Publications

Recurrent Periodicities in Very Tall Disks Packings

Royal Society of Chemistry

(submitted)

 

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

(submitted)

 

Microgravity spreading of water spheres on Hydrophobic capillary plates

Powders and Grains 2017

(submitted)

 

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

(submitted)

 

Weight of an Hourglass – Theory and Experiment in Quantitative Comparison

American Journal of Physics

(in print)

 

Homogeneous cooling state of granular gases of charged particles

(submitted)

 

Velocity distribution of a homogeneously driven two-dimensional granular gas

(submitted)

 

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

(submitted)

 

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

(submitted)

 

Vertical motion of particles in vibration-induced granular capillarity

(submitted)

 

Granular Capillarity

(submitted)

 

High speed movies of a dripping faucet

(submitted)

 

Inelastic collapse of perfectly inelastic particles

(submitted)

 

Instability of SPH applied to Poiseuille flow

(submitted)

 

Energy decay in a granular gas collapse

New Journal of Physics 19, 013001

(2017)

 

Effect of particle shape on the efficiency of granular dampers

New Journal of Physics 18 073049

(2016)

 

Heaping and secondary flows in sheared granular materials

New Journal of Physics 18, 113006

(2016)

 

Ratcheting and tumbling motion of Vibrots

New Journal of Physics 18, 123001

(2016)

 

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

Computational Partical Mechanics 3, 389

(2016)

 

Granular dampers: Does particle shape matter?

New Journal of Physics 18, 073049

(2016)

 

Dissipation of Energy by Dry Granular Matter in a Rotating Cylinder

Scientific Reports 6, 26833

(2016)

 

Exact calculation of the overlap volume of spheres and mesh elements

Journal of Computational Physics 311, 158-172

(2016)

 

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

European Journal of Physics 37, 055305

(2016)

 

Homogeneous cooling of mixtures of particle shapes

Physics of Fluids 28, 073301

(2016)

 

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

Computational Partical Mechanics 3, 383-388

(2016)

 

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

Granular Matter

(2016)

 

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

New Journal of Physics 18, 118004

(2016)

 

Actively rotating granular particles manufactured by rapid prototyping

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

(2016)

 

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

Soft Matter 12, 3184

(2016)

 

Particle-based simulation of powder application in additive manufacturing

Powder Technology 288, 96-102

(2016)

 

Steepest descent ballistic deposition of complex shaped particles

Journal of Computational Physics 308, 421

(2016)

 

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

Physical Review E 93, 032901

(2016)

 

Subharmonic instability of a self-organized granular jet

Scientific Reports 6, 22520

(2016)

 

Residual defect density in random deposits of disks

Scientific Reports 5, 12703

(2015)

 

Two-dimensional airflow modeling underpredicts the wind velocity over dunes

Scientific Reports 5, 16572

(2015)

 

Positron Emission Particle Tracking in Fluidized Beds with Secondary Gas Injection

Powder Technology 279, 113-122

(2015)

 

Particle Tracking In Fluidized Beds With Secondary Gas Injection

Procedia Engineering 102, 850-857

(2015)

 

Helical inner-wall texture prevents jamming in granular pipe flows

Soft Matter 11, 4295-4305

(2015)

 

Are physicists afraid of mathematics?

New Journal of Physics 17, 013036

(2015)

 

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

Journal of Fluid Mechanics 781, 595-621

(2015)

 

Fluidization of a horizontally driven granular monolayer

Physical Review E 91, 062213

(2015)

 

Absence of Subharmonic Response in Vibrated Granular Systems under Microgravity Conditions

Physical Review Applied 3, 024007

(2015)

 

Self-organized Shocks in the Sedimentation of a Granular Gas

Physical Review E 91, 062214

(2015)

 

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

Granular Matter 17, 73-82

(2015)

 

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

New Journal of Physics 17, 013024

(2014)

 

Granular jet impact: probing the ideal fluid description

Journal of Fluid Mechanics 751, 601-626

(2014)

 

Coefficient of Restitution of Aspherical Particles

Physical Review E 90, 052204

(2014)

 

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

Chemie Ingenieur Technik 86, 365-374

(2014)

 

Stochastic behavior of the coefficient of normal restitution

Physical Review E 89, 022205

(2014)

 

Stable algorithm for event detection in event-driven particle dynamics

Computational Particle Mechanics 1, 191-198

(2014)

 

Relation of structure and history of granular sediments

Jam-Packed 2014, Erlangen, Germany, 15th – 18th

(2014)

Research Projects
Materials
 

Sedimentation and Collapse of a granular gas under gravity

Jam-Packed – Jamming and Packing of particulate systems, Erlangen, Germany, 15th – 18th September

(2014)

Research Projects
 

Attractive particle interaction forces and packing density of fine glass powders (Poster)

Packing and Jamming of Particulate Systems – Jam Packed 2014, September 15-18, Erlangen

(2014)

Research Projects
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)

 

Attractive particle interaction forces and packing density of fine glass powders

Scientific Reports 4, 6227

(2014)

 

Origins of barchan dune asymmetry: insights from numerical simulations

Aeolian Research 12, 121-133

(2014)

 

Self-organization of antiperiodic oscillations

European Physysical Journal Special Topics 223, 2857-2867

(2014)

