Nonlocal continuum field theories are concerned with material bodies whose behavior at any interior point depends on the state of all other points in the body -- rather than only on an effective field resulting from these points -- in addition to its own state and the state of some calculable external field. Nonlocal field theory extends classical field theory by describing the responses of points within the medium by functionals rather than functions (the "constitutive relations" of classical field theory). Such considerations are already well known in solid-state physics, where the nonlocal interactions between the atoms are prevalent in determining the properties of the material. The tools developed for crystalline materials, however, do not lend themselves to analyzing amorphous materials, or materials in which imperfections are a major part of the structure. Nonlocal continuum theories, by contrast, can describe these materials faithfully at scales down to the lattice parameter. This book presents a unified approach to field theories for elastic solids, viscous fluids, and heat-conducting electromagnetic solids and fluids that include nonlocal effects in both space and time (memory effects). The solutions to the field equations agree remarkably well with atomic theories and experimental observations.

Aims to give to the reader the tools necessary to apply semi-Markov processes in real-life problems.

The book is self-contained and, starting from a low level of probability concepts, gradually brings the reader to a deep knowledge of semi-Markov processes.

Presents homogeneous and non-homogeneous semi-Markov processes, as well as Markov and semi-Markov rewards processes.

The concepts are fundamental for many applications, but they are not as thoroughly presented in other books on the subject as they are here.