Partitioning of energy in highly polydisperse granular gases

A highly polydisperse granular gas is modeled by a continuous distribution of particle sizes, a, giving rise to a corresponding continuous temperature profile, T(a), which we compute approximately, generalizing previous results for binary or multicomponent mixtures. If the system is driven, it evolves towards a stationary temperature profile, which is discussed for several driving mechanisms in dependence on the variance of the size distribution. For a uniform distribution of sizes, the stationary temperature profile is nonuniform with either hot small particles (constant force driving) or hot large particles (constant velocity or constant energy driving). Polydispersity always gives rise to non-Gaussian velocity distributions. Depending on the driving mechanism the tails can be either overpopulated or underpopulated as compared to the molecular gas. The deviations are mainly due to small particles. In the case of free cooling the decay rate depends continuously on particle size, while all partial temperatures decay according to Haff's law. The analytical results are supported by event driven simulations for a large, but discrete number of species.Comment: 10 pages; 5 figure

Hydrodynamic Correlation Functions of a Driven Granular Fluid in Steady State

We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. Inelastic collisions are modeled by incomplete normal restitution, allowing for efficient simulations with an event-driven algorithm. The incoherent scattering function, F_incoh(q,t), is seen to follow time-density superposition with a relaxation time that increases significantly as volume fraction increases. The statistics of particle displacements is approximately Gaussian. For the coherent scattering function S(q,omega) we compare our results to the predictions of generalized fluctuating hydrodynamics which takes into account that temperature fluctuations decay either diffusively or with a finite relaxation rate, depending on wave number and inelasticity. For sufficiently small wave number q we observe sound waves in the coherent scattering function S(q,omega) and the longitudinal current correlation function C_l(q,omega). We determine the speed of sound and the transport coefficients and compare them to the results of kinetic theory.Comment: 10 pages, 16 figure

Random walks with imperfect trapping in the decoupled-ring approximation

We investigate random walks on a lattice with imperfect traps. In one dimension, we perturbatively compute the survival probability by reducing the problem to a particle diffusing on a closed ring containing just one single trap. Numerical simulations reveal this solution, which is exact in the limit of perfect traps, to be remarkably robust with respect to a significant lowering of the trapping probability. We demonstrate that for randomly distributed traps, the long-time asymptotics of our result recovers the known stretched exponential decay. We also study an anisotropic three-dimensional version of our model, where for sufficiently large transverse diffusion the system is described by the mean-field kinetics. We discuss possible applications of some of our findings to the decay of excitons in semiconducting organic polymer materials, and emphasize the crucial influence of the spatial trap distribution on the kinetics.Comment: 10 page

Sample-to-sample fluctuations and bond chaos in the mm-component spin glass

We calculate the finite size scaling of the sample-to-sample fluctuations of the free energy $\Delta F$ of the $m$ component vector spin glass in the large-$m$ limit. This is accomplished using a variant of the interpolating Hamiltonian technique which is used to establish a connection between the free energy fluctuations and bond chaos. The calculation of bond chaos then shows that the scaling of the free energy fluctuaions with system size $N$ is $\Delta F \sim N^\mu$ with ${1/5}\leq\mu <{3/10}$, and very likely $\mu={1}{5}$ exactly.Comment: 12 pages, 1 figur