Collapse Publications

A local view on the role of friction and shape

Soft Matter

(submitted)

Abstract

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.

Materials
 

Recurrent Periodicities in Very Tall Disks Packings

Royal Society of Chemistry

(submitted)

Abstract

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.

 

Particle-based simulations of powder coating in additive manufacturing suggest increase in powder bed roughness with coating speed

(submitted)

Abstract
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 present work, we develop such a numerical tool and apply it to investigate the characteristics of the powder layer de posited 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 part may vary over an order of magnitude during the coating process owing to the strong inhomogeneity of inter-particle 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.
Materials
 

Microgravity spreading of water spheres on Hydrophobic capillary plates

Powders and Grains 2017

(submitted)

Abstract

We created 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.

Materials
 

Analyzing X-Ray tomographies of granular packings

arXiv:1612.06639 [physics.data-an]

(submitted)

Abstract

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.

Materials
 

Effect of vibrations applied to the transport roller in the quality of the powder bed during additive manufacturing

(submitted)

Abstract

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.

Materials
 

Weight of an Hourglass – Theory and Experiment in Quantitative Comparison

American Journal of Physics

(in print)

Research Projects
Abstract

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.

Materials
 

Homogeneous cooling state of granular gases of charged particles

(submitted)

Abstract

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.

Materials
 

Velocity distribution of a homogeneously driven two-dimensional granular gas

(submitted)

Abstract

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.

Materials
 

Morphology and scale of bedforms on Pluto suggest aeolian transport of sand-sized sediments

(submitted)

Abstract

Images of Pluto sent back to Earth by New Horizons revealed a geologically active surface consisting of dark, cratered terrains alternating with huge icy mountains and flat, bright soils free of impact craters. 1 Several processes have been suggested to explain the observed features, in particular chemical reactions triggered by ultraviolet radiation from the sun, heterogeneous rates of ice sublimation and deposition induced by gradients of surface temperature, and resurfacing due to radioactive heating from within the planetary body. 2 However, the possible role of wind as a geological process on Pluto has remained uncertain. 3, 4 Here 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 5–7 , we find that the average diameter of the granular particles constituting such bedforms — assuming an aeolian origin — lies within the range 600 μm< d < 750 μm. 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.

Materials
 

Homogenization of granular pipe flow by means of helical inner-wall texture

(submitted)

Abstract

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.

Materials
 

Vertical motion of particles in vibration-induced granular capillarity

(submitted)

Abstract

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 investigated here.

Materials
 
  • Joshua A. Anderson
  • James Antonaglia
  • Jaime A. Millan
  • Michael Engel
  • Sharon C. Glotzer

Fluid-to-Solid Transition of Hard Regular Polygons

(submitted)

Abstract

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 3n14 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.

Materials
 

Granular Capillarity

(submitted)

Abstract

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 system. A scaling of the capillarity height up to which the granular material rises in the tube with the inverse of the tube diameter is found.

Materials
 

Digging on Asteroids: a Laboratory Model of Granular Dynamics in Microgravity

(submitted)

Abstract

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.

Materials
 

High speed movies of a dripping faucet

(submitted)

Abstract

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 of the formation of drops at a nozzle of high temporal and spatial resolution.

Materials
 

Inelastic collapse of perfectly inelastic particles

(submitted)

Research Projects
Abstract

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.

Materials
 

Instability of SPH applied to Poiseuille flow

(submitted)

Abstract

Weakly compressible smoothed particle hydrodynamics (WCSPH) has been widely applied to flows with free surfaces, multi-phase flow and systems with complex boundary geometry. It is known, however, that WCSPH 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 WCSPH to practical situations into doubt, where the Reynolds number is frequently large. Here, we consider Poiseuille flow for a wide range of Reynolds number and find that the instability of WCSPH can be avoided by using appropriate ratio of smoothing length to particle spacing in combination with a density re-initialization technique. We also probe the source of the instability and point out the limitations of WCSPH for wall-bounded shear flows at high Reynolds number.

Materials
 

Periodic and chaotic psychological stress variations as predicted by a social support buffered response model

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

(2017)

Abstract

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.

Materials
 
  • Haixin Lin
  • Sangmin Lee
  • Lin Sun
  • Matthew Spellings
  • Michael Engel
  • Sharon C. Glotzer
  • Chad A. Mirkin

Clathrate colloidal crystals

Science 355, 931-935

(2017)

Abstract

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.

Materials
 

Influence of humidity on tribo-electric charging and segregation in shaken granular media

Soft Matter 13, 394-401

(2017)

Abstract

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.

