Mathematical and Computational Modeling With Applications in Natural and Social Sciences, Engineering, and the Arts

Illustrates the application of mathematical and computational modeling in a variety of disciplines

With an emphasis on the interdisciplinary nature of mathematical and computational modeling, Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts features chapters written by well-known, international experts in these fields and presents readers with a host of state-of-theart achievements in the development of mathematical modeling and computational experiment methodology. The book is a valuable guide to the methods, ideas, and tools of applied and computational mathematics as they apply to other disciplines such as the natural and social sciences, engineering, and technology. The book also features:

• Rigorous mathematical procedures and applications as the driving force behind mathematical innovation and discovery
• Numerous examples from a wide range of disciplines to emphasize the multidisciplinary application and universality of applied mathematics and mathematical modeling
• Original results on both fundamental theoretical and applied developments in diverse areas of human knowledge
• Discussions that promote interdisciplinary interactions between mathematicians, scientists, and engineers

Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts is an ideal resource for professionals in various areas of mathematical and statistical sciences, modeling and simulation, physics, computer science, engineering, biology and chemistry, and industrial and computational engineering. The book also serves as an excellent textbook for graduate courses in mathematical modeling, applied mathematics, numerical methods, operations research, and optimization.

LIST OF CONTRIBUTORS xiii

PREFACE xv

SECTION 1 INTRODUCTION 1

1 Universality of Mathematical Models in Understanding Nature, Society, and Man-Made World 3
Roderick Melnik

1.1 Human Knowledge, Models, and Algorithms 3

1.2 Looking into the Future from a Modeling Perspective 7

1.3 What This Book Is About 10

1.4 Concluding Remarks 15

References 16

SECTION 2 ADVANCED MATHEMATICAL AND COMPUTATIONAL MODELS IN PHYSICS AND CHEMISTRY 17

2 Magnetic Vortices, Abrikosov Lattices, and Automorphic Functions 19
Israel Michael Sigal

2.1 Introduction 19

2.2 The Ginzburg–Landau Equations 20

2.3 Vortices 25

2.4 Vortex Lattices 30

2.5 Multi-Vortex Dynamics 48

2.6 Conclusions 51

Appendix 2.A Parameterization of the equivalence classes [L] 51

Appendix 2.B Automorphy factors 52

References 54

3 Numerical Challenges in a Cholesky-Decomposed Local Correlation Quantum Chemistry Framework 59
David B. Krisiloff, Johannes M. Dieterich, Florian Libisch, and Emily A. Carter

3.1 Introduction 59

3.2 Local MRSDCI 61

3.3 Numerical Importance of Individual Steps 67

3.4 Cholesky Decomposition 68

3.5 Transformation of the Cholesky Vectors 71

3.6 Two-Electron Integral Reassembly 72

3.7 Integral and Execution Buffer 76

3.8 Symmetric Group Graphical Approach 77

3.9 Summary and Outlook 87

References 87

4 Generalized Variational Theorem in Quantum Mechanics 92
Mel Levy and Antonios Gonis

4.1 Introduction 92

4.2 First Proof 93

4.3 Second Proof 95

4.4 Conclusions 96

References 97

SECTION 3 MATHEMATICAL AND STATISTICAL MODELS IN LIFE AND CLIMATE SCIENCE APPLICATIONS 99

5 A Model for the Spread of Tuberculosis with Drug-Sensitive and Emerging Multidrug-Resistant and Extensively Drug-Resistant Strains 101
Julien Arino and Iman A. Soliman

5.1 Introduction 101

5.2 Discussion 117

References 119

6 The Need for More Integrated Epidemic Modeling with Emphasis on Antibiotic Resistance 121
Eili Y. Klein, Julia Chelen, Michael D. Makowsky, and Paul E. Smaldino

6.1 Introduction 121

6.2 Mathematical Modeling of Infectious Diseases 122

6.3 Antibiotic Resistance, Behavior, and Mathematical Modeling 125

6.4 Conclusion 128

References 129

SECTION 4 MATHEMATICAL MODELS AND ANALYSIS FOR SCIENCE AND ENGINEERING 135

7 Data-Driven Methods for Dynamical Systems: Quantifying Predictability and Extracting Spatiotemporal Patterns 137
Dimitrios Giannakis and Andrew J. Majda

7.1 Quantifying Long-Range Predictability and Model Error through Data Clustering and Information Theory 138

7.2 NLSA Algorithms for Decomposition of Spatiotemporal Data 163

7.3 Conclusions 184

References 185

8 On Smoothness Concepts in Regularization for Nonlinear Inverse Problems in Banach Spaces 192
Bernd Hofmann

8.1 Introduction 192

8.2 Model Assumptions, Existence, and Stability 195

8.3 Convergence of Regularized Solutions 197

8.4 A Powerful Tool for Obtaining Convergence Rates 200

8.5 How to Obtain Variational Inequalities? 206

8.6 Summary 215

References 215

9 Initial and Initial-Boundary Value Problems for First-Order Symmetric Hyperbolic Systems with Constraints 222
Nicolae Tarfulea

9.1 Introduction 222

9.2 FOSH Initial Value Problems with Constraints 223

9.3 FOSH Initial-Boundary Value Problems with Constraints 230

9.4 Applications 236

References 250

10 Information Integration, Organization, and Numerical Harmonic Analysis 254
Ronald R. Coifman, Ronen Talmon, Matan Gavish, and Ali Haddad

10.1 Introduction 254

10.2 Empirical Intrinsic Geometry 257

10.3 Organization and Harmonic Analysis of Databases/Matrices 263

10.4 Summary 269

References 270

SECTION 5 MATHEMATICAL METHODS IN SOCIAL SCIENCES AND ARTS 273

11 Satisfaction Approval Voting 275
Steven J. Brams and D. Marc Kilgour

11.1 Introduction 275

11.2 Satisfaction Approval Voting for Individual Candidates 277

11.3 The Game Theory Society Election 285

11.4 Voting for Multiple Candidates under SAV: A Decision-Theoretic Analysis 287

11.5 Voting for Political Parties 291

11.6 Conclusions 295

11.7 Summary 296

References 297

12 Modeling Musical Rhythm Mutations with Geometric Quantization 299
Godfried T. Toussaint

12.1 Introduction 299

12.2 Rhythm Mutations 301

12.3 Similarity-Based Rhythm Mutations 303

12.4 Conclusion 306

References 307

INDEX 309

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