Instabilities of time-averaged configurations in thermal glasses.

In amorphous solids at finite temperatures the particles follow chaotic trajectories which, at temperatures sufficiently lower than the glass transition, are trapped in "cages." Averaging their positions for times shorter than the diffusion time, one can define a time-averaged configuration. Under strain or stress, these average configurations undergo sharp plastic instabilities.

Breakdown of nonlinear elasticity in stress-controlled thermal amorphous solids.

In recent work it was clarified that amorphous solids under strain control do not possess nonlinear elastic theory in the sense that the shear modulus exists but nonlinear moduli exhibit sample-to-sample fluctuations that grow without bound with the system size. More relevant, however, for experiments are the conditions of stress control. In the present Rapid Communication we show that also under stress control the shear modulus exists, but higher-order moduli show unbounded sample-to-sample fluctuation.

Mechanical properties and plasticity of a model glass loaded under stress control.

Much of the progress achieved in understanding plasticity and failure in amorphous solids had been achieved using experiments and simulations in which the materials were loaded using strain control. There is paucity of results under stress control. Here we present a method that was carefully geared to allow loading under stress control either at T=0 or at any other temperature, using Monte Carlo techniques.

Statistical mechanics of glass formation in molecular liquids with OTP as an example.

We extend our statistical mechanical theory of the glass transition from examples consisting of point particles to molecular liquids with internal degrees of freedom. As before, the fundamental assertion is that supercooled liquids are ergodic, although becoming very viscous at lower temperatures, and are therefore describable in principle by statistical mechanics. The theory is based on analyzing the local neighborhoods of each molecule, and a statistical mechanical weight is assigned to every possible local organization.

Stochastic processes crossing from ballistic to fractional diffusion with memory: exact results.

We address the now classical problem of a diffusion process that crosses over from a ballistic behavior at short times to a fractional diffusion (subdiffusion or superdiffusion) at longer times. Using the standard non-Markovian diffusion equation we demonstrate how to choose the memory kernel to exactly respect the two different asymptotics of the diffusion process. Having done so we solve for the probability distribution function (pdf) as a continuous function which evolves inside a ballistically expanding domain.

Theory of specific heat in glass-forming systems.

Experimental measurements of the specific heat in glass-forming systems are obtained from the linear response to either slow cooling (or heating) or to oscillatory perturbations with a given frequency about a constant temperature. The latter method gives rise to a complex specific heat with the constraint that the zero frequency limit of the real part should be identified with thermodynamic measurements. Such measurements reveal anomalies in the temperature dependence of the specific heat, including the so called "specific heat peak" in the vicinity of the glass transition.

Nonuniversality of the specific heat in glass forming systems.

We present new simulation results for the specific heat in a classical model of a binary mixture glass former in two dimensions. We show that in addition to the formerly observed specific heat peak, there is a second peak at lower temperatures which was not observable in earlier simulations. This is a surprise, as most texts on the glass transition expect a single specific heat peak.

Aging and relaxation in glass-forming systems.

We propose that there exists a generic class of glass-forming systems that have competing states (of crystalline order or not) which are locally close in energy to the ground state (which is typically unique). Upon cooling, such systems exhibit patches (or clusters) of these competing states which become locally stable in the sense of having a relatively high local shear modulus. It is in between these clusters where aging, relaxation, and plasticity under strain can take place.

Mechanical properties of glass forming systems.

We address the interesting temperature range of a glass forming system where the mechanical properties are intermediate between those of a liquid and a solid. We employ an efficient Monte Carlo method to calculate the elastic moduli, and show that in this range of temperatures the moduli are finite for short times and vanish for long times, where short and long depend on the temperature. By invoking some exact results from statistical mechanics we offer an alternative method to compute shear moduli using molecular dynamics simulations, and compare those to the Monte Carlo method.

Statistical mechanics of the glass transition in one-component liquids with an anisotropic potential.

We study a recently introduced model of one-component glass-forming liquids whose constituents interact with an anisotropic potential. This system is interesting per se and as a model of liquids such as glycerol (interacting via hydrogen bonds) which are excellent glass formers. We work out the statistical mechanics of this system, encoding the liquid and glass disorder using appropriate quasiparticles (36 of them).

Statistical mechanics of the glass transition as revealed by a Voronoi tesselation.

The statistical mechanics of simple glass forming systems in two dimensions is worked out. The glass disorder is encoded via a Voronoi tesselation, and the statistical mechanics is performed directly in this encoding. The theory provides, without free parameters, an explanation of the glass transition phenomenology, including the identification of two different temperatures, T(g) and T(c) , the first associated with jamming and the second associated with crystallization at very low temperatures.