Materials
 

Energy decay in a granular gas collapse

New Journal of Physics 19, 013001

(2017)

Research Projects
Abstract

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.

Materials
 

Effect of particle shape on the efficiency of granular dampers

New Journal of Physics 18 073049

(2016)

Abstract

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.

Materials
 
  • Luis S. Froufe-Pérez
  • Michael Engel
  • Pablo F. Damasceno
  • Nicolas Muller
  • Jakub Haberko
  • Sharon C. Glotzer
  • Frank Scheffold

Role of Short-Range Order and Hyperuniformity in the Formation of Band Gaps in Disordered Photonic Materials

Physical Review Letters 117, 053902

(2016)

Abstract

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.

Materials
 

Self-Assembly of Colloidal Nanocrystals: From Intricate Structures to Functional Materials

Chemical Reviews 116, 11220-11289

(2016)

Abstract
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.
Materials
 

A cohesive granular material with tunable elasticity

Scientific Reports 6, 35650

(2016)

Abstract

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.

Materials
 

Alignment of Lyapunov Vectors: A Quantitative Criterion to Predict Catastrophes?

Scientific Reports 6, 37102

(2016)

Abstract

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.

Materials
 

Heaping and secondary flows in sheared granular materials

New Journal of Physics 18, 113006

(2016)

Abstract

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.

Materials
 
  • Xingchen Ye
  • Juan Chen
  • Eric Irrgang
  • Michael Engel
  • Angang Dong
  • Sharon C. Glotzer
  • Christopher Murray

Quasicrystalline nanocrystal superlattice with partial matching rules

Nature Materials - Letter

(2016)

Abstract

Expanding the library of self-assembled superstructures provides insight into the behaviour of atomic crystals and supports the development of materials with mesoscale order1, 2. Here we build on recent findings of soft matter quasicrystals3, 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 tomography7, 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.

Materials
 

Method for extracting arbitrarily large orbital equations of the Pincherle map

Results in Physics 6, 561-567

(2016)

Abstract

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.

Materials
 

Ratcheting and tumbling motion of Vibrots

New Journal of Physics 18, 123001

(2016)

Research Projects
Abstract

Systems of granular rotors (Vibrots), that is, small devices that convert linear vibrational motion into rotation by frictional impact, are of scienti c interest since they could reveal various types of collective behavior. Looking at an isolated Vibrot, we note at least two di erent 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 identi ed 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.

Materials
 

Erratum to: Stable algorithm for event detection in event-driven particle dynamics: logical states

Computational Partical Mechanics 3, 389

(2016)

Abstract
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.
Materials
 

Spiking Systematics in Some CO 2 Laser Models

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

(2016)

Abstract
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.
Materials
 

Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings

Soft Matter 12, 3991

(2016)

Abstract

We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808–2812] to
determine an upper bound sub on the Edwards entropy in frictional hard-sphere packings. sub 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 j in the range 0.551–0.65. We find
that sub has a maximum in the vicinity of the Random Loose Packing Limit jRLP = 0.55 and decreases
then monotonically with increasing j to reach a minimum at j = 0.65. Further on, sub 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 j, but it decreases strongly with the contact number.

Materials
 
  • Junaid M. Laskar
  • P. Shravan Kumar
  • Stephan Herminghaus
  • Karen E. Daniels
  • Matthias Schröter

High refractive index immersion liquid for superresolution 3D imaging using sapphire-based aplanatic numerical aperture increasing lens optics

Applied Optics 55, No. 12, 3165

(2016)

Abstract
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.
Materials
 

Granular dampers: Does particle shape matter?

New Journal of Physics 18, 073049

(2016)

Abstract
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 efficiencyon the particle shape is found.
Materials
 

Synchronization properties of two mutually delay-coupled semiconductor lasers

Journal of the Optical Society of America B 33, No. 7, 65-71

(2016)

Research Projects
Abstract

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.

Materials
 
  • Robert Tchitnga
  • Tekou Nguazon
  • Patrick H. Louodop Totso
  • Jason Gallas

Chaos in a Single Op-Amp–Based Jerk Circuit: Experiments and Simulations

IEEE TRANSACTIONS ON CIRCUITS AND SYSTEMS—II: EXPRESS BRIEFS 63, No. 3

(2016)

Research Projects
Abstract

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.

Materials
 

Dissipation of Energy by Dry Granular Matter in a Rotating Cylinder

Scientific Reports 6, 26833

(2016)

Research Projects
Abstract

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.

Materials
 

Exact calculation of the overlap volume of spheres and mesh elements

Journal of Computational Physics 311, 158-172

(2016)

Research Projects
Abstract

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.

