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Edelen, Dominic G. B.

Gauge theory and defects in solids

Edelen, Dominic G. B.

9780444702999

9780444600103

9781299537644

Edelen, Dominic G. B.

Amsterdam ; New York : North-Holland ; New York, N.Y., U.S.A. : Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co., 1988.

1 online resource (x, 427 pages) : illustrations.

Mechanics and physics of discrete systems ; v. 1

Mechanics and physics of discrete systems ; v. 1.

Front Cover; Gauge Theory and Defects in Solids; Copyright Page; Introduction to the Series; Table of Contents; Chapter 1.Foundations; 1.1 Concepts from Exterior Calculus; 1.2 Antiexact Exterior Differential Forms; 1.3 Calculus of Variations and Noether's Theorems; 1.4 Elasticity via the Exterior Calculus; 1.5 The Fundamental Group of Elasticity; Chapter 2.Gauge Theory for Matrix Lie Groups; 2.1 Matter Fields and Variational Principles; 2.2 Local Inhomogeneous Action of the Symmetry Group; 2.3 Minimal Replacement

2.4 The Gauge Covariant Exterior Derivative and the Resulting Equations of Structure2.5 Minimal Coupling vs Minimal Derivative Coupling; 2.6 Orbits of the Gauge Group and the Antiexact Gauge; Chapter 3.Kinematics of Defects; 3.1 The Kinematics of Defects via the Exterior Calculus; 3.2 A 4-Dimensional Formulation; 3.3 Abelian Gauge Transformations and the Golebiewska Gauge; 3.4 Identification with the Cartan Equations of Structure; 3.5 Classic Dislocation Theory; 3.6 Unresolved Questions; Chapter 4.Inhomogeneous Action of the Fundamental Group; 4.1 A Working Geometric Model

4.2 Matrix Representation and Minimal Replacement4.3 Curvature and Torsion of the Gauge Connection; 4.4 Transformations Induced by the Gauge Group; 4.5 The Antiexact Gauge and Canonical Forms; 4.6 Complete Integrability and Reduction to Elasticity; 4.7 The Identification Problem; 4.8 The Induced Pull-Back and Push-Forward Maps; Chapter 5.Kinetics of Defects in Elastic Dielectrics; 5.1 The Lagrangian for Elastic Dielectrics; 5.2 The Yang-Mills Gauge Process; 5.3 Minimal Derivative Coupling and Invariance Identities; 5.4 Transformations Induced by the Gauge Group; 5.5 Variational Considerations

5.6 Field Equations for the Original State Variables5.7 Balance of Dislocations; 5.8 Balance of Disclinations; 5.9 Integrability Conditions and the Balance of Moment of Momentum; 5.10 The Momentum-Energy Complex and Excesses; 5.11 The Governing Equations of Defect Dynamics; 5.12 Gauge Theories for Subgroups of the Gauge Group; Chapter 6.Gauge Conditions, Observables, and Internal Space; 6.1 Transformations Induced by Local Action of the GaugeGroup; 6.2 Internal Observers and the Kröner Gauge; 6.3 The Antiexact Gauge; 6.4 A Simple Geometric Interpretation; 6.5 Mechanical Observables

6.6 Electromagnetic Observables6.7 Burgers and Frank Vectors; 6.8 Internal Space-Time and Its Geometry; 6.9 Transformations and Interpretations; Chapter 7. Boundary Conditions, Null Lagrangians, and Effective Stresses; 7.1 Evaluation of the Variational Boundary Integral; 7.2 Boundary Conditions for the Compensating Fields; 7.3 Dirichlet and Homogeneous Neumann Data for the Original State Variables; 7.4 Null Lagrangians and Inhomogeneous Neumann Data for Elastic Dielectrics; 7.5 Images of Null Lagrangians under Minimal Replacement; 7.6 Inhomogeneous Neumann Data when Defects are Present

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.

Solids -- Mathematics.

Crystals -- Defects -- Mathematics.

Gauge fields (Physics)

Champs de jauge (Physique)

Solides.

Cristaux Defauts -- Mathématiques.

SCIENCE -- Physics -- Condensed Matter.

Crystals -- Defects -- Mathematics. (OCoLC)fst00884678

Gauge fields (Physics) (OCoLC)fst00938995

Solids -- Mathematics. (OCoLC)fst01125517

Solides -- Défauts.

Solides -- Mathématiques.

Élasticité.

Eichtheorie.

Festkörper.

Gitterbaufehler.

Electronic books.

Lagoudas, Dimitris C.

ScienceDirect http://www.sciencedirect.com/science/book/9780444702999