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Gauge theory and defects in solids /
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...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Amsterdam ; New York : New York, N.Y., U.S.A. :
North-Holland ; Sole distributors for the U.S.A. and Canada, Elsevier Science Pub. Co.,
1988.
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| Colección: | Mechanics and physics of discrete systems ;
v. 1. |
| Temas: | |
| Acceso en línea: | Texto completo Texto completo |
Tabla de Contenidos:
- 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 Kr�oner 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