 

Morphodynamic modeling of aeolian dunes: Review and future plans

European Physysical Journal Special Topics 223, 2269-2283

(2014)

 

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

Physical Review Letters 110, 254301

(2013)

 

Energy Dissipation in Driven Granular Matter in the Absence of Gravity

Physical Review Letters 111, 018001

(2013)

 

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

Physics Letters A 377, 2052–2057

(2013)

 

Janus Particles at Walls Modified with Tethered Chains

Journal of Physical Chemistry B 117, 1166−1175

(2013)

 

Relaxation of a spring with an attached granular damper

New Journal of Physics 15, 093023

(2013)

 

Pattern formation in a horizontally shaken granular submonolayer

Granular Matter 15, 377–387

(2013)

 

Collective Granular Dynamics in a Shaken Container at Low Gravity Conditions

AIP Conference Proceedings 1542, 811-814

(2013)

 

Event-driven molecular dynamics of soft particles

Physical Review E 87, 033301

(2013)

 

Erratum: Collision dynamics of granular particles with adhesion [Physical Review E 76, 051302 (2007)]

Physical Review E 87, 039904(E)

(2013)

 

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

New Journal of Physics 15, 093030

(2013)

 

Event-driven DEM of soft spheres

AIP Conference Proceedings 1542, 149-152

(2013)

 

Micro-mechanics and dynamics of cohesive particle systems

Granular Matter 15, 389-390

(2013)

 

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

Philosophical Magazine 93, 4090-4107

(2013)

 

Modeling the packing of nano-powders

EAM Summerschool, Kloster Banz, Germany

(2013)

Research Projects
Materials
 

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

New Journal of Physics 15, 043044

(2013)

 

Numerical modeling of the wind flow over a transverse dune

Scientific Reports 3, 2858

(2013)

 

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

Physical Review E 87, 042907

(2013)

 

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)

 

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

European Physical Journal D 67, 149

(2013)

 

Antiperiodic oscillations

Scientific Reports 3, 1958

(2013)

 

Discontinuous spirals of stable periodic oscillations

Scientific Reports 3, 3350

(2013)

 

Modeling the turbulent wind flow over transverse dunes

Presented at Powders and Grains 2013, Sydney, Australia, 08th – 12th

(2013)

Research Projects
Materials
 

Poly-directional Stability of Granular Matter

Physical Review Letters 111, 168003

(2013)

 

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

AIP Conference Proceedings 1501, 993-1000

(2012)

 

Special Issue: Isaac Goldhirsch – A Pioneer of Granular Matter Theory

Granular Matter 14, 2, Springer

(2012)

 

Recurrent Inflation and Collapse in Horizontally Shaken Granular Materials

Physical Review E 85, 031307

(2012)

 

Circular ratchets as transducers of vertical vibrations into rotations

Physical Review E 86, 061310

(2012)

 

Granular dampers for the reduction of vibrations of an oscillatory saw

Physica A 391, 4442-4447

(2012)

 

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

Granular Matter 14, 115-120

(2012)

 

Negative coefficient of normal restitution

Physical Review E 85, 041306

(2012)

 

Structure of granular packings

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

(2012)

 

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

Physical Review Letters 109, 128001

(2012)

 

Non-Uniformities in the angle of repose and packing fraction of large heaps of granular matter

EAM Summerschool, Kloster Banz, Germany

(2012)

Research Projects
 

Stern-Brocot trees in spiking and bursting of sigmoidal maps

Europhysics Letters 100, 48002

(2012)

 

Periodicity Hubs with Discontinuous Spirals in a Noiseless Duffing Proxy: Experiment and Theory

(2012)

Research Projects
 

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

Physical Review E 84, 021302

(2011)

 

Coefficient of restitution as a fluctuating quantity

Physical Review E 84, 041306

(2011)

 

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

Physical Review E 83, 041304

(2011)

 

Movers and shakers: Granular damping in microgravity

Physical Review E 84, 011301

(2011)

 

Force Statistics and Correlations in Dense Granular Packings

Chemical Physics 375, 600-605

(2010)

 
  • 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)

 

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)

 

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)

 

Granular Gases: Beyond the Dilute Limit

The European Physical Journal Special Topics 179, 1, Springer

(2009)

 

Fractal Substructures due to Fragmentation and Reagglomeration

AIP Conference Proceedings 1145, 859-862

(2009)

 

Granular hydrodynamics and pattern formation in vertically oscillated granular disks layers

J. Fluid Mech., 597, 119-144

(2008)

Research Projects
Abstract

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

Materials
 

Coefficient of tangential restitution for viscoelastic spheres

European Physical Journal, 27, 107-114

(2008)

Research Projects
Abstract

We consider the collision of frictional granular particles where the normal part of the interaction force is due to viscoelastic spheres and the tangential part is described by the model by Cundall and Strack being the most popular tangential collision model in Molecular Dynamics simulations. Albeit being a rather complicated model, governed by 7 phenomenological parameters, we find that it depends on 3 independent parameters only. Surprisingly, in a wide range of parameters the corresponding coefficient of tangential restitution, ε_t, is well described by the simple Coulomb law with a cut-off at ε_t=0. A more complex behavior of the coefficient of restitution as a function on the normal and tangential components of the impact velocity, g_n and g_t, including negative values of ε_t is found only for very small ratio g_t/g_n.

