Mathematical and Computational Modeling – With Applications in the Natural and Social Sciences, Engineering, and the Arts
With Applications in Natural and Social Sciences, Engineering, and the Arts
Samenvatting
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–the–art 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. Mathematical and Computational Modeling: With Applications in the Natural and Social Sciences, Engineering, and the Arts 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, 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.
Specificaties
Inhoudsopgave
<p>PREFACE xv</p>
<p>SECTION 1 INTRODUCTION 1</p>
<p>1 Universality of Mathematical Models in Understanding Nature, Society, and Man–Made World 3<br />Roderick Melnik</p>
<p>1.1 Human Knowledge, Models, and Algorithms 3</p>
<p>1.2 Looking into the Future from a Modeling Perspective 7</p>
<p>1.3 What This Book Is About 10</p>
<p>1.4 Concluding Remarks 15</p>
<p>References 16</p>
<p>SECTION 2 ADVANCED MATHEMATICAL AND COMPUTATIONAL MODELS IN PHYSICS AND CHEMISTRY 17</p>
<p>2 Magnetic Vortices, Abrikosov Lattices, and Automorphic Functions 19<br />Israel Michael Sigal</p>
<p>2.1 Introduction 19</p>
<p>2.2 The Ginzburg Landau Equations 20</p>
<p>2.3 Vortices 25</p>
<p>2.4 Vortex Lattices 30</p>
<p>2.5 Multi–Vortex Dynamics 48</p>
<p>2.6 Conclusions 51</p>
<p>Appendix 2.A Parameterization of the equivalence classes [L] 51</p>
<p>Appendix 2.B Automorphy factors 52</p>
<p>References 54</p>
<p>3 Numerical Challenges in a Cholesky–Decomposed Local Correlation Quantum Chemistry Framework 59<br />David B. Krisiloff, Johannes M. Dieterich, Florian Libisch, and Emily A. Carter</p>
<p>3.1 Introduction 59</p>
<p>3.2 Local MRSDCI 61</p>
<p>3.3 Numerical Importance of Individual Steps 67</p>
<p>3.4 Cholesky Decomposition 68</p>
<p>3.5 Transformation of the Cholesky Vectors 71</p>
<p>3.6 Two–Electron Integral Reassembly 72</p>
<p>3.7 Integral and Execution Buffer 76</p>
<p>3.8 Symmetric Group Graphical Approach 77</p>
<p>3.9 Summary and Outlook 87</p>
<p>References 87</p>
<p>4 Generalized Variational Theorem in Quantum Mechanics 92<br />Mel Levy and Antonios Gonis</p>
<p>4.1 Introduction 92</p>
<p>4.2 First Proof 93</p>
<p>4.3 Second Proof 95</p>
<p>4.4 Conclusions 96</p>
<p>References 97</p>
<p>SECTION 3 MATHEMATICAL AND STATISTICAL MODELS IN LIFE AND CLIMATE SCIENCE APPLICATIONS 99</p>
<p>5 A Model for the Spread of Tuberculosis with Drug–Sensitive and Emerging Multidrug–Resistant and Extensively Drug–Resistant Strains 101<br />Julien Arino and Iman A. Soliman</p>
<p>5.1 Introduction 101</p>
<p>5.2 Discussion 117</p>
<p>References 119</p>
<p>6 The Need for More Integrated Epidemic Modeling with Emphasis on Antibiotic Resistance 121<br />Eili Y. Klein, Julia Chelen, Michael D. Makowsky, and Paul E. Smaldino</p>
<p>6.1 Introduction 121</p>
<p>6.2 Mathematical Modeling of Infectious Diseases 122</p>
<p>6.3 Antibiotic Resistance, Behavior, and Mathematical Modeling 125</p>
<p>6.4 Conclusion 128</p>
<p>References 129</p>
<p>SECTION 4 MATHEMATICAL MODELS AND ANALYSIS FOR SCIENCE AND ENGINEERING 135</p>
<p>7 Data–Driven Methods for Dynamical Systems: Quantifying Predictability and Extracting Spatiotemporal Patterns 137<br />Dimitrios Giannakis and Andrew J. Majda</p>
<p>7.1 Quantifying Long–Range Predictability and Model Error through Data Clustering and Information Theory 138</p>
<p>7.2 NLSA Algorithms for Decomposition of Spatiotemporal Data 163</p>
<p>7.3 Conclusions 184</p>
<p>References 185</p>
<p>8 On Smoothness Concepts in Regularization for Nonlinear Inverse Problems in Banach Spaces 192<br />Bernd Hofmann</p>
<p>8.1 Introduction 192</p>
<p>8.2 Model Assumptions, Existence, and Stability 195</p>
<p>8.3 Convergence of Regularized Solutions 197</p>
<p>8.4 A Powerful Tool for Obtaining Convergence Rates 200</p>
<p>8.5 How to Obtain Variational Inequalities? 206</p>
<p>8.6 Summary 215</p>
<p>References 215</p>
<p>9 Initial and Initial–Boundary Value Problems for First–Order Symmetric Hyperbolic Systems with Constraints 222<br />Nicolae Tarfulea</p>
<p>9.1 Introduction 222</p>
<p>9.2 FOSH Initial Value Problems with Constraints 223</p>
<p>9.3 FOSH Initial–Boundary Value Problems with Constraints 230</p>
<p>9.4 Applications 236</p>
<p>References 250</p>
<p>10 Information Integration, Organization, and Numerical Harmonic Analysis 254<br />Ronald R. Coifman, Ronen Talmon, Matan Gavish, and Ali Haddad</p>
<p>10.1 Introduction 254</p>
<p>10.2 Empirical Intrinsic Geometry 257</p>
<p>10.3 Organization and Harmonic Analysis of Databases/Matrices 263</p>
<p>10.4 Summary 269</p>
<p>References 270</p>
<p>SECTION 5 MATHEMATICAL METHODS IN SOCIAL SCIENCES AND ARTS 273</p>
<p>11 Satisfaction Approval Voting 275<br />Steven J. Brams and D. Marc Kilgour</p>
<p>11.1 Introduction 275</p>
<p>11.2 Satisfaction Approval Voting for Individual Candidates 277</p>
<p>11.3 The Game Theory Society Election 285</p>
<p>11.4 Voting for Multiple Candidates under SAV: A Decision–Theoretic Analysis 287</p>
<p>11.5 Voting for Political Parties 291</p>
<p>11.6 Conclusions 295</p>
<p>11.7 Summary 296</p>
<p>References 297</p>
<p>12 Modeling Musical Rhythm Mutations with Geometric Quantization 299<br />Godfried T. Toussaint</p>
<p>12.1 Introduction 299</p>
<p>12.2 Rhythm Mutations 301</p>
<p>12.3 Similarity–Based Rhythm Mutations 303</p>
<p>12.4 Conclusion 306</p>
<p>References 307</p>
<p>INDEX 309</p>