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E-raamat: Mathematical and Computational Modeling: With Applications in Natural and Social Sciences, Engineering, and the Arts

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Mathematical and Computational Modeling 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(16)
1 Universality of Mathematical Models in Understanding Nature, Society, and Man-Made World
3(14)
Roderick Melnik
1.1 Human Knowledge, Models, and Algorithms,
3(4)
1.2 Looking into the Future from a Modeling Perspective,
7(3)
1.3 What This Book Is About,
10(5)
1.4 Concluding Remarks,
15(1)
References,
16(1)
Section 2 Advanced Mathematical And Computational Models In Physics And Chemistry 17(82)
2 Magnetic Vortices, Abrikosov Lattices, and Automorphic Functions
19(40)
Israel Michael Sigal
2.1 Introduction,
19(1)
2.2 The Ginzburg—Landau Equations,
20(5)
2.2.1 Ginzburg—Landau energy,
21(1)
2.2.2 Symmetries of the equations,
21(1)
2.2.3 Quantization of flux,
22(1)
2.2.4 Homogeneous solutions,
22(1)
2.2.5 Type I and Type II superconductors,
23(1)
2.2.6 Self-dual case κ =1/square root of 2,
24(1)
2.2.7 Critical magnetic fields,
24(1)
2.2.8 Time-dependent equations,
25(1)
2.3 Vortices,
25(5)
2.3.1 n-vortex solutions,
25(1)
2.3.2 Stability,
26(4)
2.4 Vortex Lattices,
30(18)
2.4.1 Abrikosov lattices,
31(1)
2.4.2 Existence of Abrikosov lattices,
31(3)
2.4.3 Abrikosov lattices as gauge-equivariant states,
34(1)
2.4.4 Abrikosov function,
34(1)
2.4.5 Comments on the proofs of existence results,
35(5)
2.4.6 Stability of Abrikosov lattices,
40(2)
2.4.7 Functions γδ(τ), δ > 0,
42(3)
2.4.8 Key ideas of approach to stability,
45(3)
2.5 Multi-Vortex Dynamics,
48(3)
2.6 Conclusions,
51(1)
Appendix 2.A Parameterization of the equivalence classes [ L],
51(1)
Appendix 2.B Automorphy factors,
52(2)
References,
54(5)
3 Numerical Challenges in a Cholesky-Decomposed Local Correlation Quantum Chemistry Framework
59(33)
David B. Krisiloff
Johannes M. Dieterich
Florian Libisch
Emily A. Carter
3.1 Introduction,
59(2)
3.2 Local MRSDCI,
61(6)
3.2.1 MRSDCI,
61(1)
3.2.2 Symmetric group graphical approach,
62(2)
3.2.3 Local electron correlation approximation,
64(2)
3.2.4 Algorithm summary,
66(1)
3.3 Numerical Importance of Individual Steps,
67(1)
3.4 Cholesky Decomposition,
68(3)
3.5 Transformation of the Cholesky Vectors,
71(1)
3.6 Two-Electron Integral Reassembly,
72(4)
3.7 Integral and Execution Buffer,
76(1)
3.8 Symmetric Group Graphical Approach,
77(10)
3.9 Summary and Outlook,
87(1)
References,
87(5)
4 Generalized Variational Theorem in Quantum Mechanics
92(7)
Mel Levy
Antonios Gonis
4.1 Introduction,
92(1)
4.2 First Proof,
93(2)
4.3 Second Proof,
95(1)
4.4 Conclusions,
96(1)
References,
97(2)
Section 3 Mathematical And Statistical Models In Life And Climate Science Applications 99(36)
5 A Model for the Spread of Tuberculosis with Drug-Sensitive and Emerging Multidrug-Resistant and Extensively Drug-Resistant Strains
101(20)
Julien Arino
Iman A. Soliman
5.1 Introduction,
101(16)
5.1.1 Model formulation,
102(5)
5.1.2 Mathematical Analysis,
107(1)
5.1.2.1 Basic properties of solutions,
107(1)
5.1.2.2 Nature of the disease-free equilibrium,
108(1)
5.1.2.3 Local asymptotic stability of the DFE,
108(1)
5.1.2.4 Existence of subthreshold endemic equilibria,
110(1)
5.1.2.5 Global stability of the DFE when the bifurcation is "forward",
113(1)
5.1.2.6 Strain-specific global stability in "forward" bifurcation cases,
115(2)
5.2 Discussion,
117(2)
References,
119(2)
6 The Need for More Integrated Epidemic Modeling with Emphasis on Antibiotic Resistance
121(14)
Eili Y. Klein
Julia Chelen
Michael D. Makowsky
Paul E. Smaldino
6.1 Introduction,
121(1)
6.2 Mathematical Modeling of Infectious Diseases,
122(3)
6.3 Antibiotic Resistance, Behavior, and Mathematical Modeling,
125(3)
6.3.1 Why an integrated approach?,
125(2)
6.3.2 The role of symptomology,
127(1)
6.4 Conclusion,
128(1)
References,
129(6)
Section 4 Mathematical Models And Analysis For Science And Engineering 135(138)
7 Data-Driven Methods for Dynamical Systems: Quantifying Predictability and Extracting Spatiotemporal Patterns
137(55)
Dimitrios Giannakis
Andrew J. Majda
7.1 Quantifying Long-Range Predictability and Model Error through Data Clustering and Information Theory,
138(25)
7.1.1 Background,
138(2)
7.1.2 Information theory, predictability, and model error,
140(1)
7.1.2.1 Predictability in a perfect-model environment,
140(1)
7.1.2.2 Quantifying the error of imperfect models,
143(1)
7.1.3 Coarse-graining phase space to reveal long-range predictability,
144(1)
7.1.3.1 Perfect-model scenario,
144(1)
7.1.3.2 Quantifying the model error in long-range forecasts,
147(2)
