Institute for Multiscale Simulation: Publications

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We report an autonomous circuit containing periodicity hubs with surprisingly broad spirals. Knowledge of broad spirals is important because all presently known spirals are compressed along specific directions in parameter space making them difficult to study experimentally and theoretically. We characterize the performance of the circuit by computing stability diagrams for relevant sections of the control space. In addition, the alternation of chaotic and periodic spiral phases is contrasted with equivalent alternations obtained from an experimental implementation of the circuit.

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InProceedings
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Additive manufacturing constitutes a promising production technology with potential application in a broad range of industrial areas. In this type of manufacturing process, objects are created from powder particles by adding layers of material upon one another through selectively melting particles from the powder bed. However, understanding the mechanical behavior of the powder during manufacturing as a function of material properties and particle shape is an essential pre-requisite for optimizing the production process. Here we develop a numerical tool for modeling the dynamics of powder particles during additive manufacturing based on force-based simulations by means of the Discrete Element Method (DEM). An existing DEM software (LIGGGHTS) is extended in order to study the transport of powder particles of complex geometric shapes through accounting for the boundary conditions inherent to the manufacturing process.

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We experimentally investigate the energy dissipation rate in sinusoidally driven boxes which are partly filled by granular material under conditions of weightlessness. We identify two different modes of granular dynamics, depending on the amplitude of driving, A. For intense forcing, A > A0, the material is found in the collectand-collide regime where the center of mass of the granulate moves synchronously with the driven container while for weak forcing, A < A0, the granular material exhibits gas-like behavior. Both regimes correspond to different dissipation mechanisms, leading to different scaling with amplitude and frequency of the excitation and with the mass of the granulate. For the collect-and-collide regime, we explain the dependence on frequency and amplitude of the excitation by means of an effective one-particle model. For both regimes, without using any adjustable parameter the results may be collapsed to a single curve characterizing the physics of granular dampers.
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Article
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We investigate jammed granular matter in a slowly rotating drum partially filled with granular material and find a state of poly-directional stability. In this state, the material responds elastically to small stresses in a wide angular interval while it responds by plastic deformation when subjected to small stresses outside this interval of directions. We describe the evolution of the granulate by means of a rate equation and find quantitative agreement with the experiment. The state of poly-directional stability complements the fragile state, where the material responds elastically to small applied stresses only in a certain direction but even very small stresses in any other direction would lead to plastic deformations. Similar to fragile matter, poly-directionally stable matter is created in a dynamic process by self-organization.
Article
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We investigate the coefficient of normal restitution as a function of the impact velocity, ε(v), for inelastic spheres. We observe oscillating behavior of ε(v) which is superimposed to the known decay of the coefficient of restitution as a function of impact velocity. This remarkable effect was so far unnoticed because under normal circumstances it is screened by statistical scatter. We detected its clear signature by recording large amounts of data using an automated experiment. The new effect may be understood as an interplay between translational and vibrational degrees of freedom of the colliders. Both characteristics of the oscillation, the wave length and the amplitude agree quantitatively with a theoretical description of the experiment.
Article
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This paper reports a detailed numerical investigation of the geometrical and structural prop- erties of three-dimensional heaps of particles. Our goal is the characterization of very large heaps produced by ballistic deposition from extended circular dropping areas. First, we pro- vide an in-depth study of the formation of monodisperse heaps of particles. We find very large heaps to contain three new geometrical characteristics: they may display two external angles of repose, one internal angle of repose, and four distinct packing fraction (density) regions. Such features are found to be directly connected with the size of the dropping zone. We derive a differential equation describing the elevation of an unexpected triangular packing fraction formed under the dropping area. We investigate the impact that noise during the deposition has on the final heap structure. In addition, we perform two complementary experiments designed to test the robustness of the novel features found. The first experiment considers changes due to polydispersity. The second checks what happens when letting the extended dropping zone to become a point-like source of particles, the more common type of source.
Article
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Some dynamical properties for a dissipative time-dependent Lorentz gas are studied. We assume that the size of the scatterers change periodically in time and we introduce in-flight dissipation into the system where the dissipative force is given by F = −μmg. We consider the parameter space, namely the amplitude of oscillation and the dissipation parameter and we show that for some combination of them the particles come to a complete stop between the scatterers, but for some other cases, the average velocity grows unbounded. This is the first time that the phenomenon of Fermi acceleration is observed in a dissipative system. Finally, we study the behavior of the average velocity as a function of the number of collisions and we show that the system is scaling invariant with very well defined scaling exponents.
Article
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A numerical study that aims to analyze the thermal mechanisms of unsteady, supersonic granular flow by means of hydrodynamic simulations of the Navier–Stokes granular equation is reported in this paper. For this purpose, a paradigmatic problem in granular dynamics such as the Faraday instability is selected. Two different approaches for the Navier–Stokes transport coefficients for granular materials are considered, namely the traditional Jenkins–Richman theory for moderately dense quasi-elastic grains and the improved Garz´o–Dufty–Lutsko theory for arbitrary inelasticity, which we also present here. Both the solutions are compared with event-driven simulations of the same system under the same conditions, by analyzing the density, temperature and velocity field. Important differences are found between the two approaches, leading to interesting implications. In particular, the heat transfer mechanism coupled to the density gradient, which is a distinctive feature of inelastic granular gases, is responsible for a major discrepancy in the temperature field and hence in the diffusion mechanisms.

