Category - "States of Matter"

This monograph focuses on the modeling of continua that exhibit the
property of singularities in fields. A rational theory of continuum
thermomechanics that takes into account the existence and distribution
of scalar and vector discontinuities is presented. The required
mathematical background is given; basic understanding of differential
geometry and tensor analysis is helpful. Largely self-contained work
should serve a readership of graduate students, researchers, and
engineers in applied mathematics, mechanics, and physics.

A defining feature of nonlinear hyperbolic equations is the occurrence of shock waves. Most computational fluid dynamics for this class of problems centers on how to effectively deal with shocks using shock capturing techniques. An alternative approach is the shock-fitting method, which treats shock waves as well as other singularities as discontinuous surfaces satisfying Rankine–Hugoniot jump conditions. This book provides a self-contained treatment of shock-fitting methods. It covers shock detection, shocks as boundaries, and shocks imbedded in the flow. Numerous examples illustrate the techniques using MATLAB and a companion CD-ROM provides all of the codes.

This second edition conducts a grand tour of the fundamental theories that shape our modern understanding of the physical world. The book covers the central themes of space-time geometry and the general relativistic account of gravity, quantum mechanics and quantum field theory, gauge theories and the fundamental forces of nature, statistical mechanics, and the theory of phase transitions. The basic structure of each theory is explained in explicit mathematical detail with emphasis on conceptual understanding rather than on the technical details of specialized applications. The book gives straightforward accounts of the standard models of particle physics and cosmology.

Through the 'magic' of averages it is shown that Maxwell's equations can be used in a simple way to describe filamentary composites as well as pure bulk superconductors. The second edition of AC Loss and Macroscopic Theory of Superconductors, like the first edition, is written for both physicists and engineers. It starts with a rigorous and partially new derivation of Maxwell's equations as they apply to superconductors, and the remainder of the book is devoted to loss approximations for a wide range of applications. The chapters on high-Tc materials were updated and include a change to SI units and the addition of some historical perspective.