Applied Thermal Engineering

(submitted)

Applied Thermal Engineering

(submitted)

We study the mixing of rarefied gases in a T-shape micromixer by means of fully three-dimensional Monte-Carlo direct simulations. In contrast to previous 2D-results, the characteristics of the channel walls (thermal or specular) have significant effect on the mixing efficiency. For the 3D case, we characterize the mixing efficiency in dependence on temperature and mass density of the gases. Based on kinetic theory arguments, we develop a theoretical model in good agreement with the simulation results. In particular, the theoretical prediction of system size scaling agrees well with the situation.

Journal of Aerospace Engineering

(in print)

Understanding the mechanical behaviour of lunar regolith is of great importance to address the building of structures on the Moon, as well as for predicting the response of some equipments or facilities interacting with the lunar soil (i.e. rovers). Since the amount of lunar regolith samples on Earth is quite low due to the difficulties to bring it back during space missions, in the last decades researchers started to develop similar materials, usually named lunar regolith simulants. This paper reports the geotechnical characterization of DNA “De NoArtri” lunar simulant carried out in the laboratory. Compositional analyses and mechanical tests have been carried out to characterize this simulant: particle-size distribution analysis, chemical analysis, scanning electron microscope (SEM) analysis have been performed, to identify the DNA-1A from a compositional point of view, as well as triaxial compression tests, direct shear tests and oedometer tests for depicting its mechanical behaviour, with some comparison with the original lunar soil and other simulants.

Studia Geotechnica et Mechanica

(submitted)

Scale modelling should be a very useful strategy for the design of lunar structures. Preventing structural damages in the lunar environment is crucial and scale models are helpful to achieve this aim. The size of these models must be scaled to take into account the different gravitational levels. Since the lunar gravity acceleration is about one-sixth of the terrestrial one, it follows that the models on Earth will be very smaller than the prototype to be realized on the Moon. This strategy will represent an opportunity for engineers working on lunar structure design, provided that the errors, both computational and experimental, related to the change of scale are quantified, allowing reliable extension of the physical scale modelling results to the prototype. In this work, a three-dimensional finite element analysis of walls retaining lunar regolith backfill is described and discussed, in order to provide preliminary results, which can guide a future experimental investigation based on physical scale-modelling. In particular, computational errors related to the scale effects are assessed, with respect to a virtual prototype of the lunar geotechnical structure, and compared with errors from other sources of discrepancy, like the adopted constitutive model, the variability of the geotechnical parameters and the calculation section used in the 3D analysis. The results seem to suggest the soundness of this strategy of modelling and are likely to encourage new research, both numerical and experimental, supporting the structure serviceability assessment.

(submitted)

The dynamics of rapid granular flows is governed by dissipative interactions of particles with each other and with the system walls. To adequately describe these interactions, roughness and particle shape must be taken into account. The coefficient of restitution for arbitrary particles thus depends not only on material properties and impact velocity but also on the angular orientation at the instant of the collision. By measurements of the coefficient of restitution from the sound signal emitted by a sphere bouncing repeatedly off the ground, it was found that small deviations from the perfect shape of the sphere lead to large measurement errors. Using stochastic methods, the effective coefficient of restitution for the collision of a rough sphere with a plane was described as a fluctuating quantity, characterized by a rather uncommon probability density function. It was shown that modelling the coefficient of restitution as a stochastic variable significantly affects the dynamics of particles under rapid granular flows. The decay of temperature of rapid granular flows in the homogeneous cooling state deviates from Haff’s law for gases of particles interacting via a constant coefficient of restitution also from the scaling law for gases of viscoelastic particles.

(in print)

The underlying structure in apparently ”randomly-packed” packed beds is a subject of topical interest, particularly in the context of deep processing, such as deep hydrodesulfurization. Packed beds typically exhibit ”packing defects” ; for instance, surface abnormalities such as a slope, a bump (convex surface), a hollow (concave surface), or even donut-shaped rings on the top surface of a packed bed. While these defects are observed at the top free surface of the packed bed, there are concerns that this may continue to propagate down the height, and in turn, cause local flow variations and differential wetting, which affect reactor performance, catalyst life, and formation of local hot spots. These defects come because of different protocols that are followed for packing particles, which are mainly developed out of empiricism since the physics of granular flow in confinements (such as a vertical cylindrical reactor vessel) is as yet not well understood. Earlier work on the structure of packed beds relates only to the spatial distribution of voidage, and not on how the particles are arranged with respect to each other in the reactor. This work is an attempt in that direction. We present first the use of Sequential Ballistic Deposition (SBD) algorithm to model the packing process itself, i.e., how the method of packing (modeled in this work through some simple protocols) yields a certain structure of the bed. Second, we show the use of Voronoi tessellation and the use of two of the Minkowski tensors (the Volume Moment Tensor and the Surface Orientation Tensor) to characterize the packed bed structure. Further analysis is presented which shows that we are able to fingerprint the packed bed formed through different packing methods, hence creating a link between the two.

(submitted)

The collision of gas-borne particles with surfaces plays an important role in many processes of particle technology such as particle separation, dry dispersion of powders and particle measuring techniques. While for coarse particles comprehensive investigations have been performed regarding sticking and bouncing behavior, in the range of nanoparticles new issues arise e.g. the influence of adhesive forces and of restructuring during plastic deformation on the impact process. In this contribution the different interactions (elastic and plastic deformation, friction, adhesion, charge transfer) between single particles as well as agglomerates impacting on solid substrates are elucidated by a combination of simulations and experiments. It was found, that size-dependent material parameters can be used to describe the collision of nanoparticles with solid substrates using continuum approaches. The effect of the impaction on the restructuring and fragmentation was investigated leading towards a dry dispersion method for nanoparticle agglomerates at ambient pressure.

(submitted)

An impressive ping-pong ball cannon can be made by placing a bottle of liquid nitrogen at the bottom of a container and quickly covering it with, say, 1,500 ping-pong balls. The liquid turns rapidly into a gas whose mounting pressure explodes the bottle, sending a swarm of balls upward out of the container. Surprisingly, the container also moves upward. This is a counterintuitive effect because the balance of forces, that is, Newton’s third law seems not allow the container to move upwards. We explain the effect as a consequence of granular jamming in combination with Coulomb’s friction law.

Computers & Mathematics with Applications

(in print)

Smoothed particle hydrodynamics (SPH) has been widely applied to flows with free surface, multi-phase flow, and systems with complex boundary geometry. However, it has been shown that SPH suffers from transverse instability when applied to simple wall-bounded shear flows such as Poiseuille and Couette flows at moderate and high Reynolds number, Re >~ 1, casting the application of SPH to practical situations into doubt, where the Reynolds number is frequently large. Here, we consider Poiseuille flows for a wide range of Reynolds number and find that the documented instability of SPH can be avoided by using appropriate ratio of smoothing length to particle spacing in combination with a density re-initialization technique, which has not been systematically investigated in simulations of simple shear flows. We also probe the source of the instability and point out the limitations of SPH for wall-bounded shear flows at high Reynolds number.

Powder Technology

(submitted)

When investigating dynamical processes in granular systems, it is frequently necessary to measure the time-resolved local material density. Recently, x-ray radiography facilities became available in many laboratories and can be used to measure the volume fraction via the attenuation of x-ray radiation along the beam direction. Naive application of the Beer-Lambert law yields, however, unacceptably large systematic errors due to beam hardening. We present a calibration protocol which allows to reliably measure the local volume fraction based exclusively on reference measurement of known packing fraction.

Powder Technology

(submitted)

The packing characteristics of micrometer to millimeter-sized spherical particles of glass, zirconia and copper are assessed both, by experimental methods, namely the measurement of bulk density and X-ray microtomography (CT), and by simulations of the packings using a 3d discrete element method (DEM) approach taking adhesion forces (JKR) and non-bonded van der Waals interactions and the experimental particle size distributions and realistic material properties into account. Bulk densities for the aforementioned model systems were obtained by the determination of the mass of powder poured via a funnel into a cylinder of known volume. The particle size distribution of the model systems was carefully evaluated by laser diffraction particle sizing and optical image analysis, respectively. Good agreement of the packing densities predicted by DEM and observed in the experiments (bulk density determination & CT) is found. The dependency of the packing fraction on the average particle diameter of the polydisperse powders could be described by a simple empirical correlation. The maximum packing fraction found for large particles (c.f. dominance of gravitational forces) was close to 0.64, which is the limiting packing fraction known for random close packing. Moreover, from the DEM simulations the average (first) coordination number in the respective packing is extracted and discussed with respect to the experimentally obtained direct neighbourhood detection from X-ray tomography and previous works. The coordination number has been found to show a remarkable dependency on the definition of particle contact, thus caution is advised when evaluating coordination numbers with this quantity being highly dependent on the instrumental resolution.

Computer Physics Communication

(submitted)

For most particle simulations, a time-dependent mapping between the particles’ positions and an underlying grid is an important component and is used, for example, to increase the eciency during the collision detection step. In the case of unstructured grids, which are frequently employed to handle domains of complex shape, obtaining this mapping is computationally expensive. The process can be accelerated by performing particle tracking, that is, the repeated localization of particles within a grid by means of tracking the trajectories of the particles. In fact, particle tracking is an application of event-driven particle dynamics (EDPD), hence, in this work, recent advances in stable EDPD algorithms are applied to the problem of particle tracking to address inconsistencies which arise due to numerical errors or imperfect meshes. It is illustrated how interactions of the particles with the system boundaries can be integrated into the new algorithm consistently. Additionally, it is demonstrated that the modeling of solid objects via constructive solid geometry can be combined with event-driven particle tracking algorithms to provide a fully analytical description of complex objects defining or embedded into the simulation domain. A robust particle tracking algorithm is presented, along with several optimizations with respect to the computational eciency. The capabilities of the developed method are exemplified via the simulation of a gas flow through a highly porous medium.

Royal Society of Chemistry

(submitted)

We report startling evidence of a systematic onset of periodic structures in large piles of disks deposited between rigid walls, independently of the pile width, observed in numerically constructed monodisperse packings with up to 107 disks. Disordered transient phases preceding the periodicity onset are found to obey power-laws as a function of the channel height. Independently of the width, we invariably find packings to be asymptotically periodic after disordered transients which, however, may become very large as the channel width grows without bound. The probability density of finding periodic structures of a given period displays a series of discrete peaks which, however, are washed out when the channel width grows indefinitely.

(submitted)

Characterizing the fluid-to-solid transition (conversely the melting transition) of two-dimensional systems is a fundamental problem in condensed matter physics that has advanced significantly through the application of computational resources and algorithms. Here we report a comprehensive simulation study of the phase behavior near the melting transition of all hard regular polygons with 3≤n≤14 vertices using massively parallel Monte Carlo simulations of up to one million particles. We find that regular polygons with seven or more edges behave like hard disks and melt continuously from a solid to a hexatic fluid and then undergo a first-order transition from the hexatic phase to the fluid phase. Strong directional entropic forces align polygons with fewer than seven edges and improve local ordering in the fluid. These forces can enhance or suppress the discontinuous character of the transition depending on whether the local order in the fluid is compatible with the local order in the solid. Triangles, squares, and hexagons exhibit a KTHNY-type continuous transition between fluid and hexatic, tetratic, and hexatic phases, respectively, and a continuous transition from the appropriate x-atic to the solid. In contrast, pentagons and plane-filling 4-fold pentilles display a one-step first-order melting of the solid to the fluid with no intermediate phase. The thirteen studied systems thus comprise examples of three distinct two-dimensional melting scenarios.

(submitted)

One of the most intensively discussed subjects in the dynamics of dissipative hard sphere systems is the effect of inelastic collapse, where the entire kinetic energy of the relative motion of a set of particles is dissipated in finite time due to an infinite sequence of collisions. The known collapse scenarios imply two preconditions: inertia of the particles and at least some degree of elasticity. For completely inelastic particles, collapse scenarios degenerate to a single sticky contact. By considering the overdamped motion of a frictional particle along the steepest descent in a rigid landscape, we will show that there exist collapse scenarios even if neither of these preconditions hold true. By means of numerical simulations we show that such collapses are no rare events due to particular particle shape and/or initial conditions and, thus, may lead to serious problems in article

simulations.

Physical Review Letters **120**, 148002

(2018)

We report evidence of a surprising systematic onset of periodic patterns in very tall piles of disks deposited randomly between rigid walls. Independently of the pile width, periodic structures are always observed in monodisperse deposits containing up to 107 disks. The probability density function of the lengths of disordered transient phases that precede the onset of periodicity displays an approximately exponential tail. These disordered transients may become very large when the channel width grows without bound. For narrow channels, the probability density of finding periodic patterns of a given period displays a series of discrete peaks, which, however, are washed out completely when the channel width grows.

Journal of Materials in Civil Engineering ** 30**, 6

(2018)

Reduction in pore water pressure is a useful strategy to improve the stability of slopes. Deep draining trenches can be used for this purpose. For the realization of deep trenches, the usual conventional construction techniques are not adequate and the use of adjacent vertical panels, built by means of the methods well-established for diaphragm walls, is necessary. However, unbonded materials (i.e., gravels) cannot be used, because the excavation of a panel adjacent to one already built will cause instability. For this scope a bonded material such as pervious concrete can be used. It must have high permeability; filtering capacity, in order to prevent internal erosion of the soil in which the trench drain is installed; and sufficient shear strength after a short curing time to avoid the instability of adjacent previously built panels. This paper reports the hydraulic characterization of two mixtures of pervious concrete carried out in the laboratory. Hydraulic conductivity was measured in saturated conditions. Then, the water retention functions of the mixtures were experimentally deduced by investigating different calculation options and their impact on the simulation of seepage processes through an unsaturated soil mass, in which an ideal trench is located.

Review of Scientific Instruments **89**, 075103

(2018)

Physical Review Fluids **3**, 024304

(2018)

We investigate experimentally the impact of heterogeneity on the capillary pressure hysteresis in fluid invasion of model porous media. We focus on symmetric heterogeneity, where the contact angles the fluid interface makes with the oil-wet (θ1) and the water-wet (θ2) beads add up to π. While enhanced heterogeneity is usually known to increase hysteresis phenomena, we find that hysteresis is greatly reduced when heterogeneities in wettability are introduced. On the contrary, geometric heterogeneity (like bidisperse particle size) does not lead to such an effect. We provide a qualitative explanation of this surprising result, resting on rather general geometric arguments.

Nature Communications **9**, 931

(2018)

Biological organisms and artificial active particles self-organize into swarms and patterns. Open questions concern the design of emergent phenomena by choosing appropriate forms of activity and particle interactions. A particularly simple and versatile system are 3D-printed robots on a vibrating table that can perform self-propelled and self-spinning motion. Here we study a mixture of minimalistic clockwise and counter-clockwise rotating robots, called rotors. Our experiments show that rotors move collectively and exhibit super-diffusive interfacial motion and phase separate via spinodal decomposition. On long time scales, confinement favors symmetric demixing patterns. By mapping rotor motion on a Langevin equation with a constant driving torque and by comparison with computer simulations, we demonstrate that our macroscopic system is a form of active soft matter.

Nature Communications **9**, 797

(2018)

The kinetic energy of a force-free granular gas decays monotonously due to inelastic collisions of the particles. For a homogeneous granular gas of identical particles, the corresponding decay of granular temperature is quantified by Haff’s law. Here, we report that for a granular gas of aggregating particles, the granular temperature does not necessarily decay but may even increase. Surprisingly, the increase of temperature is accompanied by the continuous loss of total gas energy. This stunning effect arises from a subtle interplay between decaying kinetic energy and gradual reduction of the number of degrees of freedom associated with the particles’ dynamics. We derive a set of kinetic equations of Smoluchowski type for the concentrations of aggregates of different sizes and their energies. We find scaling solutions to these equations and a condition for the aggregation mechanism predicting growth of temperature. Numerical direct simulation Monte Carlo results confirm the theoretical predictions.

Physical Review Letters **120**, 055701

(2018)

We present an experiment on crystallization of packings of macroscopic granular spheres. This system is often considered to be a model for thermally driven atomic or colloidal systems. Cyclically shearing a packing of frictional spheres, we observe a first order phase transition from a disordered to an ordered state. The ordered state consists of crystallites of mixed fcc and hcp symmetry that coexist with the amorphous bulk. The transition, initiated by homogeneous nucleation, overcomes a barrier at 64.5% volume fraction. Nucleation consists predominantly of the dissolving of small nuclei and the growth of nuclei that have reached a critical size of about ten spheres.

Physics of Fluids **30**, 013603

(2018)

Stochastic Rotation Dynamics (SRD) is a valuable numerical tool extensively used in many domains of hydrodynamics simulations including colloidal suspensions. We investigate the dynamics of two colloidal particles in the regime of low Reynolds number by means of SRD in 3D. In contrast to well-known analytical and experimental results, no long-range interaction between the suspended particles could be found, independent of the size of the particles and the Mach and Péclet numbers. We attribute this behavior to the compressible nature and low sound velocity in the SRD solvent. The inability of representing long-range interactions poses an important limitation to the applicability of SRD to certain physical systems. We provide an estimation of typical length scales for which SRD can be applied.

Biosensors and Bioelectronics **102**, 589-599

(2018)

We engineered an automated biomechatronics system, *MyoRobot*, for robust objective and versatile assessment of muscle or polymer materials (bio-)mechanics. It covers multiple levels of muscle biosensor assessment, e.g. membrane voltage or contractile apparatus Ca^{2+} ion responses (force resolution 1 µN, 0–10 mN for the given sensor; [Ca^{2+}] range ~ 100 nM–25 µM). It replaces previously tedious manual protocols to obtain exhaustive information on active/passive biomechanical properties across various morphological tissue levels. Deciphering mechanisms of muscle weakness requires sophisticated force protocols, dissecting contributions from altered Ca^{2+} homeostasis, electro-chemical, chemico-mechanical biosensors or visco-elastic components. From whole organ to single fibre levels, experimental demands and hardware requirements increase, limiting biomechanics research potential, as reflected by only few commercial biomechatronics systems that can address resolution, experimental versatility and mostly, automation of force recordings. Our *MyoRobot* combines optical force transducer technology with high precision 3D actuation (e.g. voice coil, 1 µm encoder resolution; stepper motors, 4 µm feed motion), and customized control software, enabling modular experimentation packages and automated data pre-analysis. In small bundles and single muscle fibres, we demonstrate automated recordings of (i) caffeine-induced-, (ii) electrical field stimulation (EFS)-induced force, (iii) pCa-force, (iv) *slack-tests* and (v) passive length-tension curves. The system easily reproduces results from manual systems (two times larger stiffness in slow over fast muscle) and provides novel insights into unloaded shortening velocities (declining with increasing slack lengths). The *MyoRobot* enables automated complex biomechanics assessment in muscle research. Applications also extend to material sciences, exemplarily shown here for spider silk and collagen biopolymers.

Physical Review E **98**, 022902

(2018)

The mechanical properties of nanoparticles cannot be reliably described by bulk material characteristics due to their atomic structure, leading to pronounced anisotropic behavior. By means of molecular dynamics simulations, we study the impact of 5-nm Ag particles on an adhesive rigid wall. We show that the main characteristics of the impact such as the coefficient of normal restitution, the sticking probability, the maximal contact force, and the degree of plastic deformation of the particle depend sensitively on the angular orientation of the nanoparticle prior to the impact. We introduce the scalar parameter Ω describing the orientation and show that the impact characteristics can be described as functions of Ω.

Chemical Engineering Science **176**, 192-204

(2018)

Grid based fluid simulation methods are not able to solve complex non-linear dynamics like the rupture of a dynamic liquid bridge between freely colliding solids–an exemplary scenario of capillary forces competing with inertial forces in engineering applications–using a monolithic formulation for the solid and liquid phases present. We introduce a new Incompressible Smoothed Particle Hydrodynamics method for simulating three dimensional fluid-solid interaction flows with capillary (wetting and surface tension) effects at free surfaces. This meshless approach presents significant advantages over grid based approaches in terms of being monolithic and in handling interaction with free solids. The method is validated for accuracy and stability in dynamic scenarios involving surface tension and wetting. We then present three dimensional simulations of crown forming instability following the splash of a liquid drop, and the rupture of a liquid bridge between two colliding solid spheres, to show the method’s advantages in the study of dynamic micromechanical phenomena involving capillary flows.

EPJ Web of Conferences **140**, 09005

(2017)

Unsaturated wet granular media are usually modelled using force laws based on analytical and empirical results of liquid bridge forces between pairs of grains. These models make ad-hoc assumptions on the liquid volume present in the bridges and its distribution. The force between grains and rupture criterion of the bridge are a function of this assumed volume of liquid, in addition to other parameters like contact angle of the liquid, geometry of the grains and the inter grain distance. To study the initial volume and morphology of liquid bridges, hydrodynamic simulation of dynamic effects leading to formation of liquid bridges at grain scale are indispensable. We use a Smoothed Particle Hydrodynamics algorithm to simulate the hydrodynamics of the evolution of the free surface using a novel freesurface-capillary model, inspired by the molecular basis of surface tension. We present validations for the model and simulations of formation and rupture of liquid bridges.

EPJ Web of Conferences **140**, 14010

(2017)

We show that the orientation and morphology of bedforms occurring on top of Pluto’s smooth ice coats are consistent with an aeolian origin under conditions of unidirectional flow. From scaling relations for dune size as a function of attributes of atmosphere and sediments, we find that the average diameter of the granular particles constituting such bedforms — assuming an aeolian origin — lies within the range 600 *μ*m< d < 750 *μ*m. Our findings show that, owing to the effect of hysteresis in the minimal threshold wind velocity for saltation, dune migration on Pluto can occur under wind speeds that are common to Earth and Mars.

V International Conference on Particle-based Methods – Fundamentals and Applications. PARTICLES 2017 (P. Wriggers, M. Bischoff, E. Oñate, D.R.J. Owen, T. Zohdi). 429-439. Hannover.

(2017)

Part of the optimization steps for additive manufacturing is related to the correct understanding of the mechanical behavior of the powder used in the process. Obtain this understanding based purely on experiments might be a difficult and sometimes prohibitive task. A particle-based numerical tool can provide critical information for correct understanding of powder deposition process. Numerical simulations through the *Discrete Element Method* (DEM) provide a useful mean to investigate the additive manufacturing process, given the possibility to study particle-scale information that are difficult to access experimentally.

The characteristics of the recoated powder bed are investigated in the packed bed region and onto the manufactured part using PA12 commercial powder. Particle size distribution, contact and non-contact cohesive forces are incorporated in the numerical model. Furthermore, the non-spherical shape of real particles is taken explicitly into account in numerical simulations. A blade-type recoating system is used to form the powder bed and its roughness is calculated.

Experimental measurements are performed by fringe projection. Several areas of the recoated powder layers can be scanned with this optical measurement method. Thus, the analyzed surface roughness can be compared with the simulated quantities to validate the numerical model.

The sintered part is modelled as a prescribed rigid static region in the simulated system. The powder recoated in the sintered region may have different characteristics (packing, roughness) compared to the powder bed region. Recoating process is modelled using two different shapes for the sintered region. The amount of material recoated and the surface roughness are then calculated for the powder bed as well as for the sintered region.

Scientific Reports **7**, 12723

(2017)

Ratchets are simple mechanical devices which combine spatial asymmetry and nonequilibrium to produce counterintuitive transport of particles. The operation and properties of *linear* ratchets have already been extensively explored. However, very little is known about *circular granular* ratchets, startling devices able to convert vertical vibrations into rotations of the device. Here, we report results of systematic numerical investigations of the operational characteristics of circular granular ratchets. Several distinct behaviors are identified and explained in terms of the inner flow fields of the ratchet. All dynamical regimes found are robust and should not be difficult to observe in laboratory experiments.