Materials
 

Coefficient of tangential restitution for the linear dashpot model

Physical Review E, 77, 011304

(2008)

Research Projects
Abstract

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

Materials
 

Hourglass of constant weight

Granular Matter, 10, 231-232

(2008)

Research Projects
Abstract

In contrast to a still common belief, a steadily flowing hourglass changes its weight in the course of time. We will show that, nevertheless, it is possible to construct hourglasses that do not change their weight.

Materials
 

Coefficient of Restitution for Viscoelastic Spheres: The Effect of Delayed Recovery

Physical Review E, 78, 051304

(2008)

Research Projects
Abstract

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

Materials
 

Fractal Substructure of a Nanopowder

Physical Review Letters 100, 218002

(2008)

Research Projects
Abstract

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

Materials
 
  • R. Bauer
  • P. E. Bourne
  • A. Formella
  • C. Frömmel
  • C. Gille
  • A. Goede
  • A. Guerler
  • A. Hoppe
  • E.-W. Knapp
  • Thorsten Pöschel
  • B. Wittig
  • V. Ziegler
  • R. Preissner

Superimposé: A 3D structural superposition server

Nucleic Acids Research 36, W47–W54

(2008)

Research Projects
Abstract

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

Materials
 

Contact of granular particles and the simulation of rapid flows using event-driven molecular dynamics

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

(2008)

Research Projects
Abstract

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

Materials
 

Granular gas cooling and relaxation to the steady state in regard to the overpopulated tail of the velocity distribution

Int. J. Mod. Phy. C, 18, 701-711

(2007)

Research Projects
Abstract

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

Materials
 

Translations and Rotations are correlated in Granular Gases

Physical Review Letters, 98, 128001

(2007)

Research Projects
Abstract

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

Materials
 

Traffic and Granular Flow'05

(Andreas Schadschneider, Thorsten Pöschel, Reinhard Kühne, Michael Schreckenberg, Dietrich E. Wolf), Springer

(2007)

Research Projects
Materials
 

Close-packed granular clusters: hydrostatics and persistent Gaussian fluctuations

Granular Matter, 10, 21-27

(2007)

Research Projects
Abstract

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

Materials
 

Coefficient of restitution and linear dashpot model revisited

Granular Matter, 9, 465-469

(2007)

Research Projects
Abstract

With the assumption of a linear-dashpot interaction force, the coefficient of restitution, ε_d^0(k, gamma), can be computed as a function of the elastic and dissipative material constants, k and gamma by integrating Newton’s equation of motion for an isolated pair of colliding particles. If we require further that the particles interact exclusively repulsive, which is a common assumption in granular systems, we obtain an expression ε_d(k, gamma) which differs even qualitatively from the known result ε_d^0(k, gamma) . The expression ε_d(k, gamma) allows to relate Molecular Dynamics simulations to event-driven Molecular Dynamics for a widely used collision model.

Materials
 

Collision dynamics of granular particles with adhesion

Physical Review E, 76, 051302

(2007)

Research Projects
Abstract

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

Materials
 

Long-time behavior of granular gases

Modelling and numerics of kinetic dissipative systems (Pareschi, L. and Russo, G. and Toscani, G.), Nova Science, Hauppauge NY

(2006)

Research Projects
Abstract

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

 

Markovsche Analyse nasser Gemeinschaften

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

(2006)

Research Projects
Abstract

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

Materials
 

Efficient numerical simulation of granular matter using the Bottom-To-Top Reconstruction method

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

(2006)

Research Projects
Abstract

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

Materials
 

Impact of high-energy tails on granular gas properties

Physical Review E, 74, 041302

(2006)

Research Projects
Abstract

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

Materials
 

Irreversible Prozesse und Selbstorganisation

Logos, Berlin

(2006)

Research Projects
Materials
 

Breakdown of the Sonine expansion for the velocity distribution in granular gases

Europhysics Letters, 74, 424-430

(2006)

Research Projects
Abstract

The velocity distribution of a granular gas is analyzed in terms of the Sonine polynomials expansion. We derive an analytical expression for the third Sonine coefficient a_3. In contrast to frequently used assumptions this coefficient is of the same order of magnitude as the second Sonine coefficient a_2. For small inelasticity the theoretical result is in good agreement with numerical simulations. The next-order Sonine coefficients a_4, a_5 and a_6 are determined numerically. While these coefficients are negligible for small dissipation, their magnitude grows rapidly with increasing inelasticity for 0< ε < 0.6. We conclude that this behavior of the Sonine coefficients manifests the break down of the Sonine polynomial expansion caused by the increasing impact of the overpopulated high-energy tail of the distribution function.

