## Prof. Dr. Thorsten Pöschel

**Research Projects**

**Function**

Head of the institute

**Phone**

09131 85-20865

**Room**

02.316

**Teaching**

Head of the institute

09131 85-20865

02.316

Royal Society of Chemistry

(submitted)

Powders and Grains 2017

(submitted)

American Journal of Physics

(in print)

(submitted)

(submitted)

(submitted)

(submitted)

New Journal of Physics **19**, 013001

(2017)

New Journal of Physics **18** 073049

(2016)

New Journal of Physics **18**, 113006

(2016)

New Journal of Physics **18**, 123001

(2016)

Computational Partical Mechanics **3**, 389

(2016)

New Journal of Physics **18**, 073049

(2016)

Scientific Reports **6**, 26833

(2016)

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

(2016)

European Journal of Physics **37**, 055305

(2016)

Physics of Fluids **28**, 073301

(2016)

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

(2016)

Granular Matter

(2016)

New Journal of Physics **18**, 118004

(2016)

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

(2016)

Soft Matter **12**, 3184

(2016)

Powder Technology **288**, 96-102

(2016)

Journal of Computational Physics **308**, 421

(2016)

Physical Review E **93**, 032901

(2016)

Scientific Reports **6**, 22520

(2016)

Scientific Reports **5**, 12703

(2015)

Scientific Reports **5**, 16572

(2015)

Powder Technology **279**, 113-122

(2015)

Procedia Engineering **102**, 850-857

(2015)

Soft Matter **11**, 4295-4305

(2015)

New Journal of Physics **17**, 013036

(2015)

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

(2015)

Physical Review E **91**, 062213

(2015)

Physical Review Applied **3**, 024007

(2015)

Physical Review E **91**, 062214

(2015)

Granular Matter **17**, 73-82

(2015)

New Journal of Physics **17**, 013024

(2014)

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

(2014)

Physical Review E **90**, 052204

(2014)

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

(2014)

Physical Review E **89**, 022205

(2014)

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

(2014)

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

(2014)

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

(2014)

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

(2014)

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

(2014)

Scientific Reports **4**, 6227

(2014)

Aeolian Research **12**, 121-133

(2014)

European Physysical Journal Special Topics **223**, 2857-2867

(2014)

European Physysical Journal Special Topics **223**, 2269-2283

(2014)

Physical Review Letters **110**, 254301

(2013)

Physical Review Letters **111**, 018001

(2013)

Physics Letters A **377**, 2052–2057

(2013)

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

(2013)

New Journal of Physics **15**, 093023

(2013)

Granular Matter **15**, 377–387

(2013)

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

(2013)

Physical Review E **87**, 033301

(2013)

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

(2013)

New Journal of Physics **15**, 093030

(2013)

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

(2013)

Granular Matter **15**, 389-390

(2013)

Philosophical Magazine **93**, 4090-4107

(2013)

EAM Summerschool, Kloster Banz, Germany

(2013)

New Journal of Physics **15**, 043044

(2013)

Scientific Reports **3**, 2858

(2013)

Physical Review E **87**, 042907

(2013)

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

(2013)

European Physical Journal D **67**, 149

(2013)

Scientific Reports **3**, 1958

(2013)

Scientific Reports **3**, 3350

(2013)

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

(2013)

Physical Review Letters **111**, 168003

(2013)

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

(2012)

Granular Matter **14**, 2, Springer

(2012)

Physical Review E **85**, 031307

(2012)

Physical Review E **86**, 061310

(2012)

Physica A **391**, 4442-4447

(2012)

Granular Matter **14**, 115-120

(2012)

Physical Review E **85**, 041306

(2012)

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

(2012)

Physical Review Letters **109**, 128001

(2012)

EAM Summerschool, Kloster Banz, Germany

(2012)

Europhysics Letters **100**, 48002

(2012)

(2012)

Physical Review E **84**, 021302

(2011)

Physical Review E **84**, 041306

(2011)

Physical Review E **83**, 041304

(2011)

Physical Review E **84**, 011301

(2011)

Chemical Physics **375**, 600-605

(2010)

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

(2010)

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)

European Physical Journal Special Topics **179**, 91-111

(2009)

The European Physical Journal Special Topics **179**, 1, Springer

(2009)

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

(2009)

J. Fluid Mech., **597**, 119-144

(2008)

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

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

(2008)

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.

Physical Review E, **77**, 011304

(2008)

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

Granular Matter, **10**, 231-232

(2008)

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

Physical Review E, **78**, 051304

(2008)

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

Physical Review Letters **100**, 218002

(2008)

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

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

(2008)

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

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

(2008)

We discuss several models for granular particles commonly used in Molecular

Dynamics simulations of granular materials, including spheres with linear dashpot force, viscoelastic

spheres and adhesive viscoelastic spheres. Starting from the vectorial interaction

forces we derive the coefficients of normal and tangential restitution as functions of the

vectorial impact velocity and of the material constants. We review the methods of

measurements of the coefficients of restitution and characterize the coefficient of normal

restitution as a fluctuating quantity. Moreover, the scaling behavior and the influence of

different force laws on the dynamical system behavior are discussed. The powerful method of

event-driven Molecular Dynamics is described and the algorithmic simulation technique is

explained in detail. Finally we discuss the limitations of event-driven MD.

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

(2007)

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

Physical Review Letters, **98**, 128001

(2007)

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

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

(2007)

Granular Matter, **10**, 21-27

(2007)

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

Granular Matter, **9**, 465-469

(2007)

With the assumption of a linear-dashpot interaction force, the coefficient of restitution, 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.

