arXiv subjects

Thorsten Poeschel

Publications and source records attributed to Thorsten Poeschel.

At least 55 records · Page 3Linked to original sources

arXiv2005

Breakdown of the Sonine expansion for the velocity distribution of Granular Gases

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< epsilon < 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.

cond-mat.stat-mech↗

arXiv2005

Collision of Adhesive Viscoelastic Particles

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-static 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.

cond-mat.stat-mech↗

arXiv2005

Adhesive interactions of viscoelastic spheres

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.

cond-mat.mtrl-sci↗

arXiv2005

Rolling friction and bistability of rolling motion

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.

cond-mat.mtrl-sci↗

arXiv2005

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

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 $ε$ which for realistic material properties depends on the impact velocity. First, we consider self-diffusion using a constant coefficient of restitution, $ε=$const, as frequently used to simplify the analysis. Second, self-diffusion is studied for a simplified (stepwise) dependence of $ε$ on the impact velocity. Finally, diffusion is considered for gases of realistic viscoelastic particles. We find that for $ε=$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.

cond-mat.stat-mech↗

arXiv2004

Peptide size dependent active transport in the proteasome

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.

q-bio.BM↗

arXiv2004

Transient structures in a Granular Gas

A force-free granular gas is considered with 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.

cond-mat.stat-mech↗

arXiv2004

Bistability and noise-enhanced velocity of rolling motion

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.

cond-mat.mtrl-sci↗

arXiv2004

Correction algorithm for finite sample statistics

Assume in a sample of size M one finds M_i representatives of species i with i=1...N^*. The normalized frequency p^*_i=M_i/M, based on the finite sample, may deviate considerably from the true probabilities p_i. We propose a method to infer rank-ordered true probabilities r_i from measured frequencies M_i. We show that the rank-ordered probabilities provide important informations on the system, e.g., the true number of species, the Shannon- and the Renyi-entropies.

q-bio.OT↗

arXiv2004

Online tool for the discrimination of equi-distributions

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.

q-bio.GN↗

arXiv2003

Giant fluctuations at a granular phase separation threshold

We investigate a phase separation instability that occurs 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 hydrostatics predict phase separation: the formation of a high-density region coexisting with a low-density region along the wall that is opposite to the thermal wall. Event-driven molecular dynamic simulations confirm this prediction. The theoretical bifurcation curve agrees with the simulations quantitatively well below and well above the threshold. However, in a wide region of aspect ratios around the threshold, the system is dominated by fluctuations, and the hydrostatic theory breaks down. Two possible scenarios of the origin of the giant fluctuations are discussed.

cond-mat.soft↗

arXiv2003

Kinetic Integrals in the Kinetic Theory of dissipative gases

The kinetic theory of gases, including Granular Gases, is based on the Boltzmann equation. Many properties of the gas, from the characteristics of the velocity distribution function to the transport coefficients may be expressed in terms of functions of the collision integral which we call kinetic integrals. Although the evaluation of these functions is conceptually straightforward, technically it is frequently rather cumbersome. We report here a method for the analytical evaluation of kinetic integrals using computer algebra. We apply this method for the computation of some properties of Granular Gases, ranging from the moments of the velocity distribution function to the transport coefficients. For their technical complexity most of these quantities cannot be computed manually.

cond-mat.stat-mech↗

arXiv2003

Close-packed floating clusters: granular hydrodynamics beyond the freezing point?

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.

cond-mat.soft↗

arXiv2003

Long-time behavior of Granular Gases with impact-velocity dependent coefficient of restitution

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.

cond-mat.stat-mech↗

arXiv2003

Hydrodynamics and transport coefficients for Granular Gases

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.

cond-mat.stat-mech↗

arXiv2002

Violation of Molecular Chaos in dissipative gases

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.

cond-mat.stat-mech↗

arXiv2002

How to decide whether small samples comply with an equidistribution

The decision whether a measured distribution complies with an equidistribution is a central element of many biostatistical methods. High throughput 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. chi^2) fail. Our method will have a major impact on several problems of computational biology where rare events baffle a reliable assessment of frequency distributions.

cond-mat.dis-nn↗

arXiv2002

Rigid body dynamics of railway ballast

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.

cond-mat.mtrl-sci↗