Materials
 

Adhesive interactions of viscoelastic spheres

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

(2005)

Research Projects
Abstract

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

Materials
 

Rolling friction and bistability of rolling motion

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

(2005)

Research Projects
Abstract

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

Materials
 

Computational Granular Dynamics - Models and Algorithms

Springer, Berlin, Heidelberg, New York

(2005)

Research Projects
 

Self-diffusion in granular gases: Green-Kubo versus Chapman-Enskog

Chaos 15, 026108

(2005)

Research Projects
Abstract

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

Materials
 

Peptide size dependent active transport in the proteasome

Europhysics Letters, 69, 725-731

(2005)

Research Projects
Abstract

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

Materials
 

Bistability and noise-induced acceleration in rolling motion

Europhysics Letters, 69, 371-377

(2005)

Research Projects
Abstract

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

Materials
 

Transient clusters in granular gases

J.Phys.: Condens. Matter, 17, S2705–S2713

(2005)

Research Projects
Abstract

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

Materials
 

Collision of adhesive viscoelastic particles

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

(2004)

Research Projects
Abstract

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

Materials
 

Transient structures in a Granular Gases

Physical Review Letters, 93, 134301

(2004)

Research Projects
Abstract

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

Materials
 

Kinetic Theory of Granular Gases

Oxford University Press, Oxford

(2004)

Research Projects
 

Giant fluctuations at a granular phase separation threshold

Physical Review E, 69, 021302

(2004)

Research Projects
Abstract

Granular hydrodynamics is tested in a system of nearly elastically colliding hard spheres driven by a thermal wall. If the aspect ratio of the confining box exceeds a threshold value, granular hydrodynamics predicts phase separation and formation of a localized almost densely packed domain. Event-driven molecular dynamic simulations confirm this prediction. However, the hydrodynamic bifurcation curve agrees with the simulations quantitatively only well below and well above the threshold. In a wide region of aspect ratios around the threshold the system is dominated by fluctuations, and granular hydrodynamics fails to give an accurate description.

Materials
 

Granular Gases: Kinetic theory meets computer simulations

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

(2003)

Research Projects
 

Kinetic Integrals in the Theory of Dissipative Gases

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

(2003)

Research Projects
Abstract

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

Materials
 

How to decide whether small samples comply with an equidistribution

BioSystems, 69, 63-72

(2003)

Research Projects
Abstract

The decision whether a measured distribution complies withan equidistribution is a central element of many biostatistical methods. High through put differential expression measurements, for instance, necessitate to judge possible over-representation of genes. The reliability of this judgement, however, is strongly affected when rarely expressed genes are pooled. We propose a method that can be applied to frequency ranked distributions and that yields a simple but efficient criterion to assess the hypothesis of equiprobable expression levels. By applying our technique to surrogate data we exemplify how the decision criterion can differentiate between a true equidistribution and a triangular distribution. The distinction succeeds even for small sample sizes where standard tests of significance (e.g. chi²) fail. Our method will have a major impact on several problems of computational biology where rare events baffle a reliable assessment of frequency distributions.

Materials
 

Hydrodynamics and transport coefficients for Granular Gases

Physical Review E, 67, 061304

(2003)

Research Projects
Abstract

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

Materials
 

Close-Packed Floating Clusters: Granular Hydrodynamics Beyond the Freezing Point?

Physical Review Letters, 91, 024301

(2003)

Research Projects
Abstract

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

Materials
 

Kinetics of Prion Growth: Mathematical Aspects

Biophys. J., 85, 3460-3474

(2003)

Research Projects
Abstract

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

Materials
 

Correction algorithm for finite sample statistics

European Physical Journal, 12, 531-541

(2003)

Research Projects
Abstract

Assume one finds in a set of M samples, M_j representatives of species j with j=1…N*. We show that due to the finite value of the sampling size,M, the observed number of species N*, may be much smaller than the real number of species in the system N. Also the naively calculated concentrations c*_j= M_j/M may deviate considerably from the true values. In this work we propose a method to deduce the true system size N and the true concentrations c_j from the measured frequencies M_j.

Materials
 

Online tool to decide whether frequencies are equidistributed

BMC Bioinformatics 4, 58 - 64

(2003)

Research Projects
Abstract

For many applications one wishes to decide whether a certain set of numbers originates from an equiprobability distribution or whether they are unequally distributed. Distributions of relative frequencies may deviate significantly from the corresponding probability distributions due to finite sample effects. Hence, it is not trivial to discriminate between an equiprobability distribution and non-equally distributed probabilities when knowing only frequencies. Based on analytical results we provide a software tool which allows to decide whether data correspond to an equiprobability distribution. The tool is available at http://bioinf.charite.de/equifreq/. Its application is demonstrated for the distribution of point mutations in coding genes.

Materials
 

Violation of Molecular Chaos in dissipative gases

Int. J. Mod. Phys. C, 13, 1263-1272

(2002)

Research Projects
Abstract

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

Materials
 

Mechanik körniger Medien

Perspectives of Science and its Funding (in German), Wiley-VCH

(2002)

Research Projects
 

Finite-sample frequency distributions originating from an equiprobability distribution

Physical Review E, 66, 026103

(2002)

Research Projects
Abstract

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

Materials
 

Hydrodynamics of dense granular systems

SPIE, 3045

(2002)

Research Projects
Abstract

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

 

Materials
 

Hydrodynamics of Granular Gases of viscoelastic particles

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

(2002)

Research Projects
Abstract

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

Materials
 

Rigid body dynamics of railway ballast

System Dynamics and Long-Term Behaviour of Railway Vehicles, Track and Subgrade (Lecture Notes in Applied Mechanics) (Popp, K. and Schiehlen, W.), 451-470, Springer, Berlin, Heidelberg, New York