Materials
 

Inexpensive Mie scattering experiment for the classroom manufactured by 3D printing

European Journal of Physics 37, 055305

(2016)

Research Projects
Abstract

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.

Materials
 

Homogeneous cooling of mixtures of particle shapes

Physics of Fluids 28, 073301

(2016)

Research Projects
Abstract

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.

Materials
 

Impact of delayed feedback of arbitrary duration in self-pulsations of a CO 2 laser

Optical Society of America B 33, 373

(2016)

Research Projects
Abstract

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.

Materials
 
  • Riccardo Meucci
  • Stefano Euzzor
  • Eugenio Pugliese
  • Samuel Zambrano
  • Marcia R. Gallas
  • Jason Gallas

Optimal phase-control strategy for damped-driven Duffing oscillators

Physical Review Letters 116, 044101

(2016)

Research Projects
Abstract

Phase-control techniques of chaos aim to extract periodic behaviors from chaotic systems by applying weak harmonic perturbations with 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 vs. 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 and to the quartic term of the single-well Duffing.

Materials
 

Manifold angles, the concept of self-similarity, and angle-enhanced bifurcation diagrams

Scientific Reports 6, 18859

(2016)

Research Projects
Abstract

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.

Materials
 

Stable algorithm for event detection in event-driven particle dynamics: logical states

Computational Partical Mechanics 3, 383-388

(2016)

Research Projects
Abstract

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.

Materials
 

Fractal Substructure of a nanopowder generated by repeated fragmentation and sedimentation: The role of the dust

Granular Matter

(2016)

Abstract

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.

Materials
 

Reply to comment on ‘Are physicists afraid of mathematics?’

New Journal of Physics 18, 118004

(2016)

Research Projects
Abstract

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.

Materials
 

Actively rotating granular particles manufactured by rapid prototyping

Revista Cubans de Físika 31, No. 1, 37-38

(2016)

Research Projects
Abstract

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.

Materials
 

The microscopic structure of mono-disperse granular heaps and sediments of particles on inclined surfaces

Soft Matter 12, 3184

(2016)

Abstract

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.

Materials
 

Particle-based simulation of powder application in additive manufacturing

Powder Technology 288, 96-102

(2016)

Abstract

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.

Materials
 

Steepest descent ballistic deposition of complex shaped particles

Journal of Computational Physics 308, 421

(2016)

Research Projects
Abstract

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.

Materials
 

Can we obtain the coefficient of restitution from the sound of a bouncing ball?

Physical Review E 93, 032901

(2016)

Research Projects
Abstract

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.

Materials
 

Subharmonic instability of a self-organized granular jet

Scientific Reports 6, 22520

(2016)

Research Projects
Abstract

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.

Materials
 

Análisis del plano de fases de un modelo discreto de neurona basado en la determinación de periodicidades. Phase plan analysis of a neuron map-based model by determining periodicities

Revista Boliviana de Fisika 27, No. 27, 1–9

(2015)

Research Projects
Abstract

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.

Materials
 

Periodic oscillations of the forced Brusselator

Modern Physics Letters B 29, 1530018

(2015)

Research Projects
Abstract

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.

Materials
 

Pattern-fluid interpretation of chemical turbulence

Physical Review E 91, 042097

(2015)

Research Projects
Abstract

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)].

Materials
 
  • Dwight Barkley
  • Baofang Song
  • Vasudevan Mukund
  • Grégoire Lemoult
  • Marc Avila
  • Björn Hof

The rise of fully turbulent flow

Nature - Letter 526, 550-553

(2015)

Research Projects
Abstract

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 flow1, 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 turbulence7 and fully turbulent flows8, 9.

Materials
 
  • Christian Scholz
  • Frank Wirner
  • Michael A. Klatt
  • Daniel Hirneise
  • Gerd E. Schröder-Turk
  • Klaus Mecke
  • Clemens Bechinger

Direct relations between morphology and transport in Boolean models

Physical Review E 92, 043023

(2015)

Abstract

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.

Materials
 

Residual defect density in random deposits of disks

Scientific Reports 5, 12703

(2015)

Research Projects
Abstract

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.

Materials
 

Two-dimensional airflow modeling underpredicts the wind velocity over dunes

Scientific Reports 5, 16572

(2015)

Research Projects
Abstract

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.

Materials
 

Positron Emission Particle Tracking in Fluidized Beds with Secondary Gas Injection

Powder Technology 279, 113-122

(2015)

Abstract

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.

Materials
 

Particle Tracking In Fluidized Beds With Secondary Gas Injection

Procedia Engineering 102, 850-857

(2015)

Abstract

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.