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InProceedings
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In this paper an algorithm is described which combines the efficiency of event-driven Molecular-Dynamics (eMD) and the physical correctness of force-based Molecular-Dynamics (MD) for dilute granular systems of frictionless spheres.

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A remarkably regular organization of spirals converging to a focal point in control parameter space was recently predicted and then observed in a nonlinear circuit containing two diodes. Such spiral organizations are relatively hard to observe experimentally because they usually emerge very compressed. Here we show that a circuit with a tunnel diode displays not one but two large spiral cascades. We show such cascades to exist over wide parameter ranges and, therefore, we expect them to be easier to observe experimentally.

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InProceedings
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We investigate the collective dissipative behavior of a model granular material (steel beads) when subjected to vibration. To this end, we study the attenuation of the amplitude of an oscillating leaf spring whose free end carries a rectangular box partly filled with granulate. To eliminate the perturbing influence of gravity, the experiment was performed under conditions of microgravity during parabolic flights. Different regimes of excitation could be distinguished, namely, a gas-like state of disordered particle motion and a state where the particles slosh back and forth between the container walls in a collective way, referred to as collect-and-collide regime. For the latter regime, we provide an expression for the container size leading to maximal dissipation of energy, that also marks the transition to the gas like regime. Also for systems driven at fixed amplitude and frequency, we find both the gas regime and the collect-and-collide regime resulting in similar dissipative behavior as in the case of the attenuating vibration.

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We investigate the structure and adsorption of amphiphilic molecules at planar walls modified by tethered chain molecules using density functional theory. The molecules are modeled as spheres composed of a hydrophilic and hydrophobic part. The pinned chains are treated as tangentially jointed spheres that can interact with fluid molecules via orientation-dependent forces. Our density functional approach involves fundamental measure theory, thermodynamic perturbation theory for chains, and a meanfield approximation for describing the anisotropic interactions. We study the adsorption of the particles, focusing on the competition between the external field (due to the surface and due to attached chain molecules) and the interaction-induced ordering phenomena.

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We report numerical evidence showing that periodic oscillations can produce unexpected and wide-ranging zig-zag parameter networks embedded in chaos in the control space of nonlinear systems. Such networks interconnect shrimp-like windows of stable oscillations and are illustrated here for a tunnel diode, for an erbiumdoped fiber-ring laser, and for the Hénon map, a proxy of certain CO2 lasers. Networks in maps can be studied without the need for solving differential equations. Tuning parameters along zig-zag networks allows one to continuously modify wave patterns without changing their chaotic or periodic nature. In addition, we report convenient parameter ranges where such networks can be detected experimentally.