(2002)

Research Projects
Abstract

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

Materials
 

Long-time behavior of granular gases with impact-velocity dependent

Physica A, 325, 274-283

(2002)

Research Projects
Abstract

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

Materials
 

Chains of viscoelastic spheres

Granular Gases (Lecture Notes in Physics) (Pöschel, T. and Luding, S), 564, 203-212, Springer, Berlin, Heidelberg, New York

(2001)

Research Projects
Abstract

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

Materials
 

Scaling properties of granular materials

Continuous and Discontinuous Modelling of Cohesive Frictional Materials (P. A. Vermeer, S. Diebels, W. Ehlers, H. J. Herrmann, S. Luding, and E. Ramm (eds.)), 173-184, Springer, Berlin

(2001)

Research Projects
Abstract

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

Materials
 

Extremal collision sequences of particles on a line: Optimal transmission of kinetic energy

Physical Review Letters, 63, 021505

(2001)

Research Projects
Abstract

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

Materials
 

Scaling properties of granular materials

Physical Review E, 64, 011308

(2001)

Research Projects
Abstract

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

Materials
 

Can we scale granular systems?

Powders & Grains'2001 (Kishino), 439-442, Balkema, Rotterdam

(2001)

Research Projects
Abstract

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

Materials
 

Granular gases with impact-velocity dependend restitution coefficient

Granular Gases (Lecture Notes in Physics) (Pöschel, T. and Luding, S), 564, 100-124, Springer, Berlin, Heidelberg, New York

(2001)

Research Projects
Abstract

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

Materials
 

Vertically shaken column of spheres. Onset of fluidization

European Physical Journal, 4, 233-239

(2001)

Research Projects
Abstract

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

Materials
 

Granular Gases - The early stage

Coherent Structures in Complex Systems (Lecture Notes in Physics) (D. Reguera, L.L. Bonilla, M. Rubi), 567, 408-419, Springer, Berlin, Heidelberg, New York

(2001)

Research Projects
Abstract

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

Materials
 

Dynamics of granular systems (in German)

Logos, Berlin

(2001)

Research Projects
 

Molecular Dynamics of comminution in ball mills

Bulk Solids Handling, 20, 159-172

(2000)

Research Projects
Abstract

We investigate autogenous fragmentation of dry granular material in rotating cylinders using two-dimensional molecular dynamics. By evaluation of spatial force distributions achieved numerically for various rotation velocities we argue that comminution occurs mainly due to the existence of force chains. A statistical analysis of these force chains explains the spatial distribution of comminution efficiency in ball mills as measured experimentally by Rothkegel [1] and Rolf [2]. For animated sequences of our simulations see url http://www.mss.cbi.uni-erlangen.de/index.php?p1=research&p2=articles&r=granular/RotatingCylinder/Comminution

Materials
 

Convection patterns in horizontally shaken granular material

European Physical Journal E, 1, 55-59

(2000)

Research Projects
Abstract

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

Materials
 

Deviation from Maxwell distribution in granular gases with constant restitution coefficient

Physical Review E, 61, 2809 – 2812

(2000)

Research Projects
Abstract

We analyze the velocity distribution function of force-free granular gases in the regime of homogeneous cooling when deviations from the Maxwellian distribution may be accounted only by the leading term in the Sonine polynomial expansion, quantified by the second coefficient a_2. We go beyond the linear approximation for a₂ and find three different values (three roots) for this coefficient which correspond to a scaling solution of the Boltzmann equation. The stability analysis performed showed, however, that among these three roots only one corresponds to a stable scaling solution. This is very close to a_2, obtained in previous studies in a linear with respect to a_2 approximation.

Materials
 

Molekulardynamische Untersuchung von Zerkleinerungsprozessen in Kugelmühlen

Schüttgut, 6, 11-24

(2000)

Research Projects
Abstract

Molekulardynamische Untersuchungen eignen sich zur Simulation des Verhaltens makroskopischer Mengen granularen Materials unter bestimmten, technologisch relevanten Beanspruchungen. Wir untersuchen das Zerkleinerungsverhalten von Mahlgut in einer Kugelmühle, insbesondere im Hinblick auf die Effizienz als Funktion der Drehzahl und auf die räumliche Verteilung von Beanspruchungen. Die Untersuchung der Verteilung von Kraftketten liefert eine Erklärung des Experiments von Rothkegel [1] und Rolf. Für animierte Sequenzen der Simulationen s. url: http://www.mss.cbi.uni-erlangen.de/index.php?p1=research&p2=articles&r=granular/RotatingCylinder/Comminution

Materials
 

Granular Gases

Lecture Notes in Physics, 564, Springer, Berlin, Heidelberg, New York

(2000)

Research Projects
Materials
 

Self-diffusion in granular gases

Physical Review E, 61, 1716-1721

(2000)

Research Projects
Abstract

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

Materials
 

Velocity distribution in granular gases of viscoelastic particles

Physical Review E, 61, 5573-5587

(2000)

Research Projects
Abstract

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

Materials
 

From ''solid'' to to ''fluid'': Time dependent hydrodynamical analysis of dense granular flows

Proceed. ICTAM, Chicago

(2000)