Materials
 
  • Joana Freire
  • Riccardo Meucci
  • Fortunato Arecchi
  • Jason Gallas

Self-organization of pulsing and bursting in a CO 2 laser with opto-electronic feedback

Chaos: An Interdisciplinary Journal of Nonlinear Science 25, 097607

(2015)

Abstract

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.

Materials
 

Helical inner-wall texture prevents jamming in granular pipe flows

Soft Matter 11, 4295-4305

(2015)

Research Projects
Abstract

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.

Materials
 
  • Laura M. Perez
  • Jean Bragard
  • Hector Mancini
  • Jason Gallas
  • Ana Cabanas
  • Omar J. Suarez
  • David Laroze

Effect of anisotropies on the magnetization dynamics

Networks and Heterogeneous Media 10, No. 1, 209-221

(2015)

Research Projects
Abstract

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 preferen- tial axes. The dynamical behavior of the system is represented in Lyapunov phase diagrams, and by calculating bifurcation diagrams, Poincar ́e sections and Fourier spectra. We find an intricate distribution of shrimp-shaped regular is- land embedded in wide chaotic phases. Anisotropy effects are found to play a key role in defining the symmetries of regular and chaotic stability phases.

Materials
 

Are physicists afraid of mathematics?

New Journal of Physics 17, 013036

(2015)

Research Projects
Abstract

A recent study of statistical trends in the distribution of citations among biologists, lead the authors to the conclusion that heavy use of equations impedes communication among biologists (Fawcett & Higginson, PNAS 109:11735). It was suggested that the density of equations in papers should be reduced, that equations should be moved to appendices, and that math training among biologists should be improved in order to increase the probability of citation. Motivated by these rather startling suggestions, we study here citation habits of physicists, a community that has traditionally strong training and dependence in mathematical formulations. Is it possible to correlate statistical citation patterns and fear of mathematics also in a community whose work strongly depends of equations? Analysis of the citation counts of papers published in one of the leading journals covering all branches of physics reveals 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 for the lack of citations. We digress briefly on other statistical trends that apparently would also enhance citation success.

Materials
 

Hydrodynamics of binary mixtures of granular gases with stochastic coefficient of restitution

Journal of Fluid Mechanics 781, 595-621

(2015)

Research Projects
Abstract

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.

Materials
 

Fluidization of a horizontally driven granular monolayer

Physical Review E 91, 062213

(2015)

Research Projects
Abstract

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.

Materials
 

Absence of Subharmonic Response in Vibrated Granular Systems under Microgravity Conditions

Physical Review Applied 3, 024007

(2015)

Research Projects
Abstract

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.

Materials
 

Self-organized Shocks in the Sedimentation of a Granular Gas

Physical Review E 91, 062214

(2015)

Research Projects
Abstract

A granular gas in gravity heated from below develops a certain stationary density profile. When the heating is switched off, the granulate sediments and one observes cycles of diffusive and inertial behavior. During this process, self-organized shocks appear, accompanied by a steep temperature front propagating upward.

Materials
 

Probing the Validity of an Effective-One-Particle Description of Granular Dampers in Microgravity

Granular Matter 17, 73-82

(2015)

Research Projects
Abstract

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.

Materials
 

Nonchaos-Mediated Mixed-Mode Oscillations in an Enzyme Reaction System

Journal of Physical Chemistry Letters 5, 4187-4193

(2014)

Research Projects
Abstract

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.

Materials
 

Structure of a three-dimensional nano-powder subjected to repeated fragmentation and sedimentation

New Journal of Physics 17, 013024

(2014)

Research Projects
Abstract

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 di erent settling kinetics of the fragments leads to di erent anisotropies, the fractal properties are not a ffected.

Materials
 
  • Nina Gunkelmann
  • Eduardo M. Bringa
  • Diego R. Tramontina
  • Carlos J. Ruestes
  • Matthew J. Suggit
  • Andrew Higginbotham
  • Justin S. Wark
  • Herbert M. Urbassek

Shock waves in polycrystalline iron: Plasticity and phase transitions

Physical Review B 89, 140102

(2014)

Research Projects
Abstract

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.

Materials
 
  • Nina Gunkelmann
  • Diego R. Tramontina
  • Eduardo M. Bringa
  • Herbert M. Urbassek

Interplay of plasticity and phase transformation in shock wave propagation in nanocrystalline iron

New Jounal of Physics 16, 093032

(2014)

Research Projects
Abstract

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.

Materials
 

Granular jet impact: probing the ideal fluid description

Journal of Fluid Mechanics 751, 601-626

(2014)

Research Projects
Abstract

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.

