Goldstein / Rosencrans / Sod Mathematics Applied to Science

In Memoriam Edward D. Conway
1. Auflage 2014
ISBN: 978-1-4832-7198-9
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 332 Seiten, Web PDF

Mathematics Applied to Science: In Memoriam Edward D. Conway presents a compilation of articles as a lasting tribute to Edward Conway III. This book covers a variety of topics, including molecular electronic energies, partial differential equations, density matrix, electron density functional, and climate change. Organized into 13 chapters, this book begins with an overview of the large-time behavior of one-dimensional motion in a model gas whose particles have a discrete set of allowed velocities. This text then explores the operator splitting techniques for the solution of time dependent differential equations. Other chapters describe a Monte Carlo simulation procedure for evaluating the relaxation rate of an excited state vibrational population of a diatomic in a simple solvent. This book discusses as well the numerical solution of nonlinear differential equations. The final chapter deals with the physical, thermal, and dynamical properties near the surface of the Earth. This book is a valuable resource for mathematicians.

Autoren/Hrsg.

Goldstein, Jerome

Rosencrans, Steven

Sod, Gary

Inhaltsverzeichnis

1;Front Cover;1
2;Mathematics Applied to Science: In Memoriam Edward D. Conway;4
3;Copyright Page;5
4;Table of Contents;6
5;Contributors;8
6;Preface;10
7;Biographical Sketch of Edward D. Conway;14
8;Scientific Biographical Sketch of Edward D. Conway;16
9;List of Articles by Edward D. Conway;20
10;CHAPTER 1. LARGE-TIME BEHAVIOR OF MODEL GASES WITH A DISCRETE SET OF VELOCITIES;24
10.1;1. INTRODUCTION;24
10.2;2. FUNDAMENTAL PROPERTIES;27
10.3;3. ESTIMATES IN HIGHER NORMS;29
10.4;4. ASYMPTOTIC BEHAVIOR IN L;31
10.5;5. CONCLUSION;33
10.6;REFERENCES;35
11;CHAPTER 2. APPLICATIONS OF OPERATOR SPLITTING METHODS TO THE NUMERICAL SOLUTION OF NONLINEAR PROBLEMS IN CONTINUUM MECHANICS AND PHYSICS;36
11.1;ABSTRACT;36
11.2;1. GENERALITIES AND SYNOPSIS;36
11.3;2. DESCRIPTION OF SOME BASIC OPERATOR SPLITTING METHODS FOR TIME DEPENDENT PROBLEMS;37
11.4;3. APPLICATION TO THE NAVIER-STOKES EQUATIONS FOR INCOMPRESSIBLE VISCOUS FLUIDS;50
11.5;4. APPLICATION TO LINEAR AND NONLINEAR EIGENVALUE PROBLEMS;68
11.6;5. APPLICATION TO LIQUID CRYSTAL CALCULATIONS;74
11.7;6. CONCLUSION;83
11.8;ACKNOWLEDGEMENTS;83
11.9;REFERENCES;84
12;CHAPTER 3. ON AN ASYMPTOTIC MODEL FOR MACH STEM FORMATION IN PLANAR DETONATIONS;88
12.1;1. INTRODUCTION;88
12.2;2. THE MAJDA-ROSALES SCHEME;90
12.3;3. ANALYTICAL RESULTS;94
12.4;REFERENCES;101
13;CHAPTER 4. GROWTH OF CELL POPULATIONS VIA ONE-PARAMETER SEMIGROUPS OF POSITIVE OPERATORS;102
13.1;1. AN EQUATION DESCRIBING CELL SIZE DISTRIBUTION AS A CONCRETE AND ABSTRACT CAUCHY PROBLEM;103
13.2;2. WELL-POSED ABSTRACT CAUCHY PROBLEMS AND STRONGLY CONTINUOUS SEMIGROUPS;104