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We study the mechanism leading to the formation of stripe-like patterns in a rectangular container filled with a sub-monolayer of frictional spherical particles when it is subjected to horizontal oscillations. By means of Molecular Dynamics simulations we could reproduce the experimental results. Systematic simulations allow to identify friction to be responsible for the pattern formation, that is, the tangential interaction between contacting particles and between the particles and the floor of the container. When particles are in contact with the floor and other adjacent particles simultaneously, there emerges a frustrated situation in which the particles are prevented from rolling on the floor. This effect leads to local jamming and eventually to stripe-like pattern formation. In the long time evolution, the stripes are unstable. Stripes may merge as well as disintegrate.

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Some dynamical properties for a bouncing ball model are studied. We show that when dissipation is introduced the structure of the phase space is changed and attractors appear. Increasing the amount of dissipation, the edges of the basins of attraction of an attracting fixed point touch the chaotic attractor. Consequently the chaotic attractor and its basin of attraction are destroyed given place to a transient described by a power law with exponent −2. The parameter-space is also studied and we show that it presents a rich structure with infinite self-similar structures of shrimp-shape.

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The dynamics of dissipative soft-sphere gases obeys Newton’s equations of motion, which are commonly solved numerically by (force-based) Molecular Dynamics (MD) schemes. With the assumption of instantaneous, pairwise collisions, the simulation can be accelerated considerably using event-driven MD, where the coefficient of restitution is derived from the interaction force between particles. Recently it was shown, however, that this approach may fail dramatically, that is, the obtained trajectories deviate significantly from the ones predicted by Newton’s equations. In this paper, we generalize the concept of the coefficient of restitution and derive a numerical scheme which, in the case of dilute systems and frictionless interaction, allows us to perform highly efficient event-driven MD simulations even for noninstantaneous collisions. We show that the particle trajectories predicted by our scheme agree perfectly with the corresponding (force-based) MD, except for a short transient period whose duration corresponds to the duration of the contact. Thus, the new algorithm solves Newton’s equations of motion like force-based MD while preserving the advantages of event-driven simulations.

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The transport of sand and dust by wind is a potent erosional force, creates sand dunes and ripples, and loads the atmosphere with suspended dust aerosols. This paper presents an extensive review of the physics of wind-blown sand and dust on Earth and Mars. Specifically, we review the physics of aeolian saltation, the formation and development of sand dunes and ripples, the physics of dust aerosol emission, the weather phenomena that trigger dust storms, and the lifting of dust by dust devils and other small-scale vortices. We also discuss the physics of wind-blown sand and dune formation on Venus and Titan.

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Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F ¼ gV2; (iii) F ¼ gVl with l 6¼ 1 and l 6¼ 2 and; (iv) F ¼ gV, where g is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined.

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It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important —moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles.

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We study some dynamical properties for the problem of a charged particle in an electric field considering both the low velocity and relativistic cases. The dynamics for both approaches is described in terms of a two-dimensional and nonlinear mapping. The structure of the phase spaces is mixed and we introduce a hole in the chaotic sea to let the particles to escape. By changing the size of the hole we show that the survival probability decays exponentially for both cases. Additionally, we show for the relativistic dynamics, that the introduction of dissipation changes the mixed phase space and attractors appear. We study the parameter space by using the Lyapunov exponent and the average energy over the orbit and show that the system has a very rich structure with infinite family of self-similar shrimp shaped embedded in a chaotic region.

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Granular ratchets are well-known devices that when driven vertically produce a counterintuitive horizontal transport of particles. Here we report the experimental observation of a complementary effect: the striking ability of circular ratchets to convert their vertical vibration into their own rotation.The average revolution speed shows a maximum value for an optimal tooth height. With no special effort the rotation speed could be maintained steady during several hours. Unexpected random arrests and reversals of the velocity were also observed abundantly.

