Elastic Energy, Fluctuations and Temperature for Granular Materials

We probe, using a model system, elastic and kinetic energies for sheared granular materials. For large enough $P/E_y$ (pressure/Young's modulus) and $P/\rho v^2$ ($P/$kinetic energy density) elastic dominates kinetic energy, and energy fluctuations become primarily elastic in nature. This regime has likely been reached in recent experiments. We consider a generalization of the granular temperature, $T_g$, with both kinetic and elastic terms and that changes smoothly from one regime to the other. This $T_g$ is roughly consistent with a temperature adapted from equilibrium statistical mechanics.Comment: 4 pages, 4 figure

Sliding Phases in XY-Models, Crystals, and Cationic Lipid-DNA Complexes

We predict the existence of a totally new class of phases in weakly coupled, three-dimensional stacks of two-dimensional (2D) XY-models. These ``sliding phases'' behave essentially like decoupled, independent 2D XY-models with precisely zero free energy cost associated with rotating spins in one layer relative to those in neighboring layers. As a result, the two-point spin correlation function decays algebraically with in-plane separation. Our results, which contradict past studies because we include higher-gradient couplings between layers, also apply to crystals and may explain recently observed behavior in cationic lipid-DNA complexes.Comment: 4 pages of double column text in REVTEX format and 1 postscript figur

Karhunen-Lo`eve Decomposition of Extensive Chaos

We show that the number of KLD (Karhunen-Lo`eve decomposition) modes D_KLD(f) needed to capture a fraction f of the total variance of an extensively chaotic state scales extensively with subsystem volume V. This allows a correlation length xi_KLD(f) to be defined that is easily calculated from spatially localized data. We show that xi_KLD(f) has a parametric dependence similar to that of the dimension correlation length and demonstrate that this length can be used to characterize high-dimensional inhomogeneous spatiotemporal chaos.Comment: 12 pages including 4 figures, uses REVTeX macros. To appear in Phys. Rev. Let

Loose packings of frictional spheres

We have produced loose packings of cohesionless, frictional spheres by sequential deposition of highly-spherical, monodisperse particles through a fluid. By varying the properties of the fluid and the particles, we have identified the Stokes number (St) - rather than the buoyancy of the particles in the fluid - as the parameter controlling the approach to the loose packing limit. The loose packing limit is attained at a threshold value of St at which the kinetic energy of a particle impinging on the packing is fully dissipated by the fluid. Thus, for cohesionless particles, the dynamics of the deposition process, rather than the stability of the static packing, defines the random loose packing limit. We have made direct measurements of the interparticle friction in the fluid, and present an experimental measurement of the loose packing volume fraction, \phi_{RLP}, as a function of the friction coefficient \mu_s.Comment: 6 pages, 5 figure

Random Packings of Frictionless Particles

We study random packings of frictionless particles at T=0. The packing fraction where the pressure becomes nonzero is the same as the jamming threshold, where the static shear modulus becomes nonzero. The distribution of threshold packing fractions narrows and its peak approaches random close-packing as the system size increases. For packing fractions within the peak, there is no self-averaging, leading to exponential decay of the interparticle force distribution.Comment: 4 pages, 3 figure

Spatial and temporal resolution of fluid flows: LDRD final report

This report describes a Laboratory Directed Research and Development (LDRD) activity to develop a diagnostic technique for simultaneous temporal and spatial resolution of fluid flows. The goal is to obtain two orders of magnitude resolution in two spatial dimensions and time simultaneously. The approach used in this study is to scale up Particle Image Velocimetry (PIV) and Planar Laser Induced Fluorescence (PLIF) to acquire meter-size images at up to 200 frames/sec. Experiments were conducted in buoyant, fully turbulent, non-reacting and reacting plumes with a base diameter of one meter. The PIV results were successful in the ambient gas for all flows, and in the plume for non-reacting helium and reacting methane, but not reacting hydrogen. No PIV was obtained in the hot combustion product region as the seed particles chosen vaporized. Weak signals prevented PLIF in the helium. However, in reacting methane flows, PLIF images speculated to be from Poly-Aromatic-Hydrocarbons were obtained which mark the flame sheets. The results were unexpected and very insightful. A natural fluorescence from the seed particle vapor was also noted in the hydrogen tests