This new series Mechanics and Physics of Discrete Systems aims to provide a coherent picture of the modern development of discrete physical systems. Each volume will offer an orderly perspective of disciplines such as molecular dynamics, crystal mechanics and/or physics, dislocation, etc. Emphasized in particular are the fundamentals of mechanics and physics that play an essential role in engineering applications.Volume 1, Gauge Theory and Defects in Solids, presents a detailed development of a rational theory of the dynamics of defects and damage in solids. Solutions to field equations are used to determine stresses, dislocation densities and currents that arise from histories of loading of boundaries of bodies. Analysed in detail is a gauge theory with a gauge group that is not semi-simple, and whose action occurs at the classical macroscopic level. Yang-Mills theory is applied where the state variables are elastic displacements in solids, determination of mechanical and electromagnetic observables by choice of gauge conditions is demonstrated, and practices of classical dislocation theory are derived from first principles.

The importance of gauge theory for elementary particle physics is by now firmly established. Recent experiments have yielded convincing evidence for the existence of intermediate bosons, the carriers of the electroweak gauge force, as well as for the presence of gluons, the carriers of the strong gauge force, in hadronic interactions. For the gauge theory of strong interactions, however, a number of important theoretical problems remain to be definitely resolved. They include the quark confinement problem, the quantitative study of the hadron mass spectrum as well as the role of topology in quantum gauge field theory. These problems require for their solution the development and application of non-perturbative methods in quantum gauge field theory. These problems, and their non-perturbative analysis, formed the central interest of the 1983 Cargese summer institute on "Progress in Gauge Field Theory. " In this sense it was a natural sequel to the 1919 Cargese summer institute on "Recent Developments in Gauge Theories. " Lattice gauge theory provides a systematic framework for the investigation of non-perturbative quantum effects. Accordingly, a large number of lectures dealt with lattice gauge theory. Following a systematic introduction to the subject, the renormalization group method was developed both as a rigorous tool for fundamental questions, and in the block-spin formulation, the computations by Monte Carlo programs. A detailed analysis was presented of the problems encountered in computer simulations. Results obtained by this method on the mass spectrum were reviewed.

This book is an homage to the pioneering works of E. Aero and G. Maugin in the area of analytical description of generalized continua. It presents a collection of contributions on micropolar, micromorphic and strain gradient media, media with internal variables, metamaterials, beam lattices, liquid crystals, and others. The main focus is on wave propagation, stability problems, homogenization, and relations between discrete and continuous models.

Yi-Shi Duan (1927-2016) was one of the world-renowned pioneers in the study of gauge field theory and general relativity. Trained in the former Soviet Union, Prof. Duan returned to China in 1957 to work in Lanzhou University for 60 years. In 1963, he came up with a general co-variant form of the conservation law of the energy-momentum tensor in general relativity. In 1979, he suggested that the gauge potential could be decomposed, which has important implications to gauge field theory. He trained in China a big team of talents in theoretical physics. His contributions to theoretical physics in China have earned him praise from both Professor Shiing-Shen Chern and Professor Chen-Ning Yang.

This volume introduces a comprehensive theory of deformation and fracture to engineers and applied scientists. Here “comprehensive” means that the theory can describe all stages of deformation from elastic to plastic and plastic to fracturing stage on the same basis (equations). The comprehensive approach is possible because the theory is based on a fundamental physical principle called the local symmetry, or gauge invariance, as opposed to phenomenology. Professor Yoshida explains the gist of local symmetry (gauge invariance) intuitively so that engineers and applied physicists can digest it easily, rather than describing physical or mathematical details of the principle. The author also describes applications of the theory to practical engineering, such as nondestructive testing in particular, with the use of an optical interferometric technique called ESPI (Electronic Speckle-Pattern Interferometry).The book is not a manual of applications. Instead, it provides information on how to apply physical concepts to engineering applications.

This volume comprises the Proceedings of the Yamada Conference IX on Dislocations in Solids, held in August 1984 in Tokyo. The purpose of the conference was two-fold: firstly to evaluate the increasing data on basic properties of dislocations and their interaction with other types of defects in solids and, secondly, to increase understanding of the material properties brought about by dislocation-related phenomena. Metals and alloys, semi-conductors and ions crystals were discussed. One of the important points of contention was the electronic state at the core of dislocation. Another was the dislocation model of amorphous structure.

In their 1909 publication Théorie des corps déformables, Eugène and François Cosserat made a historic contribution to materials science by establishing the fundamental principles of the mechanics of generalized continua. The chapters collected in this volume showcase the many areas of continuum mechanics that grew out of the foundational work of the Cosserat brothers. The included contributions provide a detailed survey of the most recent theoretical developments in the field of generalized continuum mechanics and can serve as a useful reference for graduate students and researchers in mechanical engineering, materials science, applied physics and applied mathematics.