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

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