Physical Review X **7**, 021001

(2017)

The melting transition of two-dimensional systems is a fundamental problem in condensed matter and statistical physics that has advanced significantly through the application of computational resources and algorithms. Two-dimensional systems present the opportunity for novel phases and phase transition scenarios not observed in 3D systems, but these phases depend sensitively on the system and, thus, predicting how any given 2D system will behave remains a challenge. Here, we report a comprehensive simulation study of the phase behavior near the melting transition of all hard regular polygons with 3≤n≤14 vertices using massively parallel Monte Carlo simulations of up to 1×106 particles. By investigating this family of shapes, we show that the melting transition depends upon both particle shape and symmetry considerations, which together can predict which of three different melting scenarios will occur for a given n. We show that systems of polygons with as few as seven edges behave like hard disks; they melt continuously from a solid to a hexatic fluid and then undergo a first-order transition from the hexatic phase to the isotropic fluid phase. We show that this behavior, which holds for all 7≤n≤14, arises from weak entropic forces among the particles. Strong directional entropic forces align polygons with fewer than seven edges and impose local order in the fluid. These forces can enhance or suppress the discontinuous character of the transition depending on whether the local order in the fluid is compatible with the local order in the solid. As a result, systems of triangles, squares, and hexagons exhibit a Kosterlitz-Thouless-Halperin-Nelson-Young (KTHNY) predicted continuous transition between isotropic fluid and triatic, tetratic, and hexatic phases, respectively, and a continuous transition from the appropriate x-atic to the solid. In particular, we find that systems of hexagons display continuous two-step KTHNY melting. In contrast, due to symmetry incompatibility between the ordered fluid and solid, systems of pentagons and plane-filling fourfold pentilles display a one-step first-order melting of the solid to the isotropic fluid with no intermediate phase.

Physical Review E **96**, 040901(R)

(2017)

Analogies between fluid flows and granular flows are useful because they pave the way for continuum treatments of granular media. However, in practice it is impossible to predict under what experimental conditions the dynamics of fluids and granulates are qualitatively similar. In the case of unsteadily driven systems no such analogy is known. For example, in a partially filled container subject to horizontal oscillations liquids slosh, whereas granular media of complex particles exhibit large-scale convection rolls. We here show that smooth monodisperse steel spheres exhibit liquidlike sloshing dynamics. Our findings highlight the role of particle material and geometry for the dynamics and phase transitions of the system.

Physical Review E **96**, 042902

(2017)

The decay of energy within particulate media subjected to an impulse is an issue of significant scientific interest, but also one with numerous important practical applications. In this paper, we study the dynamics of a

granular system exposed to energetic impulses in the form of discrete taps from a solid surface. By considering a one-dimensional toy system, we develop a simple theory, which successfully describes the energy decay within the system following exposure to an impulse. We then extend this theory so as to make it applicable also to more realistic, three-dimensional granular systems, assessing the validity of the model through direct comparison with discrete particle method simulations. The theoretical form presented possesses several notable consequences; in particular, it is demonstrated that for suitably large systems, effects due to the bounding walls may be entirely neglected. We also establish the existence of a threshold system size above which a granular bed may be considered fully three dimensional.

American Journal of Physics **85**, 649

(2017)

Besides its importance for science and engineering, the process of drop formation from a homogeneous jet or at a nozzle is of great aesthetic appeal. In this paper, we introduce a low-cost setup for classroom use to produce quasi-high-speed recordings with high temporal and spatial resolution of the formation of drops at a nozzle. The visualization of the process can be used for quantitative analysis of the underlying physical phenomena.

RSC Advances **7**, 42218-42224

(2017)

As an environment for rich pattern formation, the electroconvection (EC) of nematic liquid crystals (LCs) is studied via fully nonlinear simulations for the first time. Previously, EC was mostly studied by experiments or

by linear/weakly nonlinear hydrodynamic theory for its instability criteria. While the negative dielectric LCs are used in most EC analytical and experimental investigations, EC with positive dielectric LCs is limited to

experiments only, due to their more complex nonlinear behavior. In this work we take a step beyond the existing weakly nonlinear EC research by using a fully nonlinear particle-based simulation. To investigate

the distinct dynamics of positive and negative dielectric LCs, we modified the molecular potential in the LC stochastic rotational model (LC SRD) [Lee et al., J. Chem. Phys., 2015, 142, 164110] to incorporate the

dielectric characteristics and the field-particle interaction. As a result, different convection patterns known in the EC experiments were observed in our simulations, for which those patterns appeared orderly, as a function of external field strength. The simulated director and flow fields correspond to each other well, as found in our experiments. For the positive dielectric LC, we discovered a net directional flow accompanying the travelling EC rolls. This numerical model and its hydrodynamic analysis could be used for precise flow control at the micro-scale, such as nematic colloidal transportation in microfluidics.

Revista Cubana de Física **34**, 69

(2017)

In [1] the rotational frequency of a single Vibrot was incorrectly plotted as a function of the excitation amplitude *A*. Instead the figure shows the data in dependence of the dimensionless acceleration Γ= A(2πƒ_{D})^{2}/g, where g is the gravitational acceleration. Only in the case of ƒ_{D} = 50 Hz *A* = 1,3 mm corresponds to Γ = 1.3 g and vice versa. The corresponding paragraph of the original manuscript must then be replaced by the following: „Figure 4 shows ϖ vs. ƒ_{D} for two different values of the dimensionless acceleration Γ =*A* (2πƒ_{D})^{2}/g. For a low Γ the particle performs slow rotation where ƒ_{D} depends non-monotonously on the frequency characterized by a minimum at ƒ_{D} = 50 Hz. For large Γ, we observe slow rotation at low frequency and tumbling motion for ƒ_{D} ≥ 30 Hz, where the rotational velocity decreases with increasing ƒ_{D}.“ The corrected version of the plot is shown in Fig. 4.

EPJ Special Topics **226**, 1987-1995

(2017)

We report a startling mosaic-like organization of stability phases found in the low-frequency limit of a driven Brusselator. Such phases correspond to periodic oscillations having a constant number of spikes per period. The mosaic is free from chaotic oscillations and is formed by an apparently infinite cascade of oscillations whose number of spikes grow without bound. Wide windows free from chaos but supporting unbounded quantities of complex oscillations are potentially of interest to operate driven oscillators such as lasers, electronic circuits, and biochemical pacemakers.

Physical Review Fluids **2**, 124204

(2017)

Stochastic rotation dynamics (SRD) is a widely used method for the mesoscopic modeling of complex fluids, such as colloidal suspensions or multiphase flows. In this method, however, the underlying Cartesian grid defining the coarse-grained interaction volumes induces anisotropy. We propose an isotropic, lattice-free variant of stochastic rotation dynamics, termed iSRD. Instead of Cartesian grid cells, we employ randomly distributed spherical interaction volumes. This eliminates the requirement of a grid shift, which is essential in standard SRD to maintain Galilean invariance. We derive analytical expressions for the viscosity and the diffusion coefficient in relation to the model parameters, which show excellent agreement with the results obtained in iSRD simulations. The proposed algorithm is particularly suitable to model systems bound by walls of complex shape, where the domain cannot be meshed uniformly. The presented approach is not limited to SRD but is applicable to any other mesoscopic method, where particles interact within certain coarse-grained volumes.

Soft Matter **13**, 8816-8823

(2017)

We consider electroconvection as the response of nematic liquid crystal to an external electric AC field, in the absence of free charge carriers. Previous experimental and theoretical results emphasized charge carriers as a necessary precondition of electroconvection because free-charges in the fluid can response to the external electric field. Therefore, ionized molecules are considered as responsible for the driving of electroconvective flows. In experiments, finite conductivity is achieved by adding charge-carrying dye molecules or in non-dyed liquid crystals by impurities of the samples. The phenomenon of electroconvection is explained by the Carr-Helfrich theory, supported by numerical simulations. In the present paper, we show that electroconvection may occur also in pure nematic liquid crystals. By means of particle-based numerical simulation we found that bound charges emerge by alignment of polarized liquid crystal molecules in response to the external electric field. In our simulations we could reproduce the characteristic features of electroconvection, such as directorflow patterns, the phase-transition in the voltage-frequency diagram, and dislocation climb/glide motion, which are well known from experiments and hydrodynamic simulations under the assumption of free charge carriers.

Physical Review Letters **118**, 218001

(2017)

When a thin tube is dipped into water, the water will ascend to a certain height, against the action of gravity. While this effect, termed capillarity, is well known, recent experiments have shown that agitated granular matter reveals a similar behavior. Namely, when a vertical tube is inserted into a container filled with granular material and is then set into vertical vibration, the particles rise up along the tube. In the present Letter, we investigate the effect of granular capillarity by means of numerical simulations and show that the effect is caused by convection of the granular material in the container. Moreover, we identify two regimes of behavior for the capillary height H_{c}∞ depending on the tube-to-particle-diameter ratio, D/d. For large D/d, a scaling of H_{c}∞ with the inverse of the tube diameter, which is reminiscent of liquids, is observed. However, when D/d decreases down to values smaller than a few particle sizes, a uniquely granular behavior is observed where H_{c}∞ increases linearly with the tube diameter.

Review of Scientific Instruments **88**, 051701

(2017)

Granular materials are complex multi-particle ensembles in which macroscopic properties are largely determined by inter-particle interactions between their numerous constituents. In order to understand and to predict their macroscopic physical behavior, it is necessary to analyze the composition and interactions at the level of individual contacts and grains. To do so requires the ability to image individual particles and their local configurations to high precision. A variety of competing and complementary imaging techniques have been developed for that task. In this introductory paper accompanying the Focus Issue, we provide an overview of these imaging methods and discuss their advantages and drawbacks, as well as their limits of application.

EPJ Web of Conferences **140**, 06007

(2017)

We describe the development of a new software tool, called “Pomelo”, for the calculation of Set Voronoi diagrams. Voronoi diagrams are a spatial partition of the space around the particles into separate Voronoi cells, e.g. applicable to granular materials. A generalization of the conventional Voronoi diagram for points or monodisperse spheres is the Set Voronoi diagram, also known as navigational map or tessellation by zone of influence. In this construction, a Set Voronoi cell contains the volume that is closer to the surface of one particle than to the surface of any other particle. This is required for aspherical or polydisperse systems. Pomelo is designed to be easy to use and as generic as possible. It directly supports common particle shapes and offers a generic mode, which allows to deal with any type of particles that can be described mathematically. Pomelo can create output in different standard formats, which allows direct visualization and further processing. Finally, we describe three applications of the Set Voronoi code in granular and soft matter physics, namely the problem of packings of ellipsoidal particles with varying degrees of particle-particle friction, mechanical stable packings of tetrahedra and a model for liquid crystal systems of particles with shapes reminiscent of pears.

Physical Review E **95**, 062903

(2017)

Equal volume mixtures of small and large polytetrafluorethylene (PTFE) spheres are shaken in an atmosphere of controlled humidity which allows to also control their tribo-charging. We find that the contact numbers are charge-dependent: as the charge density of the beads increases, the number of same-type contacts decreases and the number of opposite-type contacts increases. This change is not caused by a global segregation of the sample. Hence, tribo-charging can be a way to tune the local composition of a granular material.

EG 2017 - Posters (P. Benard, D. Sykora). The Eurographics Association.

(2017)

We propose a new scheme for the two-way coupling of incompressible fluids and deformable bodies, where we focus on a medical application; in particular, secondary bone healing. Our method allows for accurate simulation and visualisation of the secondary bone healing process, which is used to optimise clinical treatment of bone fractures. In our simulation, the soft tissues are simulated as elastic materials using Strain Based Dynamics (SBD), and fluid is simulated using Incompressible Smoothed Particle Hydrodynamics (ISPH). The interaction model we propose works with any type of deformation technique as long as the object surface is represented by a polygonal mesh and the fluid by Lagrangian particles.

EPJ Web of Conferences **140**, 01008

(2017)

Leibniz said „Naturam cognosci per analogiam“: nature is understood by making analogies. This statement describes a seminal epistemological principle. But one has to be aware of its limitations: quantum mechanics for example at some point had to push Bohr’s model of the atom aside to make progress. This article claims that the physics of granular packings has to move beyond the analogy of frictionless spheres, towards local models of contact formation.

Communications in Nonlinear Science and Numerical Simulation **49**, 135-144

(2017)

Recent work has introduced social dynamic models of people’s stress-related processes, some including amelioration of stress symptoms by support from others. The effects of support may be “direct”, depending only on the level of support, or “buffering”, depending on the product of the level of support and level of stress. We focus here on the nonlinear buffering term and use a model involving three variables (and 12 control parameters), including stress as perceived by the individual, physical and psychological symptoms, and currently active social support. This model is quantified by a set of three nonlinear differential equations governing its stationary-state stability, temporal evolution (sometimes oscillatory), and how each variable affects the others. Chaos may appear with periodic forcing of an environmental stress parameter. Here we explore this model carefully as the strength and amplitude of this forcing, and an important psychological parameter relating to self-kindling in the stress response, are varied. Three significant observations are made: 1. There exist many complex but orderly regions of periodicity and chaos, 2. there are nested regions of increasing number of peaks per cycle that may cascade to chaos, and 3. there are areas where more than one state, e.g., a period-2 oscillation and chaos, coexist for the same parameters; which one is reached depends on initial conditions.

Science **355**, 931-935

(2017)

DNA-programmable assembly has been used to deliberately synthesize hundreds of different colloidal crystals spanning dozens of symmetries, but the complexity of the achieved structures has so far been limited to small unit cells. We assembled DNA-modified triangular bipyramids (~250-nanometer long edge, 177-nanometer short edge) into clathrate architectures. Electron microscopy images revealed that at least three different structures form as large single-domain architectures or as multidomain materials. Ordered assemblies, isostructural to clathrates, were identified with the help of molecular simulations and geometric analysis. These structures are the most sophisticated architectures made via programmable assembly, and their formation can be understood based on the shape of the nanoparticle building blocks and mode of DNA functionalization.

EPJ Web of Conferences **140**, 15013

(2017)

We have developed the first particle-based numerical tool to simulate the coating of powder particles in additive manufacturing devices. Our Discrete Element Method considers realistic particle shapes and incorporates attractive interaction (van-der-Waals) forces between the particles. From simulations of powder coating using a roller as coating device, we find that the surface roughness of the powder bed scales with the square of coating speed. Moreover, we find that using fine, highly polydisperse powders may lead to larger powder bed roughness, compared to process simulations using coarser powders, due to the formation of agglomerates resulting from cohesive forces.

EPJ Web of Conferences **140**, 16001

(2017)

We create nearly perfect centimetric spheres of water by splitting a cavity consisting of two metal hemispheres coated with a hydrophobic paint and under-filled with liquid, while releasing the apparatus in free-fall. A high-speed camera captured how water spread on hydrophobic aluminum and polycarbonate plates perforated with cylindrical capillaries. We compare observations at the ZARM drop tower in Bremen with Lattice-Boltzmann numerical simulations of Frank, Perre and Li for the inertial phase of imbibition.

Review of Scientific Instruments **88**, 051809

(2017)

Starting from three-dimensional volume data of a granular packing, as e.g. obtained by X-ray Computed Tomography, we discuss methods to first detect the individual particles in the sample and then analyze their properties. This analysis includes the pair correlation function, the volume and shape of the Voronoi cells and the number and type of contacts formed between individual particles. We mainly focus on packings of monodisperse spheres, but we will also comment on other monoschematic particles such as ellipsoids and tetrahedra. This paper is accompanied by a package of free software containing all programs (including source code) and an example three-dimensional dataset which allows the reader to reproduce and modify all examples given.

Physics of Fluids **29**, 083303

(2017)

We describe the velocity distribution function of a granular gas of electrically charged particles by means of a Sonine polynomial expansion and study the decay of its granular temperature. We find a dependence of the first non-trivial Sonine coefficient, *a*_{2}, on time through the value of temperature. In particular, we find a sudden drop of *a*_{2} when temperature approaches a characteristic value, T∗, describing the electrostatic interaction. For lower values of *T*, the velocity distribution function becomes Maxwellian. The theoretical calculations agree well with numerical direct simulation Monte Carlo to validate our theory.

Soft Matter **13**, 394-401

(2017)

We study the effect of humidity on the charge accumulation of polymer granulates shaken vertically in a stainless steel container. This setup allows us to control the humidity level from 5% to 100%RH while performing automated charge measurements in a Faraday cup directly connected to the shaking container. We find that samples of approximately 2000 polymer spheres become highly charged at low humidity levels (<30%RH), but acquire almost no charge for humidity levels above 80%RH. The transition between these two regimes does depend on the material, as does the sign of the charge. For the latter we find a correlation with the contact angle of the polymer with only very hydrophilic particles attaining positive charges. We show that this humidity dependence of tribo-charging can be used to control segregation in shaken binary mixtures.

Physical Review Letters **118**, 198003

(2017)

The theory of homogeneously driven granular gases of hard particles predicts that the stationary state is characterized by a velocity distribution function with overpopulated high-energy tails as compared to the exponential decay valid for molecular gases. While this fundamental theoretical re- sult was confirmed by numerous numerical simulations, an experimental confirmation is still missing. Using self-rotating active granular particles, we find a power-law decay of the velocity distribution whose exponent agrees well with the theoretic prediction.

EPJ Web of Conferences **140**, 03069

(2017)

The homogenization of granular flows through narrow pipes is important for a broad range of technological and industrial applications. Here we show, by means of molecular dynamics simulations, that such homogenization can be achieved by adding a helical inner-wall texture to the pipe, without the need for energy input from any external source. By using such a texture, jamming is prevented and the granular flux can be predicted using a modified Beverloo equation that accounts for the wavelength of the helical texture.

EPJ Web of Conferences **140**, 16008

(2017)

When a narrow tube inserted into a static container filled with particles is subjected to vertical vibration, the particles rise in the tube, much resembling the ascending motion of a liquid column in a capillary tube. To gain insights on the particle dynamics dictating this phenomenon – which we term **granular capillarity** – we numerically investigate the system using the Discrete Element Method (DEM). We reproduce the dynamical process of the granular capillarity and analyze the vertical motion of the individual particles in the tube, as well as the average vertical velocities of the particles. Our simulations show that the height of the granular column fluctuates in a periodic or period-doubling manner as the tube vibrates, until a steady-state (capillary) height is reached. Moreover, our results for the average vertical velocity of the particles in the tube at different radial positions suggest that granular convection is one major factor underlying the particle-based dynamics that lead to the granular capillarity phenomenon.

Nature Materials **16**, 214-219

(2017)

Expanding the library of self-assembled superstructures provides insight into the behaviour of atomic crystals and supports the development of materials with mesoscale order^{1, 2}. Here we build on recent findings of soft matter quasicrystals^{3, 4, 5, 6} and report a quasicrystalline binary nanocrystal superlattice that exhibits correlations in the form of partial matching rules reducing tiling disorder. We determine a three-dimensional structure model through electron tomography^{7, 8} and direct imaging of surface topography. The 12-fold rotational symmetry of the quasicrystal is broken in sublayers, forming a random tiling of rectangles, large triangles and small triangles with 6-fold symmetry. We analyse the geometry of the experimental tiling and discuss factors relevant for the stabilization of the quasicrystal. Our joint experimental–computational study demonstrates the power of nanocrystal superlattice engineering and further narrows the gap between the richness of crystal structures found with atoms and in soft matter assemblies.

New Journal of Physics **19**, 013001

(2017)

An inelastic hard ball bouncing repeatedly off the ground comes to rest in finite time by performing an infinite number of collisions. Similarly, a granular gas under the influence of external gravity, condenses at the bottom of the confinement due to inelastic collisions. By means of hydrodynamical simulations, we find that the condensation process of a granular gas reveals a similar dynamics as the bouncing ball. Our result is in agreement with both experiments and particle simulations, but disagrees with earlier simplified hydrodynamical description. Analyzing the result in detail, we find that the adequate modeling of pressure plays a key role in continuum modeling of granular matter.

American Journal of Physics **85**, 98

(2017)

A flowing hourglass changes its weight in the course of time because of the accelerated motion of its center of mass. While this insight is not new, it is frequently said that the effect is tiny and hardly measurable. Here we present a simple experiment which allows to monitor the weight as a function of time revealing different stages, in quantitative agreement with theory.

New Journal of Physics **18**, 073049

(2016)

By means of particle-based numerical simulations using the discrete element method, we address the question of how the performance of granular dampers is affected by the shape of the granular particles. In consistence with previous experiments performed with nearly spherical particles we find that independently of the particles‘ shape, the granular system is characterized by a gas-like regime for small amplitudes of the container’s oscillation and by a collect-and-collide regime for large amplitude forcing. Both regimes are separated by an optimal operation mode—the critical amplitude of the damping oscillation for which the energy dissipation is maximal—which is independent of the particle shape for given conditions of particle mass, material properties and number of particles. However, in the gas-like regime, we find that spherical particles lead to more efficient energy dissipation compared to complex shaped particles of the same mass. In this regime, a dependence on the damper’s efficiency on the particle shape is found.

Physical Review Letters **117**, 053902

(2016)

We study photonic band gap formation in two-dimensional high-refractive-index disordered materials where the dielectric structure is derived from packing disks in real and reciprocal space. Numerical calculations of the photonic density of states demonstrate the presence of a band gap for all polarizations in both cases. We find that the band gap width is controlled by the increase in positional correlation inducing short-range order and hyperuniformity concurrently. Our findings suggest that the optimization of short-range order, in particular the tailoring of Bragg scattering at the isotropic Brillouin zone, are of key importance for designing disordered PBG materials.

Chemical Reviews **116**, 11220-11289

(2016)

Chemical methods developed over the past two decades enable preparation of colloidal nanocrystals with uniform size and shape. These Brownian objects readily order into superlattices. Recently, the range of accessible inorganic cores and tunable surface chemistries dramatically increased, expanding the set of nanocrystal arrangements experimentally attainable. In this review, we discuss efforts to create next-generation materials via bottom-up organization of nanocrystals with preprogrammed functionality and self-assembly instructions. This process is often driven by both interparticle interactions and the influence of the assembly environment. The introduction provides the reader with a practical overview of nanocrystal synthesis, self-assembly, and superlattice characterization. We then summarize the theory of nanocrystal interactions and examine fundamental principles governing nanocrystal self- assembly from hard and soft particle perspectives borrowed from the comparatively established fields of micrometer colloids and block copolymer assembly. We outline the extensive catalog of superlattices prepared to date using hydrocarbon-capped nanocrystals with spherical, polyhedral, rod, plate, and branched inorganic core shapes, as well as those obtained by mixing combinations thereof. We also provide an overview of structural defects in nanocrystal superlattices. We then explore the unique possibilities offered by leveraging nontraditional surface chemistries and assembly environments to control superlattice structure and produce nonbulk assemblies. We end with a discussion of the unique optical, magnetic, electronic, and catalytic properties of ordered nanocrystal superlattices, and the coming advances required to make use of this new class of solids.

Scientific Reports **6**, 35650

(2016)

By mixing glass beads with a curable polymer we create a well-defined cohesive granular medium, held together by solidified, and hence elastic, capillary bridges. This material has a geometry similar to a wet packing of beads, but with an additional control over the elasticity of the bonds holding the particles together. We show that its mechanical response can be varied over several orders of magnitude by adjusting the size and stiffness of the bridges, and the size of the particles. We also investigate its mechanism of failure under unconfined uniaxial compression in combination with *in situ* x-ray microtomography. We show that a broad linear-elastic regime ends at a limiting strain of about 8%, whatever the stiffness of the agglomerate, which corresponds to the beginning of shear failure. The possibility to finely tune the stiffness, size and shape of this simple material makes it an ideal model system for investigations on, for example, fracturing of porous rocks, seismology, or root growth in cohesive porous media.