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We study the global organization of oscillations in sigmoidal maps, a class of models which reproduces complex locking behaviors commonly observed in lasers, neurons, and other systems which display spiking, bursting, and chaotic sequences of spiking and bursting. We ﬁnd periodic oscillations to emerge organized regularly according to the elusive Stern-Brocot tree, a symmetric and more general tree which contains the better-known asymmetric Farey tree as a sub-tree. The Stern-Brocot tree provides a natural and encompassing organization to classify nonlinear oscillations. The mathematical algorithm for generating both trees is exactly the same, differing only in the initial conditions. Such degeneracy suggests that the wrong tree might have been attributed to locking phenomena reported in some of the earlier works.

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We report a numerical investigation of the structural properties of very large three-dimensional heaps of particles produced by ballistic deposition from extended circular dropping areas. Very large heaps are found to contain three new geometrical characteristics not observed before: they may have two external angles of repose, an internal angle of repose, and four distinct packing fraction (density) regions. Such characteristics are shown to be directly correlated with the size of the dropping zone. In addition, we also describe how noise during the deposition affects the ﬁnal heap structure.

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InProceedings
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We perform two-dimensional hydrodynamic simulations on a paradigmatic problem of granular dynamics, the Faraday instability, using two different approximations to the Navier-Stokes granular equations: the constitutive equations and kinetic coefficients derived from the assumption of vanishing inelasticity (Jenkins-Richman approach) obtained by solving the Enskog equation disks by means of Grad’s method, and the ones obtained by solving the Enskog equation with the Chapman-Enskog method (Garzó-Dufty-Lutsko approach). The comparison reveals important qualitative and quantitative differences with respect to the hydrodynamic fields obtained by averaging results from particle simulations of the same system.

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Instruments for surgical and dental application based on oscillatory mechanics submit unwanted vibrations to the operator’s hand. Frequently the weight of the instrument’s body is increased to dampen its vibration. Based on recent research regarding the optimization of granular damping we developed a prototype granular damper that attenuates the vibrations of an oscillatory saw twice as efficiently as a comparable solid mass.

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InProceedings
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We report a numerical investigation of the structural properties of very large three-dimensional heaps of granular material produced by ballistic deposition from extended circular dropping areas. Very large heaps are found to contain three new geometrical characteristics not observed before: they may have two external angles of repose, an internal angle of repose, and four distinct packing fraction (density) regions. Such characteristics are shown to be directly correlated with the size of the dropping zone. In addition, we also describe how noise during the deposition affects the ﬁnal heap structure.

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Article
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We describe some remarkable continuous deformations which create and destroy peaks in periodic oscillations of the Mackey–Glass equation, a paradigmatic example of a delayed feedback system. Peak creation and destruction results in richer bifurcation diagrams which, in addition to the familiar branches arising from period-doubling and peak-adding bifurcations, may also display arbitrary combinations of doubling and adding, leading to highly complex mosaics of stability domains in control parameter space. In addition, we show that the onset of higher dimensionality does not alter the prevailing dynamics instantaneously and, remarkably, even may have no effect at all, a result that cannot be predicted analytically with standard methods.

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This paper shows that negative coefficients of normal restitution occur inevitably when the interaction force between colliding particles is finite. We derive an explicit criterion showing that for any set of material properties there is always a collision geometry leading to negative restitution coefficients. While from a phenomenological point of view, negative coefficients of normal restitution appear rather artificial, this phenomenon is generic and implies an important overlooked limitation of the widely used hard sphere model. The criterion is explicitly applied to two paradigmatic situations: for the linear dashpot model and for viscoelastic particles. In addition, we show that for frictional particles the phenomenon is less pronounced than for smooth spheres.

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We report a striking effect observed experimentally in several granular materials when shaken horizontally:The material displays a recurrent alternation between a slow inﬂation phase, characterized by an increase in its volume, and a fast collapse phase, when the volume abruptly returns to its original value. The frequency of such phase alternations is totally decoupled from the frequency of the external drive. We argue that the inﬂation and collapse alternation arises from an interplay between the mechanical stability of the material and Reynolds dilatancy due to convective motion.