13.3;3. ASYMPTOTIC BEHAVIOR OF STRONGLY CONTINUOUS SEMIGROUPS;108
13.4;4. ASYMPTOTIC BEHAVIOR OF POSITIVE SEMIGROUPS;113
13.5;5. AN EXAMPLE;120
13.6;REFERENCES;127
14;CHAPTER 5. SOLVENT INDUCED RELAXATION OF EXCITED STATE VIBRATIONAL POPULATIONS OF DIATOMICS: A MIXED QUANTUM-CLASSICAL SIMULATION;130
14.1;ABSTRACT;130
14.2;I. INTRODUCTION;130
14.3;II. THEORY;132
14.4;3. RESULTS AND DISCUSSION;145
14.5;4. SUMMARY;148
14.6;ACKNOWLEDGEMENT;149
14.7;REFERENCES;149
15;CHAPTER 6. MOVING MESH METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS;152
15.1;ABSTRACT;152
15.2;1. INTRODUCTION;152
15.3;2. SOFTWARE DESIGN;156
15.4;3. TIME DISCRETIZATION;157
15.5;4. DYNAMIC REZONING;158
15.6;5. MESH REGULARITY;166
15.7;6. NUMERICAL EXAMPLE;171
15.8;7. CONCLUSIONS;173
15.9;ACKNOWLEDGMENTS;174
15.10;REFERENCES;174
16;CHAPTER 7. OSCILLATORY SOLUTIONS OF PARTIAL DIFFERENTIAL AND DIFFERENCE EQUATIONS;178
16.1;ACKNOWLEDGEMENTS;192
16.2;REFERENCES;192
17;8. THE QUANTUM-MECHANICAL HARTREE-FOCK STAIRCASE METHOD FOR MOLECULAR ELECTRONIC ENERGIES;194
17.1;ABSTRACT;194
17.2;I. INTRODUCTION;194
17.3;2. HARTREE-FOCK STAIRCASE METHOD;197
17.4;3. ANALYSIS OF THE STAIRCASE METHOD;203
17.5;4. AN OPEN MATHEMATICAL QUESTION AND CONCLUDING REMARKS;207
17.6;REFERENCES;209
18;CHAPTER 9. ELECTRON DENSITY FUNCTIONALS FROM THE GRADIENT EXPANSION OF THE DENSITY MATRIX: THE TROUBLE WITH LONG-RANGE INTERACTIONS;210
18.1;ABSTRACT;210
18.2;1. DENSITY FUNCTIONAL THEORY;211
18.3;2. KINETIC AND EXCHANGE ENERGIES;213
18.4;3. DENSITY MATRIX AND ITS GRADIENT EXPANSION;216
18.5;4. GRADIENT EXPANSION OF THE EXCHANGE ENERGY;222
18.6;5. INCONCLUSIVE NUMERICAL EXPERIMENT ON THE GRADIENT COEFFICIENT;226
18.7;6. DERIVATIONS FROM LINEAR-RESPONSE THEORY;228
18.8;REFERENCES;231
19;CHAPTER 10. DYNAMICS OF SYSTEMS IN CLOSE-TO-CONTINUUM CONDITIONS;234
19.1;ABSTRACT;234
19.2;1. OUTLINE OF THE METHOD;234
19.3;2. APPLICATIONS (Summary);239
19.4;REFERENCES;241
20;CHAPTER 11. HAMILTONIAN DYNAMICS OF RIEMANN ELLIPSOIDS;242
20.1;1. INTRODUCTION;242
20.2;2. RIEMANN ELLIPSOIDS;248
20.3;3. OBSERVABLES;251
20.4;4. EULER EQUATIONS;252
20.5;5. LAGRANGE FORMULATION;254
20.6;6. HAMILTONIAN FORMULATION;256
20.7;7. S-TYPE RIEMANN ELLIPSOIDS;261
20.8;8. GEOMETRIC QUANTIZATION;264
20.9;9. CONCLUSION;266
20.10;REFERENCES;268
21;CHAPTER 12. ASYMMETRIC SOLUTIONS OF PROBLEMS WITH SYMMETRY;272
21.1;1. INTRODUCTION;272
21.2;2. POSITIVE SOLUTIONS OF THE DIRICHLET PROBLEM;275
21.3;3. GENERAL BOUNDARY CONDITIONS; A UNIVERSALITY THEOREM;279
21.4;REFERENCES;284
22;CHAPTER 13. THE MATHEMATICS IN CLIMATE CHANGE;286
22.1;1. INTRODUCTION;286
22.2;2. THE THINGS THAT NEED TO BE EXPLAINED;290
22.3;3. THE OVERALL PHILOSOPHY OF THE PRESENT APPROACH;299
22.4;ORGANIZATION OF THE RAMAINDER OF THIS PAPER;302
22.5;5. THE ORIGIN OF THE PLEISTOCENE ICE AGE;303
22.6;5. CLIMATES WITHIN THE OCEAN;315
22.7;6. ABRUPT CLIMATIC EVENTS;322
22.8;REFERENCES;330