Scientific Reports **6**, 37102

(2016)

We argue that the alignment of Lyapunov vectors provides a quantitative criterion to predict catastrophes, i.e. the imminence of large-amplitude events in chaotic time-series of observables generated by sets of ordinary differential equations. Explicit predictions are reported for a Rössler oscillator and for a semiconductor laser with optoelectronic feedback.

New Journal of Physics **18**, 113006

(2016)

Cylindrical containers with a rotating bottom disk (so-called split-bottom geometry) are well established devices to shear granular materials in a continuous way, and to generate well-defined localized shear bands in the granular bed. When material composed of shape-anisotropic grains is sheared in such a container, a secondary flow is generated that leads to the formation of a considerable heap of material near the rotation center. We demonstrate that this effect can be found not only with prolate grains, as shown in a previous study, but also for oblate particle shapes. In addition, the quantitative influence of geometric and dynamic parameters is studied systematically. It is shown that the fill height of the container has considerable influence on the time scale for heap formation, but much less effect on the heap height. Results of numerical simulations agree with the experimental findings and provide insight in the particle dynamics.

6th International Conference on Additive Technologies. iCAT 2016 (I. Drstvenšek, D. Drummer, M. Schmidt). Interesansa - zavod. Ljubljana.

(2016)

Part of the optimization steps for the additive manufacturing is related to the correct understanding of the mechanical behavior of the powder used in the process. Numerical simulations through the Discrete Element Method (DEM) provide a useful means to investigate additive manufacturing process thus assisting and complementing experimental investigations. In particular, with the help of DEM simulations, it is possible to study particle-scale processes that are difficult to access experimentally. We investigate the characteristics of the powder bed deposited onto the manufactured part using a roller as the coating system. Furthermore, the non-spherical shape of real particles is also taken explicitly into account in the numerical simulations. A combination of translational velocity and sinusoidal vibration is used in the roller. The effect of varying the translational velocity, vibration frequency and amplitude in the density and roughness of the formed bed is investigated.

Results in Physics **6**, 561-567

(2016)

We report an algorithm to extract equations of motion for orbits of arbitrarily high periods generated by iteration of the Pincherle map, the operational kernel used in the so-called chaotic computers. The performance of the algorithm is illustrated explicitly by extracting expeditiously, among others, an orbit buried inside a polynomial cluster of equations with degree exceeding one billion, out of reach by ordinary brute-force factorization. Large polynomial clusters are responsible for the organization of the phasespace and knowledge of this organization requires decomposing such clusters.

New Journal of Physics **18**, 123001

(2016)

Systems of granular rotors (Vibrots), that is, small devices that convert linear vibrational motion into rotation by frictional impact, are of scientic interest since they could reveal various types of collective behavior. Looking at an isolated Vibrot, we note at least two dierent dynamical modes, depending on the parameters of the vibrational driving. By means of Finite Element simulations, we reveal the driving mechanism for both cases which may be correspondingly identied as ratcheting and tumbling. The transition between both modes resembles period doubling in certain bouncing ball problems leading eventually to chaotic motion in such systems.

Computational Particle Mechanics **3**, 389

(2016)

The original publication of the article contains an error in line number 8 of Algorithm 2. The correct version of the Algorithm 2 is provided in this erratum.

Advances In Atomic, Molecular, and Optical Physics **65**, 127-191

(2016)

The CO2 laser is a complex dynamical system that has been investigated extensively both experimentally and through numerical simulations. As a result, a number of models exist for this laser, famed for providing satisfactory agreement between numerical and experimental observations. But the laser involves a large number of freely tunable control parameters whose impact on its performance and stability is not known in detail. The spontaneous emergence and organization of laser stability phases are also poorly understood. Here, we review recent progress in the classification of laser spiking, periodic or nonperiodic self-pulsations, predicted for CO2 lasers with modulated parameters and with feedback, instantaneous or delayed. The unfolding of spiking is classified with the help of numerically obtained high-resolution stability charts for experimentally accessible control parameters. Such stability charts display novel regular and irregular features, suggesting that the laser control parameter planes harbor remarkable symme- tries not yet accounted for theoretically but which are experimentally within reach. High-resolution stability charts put stringent tests on the reliability and accuracy of current models in forecasting laser dynamics.

Soft Matter **12**, 3991-4006

(2016)

We extend the Widom particle insertion method [B. Widom, *J. Chem. Phys.*, 1963, **39**, 2808–2812] to determine an upper bound *s*_{ub} on the Edwards entropy in frictional hard-sphere packings. *s*_{ub} corresponds to the logarithm of the number of mechanically stable configurations for a given volume fraction and boundary conditions. To accomplish this, we extend the method for estimating the particle insertion probability through the pore-size distribution in frictionless packings [V. Baranau, *et al.*, *Soft Matter*, 2013, **9**, 3361–3372] to the case of frictional particles. We use computer-generated and experimentally obtained three-dimensional sphere packings with volume fractions *φ* in the range 0.551–0.65. We find that *s*_{ub} has a maximum in the vicinity of the Random Loose Packing Limit *φ*_{RLP} = 0.55 and decreases then monotonically with increasing *φ* to reach a minimum at *φ* = 0.65. Further on, *s*_{ub} does not distinguish between real mechanical stability and packings in close proximity to mechanical stable configurations. The probability to find a given number of contacts for a particle inserted in a large enough pore does not depend on *φ*, but it decreases strongly with the contact number.

Applied Optics **55**, 3165-3169

(2016)

Optically transparent immersion liquids with refractive index (n~1.77) to match the sapphire-based aplanatic numerical aperture increasing lens (aNAIL) are necessary for achieving deep 3D imaging with high spatial resolution. We report that antimony tribromide (SbBr3) salt dissolved in liquid diiodomethane (CH2I2) provides a new high refractive index immersion liquid for optics applications. The refractive index is tunable from n=1.74 (pure) to n=1.873 (saturated), by adjusting either salt concentration or temperature; this allows it to match (or even exceed) the refractive index of sapphire. Importantly, the solution gives excellent light transmittance in the ultraviolet to near-infrared range, an improvement over commercially available immersion liquids. This refractive-index-matched immersion liquid formulation has enabled us to develop a sapphire-based aNAIL objective that has both high numerical aperture (NA=1.17) and long working distance (WD=12mm). This opens up new possibilities for deep 3D imaging with high spatial resolution.

Journal of the Optical Society of America B **33**, C65-C71

(2016)

This paper reports a detailed numerical study of the synchronization properties of two mutually delay-coupled semiconductor lasers in the framework of the Lang-Kobayashi model. By computing high-definition stability diagrams we predict the complex distribution of periodic and chaotic laser oscillations on the coupling versus detuning control parameter plane. Such diagrams provide details concerning the behavior of the laser intensities, quantify objectively the synchronization between their electric fields, and display in-phase and out-of-phase laser behavior. In addition, we also describe the presence of a conspicuous abrupt change in the optimal shift for the greatest value of the cross-correlation function when varying the detuning between the optical angular frequencies of the lasers.

IEEE Transactions on Circuits and Systems II: Express Briefs **63**, 239-243

(2016)

We report a five-component autonomous chaotic oscillator of jerky type, hitherto the simplest of its kind, using only one operational amplifier. The key component of the circuit is a junction field-effect transistor operating in its triode region, which provides a nonlinear resistor of antisymmetrical current–voltage characteristic, emulating a Colpitts-like chaotic circuit. We describe the experimental results illustrating the dynamical behavior of the circuit. In addition, we report numerical simulations of a model of the circuit which display good agreement with our measurements.

ASCE Proceedings for Earth & Space Conference, At Orlando, FL

(2016)

As NASA prepares to visit asteroids and other poorly-consolidated near-earth-objects (NEOs), it will be important to safely interact with the granular materials at the surface of these objects. A particular concern is the low elastic modulus of granular materials: rubblepile asteroids are only held together by weak gravitational and van der Waals forces. This means that both the escape velocity and the sound velocity are low compared to their values on earth. To better predict the dynamics of the granular flows resulting from surface explorations such as digging, sample-collection, anchoring, or lift-off, we develop microgravity experiments which are able to predict the circumstances under which the NEO material will remain intact or become unstable. In our experiments, we insert a flexible probe into a granular material under simulated conditions of low gravity. We show that low-speed interactions reduce the effects of shock wave creation and observe that thinner diggers allow the grains to rearrange and minimize the possibility of ejecta.

Scientific Reports **6**, 26833

(2016)

We study experimentally the dissipation of energy in a rotating cylinder which is partially filled by granular material. We consider the range of angular velocity corresponding to continous and stationary flow of the granulate. In this regime, the stationary state depends on the angular velocity and on the filling mass. For a wide interval of filling levels we find a universal behavior of the driving torque required to sustain the stationary state as a function of the angular velocity. The result may be of relevance to industrial applications, e.g. to understand the power consumption of ball mills or rotary kilns and also for damping applications where mechanical energy has to be dissipated in a controlled way.

Journal of Computational Physics **311**, 158-172

(2016)

An algorithm for the exact calculation of the overlap volume of a sphere and a tetrahedron, wedge, or hexahedron is described. The method can be used to determine the exact local solid fractions for a system of spherical, non-overlapping particles contained in a complex mesh, a question of significant relevance for the numerical solution of many fluid-solid interaction problems. While challenging due to the limited machine precision, a numerically robust version of the calculation maintaining high computational efficiency is devised. The method is evaluated with respect to the numerical precision and computational cost. It is shown that the exact calculation is only limited by the machine precision and can be applied to a wide range of size ratios, contrary to previously published methods. Eliminating this constraint enables the usage of meshes with higher resolution near the system boundaries for coupled CFD–DEM simulations. The numerical robustness is further illustrated by applying the method to highly deformed mesh elements. The full source code of the reference implementation is made available under an open-source license.

European Journal of Physics **37**, 055305

(2016)

Scattering experiments are fundamental for structure elucidation of matter on molecular, atomic and sub-atomic length scales. In contrast, it is not standard to demonstrate optical scattering experiments on the undergraduate level beyond simple diffraction gratings. We present an inexpensive Mie-scattering setup for the classroom manufactured by 3D printing. This experiment allows to determine the particle size in dilute monodisperse suspensions and is, thus, suitable to demonstrate relations between scattering measurements and microscopic properties of particles within undergraduate lab course projects.

Physics of Fluids **28**, 073301

(2016)

In this work, we examine theoretically the cooling dynamics of binary mixtures of spheres and rods. To this end, we introduce a generalized mean field analytical theory, which describes the free cooling behavior of the mixture. The relevant characteristic time scale for the cooling process is derived, depending on the mixture composition and the aspect ratio of the rods. We simulate mixtures of spherocylinders and spheres using a molecular dynamics algorithm implemented on graphics processing unit (GPU) architecture. We systematically study mixtures composed of spheres and rods with several aspect ratios and varying the mixture composition. A homogeneous cooling state, where the time dependence of the system’s intensive variables occurs only through a global granular temperature, is identified. We find cooling dynamics in excellent agreement with Haff’s law, when using an adequate time scale. Using the scaling properties of the homogeneous cooling dynamics, we estimated numerically the efficiency of the energy interchange between rotational and translational degrees of freedom for collisions between spheres and rods.

Optical Society of America B **33**, 373-381

(2016)

We report a systematic investigation of the stability of a CO 2 laser subjected to delayed electro-optical feedback. Such laser displays roughly three operational intervals of stability which we characterize using high-resolution stability charts and a video. Contrary to current belief, we find delays smaller than ∼ 1 μs to strongly “clean complexity”, namely to prevent chaos and periodic pulsations with many spikes. In contrast, complex pulsations and chaos are significantly enhanced for τ > 1 μs. In this range, one finds a complex alternation of periodic and chaotic phases which are very sensitive to the delay duration.

Physical Review Letters **116**, 044101

(2016)

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with a suitably chosen phase. However, little is known about the best strategy for selecting adequate perturbations to reach desired states. Here we use experimental measures and numerical simulations to assess the benefits of controlling individually the three terms of a Duffing oscillator. Using a real-time analog indicator able to discriminate on-the-fly periodic behaviors from chaos, we reconstruct experimentally the phase versus perturbation strength stability areas when periodic perturbations are applied to different terms governing the oscillator. We verify the system to be more sensitive to perturbations applied to the quadratic term of the double-well Duffing oscillator and to the quartic term of the single-well Duffing oscillator.

Scientific Reports **6**, 18859

(2016)

Chaos and regularity are routinely discriminated by using Lyapunov exponents distilled from the norm of orthogonalized Lyapunov vectors, propagated during the temporal evolution of the dynamics. Such exponents are mean-field-like averages that, for each degree of freedom, squeeze the whole temporal evolution complexity into just a single number. However, Lyapunov vectors also contain a step-by-step record of what exactly happens with the angles between stable and unstable manifolds during the whole evolution, a big-data information permanently erased by repeated orthogonalizations. Here, we study changes of angles between invariant subspaces as observed during temporal evolution of Henon’s system. Such angles are calculated numerically and analytically and used to characterize self-similarity of a chaotic attractor. In addition, we show how standard tools of dynamical systems may be angle-enhanced by dressing them with informations not difficult to extract. Such angle-enhanced tools reveal unexpected and practical facts that are described in detail. For instance, we present a video showing an angle-enhanced bifurcation diagram that exposes from several perspectives the complex geometrical features underlying the attractors. We believe such findings to be generic for extended classes of systems.

Computational Particle Mechanics **3**, 383-388

(2016)

Following the recent development of a stable event-detection algorithm for hard-sphere systems, the implications of more complex interaction models are examined. The relative location of particles leads to ambiguity when it is used to determine the interaction state of a particle in stepped potentials, such as the square-well model. To correctly predict the next event in these systems, the concept of an additional state that is tracked separately from the particle position is introduced and integrated into the stable algorithm for event detection.

Granular Matter **18**, 31

(2016)

Packings of cohesive nanoparticles, that is nano powders, may be obtained as the result of repeated fragmentation–reagglomeration cycles (Schwager et al. in Phys Rev Lett 100:218002, 2008) such that the resulting sediment reveals a fractal structure. The size distribution of the fragments after a fragmentation step is a superposition of a narrow distribution of large particles (chunks) whose size is determined by the cutting length and a power-law distribution for small particles, representing scale invariant dust. It was shown that the exponent of the power-law, τ, is in non-trivial relation to the fractal dimension, d f , via d f (2 − τ) = 1. This poses the question for the structure of the sediment created by repeated fragmentation–reagglomeration cycles when the dust particles are excluded from the reagglomeration step. We found that even in this case, repeated fragmentation-reagglomeration cycles yield a sediment of fractal structure with slightly reduced fractal dimension while the dust exponent, τ, remains unchanged.

New Journal of Physics **18**, 118004

(2016)

Based on citation data of biologists and physicists, we reiterate that trends in statistical indicators are not reliable to unambiguously blame mathematics for the existence or lack of paper citations. We further clarify that, contrary to claims in the Comment (Higginson and Fawcett 2016 *New J. Phys.*18 118003), a clear statistical correlation between the number of equations and the citation success is not possible because the data is too noisy and not reliable for identifying trends unambiguously. Concerning their conclusions, we stress the well-know fact in statistics that even if correlation could be found, it by no means imply causality. Concerning their conclusions, we stress the well-know fact in statistics that even if correlation could be found, it by no means implies causality. Accordingly, to discuss ways of increasing citation rates by suppressing or hiding equations in appendices cannot be justified with statistics, even less so when based on small sets of very noisy data.

Revista Cubana de Física **33**, 37-38

(2016)

We study actively rotating granular particles manufactured by rapid prototyping. Such particles, as introduced in Ref. [1], convert vibrational motion into rotational motion via tilted elastic legs in a circular arrangement at the bottom of the particle. We extend the original design of the particles to make them suitable for mass-fabrication via rapid prototyping. The rotational velocity is measured in dependence of the driving frequency and amplitude. We find two different regimes of motion. For small amplitudes the particle performs a slow and stable rotation, while above a certain threshold the particle starts to perform a precission and consequently rotates significantly faster.

Soft Matter **12**, 3184-3188

(2016)

Granular heaps of particles created by deposition of mono-disperse particles raining from an extended source of finite size are characterized by a non-homogeneous field of density. It was speculated that this inhomogeneity is due to the transient shape of the sediment during the process of construction of the heap, thus reflecting the history of the creation of the heap. By comparison of structural characteristics of the heap with sediments created on top of inclined planes exploiting the method of Minkowski tensors, we provide further evidence to support this hypothesis. Moreover, for the case of sediments generated by homogeneous rain on surfaces, we provide relationships between the inclination of the surface and the Minkowski measures characterizing the isotropy of local particle environments.

Powder Technology **288**, 96-102

(2016)

The development of reliable strategies to optimize part production in additive manufacturing technologies hinges, to a large extent, on the quantitative understanding of the mechanical behavior of the powder particles during the application process. Since it is difficult to acquire this understanding based on experiments alone, a particle-based numerical tool for the simulation of powder application is required. In the presentwork,we develop such a numerical tool and apply it to investigate the characteristics of the powder layer deposited onto the part using a roller as the coating system. In our simulations, the complex geometric shapes of the powder particles are taken explicitly into account. Our results show that increasing the coating speed leads to an increase in the surface roughness of the powder bed, which is known to affect part quality.We also find that, surprisingly, powders with broader size distributions may lead to larger values of surface roughness as the smallest particles are most prone to form large agglomerates thus increasing the packing’s porosity. Moreover, we find that the load on the partmay vary over an order of magnitude during the coating process owing to the strong inhomogeneity of interparticle forces in the granular packing. Our numerical tool can be used to assist — and partially replace — experimental investigations of the flowability and packing behavior of different powder systems as a function of material and process parameters.

Journal of Computational Physics **308**, 421-437

(2016)

We propose an efficient event-driven algorithm for sequential ballistic deposition of complex-shaped rigid particles. Each of the particles consists of hard spheres (typically 5 … 1000) located at invariant relative positions. The sizes and relative positions of the spheres may be chosen such that the surface of the resulting particle appears smooth. In the sequential deposition process, by performing steps of rolling and linear motion, the particles move along the steepest descent in a landscape formed by the boundaries and previously deposited particles. The proposed algorithm generalizes the Visscher-Bolsterli algorithm [1] which is frequently used for packing of spheres, to non-spherical particles. The event-driven scheme of the algorithms allows simulation of multi-million particle systems using desktop computers.

Physical Review E **93**, 032901

(2016)

The coefficient of restitution may be determined from the sound signal emitted by a sphere bouncing repeatedly off the ground. Although there is a large number of publications exploiting this method, so far, there is no quantitative discussion of the error related to this type of measurement. Analyzing the main error sources, we find that even tiny deviations of the shape from the perfect sphere may lead to substantial errors that dominate the overall error of the measurement. Therefore, we come to the conclusion that the well-established method to measure the coefficient of restitution through the emitted sound is applicable only for the case of nearly perfect spheres. For larger falling height, air drag may lead to considerable error, too.

Scientific Reports **6**, 22520

(2016)

Downhill flows of granular matter colliding in the lowest point of a valley, may induce a selforganized jet. By means of a quasi two-dimensional experiment where fine grained sand flows in a vertically sinusoidally agitated cylinder, we show that the emergent jet, that is, a sheet of ejecta, does not follow the frequency of agitation but reveals subharmonic response. The order of the subharmonics is a complex function of the parameters of driving.

Revista Boliviana de Fisica **27**, 1–9

(2015)

We study the Rulkov model phase plane, a two-dimensional map-based model that describes the behavior of a neuron. Keeping constant one of the three parameters, we obtain phase planes showing well-defined periodicities. We show the importance of the parameter identifying the periodicities and the number of spikes per burst, quantities that are related between them by a linear relationship. The zones in which these periodicities are well-definedexhibit in some cases, shapes similar to those appearing in some palm-tree patterns observed both in trunks and in leaves. The detailed determination and description of these periodicity zones could be the basis for a further study on synchronization of nonidentical neurons in regions in which the domain of the parameter values ensure the fact to work with the same periodicity. We also analyze the reliability and the limitations of this method.

Modern Physics Letters B **29**, 1530018

(2015)

We study the organization of stability phases in the control parameter space of a periodically driven Brusselator. Specifically, we report high-resolution stability diagrams classifying periodic phases in terms of the number of spikes per period of their regular oscillations. Such diagrams contain accumulations of periodic oscillations with an apparently unbounded growth in the number of their spikes. In addition to the entrainment horns, we investigate the organization of oscillations in the limit of small frequencies and amplitudes of the drive. We find this limit to be free from chaotic oscillations and to display an extended and regular tiling of periodic phases. The Brusselator contains also several features discovered recently in more complex scenarios like, e.g. in lasers and in biochemical reactions, and exhibits properties which are helpful in the generic classification of entrainment in driven systems. Our stability diagrams reveal snippets of how the full classification of oscillations might look like for a wide class of flows.

Physical Review E **91**, 042907

(2015)

The spontaneous formation of heterogeneous patterns is a hallmark of many nonlinear systems, from biological tissue to evolutionary population dynamics. The standard model for pattern formation in general, and for Turing patterns in chemical reaction-diffusion systems in particular, are deterministic nonlinear partial differential equations where an unstable homogeneous solution gives way to a stable heterogeneous pattern. However, these models fail to fully explain the experimental observation of turbulent patterns with spatio-temporal disorder in chemical systems. Here we introduce a pattern-fluid model as a general concept where turbulence is interpreted as a weakly interacting ensemble obtained by random superposition of stationary solutions to the underlying reaction-diffusion system. The transition from turbulent to stationary patterns is then interpreted as a condensation phenomenon, where the nonlinearity forces one single mode to dominate the ensemble. This model leads to better reproduction of the experimental concentration profiles for the “stationary phases” and reproduces the turbulent chemical patterns observed by Q. Ouyang and H. L. Swinney [Chaos 1, 411 (1991)].

Nature **526**, 550-553

(2015)

Over a century of research into the origin of turbulence in wall-bounded shear flows has resulted in a puzzling picture in which turbulence appears in a variety of different states competing with laminar background flow^{1, 2, 3, 4, 5, 6}. At moderate flow speeds, turbulence is confined to localized patches; it is only at higher speeds that the entire flow becomes turbulent. The origin of the different states encountered during this transition, the front dynamics of the turbulent regions and the transformation to full turbulence have yet to be explained. By combining experiments, theory and computer simulations, here we uncover a bifurcation scenario that explains the transformation to fully turbulent pipe flow and describe the front dynamics of the different states encountered in the process. Key to resolving this problem is the interpretation of the flow as a bistable system with nonlinear propagation (advection) of turbulent fronts. These findings bridge the gap between our understanding of the onset of turbulence^{7} and fully turbulent flows^{8, 9}.

Physical Review E **92**, 043023

(2015)

We study the relation of permeability and morphology for porous structures composed of randomly placed overlapping circular or elliptical grains, so-called Boolean models. Microfluidic experiments and lattice Boltzmann simulations allow us to evaluate a power-law relation between the Euler characteristic of the conducting phase and its permeability. Moreover, this relation is so far only directly applicable to structures composed of overlapping grains where the grain density is known a priori. We develop a generalization to arbitrary structures modeled by Boolean models and characterized by Minkowski functionals. This generalization works well for the permeability of the void phase in systems with overlapping grains, but systematic deviations are found if the grain phase is transporting the fluid. In the latter case our analysis reveals a significant dependence on the spatial discretization of the porous structure, in particular the occurrence of single isolated pixels. To link the results to percolation theory we performed Monte Carlo simulations of the Euler characteristic of the open cluster, which reveals different regimes of applicability for our permeability-morphology relations close to and far away from the percolation threshold.

Scientific Reports **5**, 12703

(2015)

We investigate the residual distribution of structural defects in very tall packings of disks deposited randomly in large channels. By performing simulations involving the sedimentation of up to 50 × 10^9 particles we find all deposits to consistently show a non-zero residual density of defects obeying a characteristic power-law as a function of the channel height. This remarkable finding corrects the wide-spread belief that the density of defects should vanish algebraically with growing height. A non-zero residual density of defects implies a type of long-range spatial order in the packing, as opposed to only local ordering. In addition, we find deposits of particles to involve considerably less randomness than generally presumed.

