Thorsten Pöschel

Kinetic Theory of Granular Gases

topics covered. For example, one could use Fourier-transform techniques and Gaussian statistics to provide an alternative derivation for the significance of sequence-alignment scores from random-walk models. One could also use cumulant expansions or steepestdescent methods and the Cramer function in a discussion of the rare events that lead to nonuniform convergence of a sum of random variables to the central limit. The discussion of maximumlikelihood estimation might be simplified to introduce readers to estimation theory and its importance as a statistical tool. Introduction to Mathematical Methods in Bioinformatics is a strong description of the theory behind the standard methods of computational sequence analysis. The book serves as a springboard for considering current bioinformatics research problems— such as the analysis of gene chip data—whose solutions entail a mixture of mathematics, statistics, engineering, and physics. With some additional work on the reader’s or instructor’s part, the text may also serve as an introduction to computational biology in general. Michael W. Deem Rice University Houston, Texas Kinetic Theory of Granular Gases

Granular gas dynamics

Dynamics of inelastic gases are studied within the framework of random collision processes. The corresponding Boltzmann equation with uniform collision rates is solved analytically for gases, impurities, and mixtures. Generally, the energy dissipation leads to a significant departure from the elastic case. Specifically, the velocity distributions have overpopulated high energy tails and different velocity components are correlated. In the freely cooling case, the velocity distribution develops an algebraic high-energy tail, with an exponent that depends sensitively on the dimension and the degree of dissipation. Moments of the velocity distribution exhibit multiscaling asymptotic behavior, and the autocorrelation function decays algebraically with time. In the forced case, the steady state velocity distribution decays exponentially at large velocities. An impurity immersed in a uniform inelastic gas may or may not mimic the behavior of the background, and the departure from the background behavior is characterized by a series of phase transitions.Part I: Kinetic Theory.- Asymptotic Solutions of the Nonlinear Boltzmann Equation for Dissipative Systems.- The Homogeneous Cooling State Revisited.- The Inelastic Maxwell Model.- Cooling Granular Gases: The Role of Correlations in the Velocity Field.- Self-Similar Asymptotics for the Boltzmann Equation With Inelastic Interactions.- Kinetic Integrals in the Kinetic Theory of Dissipative Gases.- Kinetics of Fragmenting Freely Evolving Granular Gases.- Part II: Granular Hydrodynamics.- Shock Waves in Granular Gases.- Linearized Boltzmann Equation and Hydrodynamics for Granular Gases.- Development of a Density Invesion in Driven Granular Gases.- Kinetic Theory for Inertia Flows of Dilute Turbulent Gas-Solids Two-Phase Mixtures.- Part III: Driven Gases and Structure Formation.- Driven Granular Gases.- Van der Waals-Like Transition in Fluidized Granular Matter.- Birth and Sudden Death of Granular Cluster.- Vibrated Granular Media as Experimentally Realized Granular Gases.

Dissipative properties of vibrated granular materials

We investigate collective dissipative properties of vibrated granular materials by means of moleculardynamics simulations. Rates of energy losses indicate three different regimes or ‘‘phases’’ in the amplitudefrequency 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. @S1063-651X~99!07304-3# PACS number~s!: 83.70.Fn, 05.40.2a, 45.05.1x The dominating approach in the world of vibration control and suppression by granular systems has been mainly practical @1#. Granular motion relaxes rapidly once the energy supply is switched off, and dampers can efficiently absorb energy released by shocks of external forcing. Engineers classify granular dampers as passive ones. For the case of ‘‘granular gases,’’ i.e., particulate systems in a state where the mean free path is large as compared with particle sizes, the cooling rate, which is the dissipation rate of the system, has been investigated @2#, and applications of this work require an analysis of granular gas ~hydro!dynamics in a given experimental setup. Damping in dense granular arrangements is a much more difficult problem which is mostly studied experimentally. In this work, by using molecular-dynamics simulations, we show that granular systems reveal different damping regimes indicating collective dissipation modes. Our study of these regimes leads to a ‘‘phase diagram’’ of horizontally vibrated granular systems ~see Fig. 4!. By using this diagram along with the presented estimates for damping decrements, practitioners may accelerate the design and testing procedures. In simulations we focus on two-dimensional containers which are partially filled with granular material and shaken horizontally. The motion of the container is sinusoidal, x(t) 5A sin(vt); it mimics practical situations where dampers are tested in the vicinity of the eigenmodes of the vibrating mechanism. We study the reaction of the system to the choice of parameters of shaking A and v, keeping all other parameters ~size, roughness and hardness of particles, filling factor, and size and shape of the apparatus! fixed@3#.

Attractive particle interaction forces and packing density of fine glass powders

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

Transient structures in a granular gas.

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.

Superimposé: a 3D structural superposition server

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://bioinformatics.charite.de/superimpose.

Self-diffusion in granular gases

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.

SIMULATION OF ROTATING DRUM EXPERIMENTS USING NON-CIRCULAR PARTICLES

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.

Translations and Rotations Are Correlated in Granular Gases

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.

Coefficient of restitution as a fluctuating quantity.

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