Research Projects
Abstract

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

Materials
 

Diffusion in granular gases of viscoelastic particles

Stochastic Processes in Physics, Chemistry, and Biology (Lecture Notes in Physics) (Freund, J. A. and Pöschel, T.), 557, 107-117, Springer, Berlin, Heidelberg, New York

(2000)

Research Projects
Abstract

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

Materials
 

Molecular Dynamics of comminution in ball mills

European Physical Journal, 16, 169-182

(2000)

Research Projects
Abstract

We investigate autogenous fragmentation of dry granular material in rotating cylinders using two-dimensional molecular dynamics. By evaluation of spatial force distributions achieved numerically for various rotation velocities we argue that comminution occurs mainly due to the existence of force chains. A statistical analysis of these force chains explains the spatial distribution of comminution efficiency in ball mills as measured experimentally by Rothkegel [1] and Rolf [2]. For animated sequences of our simulations see url http://www.mss.cbi.uni-erlangen.de/php/research/granular/RotatingCylinder/Comminution/

Materials
 

Onset of fluidization in vertically shaken granular material

Physical Review E, 62, 1361-1367

(2000)

Research Projects
Abstract

When granular material is shaken vertically one observes convection, surface fluidization, spontaneous heap formation and other effects. There is a controversial discussion in literature whether there exists a threshold for the Froude number Γ=(A_0ω_0^2)/g below which these effects cannot be observed anymore. By means of theoretical analysis and computersimulation we find that there is no such single threshold. Instead we propose a modified criterion which coincides with critical Froude number Γ_c=1 for small driving frequency ω_0

Materials
 

Stochastic Processes in Physics, Chemistry, and Biology

Lecture Notes in Physics, 557, Springer, Berlin, Heidelberg, New York

(2000)

Research Projects
 

Granular Gases

Phys. Bl., 55

(1999)

Research Projects
 

Rolling friction of a hard cylinder on a viscous plane

European Physical Journal B, 10, 169-174

(1999)

Research Projects
Abstract

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

 

Materials
 

Rolling as a continuing collision

European Physical Journal B, 12, 299-301

(1999)

Research Projects
Abstract

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

Materials
 

Dissipative properties of vibrated granular materials

Physical Review E, 59, 4422-4425

(1999)

Research Projects
Abstract

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

Materials
 

Coefficient of restitution of colliding spheres

Physical Review E, 60, 4465-4472

(1999)

Research Projects
Abstract

We perform a dimension analysis for colliding viscoelastic spheres to show that the coefficient of normal restitution epsilon depends on the impact velocity g as ε= 1-gamma_1 g^(1/5) + gamma_2 g^(2/5) …, in accordance with recent findings. We develop a simple theory to find explicit expressions for coefficients gamma1 and gamma2. Using these and few next expansion coefficients for ε (g) we construct a Padé approximation for this function which may be used for a wide range of impact velocities where the concept of the viscoelastic collision is valid. The obtained expression reproduces quite accurately the existing experimental dependence ε(g) for ice particles.

Materials
 

Dynamics of granular systems - Theory, experiments, and numerical experiments (in German)

habilitation thesis, Humboldt-University Berlin

(1999)

Research Projects
Materials
 

Comment on: Frank Spahn, Udo Schwarz, and Jürgen Kurths. Clustering of granular Assemblies with temperature dependent restitution under Keplerian differential rotation. Phys. Rev. Lett. 78, 1596-1599 (1997)

Physical Review Letters, 80, 5708

(1998)

Research Projects
Materials
 

Rolling friction of a viscous sphere on a hard plane

Europhysics Letters, 42, 511-516

(1998)

Research Projects
Abstract

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

Materials
 

Interaction of a granular stream with an obstacle

Granular Matter, 1, 33-41

(1998)

Research Projects
Abstract

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

Materials
 

Coefficient of restitution of viscous particles and cooling rate of granular gases

Physical Review E, 57, 650-654

(1998)

Research Projects
Abstract

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

Materials
 

Is there a critical acceleration for the onset of convection?

Physics of Dry Granular Materials (H. J. Herrmann and J.-P. Hovi and S. Luding), 625-631, Kluwer, Dortrecht

(1998)

Research Projects
Abstract

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

Materials
 

Dissipative properties of granular ensembles

Proceedings of the SPIE's Conference on Smart Structures and Materials, Passive Damping and Isolation, 3327, 19 - 26

(1998)

Research Projects
Abstract

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

Materials
 

The granular phase diagram

Journal of Statistical Physics, 86, 1385-1395

(1997)

Research Projects
Abstract

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

Materials
 

Stochastic Dynamics

Lecture Notes in Physics, 484, Springer, Berlin, Heidelberg, New York

(1997)

Research Projects
 

Langevin equation approach to granular flow in a narrow pipe

J. Stat. Phys, 86, 421-430

(1997)

Research Projects
Abstract

The flow of granular material through a rough narrow pipe is described by the Langevin equation formalism. The stochastic force is caused by irregular interaction between the wall and the granular particles. In correspondence with experimental observations we find clogging and density waves in the flowing material.