Scientific Reports **5**, 16572

(2015)

We investigate the average turbulent wind field over a barchan dune by means of Computational Fluid Dynamics. We find that the fractional speed-up ratio of the wind velocity over the three-dimensional barchan shape differs from the one obtained from two-dimensional calculations of the airflow over the longitudinal cut along the dune’s symmetry axis — that is, over the equivalent transverse dune of same size. This finding suggests that the modeling of the airflow over the central slice of barchan dunes is insufficient for the purpose of the quantitative description of barchan dune dynamics as three-dimensional flow effects cannot be neglected.

Powder Technology **279**, 113-122

(2015)

We apply positron emission particle tracking (PEPT) to a gas-solid fluidized bed with injection of a secondary gas through a centrally arranged nozzle and present a method to compute stationary fluid-dynamic characteristics of the system from the trajectories of a test particle. In order to evaluate this non-invasive method we compare the field of density obtained by PEPT with the density obtained by a traditional, well-established and approved, yet invasive, measurement technique to find good agreement. Besides the penetration depth of the jet region and the opening angle of the jet which are inferred from the density field, we use PEPT to measure quantities whose measurement using traditional methods is rather sophisticated, including the residence time of particles in the jet region and the suspended phase, the coefficients of axial and radial dispersion and the material flux across the jet boundaries. We conclude that PEPT is a reliable and at the same time versatile technique to measure stationary fluid-dynamic properties of dynamical particle systems at spatial resolution only limited by the duration of the measurement.

Procedia Engineering **102**, 850-857

(2015)

Fluidized beds with secondary gas injection enjoy great popularity in process industry. Owing to their characteristic properties such as intense mixing of solids, excellent mass and heat transfer conditions as well as easy handling of solids, this type of apparatus is applied in various fields of process engineering nowadays. In the past decades research concerning fluidized beds with secondary gas injection has focused on understanding how solid particles and the injected gas are distributed within the apparatus. With the aid of invasive measurement techniques the region surrounding the injector nozzle was investigated with respect to the penetration depth of the gas jet above the nozzle orifice as well as the jet opening angle. A major drawback of the previously used measurement techniques consists in their invasive nature. Penetration of the injection zone by a probe can severely influence the local flow pattern and consequently has a detrimental effect on the reliability of the measured data. Therefore in the presented work for the first time the solids distribution as well as the motion of a single particle in a fluidized bed with secondary gas injection has been investigated by positron emission particle tracking (PEPT). This on-invasive technique is based on labeling one single particle, randomly selected from the bulk, radioactively, which allows for tracking its motion with high temporal and spatial resolution. The obtained data are compared with results derived from invasive measurements. Moreover PEPT-data have been used to perform investigations on the residence time behavior of particles within the jet region and the suspended phase. It could be found that the combination of invasive measurements and PEPT provide valuable information for the design and optimization of fluidized bed reactors with a well-defined injection zone.

Chaos **25**, 097607

(2015)

We report a detailed investigation of the stability of a CO_{2} laser with feedback as described by a six-dimensional rate-equations model which provides satisfactory agreement between numerical and experimental results. We focus on experimentally accessible parameters, like bias voltage, feedback gain, and the bandwidth of the feedback loop. The impact of decay rates and parameters controlling cavity losses are also investigated as well as control planes which imply changes of the laser physical medium. For several parameter combinations, we report stability diagrams detailing how laser spiking and bursting is organized over extended intervals. Laser pulsations are shown to emerge organized in several hitherto unseen regular and irregular phases and to exhibit a much richer and complex range of behaviors than described thus far. A significant observation is that qualitatively similar organization of laser spiking and bursting can be obtained by tuning rather distinct control parameters, suggesting the existence of unexpected symmetries in the laser control space.

CO_{2} laser with feedback is a complex system that has been investigated extensively both experimentally and through numerical simulations. As a result, a highly tested model exists for this laser, famed for providing quite satisfactory agreement between numerical and experimental observations. However, the laser involves a large number of freely tunable control parameters, whose impact on the laser performance and stability has not yet been investigated. In the present paper, we bridge this gap by performing a systematic numerical classification of complex dynamical phenomena observed in the CO_{2} laser with feedback as a function of its several control parameters. More specifically, we report high-resolution stability diagrams for accessible control parameters and for parameters that imply more subtle changes of the physical characteristics of the laser medium. Such diagrams describe the self-organization and the extension of stable spiking and bursting laser phases. Laser pulsations are shown to display novel regular and irregular features. In particular, our stability diagrams suggest that the laser control space harbors remarkable symmetries that were not yet accounted for but which are experimentally accessible. In addition, our stability diagrams provide stringent tests of the reliability and accuracy of the laser model investigated, currently the best model available for such laser.

Soft Matter **11**, 4295-4305

(2015)

Granular pipe flows are characterized by intermittent behavior and large, potentially destructive solid fraction variations in the transport direction. By means of particle-based numerical simulations of gravity-driven flows in vertical pipes, we show that it is possible to obtain steady material transport by adding a helical texture to the pipe’s inner-wall. The helical texture leads to more homogeneous mass flux along the pipe, prevents the emergence of large density waves and substantially reduces the probability of plug formation thus avoiding jamming of the particulate flow. We show that the granular mass flux Q through a pipe diameter D with an helical texture of wavelength λ follows the equation Q = Q0 · {1 − B sin [arctan(2π D/λ )]}, where Q0 is the flow without helix, predicted from the well-known Beverloo equation. Our new expression yields, thus, a modification of the Beverloo equation with only one additional fit parameter, B, and describes the particle mass flux with the helical texture with excellent quantitative agreement with simulation results. The future application of the method proposed here has the potential to improve granular pipe flows in a broad range of processes without the need of energy input from any external source.

Networks and Heterogeneous Media **10**, 209-221

(2015)

We report a systematic investigation of the magnetic anisotropy effects observed in the deterministic spin dynamics of a magnetic particle in the presence of a time-dependent magnetic field. The system is modeled by the Landau-Lifshitz-Gilbert equation and the magnetic field consists of two terms, a constant term and a term involving a harmonic time modulation. We consider a general quadratic anisotropic energy with three different preferential axes. The dynamical behavior of the system is represented in Lyapunov phase diagrams, and by calculating bifurcation diagrams, Poincaré sections and Fourier spectra. We find an intricate distribution of shrimp-shaped regular island embedded in wide chaotic phases. Anisotropy effects are found to play a key role in defining the symmetries of regular and chaotic stability phases.

New Journal of Physics **17**, 013036

(2015)

A recent study claimed that heavy use of equations impedes communication among biologists, as measured by the ability to attract citations from peers. It was suggested that to increase the probability of being cited one should reduce the density of equations in papers, that equations should be moved to appendices, and that math training among biologists should be improved. Here, we report a detailed study of the citation habits among physicists, a community that has traditionally strong training and dependence on mathematical formulations. Is it possible to correlate statistical citation patterns and fear of mathematics in a community whose work strongly depends on equations? By performing a systematic analysis of the citation counts of papers published in one of the leading journals in physics covering all its disciplines, we find striking similarities with distribution of citations recorded in biological sciences. However, based on the standard deviations in citation data of both communities, biologists and physicists, we argue that trends in statistical indicators are not reliable to unambiguously blame mathematics for the existence or lack of citations. We digress briefly about other statistical trends that apparently would also enhance citation success.

Journal of Fluid Mechanics **781**, 595-621

(2015)

A hydrodynamic description of dilute binary gas mixtures comprising smooth inelastic spheres interacting by binary collisions with a random coefficient of restitution is presented. Constitutive relations are derived using the Chapman-Enskog perturbative method, associated with a computer-aided method to allow high order Sonine polynomial expansions. The transport coefficients obtained are checked against DSMC simulations. The resulting equations are applied to the analysis of a vertically vibrated system. It is shown that differences in the shape of the distributions of coefficient of restitution are sufficient to produce partial segregation.

Physical Review E **91**, 062213

(2015)

We consider the transition of a horizontally vibrated monodisperse granular monolayer between its condensed state and its three-dimensional gaseous state as a function of the vibration parameters. The transition is characterized by an abrupt change of the dynamical state which leaves its fingerprints in several measurable quantities including dissipation rate, sound emission and a gap size which characterizes the sloshing motion of the material. We observe a pronounced hysteresis of the transition which can be explained by the collective motion of the particles relative to the container.

Physical Review Applied **3**, 024007

(2015)

By means of experiments in microgravity conditions we show that granular systems subjected to sinusoidal vibrations respond either by harmonic or gas-like dynamics, depending on the parameters of the vibration, amplitude and frequency, and the container size while subharmonic response is un- stable, except for extreme material properties and particular initial conditions. Extensive Molecular Dynamics simulations support our findings.

Physical Review E **91**, 062214

(2015)

A granular gas in gravity heated from below develops a certain stationary density profile. When the heating is switched off, the granular gas collapses. We investigate the process of sedimentation using computational hydrodynamics, based on the Jenkins-Richman theory, and find that the process is significantly more complex than generally acknowledged. In particular, during its evolution, the system passes several stages which reveal distinct spatial regions of inertial (supersonic) and diffusive (subsonic) dynamics. During the supersonic stages, characterized by Mach>1, the system develops supersonic shocks which are followed by a steep front of the hydrodynamic fields of temperature and density, traveling upward.

Granular Matter **17**, 73-82

(2015)

We consider the attenuation of the oscilla- tion of a flat spring due to the action of a granular damper. The efficiency of the damper is quantified by evaluating the position of the oscillator as a function of time using a Hall effect based position sensor. Perform- ing experiments for a large abundance of parameters under conditions of microgravity, we confirm a recent theory for granular damping [1] and show that the the- ory remains approximately valid even beyond the limits of its derivation.

Journal of Physical Chemistry Letters **5**, 4187-4193

(2014)

We report numerical evidence of a new type of wide-ranging organization of mixed-mode oscillations (MMOs) in a model of the peroxidase−oxidase reaction, in the control parameter plane defined by the supply of the reactant NADH and the pH of the medium. In classic MMOs, the intervals of distinct periodic oscillations are always separated from each other by windows of chaos. In contrast, in the new unfolding, such windows of chaos do not exist. Chaos-mediated and nonchaos-mediated MMO phases are separated by a continuous transition boundary in the control parameter plane. In addition, for low pH values, we find an exceptionally wide and intricate mosaic of MMO phases that is described by a detailed phase diagram.

New Journal of Physics **17**, 013024

(2014)

We revisit the problem of the structure of a nano-powder subjected to repeated fragmentation and sedimentation, and extend the analysis to the more relevant three-dimensional (3D) case. One important question not addressed previously is how the fractal dimension and dust exponent depend on space dimension. We find that qualitative behavior of the nano-powder in three dimensions is similar to the one in two dimensions. But the fractal dimension changes from 1.6 ± 0.1 in two dimensions to 2.1 ± 0.1 in three dimensions. The scaling relation between the fractal dimension and the dust exponent characterizing the fragment size distribution is the same as in two dimensions. The universality of these exponents is addressed by comparing the results with a much simpler lattice model. Although the dierent settling kinetics of the fragments leads to dierent anisotropies, the fractal properties are not affected.

Physical Review B ** 89**, 140102(R)

(2014)

At a pressure of around 13 GPa iron undergoes a structural phase transition from the bcc to the hexagonal close-packed phase. Atomistic simulations have provided important insights into this transition. However, while experiments in polycrystals show clear evidence that the α-ε transition is preceded by plasticity, simulations up to now could not detect any plastic activity occurring before the phase change. Here we study shock waves in polycrystalline Fe using an interatomic potential which incorporates the α-ε transition faithfully. Our simulations show that the phase transformation is preceded by dislocation generation at grain boundaries, giving a three-wave profile. The α-ε transformation pressure is much higher than the equilibrium transformation pressure but decreases slightly with increasing loading ramp time (decreasing strain rate). The transformed phase is mostly composed of hcp grains with large defect density. Simulated x-ray diffraction displays clear evidence for this hcp phase, with powder-diffraction-type patterns as they would be seen using current experimental setups.

New Jounal of Physics **16**, 093032

(2014)

Strong shock waves create not only plasticity in Fe, but also phase transform the material from its bcc phase to the high-pressure hcp phase. We perform molecular-dynamics simulations of large, 8-million atom nanocrystalline Fe samples to study the interplay between these two mechanisms. We compare results for a potential that describes dislocation generation realistically but excludes phase change with another which in addition faithfully features the bcc → hcp transformation. With increasing shock strength, we find a transition from a two-wave structure (elastic and plastic wave) to a three-wave structure (an additional phase-transformation wave), in agreement with experiment. Our results demonstrate that the phase transformation is preceded by dislocation generation at the grain boundaries (GBs). Plasticity is mostly given by the formation of dislocation loops, which cross the grains and leave behind screw dislocations. We find that the phase transition occurs for a particle velocity between 0.6 and 0.7 km s^{−1}. The phase transition takes only about 10 ps, and the transition time

decreases with increasing shock pressure.

Journal of Fluid Mechanics **751**, 601-626

(2014)

We investigate the impact of a granular jet on a finite target by means of particle simulations. The resulting hydrodynamic fields are compared with theoretical predictions for the corresponding flow of an incompressible and rotation-free fluid. The degree of coincidence between the field obtained from the discrete granular system and the idealized continuous fluid flow depends on the characteristics of the granular system, such as granularity, packing fraction, inelasticity of collisions, friction and target size. In certain limits we observe a granular-continuum transition under which the geometric and dynamic properties of the particle jet and the fluid jet become almost identical.

European Physical Journal Special Topics **223**, 2131-2144

(2014)

We study complex oscillations generated by the de Pillis-Radunskaya model of cancer growth, a model including interactions between tumor cells, healthy cells, and activated immune system cells. We report a wide-ranging systematic numerical classification of the oscillatory states and of their relative abundance. The dynamical states

of the cell populations are characterized here by two independent and complementary types of stability diagrams: Lyapunov and isospike diagrams. The model is found to display stability phases organized regularly in old and new ways: Apart from the familiar spirals of stability, it displays exceptionally long zig-zag networks and intermixed cascades of two- and three-doubling flanked stability islands previously detected only in feedback systems with delay. In addition, we also characterize the interplay between continuous spike-adding and spike-doubling mechanisms responsible for the unbounded complexification of periodic wave patterns. This article is dedicated to Prof. Hans Jürgen Herrmann on the occasion of his 60th birthday.

Physical Review E **90**, 052204

(2014)

We consider the motion of an aspherical inelastic particle of dumbbell type bouncing repeatedly on a horizontal flat surface. The coefficient of restitution of such a particle depends not only on material properties and impact velocity but also on the angular orientation at the instant of the collision whose variance is considerable, even for small eccentricity. Assuming random angular orientation of the particle at the instant of contact we characterize the measured coefficient of restitution as a fluctuating quantity and obtain a wide probability density function including a finite probability for negative values of the coefficient of restitution. This may be understood from the partial exchange of translational and rotational kinetic energy.

Computational Materials Science **82**, 399–404

(2014)

Using molecular dynamics simulation, we study the austenitic and the martensitic solid–solid phase transformation in the Fe–C system. Random alloys with C contents up to 1 at% are subjected to a heating/ cooling cycle. The martensite and austenite phase transition temperatures can be determined from the hysteresis of the system volume with temperature. The martensite temperature decreases with C content, as in experiment. The influence of the C atom position on the phase transformation and the pathways of the transition are analyzed. The transformed austenite phase shows strong twinning.

Chemie Ingenieur Technik **86**, 365-374

(2014)

A modified single-stage low pressure impactor is described to measure the coefficient of normal restitution *e*_{n} for nanoparticles. The device is analysed numerically using CFD, and the gas flow inside the structured impaction plate is studied. A formula for the calculation of *e*_{n} is derived and first measurements of *e*_{n} for spherical silver particles are presented together with numerical data obtained from force-based molecular dynamics simulations. Furthermore, the simulation data for *e*_{n} and the sticking probability are investigated in detail for the elastic, and partly for the plastic impaction regime.

Physical Review E **89**, 022205

(2014)

We consider the collision of a rough sphere with a plane by detailed analysis of the collision geometry. Using stochastic methods, the effective coefficient of restitution may be described as a fluctuating quantity whose probability density follows an asymmetric Laplace distribution. This result agrees with recent experiments by Montaine et al. [Phys. Rev. E 84, 041306 (2011)].

Computational Particle Mechanics **1**, 191-198

(2014)

Event-driven particle dynamics is a fast and precise method to simulate particulate systems of all scales. In

this work it is demonstrated that, despite the high accuracy of the method, the finite machine precision leads to simulations entering invalid states where the dynamics are undefined. A general event-detection algorithm is proposed which handles these situations in a stable and efficient manner. This requires a definition of the dynamics of invalid states and leads to improved algorithms for event-detection in hard-sphere systems.

85th Annual Meeting of the International Association of Applied Mathematics and Mechanics – GAMM 2014, March 10-14

(2014)

Numerical simulations by means of the Discrete Element Method (DEM) can provide a helpful tool in the investigation of the packing behavior of powders. In this type of numerical simulations, the Newton’s equations of motion for every single particle in the system are solved by taking into account all forces and torques acting on it, both due to external fields and due to interactions with other particles in the system. However, in order to make reliable predictions of the behavior of the bulk from DEM simulations, an accurate physical modeling of the relevant forces governing the interactions between the particles is required. In the present work, we perform DEM simulations of polydisperse packings of glass beads using several particle size distributions, with average particle diameter〈d〉varying within the range between 6.5μm and 56μm. […]

Scientific Reports **4**, 6227

(2014)

We study the packing of fine glass powders of mean particle diameter in the range (4–52) *μ*m both experimentally and by numerical DEM simulations. We obtain quantitative agreement between the experimental and numerical results, if both types of attractive forces of particle interaction, adhesion and non-bonded van der Waals forces are taken into account. Our results suggest that considering only viscoelastic and adhesive forces in DEM simulations may lead to incorrect numerical predictions of the behavior of fine powders. Based on the results from simulations and experiments, we propose a mathematical expression to estimate the packing fraction of fine polydisperse powders as a function of the average particle size.

Encyclopedia of Planetary Landforms. Springer. New York, NY.

(2014)

**Definition
**Straight to curvilinear longitudinal dune formed downwind of domes or barchans (Schatz et al. 2006).

A type of linear dune.

Encyclopedia of Planetary Landforms. Springer. New York, NY.

(2014)

**Formation
**Drop dunes form in areas where sand supply is low and subject to a bimodal wind regime where the directions of the winds differ by >120° (Parteli and Herrmann 2007; Parteli et al. 2009a; Reffet et al. 2010). It originates from a wedge dune whose downwind tail elongates, leading to a longitudinal dune (Parteli et al. 2009a; Fig. 1).

**Degradation
**They decay into a train of rounded barchans after a decrease of wind divergence angle down to 80° (dune convoy) (Parteli and Herrmann 2007; Parteli et al. 2009b).

Encyclopedia of Planetary Landforms. Springer. New York, NY.

(2014)

**Definition
**Circular to elliptical, relatively flat mounds often without external slip faces.

Domes may also be dunes smaller than the critical size for a barchan development where slip faces and horns are not able to evolve (Parteli 2007).

Aeolian Research **12**, 121-133

(2014)

Barchan dunes – crescent-shaped dunes that form in areas of unidirectional winds and low sand availability

– commonly display an asymmetric shape, with one limb extended downwind. Several factors have been identified as potential causes for barchan dune asymmetry on Earth and Mars: asymmetric bimodal wind regime, topography, influx asymmetry and dune collision. However, the dynamics and potential range of barchan morphologies emerging under each specific scenario that leads to dune asymmetry are far from being understood. In the present work, we use dune modeling in order to investigate the formation and evolution of asymmetric barchans. We find that a bimodal wind regime causes limb extension when the divergence angle between primary and secondary winds is larger than 90°, whereas the extended limb evolves into a seif dune if the ratio between secondary and primary transport rates is larger than 25%. Calculations of dune formation on an inclined surface under constant wind direction also lead to barchan asymmetry, however no seif dune is obtained from surface tilting alone. Asymmetric barchans migrating along a tilted surface move laterally, with transverse migration velocity proportional to the slope of the terrain. Limb elongation induced by topography can occur when a barchan crosses a topographic rise. Furthermore, transient asymmetric barchan shapes with extended limb also emerge during collisions between dunes or due to an asymmetric influx. Our findings can be useful for making quantitative inference on local wind regimes or spatial heterogeneities in transport conditions of planetary

dune fields hosting asymmetric barchans.

Chaos, Solitons & Fractals **59**, 129-134

(2014)

A recent conjecture in this Journal, concerning the existence of spiral stability phases in Hartley’s oscillator, is corroborated amply. We report numerically computed stability phase diagrams indicating precisely where spirals of periodicity and chaos may be found in several control planes of the system. In addition, we describe some remarkable parameter loops in control space which allow one to trace identical dynamical behaviors by tuning totally independent parameters.

EPJ Special Topics **223**, 2857-2867

(2014)

*Antiperiodic* oscillations forming innite cascades of spirals were recently found experimentally and numerically in the control parameter space of an autonomous electronic circuit. They were discovered while recording one specific voltage of the circuit. Here, we show that such regular self-organization may be measured in any of the four variables of the circuit. Although the relative size of individual phases, their boundaries and the number of peaks of each characteristic oscillation depends on the physical quantity used to record them, the global structural organization of the complex phase diagrams is an invariant of the circuit. Tunable families of antiperiodic oscillations cast fresh light on new intricate behavior of nonlinear systems and open the possibility of studying hitherto unobserved phenomena.

Physical Review E **89**, 052213

(2014)

The transport of sediment by a fluid along the surface is responsible for dune formation, dust entrainment, and a rich diversity of patterns on the bottom of oceans, rivers, and planetary surfaces. Most previous models of sediment transport have focused on the equilibrium (or saturated) particle flux. However, the morphodynamics of sediment landscapes emerging due to surface transport of sediment is controlled by situations out of equilibrium. In particular, it is controlled by the saturation length characterizing the distance it takes for the particle flux to reach a new equilibrium after a change in flow conditions. The saturation of mass density of particles entrained into transport and the relaxation of particle and fluid velocities constitute the main relevant relaxation mechanisms leading to saturation of the sediment flux. Here we present a theoretical model for sediment transport which, for the first time, accounts for both these relaxation mechanisms and for the different types of sediment entrainment prevailing under different environmental conditions. Our analytical treatment allows us to derive a closed expression for the saturation length of sediment flux, which is general and thus can be applied under different physical conditions.

EPJ Special Topics **223**, 2269-2283

(2014)

Sand dunes are ubiquitous in deserts, on coasts, on the sea bottom, and on the surface of Mars, Venus and Titan. The quantitative understanding of dune dynamics is thus of relevance for a broad range of physical, geological and planetary sciences. A morphodynamic model for dunes, which combines an analytical description of the average turbulent wind field over the topography with a continuum saltation model, has proven successful to quantitatively reproduce the shape of aeolian dunes of different types. We present a short review on the physics of dune formation and model development, as well as some future plans for further developments and applications.

Physica A **410**, 313-318

(2014)

We study the distribution of periodic orbits in one-dimensional two-parameter maps. Specifically, we report an exact expression to quantify the growth of the number of periodic orbits for discrete-time dynamical systems governed by polynomial equations of motion of arbitrary degree. In addition, we compute high-resolution phase diagrams for quartic and for both normal forms of cubic dynamics and show that their stability phases emerge all distributed in a similar way, preserving a characteristic invariant ordering. Such coincidences are remarkable since our exact expression shows the total number of orbits of these systems to differ dramatically by more than several millions, even for quite low periods. All this seems to indicate that, surprisingly, the total number and the distribution of stable phases is not significantly affected by the specific nature of the nonlinearity present in the equations of motion.

