What is in a pebble shape?

We propose to characterize the shapes of flat pebbles in terms of the statistical distribution of curvatures measured along the pebble contour. This is demonstrated for the erosion of clay pebbles in a controlled laboratory apparatus. Photographs at various stages of erosion are analyzed, and compared with two models. We find that the curvature distribution complements the usual measurement of aspect ratio, and connects naturally to erosion processes that are typically faster at protruding regions of high curvature.Comment: Phys. Rev. Lett. (to appear

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

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

Rheological constitutive equation for model of soft glassy materials

We solve exactly and describe in detail a simplified scalar model for the low frequency shear rheology of foams, emulsions, slurries, etc. [P. Sollich, F. Lequeux, P. Hebraud, M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)]. The model attributes similarities in the rheology of such ``soft glassy materials'' to the shared features of structural disorder and metastability. By focusing on the dynamics of mesoscopic elements, it retains a generic character. Interactions are represented by a mean-field noise temperature x, with a glass transition occurring at x=1 (in appropriate units). The exact solution of the model takes the form of a constitutive equation relating stress to strain history, from which all rheological properties can be derived. For the linear response, we find that both the storage modulus G' and the loss modulus G'' vary with frequency as \omega^{x-1} for 1<x<2, becoming flat near the glass transition. In the glass phase, aging of the moduli is predicted. The steady shear flow curves show power law fluid behavior for x<2, with a nonzero yield stress in the glass phase; the Cox-Merz rule does not hold in this non-Newtonian regime. Single and double step strains further probe the nonlinear behavior of the model, which is not well represented by the BKZ relation. Finally, we consider measurements of G' and G'' at finite strain amplitude \gamma. Near the glass transition, G'' exhibits a maximum as \gamma is increased in a strain sweep. Its value can be strongly overestimated due to nonlinear effects, which can be present even when the stress response is very nearly harmonic. The largest strain \gamma_c at which measurements still probe the linear response is predicted to be roughly frequency-independent.Comment: 24 pages, REVTeX, uses multicol, epsf and amssymp; 20 postscript figures (included). Minor changes to text (relation to mode coupling theory, update on recent foam simulations etc.) and figures (emphasis on low frequency regime); typos corrected and reference added. Version to appear in Physical Review

The shape and erosion of pebbles

The shapes of flat pebbles may be characterized in terms of the statistical distribution of curvatures measured along their contours. We illustrate this new method for clay pebbles eroded in a controlled laboratory apparatus, and also for naturally-occurring rip-up clasts formed and eroded in the Mont St.-Michel bay. We find that the curvature distribution allows finer discrimination than traditional measures of aspect ratios. Furthermore, it connects to the microscopic action of erosion processes that are typically faster at protruding regions of high curvature. We discuss in detail how the curvature may be reliable deduced from digital photographs.Comment: 10 pages, 11 figure

Stress in frictionless granular material: Adaptive Network Simulations

We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with no tensile contact forces. The procedure works by sequentially removing and adding individual contacts between adjacent beads, while the bead positions are not modified. In a series of two-dimensional realizations, the resulting force networks are shown to satisfy a linear constraint among the three components of average stress, as anticipated by recent theories. The coefficients in the linear constraint remain nearly constant for a range of shear loadings up to about .6 of the normal loading. The spatial distribution of contact forces shows strong concentration along ``force chains". The probability of contact forces of magnitude f shows an exponential falloff with f. The response to a local perturbing force is concentrated along two characteristic rays directed downward and laterally.Comment: 8 pages, 8 figure

Deformation of Small Compressed Droplets

We investigate the elastic properties of small droplets under compression. The compression of a bubble by two parallel plates is solved exactly and it is shown that a lowest-order expansion of the solution reduces to a form similar to that obtained by Morse and Witten. Other systems are studied numerically and results for configurations involving between 2 and 20 compressing planes are presented. It is found that the response to compression depends on the number of planes. The shear modulus is also calculated for common lattices and the stability crossover between f.c.c.\ and b.c.c.\ is discussed.Comment: RevTeX with psfig-included figures and a galley macr

Diffusing-wave spectroscopy of nonergodic media

We introduce an elegant method which allows the application of diffusing-wave spectroscopy (DWS) to nonergodic, solid-like samples. The method is based on the idea that light transmitted through a sandwich of two turbid cells can be considered ergodic even though only the second cell is ergodic. If absorption and/or leakage of light take place at the interface between the cells, we establish a so-called "multiplication rule", which relates the intensity autocorrelation function of light transmitted through the double-cell sandwich to the autocorrelation functions of individual cells by a simple multiplication. To test the proposed method, we perform a series of DWS experiments using colloidal gels as model nonergodic media. Our experimental data are consistent with the theoretical predictions, allowing quantitative characterization of nonergodic media and demonstrating the validity of the proposed technique.Comment: RevTeX, 12 pages, 6 figures. Accepted for publication in Phys. Rev.

Sheared Solid Materials

We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure. With this new ingredient, solving the equations yields formation of dislocation dipoles or slips. In plastic flow high-density dislocations emerge at large strains to accumulate and grow into shear bands where the strains are localized. In addition to the elastic displacement, we also introduce the local free volume {\it m}. For very small $m$ the defect structures are metastable and long-lived where the dislocations are pinned by the Peierls potential barrier. However, if the shear modulus decreases with increasing {\it m}, accumulation of {\it m} around dislocation cores eventually breaks the Peierls potential leading to slow relaxations in the stress and the free energy (aging). As another application of our scheme, we also study dislocation formation in two-phase alloys (coherency loss) under shear strains, where dislocations glide preferentially in the softer regions and are trapped at the interfaces.Comment: 16pages, 11figure