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.Granular media such as sand provide an attractive opportunity to revisit a number of topics in classical physics, and contribute new angles. In this paper we describe the granular phase diagram which we hope will be helpful to a broad community given the raising interest in granular systems [1]. The researchers interested in diluted granular gases, such as in astrophysical applications [2], and researchers who study, say, compaction of sand [3] use different approaches. The phase diagram may represent a ground for communication.The phase of granular system depends on inelasticity of collisions, r, (restitution coefficient approximation, [4, 5, 6]), particle density, ρ, particle size, a, system size, * J. Stat. Phys. (in press)

Proteus mirabilis colonies exhibit striking geometric regularity. Basic microbiological methods and imaging techniques were used to measure periodic macroscopic events in swarm colony morphogenesis. We distinguished three initial phases (lag phase, first swarming phase, and first consolidation phase) followed by repeating cycles of subsequent swarming plus consolidation phases. Each Proteus swarm colony terrace corresponds to one swarming-plus-consolidation cycle. The duration of the lag phase was dependent upon inoculation density in a way that indicated the operation of both cooperative and inhibitory multicellular effects. On our standard medium, the second and subsequent swarm phases displayed structure in the form of internal waves visible with reflected and dark-field illumination. These internal waves resulted from organization of the migrating bacteria into successively thicker cohorts of swarmer cells. Bacterial growth and motility were independently modified by altering the composition of the growth medium. By varying the glucose concentration in the substrate, it was possible to alter biomass production without greatly affecting the kinetics of colony surface area expansion. By varying the agar concentration in the substrate, initial bacterial biomass production was unaffected but colony expansion dynamics were significantly altered. Higher agar concentrations led to slower, shorter swarm phases and longer consolidation phases. Thus, colony growth was restricted by higher agar concentrations but the overall timing of the swarming-plus-consolidation cycles remained constant. None of a variety of factors which had significant effects on colony expansion altered terracing frequencies at 32؇C, but the length of the swarming-plus-consolidation cycle was affected by temperature and medium enrichment. Some clinical isolates displayed significant differences in terracing frequencies at 32؇C. Our results defined a number of readily quantifiable parameters in swarm colony development. The data showed no connection between nutrient (glucose) depletion and the onset of different phases in swarm colony morphogenesis. Several observations point to the operation of density-dependent thresholds in controlling the transitions between distinct phases.Proteus mirabilis colonies have fascinated microbiologists for over a century (13). On typical laboratory media, mature P. mirabilis swarm colonies display striking patterns characterized by circular symmetry and regularly spaced concentric terraces or zones (Fig. 1) (6). These terraces develop as a result of periodic events during colony growth, most notably the cyclic repetition of alternating phases: swarming (active migration) and consolidation (growth without movement of the colony perimeter) (2, 3). Colony expansion is a dynamic process involving movement over the solid substrate by multicellular rafts of specially differentiated swarmer cells (7,18,30,32). The swarmer cells are elongated and hyperflagellated but have the same DNA/length ratio as the shorter oligofla...

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This paper compares theory and experiment for the kinetics of time-dependent sedimentation. We discuss non-interacting suspensions and colloids which may exhibit behavior similar to the one-dimensional motion of compressible gas. The velocity of sedimentation (or creaming) depends upon the volume fraction of the constituting particles and leads to Burgers-like equations for concentration profiles.It is shown that even the bi-dispersive system of two coupled Burgers equations has rich dynamics. The study of polydispersive case reveals a continuous "renormalization" of the polydispersity. We compare the Burgers system evolution with the experimental results on mono-and polydispersive sedimentation. The influence of thermal fluctuations is briefly discussed.

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 gas-like regimes. The behavior of effective damping decrement in the solid regime is glassy. Practical applications are dicussed.PACS: 05.40. -y, 46.10 +z, 83.70 Fn.The dominating approach in the world of vibration control and suppression by granular systems has been mainly practical [1]. Granular motion relaxes rapidly once the energy supply is switched off, and dampers can efficiently absorb energy released by shocks of external forcing. Engineers classify granular dampers as passive ones.For the case of "granular gases", i.e. particulate systems in a state where the mean free path is large as compared with particle sizes the cooling rate, the dissipation rate of the system has been investigated [2], and applications of this work require an analysis of granular gas (hydro)dynamics in a given experimental setup. Damping in dense granular arrangements is a much more difficult problem which is mostly studied experimentally.In this work, by using molecular dynamics simulations, we show that granular systems reveal different damping regimes indicating collective dissipation modes. Our study of these regimes leads to a "phase diagram" of horizontally vibrated granular systems (see Fig. 4). By using this diagram along with the presented estimates for damping decrements, practitioners may accelerate the design and testing procedures.In simulations we focus on two dimensional containers which are partially filled with granular material and shaken horizontally. The motion of the container is sinusoidal, x(t) = A sin(ωt); it mimics practical situations where dampers are tested in the vicinity of the eigenmodes of the vibrating mechanism. We study the reaction of the system to the choice of parameters of shaking A and ω, keeping all other parameters (size, roughness and hardness of particles, filling factor, size and shape of the apparatus) fixed [3].Our primary objective is the rate of energy dissipation, computed by cycle averaging under steady conditions of oscillatory motion. Dissipation is obtained by using two different ways to ensure consistency of the data: (i) from the total power transmitted to the container walls, and (ii) from the dissipative work in inter-particle collisions. Numerically, both results coincide within a few percent.For the molecular dynamics simulations, we use a modified soft-particle model by Cundall and Strack [4]: Two particles i and j, with radii R i and R j and position vectors r i and r j , interact if their compression ξ ij = R i + R j − | r i − r j | is positive. In this case the colliding spheres feel forces F