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When granular systems are modeled by fric- tionless hard spheres, particle-particle collisions are considered as instantaneous events. This implies that while the velocities change according to the collision rule, the positions of the particles are the same before and after such an event. We show that depending on the material and system parameters, this assumption may fail. For the case of viscoelastic particles we present a univer- sal condition which allows to assess whether the hard- sphere modeling and, thus, event-driven Molecular Dynamics simulations are justified.

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We study the deterministic spin dynamics of an anisotropic magnetic particle in the presence of a magnetic field with a constant longitudinal and a time-dependent transverse component using the Landau-Lifshitz-Gilbert equation. We characterize the dynamical behavior of the system through calculation of the Lyapunov exponents, Poincare ́ sections, bifurcation diagrams, and Fourier power spectra. In particular we explore the positivity of the largest Lyapunov exponent as a function of the magnitude and frequency of the applied magnetic field and its direction with respect to the main anisotropy axis of the magnetic particle. We find that the system presents multiple transitions between regular and chaotic behaviors. We show that the dynamical phases display a very complicated structure of intricately intermingled chaotic and regular phases.

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Infinite cascades of periodicity hubs were predicted and very recently observed experimentally to organize stable oscillations of some dissipative flows. Here we describe the global mechanism underlying the genesis and organization of networks of periodicity hubs in control parameter space of a simple prototypical flow, namely a Ro ̈ssler’s oscillator. We show that spirals associated with periodicity hubs emerge and accumulate at the folding of certain fractal-like sheaves of Shilnikov homoclinic bifurcations of a common saddle-focus equilibrium. The specific organization of hub networks is found to depend strongly on the interaction between the homoclinic orbits and the global structure of the underlying attractor.

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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 non-trivial (non-Gaussian) fluctuations of the measured values. For a fixed impact velocity, the probability density of the coefficient of restitution, $p(epsilon)$, 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.

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A computer aided method using symbolic computations that enables the calculation of the source terms (Boltzmann) in Grad’s method of moments is presented. The method is extremely powerful, easy to program and allows the derivation of balance equations to very high moments (limited only by computer resources). For sake of demonstration the method is applied to a simple case: the one-dimensional stationary granular gas under gravity. The method should find applica- tions in the field of rarefied gases, as well. Questions of convergence, closure are beyond the scope of this article.

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

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Molecular-dynamics algorithms for systems interacting through discrete or "hard" potentials are fundamentally different to the methods for continuous or "soft" potential systems. Although many software packages have been developed for continuous potential systems, software for discrete potential systems based on event-driven algorithms are relatively scarce and fairly specialized. We present DYNAMO, a general event-driven simulation package which displays the optimal asymptotic scaling of the computational cost with system size. DYNAMO provides reference implementations of the best available event-driven algorithms. These techniques allow the rapid simulation of both complex and large (> 10^6 particles) systems for long times. This software and its documentation are distributed under the GNU General Public license and can be freely downloaded from this http URL

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The response of an oscillating granular damper to an initial perturbation is studied using experiments performed in microgravity and granular dynamics simulations. High-speed video and image processing techniques are used to extract experimental data. An inelastic hard sphere model is developed to perform simulations and the results are in excellent agreement with the experiments. The granular damper behaves like a frictional damper and a linear decay of the amplitude is observed. This is true even for the simulation model, where friction forces are absent. A simple expression is developed which predicts the optimal damping conditions for a given amplitude and is independent of the oscillation frequency and particle inelasticities.

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The main precondition of simulating systems of hard particles by means of event-driven modeling is theassumption of instantaneous collisions. The aim of this paper is to quantify the deviation of event-driven modeling from the solution of Newton’s equation of motion using a paradigmatic example: If a tennis ball is held above a basketball with their centers vertically aligned, and the balls are released to collide with the ﬂoor, the tennis ball may rebound at a surprisingly high speed. We show in this article that the simple textbook explanation of this effect is an oversimpliﬁcation, even for the limit of perfectly elastic particles. Instead, there may occur a rather complex scenario including multiple collisions which may lead to a very different ﬁnal velocity as compared with the velocity resulting from the oversimpliﬁed model.

