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

Sliding Columnar Phase of DNA-Lipid Complexes

We introduce a simple model for DNA-cationic-lipid complexes in which galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices that couple orientationally and positionally to lattices in neighboring galleries. We identify a new equilibrium phase in which there are long-range orientational but not positional correlations between DNA lattices. We discuss properties of this new phase such as its X-ray structure factor S(r), which exhibits unusual exp(- const.ln^2 r) behavior as a function of in-plane separation r.Comment: This file contains 4 pages of double column text and one postscript figure. This version includes interactions between dislocations in a given gallery and presents an improved estimate of the decoupling temperature. It is the published versio

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

Constraints and vibrations in static packings of ellipsoidal particles

We numerically investigate the mechanical properties of static packings of ellipsoidal particles in 2D and 3D over a range of aspect ratio and compression $\Delta \phi$. While amorphous packings of spherical particles at jamming onset ($\Delta \phi=0$) are isostatic and possess the minimum contact number $z_{\rm iso}$ required for them to be collectively jammed, amorphous packings of ellipsoidal particles generally possess fewer contacts than expected for collective jamming ($z < z_{\rm iso}$) from naive counting arguments, which assume that all contacts give rise to linearly independent constraints on interparticle separations. To understand this behavior, we decompose the dynamical matrix $M=H-S$ for static packings of ellipsoidal particles into two important components: the stiffness $H$ and stress $S$ matrices. We find that the stiffness matrix possesses $N(z_{\rm iso} - z)$ eigenmodes ${\hat e}_0$ with zero eigenvalues even at finite compression, where $N$ is the number of particles. In addition, these modes ${\hat e}_0$ are nearly eigenvectors of the dynamical matrix with eigenvalues that scale as $\Delta \phi$, and thus finite compression stabilizes packings of ellipsoidal particles. At jamming onset, the harmonic response of static packings of ellipsoidal particles vanishes, and the total potential energy scales as $\delta^4$ for perturbations by amplitude $\delta$ along these `quartic' modes, ${\hat e}_0$. These findings illustrate the significant differences between static packings of spherical and ellipsoidal particles.Comment: 18 pages, 21 figure

Numerical Study of the Stress Response of Two-Dimensional Dense Granular Packings

We investigate the Green function of two-dimensional dense random packings of grains in order to discriminate between the different theories of stress transmission in granular materials. Our computer simulations allow for a detailed quantitative investigation of the dynamics which is difficult to obtain experimentally. We show that both hyperbolic and parabolic models of stress transmission fail to predict the correct stress distribution in the studied region of the parameters space. We demonstrate that the compressional and shear components of the stress compare very well with the predictions of isotropic elasticity for a wide range of pressures and porosities and for both frictional and frictionless packings. However, the states used in this study do not include the critical isostatic point for frictional particles, so that our results do not preclude the fact that corrections to elasticity may appear at the critical point of jamming, or for other sample preparation protocols, as discussed in the main text. We show that the agreement holds in the bulk of the packings as well as at the boundaries and we validate the linear dependence of the stress profile width with depth.Comment: 7 pages, 5 figure

Force distributions near the jamming and glass transitions

We calculate the distribution of interparticle normal forces $P(F)$ near the glass and jamming transitions in model supercooled liquids and foams, respectively. $P(F)$ develops a peak that appears near the glass or jamming transitions, whose height increases with decreasing temperature, decreasing shear stress and increasing packing density. A similar shape of $P(F)$ was observed in experiments on static granular packings. We propose that the appearance of this peak signals the development of a yield stress. The sensitivity of the peak to temperature, shear stress and density lends credence to the recently proposed generalized jamming phase diagram.Comment: 4 pages, 3 postscript figures;Version 3 replaces figure 1 and removes figure 2 from version 1. Significant rewording of version 1 to emphasize the formation of peak in P(F) when these systems jam along five different routes of the recently proposed jamming phase diagram. Version 2 displayed the incorrect abstrac

Lyapunov spectral analysis of a nonequilibrium Ising-like transition

By simulating a nonequilibrium coupled map lattice that undergoes an Ising-like phase transition, we show that the Lyapunov spectrum and related dynamical quantities such as the dimension correlation length~$\xi_\delta$ are insensitive to the onset of long-range ferromagnetic order. As a function of lattice coupling constant~$g$ and for certain lattice maps, the Lyapunov dimension density and other dynamical order parameters go through a minimum. The occurrence of this minimum as a function of~$g$ depends on the number of nearest neighbors of a lattice point but not on the lattice symmetry, on the lattice dimensionality or on the position of the Ising-like transition. In one-space dimension, the spatial correlation length associated with magnitude fluctuations and the length~$\xi_\delta$ are approximately equal, with both varying linearly with the radius of the lattice coupling.Comment: 29 pages of text plus 15 figures, uses REVTeX macros. Submitted to Phys. Rev. E

Glass Transition Behavior of Polymer Films of Nanoscopic Dimensions

Glass transition behavior of nanoscopically thin polymer films is investigated by means of molecular dynamics simulations. A thin polymer film that is composed of bead-spring model chains and supported on an idealized, fcc lattice substrate surface is studied in this work.Comment: in review, macromolecule

The Batten Disease Palmitoyl Protein Thioesterase 1 Gene Regulates Neural Specification and Axon Connectivity during Drosophila Embryonic Development

Palmitoyl Protein Thioesterase 1 (PPT1) is an essential lysosomal protein in the mammalian nervous system whereby defects result in a fatal pediatric disease called Infantile Neuronal Ceroids Lipofuscinosis (INCL). Flies bearing mutations in the Drosophila ortholog Ppt1 exhibit phenotypes similar to the human disease: accumulation of autofluorescence deposits and shortened adult lifespan. Since INCL patients die as young children, early developmental neural defects due to the loss of PPT1 are postulated but have yet to be elucidated. Here we show that Drosophila Ppt1 is required during embryonic neural development. Ppt1 embryos display numerous neural defects ranging from abnormal cell fate specification in a number of identified precursor lineages in the CNS, missing and disorganized neurons, faulty motoneuronal axon trajectory, and discontinuous, misaligned, and incorrect midline crossings of the longitudinal axon bundles of the ventral nerve cord. Defects in the PNS include a decreased number of sensory neurons, disorganized chordotonal neural clusters, and abnormally shaped neurons with aberrant dendritic projections. These results indicate that Ppt1 is essential for proper neuronal cell fates and organization; and to establish the local environment for proper axon guidance and fasciculation. Ppt1 function is well conserved from humans to flies; thus the INCL pathologies may be due, in part, to the accumulation of various embryonic neural defects similar to that of Drosophila. These findings may be relevant for understanding the developmental origin of neural deficiencies in INCL