Tomarelli Variational Problems in Materials Science

1. Auflage 2006
ISBN: 978-3-7643-7565-2
Verlag: Springer
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 162 Seiten

This volume contains the proceedings of the international workshop Variational Problems in Materials Science. Coverage includes the study of BV vector fields, path functionals over Wasserstein spaces, variational approaches to quasi-static evolution, free-discontinuity problems with applications to fracture and plasticity, systems with hysteresis or with interfacial energies, evolution of interfaces, multi-scale analysis in ferromagnetism and ferroelectricity, and much more.

Autoren/Hrsg.

Tomarelli, Franco

Inhaltsverzeichnis

1;Contents;5
2;Preface;6
3;Invited Lectures;8
4;Remarks on a Multiscale Approach to;10
5;Grain Growth in Polycrystals;10
5.1;Introduction;10
5.2;1. Recapitulation of grain growth;11
5.3;2. Master equation approach to evolution;12
5.4;3. Comparison with experiments;17
5.5;References;19
6;Another Brick in the Wall;21
6.1;1. Introduction;21
6.2;2. Statement of the problem and main result;23
6.3;3. Proof of the result;27
6.4;4. Perspectives;31
6.5;References;31
7;Variational Problems for Functionals Involving the Value Distribution;33
7.1;1. Introduction;33
7.2;2. Value distributions and optimization problems;35
7.3;3. Generalized volume constraints;39
7.4;4. Symmetry breaking solutions;45
7.5;References;48
8;Bi-Modal Cohesive Energies;50
8.1;1. Introduction;50
8.2;2. The model;51
8.3;3. Equilibrium;52
8.4;4. Energy minimizers;53
8.5;5. Equilibrium branches and response curves;54
8.6;6. Response curves for a bi-modal cohesive energy;55
8.7;7. Stress oscillation and damage;58
8.8;References;61
9;Asymptotics of Boundary Value Problems for Supercritical Ginzburg-Landau Energies;82
9.1;1. Introduction;82
9.2;2. Notation and preliminaries;84
9.3;3. Results;86
9.4;4. Comments and remarks;89
9.5;References;91
10;An Introduction to H-measures and Their Applications;92
10.1;1. Introduction;92
10.2;2. H-measures or microlocal defect measures;96
10.3;3. A compactness theorem for the wave equation;107
10.4;References;117
11;A Singular Perturbation Result with a Fractional Norm;118
11.1;1. Introduction;118
11.2;2. The;120
11.3;convergence;120
11.4;result;120
11.5;3. The optimal pro.le problem;121
11.6;4. Compactness;126
11.7;5. Lower bound inequality;128
11.8;6. Upper bound inequality;131
11.9;References;132
12;Smooth and Creased Equilibria for Elastic-plastic Plates and Beams;134
12.1;1. Introduction;134
12.2;2. Regular minimizers for clamped elastic-plastic plates;135
12.3;3. The clamped elastic-plastic beam;136
12.4;4. Existence and properties of creased minimizers;140
12.5;References;143
13;On Concentrated Contact Interactions;144
13.1;1. Introduction;144
13.2;2. The Flamant stress .eld in a half-plane;146
13.3;3. Sutured Flamant stress .elds in a plane;150
13.4;4. Concentrated couple applied at the boundary of a half-plane;152
13.5;References;154
14;Discontinuous Hysteresis and P.D.E.s;155
14.1;1. Hysteresis;155
14.2;2. Discontinuous hysteresis and the Preisach model;158
14.3;3. On First-order P.D.E. with discontinuous hysteresis;161
14.4;References;164
15;List of Registered Participants;166