Physical Review Letters **110**, 254301

(2013)

We investigate the coefficient of normal restitution as a function of the impact velocity, e(v), for inelastic spheres. We observe oscillating behavior of e(v) which is superimposed to the known decay of the coefficient of restitution as a function of impact velocity. This remarkable effect was so far unnoticed because under normal circumstances it is screened by statistical scatter. We detected its clear signature by recording large amounts of data using an automated experiment. The new effect may be understood as an interplay between translational and vibrational degrees of freedom of the colliders. Both characteristics of the oscillation, the wavelength and the amplitude, agree quantitatively with a theoretical description of the experiment.

Physica A **392**, 1762–1769

(2013)

Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent −2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape.

Physical Review Letters **111**, 018001

(2013)

We experimentally investigate the energy dissipation rate in sinusoidally driven boxes which are partly filled by granular material under conditions of weightlessness. We identify two different modes of granular dynamics, depending on the amplitude of driving, A. For intense forcing, A > A_{0}, the material is found in the* collect-and-collide* regime where the center of mass of the granulate moves synchronously with the driven container while for weak forcing, A < A_{0}, the granular material exhibits gas-like behavior. Both regimes correspond to different dissipation mechanisms, leading to different scaling with amplitude and frequency of the excitation and with the mass of the granulate. For the collect-and-collide regime, we explain the dependence on frequency and amplitude of the excitation by means of an effective one-particle model. For both regimes, without using any adjustable parameter the results may be collapsed to a single curve characterizing the physics of granular dampers.

Physics Letters A **377**, 2052–2057

(2013)

Some dynamical properties for a dissipative time-dependent Lorentz gas are studied. We assume that the size of the scatterers change periodically in time. We show that for some combination of the control parameters the particles come to a complete stop between the scatterers, but for some other cases, the average velocity grows unbounded. This is the first time that the unlimited energy growth is observed in a dissipative system. Finally, we study the behavior of the average velocity as a function of the number of collisions and we show that the system is scaling invariant with scaling exponents well defined.

Journal of Physical Chemistry B **117**, 1166−1175

(2013)

We investigate the structure and adsorption of amphiphilic molecules at planar walls modified by tethered chain molecules using density functional theory. The molecules are modeled as spheres composed of a hydrophilic and hydrophobic part. The pinned chains are treated as tangentially jointed spheres that can interact with fluid molecules via orientation-dependent forces. Our density functional approach involves fundamental measure theory, thermodynamic perturbation theory for chains, and a meanfield approximation for describing the anisotropic interactions. We study the adsorption of the particles, focusing on the competition between the external field (due to the surface and due to attached chain molecules) and the interaction-induced ordering phenomena.

New Journal of Physics **15**, 093023

(2013)

The oscillation of a spring may be attenuated by means of a granular damper. In difference to viscous dampers, the amplitude decays nearly *linearly* in time up to a finite value, from there on it decays much slower. We quantitatively explain the linear decay, which was a long-standing question.

Granular Matter **15**, 377–387

(2013)

We study the mechanism leading to the formation of stripe-like patterns in a rectangular container filled with a sub-monolayer of frictional spherical particles when it is subjected to horizontal oscillations. By means of Molecular Dynamics simulations we could reproduce the experimental results. Systematic simulations allow to identify friction to be responsible for the pattern formation, that is, the tangential interaction between contacting particles and between the particles and the floor of the container. When particles are in contact with the floor and other adjacent particles simultaneously, there emerges a frustrated situation in which the particles are prevented from rolling on the floor. This effect leads to local jamming and eventually to stripe-like pattern formation. In the long time evolution, the stripes are unstable. Stripes may merge as well as disintegrate.

AIP Conference Proceedings **1542**, 811-814

(2013)

We investigate the collective dissipative behavior of a model granular material (steel beads) when subjected to vibration. To this end, we study the attenuation of the amplitude of an oscillating leaf spring whose free end carries a rectangular box partly filled with granulate. To eliminate the perturbing influence of gravity, the experiment was performed under conditions of microgravity during parabolic flights. Different regimes of excitation could be distinguished, namely, a gas-like state of disordered particle motion and a state where the particles slosh back and forth between the container walls in a collective way, referred to as *collect-and-collide* regime. For the latter regime, we provide an expression for the container size leading to maximal dissipation of energy, that also marks the transition to the gas like regime. Also for systems driven at fixed amplitude and frequency, we find both the gas regime and the *collect-and-collide* regime resulting in similar dissipative behavior as in the case of the attenuating vibration.

Physical Review E **87**, 033301

(2013)

The dynamics of dissipative soft-sphere gases obeys Newton’s equations of motion, which are commonly solved numerically by (force-based) Molecular Dynamics (MD) schemes.With the assumption of instantaneous, pairwise collisions, the simulation can be accelerated considerably using event-driven MD, where the coefficient of restitution is derived from the interaction force between particles. Recently it was shown, however, that this approach may fail dramatically, that is, the obtained trajectories deviate significantly from the ones predicted by Newton’s equations. In this paper, we generalize the concept of the coefficient of restitution and derive a numerical scheme which, in the case of dilute systems and frictionless interaction, allows us to perform highly efficient event-driven MDsimulations even for noninstantaneous collisions.We show that the particle trajectories predicted by our scheme agree perfectly with the corresponding (force-based) MD, except for a short transient period whose duration corresponds to the duration of the contact. Thus, the new algorithm solves Newton’s equations of motion like force-based MD while preserving the advantages of event-driven simulations.

Physical Review E **87**, 039904(E)

(2013)

New Journal of Physics **15**, 093030

(2013)

The decay of temperature of a force-free granular gas in the homogeneous cooling state depends on the specific model for particle interaction. For the case of rough spheres, in recent experimental and theoretical work, the coefficient of restitution was characterized as a fluctuating quantity. We show that for such particles, the decay of temperature with time follows the law *T *∼* t*^{−50/29} which deviates from Haff’s law, *T* ∼ *t*^{−2}, obtained for gases of particles interacting via a constant coefficient of restitution also from *T* ∼ *t*^{−5/3 }obtained for gases of viscoelastic particles. Our results are obtained from kinetic theory and are in very good agreement with Monte Carlo simulations.

AIP Conference Proceedings **1542**, 149-152

(2013)

In this paper an algorithm is described which combines the efficiency of event-driven Molecular-Dynamics (eMD) and the physical correctness of force-based Molecular-Dynamics (MD) for dilute granular systems of frictionless spheres.

Granular Matter **15**, 389-390

(2013)

Cohesive particle systems are ubiquitous in nature and industrial applications. Besides the ordinary repulsive interaction between particles, the macroscopic behavior of cohesive systems is determined by attractive interactions between particles, such as van der Waals forces, liquid bridges and electrostatics.

Much insight in the dynamics of cohesive granular materials was obtained by means of discrete element modeling (DEM). First introduced by Cundall and Strack [1], this method offers a robust numerical approach to explore the macroscopic behaviour of granular materials with detailed analysis of particle interactions. As one of the pioneers in DEM, Colin Thornton and his co-workers have advanced DEM significantly, in particular, in modeling cohesive particle systems, e.g. [2, 3, 4, 5, 6, 7, 8, 9, 10]. Thornton’s work inspired the research in this area significantly.

Cohesive forces in particle systems can be caused by van der Waals interactions [2, 3, 4, 5, 6, 7, 8, 9], liquid bridges [10, 11] and electrostatic interaction [12]. The systematic investigation of cohesive particle systems was much inspired by the seminal work on impact of elastic spheres with adhesion [2], in which theories of Hertz [13], Mindlin and Deresiewicz [14] were adapted to model the normal and tangential interaction of elastic particles, and the classical JKR model [15, 16] was used for modelling the adhesive interaction. In particular, this was used to study the agglomerate breakage during impacts [6, 7] and diametrical compression [8] whose implications can be considered as main achievements.

Beginning with the aforementioned pioneering work, the knowledge on cohesive particle systems has progressed dramatically. The present topical issue on “Micro-mechanics and Dynamics of Cohesive Particle Systems” includes ten invited papers addressing the recent development in understanding micro-mechanics and dynamics of cohesive particle systems and reflecting the state of the art in this field. They cover the measurement of motion of particles in cohesive granular systems [17], modeling of adhesion of particles due to van der Waals forces [18, 19], rheology [20], dynamics and segregation of wet granular systems [21, 22, 23], packing and fluidization of particles with electrostatic and magnetic forces [24, 25], and the measurement of the horizontal-to-vertical stress ratio of cohesive powders [26].

The authors and editors of this *Topical Issue* dedicate this volume to their highly esteemed scientific colleague, teacher and personal friend, Prof. Colin Thornton, on the occasion of his 70th birthday.

Philosophical Magazine **93**, 4090-4107

(2013)

This paper reports a detailed numerical investigation of the geometrical and structural properties of three-dimensional heaps of particles. Our goal is the characterization of very large heaps produced by ballistic deposition from extended circular dropping areas. First, we provide an in-depth study of the formation of monodisperse heaps of particles. We find very large heaps to contain three new geometrical characteristics: they may display two external angles of repose, one internal angle of repose, and four distinct packing fraction (density) regions. Such features are found to be directly connected with the size of the dropping zone. We derive a differential equation describing the boundary of an unexpected triangular packing fraction zone formed under the dropping area.We investigate the impact that noise during the deposition has on the final heap structure. In addition, we perform two complementary experiments designed to test the robustness of the novel features found. The first experiment considers changes due to polydispersity. The second checks what happens when letting the extended dropping zone to become a point-like source of particles, the more common type of source.

New Journal of Physics **15**, 043044

(2013)

A numerical study that aims to analyze the thermal mechanisms of unsteady, supersonic granular flow by means of hydrodynamic simulations of the Navier–Stokes granular equation is reported in this paper. For this purpose, a paradigmatic problem in granular dynamics such as the Faraday instability is selected. Two different approaches for the Navier–Stokes transport coefficients for granular materials are considered, namely the traditional Jenkins–Richman theory for moderately dense quasi-elastic grains and the improved Garz´o–Dufty–Lutsko theory for arbitrary inelasticity, which we also present here. Both the solutions are compared with event-driven simulations of the same system under the same conditions, by analyzing the density, temperature and velocity field. Important differences are found between the two approaches, leading to interesting implications. In particular, the heat transfer mechanism coupled to the density gradient, which is a distinctive feature of inelastic granular gases, is responsible for a major discrepancy in the temperature field and hence in the diffusion mechanisms.

Proceedings of the 6^{th} International Conference on Discrete Element Methods, pp. 217 - 222

(2013)

The multisphere method is commonly used as an approximation for modeling particles of complex geometric shapes in DEM simulations. However, typically the mass and moment of inertia of the resulting sphere clumps are incorrectly computed as a result of the (artifactual) contribution of the sphere-sphere overlaps. We adapted the current public release of LIGGGHTS in order to perform DEM simulations of rigid bodies using the mass and moment of inertia of the particles as obtained through an analytical (exact) method.

AIP Conference Proceedings **1542**, 185-188

(2013)

Additive manufacturing constitutes a promising production technology with potential application in a broad range of industrial areas. In this type of manufacturing process, objects are created from powder particles by adding layers of material upon one another through selectively melting particles from the powder bed. However, understanding the mechanical behavior of the powder during manufacturing as a function of material properties and particle shape is an essential pre-requisite for optimizing the production process. Here we develop a numerical tool for modeling the dynamics of powder particles during additive manufacturing based on force-based simulations by means of the Discrete Element Method (DEM). An existing DEM software (LIGGGHTS) is extended in order to study the transport of powder particles of complex geometric shapes through accounting for the boundary conditions inherent to the manufacturing process.

Scientific Reports **3**, 2858

(2013)

Transverse dunes, which form under unidirectional winds and have fixed profile in the direction perpendicular to the wind, occur on all celestial objects of our solar system where dunes have been detected. Here we perform a numerical study of the average turbulent wind flow over a transverse dune by means of computational fluid dynamics simulations. We find that the length of the zone of recirculating flow at the dune lee – the *separation bubble* – displays a surprisingly strong dependence on the wind shear velocity, *u _{*}*: it is nearly independent of

Physical Review E **87**, 042907

(2013)

We report numerical evidence showing that periodic oscillations can produce unexpected andwide-ranging zigzag parameter networks embedded in chaos in the control space of nonlinear systems. Such networks interconnect shrimplikewindows of stable oscillations and are illustrated here for a tunnel diode, for an erbium-doped fiber-ring laser, and for the Hénon map, a proxy of certain CO_{2} lasers. Networks in maps can be studied without the need for solving differential equations. Tuning parameters along zig-zag networks allows one to continuously modify wave patterns without changing their chaotic or periodic nature. In addition, we report convenient parameter ranges where such networks can be detected experimentally.

Selected Topics in Nonlinear Dynamics and Theoretical Electrical Engineering (Kyamakya K., Halang W., Mathis W., Chedjou J., Li Z.; Eds.) **SCI 459**. 161-177. Springer. Berlin, Heidelberg.

(2013)

A remarkably regular organization of spirals converging to a focal point in control parameter space was recently predicted and then observed in a nonlinear circuit containing two diodes. Such spiral organizations are relatively hard to observe experimentally because they usually emerge very compressed. Here we show that a circuit with a tunnel diode displays not one but two large spiral cascades. We show such cascades to exist over wide parameter ranges and, therefore, we expect them to be easier to observe experimentally.

Chaos, Solitons & Fractals **52** , 59-65

(2013)

We report an autonomous circuit containing periodicity hubs with surprisingly broad spirals. Knowledge of broad spirals is important because all presently known spirals are compressed along specific directions in parameter space making them difficult to study experimentally and theoretically. We characterize the performance of the circuit by computing stability diagrams for relevant sections of the control space. In addition, the alternation of chaotic and periodic spiral phases is contrasted with equivalent alternations obtained from an experimental implementation of the circuit.

The European Physical Journal D **67**, 149

(2013)

We report a numerical characterization of the stability of semiconductor lasers with delayed feedback under the simultaneous variation of the delay time τ and the pump current *P*. Changes in the number of External Cavity Modes are studied as a function of the delay time while the Regular Pulse Package regime is characterized as a function of the pump current. In addition, we describe some remarkable structures observed in the *τ × P* control plane, delimiting where these and other complex regimes of laser operation exist.

Scientific Reports **3**, 1958

(2013)

The investigation of regular and irregular patterns in nonlinear oscillators is an outstanding problem in physics and in all natural sciences. In general, regularity is understood as tantamount to periodicity. However, there is now a flurry of works proving the existence of ‘‘antiperiodicity’’, an unfamiliar type of regularity. Here we report the experimental observation and numerical corroboration of antiperiodic oscillations. In contrast to the isolated solutions presently known, we report infinite hierarchies of antiperiodic waveforms that can be tuned continuously and that form wide spiral-shaped stability phases in the control parameter plane. The waveform complexity increases towards the focal point common to all spirals, a key hub interconnecting them all.

Scientific Reports **3**, 3350

(2013)

We report the experimental discovery of a remarkable organization of the set of self-generated periodic oscillations in the parameter space of a nonlinear electronic circuit. When control parameters are suitably tuned, the wave pattern complexity of the periodic oscillations is found to increase orderly without bound. Such complex patterns emerge forming self-similar discontinuous phases that combine in an artful way to produce large discontinuous spirals of stability. This unanticipated discrete accumulation of stability phases was detected experimentally and numerically in a Duffing-like proxy specially designed to bypass noisy spectra conspicuously present in driven oscillators. Discontinuous spirals organize the dynamics over extended parameter intervals around a focal point. They are useful to optimize locking into desired oscillatory modes and to control complex systems. The organization of oscillations into discontinuous spirals is expected to be generic for a class of nonlinear oscillators.

Physical Review Letters **111**, 168003

(2013)

We investigate jammed granular matter in a slowly rotating drum partially filled with granular material and find a state of polydirectional stability. In this state, the material responds elastically to small stresses in a wide angular interval while it responds by plastic deformation when subjected to small stresses outside this interval of directions. We describe the evolution of the granulate by means of a rate equation and find quantitative agreement with the experiment. The state of polydirectional stability complements the fragile state, where the material responds elastically to small applied stresses only in a certain direction but even very small stresses in any other direction would lead to plastic deformations. Similar to fragile matter, polydirectionally stable matter is created in a dynamic process by self-organization.

Physical Review Letters **111**, 218002

(2013)

Sediment transport along the surface drives geophysical phenomena as diverse as wind erosion and dune formation. The main length scale controlling the dynamics of sediment erosion and deposition is the saturation length *L _{s}*, which characterizes the flux response to a change in transport conditions. Here we derive, for the first time, an expression predicting

AIP Conference Proceedings **1501**, 993-1000

(2012)

We perform two-dimensional hydrodynamic simulations on a paradigmatic problem of granular dynamics, the Faraday instability, using two different approximations to the Navier-Stokes granular equations: the constitutive equations and kinetic coefficients derived from the assumption of vanishing inelasticity (Jenkins-Richman approach) obtained by solving the Enskog equation disks by means of Grad’s method, and the ones obtained by solving the Enskog equation with the Chapman-Enskog method (Garzó-Dufty-Lutsko approach). The comparison reveals important qualitative and quantitative differences with respect to the hydrodynamic fields obtained by averaging results from particle simulations of the same system.

Chaos **22**, 026123

(2012)

Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F=−ηV2; (iii) F=−ηVμ with μ≠1 and μ≠2 and; (iv) F=−ηV, where η is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined.

We revisit the problem of non-interacting particles in a time dependent Lorentz gas. We describe the model by using a four dimensional nonlinear map. As it is known, the phase space of the Lorentz gas with static scatterers is fully chaotic and the velocity of the particle is constant. However, when a time dependent perturbation is introduced to the boundary, the energy is no longer conserved and the unlimited energy growth is observed for the conservative case. On the other hand, our results show that when dissipation is introduced into the system, either by collisional dissipation or dissipation during the flight, the unlimited energy growth is no longer observed. Depending on the strength of the dissipation and considering short time, the average velocity can either grows and reaches a constant plateau or decays until the particle reaches the state of rest. For the cases, when the dynamics does not stop between the scatterers, the behaviour of the average velocity is described by using scaling arguments and once the scaling exponents are known, classes of universalities are defined.

Europhysics Letters **100**, 2005

(2012)

It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important —moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles.

Physics Letters A **376**, 3630-3637

(2012)

We study some dynamical properties for the problem of a charged particle in an electric field considering both the low velocity and relativistic cases. The dynamics for both approaches is described in terms of a two-dimensional and nonlinear mapping. The structure of the phase spaces is mixed and we introduce a hole in the chaotic sea to let the particles to escape. By changing the size of the hole we show that the survival probability decays exponentially for both cases. Additionally, we show for the relativistic dynamics, that the introduction of dissipation changes the mixed phase space and attractors appear. We study the parameter space by using the Lyapunov exponent and the average energy over the orbit and show that the system has a very rich structure with infinite family of self-similar shrimp shaped embedded in a chaotic region.

Granular Matter **14**, 77

(2012)

Physical Review E **85**, 031307

(2012)

We report a striking effect observed experimentally in several granular materials when shaken horizontally:The material displays a recurrent alternation between a slow inﬂation phase, characterized by an increase in its volume, and a fast collapse phase, when the volume abruptly returns to its original value. The frequency of such phase alternations is totally decoupled from the frequency of the external drive. We argue that the inﬂation and collapse alternation arises from an interplay between the mechanical stability of the material and Reynolds dilatancy due to convective motion.

Physical Review E **86**, 061310

(2012)

Granular ratchets are well-known devices that when driven vertically produce a counterintuitive horizontal transport of particles. Here we report the experimental observation of a complementary effect: the striking ability of circular ratchets to convert their vertical vibration into their own rotation. The average revolution speed shows a maximum value for an optimal tooth height. With no special effort the rotation speed could be maintained steady during several hours. Unexpected random arrests and reversals of the velocity were also observed abundantly.

Physica A **391**, 4442-4447

(2012)

Instruments for surgical and dental application based on oscillatory mechanics submit unwanted vibrations to the operator’s hand. Frequently the weight of the instrument’s body is increased to dampen its vibration. Based on recent research regarding the optimization of granular damping we developed a prototype granular damper that attenuates the vibrations of an oscillatory saw twice as efficiently as a comparable solid mass.

Granular Matter **14**, 115-120

(2012)

When granular systems are modeled by hard spheres, particle–particle collisions are considered as instantaneous events. This implies that while the velocities change according to the collision rule, the positions of the particles are the same before and after such an event. We show that depending on the material and system parameters, this assumption may fail. For the case of viscoelastic particles we present a universal condition which allows to assess whether hard-sphere modeling and, thus, event-driven Molecular Dynamics simulations are justified.

Physical Review E **85**, 041306

(2012)

This paper shows that negative coefficients of normal restitution occur inevitably when the interaction force between colliding particles is finite. We derive an explicit criterion showing that for any set of material properties there is *always* a collision geometry leading to negative restitution coefficients. While from a phenomenological point of view, negative coefficients of normal restitution appear rather artificial, this phenomenon is generic and implies an important overlooked limitation of the widely used hard sphere model. The criterion is explicitly applied to two paradigmatic situations: for the linear dashpot model and for viscoelastic particles. In addition, we show that for frictional particles the phenomenon is less pronounced than for smooth spheres.

Proceedings XXIII ICTAM, 19th – 24th August 2012, Beijing, China

(2012)

We report a numerical investigation of the structural properties of very large three-dimensional heaps of granular material produced by ballistic deposition from extended circular dropping areas. Very large heaps are found to contain three new geometrical characteristics not observed before: they may have two external angles of repose, an internal angle of repose, and four distinct packing fraction (density) regions. Such characteristics are shown to be directly correlated with the size of the dropping zone. In addition, we also describe how noise during the deposition affects the final heap structure.

Physical Review Letters **109**, 128001

(2012)

We report a numerical investigation of the structural properties of very large three-dimensional heaps of particles produced by ballistic deposition from extended circular dropping areas. Very large heaps are found to contain three new geometrical characteristics not observed before: they may have two external angles of repose, an internal angle of repose, and four distinct packing fraction (density) regions. Such characteristics are shown to be directly correlated with the size of the dropping zone. In addition, we also describe how noise during the deposition affects the final heap structure.

Industriekolloqium des Sonderforschungsbereichs 814 – Additive Fertigung (Drummer, D.; Ed.), 117 – 130

(2012)

Additive Fertigungsprozesse erfahren zurzeit zunehmendes Inte-resse aus Wirtschaft und Forschung, so zum Beispiel durch den Sonderforschungsbereich 814 (SFB 814) an der Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU). Der Arbeitskreis Modellierung innerhalb des SFB 814 widmet sich hierbei dem Auf- und Ausbau von grundlegendem Prozessverständnis mit dem Schwerpunkt auf pulver- und strahlbasierten Fertigungs-prozessen. Dies wird durch Anwendung komplexer Modelle er-reicht, welche die unterschiedlichen physikalischen Skalen und Effekte nachbilden. Der Schlüssel zum tieferen Prozessver-ständnis liegt dabei neben der eigentlichen Modellierung in der Verknüpfung der Einflüsse, die aus Effekten unterschiedlicher Größen- und Zeitskalen stammen. Das Ziel ist dabei stets die Optimierung des resultierenden Bauteils, vor allem hinsichtlich der Qualität der Oberfläche, der mechanischen Eigenschaften und der Wirtschaftlichkeit des Herstellungsprozesses.

Third International Planetary Dunes Workshop, 7007

(2012)

It has recently been established that sand is mobile under the current Martian cli-mate, including at the North Pole [1,2]. Here we present a detailed study of the morphometry and migration of barchan and dome dunes in the North Polar Region of Mars.