Materials
 

Distribution of chaos and periodic spikes in a three-cell population model of cancer. Auto-organization of oscillatory phases in parameter planes

European Physical Journal Special Topics 223, 2131-2144

(2014)

Research Projects
Abstract

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.

Materials
 

Coefficient of Restitution of Aspherical Particles

Physical Review E 90, 052204

(2014)

Research Projects
Abstract

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.

Materials
 

Molecular-dynamics study of the α ↔ γ phase transition in Fe–C

Computational Materials Science 82, 399–404

(2014)

Research Projects
Abstract

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.

Materials
 

Introduction of a new technique to measure the coefficient of restitution for nanoparticles

Chemie Ingenieur Technik 86, 365-374

(2014)

Research Projects
Abstract

A modified single-stage low pressure impactor is described to measure the coefficient of normal restitution en 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 en is derived and first measurements of en for spherical silver particles are presented together with numerical data obtained from force-based molecular dynamics simulations. Furthermore, the simulation data for en and the sticking probability are investigated in detail for the elastic, and partly for the plastic impaction regime.

Materials
 

Stochastic behavior of the coefficient of normal restitution

Physical Review E 89, 022205

(2014)

Research Projects
Abstract

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)].

Materials
 

Stable algorithm for event detection in event-driven particle dynamics

Computational Particle Mechanics 1, 191-198

(2014)

Research Projects
Abstract

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.

Materials
 

Numerical study of the packing density of fine powders by means of the Discrete Element Method

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

(2014)

Research Projects
Abstract

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….

Materials
 

Attractive particle interaction forces and packing density of fine glass powders

Scientific Reports 4, 6227

(2014)

Research Projects
Abstract

We study the packing of fine glass powders of mean particle diameter in the range (4–52) μm 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.

Materials
 

Rectilinear Dune

Encyclopedia of Planetary Landforms (Eds. Hargitai, H., Kereszturi, Ákos), 1-3, Springer New York

(2014)

Research Projects
Abstract

Definition
Straight to curvilinear longitudinal dune formed downwind of domes or barchans (Schatz et al. 2006).
A type of linear dune.
Description
Linear dunes showing sharp crest intermingling with barchan dunes (Tsoar 2008).
Formation
Adjacent barchans indicate unidirectional wind regime. Their sharp crest suggests that their formation is related to terrestrial seif dunes and not linear dunes whose crest is rounded. However, terrestrial seif dunes are sinuous whereas Martian’s are rectilinear. Differences may stem from the induration of Martian dunes (Herrmann et al. 2008) either by geochemical processes or by ice. Indurated Martian barchans may function as obstacle dunes. Consequently, sand transported from upwind direction will be accumulated on the lee side as a short, linear, sharp-crested lee dune. This initial dune stabilizes in time but continues to lengthen parallel to the wind. As induration crust is removed, it disintegrates into a dune convoy (Tsoar 2008). Numerical simulations …

Materials
 

Drop Dune

Encyclopedia of Planetary Landforms (Eds. Hargitai, H., Kereszturi, Ákos), 1-2, Springer New York

(2014)

Research Projects
Abstract

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).
Studied Locations
Mars
Related Landforms
Rectiliniar dune, wedge dune

Materials
 

Dome Dune

Encyclopedia of Planetary Landforms (Eds. Hargitai, H., Kereszturi, Ákos), 1-3, Springer New York

(2014)

Research Projects
Abstract

Definition
Circular to elliptical, relatively flat mounds often without external slip faces.
Synonyms
Dome; Shield dune (obsolete)
Morphometry
On Mars, they are 40–100 m across and <30 m high with 100–1,000 m spacing (De Hon 2006).
Formation
They form where dune height is inhibited by unobstructed strong winds. Strong unidirectional winds retard normal upward growth of dune crests, leading to the formation of dome dunes. Alternatively, they may form when wind velocities are low (Pye and Tsoar 1990 and references therein). Dome dunes may transform into other dune forms. Computer modeling (Parteli et al. 2009) suggests that dome dunes may form if the wind oscillates between two prevailing directions with a period shorter than 0.01 % of the dune’s turnover time, which is the time needed for the dune to cover a distance equal to its own size.

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).

On Mars, do …

Materials
 

Origins of barchan dune asymmetry: insights from numerical simulations

Aeolian Research 12, 121-133

(2014)

Research Projects
Abstract

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.

Materials
 

Cyclic organization of stable periodic and chaotic pulsations in Hartley´s oscillator

Chaos, Solitons & Fractals 59, 129-134

(2014)

Research Projects
Abstract

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.

Materials
 

Self-organization of antiperiodic oscillations

European Physysical Journal Special Topics 223, 2857-2867

(2014)

Research Projects
Abstract

Antiperiodic oscillations forming in nite 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.