Materials
 

A measure of the information content of neural spike trains

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

(1997)

Research Projects
Abstract

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

Materials
 

Adaptive evolutionary optimization of team work

Int. J. Bifurc. Chaos, 7, 751-757

(1997)

Research Projects
Abstract

A complex optimisation problem is studied using an evolution game. Each individual which undergoes evolution is a set of points in the plane. During the evolution process the positions of the points in the plane and the number of points which belong to each individual are optimised. It is shown that in certain cases it might be more effective to solve a sequence of problems which degree of complexity is increased stepwise than to solve the original difficult problem at once.

Materials
 

Cluster Statistics and Traffic on a Lattice

Stochastic Dynamics (Lecture Notes in Physics) (Schimansky-Geier, L. and Pöschel, T.), 484, 220-231, Springer, Berlin, Heidelberg, New York

(1997)

Research Projects
Abstract

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

Materials
 

Hydrodynamic fluctuations and averaging problems in dense granular flows

Powders and Grains'97 (R. P. Behringer and J. T. Jenkins), 341-344, Balkema, Rotterdam

(1997)

Research Projects
Abstract

We analize the properties of dense granular systems by assuming a hydrodynamical description, based on conservation laws for the particle number density and linear momentum. We combine analytical methods and experimental and numerical results obtained by ensemble-averaging of data on creep during compaction and molecular dynamics simulations of convective flow.

Materials
 

Contact of viscous spheres

Friction, Arching and Contact Dynamics (Wolf, D. E. and Grassberger, P.), 293-299, World Scientific, Singapore

(1997)

Research Projects
Abstract

In a recent paper an implicit equation for contacting viscoelastic spheres was derived [1]. Integrating this equation it can be shown that the coefficient of normal restitution ε depends on the impact velocity g as 1- ε ∼ g^⅕

 

Materials
 

Force Distribution and Comminution in Ball Mills

Friction, Arching and Contact Dynamics (Wolf, D. E. and Grassberger, P.), 265-273, World Scientific, Singapore

(1997)

Research Projects
Abstract

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

Materials
 

Molecular dynamics simulation of size segregation in three dimensions

Journal of Statistical Physics, 82, 443-450

(1996)

Research Projects
Abstract

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

Materials
 

A model for collisions in granular gases

Physical Review E, 53, 5382-5392

(1996)

Research Projects
Abstract

We propose a model for collisions between particles of a granular material and calculate the restitution coefficients for the normal and tangential motion as functions of the impact velocity from considerations of dissipative viscoelastic collisions. Existing models of impact with dissipation as well as the classical Hertz impact theory are included in the present model as special cases. We find that the type of collision (smooth, reflecting or sticky) is determined by the impact velocity and by the surface properties of the colliding grains. We observe a rather nontrivial dependence of the tangential restitution coefficient on the impact velocity. ©1996 The American Physical Society.

Materials
 

The hypercube structure of the genetic code explains conservative and non-conservative aminoacid substitutions in vivo and in vitro

BioSystems, 39, 117-125

(1996)

Research Projects
Abstract

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

Materials
 

The collision of particles in granular systems

Physica A, 231, 417-424

(1996)

Research Projects
Abstract

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

Materials
 

Swirling granular matter: from rotation to reptation

Physical Review E, 54, R4560-R4563

(1996)

Research Projects
Abstract

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

Materials
 

Avalanche statistics of sand heaps

Journal of Statistical Physics, 84, 1373-1378

(1996)

Research Projects
Abstract

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

Materials
 

Entropy and compressibility of symbol sequences

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

(1996)

Research Projects
Abstract

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

Materials
 

Cooling rate of a granular gas (in German)

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

(1996)

Research Projects
Abstract

Das dissipative Verhalten granularer Gase ist wegen seiner ungewöhnlichen Eigenschaften von großem wissenschaftlichen Interesse. Goldhirsch and Zanetti [1] und McNamara und Young [2] zeigten, dass ein homogen initialisiertes granulares Gas im Laufe der Zeit instabil ist – nach einiger Zeit der Abkühlung durch dissipative Stöße bilden sich räumliche Dichteinhomogenitäten und schließlich Cluster.

Materials
 

Can we measure the entropy of symbol sequences by means of compressibility? (in German)

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

(1996)

Research Projects
Materials
 

Complex flow of granular material in a rotating cylinder

Chaos, Solitons and Fractals, 5, 1901-1912

(1995)

Research Projects
Abstract

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

Materials
 

A statistical approach to vehicular traffic

Physica A, 219, 95-113

(1995)

Research Projects
Abstract

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

Materials
 

Guessing probability distributions from small samples

Journal of Statistical Physics, 80, 1443-1452

(1995)

Research Projects
Abstract

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

Materials
 

Size segregation and convection

Europhysics Letters, 29, 123-129

(1995)

Research Projects
Abstract

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

Materials
 

Simulation of rotating drum experiments using non-circular particles

Physica A, 216, 199-212

(1995)

Research Projects
Abstract

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

Materials
 

Entropy, transinformation and word distribution of information-carrying sequences

Int. J. Bifurc. Chaos, 5, 51-61

(1995)

Research Projects
Abstract

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

Materials
 

Molecular dynamics of arbitrarily shaped granular particles

J. Phys. I. France, 5, 1431-1455

(1995)

Research Projects
Abstract

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

Materials
 

SYNTAX: A computer program to compress a sequence and to estimate its information content

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

(1995)