Reports on Progress in Physics **75**, 106901

(2012)

The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This paper presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.

Physics Letters A **376**, 2109-2116

(2012)

We describe some remarkable *continuous deformations* which create and destroy peaks in periodic oscillations of the Mackey–Glass equation, a paradigmatic example of a delayed feedback system. Peak creation and destruction results in richer bifurcation diagrams which, in addition to the familiar branches arising from period-doubling and peak-adding bifurcations, may also display arbitrary combinations of doubling and adding, leading to highly complex mosaics of stability domains in control parameter space. In addition, we show that the onset of higher dimensionality does not alter the prevailing dynamics instantaneously and, remarkably, even may have no effect at all, a result that cannot be predicted analytically with standard methods.

Europhysics Letters **100**, 48002

(2012)

We study the global organization of oscillations in sigmoidal maps, a class of models which reproduces complex locking behaviors commonly observed in lasers, neurons, and other systems which display spiking, bursting, and chaotic sequences of spiking and bursting. We find periodic oscillations to emerge organized regularly according to the elusive Stern-Brocot tree, a *symmetric* and more general tree which contains the better-known *asymmetric* Farey tree as a sub-tree. The Stern-Brocot tree provides a natural and encompassing organization to classify nonlinear oscillations. The mathematical algorithm for generating both trees is exactly the same, differing only in the initial conditions. Such degeneracy suggests that the wrong tree might have been attributed to locking phenomena reported in some of the earlier works.

Physical Review E **84**, 021302

(2011)

The coefficient of restitution of colliding viscoelastic spheres is known analytically as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While being analytically exact, this result is not suitable for applications in efficient event-driven molecular dynamics (eMD) or direct simulation Monte Carlo (DSMC) methods. Based on the analytic result, here we derive expressions for the coefficient of restitution that allow for application in efficient eMD and DSMC simulations of granular systems.

Physical Review E **84**, 041306

(2011)

The coefficient of restitution of a spherical particle in contact with a flat plate is investigated as a function of the impact velocity. As an experimental observation we notice nontrivial (non-Gaussian) fluctuations of the measured values. For a fixed impact velocity, the probability density of the coefficient of restitution, p(ε), is formed by two exponential functions (one increasing, one decreasing) of different slope. This behavior may be explained by a certain roughness of the particle which leads to energy transfer between the linear and rotational degrees of freedom.

Physical Review E **83**, 041304

(2011)

The main precondition of simulating systems of hard particles by means of event-driven modeling is theassumption of instantaneous collisions. The aim of this paper is to quantify the deviation of event-driven modeling from the solution of Newton’s equation of motion using a paradigmatic example: If a tennis ball is held above a basketball with their centers vertically aligned, and the balls are released to collide with the ﬂoor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple textbook explanation of this effect is an oversimpliﬁcation, even for the limit of perfectly elastic particles. Instead, there may occur a rather complex scenario including multiple collisions which may lead to a very different ﬁnal velocity as compared with the velocity resulting from the oversimpliﬁed model.

Physical Review E **84**, 011301

(2011)

The response of an oscillating granular damper to an initial perturbation is studied using experiments performed in microgravity and granular dynamics simulations. High-speed video and image processing techniques are used to extract experimental data. An inelastic hard sphere model is developed to perform simulations and the results are in excellent agreement with the experiments. The granular damper behaves like a frictional damper and a linear decay of the amplitude is observed. This is true even for the simulation model, where friction forces are absent. A simple expression is developed which predicts the optimal damping conditions for a given amplitude and is independent of the oscillation frequency and particle inelasticities.

Journal of Computational Chemistry **32**, 3329-3338

(2011)

Molecular dynamics algorithms for systems of particles interacting through discrete or “hard” potentials are fundamentally different to the methods for continuous or “soft” potential systems. Although many software packages have been developed for continuous potential systems, software for discrete potential systems based on event‐driven algorithms are relatively scarce and specialized. We present DynamO, a general event‐driven simulation package, which displays the optimal (*N*) asymptotic scaling of the computational cost with the number of particles *N*, rather than the (*N* log *N*) scaling found in most standard algorithms. DynamO provides reference implementations of the best available event‐driven algorithms. These techniques allow the rapid simulation of both complex and large (>10^{6} particles) systems for long times. The performance of the program is benchmarked for elastic hard sphere systems, homogeneous cooling and sheared inelastic hard spheres, and equilibrium Lennard–Jones fluids. This software and its documentation are distributed under the GNU General Public license and can be freely downloaded from http://marcusbannerman.co.uk/dynamo.

Mathematical Modelling of Natural Phenomena **6**, 151-174

(2011)

A computer aided method using symbolic computations that enables the calculation of the source terms (Boltzmann) in Grad’s method of moments is presented. The method is extremely powerful, easy to program and allows the derivation of balance equations to very high moments (limited only by computer resources). For sake of demonstration the method is applied to a simple case: the one-dimensional stationary granular gas under gravity. The method should find applications in the field of rarefied gases, as well. Questions of convergence, closure are beyond the scope of this article.

Physical Review E **84**, 016216

(2011)

Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow, namely a Rössler’s oscillator. We show that spirals associated with periodicity hubs emerge and accumulate at the folding of certain fractal-like sheaves of Shilnikov homoclinic bifurcations of a common saddle-focus equilibrium. The specific organization of hub networks is found to depend strongly on the interaction between the homoclinic orbits and the global structure of the underlying attractor.

Physical Review E **84**, 037202

(2011)

We study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a magnetic field with a constant longitudinal and a time-dependent transverse component using the Landau-Lifshitz-Gilbert equation. We characterize the dynamical behavior of the system through calculation of the Lyapunov exponents, Poincar´e sections, bifurcation diagrams, and Fourier power spectra. In particular we explore the positivity of the largest Lyapunov exponent as a function of the magnitude and frequency of the applied magnetic field and its direction with respect to the main anisotropy axis of the magnetic particle. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated structure of intricately intermingled chaotic and regular phases.

Chemical Physics **375**, 600-605

(2010)

In dense, static, polydisperse granular media under isotropic pressure, the probability density and the correlations of particle-wall contact forces are studied. Furthermore, the probability density functions of the populations of pressures measured with different sized circular pressure cells is examined. The questions answered are: (i) What is the number of contacts that has to be considered so that the measured pressure lies within a certain error margin from its expectation value? (ii) What is the statistics of the pressure probability density as function of the size of the pressure cell? Astonishing non-random correlations between contact forces are evidenced, which range at least 10 to 15 particle diameter. Finally, an experiment is proposed to tackle and better understand this issue.

Journal of Fluid Mechanics **655**, 1–2

(2010)

Professor Isaac Goldhirsch, the Raquel and Manuel Klachky Chair of Rheological Flows at the School of Mechanical Engineering of Tel-Aviv University, Israel, died unexpectedly on April 29 at age 60 while on sabbatical leave at the University of Erlangen–Nuremberg, Germany.

Journal of Chemical Physics **133**, 124506

(2010)

The properties of systems composed of atoms interacting though discrete potentials are dictated by a series of events which occur between pairs of atoms. There are only four basic event types for pairwise discrete potentials and the square-well/shoulder systems studied here exhibit them all. Closed analytical expressions are derived for the on-event kinetic energy distribution functions for an atom, which are distinct from the Maxwell–Boltzmann distribution function. Exact expressions are derived that directly relate the pressure and temperature of equilibrium discrete potential systems to the rates of each type of event. The pressure can be determined from knowledge of only the rate of core and bounce events. The temperature is given by the ratio of the number of bounce events to the number of disassociation/association events. All these expressions are validated with event-driven molecular dynamics simulations and agree with the data within the statistical precision of the simulations.

Journal of Chemical Physics **132**, 084507

(2010)

Hard-sphere molecular dynamics (MD) simulation results, with six-figure accuracy in the

thermodynamic equilibrium pressure, are reported and used to test a closed-virial equation-of-state.

This latest equation, with no adjustable parameters except known virial coefficients, is comparable

in accuracy both to Padé approximants, and to numerical parameterizations of MD data. There is no

evidence of nonconvergence at stable fluid densities. The virial pressure begins to deviate

significantly from the thermodynamic fluid pressure at or near the freezing density, suggesting that

the passage from stable fluid to metastable fluid is associated with a higher-order phase transition;

an observation consistent with some previous experimental results. Revised parameters for the

crystal equation-of-state [R. J. Speedy, J. Phys.: Condens. Matter **10**, 4387 (1998)] are also

reported.

New Trends in Artificial Intelligence. 14th Portuguese Conference on Artificial Intelligence. EPIA 2009. Aveiro, October 12-15, 2009. Proceedings (Luís Seabra Lopes, Nuno Lau, Pedro Mariano, Luís M. Rocha), 101-112

(2009)

We present three heuristics including the usage of domain specific knowledge to improve a general purpose algorithm for the 3D approximate point set match problem and its application to the task of finding 3D motifs (like surface patterns or binding sites) in proteins. The domain specific knowledge and further heuristics are used, under certain conditions, to reduce the run time for the search and to adapt the number of reported matches to the expectations of the user. Compared to the general purpose algorithm, the new version is twice as fast, and can be further improved especially for small tolerances in the matches by means of analyzing the distance distributions of the atoms.

EPJ Special Topics **179**, 91-111

(2009)

In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a steady-state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analyzed systematically for a wide range of system parameters, including the coefficients of tangential and normal restitution as well as the moment of inertia of the particles. For most parameter values the axis of rotation and the direction of linear momentum are perpendicular like in a sliced tennis ball, while parallel orientation, like in a rifled bullet, occurs only for a small range of parameters. The limit of smooth spheres is singular: any arbitrarily small roughness unavoidably causes significant translation-rotation correlations, whereas for perfectly smooth spheres the rotational degrees of freedom are completely decoupled from the dynamic evolution of the gas.

EPJ Special Topics **179**

(2009)

Journal of Statistical Physics **136**, 715-732

(2009)

The fluid and solid equations of state for hard parallel squares and cubes are reinvestigated here over a wide range of densities. We use a novel single-speed version of molecular dynamics. Our results are compared with those from earlier simulations, as well as with the predictions of the virial series, the cell model, and Kirkwood’s many-body single-occupancy model. The singleoccupancy model is applied to give the absolute entropy of the solid phases just as was done earlier for hard disks and hard spheres. The excellent agreement found here with all relevant previous work shows very clearly that configurational properties, such as the equation of state, do not require the maximum-entropy Maxwell-Boltzmann velocity distribution. For both hard squares and hard cubes the free-volume theory provides a good description of the high-density solid-phase pressure. Hard parallel squares appear to exhibit a second-order melting transition at a density of 0.79 relative to close-packing. Hard parallel cubes have a more complicated equation of state, with several relatively-gentle curvature changes, but nothing so abrupt as to indicate a first-order melting transition. Because the number-dependence for the cubes is relatively large the exact nature of the cube transition remains unknown.

Physical Review E **80**, 021801

(2009)

Recently, it has been demonstrated [Magee et al., Phys. Rev. Lett. **96**, 207802 (2006)] that isolated, square-well homopolymers can spontaneously break chiral symmetry and freeze into helical structures at sufficiently low temperatures. This behavior is interesting because the square-well homopolymer is itself achiral. In this work, we use event-driven molecular dynamics, combined with an optimized parallel tempering scheme, to study this polymer model over a wide range of parameters. We examine the conditions where the helix structure is stable and determine how the interaction parameters of the polymer govern the details of the helix structure. The width of the square well (proportional to lambda) is found to control the radius of the helix, which decreases with increasing well width until the polymer forms a coiled sphere for sufficiently large wells. The helices are found to be stable for only a window of molecular weights. If the polymer is too short, the helix will not form. If the polymer is too long, the helix is no longer the minimum energy structure, and other folded structures will form. The size of this window is governed by the chain stiffness, which in this model is a function of the ratio of the monomer size to the bond length. Outside this window, the polymer still freezes into a locked structure at low temperature, however, unless the chain is sufficiently stiff, this structure will not be unique and is similar to a glassy state.

Journal of Chemical Physics **130**, 164507

(2009)

The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of σB/σA=0.1 and a mass ratio of mB/mA=0.001 are investigated using event driven molecular dynamics. The contact values of the pair correlation functions are found to compare favorably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of the revised Enskog theory using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, the Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (xA=0.01) examined. A “fines effect” was observed at higher packing fractions, where adding smaller spheres to a system of large spheres decreases the viscosity of the mixture; this effect is not captured by the Enskog theory.

Physical Review E **79**, 041308

(2009)

The dynamics of sheared inelastic-hard-sphere systems are studied using non-equilibrium molecular dynamics simulations and direct simulation Monte Carlo. In the molecular dynamics simulations Lees-Edwards boundary conditions are used to impose the shear. The dimensions of the simulation box are chosen to ensure that the systems are homogeneous and that the shear is applied uniformly. Various system properties are monitored, including the one-particle velocity distribution, granular temperature, stress tensor, collision rates, and time between collisions. The one-particle velocity distribution is found to agree reasonably well with an anisotropic Gaussian distribution, with only a slight overpopulation of the high velocity tails. The velocity distribution is strongly anisotropic, especially at lower densities and lower values of the coefficient of restitution, with the largest variance in the direction of shear. The density dependence of the compressibility factor of the sheared inelastic hard sphere system is quite similar to that of elastic hard sphere fluids. As the systems become more inelastic, the glancing collisions begin to dominate more direct, head-on collisions. Examination of the distribution of the time between collisions indicates that the collisions experienced by the particles are strongly correlated in the highly inelastic systems. A comparison of the simulation data is made with DSMC simulation of the Enskog equation. Results of the kinetic model of Montanero et al. [Montanero et al., J. Fluid Mech. **389**, 391 (1999)] based on the Enskog equation are also included. In general, good agreement is found for high density, weakly inelastic systems.

AIP Conference Proceedings **1145**, 859-862

(2009)

Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale , where the fragments are subsequently allowed to settle under gravity. If this fragmentation-reagglomeration cycle is repeated sufficiently often, the powder develops a fractal substructure with robust statistical properties. The structural evolution is discussed for two different models: The first one is an off-lattice model, in which a fragment does not stick to the surface of other fragments that have already settled, but rolls down until it finds a locally stable position. The second one is a simpler lattice model, in which a fragment sticks at first contact with the agglomerate of fragments that have already settled. Results for the fragment size distribution are shown as well. One can distinguish scale invariant dust and fragments of a characteristic size. Their role in the process of structure formation will be addressed.

Journal of Fluid Mechanics **597**, 119-144

(2008)

The goal of this study is to demonstrate numerically that certain hydrodynamic systems, derived from inelastic kinetic theory, give fairly good descriptions of rapid granular flows even if they are way beyond their supposed validity limits. A numerical hydrodynamic solver is presented for a vibrated granular bed in two dimensions. It is based on a highly accurate shock capturing state-of-the-art numerical scheme applied to a compressible Navier-Stokes system for granular flow. The hydrodynamic simulation of granular flows is challenging, particularly in systems where dilute and dense regions occur at the same time and interact with each other. As a benchmark experiment, we investigate the formation of Faraday waves in a two-dimensional thin layer exposed to vertical vibration in the presence of gravity. The results of the hydrodynamic simulations are compared with those of event-driven molecular dynamics and the overall quantitative agreement is good at the level of the formation and structure of periodic patterns. The accurate numerical scheme for the hydrodynamic description improves the reproduction of the primary onset of patterns compared to previous literature. To our knowledge, these are the first hydrodynamic results for Faraday waves in two-dimensional granular beds that accurately predict the wavelengths of the two-dimensional standing waves as a function of the perturbation’s amplitude. Movies are available with the online version of the paper.

The European Physical Journal E, **27**, 107-114

(2008)

The collision of frictional granular particles may be described by an interaction force whose normal component is that of viscoelastic spheres while the tangential part is described by the model by Cundall and Strack (Géotechnique **29**, 47 (1979)) being the most popular tangential collision model in Molecular Dynamics simulations. Albeit being a rather complicated model, governed by 5 phenomenological parameters and 2 independent initial conditions, we find that it is described by 3 independent parameters only. Surprisingly, in a wide range of parameters the corresponding coefficient of tangential restitution, ε_{t}, is well described by the simple Coulomb law with a cut-off at ε_{t} = 0. A more complex behavior of the coefficient of restitution as a function on the normal and tangential components of the impact velocity, *g* _{ n } and *g* _{ t }, including negative values of ε_{ n }, is found only for very small ratio *g* _{ t }/*g* _{ n }. For the analysis presented here we neglect dissipation of the interaction in normal direction.

Physical Review E, **77**, 011304

(2008)

The linear dashpot model for the inelastic normal force between colliding spheres leads to a constant coefficient of normal restitution, ε_n=const., which makes this model very popular for the investigation of dilute and moderately dense granular systems. For two frequently used models for the tangential interaction force we determine the coefficient of tangential restitution ε_t, both analytically and by numerical integration of Newton’s equation. Although ε_n=const. for the linear-dashpot model, we obtain pronounced and characteristic dependencies of the tangential coefficient on the impact velocity ε_t=ε_t(**g**). The results may be used for event-driven simulations of granular systems of frictional particles.

Granular Matter **10**, 231-232

(2008)

In contrast to a still common belief, a steadily flowing hourglass changes its weight over the course of time (Shen and Scott in Am J Phys 53(8):787–788, 1985). We will show that, nevertheless, it is possible to construct hourglasses that do not change their weight.

Physical Review E, **78**, 051304

(2008)

The coefficient of normal restitution of colliding viscoelastic spheres is computed as a function of the material properties and the impact velocity. From simple arguments it becomes clear that in a collision of purely repulsively interacting particles, the particles loose contact slightly before the distance of the centers of the spheres reaches the sum of the radii, that is, the particles recover their shape only after they lose contact with their collision partner. This effect was neglected in earlier calculations which leads erroneously to attractive forces and, thus, to an underestimation of the coefficient of restitution. As a result we find a novel dependence of the coefficient of restitution on the impact rate.

Physical Review Letters **100**, 218002

(2008)

The structural evolution of a nano-powder by repeated dispersion and settling can lead to characteristic fractal substructures. This is shown by numerical simulations of a two-dimensional model agglomerate of adhesive rigid particles. The agglomerate is cut into fragments of a characteristic size l, which then are settling under gravity. Repeating this procedure converges to a loosely packed structure, the properties of which are investigated: a) The final packing density is independent of the initialization, b) the short-range correlation function is independent of the fragment size, c) the structure is fractal up to the fragmentation scale l with a fractal dimension close to 1.7, and d) the relaxation time increases linearly with l.

Nucleic Acids Research **36**, W47–W54

(2008)

The Superimposé webserver performs structural similarity searches with a preference towards 3D structure-based methods. Similarities can be detected between small molecules (e.g. drugs),parts of large structures (e.g. binding sites of proteins) and entire proteins. For this purpose, a number of algorithms were implemented and various databases are provided. Superimposé assists the user regarding the selection of a suitable combination of algorithm and database. After the computation on our server infrastructure, a visual assessment of the results is provided. The structure-based in silico screening for similar drug-like compounds enables the detection of scaffold-hoppers with putatively similar effects. The possibility to find similar binding sites can be of special interest in the functional analysis of proteins. The search for structurally similar proteins allows the detection of similar folds with different backbone topology. The Superimposé server is available at: http://farnsworth.charite.de/superimpose-web/

European Journal of Environmental and Civil Engineering **12**, 827-870

(2008)

We discuss several models for granular particles commonly used in Molecular Dynamics simulations of granular materials, including spheres with linear dashpot force, viscoelastic spheres and adhesive viscoelastic spheres. Starting from the vectorial interaction forces we derive the coefficients of normal and tangential restitution as functions of the vectorial impact velocity and of the material constants. We review the methods of measurements of the coefficients of restitution and characterize the coefficient of normal restitution as a fluctuating quantity. Moreover, the scaling behavior and the influence of different force laws on the dynamical system behavior are discussed. The powerful method of event-driven Molecular Dynamics is described and the algorithmic simulation technique is explained in detail. Finally we discuss the limitations of event-driven MD.

International Journal of Modern Physics C **18**, 701-711

(2007)

We present a universal description of the velocity distribution function of granular gases, f(v), valid for both, small and intermediate velocities where v is close to the thermal velocity and also for large v where the distribution function reveals an exponentially decaying tail. By means of large-scale Monte Carlo simulations and by kinetic theory we show that the deviation from the Maxwell distribution in the high-energy tail leads to small but detectable variation of the cooling coefficient and to extraordinary large relaxation time.

Physical Review Letters **98**, 128001

(2007)

In a granular gas of rough particles the axis of rotation is shown to be correlated with the translational velocity of the particles. The average relative orientation of angular and linear velocities depends on the parameters which characterize the dissipative nature of the collision. We derive a simple theory for these correlations and validate it with numerical simulations for a wide range of coefficients of normal and tangential restitution. The limit of smooth spheres is shown to be singular: even an arbitrarily small roughness of the particles gives rise to orientational correlations.

Granular Matter **10**, 21-27

(2007)

Dense granular clusters often behave like macro-particles. We address this interesting phenomenon in a model system of inelastically colliding hard disks inside a circular box, driven by a thermal wall at zero gravity. Molecular dynamics simulations show a close-packed cluster of almost circular shape, weakly fluctuating in space and isolated from the driving wall by a low-density gas. The density profile of the system agrees very well with the azimuthally symmetric solution of granular hydrostatic equations employing constitutive relations by Grossman et al., whereas the widely used Enskog-type constitutive relations show poor accuracy. We find that fluctuations of the center of mass of the system are Gaussian. This suggests an effective Langevin description in terms of a macro-particle, confined by a harmonic potential and driven by delta-correlated noise. Surprisingly, the fluctuations persist when increasing the number of particles in the system.

Granular Matter **9**, 465-469

(2007)

With the assumption of a linear–dashpot interaction force, the coefficient of restitution, ε0d(k,γ), can be computed as a function of the elastic and dissipative material constants, *k* and γ by integrating Newton’s equation of motion for an isolated pair of colliding particles. If we require further that the particles interact exclusively repulsive, which is a common assumption in granular systems, we obtain an expression εd(k,γ) which differs even qualitatively from the known result ε0d(k,γ). The expression εd(k,γ) allows to relate Molecular Dynamics simulations to event-driven Molecular Dynamics for a widely used collision model.

Physical Review E **76**, 051302

(2007)

We investigate the collision of adhesive viscoelastic spheres in quasistatic approximation where the adhesive interaction is described by the Johnson, Kendall, and Roberts (JKR) theory. The collision dynamics, based on the dynamic contact force, describes both restitutive collisions quantified by the coefficient of restitution ε as well as aggregative collisions, characterized by the critical aggregative impact velocity gcr. Both quantities ε and gcr depend sensitively on the impact velocity and particle size. Our results agree well with laboratory experiments.

Europhysics Letters **75**, 188

(2006)

Irreversible Prozesse und Selbstorganisation (Pöschel, T.; Malchow, H.; and Schimansky-Geier, L.), 281 - 292. Berlin: Logos.

(2006)

In ökologischen Systemen ist die saisonal variierende Präsenz von Arten sowohl durch die jahreszeitlich schwankenden Umgebungsbedingungen, als auch durch die Wechselwirkungen zwischen den Arten bedingt. Letztere erfahren ihre Ausprägung in Sukzession und Koexistenz. Wir wollen die zyklische Wiederkehr der Arten im Jahresgang wahrscheinlichkeitstheoretisch beschreiben, wobei der Wechsel von Jahr zu Jahr im Rahmen einer Markovschen Kette modelliert wird. Neben allgemeinen Ausführungen zu dieser modellhaften Art der Analyse werden wir als eine konkrete Anwendung die Zeitreihen (Zellzahlen) dreier prominenter Algenarten der südlichen Nordsee analysieren. Über den Aspekt einer quantitativen Beschreibung der Verhältnisse im marinen Habitat hinaus zielt eine derartige Untersuchung insbesondere auf einen Nachweis möglicher Veränderungen des ökologischen Systems der „nassen Gemeinschaft“ vor dem Hintergrund einer bereits beobachteten Temperaturerhöhung des Meerwassers bei Helgoland.