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Hard-sphere molecular dynamics (MD) simulation results, with six-figure accuracy in the
thermodynamic equilibrium pressure, are reported and used to test a closed-virial equation-of-state.
This latest equation, with no adjustable parameters except known virial coefficients, is comparable
in accuracy both to Padé approximants, and to numerical parameterizations of MD data. There is no
evidence of nonconvergence at stable fluid densities. The virial pressure begins to deviate
significantly from the thermodynamic fluid pressure at or near the freezing density, suggesting that
the passage from stable fluid to metastable fluid is associated with a higher-order phase transition;
an observation consistent with some previous experimental results. Revised parameters for the
crystal equation-of-state [R. J. Speedy, J. Phys.: Condens. Matter 10, 4387 (1998)] are also
reported.

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The properties of systems composed of atoms interacting though discrete potentials are dictated by a series of events which occur between pairs of atoms. There are only four basic event types for pairwise discrete potentials and the square-well/shoulder systems studied here exhibit them all. Closed analytical expressions are derived for the on-event kinetic energy distribution functions for an atom, which are distinct from the Maxwell–Boltzmann distribution function. Exact expressions are derived that directly relate the pressure and temperature of equilibrium discrete potential systems to the rates of each type of event. The pressure can be determined from knowledge of only the rate of core and bounce events. The temperature is given by the ratio of the number of bounce events to the number of disassociation/association events. All these expressions are validated with event-driven molecular dynamics simulations and agree with the data within the statistical precision of the simulations.

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In dense, static, polydisperse granular media under isotropic pressure, the probability density and the correlations of particle-wall contact forces are studied. Furthermore, the probability density functions of the populations of pressures measured with different sized circular pressure cells is examined. The questions answered are: (i) What is the number of contacts that has to be considered so that the measured pressure lies within a certain error margin from its expectation value? (ii) What is the statistics of the pressure probability density as function of the size of the pressure cell? Astonishing non-random correlations between contact forces are evidenced, which range at least 10 to 15 particle diameter. Finally, an experiment is proposed to tackle and better understand this issue.

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The dynamics of sheared inelastic-hard-sphere systems are studied using non-equilibrium molecular dynamics simulations and direct simulation Monte Carlo. In the molecular dynamics simulations Lees-Edwards boundary conditions are used to impose the shear. The dimensions of the simulation box are chosen to ensure that the systems are homogeneous and that the shear is applied uniformly. Various system properties are monitored, including the one-particle velocity distribution, granular temperature, stress tensor, collision rates, and time between collisions. The one-particle velocity distribution is found to agree reasonably well with an anisotropic Gaussian distribution, with only a slight overpopulation of the high velocity tails. The velocity distribution is strongly anisotropic, especially at lower densities and lower values of the coefficient of restitution, with the largest variance in the direction of shear. The density dependence of the compressibility factor of the sheared inelastic hard sphere system is quite similar to that of elastic hard sphere fluids. As the systems become more inelastic, the glancing collisions begin to dominate more direct, head-on collisions. Examination of the distribution of the time between collisions indicates that the collisions experienced by the particles are strongly correlated in the highly inelastic systems. A comparison of the simulation data is made with DSMC simulation of the Enskog equation. Results of the kinetic model of Montanero et al. [Montanero et al., J. Fluid Mech. 389, 391 (1999)] based on the Enskog equation are also included. In general, good agreement is found for high density, weakly inelastic systems.