Research Projects
Abstract

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

Materials
 

Dynamic entropies, long-range correlations and fluctuations in complex linear structures

Coherent Approaches to Fluctuations (Proc. Hayashibara Forum 95) (M. Suzuki and N. Kawashima), 59-64,World Scientific, Singapore

(1995)

Research Projects
Abstract

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

Materials
 

Numerical investigation of the evolution of sandpiles

Physica A, 202, 390-401

(1994)

Research Projects
Abstract

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

Materials
 

On collisions between granular particles: Application to planetary rings

Bull. Am. Astron. Soc., 26, 1143-1144

(1994)

Research Projects
 

Entropy and long range correlations in literary English

Europhysics Letters, 26, 241-246

(1994)

Research Projects
Abstract

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

Materials
 

A simple model for the growth of ramificated leaf structures

Chaos, Solitons and Fractals, 4, 1883-1888

(1994)

Research Projects
Abstract

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

Materials
 

Synchronization effects in the dynamic behavior of elevators

Physical Review E, 50, 2654-2659

(1994)

Research Projects
Abstract

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

Materials
 

Recurrent clogging and density waves of granular material flowing in a narrow pipe

J. Phys. I. France, 4, 499-506

(1994)

Research Projects
Abstract

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

Materials
 

Correlation functions, entropy, and word distribution of information-carrying sequences

(1994)

Research Projects
Abstract

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

 

On the hypercube structure of the genetic code

Proc. 3. Int. Conf. on Bioinformatics and Genome Research (Lim, H. A. and Cantor, C. A.), 445, World Scientific, Singapore

(1994)

Research Projects
Abstract

A representation of the genetic code as a six-dimensional Boolean hypercube is proposed. It is assumed here that this structure is the result of the hierarchical order of the interaction energies of the bases in codon-anticodon recognition. The proposed structure demonstrates that in the genetic code there is a balance between conservatism and innovation. Comparing aligned positions in homologous protein sequences two different behaviors are found: a) There are sites in which the different amino acids present may be explained by one or two „attractor nodes“ (coding for the dominating amino acid(s)) and their one-bit neighbors in the codon hypercube, and b) There are sites in which the amino acids present correspond to codons located in closed paths in the hypercube. The structure of the code facilitates evolution: the variation found at the variable positions of proteins do not corresponds to random jumps at the codon level, but to well defined regions of the hypercube.

Materials
 

Granular material flowing down an inclined chute: A molecular dynamics simulation

J. Phys. II France, 3, 27-40

(1993)

Research Projects
Abstract

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

 

Materials
 

A vectorized algorithm for molecular dynamics of short range interacting particles

Int. J. Mod. Phys. C, 4, 1049-1057

(1993)

Research Projects
Abstract

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

Materials
 

Static friction phenomena in granular materials: Coulomb law versus particle geometry

Physical Review Letters, 71, 3963-3966

(1993)

Research Projects
Abstract

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

Materials
 

A simple geometrical model for solid friction

Physica A, 198, 441-448

(1993)

Research Projects
Abstract

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

Materials
 

Computer simulations of clogged pipes

KFA-Intern, 24, 3-4

(1993)

Research Projects
Abstract

Im Höchstleistungsrechenzentrum wurde der Fluß von granularen Medien durch Rohre auf dem Computer simuliert. Dabei wurde die Ausbildung von unregelmäßigen Dichtewellen entdeckt und in einem Videofilm sichtbar dargestellt. Experimente bestätigen diese Simulationsrechnungen. In der industriellen Anwendung stellen solche Stoßwellen, z.B. beim Ausfluß von Silos, schon lange ein großes Problem dar.

 

Selforganization of nonlinear networks and applications to information processing

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

(1991)

Research Projects
Materials
 

Neural Networks

Nachrichten Neuronale Netze der Fachgruppe 0.1.3., 3

(1991)

Research Projects
 

Non-linear neural networks and their application in information processing (in German)

Humboldt University, Berlin

(1990)

Research Projects
 

A multiprocessor system for high speed simulation of neural networks

J. New Generation Comp. Syst., 3, 65-76

(1990)

Research Projects
 

Modelling neural networks

Manuskripte der Humboldt-Universität 1, 46-57

(1989)

Research Projects
 

Simulation of network machines

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

(1989)

Research Projects
 

Mechanisms of photo synthesis - kinetic modelling

Manuskripte der Humboldt-Universität, 2, 35-49

(1989)

Research Projects
 

Algorithm and electronic device for the deterministic or probabilistic generation of discrete output fields from discrete input fields (in German)

Patent DD 270 161 A1

(1988)

Research Projects
Materials
 

Device and algorithms for learning processes using parallel digital computers (in German)

DD 270 162 A1

(1988)

Research Projects
Materials
 

Simulation of neural networks

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

(1988)

Research Projects
 
  • Peter Bergmann
  • Jörg Keller
  • Sylvia Melitta Müller
  • Wolfgang J. Paul
  • Thorsten Pöschel
  • Oliver Schlüter
  • Wolfgang Thiele

Implementierung eines informationstheoretischen Ansatzes zur Bilderkennung

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

(1988)

Research Projects
Materials
 

Mathematical description of a secondary electron spectrometer (in Russian)

Electrotechnical Institute, Leningrad

(1986)

Research Projects