Behavior of Granular Media (Walzel, P.; Grochowski, R.; Kruelle, C.; and Linz, S. J.), 151 - 159. Aachen: Shaker.

(2006)

The numerical simulation of granular systems of even moderate size is a challenging computational problem. In most investigations, either Molecular Dynamics or Event-driven Molecular Dynamics is applied. Here we show that in certain cases, mainly (but not exclusively) for static granular packings, the Bottom-to-top Reconstruction method allows for the efficient simulation of very large systems. We apply the method to heap formation, granular flow in a rotating cylinder and to structure formation in nano-powders. We also present an efficient implementation of the algorithm in C++, including a benchmark.

Physical Review E **74**, 041302

(2006)

The velocity distribution function of granular gases in the homogeneous cooling state as well as some heated granular gases decays for large velocities as f ∼ exp(−const. v). That is, its high-energy tail is overpopulated as compared with the Maxwell distribution. At the present time, there is no theory to describe the influence of the tail on the kinetic characteristics of granular gases. We develop an approach to quantify the overpopulated tail and analyze its impact on granular gas properties, in particular on the cooling coefficient. We observe and explain anomalously slow relaxation of the velocity distribution function to its steady state.

Europhysics Letters **74**, 424-430

(2006)

The velocity distribution of a granular gas is analyzed in terms of the Sonine polynomials expansion. We derive an analytical expression for the third Sonine coefficient *a*_{3}. In contrast to frequently used assumptions this coefficient is of the same order of magnitude as the second Sonine coefficient *a*_{2}. For small inelasticity the theoretical result is in good agreement with numerical simulations. The next-order Sonine coefficients *a*_{4}, *a*_{5} and *a*_{6} are determined numerically. While these coefficients are negligible for small dissipation, their magnitude grows rapidly with increasing inelasticity for 0 < ε0.6. We conclude that this behavior of the Sonine coefficients manifests the breakdown of the Sonine polynomial expansion caused by the increasing impact of the overpopulated high-energy tail of the distribution function.

Powders & Grains 2005: Proceedings of the 5th International Conference on Micromechanics of Granular Media (Garcia-Rojo, R., Herrmann, H. J., McNamara, S.), 1247-1253. Taylor & Francis.

(2005)

We develop an analytical theory of adhesive interaction of viscoelastic spheres in quasistatic approximation. Deformations and deformation rates are assumed to be small, which allows for the application of the Hertz contact theory, modified to account for viscoelastic forces. The adhesion interactions are described by the Johnson, Kendall, and Roberts theory. Using the quasistatic approximation we derive the total force between the bodies which is not sufficiently described by the superposition of elastic, viscous and adhesive contributions, but instead an additional cross-term appears, which depends on the elastic, viscous and adhesive parameters of the material. Using the derived theory we estimate the contribution of adhesive forces to the normal coefficient of restitution and derive a criterion for the validity of the viscoelastic collision model.

Powders & Grains 2005: Proceedings of the 5th International Conference on Micromechanics of Granular Media (Garcia-Rojo, R., Herrmann, H. J., McNamara, S.) **2**, 505-509. Taylor & Francis.

(2005)

The rolling motion of a rigid cylinder on an inclined flat viscous surface is investigated and the nonlinear resistance force against rolling, F_R(v), is derived. For small velocities F_R(v) increases with velocity due to increasing deformation rate of the surface material. For larger velocity it decreases with velocity due to decreasing contact area between the rolling cylinder and the deformed surface. The cylinder is, moreover, subjected to a viscous drag force and stochastic fluctuations due to a surrounding medium (air). For this system, in a wide range of parameters we observe bistability of the rolling motion. Depending on the material parameters, increasing the noise level may lead to increasing or decreasing average velocity.

Chaos **15**, 026108

(2005)

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green–Kubo relation and the Chapman–Enskog approach. The dissipative particle collisions are described by the coefficient of restitution ε which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, ε=const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of ε on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for ε=const both methods lead to the same result for the self-diffusion coefficient. For the case of impact-velocity dependent coefficients of restitution, the Green–Kubo method is, however, either restrictive or too complicated for practical application, therefore we compute the diffusion coefficient using the Chapman–Enskog method. We conclude that in application to granular gases, the Chapman–Enskog approach is preferable for deriving kinetic coefficients.

The diffusion of tracer particles (self-diffusion) in a force-free gas of dissipatively colliding particles, also called granular gases, is studied. Main theoretical approaches for the calculation of transport coefficients are the Green–Kubo and Chapman–Enskog methods. The former is based on fluctuation–dissipation relations, which express transport coefficients in terms of the time correlation function of dynamical variables. The latter approach is based on the Boltzmann equation, that describes the evolution of the distribution function of tracers. The dissipative nature of the gas is characterized by the coefficient of restitution, ε which is the central quantity in the theory of granular gases. This coefficient quantifies the loss of kinetic energy due to a single particle collision. We consider three different models for the coefficient of restitution (i) ε=const, (ii) a stepwise dependence of ε on the impact velocity, which mimics the basic property of this coefficient, and (iii) a realistic model for ε as a function of the impact velocity, derived from the contact mechanics of viscoelastic bodies. For the simplest model (i), both theoretical methods yield the same coefficient of diffusion. For the more realistic models (ii) and (iii), however, the Green–Kubo approach is either restrictive or too complicated for practical application. Therefore we conclude that the Chapman–Enskog method is preferable for deriving kinetic coefficients of granular gases.

Europhysics Letters **69**, 725-731

(2005)

We investigate the transport of proteins inside the proteasome and propose an active-transport mechanism based on a spatially asymmetric interaction potential of peptide chains. The transport is driven by fluctuations which are always present in such systems. We compute the peptide-size dependent transport rate which is essential for the functioning of the proteasome. In agreement with recent experiments, varying temperature changes the transport mechanism qualitatively.

Europhysics Letters **69**, 371-377

(2005)

We investigate the motion of a hard cylinder rolling down a soft inclined plane. The cylinder is subjected to a viscous drag force and stochastic fluctuations due to the surrounding medium. In a wide range of parameters we observe bistability of the rolling velocity. In dependence on the parameters, increasing noise level may lead to increasing or decreasing average velocity of the cylinder. The approximative analytical theory agrees with numerical results.

Journal of Physics: Condensed Matter **17**, S2705–S2713

(2005)

The most striking phenomenon in the dynamics of granular gases is the formation of clusters and other structures. We investigate a gas of dissipatively colliding particles with a velocity dependent coefficient of restitution where cluster formation occurs as a transient phenomenon. Although for small impact velocity the particles collide elastically, surprisingly the temperature converges to zero.

Physical Review E **69**, 059905

(2004)

The Physics of Granular Media (Hinrichsen, H. and Wolf, D. E.), 189-209. Amsterdam: Wiley.

(2004)

The collision of convex bodies is considered for small impact velocity, when plastic deformation and fragmentation may be disregarded. In this regime the contact is governed by forces according to viscoelastic deformation and by adhesion. The viscoelastic interaction is described by a modified Hertz law, while for the adhesive interactions, the model by Johnson, Kendall and Roberts (JKR) is adopted. We solve the general contact problem of convex viscoelastic bodies in quasi-sstatic approximation, which implies that the impact velocity is much smaller than the speed of sound in the material and that the viscosity relaxation time is much smaller than the duration of a collision. We estimate the threshold impact velocity which discriminates restitutive and sticking collisions. If the impact velocity is not large as compared with the threshold velocity, adhesive interaction becomes important, thus limiting the validity of the pure viscoelastic collision model.

Physical Review Letters **93**, 134301

(2004)

A force-free granular gas is considered with an impact-velocity-dependent coefficient of restitution as it follows from the model of viscoelastic particles. We analyze structure formation in this system by means of three independent methods: molecular dynamics, numerical solution of the hydrodynamic equations, and linear stability analysis of these equations. All these approaches indicate that structure formation occurs in force-free granular gases only as a transient process.

Physical Review E **69**, 021302

(2004)

We investigate a phase separation instability that occurs in a system of nearly elastically colliding hard spheres driven by a thermal wall. If the aspect ratio of the confining box exceeds a threshold value, granular hydrostatics predict phase separation: the formation of a high-density region coexisting with a low-density region along the wall that is opposite to the thermal wall. Event-driven molecular dynamics simulations confirm this prediction. The theoretical bifurcation curve agrees with the simulations quantitatively well below and well above the threshold. However, in a wide region of aspect ratios around the threshold, the system is dominated by fluctuations, and the hydrostatic theory breaks down. Two possible scenarios of the origin of the giant fluctuations are discussed.

Proceed. 7th APCTP Winter School on Granular Material and Complex Systems (Lee, J.). Phoenix Park, Kangwondo, Korea: Asia Pacific Center for Theoretical Physics.

(2003)

Granular Gas Dynamics (Lecture Notes in Physics) (Pöschel, T. and Brilliantov, N. V) **624**, 131-162. Berlin: Springer.

(2003)

The gaskinetic theory, including the theory of Granular Gases is based on the Boltzmann equation with the collision integral. Many properties of the gas, from the characteristics of the velocity distribution function to transport coefficients may be expressed in terms of functions of the collision integral which we call kinetic integrals. Although evaluation of these functions is conceptually straightforward, technically it is rather cumbersome. We report here a method of analytic evaluation of kinetic integrals based on the symbolic programming. The method is illustrated for various properties of the Granular Gas, ranging from the moments of the velocity distribution function to the transport coefficients. Most of these quantities and may not be found in practice manually.

Biosystems **69**, 63-72

(2003)

The decision whether a measured distribution complies with an equidistribution is a central element of many biostatistical methods. High throughput differential expression measurements, for instance, necessitate to judge possible over-representation of genes. The reliability of this judgement, however, is strongly affected when rarely expressed genes are pooled. We propose a method that can be applied to frequency ranked distributions and that yields a simple but efficient criterion to assess the hypothesis of equiprobable expression levels. By applying our technique to surrogate data we exemplify how the decision criterion can differentiate between a true equidistribution and a triangular distribution. The distinction succeeds even for small sample sizes where standard tests of significance (e.g. *χ*^{2}) fail. Our method will have a major impact on several problems of computational biology where rare events baffle a reliable assessment of frequency distributions. The program package is available upon request from the authors.

Physical Review E **67**, 061304

(2003)

The hydrodynamics of granular gases of viscoelastic particles, whose collision is described by an impact-velocity dependent coefficient of restitution, is developed using a modified Chapman-Enskog approach. We derive the hydrodynamic equations and the according transport coefficients with the assumption that the shape of the velocity distribution function follows adiabatically the decaying temperature. We show numerically that this approximation is justified up to intermediate dissipation. The transport coefficients and the coefficient of cooling are expressed in terms of the elastic and dissipative parameters of the particle material and by the gas parameters. The dependence of these coefficients on temperature differs qualitatively from that obtained with the simplifying assumption of a constant coefficient of restitution which was used in previous studies. The approach formulated for gases of viscoelastic particles may be applied also for other impact-velocity dependencies of the restitution coefficient.

Physical Review Letters **91**, 024301

(2003)

Monodisperse granular flows often develop regions with hexagonal close packing of particles. We investigate this effect in a system of inelastic hard spheres driven from below by a “thermal” plate. Molecular dynamics simulations show, in a wide range of parameters, a close-packed cluster supported by a low-density region. Surprisingly, the steady-state density profile, including the close-packed cluster part, is well described by a variant of Navier-Stokes granular hydrodynamics (NSGH). We suggest a simple explanation for the success of NSGH beyond the freezing point.

Biophysical Journal **85**, 3460-3474

(2003)

We study the kinetics of prion fibril growth, described by the nucleated polymerization model analytically and by means of numerical experiments. The elementary processes of prion fibril formation lead us to a set of differential equations for the number of fibrils, their total mass and the number of prion monomers. In difference to previous studies we analyze this set by explicitely taking into account the time dependence of the prion monomer concentration. The theoretical results agree with experimental data whereas the generally accepted hypothesis of constant monomer concentration leads to a fibril growth behavior which is not in agreement with experiments. The obtained size distribution of the prion fibril aggregates is shifted significantly towards shorter lengths as compared to earlier results, which leads to a enhanced infectivity of the prion material. Finally we study the effect of filtering of the inoculated material on the incubation time of the disease.

European Physical Journal E **12**, 531-541

(2003)

Assume in a sample of size *M* one finds *M*_{i }representatives of species *i* with i=1…N∗. The normalized frequency p∗i≡Mi/M, based on the finite sample, may deviate considerably from the true probabilities *p*_{i}. We propose a method to infer rank-ordered true probabilities *r*_{i } from measured frequencies *M*_{i}. We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon- and the Renyi-entropies.

BMC Bioinformatics **4**, 58-64

(2003)

**Background**

For many applications one wishes to decide whether a certain set of numbers originates from an equiprobability distribution or whether they are unequally distributed. Distributions of relative frequencies may deviate significantly from the corresponding probability distributions due to finite sample effects. Hence, it is not trivial to discriminate between an equiprobability distribution and non-equally distributed probabilities when knowing only frequencies.

**Results**

Based on analytical results we provide a software tool which allows to decide whether data correspond to an equiprobability distribution. The tool is available at http://bioinf.charite.de/equifreq/.

Its application is demonstrated for the distribution of point mutations in coding genes.

International Journal of Modern Physics C **13**, 1263-1272

(2002)

Numerical simulations of a dissipative hard sphere gas reveal a dependence of the cooling rate on correlation of the particle velocities due to inelastic collisions. We propose a coefficient which characterizes the velocity correlations in the two-particle velocity distribution function and express the temperature decay rate in terms of this coefficient. The analytical results are compared with numerics.

Perspektiven der Forschung und ihrer Förderung, 417-427. Weinheim: Wiley-VCH.

(2002)

Physical Review E **66**, 026103

(2002)

Given an equidistribution for probabilities p(i)=1/N, i=1..N. What is the expected corresponding rank ordered frequency distribution f(i), i=1..N, if an ensemble of M events is drawn?

Philosophical Transactions of the Royal Society A **360**, 415-428

(2002)

Our study examines the long-time behaviour of a force-free Granular Gas of viscoelastic particles, for which the coefficient of restitution depends on the impact velocity, as it follows from the solution of the impact problem for viscoelastic spheres. Starting from the Boltzmann equation, we derived the hydrodynamic equations and obtained microscopic expressions for the transport coefficients in terms of the elastic and dissipative parameters of the particle material. We performed the stability analysis of the linearised set of equations and found that any inhomogeneities and vortices vanish after long time and the system approaches the flow-free stage of homogeneous density. This behaviour is in contrast to that of a gas consisting of particles which interact via a (non-realistic) constant coefficient of restitution, for which inhomogeneities (clusters) and vortex patterns have been proven to arise and to continuously develop.

System Dynamics and Long-Term Behaviour of Railway Vehicles, Track and Subgrade (Popp, K., and Schiehlen, W.), 451-470. Berlin: Springer.

(2002)

A method for the discrete particle simulation of of almost rigid, sharply edged frictional particles, such as railway ballast is proposed. In difference to Molecular Dynamics algorithms, the method does not require knowledge about the deformation-force law of the material. Moreover, the method does not suffer from numerical instability which is encountered in MD simulations of very stiff particles.

Physica A **325**, 274-283

(2002)

A gas of particles which collide inelastically if their impact velocity exceeds a certain value is investigated. In difference to common granular gases, cluster formation occurs only as a transient phenomenon. We calculate the decay of temperature due to inelastic collisions. In spite of the drastically reduced dissipation at low temperature the temperature surprisingly converges to zero.

Granular Gases (Pöschel, T. and Luding, S) **564**, 203-212. Berlin: Springer.

(2001)

Given a chain of viscoelastic spheres with fixed masses of the first and last particles. We raise the question: How to chose the masses of the other particles of the chain to assure maximal energy transfer? The results are compared with a chain of particles for which a constant coefficient of restitution is assumed. Our simple example shows that the assumption of viscoelastic particle properties has not only important consequences for very large systems (see [1]) but leads also to qualitative changes in smallsystems as compared with particles interacting via a constant restitution coefficient.

Physical Review E **64**, 011308

(2001)

Given an assembly of viscoelastic spheres with certain material properties, we raise the question how the macroscopic properties of the assembly will change if all lengths of the system, i.e. radii, container size etc., are scaled by a constant. The result leads to a method to scale down experiments to lab size.

Physical Review Letters **63**, 021505

(2001)

The transmission of kinetic energy through chains of inelastically colliding spheres is investigated for the case of constant coefficient of restitution ε = const and impact-velocity dependent coefficient ε(v) for viscoelastic particles. We derive a theory for the optimal distribution of particle masses which maximize the energy transfer along the chain and check it numerically. We found that for ε = const the mass distribution is a monotonous function which does not depend on the value of ε. In contrast, for ε(v) the mass distribution reveals a pronounced maximum, depending on the particle properties and on the chain length. The system investigated demonstrates that even for small and simple systems the velocity dependence of the coefficient of restitution may lead to new effects with respect to the same systems under the simplifying approximation ε = const.

Powders and Grains 2001: Proceedings of the Fourth International Conference on Micromechanics of Granular Media, Sendai, 21-25 May 2001 (Kishino, Y.), 439-442. Rotterdam: Balkema.

(2001)

For the experimental investigation of large scale phenomena in the laboratory such as in geophysical or industrial applications one has to scale down all length in the system, e.g. particle size, container size. We show that besides length scaling one as to scale the material properties too to achieve identical behavior of the scaled and the original systems. We provide the scaling laws for a system of viscoelastic spheres.

Granular Gases (Pöschel, T. and Luding, S) **564**, 100-124. Berlin: Springer.

(2001)

We consider collisional models for granular particles and analyze the conditions under which the restitution coefficient might be a constant. We show that these conditions are not consistent with known collision laws. From the generalization of the Hertz contact law for viscoelastic particles we obtain the coefficient of normal restitution ε as a function of the normal component of the impact velocity v_imp. Using ε(v_imp) we describe the time evolution of temperature and of the velocity distribution function of a granular gas in the homogeneous cooling regime, where the particles collide according to the viscoelastic law. We show that for the studied systems the simple scaling hypothesis for the velocity distribution function is violated, i.e. that its evolution is not determined only by the time dependence of the thermal velocity. We observe, that the deviation from the Maxwellian distribution, which we quantify by the value of the second coefficient of the Sonine polynomial expansion of the velocity distribution function, does not depend on time monotonously. At first stage of the evolution it increases on the mean-collision time-scale up to a maximum value and then decays to zero at the second stage, on the time scale corresponding to the evolution of the granular gas temperature. For granular gas in the homogeneous cooling regime we also evaluate the time-dependent self-diffusion coefficient of granular particles. We analyze the time dependence of the mean-square displacement and discuss its impact on clustering. Finally, we discuss the problem of the relevant internal time for the systems of interest.

European Physical Journal E **4**, 233-239

(2001)

The onset of surface fluidization of granular material in a vertically vibrated container, z=A cos(ω t), is studied experimentally. Recently, for a column of spheres it has been theoretically found that the particles lose contact if a certain condition for the acceleration amplitude d²z/dt² = Aω²/g = f(ω) holds. This result is in disagreement with other findings where the criterion (d²z/dt² = d²z/dt²)_crit = const. was found to be the criterion of fluidization. We show that for a column of spheres a critical acceleration is not a proper criterion for fluidization and compare the results with theory.

Coherent Structures in Complex Systems - Selected Papers of the XVII Sitges Conference on Statistical Mechanics Held at Sitges, Barcelona, Spain, 5-9 June 2000 (D. Reguera, L.L. Bonilla, and M. Rubi) **567**, 408-419. Berlin: Springer.

(2001)

We investigate the evolution of the velocity distribution function of a granular gas composed of viscoelastic particles in the homogeneous cooling state, i.e. before clustering occurs. The deviation of the velocity distribution function from the Maxwellian distribution is quantified by a Sonine polynomials expansion. The first non-vanishing Sonine coefficient a_2(t), reveals a complex time dependence which allows to assign the granular gas the property of an age. We discuss the possibility to measure the age of a granular gas.

Mechanics for a New Millennium - Proceedings of the 20th International Congress on Theoretical and Applied Mechanics, held in Chicago, USA, 27 August - 2 September 2000 (Aref, H. and Philips, J.W.). Dortrecht: Kluwer.

(2000)

Zahnärzteblatt der Landeszahnärztekammer Thüringen

(2000)

European Physical Journal B **16**, 169–182

(2000)

We investigate autogenous fragmentation of dry granular material in rotating cylinders using two-dimensional molecular dynamics. By evaluation of spatial force distributions achieved numerically for various rotation velocities we argue that comminution occurs mainly due to the existence of force chains. A statistical analysis of these force chains explains the spatial distribution of comminution efficiency in ball mills as measured experimentally by Rothkegel [1] and Rolf [2].

European Physical Journal E **1**, 55-59

(2000)

In horizontally shaken granular material different types of pattern formation have been reported. We want to deal with the convection instability which has been observed in experiments and which recently has been investigated numerically. Using two dimensional molecular dynamics we show that the convection pattern depends crucially on the inelastic properties of the material. The concept of restitution coefficient provides arguments for the change of the behaviour with varying inelasticity.

Physical Review E **61**, 2809 – 2812

(2000)

We analyze the velocity distribution function of force-free granular gases in the regime of homogeneous cooling when deviations from the Maxwellian distribution may be accounted only by the leading term in the Sonine polynomial expansion, quantified by the second coefficient a_{2}. We go beyond the linear approximation for a_{2} and find three different values (three roots) for this coefficient which correspond to a scaling solution of the Boltzmann equation. The stability analysis performed showed, however, that among these three roots only one corresponds to a stable scaling solution. This is very close to a_{2}, obtained in previous studies in a linear with respect to a_{2} approximation.

Schüttgut **6**, 11-24

(2000)

Molekulardynamische Untersuchungen eignen sich zur Simulation des Verhaltens makroskopischer Mengen granularen Materials unter bestimmten, technologisch relevanten Beanspruchungen. Wir untersuchen das Zerkleinerungsverhalten von Mahlgut in einer Kugelmühle, insbesondere im Hinblick auf die Effizienz als Funktion der Drehzahl und auf die räumliche Ver-teilung von Beanspruchungen. Die Untersuchung der Verteilung von Kraftket-ten (force chains) liefert eine Erklärung des Experiments von Rothkegel [1] und Rolf.

Physical Review E **61**, 1716-1721

(2000)

The coefficient of self-diffusion for a homogeneously cooling granular gas changes significantly if the impact-velocity dependence of the restitution coefficient epsilon is taken into account. For the case of a constant epsilon the particles spread logarithmically slowly with time, whereas a velocity-dependent coefficient yields a power law time dependence. The impact of the difference in these time dependences on the properties of a freely cooling granular gas is discussed.

Physical Review E **61**, 5573-5587

(2000)

The velocity distribution in a homogeneously cooling granular gas has been studied in the viscoelastic regime, when the restitution coefficient of colliding particles depends on the impact velocity. We show that for viscoelastic particles a simple scaling hypothesis is violated, i.e., that the time dependence of the velocity distribution does not scale with the mean square velocity as in the case of particles interacting via a constant restitution coefficient. The deviation from the Maxwellian distribution does not depend on time monotonically. For the case of small dissipation we detected two regimes of evolution of the velocity distribution function: Starting from the initial Maxwellian distribution, the deviation first increases with time on a collision time scale saturating at some maximal value; then it decays to zero on a much larger time scale which corresponds to the temperature relaxation. For larger values of the dissipation parameter there appears an additional intermediate relaxation regime. Analytical calculations for small dissipation agree well with the results of a numerical analysis.

