In this second edition several new topics of technological interest have been added. These include: coupled mechanical and nonmechanical overall properties of heterogeneous piezoelectric materials, new upper and lower bounds for these coupled properties, a systematic comparison between the average-field theory and the results obtained using multi-scale perturbation theory, an account of the uniform-field theory, improveable bounds on overall moduli of heterogeneous materials which remain finite even when isolated cavities and rigid inclusions are present, and a brief account of a fundamental...

Most of the natural and biological phenomena such as solute transport in porous media exhibit variability which can not be modeled by using deterministic approaches. There is evidence in natural phenomena to suggest that some of the observations can not be explained by using the models which give deterministic solutions. Stochastic processes have a rich repository of objects which can be used to express the randomness inherent in the system and the evolution of the system over time. The attractiveness of the stochastic differential equations (SDE) and stochastic partial differential equations...

This book deals with the impact of uncertainty in input data on the outputs of mathematical models. Uncertain inputs as scalars, tensors, functions, or domain boundaries are considered. In practical terms, material parameters or constitutive laws, for instance, are uncertain, and quantities as local temperature, local mechanical stress, or local displacement are monitored. The goal of the worst scenario method is to extremize the quantity over the set of uncertain input data.

A general mathematical scheme of the worst scenario method, including approximation by finite element methods, is...

This volume emphasises studies related to
classical Stefan problems. The term "Stefan problem" is
generally used for heat transfer problems with
phase-changes such
as from the liquid to the solid. Stefan problems have some
characteristics that are typical of them, but certain problems
arising in fields such as mathematical physics and engineering
also exhibit characteristics similar to them. The term
classical" distinguishes the formulation of these problems from
their weak formulation, in which the solution need not possess
classical derivatives. Under suitable...