Materials
 

Analytical model for flux saturation in sediment transport

Physical Review E 89, 052213

(2014)

Research Projects
Abstract

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.

Materials
 

Morphodynamic modeling of aeolian dunes: Review and future plans

European Physysical Journal Special Topics 223, 2269-2283

(2014)

Research Projects
Abstract

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.

Materials
 

What is the effective impact of the explosive orbital growth in discrete-time one-dimensional polynomial dynamical systems?

Physica A 410, 313-318

(2014)

Research Projects
Abstract

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.

Materials
 

Complex Velocity Dependence of the Coefficient of Restitution of a Bouncing Ball

Physical Review Letters 110, 254301

(2013)

Research Projects
Abstract

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.

Materials
 

Some dynamical properties of a classical dissipative bouncing ball model with two nonlinearities

Physica A 392, 1762–1769

(2013)

Research Projects
Abstract

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.

Materials
 

Energy Dissipation in Driven Granular Matter in the Absence of Gravity

Physical Review Letters 111, 018001

(2013)

Research Projects
Abstract

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 > A0, 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 < A0, 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.

Materials
 

Competition between unlimited and limited energy growth in a two-dimensional time-dependent billiard

Physics Letters A 377, 2052–2057

(2013)

Research Projects
Abstract

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.

Materials
 

Janus Particles at Walls Modified with Tethered Chains

Journal of Physical Chemistry B 117, 1166−1175

(2013)

Research Projects
Abstract

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.

Materials
 

Relaxation of a spring with an attached granular damper

New Journal of Physics 15, 093023

(2013)

Research Projects
Abstract

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.

Materials
 

Pattern formation in a horizontally shaken granular submonolayer

Granular Matter 15, 377–387

(2013)

Research Projects
Abstract

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.

Materials
 

Collective Granular Dynamics in a Shaken Container at Low Gravity Conditions

AIP Conference Proceedings 1542, 811-814

(2013)

Research Projects
Abstract

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.

Materials
 

Event-driven molecular dynamics of soft particles

Physical Review E 87, 033301

(2013)

Research Projects
Abstract

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.

Materials
 
 

Temperature of a granular gas with regard to the stochastic nature of particle interactions

New Journal of Physics 15, 093030

(2013)

Research Projects
Abstract

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−50/29 which deviates from Haff’s law, Tt−2, obtained for gases of particles interacting via a constant coefficient of restitution also from Tt−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.

Materials
 
 
 

Characteristics of large threedimensional heaps of particles produced by ballistic deposition from extended sources

Philosophical Magazine 93, 4090-4107

(2013)

Research Projects
Abstract

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.

Materials
 

A numerical study of the Navier–Stokes transport coefficients for two-dimensional granular hydrodynamics

New Journal of Physics 15, 043044

(2013)

Research Projects
Abstract

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.

Materials
 

Using LIGGGHTS for performing DEM simulations of particles of complex shapes with the multisphere method

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

(2013)

Research Projects
Abstract

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.

Materials
 

DEM simulation of particles of complex shapes using the multisphere method: Application for additive manufacturing

AIP Conference Proceedings 1542, 185-188

(2013)

Research Projects
Abstract

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.

Materials
 

Numerical modeling of the wind flow over a transverse dune

Scientific Reports 3, 2858

(2013)

Research Projects
Abstract

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 u* for shear velocities within the range between 0.2 m/s and 0.8 m/s but increases linearly with u* for larger shear velocities. Our calculations show that transport in the direction opposite to dune migration within the separation bubble can be sustained if u* is larger than approximately 0.39 m/s, whereas a larger value of u* (about 0.49 m/s) is required to initiate this reverse transport.

Materials
 

Zig-zag networks of selfexcited periodic oscillations in a tunnel diode and a fiber-ring laser

Physical Review E 87, 042907

(2013)

Research Projects
Abstract

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 CO2 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.

Materials
 

Infinite Networks of Hubs, Spirals, and Zig-Zag Patterns in Self-sustained Oscillations of a Tunnel Diode and of an Erbium-doped Fiber-ring Laser

Selected Topics in Nonlinear Dynamics (K. Kyamakya et al., Eds.) SCI 459, 161-177, Springer Verlag Berlin Heidelberg

(2013)

Research Projects
Abstract

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.

Materials
 
  • Cecilia Cabeza
  • Carlos A. Briozzo
  • Rodrigo Garcia
  • Joana G. Freire
  • Arturo C. Marti
  • Jason Gallas

Periodicity hubs and wide spirals in a two-component autonomous electronic circuit

Chaos, Solitons & Fractals 52 , 59-65

(2013)

Research Projects
Abstract

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.

