Properties of exact hard-disk free volumes are determined by a combination of analytical and numerical technIques. Both the high-density fluid phase and the lower-density fluid phase are treated. These one particle free volumes are used to verify known thermodynamic information for hard disks and to calculate the shear ~odulus for the hard-disk solid phase. The free volumes are also compared to approximate free volume eslimates made from the known hard-disk entropy. The statistical distributions of free volume and free surface (perimeter of the free volume) are studied. The percolation transition, at which the free volume changes from extensive to intensive, is found to occur at about one-third pf the freezing density.
The geometric properties of polygranular microstructures of the Johnson-Mehl and cellular types have been studied through computer simulation. These prototypic microstructures arise naturally from the classical model of a phase transformation in a one-component solid through growth from a random distribution of nucleation sites. The
Using techniques drawn from the statistical theory of branching processes, we approximate the critical resolved shear stress for the athermal planar glide of a dislocation, idealized as a flexible line of constant tension, through a random mixture of immobile point obstacles
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