Mixing rate in Classical Many Body Systems.

Mixing in many body systems is intuitively understood as the change in time of the set of neighbors surrounding each particle. Its rate and its development over time hold important clues to the behavior of many body systems. For example, gas particles constantly change their position and surrounding particles, while in solids one expects the motion of the atoms to be limited by a fixed set of neighboring atoms. In other systems the situation is less clear. For example, agitated granular systems may behave like a fluid, a solid or glass, depending on various parameter such as density and friction. Thus, we introduce a parameter which describes the mixing rate in many body systems in terms of changes of a properly chosen adjacency matrix. The parameter is easily measurable in simulations but not in experiment. To demonstrate an application of the concept, we simulate a many body system, with particles interacting via a two-body potential and calculate the mixing rate as a function of time and volume fraction. The time dependence of the mixing rate clearly indicates the onset of crystallization.

Structural characterization and statistical properties of two-dimensional granular systems.

A recently developed method is used for the analysis of structures of planar disordered granular assemblies. Within this method, the assemblies are partitioned into volume elements associated either with grains or with more basic elements called quadrons. Our first aim is to compare the relative usefulness of description by quadrons or by grains for entropic characterization. The second aim is to use the method to gain better understanding of the different roles of friction and grain shape and size distributions in determining the disordered structure. Our third aim is to quantify the statistics of basic volumes used for the entropic analysis. We report the following results. (1) Quadrons are more useful than grains as basic ''quasiparticles'' for the entropic formalism. (2) Both grain and quadron volume distributions show nontrivial peaks and shoulders. These can be understood only in the context of the quadrons in terms of particular conditional distributions. (3) Increasing friction increases the mean cell size, as expected, but does not affect the conditional distributions, which is explained on a fundamental level. We conclude that grain size and shape distributions determine the conditional distributions, while their relative weights are dominated by friction and by the pack formation process. This separates sharply the different roles that friction and grain shape distributions play. (4) The analysis of the quadron volumes shows that Gamma distributions, which are accepted to describe foamlike structures well, are too simplistic for general granular systems. (5) A range of quantitative results is obtained for the ''density of states'' of quadron and grain volumes and calculations of expectation values of structural properties are demonstrated. The structural characteristics of granular systems are compared with numerically generated foamlike Dirichlet-Voronoi constructions.

Shape fluctuations of a deformable body in a randomly stirred host fluid.

We consider a deformable body immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we investigate the deformations of the body. The shape is decomposed into spherical harmonic modes. We study the correlations of these modes for a general class of random flows that include, as a special case, the flow due to thermal agitation. Our results are general, in the sense that they are applicable to a large class of deformable bodies with energy that depends only on the shape of the body, and a general class of random flows.

Diffusion of a nearly spherical deformable body in a randomly stirred host fluid.

The motion of a deformable body is investigated for cases in which the body is immersed in an incompressible fluid that is randomly stirred. Sticking to physical situations in which the body departs only slightly from its spherical shape, we show that the motion of its center is decoupled from its deformation degrees of freedom. We study the general case in which the velocity field, imposed on the system, is correlated both in space and time. We derive the mean-squared displacement of the body for the general random velocity field, and consider several useful cases including: white-noise flow, turbulence-like flow, and thermal agitation.