Physical Review E, **76**, 051302

(2007)

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

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

(2006)

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.

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

(2006)

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

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

(2006)

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

Physical Review E, **74**, 041302

(2006)

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

Logos, Berlin

(2006)

Europhysics Letters, **74**, 424-430

(2006)

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

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

(2005)

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

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

(2005)

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

Springer, Berlin, Heidelberg, New York

(2005)

Chaos **15**, 026108

(2005)

We study the diffusion of tracers (self-diffusion) in a homogeneously cooling gas of dissipative particles, using the Green-Kubo relation and the Chapman-Enskog approach. The dissipative particle collisions are described by the coefficient of restitution 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.

Europhysics Letters, **69**, 725-731

(2005)

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

Europhysics Letters, **69**, 371-377

(2005)

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

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

(2005)

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

(2004)

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

Physical Review Letters, **93**, 134301

(2004)

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

Oxford University Press, Oxford

(2004)

Physical Review E, **69**, 021302

(2004)

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.

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

(2003)

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

(2003)

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

BioSystems, **69**, 63-72

(2003)

The decision whether a measured distribution complies 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.

Physical Review E, **67**, 061304

(2003)

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

Physical Review Letters, **91**, 024301

(2003)

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

Biophys. J., **85**, 3460-3474

(2003)

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

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

(2003)

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.

BMC Bioinformatics **4**, 58 - 64

(2003)

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.

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

(2002)

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

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

(2002)

Physical Review E, **66**, 026103

(2002)

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

SPIE, **3045**

(2002)

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.

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

(2002)

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

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

(2002)

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

Physica A, **325**, 274-283

(2002)

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

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

(2001)

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

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)

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

Physical Review Letters, **63**, 021505

(2001)

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

Physical Review E, **64**, 011308

(2001)

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

(2001)

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

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

(2001)

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

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

(2001)

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

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

(2001)

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

Logos, Berlin

(2001)

Bulk Solids Handling, **20**, 159-172

(2000)

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

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

(2000)

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

Physical Review E, **61**, 2809 – 2812

(2000)

We analyze the velocity distribution function of force-free granular gases in the regime of homogeneous cooling when deviations from the Maxwellian distribution may be accounted only by the leading term in the Sonine polynomial expansion, quantified by the second coefficient a_2. We go beyond the linear approximation for 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.

Schüttgut, **6**, 11-24

(2000)

Molekulardynamische Untersuchungen eignen sich zur Simulation des Verhaltens makroskopischer Mengen granularen Materials unter bestimmten, technologisch relevanten Beanspruchungen. Wir untersuchen das Zerkleinerungsverhalten von Mahlgut in einer Kugelmühle, insbesondere im Hinblick auf die Effizienz als Funktion der Drehzahl und auf die räumliche 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

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

(2000)

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

(2000)

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

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

(2000)

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

Proceed. ICTAM, Chicago

(2000)

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

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

(2000)

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

European Physical Journal, **16**, 169-182

(2000)

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

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

(2000)

When granular material is shaken vertically one observes convection, surface fluidization, spontaneous heap formation and other effects. There is a controversial discussion in 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

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

(2000)

Phys. Bl., **55**

(1999)

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

(1999)

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

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

(1999)

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

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

(1999)

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

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

(1999)

We perform a dimension analysis for colliding viscoelastic spheres to show that the coefficient of normal restitution 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.

habilitation thesis, Humboldt-University Berlin

(1999)

Physical Review Letters, **80**, 5708

(1998)

Europhysics Letters, **42**, 511-516

(1998)

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

Granular Matter, **1**, 33-41

(1998)

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

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

(1998)

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

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

(1998)

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

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

(1998)

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

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

(1997)

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

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

(1997)

J. Stat. Phys, **86**, 421-430

(1997)

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.

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)

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.

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

(1997)

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.

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

(1997)

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

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

(1997)

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.

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

(1997)

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

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

(1997)

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

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

(1996)

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

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

(1996)

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

BioSystems, **39**, 117-125

(1996)

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

Physica A, **231**, 417-424

(1996)

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

Physical Review E, **54**, R4560-R4563

(1996)

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

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

(1996)

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

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

(1996)

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

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

(1996)

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.

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

(1996)

Chaos, Solitons and Fractals, **5**, 1901-1912

(1995)

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

Physica A, **219**, 95-113

(1995)

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

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

(1995)

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

Europhysics Letters, **29**, 123-129

(1995)

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

Physica A, **216**, 199-212

(1995)

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

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

(1995)

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

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

(1995)

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

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

(1995)

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

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

(1995)

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

Physica A, **202**, 390-401

(1994)

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

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

(1994)

Europhysics Letters, **26**, 241-246

(1994)

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.

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

(1994)

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

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

(1994)

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

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

(1994)

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

(1994)

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

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

(1994)

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.

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

(1993)

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

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

(1993)

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

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

(1993)

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

Physica A, **198**, 441-448

(1993)

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

KFA-Intern, **24**, 3-4

(1993)

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.

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

(1991)

Nachrichten Neuronale Netze der Fachgruppe 0.1.3., 3

(1991)

Humboldt University, Berlin

(1990)

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

(1990)

Manuskripte der Humboldt-Universität **1**, 46-57

(1989)

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

(1989)

Manuskripte der Humboldt-Universität, **2**, 35-49

(1989)

Patent DD 270 161 A1

(1988)

DD 270 162 A1

(1988)

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

(1988)

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

(1988)

Electrotechnical Institute, Leningrad

(1986)