Materials
 

Characterization of the stability of semiconductor lasers with delayed feedback according to the Lang- Kobayashi model

European Physical Journal D 67, 149

(2013)

Research Projects
Abstract

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.

Materials
 

Antiperiodic oscillations

Scientific Reports 3, 1958

(2013)

Research Projects
Abstract

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.

Materials
 

Discontinuous spirals of stable periodic oscillations

Scientific Reports 3, 3350

(2013)

Research Projects
Abstract

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.

Materials
 

Poly-directional Stability of Granular Matter

Physical Review Letters 111, 168003

(2013)

Research Projects
Abstract

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.

Materials
 

Flux saturation length of sediment transport

Physical Review Letters 111, 218002

(2013)

Research Projects
Abstract

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 Ls, which characterizes the flux response to a change in transport conditions. Here we derive, for the first time, an expression predicting Ls as a function of the average sediment velocity under different physical environments. Our expression accounts for both the characteristics of sediment entrainment and the saturation of particle and fluid velocities, and has only two physical parameters which can be estimated directly from independent experiments. We show that our expression is consistent with measurements of Ls in both aeolian and subaqueous transport regimes over at least 5 orders of magnitude in the ratio of fluid and particle density, including on Mars.

Materials
 

Hydrodynamics at the Navier-Stokes Level Applied to Fast, Transient, Supersonic Granular Flows

AIP Conference Proceedings 1501, 993-1000

(2012)

Research Projects
Abstract

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.

Materials
 

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

Chaos 22, 026123

(2012)

Research Projects
Abstract

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 ¼ gV2; (iii) F ¼ gVl with l 6¼ 1 and l 6¼ 2 and; (iv) F ¼ gV, where g 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.

Materials
 

Influence of boundary conditions on quantum escape

Europhysics Letters 100, 2005

(2012)

Research Projects
Abstract

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.

Materials
 

Dynamical properties for the problem of a particle in an electric field of wave packet: Low velocity and relativistic approach

Physics Letters A 376, 3630-3637

(2012)

Research Projects
Abstract

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.

Materials
 
 
 

Recurrent Inflation and Collapse in Horizontally Shaken Granular Materials

Physical Review E 85, 031307

(2012)

Research Projects
Abstract

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.

Materials
 

Circular ratchets as transducers of vertical vibrations into rotations

Physical Review E 86, 061310

(2012)

Research Projects
Abstract

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.

Materials
 

Granular dampers for the reduction of vibrations of an oscillatory saw

Physica A 391, 4442-4447

(2012)

Research Projects
Abstract

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.

Materials
 

Oblique impact of frictionless spheres: On the limitations of hard sphere models for granular dynamics

Granular Matter 14, 115-120

(2012)

Research Projects
Abstract

When granular systems are modeled by fric- tionless 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 univer- sal condition which allows to assess whether the hard- sphere modeling and, thus, event-driven Molecular Dynamics simulations are justified.

Materials
 

Negative coefficient of normal restitution

Physical Review E 85, 041306

(2012)

Research Projects
Abstract

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.

Materials
 

Structure of granular packings

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

(2012)

Research Projects
Abstract

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.

Materials
 

Nonuniformities in the angle of repose and packing fraction of large heaps of particles

Physical Review Letters 109, 128001

(2012)

Research Projects
Abstract

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.

Materials
 
  • Andreas Bauereiß
  • Eric Parteli
  • Daniel Riedlbauer
  • Michael Stingl

Numerische Simulation pulver- und strahlbasierter additiver Fertigungsprozesse

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

(2012)

Research Projects
Abstract

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.

Materials
 

Dune migration in the north polar region of Mars

Third International Planetary Dunes Workshop, 7007

(2012)

Research Projects
Abstract

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.

Materials
 
  • Jasper F. Kok
  • Eric Parteli
  • Timothy I. Michaels
  • Diana B. Karam

The physics of wind-blown sand and dust

Reports on Progress in Physics 75, 106901

(2012)

Research Projects
Abstract

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.

Materials
 
  • Britt Michelsen

Validation of Dune Simulations using OpenFOAM

Bachelor Thesis, Friedrich-Alexander Universität Erlangen-Nürnberg

(2012)

Research Projects
 

Intricate routes to chaos in the Mackey- Glass delayed feedback system

Physics Letters A 376, 2109-2116

(2012)

Research Projects
Abstract

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.

Materials
 

Stern-Brocot trees in spiking and bursting of sigmoidal maps

Europhysics Letters 100, 48002

(2012)

Research Projects
Abstract

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.

