We conduct numerical simulations of 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.

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PACS. 68.10 -Fluid surfaces and interfaces with fluids (inc. surface tension, capillarity, wetting and related phenomena). FACS. 68.80 -Dynamics of solid surfaces and interface vibrations.Abstract. -We detennine the dispersion relation for a fluid bilayer membrane, taking into account the coupling between bending and the local density of the two monolayers. Apart from important corrections to the conventional bending mode, we obtain a second slow mode which is essentially a fluctuation in the density difference of the two monolayers, damped by inter-monolayer friction. Estimates for a stack of membranes show reasonable agreement with a recent spin-echo study of membrane undulations.The traditional model for fluid phospholipid membranes treats them as a single incompressible sheet with bending rigidity [1). Actually, of course, they consist of a pair of slightly compressible monolayers bound tightly together. This bilayer structure implies that bending a membrane necessarily leads to a stretching of one monolayer and a compression of the other. Since the membrane is fluid, density inhomogeneities can relax within each monolayer by lateral lipid flow. For the investigation of static equilibrium phenomena, one ean therefore assume that the lipid density within each monolayer is homogeneous. The only effect of the bilayer structure is to add a global term to the energy, the area difference elasticity [2-4), which is important for calculating the phase diagram of vesicle shapes.Evans and Yeung [5, 6) recently stressed that for the dynamics of conformational changes of membranes the coupling between bending and relative compression is crucial, and demonstrated this in the analysis of a tether fonnation experiment. The purpose of this paper is, first, to analyse this coupling for the much simpler but paradigmatic case of the dynamical equilibrium fluctuations of an almost planar bilayer embedded in a viscous medium and then, briefly, to discuss these fluctuations for the experimentally relevant case of membrane stacks.The standard treatment [7) of the fluctuating single membrane leads to a relaxation rate y, = "q'/4~ for a plane wave excitation with wave number q within the membrane. The bending rigidity" provides the driving force, while the viscosity ~ of the surrounding liquid provides the dissipation. Does this relation hold for a bilayer in which the lipids can

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. 64.70.Pf,81.05.Rm,83.70.Hq Granular materials can flow when shaken, but jam when the shaking intensity is lowered [1]. Similarly, foams and emulsions can flow when sheared, but jam when shear stress is lowered [2]. These systems are athermal because thermal energy is insufficient to change the packing of grains, bubbles, or droplets. When the external driving force is too small to cause particle rearrangements, these materials become amorphous solids and develop a yield stress. A supercooled liquid, on the other hand, is a thermal system that turns, as temperature is lowered, into a glass-an amorphous solid with a yield stress [3]. Despite significant differences between driven, athermal systems and quiescent, thermal ones, it has been suggested that the process of jamming-developing a yield stress in an amorphous state-may lead to common behavior, and that these systems can be unified by a jamming phase diagram [4]. This implies that there should be similarities in these different systems as they approach jamming or glass transitions. We test this speculation by measuring the distribution P (F ) of interparticle normal forces F , in model supercooled liquids and foams. We find that for glasses, P (F ) is quantitatively similar to experimental results on granular materials [5].When granular materials jam, the distribution of stresses is known to be inhomogeneous [6,7]. As proposed in Ref.[7], we quantify this effect by measuring P (F ). Our aim is to determine which feature in P (F ) is associated with development of a yield stress. Experiments [5,8] and simulations [9,10] on static granular packings find that P (F ) has a plateau or small peak at small F and decays exponentially at large F . We argue that the development of a peak is the signature of jamming.For supercooled liquids, equilibrium statistical mechanics gives insight into the shape of P (F ). Since forces depend only on particle separations, P (F )dF = G(r)dr, where G(r)dr is the probability of finding a particle between r and r + dr given a particle at the origin. Thus,, where N is the number of particles, ρ is the number density, g(r) is the pair distribution function, and S D r D−1 is the surface area of a Ddimensional sphere of radius r. Although it is well known that g(r) does not change significantly as the temperature is varied through the glass transition T g , we show below that P (F ) is qu...

Fluctuations in a model of a sheared, zero-temperature foam are studied numerically. Five different quantities that independently reduce to the true temperature in an equilibrium thermal system are calculated. One of the quantities is calculated up to an unknown coefficient. The other four quantities have the same value and all five have the same shear-rate dependence. These results imply that statistical mechanics is useful for the system even though it is far from thermal equilibrium.