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The static and dynamic properties of binary mixtures of hard spheres with a diameter ratio of sigma_B/sigma_A=0.1 and a mass ratio of m_B/m_A=0.001 are investigated using event driven molecular dynamics. The contact value of the pair correlation functions are found to compare favourably with recently proposed theoretical expressions. The transport coefficients of the mixture, determined from simulation, are compared to the predictions of revised Enskog theory, using both a third-order Sonine expansion and direct simulation Monte Carlo. Overall, Enskog theory provides a fairly good description of the simulation data, with the exception of systems at the smallest mole fraction of larger spheres (x_A=0.01) examined. A "fines effect" was observed at higher packing fractions, where adding smaller spheres to a system of large spheres decreases the viscosity of the mixture; this effect is not captured by Enskog theory.

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Recently, it has been demonstrated [Magee et al., Phys. Rev. Lett. 96, 207802 (2006)] that isolated, square-well homopolymers can spontaneously break chiral symmetry and freeze into helical structures at sufficiently low temperatures. This behavior is interesting because the square-well homopolymer is itself achiral. In this work, we use event-driven molecular dynamics, combined with an optimized parallel tempering scheme, to study this polymer model over a wide range of parameters. We examine the conditions where the helix structure is stable and determine how the interaction parameters of the polymer govern the details of the helix structure. The width of the square well (proportional to lambda) is found to control the radius of the helix, which decreases with increasing well width until the polymer forms a coiled sphere for sufficiently large wells. The helices are found to be stable for only a window of molecular weights. If the polymer is too short, the helix will not form. If the polymer is too long, the helix is no longer the minimum energy structure, and other folded structures will form. The size of this window is governed by the chain stiffness, which in this model is a function of the ratio of the monomer size to the bond length. Outside this window, the polymer still freezes into a locked structure at low temperature, however, unless the chain is sufficiently stiff, this structure will not be unique and is similar to a glassy state.

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The fluid and solid equations of state for hard parallel squares and cubes are reinvestigated here over a wide range of densities. We use a novel single-speed version of molecular dynamics. Our results are compared with those from earlier simulations, as well as with the predictions of the virial series, the cell model, and Kirkwood’s many-body single-occupancy model. The singleoccupancy model is applied to give the absolute entropy of the solid phases just as was done earlier for hard disks and hard spheres. The excellent agreement found here with all relevant previous work shows very clearly that configurational properties, such as the equation of state, do not require the maximum-entropy Maxwell-Boltzmann velocity distribution. For both hard squares and hard cubes the free-volume theory provides a good description of the high-density solid-phase pressure. Hard parallel squares appear to exhibit a second-order melting transition at a density of 0.79 relative to close-packing. Hard parallel cubes have a more complicated equation of state, with several relatively-gentle curvature changes, but nothing so abrupt as to indicate a first-order melting transition. Because the number-dependence for the cubes is relatively large the exact nature of the cube transition remains unknown.

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In a granular gas of rough particles the spin of a grain is correlated with its linear velocity. We develop an analytical theory to account for these correlations and compare its predictions to numerical simulations, using Direct Simulation Monte Carlo as well as Molecular Dynamics. The system is shown to relax from an arbitrary initial state to a steady-state, which is characterized by time-independent, finite correlations of spin and linear velocity. The latter are analyzed systematically for a wide range of system parameters, including the coefficients of tangential and normal restitution as well as the moment of inertia of the particles. For most parameter values the axis of rotation and the direction of linear momentum are perpendicular like in a sliced tennis ball, while parallel orientation, like in a rifled bullet, occurs only for a small range of parameters. The limit of smooth spheres is singular: any arbitrarily small roughness unavoidably causes significant translation-rotation correlations, whereas for perfectly smooth spheres the rotational degrees of freedom are completely decoupled from the dynamic evolution of the gas.

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InProceedings
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Cohesive powders form agglomerates that can be very porous. Hence they are also very fragile. Consider a process of complete fragmentation on a characteristic length scale , where the fragments are subsequently allowed to settle under gravity. If this fragmentation-reagglomeration cycle is repeated sufficiently often, the powder develops a fractal substructure with robust statistical properties. The structural evolution is discussed for two different models: The first one is an off-lattice model, in which a fragment does not stick to the surface of other fragments that have already settled, but rolls down until it finds a locally stable position. The second one is a simpler lattice model, in which a fragment sticks at first contact with the agglomerate of fragments that have already settled. Results for the fragment size distribution are shown as well. One can distinguish scale invariant dust and fragments of a characteristic size. Their role in the process of structure formation will be addressed.