Mechanics for a New Millennium - Proceedings of the 20th International Congress on Theoretical and Applied Mechanics, held in Chicago, USA, 27 August - 2 September 2000 (Aref, H.; Philips, J.W.). Dortrecht: Kluwer.

(2000)

When dealing with dense granular flows (not far above the fluidization point of the granular material), which cannot be regarded as granular gases, multiple unresolved questions arise. Many of them are related to the necessity of constructing the right framework to handle the dynamics of void occupation, which governs granular flow athigh densities. This is a formidable task. However, hydrodynamic fields such as density, velocity, pressure and granular temperature, are easy to produce and study in numerical simulations of particles.

Stochastic Processes in Physics, Chemistry, and Biology (Freund, J. A. and Pöschel, T.) **557**, 107-117. Berlin: Springer.

(2000)

In most of the literature on granular gases it is assumed that the restitution coefficient ε, which quantifies the loss of kinetic energy upon a collision is independent on the impact velocity. Experiments as well as theoretical investigations show, however, that for real materials the restitution coefficient depends significantly on the impact velocity. We consider the diffusion process in a homogeneous granular gas, i.e. in a system of dissipatively colliding particles. We show that the mean square displacement of the particles changes drastically if we take the impact velocity dependence of ε into account. Under the oversimplifying assumption of a constant coefficient one finds that the particles spread in space logarithmically slow with time, whereas realistic particles spread due to a power law.

Physical Review E **62**, 1361-1367

(2000)

When granular material is shaken vertically one observes convection, surface fluidization, spontaneous heap formation, and other effects. There is a controversial discussion in the literature as to whether there exists a threshold for the Froude number Γ=A_{0}ω_{0}^{2}/g, below which these effects cannot be observed anymore. By means of theoretical analysis and computer simulation we find that there is no such single threshold. Instead, we propose a modified criterion that coincides with the critical Froude number Γ_{c}=1 for small driving frequency ω_{0}.

Proceedings **3672**, Smart Structures and Materials 1999: Passive Damping and Isolation

(1999)

Simulation models in space industry may allocate a few mesh points for such fine details as granular dampers embedded in mechanical parts. As a result, collective dynamics of grains inside dampers cannot be adequately resolved. A hierarchical approach to modeling and design has been explored by practitioners to study this phenomenon. Available models fail to explain the observed spectral response. This article is an attempt to examine models where dampers are replaced by calibrated linear and non-linear visco-elastic units with stochastic forcing. Namely, the parameterization of a non- linear visco-elastic unit is described. Non-linearity facilitates mode-mixing and shifts of major resonances, while stochastic forcing contributes to the overall risk assessment. Limitations of the proposed reductions of granular hydrodynamics are discussed.

Physikalische Blätter **55**, 99

(1999)

European Physical Journal B **10**, 169-174

(1999)

The resistance against rolling of a rigid cylinder on a flat viscous surface is investigated. We found that the rolling-friction coefficient reveals strongly non-linear dependence on the cylinder’s velocity. For low velocity the rolling-friction coefficient rises with velocity due to increasing deformation rate of the surface. For larger velocity, however, it decreases with velocity according to decreasing contact area and deformation of the surface.

European Physical Journal B **12**, 299-301

(1999)

We show that two basic mechanical processes, the collisionof particles and rolling motion of a sphere on a plane, are intimately related. According to our recent findings, the restitution coefficient for colliding spherical particles ε, which characterizes the energy loss upon collision, is directly related to the rolling friction coefficient µ_roll for a viscous sphere on a hard plane. We quantify both coefficients in terms of material constants which allows to determine either of them provided the other is known. This relation between the coefficients may give rise to a novel experimental technique to determine alternatively the coefficient of restitution or the coefficient of rolling friction.

Physical Review E **59**, 4422-4425

(1999)

We investigate collective dissipative properties of vibrated granular materials by means of molecular-dynamics simulations. Rates of energy losses indicate three different regimes or phases in the amplitude-frequency plane of the external forcing,namely solid, convective, and gaslike regimes. The behavior of effective damping decrement in the solid regime is glassy. Practical applications are discussed.

Physical Review E **60**, 4465-4472

(1999)

We perform a dimension analysis for colliding viscoelastic spheres to show that the coefficient of normal restitution ε depends on the impact velocity *g* as ε=1−γ_{1}g^{1/5}+γ_{2}g^{2/5}∓⋅⋅⋅, in accordance with recent findings. We develop a simple theory to find explicit expressions for coefficients γ_{1} and γ_{2}. Using these and few next expansion coefficients for ε(g) we construct a Padé approximation for this function which may be used for a wide range of impact velocities where the concept of the viscoelastic collision is valid. The obtained expression reproduces quite accurately the existing experimental dependence ε(g) for ice particles.

A Perspective Look at Nonlinear Media. Lecture Notes in Physics (Parisi J., Müller S.C., Zimmermann W.) **503**, 96-109. Berlin: Springer.

(1998)

We report on a new effect observed in horizontally shaken granular material in a rectangular box. Within a certain region of parameters of the oscillation the granular material swells recurrently with a characteristic frequency (see http://summa.physik.hu-berlin.de/GranMat/). This frequency is significantly smaller than the frequency of forcing. We claim that this new effect is caused by the the interplay between Reynolds dilatancy due to convective motion and mechanical stability of the diluted granular material in the box. Measurements of the dissipated energy per time supports this explanation.

Physical Review E **57**, 650-654

(1998)

We investigate the cooling rate of a gas of inelastically interacting particles. When we assume velocity-dependent coefficients of restitution the material cools down slower than with constant restitution. This behavior might have a large influence to clustering and structure formation processes.

Physical Review Letters **80**, 5708

(1998)

A Comment on the Letter by Frank Spahn, Udo Schwarz, and Jurgen Kurths, Phy. Rev. Lett. **78**, 1596 (1997). The authors of the Letter offer a Reply.

Europhysics Letters **42**, 511-516

(1998)

A first-principle continuum-mechanics expression for the rolling friction coefficient is obtained for the rolling motion of a viscoelastic sphere on a hard plane. It relates the friction coefficient to the viscous and elastic constants of the sphere material. The relation obtained refers to the case when the deformation of the sphere is small, the velocity of the sphere V is much less than the speed of sound in the material and when the characteristic time is much larger than the dissipative relaxation times of the viscoelastic material. To our knowledge this is the first first-principle expression of the rolling friction coefficient which does not contain empirical parameters.

Granular Matter **1**, 33-41

(1998)

We investigate numerically the interaction of a stream of granular particles with a resting obstacle in two dimensions. For the case of high stream velocity we find that the force acting on the obstacle is proportional to the square of the stream velocity, the density and the obstacle size. This behaviour is equivalent to that of non-interacting hard spheres. For low stream velocity a gap between the obstacle and the incoming stream particles appears which is filled with granular gas of high temperature and low density. As soon as the gap appears the force does not depend on the square of velocity of the stream but the dependency obeys another law.

Physics of Dry Granular Media: Proceedings of the NATO Advanced Study Institute, Cargese, France, September 15-26, 1997 (H. J. Herrmann and J.-P. Hovi and S. Luding) **350**, 625-631. Dortrecht: Kluwer.

(1998)

Suppose granular material is shaken vertically with z(t)=A_0 cos(ω_0 t). Can we expect to find convection if A_0ω_0^2 < g? By means of theoretical analysis and computer simulation we find that there is no critical Γ= |A_0|ω_0^2/g for the onset of convection. Instead we propose a modified criterion which coincides with Γ=1 for small frequency ω_0.

Proceedings **3327**, Smart Structures and Materials 1998: Passive Damping and Isolation, 19-26

(1998)

We investigate collective dissipative properties of vibrated granular materials by means of molecular dynamics simulations. The rate of energy loss indicates three di®erent phases in the amplitude-frequency plane of the external forcing, namely solid, convective and gas-like regimes. The behavior of the e®ective damping decrement is consistent with the glassy nature of granular solids. The gas-like regime is most promising for practical applications.

Journal of Statistical Physics **86**, 1385-1395

(1997)

The kinetic energy distribution function satisfying the Boltzmann equation is studied analytically and numerically for a system of inelastic hard spheres in the case of binary collisions. Analytically, this function is shown to have a similarity form in the simple cases of uniform or steady-state flows. This determines the region of validity of hydrodynamic description. The latter is used to construct the phase diagram of granular systems, and discriminate between clustering instability and inelastic collapse. The molecular dynamics results support analytical results, but also exhibit a novel fluctuational breakdown of mean-field descriptions.

Journal of Statistical Physics **86**, 421-430

(1997)

The gravity-driven flow of granular material through a rough, narrow vertical pipe is described using the Langevin equation formalism. Above a critical particle density the homogeneous flow becomes unstable with respect to short-wave length perturbations. In correspondence with experimental observations, we find clogging and density waves in the flowing material.

Biological Complexity (Mizraji, E., Acerenza, L., Alvarez, F., and Pomi, A.), 113-142. Montevideo, Uruguay: D.I.R.A.C.

(1997)

After a short review of some informational and grammatical concepts and a former algorithm to evaluate the complexity of neural spike trains, a new algorithm to build a short context-free grammar (also called program or description) that generates a given sequence is introduced. It follows the general lines of the first algorithm but it optimizes the information content, instead of the grammar complexity that was used in the previous work. It is implemented by means of the program SYNTAX and applied to estimate the information content of neural spikes trains, obtained from a sample of seven neurons, before and after penicillin treatment. A comparison of the sequences (encoding the inter-spike intervals) according to their information content, grammar complexity, and block-entropies shows that the three context dependent measures of complexity give similar results to categorize the neurons with respect to their structure or randomness, before and after the application of penicillin.

International Journal of Bifurcation and Chaos **7**, 751-757

(1997)

Stochastic Dynamics (Schimansky-Geier, L. and Pöschel, T.) **484**, 220-231. Berlin: Springer.

(1997)

We describe traffic on a two dimensional lattice modelled using a cellular automaton. The theoretical approach valid in the low density region employs cluster statistics. The derived central formula for the velocity vs. density relation nicely agrees with simulation results. In our approach the explicit traffic rules solely enter through combinatorics accounting for average crossing traffics.

Proceedings **3045**, Smart Structures and Materials 1997: Passive Damping and Isolation, 341-344

(1997)

The properties of dense granular systems are analyzed from a hydrodynamical point of view, based on conservation laws for the particle number density and linear momentum. We discuss averaging problems associated with the nature of such systems and the peculiarities of the sources of noise. We perform a quantitative study by combining analytical methods and numerical results obtained by ensemble-averaging of data on creep during compaction and molecular dynamics simulations of convective flow. We show that numerical integration of the hydrodynamic equations gives the expected evolution for the time-dependent fields.

Friction, Arching, Contact Dynamics: Proceedings of the Workshop, HLRZ, Forschungszentrum Jülich, Germany, 28-30 October 1996 (Wolf, D. E. and Grassberger, P.), 265-273. Singapore: World Scientific.

(1997)

The motion of granular material in a ball mill is investigated using molecular dynamics simulations in two dimensions. In agreement with experimental observations by Rothkegel [1] we find that local stresses – and hence the comminution efficiency – are maximal close to the bottom of the container. This effect will be explained using analysis of statistics of force chains in the material.

Dynamik, Evolution, Strukturen: Nichtlineare Dynamik und Statistik komplexer Strukturen (Freund, J.), 191-201. Berlin: Köster.

(1996)

Dynamik, Evolution, Strukturen: Nichtlineare Dynamik und Statistik komplexer Strukturen (Freund, J.), 237-246. Berlin: Köster.

(1996)

Journal of Statistical Physics **82**, 443-450

(1996)

We report the first three-dimensional molecular dynamics simulation of particle segregation by shaking. Two different containers are considered: one cylindrical and another with periodic boundary conditions. The dependence of the time evolution of a test particle inside the material is studied as a function of the shaking frequency and amplitude, damping coefficients and dispersivity.

Physical Review E **53**, 5382-5392

(1996)

We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity.

Biosystems **39**, 117-125

(1996)

A representation of the genetic code as a six-dimensional Boolean hypercube is described. This structure is the result of the hierarchical order of the interaction energies of the bases in codon-anticodon recognition. In this paper it is applied to study molecular evolution in vivo and in vitro. In the first case we compared aligned positions in homologous protein sequences and found two different behaviors: a) There are sites in which the different amino acids may be explained by one or two „attractor nodes“ (coding for the dominating amino acid(s)) and their one-bit neighbors in the codon hypercube, and b) There are sites in which the amino acids correspond to codons located in closed paths in the hypercube. In the second case we studied the „Sexual PCR“ experiment described by Stemmer and found that the success of this combination of usual PCR and recombination is in part due to the Gray code structure of the genetic code.

Physica A **231**, 417-424

(1996)

Collisions between granular particles are irreversibleprocesses causing dissipation of mechanical energy by fragmentation or heating of the colliders. The knowledge of these phenomena is essential for the understanding of the behaviour of complex systems of granular particles. We have developed a model for inelastic collisions of granular particles and calculated the velocity restitution coefficients, which describe all possible collisions in the system. The knowledge of these coefficients allows for event-driven many-particle simulations which cannot be performed in the frame of molecular dynamics. The benefit of this approach is to treat very large particle numbers necessary for the understanding of intrinsic large-scale phenomena in granular systems.

Physical Review E **54**, R4560(R)

(1996)

Experiments and numerical simulations of granular material under swirling motion of the container are presented. At low packing densities the material rotates in the same direction as the swirling motion of the container (rotation). At higher densities the cluster of granular material rotates in the opposite direction (reptation). The change of the direction of the motion of the cluster takes place at a critical packing density while the diffusion coefficient changes significantly. The measured critical density of the packing is in good agreement with results obtained by molecular-dynamics simulation.

Journal of Statistical Physics **84**, 1373-1378

(1996)

Large scale computer simulations are presented to investigate the avalanche statistics of sand piles using molecular dynamics. We could show that different methods of measurement lead to contradicting conclusions, presumably due to avalanches not reaching the end of the experimental table.

Proceedings of PhysComp96: Fourth Workshop on Physics and Computation, Boston, 22-24 November 1996 (Toffoli, T., Biafore, M. and Leão, J.), 103-107. Complex Systems Institute. Boston.

(1996)

The purpose of this paper is to investigate long-range correlations in symbol sequences using methods of statistical physics and nonlinear dynamics. Beside the principal interest in the analysis of correlations and fluctuations comprising many letters, our main aim is related here to the problem of sequence compression.

Zeitschrift für Physikalische Chemie **188**, 311

(1995)

Chaos, Solitons & Fractals **5**, 1901-1905, 1907-1912

(1995)

The flow of granular material in a rotating cylinder was simulated by molecular dynamics in two dimensions using spherical as well as nonspherical grains. At very low but constant angular velocity we found that the flow varies irregularly with time. The particles move stick-slip like i.e. there are avalanches of different size at the surface of the granular material. Observing the traces of the particles we found that there are unstable convection cells. Our results agree with recent experiments by Rajchenbach and Rolf.

Physica A **219**, 95-113

(1995)

A two-dimensional cellular automaton is introduced to model the flow and jamming of vehicular traffic in cities. Each site of the automaton represents a crossing where a finite number of cars can wait approaching the crossing from each of the four directions. The flow of cars obeys realistic traffic rules. We investigate the dependence of the average velocity of cars on the global traffic density. At a critical threshold for the density the average velocity reduces drastically caused by jamming. For the low density regime we provide analytical results which agree with the numerical results.

Journal of Statistical Physics **80**, 1443-1452

(1995)

We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution p(k) of the elements k of a population can be approximated by the frequencies f(k) of a sample provided the sample is long enough so that each element k occurs many times. Our method yields an approximation if this precondition does not hold. For a given f(k) we recalculate the Zipf-ordered probability distribution by optimization of the parameters of a guessed distribution. We demonstrate that our method yields reliable results.

Europhysics Letters **29**, 123-129

(1995)

The size segregation of granular materials in a vibrating container is investigated using Molecular Dynamics. We find that the rising of larger particles is accompanied by the existence of convection cells even in the case of the lowest possiblefrequencies. The convection can, however, also be triggered by the larger particle itself. The possibility of rising through this mechanism strongly depends on the depth of the larger particle.

Physica A **216**, 199-212

(1995)

We investigate the flow of granular material in a rotating cylinder numerically using molecular dynamics in two dimensions. The particles are described by a new model which allows to simulate geometrically complicated shaped grains. The results of the simulation agree significantly better with experiments than the results which are based on circular particles.

International Journal of Bifurcation and Chaos **5**, 51-61

(1995)

We investigate correlations in information carriers, e.g. texts and pieces of music, which are represented by strings of letters. For information carrying strings generated by one source (i.e. a novel or a piece of music) we find correlations on many length scales. The word distribution, the higher order entropies and the transinformation are calculated. The analogy to strings generated through symbolic dynamics by nonlinear systems in critical states is discussed.

Journal de Physique I France **5**, 1431-1455

(1995)

We propose a new model for the description of complex granular particles and their interaction in molecular dynamics simulations of granular material in two dimensions. The grains are composed of triangles which are connected by deformable beams. Particles are allowed to be convex or concave. We present first results of simulations using this particle model.

Guanajuato Lectures, México, 16-22 Januar 1995 (López-Peña, R. and Waelbroeck, H. and Zertuche, F.).

(1995)

The determination of block-entropies is a well established method for the investigation of discrete data, also called symbols (1). There is a large variety of such symbolic sequences, ranging from texts written in natural languages, computer programs, neural spike trains, and biosequences. In this paper a new algorithm to construct a short context-free grammar (also called program or description) that generates a given sequence is introduced. It follows the general lines of a former algorithm, employed to compress biosequences (2) and to estimate the complexity of neural spike trains (3), which uses as valuation function the, so called, grammar complexity (2). The new algorithm employs the (observed)block-entropies instead. A variant, which employs a corrected observed entropy; as discussed in (1) is also described. To illustrate its usefulness, applications of the program to the syntactic analysis of a sample biological sequences (DNA and RNA) is presented.

Coherent Approaches to Fluctuations (Proc. Hayashibara Forum 95), 59-64. Singapore: World Scientific.

(1995)

We investigate symbolic sequences and in particular information carriers as e.g. books and DNA-strings. First the higher order Shannon entropies are calculated, a characteristic root law is detected. Then the algorithmic entropy is estimated by using Lempel-Ziv compression algorithms. In the third section the correlation function for distant letters, the low frequency Fourier spectrum and the characteristic scaling exponents are calculated. We show that all these measures are able to detect long-range correlations. However, as demonstrated by shuffling experiments, different measures operate on different length scales. The longest correlations found in our analysis comprise a few hundreds or thousands of letters and may be understood as long-wave fluctuations of the composition.

Physica A **202**, 390-401

(1994)

The evolution of a pile of granular material is investigated by molecular dynamics using a new model including nonsphericity of the particles instead of introducing static friction terms. The angle of repose of the piles as well as the avalanche statistics gathered by the simulation agree with experimental results. The angle of repose of the pile is determined by the shape of the grains. Our results are compared with simulations using spherical grains and static friction.

Europhysics Letters **26**, 241-246

(1994)

We investigated long-range correlations in two literary texts, „Moby Dyck“ by H. Melville and Grimm’s tales. The analysis is based on the calculation of entropylike quantities as the mutual information for pairs of letters and the entropy, the mean uncertainty, per letter. We further estimate the number of different subwords of a given length *n.* Filtering out the contributions due to the effects of the finite length of the texts, we find correlations ranging to a few hundred letters. Scaling laws for the mutual information (decay with a power law), for the entropy per letter (decay with the inverse square root of *n*) and for the word numbers (stretched exponential growth with *n* and with a power law of the text length) were found.

Bulletin of the American Astronomical Society **26**, 1143-1144

(1994)

Chaos, Solitons & Fractals **4**, 1883-1888

(1994)

The detailed mechanism of the formation of net and branching leaf structures is not known yet. Several mathematical modelling attempts to generate those structures have been made previously, based on biochemical or purely mathematical assumptions. A very simple model with only a few plausible biophysical suppositions is presented here, showing the formation of a ramificated structure grown out of a single activated cell.

Physical Review E **50**, 2654-2659

(1994)

We simulate the dynamical behavior of M elevators serving N floors of a building in which a Poisson distribution of persons call elevators. Our simulation reproduces the jamming effect typically seen in large buildings when a large number of persons decide to leave the building simultaneously. The collective behavior of the elevators involves characteristics similar to those observed in systems of coupled oscillators. In addition, there is an apparently rule-free critical population density above which elevators start to arrive synchronously at the ground floor.

Journal de Physique I France **4**, 499-506

(1994)

We report on density waves in granular material, investigated both experimentally and numerically. When granular material falls through a long narrow pipe one observes recurrent clogging. The kinetic energy of the falling particles increases up to a characteristic threshold corresponding to the onset of recurrent clogging and density waves of no definite wavelength. The distances between regions of high density depend strongly on the initial conditions. They vary irregularly without any characteristic time and length scale. The particle-flow was investigated using 2D Molecular Dynamics simulations. Experimental investigations lead to equivalent results.

(1994)

The investigation of long-range correlations in information carriers is the main subject of this work. As typical examples of information-carrying strings we study here books which are considered as strings of letters. The main aim of the investigation is the analysis of correlations beyond the level of letters. The correlation function for distant letters, the characteristic scaling exponent, the distribution of longer subwords and the entropy are calculated. The effect of mixing on the word level and on the level of sentences is studied systematically. It is shown in this way that there exist indeed correlations on all scales. The formal analogy of information carriers to strings generated by nonlinear systems in critical states is discussed.

KFA intern **24**, 3-4

(1993)

Journal de Physique II France **3**, 27-40

(1993)

Two-dimensional Molecular Dynamics simulations are used to model the free surface flow of spheres falling down an inclined chute. The interaction between the particles in our model is assumed to be subjected to the Hertzian contact force and normal as well as shear friction. The stream of particles shows characteristic height profile, consisting of layers of different types of fluidization. The numerically observed flow properties agree qualitatively with experimental results.

International Journal of Modern Physics C **4**, 1049-1057

(1993)

We report on a lattice based algorithm, completely vectorized for molecular dynamics simulations. Its algorithmic complexity is of the order O(N), where N is the number of particles. The algorithm works very effectively when the particles have short range interaction, but it is applicable to each kind of interaction. The code was tested on a CRAY YMP EL in a simulation of flowing granular material.

Physical Review Letters **71**, 3963-3966

(1993)

The static as well as the dynamic behavior of granular material are determined by dynamic and static friction. There are well known methods to inlcude static friction in molecular dynamics simulations using scarcely understood forces. We propose an ansatz based on the geometrical shape of nonspherical particles which does not involve an explicit expression for static friction. It is shown that the simulations based on this model are close to experimental results.

Physica A **198**, 441-448

(1993)

We present a simple model for the friction of two solid bodies moving against each other. In a self consistent way we can obtain the dependence of the macroscopic friction force as a function of the driving velocity, the normal force and the ruggedness of the surfaces in contact. Our results are discussed in the context of friction laws used in earthquake models.

Neurocomputers and Attention II: Connectionism and neurocomputers (Holden, A. V. and Kryukov, V. I.), 615-627. Manchester: Manchester University Press.

(1991)

Dynamical Networks (Ebeling, W. and Peschel, M.), 128-137. Berlin: Akademie-Verlag.

(1989)

Parcella'88 (Wolf, G. and Legendy, T. and Schendel, U.). Berlin: Akademie-Verlag.

(1988)

Innovative Informations-Infrastrukturen, I.I.I.-Forum (Gollan, B. and Paul, W. J. and Schmitt, A.), 187-197. Saarbrücken.

(1988)