Related papers: Statistical theory of structures with extended def…

The growth dynamics of a single crack in a heterogeneous material under subcritical loading is an intermittent process; and many features of this dynamics have been shown to agree with simple models of thermally activated rupture. In order…

Solid state impedance spectroscopy enables the various contributions to the resistive and capacitive properties of electronically inhomogeneous condensed matter to be deconvoluted and characterized separately. The different contributions…

In this article we review classical and recent results in anomalous diffusion and provide mechanisms useful for the study of the fundamentals of certain processes, mainly in condensed matter physics, chemistry and biology. Emphasis will be…

Long range order and symmetry in heterogeneous materials architected on crystal lattices lead to elastic and inelastic anisotropies and thus limit mechanical functionalities in particular crystallographic directions. Here, we present a…

This paper studies the problem of estimation from relative measurements in a graph, in which a vector indexed over the nodes has to be reconstructed from pairwise measurements of differences between its components associated to nodes…

We consider the problem of goodness-of-fit testing for a model that has at least one unknown parameter that cannot be eliminated by transformation. Examples of such problems can be as simple as testing whether a sample consists of…

We consider the problem of determining, within an elastic isotropic nanoplate in bending, the possible presence of an inclusion made of different elastic material. Under suitable a priori assumptions on the unknown inclusion, we provide…

We study the random walk of a particle in a compartmentalized environment, as realized in biological samples or solid state compounds. Each compartment is characterized by its length $L$ and the boundaries transmittance $T$. We identify two…

In Part I of this paper we have presented a simple model capable of describing the localized failure of a massive structure. In this part, we discuss the identification of the model parameters from two kinds of experiments: a uniaxial…

A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…

For many materials, macroscopic mechanical behavior is determined by an intricate microstructure. Understanding the relation between these two scales helps scientists and engineers design better materials. The relation which maps…

The evolution of local defects such as dislocations and cracks often determines the performance of engineering materials. For a proper description and understanding of these phenomena, one needs to descend to a very small scale, at which…

Materials characterization and property measurements are a cornerstone of material science, providing feedback from synthesis to applications. Traditionally, a single sample is used to derive information on a single point in composition…

Using the superstatistics method, we propose an extension of the random matrix theory to cover systems with mixed regular-chaotic dynamics. Unlike most of the other works in this direction, the ensembles of the proposed approach are basis…

Quantitative measurements of extended defects in crystalline materials are important in understanding material behaviour. X-ray line profile analysis provides a complement to direct counting in the electron microscope, but is an indirect…

We study a generalized notion of a homogeneous skew-product extension of a probability-preserving system in which the homogeneous space fibres are allowed to vary over the ergodic decomposition of the base. The construction of such…

We study deterministic discrete time exclusion type spatially heterogeneous particle processes in continuum. A typical example of this sort is a traffic flow model with obstacles: traffic lights, speed bumps, spatially varying local…

With full knowledge of a material's atomistic structure, it is possible to predict any macroscopic property of interest. In practice, this is hindered by limitations of the chosen characterisation techniques. For example, electron…

Heterogeneity of many building materials complicates numerical modelling of structural behaviour. The material randomicity can be manifested by different values of material parameters of each material specimen. To capture inherent…

The self-assembly of complex structures from engineered subunits is a major goal of nanotechnology, but controlling their size becomes increasingly difficult in larger assemblies. Existing strategies present significant challenges, among…