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InProceedings
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We present three heuristics including the usage of domain specific knowledge to improve a general purpose algorithm for the 3D approximate point set match problem and its application to the task of finding 3D motifs (like surface patterns or binding sites) in proteins. The domain specific knowledge and further heuristics are used, under certain conditions, to reduce the run time for the search and to adapt the number of reported matches to the expectations of the user. Compared to the general purpose algorithm, the new version is twice as fast, and can be further improved especially for small tolerances in the matches by means of analyzing the distance distributions of the atoms.

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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.

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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.

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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.

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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/

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Superimposé
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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.

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Article
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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.

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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.

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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.

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The Pre-Induction Pack for Engineers (PIPE) is an online tool designed to familiarise prospective students with the university environment, and in particular with the Chemical Engineering course at The University of Manchester, before they actually start their studies. While introducing prospective students to the university, the course and university life in general, the PIPE website helps to ease the communication between prospective students and the School. Through the Ask Dr PIPE section prospectives students can make enquiries directly to staff within the School. The information from students enquiries and the students' responses to the pre-induction questionnaire allow staff within the School to get to know prospectives students better so that adequate support can be in place upon their arrival. PIPE was introduced in August 2005 aiming to help bridge the gap between school and university. An evaluation of the scheme was carried out during the first weeks of the term to obtain information about students’ experience with PIPE and also staff perceptions regarding its functionality and efficiency. Most students found that the information provided in the PIPE website was clear and useful. Most home students who responded the evaluation questionnaire found the section Chemical Engineering at The University of Manchester to be the most useful followed by the Frequently Asked Questions (FAQ) section. On the other hand, the section Working to succeed was found the most useful to the majority of overseas students who responded the evaluation questionnaire followed by Ask Dr PIPE. The majority of students using the site found it an easy and friendly way to communicate with the School at a more personal level. The scheme has been used successfuly during the first attemp although the feedback from the evaluation reveals room for improvement.

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Article
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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.

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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.

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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.

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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.

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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.

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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.

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Erratum
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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.

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InCollection
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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.

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InCollection
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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.

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lanl.arXiv.org
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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.
Article
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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.

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InProceedings
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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.

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Article
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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.
InProceedings
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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.

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lanl.arXiv.org
Article
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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.

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Article
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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.

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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.

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InProceedings
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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.

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Article
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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.

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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.

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Article
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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.

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Erratum
Article
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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.

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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.

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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.

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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.

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InProceedings
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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.

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lanl.arXiv.org
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Article
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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.

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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.

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InProceedings
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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.

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lanl.arXiv.org
Article
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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.

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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.

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Article
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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?

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InCollection
Article
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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.

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InProceedings
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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.

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lanl.arXiv.org
InProceedings
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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.

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lanl.arXiv.org
InProceedings
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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.

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Article
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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.

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Article
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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.

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

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InProceedings
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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.

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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

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Article
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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/

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InProceedings
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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.

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lanl.arXiv.org
Article
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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

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InProceedings
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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.

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Article
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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.

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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.

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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.

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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

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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lanl.arXiv.org
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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.

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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.

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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.

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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

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lanl.arXiv.org
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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.

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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.

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lanl.arXiv.org
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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.

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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.

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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.

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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.

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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.

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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.

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InProceedings
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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.

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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.

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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.

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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.

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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.

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Article
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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.

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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.

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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.

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lanl.arXiv.org
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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.

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lanl.arXiv.org
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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.

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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.

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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.

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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.

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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.

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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.

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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.

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InProceedings
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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.

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lanl.arXiv.org
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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.
Article
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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.

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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.

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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.

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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.

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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.

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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.
Article
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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.

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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.

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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.

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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.

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