Materials with negative Poisson ratios are known to have high shear rigidities – a useful property for many types of structural and functional materials. To improve upon relatively low Young’s modulus of existing auxetics, one may consider embedding such components in an elastic material...

Exact formulation for calculating effective elastic moduli of an isotropic two-phase disordered composite with ellipsoidal or elliptic inclusions are given in the mean-field approximation, which yields simple analytic expansions of effective Poisson ratio and Young's modulus to second order in...

For arbitrary random walks in any d-dimensional space, a 1/d expansion of the most probable size ratio, i.e., squared radius of gyration s2 divided by 〈s2〉 of open random walks, has been developed, which, at O(1/d3), yields a very good approximation to the exact value for chains (d ⩾ 2)...

For arbitrary random walks in any d-dimensional space, expansions in powers of 1/d of asphericity and prolateness parameters and moments of the inverse size ratio have been developed, which, at O(1/d3), yield very good approximations to exact values of the parameters for chains, rings, dumbbells...

Since the random walk problem was first presented by Pearson in 1905, the shape of a walk which is either completely random or self-avoiding has attracted the attention of generations of researchers working in such diverse fields as chemistry, physics, biology and statistics. Among many advances...

The problem of the shape of a random object such as a flexible polymer chain was first tackled by Kuhn nearly thirty years after the answer to the probability distribution of its size was publicly sought for by Pearson in 1905. Since then, significant progress in the field has been made, but the...

As an application of the model we have developed for the stress within a granular material we consider the force distribution within vertical and horizontal pipes. For a vertical pipe (with rough walls) the average forces in the system follow the arch of a catenary between the walls. For a...

We construct the equation of motion for the probability density functional for a given shape and central location of a deformable membrane. The equation is developed and solved in the regime of small deformations.

In this paper we will attempt to address the problem of the packing properties of granular materials composed of irregularly shaped grains (using configurational statistical mechanics). In particular, we will develop a model for a system of irregular grains based upon perturbing a packing of...