Stephen A. Langer

Random Packings of Frictionless Particles

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.

Force Distributions near 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.

Viscous modes of fluid bilayer membranes

We determine 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.

Effective Temperatures of a Driven System Near Jamming

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.

Labyrinthine Pattern Formation in Magnetic Fluids

A quasi two-dimensional drop of a magnetic fluid (ferrofluid) in a magnetic field is one example of the many systems, including amphiphilic monolayers, thin magnetic films, and type I superconductors, that form labyrinthine patterns. The formation of the ferrofluid labyrinth was examined both experimentally and theoretically. Labyrinth formation was found to be sensitively dependent on initial conditions, indicative of a space of configurations having a vast number of local energy minima. Certain geometric characteristics of the labyrinths suggest that these multiple minima have nearly equivalent energies. Kinetic effects on pattern selection were found in studies of fingering in the presence of timedependent magnetic fields. The dynamics of this pattern formation was studied within a simple model that yields shape evolutions in qualitative agreement with experiment.

Modelling Microstructures with OOF2

OOF2 is a program designed to compute the properties and local behaviour of material microstructures, starting from a two-dimensional representation, an image, of arbitrary geometrical complexity. OOF2 uses the finite element method to resolve the local behaviour of a material, and is designed to be used by materials scientists with little or no computational background. It can solve for a wide range of physical phenomena and can be easily extended. This paper is an introduction to some of its most basic and important features.

Statistics of shear-induced rearrangements in a two-dimensional model foam.

Under steady shear, a foam relaxes stress through intermittent rearrangements of bubbles accompanied by sudden drops in the stored elastic energy. We use a simple model of foam that incorporates both elasticity and dissipation to study the statistics of bubble rearrangements in terms of energy drops, the number of nearest neighbor changes, and the rate of neighbor-switching (T1) events. We do this for a two-dimensional system as a function of system size, shear rate, dissipation mechanism, and gas area fraction. We find that for dry foams, there is a well-defined quasistatic limit at low shear rates where localized rearrangements occur at a constant rate per unit strain, independent of both system size and dissipation mechanism. These results are in good qualitative agreement with experiments on two-dimensional and three-dimensional foams. In contrast, we find for progessively wetter foams that the event size distribution broadens into a power law that is cut off only by system size. This is consistent with criticality at the melting transition.

Effect of Ordering on Spinodal Decomposition of Liquid-Crystal/Polymer Mixtures

Partially phase-separated liquid-crystal/polymer dispersions display highly fibrillar domain morphologies that are dramatically different from the typical structures found in isotropic mixtures. To explain this, we numerically explore the coupling between phase ordering and phase-separation kinetics in model two-dimensional fluid mixtures phase separating into a nematic phase, rich in liquid crystal, coexisting with an isotropic phase, rich in polymer. We find that phase ordering can lead to fibrillar networks of the minority polymer-rich phase.

Analytical and numerical analyses for two-dimensional stress transfer

Abstract Both analytical modeling and numerical simulations were performed to analyze the stress transfer in platelet-reinforced composites in a two-dimensional sense. In the two-dimensional model, an embedded elongated plate bonded to a matrix along its long edges was considered. The system was subjected to both tensile loading parallel to the plate’s long edges and residual thermal stresses. The ends of the plate can be debonded from or bonded to the matrix during loading, and both cases were considered in the analysis. Good agreement was obtained between the present analytical and numerical solutions. However, better agreement between analytical and numerical models was obtained for the case of bonded ends than for debonded ends.

Grain‐scale thermoelastic stresses and spatiotemporal temperature gradients on airless bodies, implications for rock breakdown

Thermomechanical processes such as fatigue and shock have been suggested to cause and contribute to rock breakdown on Earth, and on other planetary bodies, particularly airless bodies in the inner solar system. In this study, we modeled grain-scale stresses induced by diurnal temperature variations on simple microstructures made of pyroxene and plagioclase on various solar system bodies. We found that a heterogeneous microstructure on the Moon experiences peak tensile stresses on the order of 100 MPa. The stresses induced are controlled by the coefficient of thermal expansion and Youngs modulus of the mineral constituents, and the average stress within the microstructure is determined by relative volume of each mineral. Amplification of stresses occurs at surface-parallel boundaries between adjacent mineral grains and at the tips of pore spaces. We also found that microscopic spatial and temporal surface temperature gradients do not correlate with high stresses, making them inappropriate proxies for investigating microcrack propagation. Although these results provide very strong evidence for the significance of thermomechanical processes on airless bodies, more work is needed to quantify crack propagation and rock breakdown rates.