Materials
 

Collision of Viscoelastic Spheres: Compact Expressions for the Coefficient of Normal Restitution

Physical Review E 84, 021302

(2011)

Research Projects
Abstract

The coefficient of restitution of colliding viscoelastic spheres is analytically known as a complete series expansion in terms of the impact velocity where all (infinitely many) coefficients are known. While beeing analytically exact, this result is not suitable for applications in efficient event-driven Molecular Dynamics (eMD) or Monte Carlo (MC) simulations. Based on the analytic result, here we derive expressions for the coefficient of restitution which allow for an application in efficient eMD and MC simulations of granular Systems.

Materials
 

Coefficient of restitution as a fluctuating quantity

Physical Review E 84, 041306

(2011)

Research Projects
Abstract

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.

Materials
 

Two-ball problem revisited: Limitations of event-driven modeling

Physical Review E 83, 041304

(2011)

Research Projects
Abstract

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.

Materials
 

Movers and shakers: Granular damping in microgravity

Physical Review E 84, 011301

(2011)

Research Projects
Abstract

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.

Materials
 

DynamO: A free O(N) general event-driven simulator

Journal of Computational Chemistry 32, 3329-3338

(2011)

Research Projects
Abstract

Molecular-dynamics algorithms for systems 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 fairly specialized. We present DYNAMO, a general event-driven simulation package which displays the optimal asymptotic scaling of the computational cost with system size. 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. This software and its documentation are distributed under the GNU General Public license and can be freely downloaded from this http URL

Materials
 

Application of the Method of Generating Functions to the Derivation of Grad’s N-Moment Equations for a Granular Gas

Mathematical Modelling of Natural Phenomena 6, No. 4, 151-174

(2011)

Research Projects
Abstract

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.

Materials
 

Global structure of periodicity hubs in Lyapunov phase diagrams of dissipative flows

Physical Review E 84, 016216

(2011)

Research Projects
Abstract

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 R¨ossler’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.

Materials
 
  • Jean Bragard
  • Harald Pleiner
  • Omar J. Suarez
  • Patricio Vargas
  • Jason Gallas
  • David Laroze

Chaotic dynamics of a magnetic nanoparticle

Physical Review E 84, 037202

(2011)

Research Projects
Abstract

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.

Materials
 

Force Statistics and Correlations in Dense Granular Packings

Chemical Physics 375, 600-605

(2010)

Research Projects
Abstract

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.

Materials
 
  • Robert Behringer
  • James Jenkins
  • Touvia Miloh
  • Steven Orszag
  • Thorsten Pöschel
  • Philip Rosenau
  • Stuart Savage
  • Zeev Schuss
  • Lev Shemer

Obituary: PROFESSOR ISAAC GOLDHIRSCH 11 October 1949–29 April 2010

Journal of Fluid Mechanics 655, 1–2

(2010)

Research Projects
Abstract

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.

Materials
 

Exact on-event expressions for discrete potential systems

Journal of Chemical Physics 133, 124506

(2010)

Research Projects
Abstract

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.

Materials
 

Thermodynamic pressures for hard spheres and closed-virial equation-of-state

Journal of Chemical Physics 132, 084507

(2010)

Research Projects
Abstract

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.

Materials
 

Approximate 3D motif search in proteins with domain specific knowledge

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)

Research Projects
Abstract

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.

Materials
 

Correlation of spin and velocity in the homogeneous cooling state of a granular gas of rough particles

European Physical Journal Special Topics 179, 91-111

(2009)

Research Projects
Abstract

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.

Materials
 
 

Single-Speed Molecular Dynamics of Hard Parallel Squares and Cubes

Journal of Statistical Physics 136, 715-732

(2009)

Research Projects
Abstract

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.

Materials
 

Structure and stability of helices in square-well homopolymers

Physical Review E 80, 021801

(2009)

Research Projects
Abstract

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.

Materials
 

Transport properties of highly asymmetric hard sphere mixtures

Journal of Chemical Physics 130, 164507

(2009)

Research Projects
Abstract

The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of sigma_B/sigma_A=0.1 and a mass ratio of m_B/m_A=0.001 are investigated using event driven molecular dynamics. The contact value of the pair correlation functions are found to compare favourably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of revised Enskog theory, using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (x_A=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 Enskog theory.

Materials
 

Collision statistics in sheared inelastic hard spheres

Physical Review E 79, 041308

(2009)

Research Projects
Abstract

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.

Materials
 

Fractal Substructures due to Fragmentation and Reagglomeration

AIP Conference Proceedings 1145, 859-862

(2009)

Research Projects
Abstract

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.

Materials