Velocity Statistics in the Two-Dimensional Granular Turbulence

We studied the macroscopic statistical properties on the freely evolving quasi-elastic hard disk (granular) system by performing a large-scale (up to a few million particles) event-driven molecular dynamics systematically and found that remarkably analogous to an enstrophy cascade process in the decaying two-dimensional fluid turbulence. There are four typical stages in the freely evolving inelastic hard disk system, which are homogeneous, shearing (vortex), clustering and final state. In the shearing stage, the self-organized macroscopic coherent vortices become dominant. In the clustering stage, the energy spectra are close to the expectation of Kraichnan-Batchelor theory and the squared two-particle separation strictly obeys Richardson law.Comment: 4 pages, 4 figures, to be published in PR

Hydrodynamics of thermal granular convection

A hydrodynamic theory is formulated for buoyancy-driven ("thermal") granular convection, recently predicted in molecular dynamic simulations and observed in experiment. The limit of a dilute flow is considered. The problem is fully described by three scaled parameters. The convection occurs via a supercritical bifurcation, the inelasticity of the collisions being the control parameter. The theory is expected to be valid for small Knudsen numbers and nearly elastic grain collisions.Comment: 4 pages, 4 EPS figures, some details adde

Symmetry-breaking instability in a prototypical driven granular gas

Symmetry-breaking instability of a laterally uniform granular cluster (strip state) in a prototypical driven granular gas is investigated. The system consists of smooth hard disks in a two-dimensional box, colliding inelastically with each other and driven, at zero gravity, by a "thermal" wall. The limit of nearly elastic particle collisions is considered, and granular hydrodynamics with the Jenkins-Richman constitutive relations is employed. The hydrodynamic problem is completely described by two scaled parameters and the aspect ratio of the box. Marginal stability analysis predicts a spontaneous symmetry breaking instability of the strip state, similar to that predicted recently for a different set of constitutive relations. If the system is big enough, the marginal stability curve becomes independent of the details of the boundary condition at the driving wall. In this regime, the density perturbation is exponentially localized at the elastic wall opposite to the thermal wall. The short- and long-wavelength asymptotics of the marginal stability curves are obtained analytically in the dilute limit. The physics of the symmetry-breaking instability is discussed.Comment: 11 pages, 14 figure

A Technique for Tensile Fatigue and Creep Testing of Fiber-Reinforced Ceramics

An experimental technique for the elevated temperature tensile fatigue and creep testing of fiber-reinforced ceramics is discussed. The experimental approach utilizes edge-loaded specimens with rectangular gage-sections. Novel furnace and grip designs which allow testing in air to 1500°C are provided. The specimen, furnace and grip designs discussed in the paper have been successfully used to test unidirectional and cross-ply SiCf/Si3N 4, SiCf/SiC, Cf/SiC and SiCf/calcium-aluminosilicate composites.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66679/2/10.1177_002199839202600608.pd

On Local Behavior of Holomorphic Functions Along Complex Submanifolds of C^N

In this paper we establish some general results on local behavior of holomorphic functions along complex submanifolds of \Co^{N}. As a corollary, we present multi-dimensional generalizations of an important result of Coman and Poletsky on Bernstein type inequalities on transcendental curves in \Co^{2}.Comment: minor changes in the formulation and the proof of Lemma 8.

Collision statistics of driven granular materials

We present an experimental investigation of the statistical properties of spherical granular particles on an inclined plane that are excited by an oscillating side-wall. The data is obtained by high-speed imaging and particle tracking techniques. We identify all particles in the system and link their positions to form trajectories over long times. Thus, we identify particle collisions to measure the effective coefficient of restitution and find a broad distribution of values for the same impact angles. We find that the energy inelasticity can take on values greater than one, which implies that the rotational degrees play an important role in energy transfer. We also measure the distance and the time between collision events in order to directly determine the distribution of path lengths and the free times. These distributions are shown to deviate from expected theoretical forms for elastic spheres, demonstrating the inherent clustering in this system. We describe the data with a two-parameter fitting function and use it to calculated the mean free path and collision time. We find that the ratio of these values is consistent with the average velocity. The velocity distribution are observed to be strongly non-Gaussian and do not demonstrate any apparent universal behavior. We report the scaling of the second moment, which corresponds to the granular temperature, and higher order moments as a function of distance from the driving wall. Additionally, we measure long time correlation functions in both space and in the velocities to probe diffusion in a dissipative gas.Comment: 12 pages, 4 figures, uses revtex

Slater-Pauling Behavior of the Half-Ferromagnetic Full-Heusler Alloys

Using the full-potential screened Korringa-Kohn-Rostoker method we study the full-Heusler alloys based on Co, Fe, Rh and Ru. We show that many of these compounds show a half-metallic behavior, however in contrast to the half-Heusler alloys the energy gap in the minority band is extremely small. These full-Heusler compounds show a Slater-Pauling behavior and the total spin-magnetic moment per unit cell (M_t) scales with the total number of valence electrons (Z_t) following the rule: M_t=Z_t-24. We explain why the spin-down band contains exactly 12 electrons using arguments based on the group theory and show that this rule holds also for compounds with less than 24 valence electrons. Finally we discuss the deviations from this rule and the differences compared to the half-Heusler alloys.Comment: 10 pages, 8 figures, revised figure 3, new text adde

Using Heavy Quark Spin Symmetry in Semileptonic BcB_c Decays

The form factors parameterizing the B_c semileptonic matrix elements can be related to a few invariant functions if the decoupling of the spin of the heavy quarks in B_c and in the mesons produced in the semileptonic decays is exploited. We compute the form factors as overlap integral of the meson wave-functions obtained using a QCD relativistic potential model, and give predictions for semileptonic and non-leptonic B_c decay modes. We also discuss possible experimental tests of the heavy quark spin symmetry in B_c decays.Comment: RevTex, 22 pages, 2 figure

Granular Solid Hydrodynamics

Granular elasticity, an elasticity theory useful for calculating static stress distribution in granular media, is generalized to the dynamic case by including the plastic contribution of the strain. A complete hydrodynamic theory is derived based on the hypothesis that granular medium turns transiently elastic when deformed. This theory includes both the true and the granular temperatures, and employs a free energy expression that encapsulates a full jamming phase diagram, in the space spanned by pressure, shear stress, density and granular temperature. For the special case of stationary granular temperatures, the derived hydrodynamic theory reduces to {\em hypoplasticity}, a state-of-the-art engineering model.Comment: 42 pages 3 fi