Most of the recent research on random surface contact mechanics has been on self-affine
surfaces. In such models, the fractal dimension (which represents the 'roughness') and the …

In this paper, we review the history, current state-of-art, and physical applications of the
spectral theory of two classes of random functions. One class consists of homogeneous and …

This paper reports a procedure to develop random fields of material properties on a
mesoscale level, coarser than the microscale level of heterogeneous material …

The paper considers mean-square continuous, wide-sense homogeneous, and isotropic
random fields taking values in a linear space of polyadics. We find a set of such fields whose …

The first group of articles concerns fractional models [1–4]. Patnaik et al.[1] propose a
fractional-order homogenization approach to model the elastic wave propagation in a bi …

The Matérn and the Generalized Cauchy families of covariance functions have a prominent
role in spatial statistics as well as in a wealth of statistical applications. The Matérn family is …

A new parametric class of covariance functions of wide-sense homogeneous and isotropic
random fields on Euclidean spaces is presented. While the new class possesses uncoupled …

Mechanics and physics of random media strongly suggest that stochastic PDEs and
stochastic finite element methods require mesoscale tensor-valued random fields (TRFs) of …

Wave propagation through random heterogeneous media is an important research area due
to its significance in engineering and science applications. This dissertation focuses on the …