7.1.4 K-means clustering with persistence,
149(3)
7.1.5 Demonstration in a double-gyre ocean model,
152(1)
7.1.5.1 Predictability bounds for coarse-grained observables,
154(1)
7.1.5.2 The physical properties of the regimes,
157(1)
7.1.5.3 Markov models of regime behavior in the 1.5-layer ocean model,
159(1)
7.1.5.4 The model error in long-range predictions with coarse-grained Markov models,
162(1)
7.2 NLSA Algorithms for Decomposition of Spatiotemporal Data,
163(21)
7.2.1 Background,
163(2)
7.2.2 Mathematical framework,
165(1)
7.2.2.1 Time-lagged embedding,
166(1)
7.2.2.2 Overview of singular spectrum analysis,
167(1)
7.2.2.3 Spaces of temporal patterns,
167(1)
7.2.2.4 Discrete formulation,
169(1)
7.2.2.5 Dynamics-adapted kernels,
171(1)
7.2.2.6 Singular value decomposition,
173(1)
7.2.2.7 Setting the truncation level,
174(1)
7.2.2.8 Projection to data space,
175(1)
7.2.3 Analysis of infrared brightness temperature satellite data for tropical dynamics,
175(1)
7.2.3.1 Dataset description,
176(1)
7.2.3.2 Modes recovered by NLSA,
176(1)
7.2.3.3 Reconstruction of the TOGA COARE MJOs,
183(1)
7.3 Conclusions,
184(1)
References,
185(7)
8 On Smoothness Concepts in Regularization for Nonlinear Inverse Problems in Banach Spaces
192(30)
Bernd Hofmann
8.1 Introduction,
192(3)
8.2 Model Assumptions, Existence, and Stability,
195(2)
8.3 Convergence of Regularized Solutions,
197(3)
8.4 A Powerful Tool for Obtaining Convergence Rates,
200(6)
8.5 How to Obtain Variational Inequalities?,
206(9)
8.5.1 Bregman distance as error measure: the benchmark case,
206(4)
8.5.2 Bregman distance as error measure: violating the benchmark,
210(3)
8.5.3 Norm distance as error measure: .0 - regularization
213(2)
8.6 Summary,
215(1)
References,
215(7)
9 Initial and Initial-Boundary Value Problems for First-Order Symmetric Hyperbolic Systems with Constraints
222(32)
Nicolae Tarfulea
9.1 Introduction,
222(1)
9.2 FOSH Initial Value Problems with Constraints,
223(7)
9.2.1 FOSH initial value problems,
224(1)
9.2.2 Abstract formulation,
225(3)
9.2.3 FOSH initial value problems with constraints,
228(2)
9.3 FOSH Initial-Boundary Value Problems with Constraints,
230(6)
9.3.1 FOSH initial-boundary value problems,
232(2)
9.3.2 FOSH initial-boundary value problems with constraints,
234(2)
9.4 Applications,
236(14)
9.4.1 System of wave equations with constraints,
237(3)
9.4.2 Applications to Einstein's equations,
240(1)
9.4.2.1 Einstein—Christoffel formulation,
243(1)
9.4.2.2 Alekseenko—Arnold formulation,
246(4)
References,
250(4)
10 Information Integration, Organization, and Numerical Harmonic Analysis
254(19)
Ronald R. Coffman
Ronen Talmon
Matan Gavish
Ali Haddad
10.1 Introduction,
254(3)
10.2 Empirical Intrinsic Geometry,
257(6)
10.2.1 Manifold formulation,
259(2)
10.2.2 Mahalanobis distance,
261(2)
10.3 Organization and Harmonic Analysis of Databases/Matrices,
263(6)
10.3.1 Haar bases,
264(1)
10.3.2 Coupled partition trees,
265(4)
10.4 Summary,
269(1)
References,
270(3)
Section 5 Mathematical Methods In Social Sciences And Arts 273(36)
11 Satisfaction Approval Voting
275(24)
Steven J. Brams
D. Marc Kilgour
11.1 Introduction,
275(2)
11.2 Satisfaction Approval Voting for Individual Candidates,
277(8)
11.3 The Game Theory Society Election,
285(2)
11.4 Voting for Multiple Candidates under SAV: A Decision-Theoretic Analysis,
287(4)
11.5 Voting for Political Parties,
291(4)
11.5.1 Bullet voting,
291(1)
11.5.2 Formalization,
292(2)
11.5.3 Multiple-party voting,
294(1)
11.6 Conclusions,
295(1)
11.7 Summary,
296(1)
References,
297(2)
12 Modeling Musical Rhythm Mutations with Geometric Quantization
299(10)
Godfried T. Toussaint
12.1 Introduction,
299(2)
12.2 Rhythm Mutations,
301(2)
12.2.1 Musicological rhythm mutations,
301(1)
12.2.2 Geometric rhythm mutations,
302(1)
12.3 Similarity-Based Rhythm Mutations,
303(3)
12.3.1 Global rhythm similarity measures,
304(2)
12.4 Conclusion,
306(1)
References,
307(2)
Index 309
RODERICK MELNIk, PhD, is Professor in the Department of Mathematics at Wilfrid Laurier University, Canada, where he is also Tier I Canada Research Chair in Mathematical Modeling. He is internationally known for his research in computational and applied mathematics, numerical analysis, and mathematical modeling for scientific and engineering applications. Dr. Melnik is the recipient of many awards, including a number of prestigious fellowships in Italy, Denmark, England and Spain. He has published over 300 refereed research papers and has served on editorial boards of numerous international journals and book series. Currently, Dr. Melnik is Director of the MS2Discovery Interdisciplinary Research Institute in Waterloo, Canada.
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