Diploma student, graduate student, postdoctoral researcher

## Dr. Thomas Schwager

**Function**

**Info**

Bruker AXS, Berlin

Diploma student, graduate student, postdoctoral researcher

Bruker AXS, Berlin

Physical Review E **84**, 041306

(2011)

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

(2009)

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.

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.

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.

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.

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.

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.

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)

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

(2005)

Physical Review Letters, **93**, 134301

(2004)

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

Physical Review E, **69**, 021302

(2004)

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.

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.

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.

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 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.

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.

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

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.

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.

Physical Review Letters, **80**, 5708

(1998)

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.

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

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.