Mathematical and Computational Modeling : With Applications in Natural and Social Sciences, Engineering, and the Arts.
Title:
Mathematical and Computational Modeling : With Applications in Natural and Social Sciences, Engineering, and the Arts.
Author:
Melnik, Roderick.
ISBN:
9781118854112
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (336 pages)
Series:
Pure and Applied Mathematics: a Wiley Series of Texts, Monographs and Tracts Ser.
Contents:
Title Page -- Copyright Page -- Contents -- List of Contributors -- Preface -- Section 1 Introduction -- Chapter 1 Universality of Mathematical Models in Understanding Nature, Society, and Man-Made World -- 1.1 Human Knowledge, Models, and Algorithms -- 1.2 Looking into the Future from a Modeling Perspective -- 1.3 What This Book Is About -- 1.4 Concluding Remarks -- References -- Section 2 Advanced Mathematical and Computational Models in Physics and Chemistry -- Chapter 2 Magnetic Vortices, Abrikosov Lattices, and Automorphic Functions -- 2.1 Introduction -- 2.2 The Ginzburg-Landau Equations -- 2.2.1 Ginzburg-Landau energy -- 2.2.2 Symmetries of the equations -- 2.2.3 Quantization of flux -- 2.2.4 Homogeneous solutions -- 2.2.5 Type I and Type II superconductors -- 2.2.6 Self-dual case κ=1/√2 -- 2.2.7 Critical magnetic fields -- 2.2.8 Time-dependent equations -- 2.3 Vortices -- 2.3.1 n-vortex solutions -- 2.3.2 Stability -- 2.4 Vortex Lattices -- 2.4.1 Abrikosov lattices -- 2.4.2 Existence of Abrikosov lattices -- 2.4.3 Abrikosov lattices as gauge-equivariant states -- 2.4.4 Abrikosov function -- 2.4.5 Comments on the proofs of existence results -- 2.4.6 Stability of Abrikosov lattices -- 2.4.7 Functions γδ(τ ),δ > 0 -- 2.4.8 Key ideas of approach to stability -- 2.5 Multi-Vortex Dynamics -- 2.6 Conclusions -- Appendix 2.A Parameterization of the equivalence classes [L] -- Appendix 2.B Automorphy factors -- Acknowledgments -- References -- Chapter 3 Numerical Challenges in a Cholesky-Decomposed Local Correlation Quantum Chemistry Framework -- 3.1 Introduction -- 3.2 Local MRSDCI -- 3.2.1 MRSDCI -- 3.2.2 Symmetric group graphical approach -- 3.2.3 Local electron correlation approximation -- 3.2.4 Algorithm summary -- 3.3 Numerical Importance of Individual Steps -- 3.4 Cholesky Decomposition -- 3.5 Transformation of the Cholesky Vectors.
3.6 Two-Electron Integral Reassembly -- 3.7 Integral and Execution Buffer -- 3.8 Symmetric Group Graphical Approach -- 3.9 Summary and Outlook -- Acknowledgments -- References -- Chapter 4 Generalized Variational Theorem in Quantum Mechanics -- 4.1 Introduction -- 4.2 First Proof -- 4.3 Second Proof -- 4.4 Conclusions -- Acknowledgments -- References -- Section 3 Mathematical and Statistical Models in Life and Climate Science Applications -- Chapter 5 A Model for the Spread of Tuberculosis with Drug-Sensitive and Emerging Multidrug-Resistant and ExtensivelyDrug-Resistant Strains -- 5.1 Introduction -- 5.1.1 Model formulation -- 5.1.2 Mathematical Analysis -- 5.1.2.1 Basic properties of solutions -- 5.1.2.2 Nature of the disease-free equilibrium -- 5.1.2.3 Local asymptotic stability of the DFE -- 5.1.2.4 Existence of subthreshold endemic equilibria -- 5.1.2.5 Global stability of the DFE when the bifurcation is "forward" -- 5.1.2.6 Strain-specific global stability in "forward" bifurcation cases -- 5.2 Discussion -- References -- Chapter 6 The Need for More Integrated Epidemic Modeling with Emphasis on Antibiotic Resistance -- 6.1 Introduction -- 6.2 Mathematical Modeling of Infectious Diseases -- 6.3 Antibiotic Resistance, Behavior, and Mathematical Modeling -- 6.3.1 Why an integrated approach? -- 6.3.2 The role of symptomology -- 6.4 Conclusion -- Acknowledgments -- References -- Section 4 Mathematical Models and Analysis for Science and Engineering -- Chapter 7 Data-Driven Methods for Dynamical Systems: Quantifying Predictability and Extracting Spatiotemporal Patterns -- 7.1 Quantifying Long-Range Predictability and Model Error through Data Clustering and Information Theory -- 7.1.1 Background -- 7.1.2 Information theory, predictability, and model error -- 7.1.2.1 Predictability in a perfect-model environment.
7.1.2.2 Quantifying the error of imperfect models -- 7.1.3 Coarse-graining phase space to reveal long-range predictability -- 7.1.3.1 Perfect-model scenario -- 7.1.3.2 Quantifying the model error in long-range forecasts -- 7.1.4 K-means clustering with persistence -- 7.1.5 Demonstration in a double-gyre ocean model -- 7.1.5.1 Predictability bounds for coarse-grained observables -- 7.1.5.2 The physical properties of the regimes -- 7.1.5.3 Markovmodels of regime behavior in the 1.5-layer ocean model -- 7.1.5.4 The model error in long-range predictions with coarse-grained Markov models -- 7.2 NLSA Algorithms for Decomposition of Spatiotemporal Data -- 7.2.1 Background -- 7.2.2 Mathematical framework -- 7.2.2.1 Time-lagged embedding -- 7.2.2.2 Overview of singular spectrum analysis -- 7.2.2.3 Spaces of temporal patterns -- 7.2.2.4 Discrete formulation -- 7.2.2.5 Dynamics-adapted kernels -- 7.2.2.6 Singular value decomposition -- 7.2.2.7 Setting the truncation level -- 7.2.2.8 Projection to data space -- 7.2.3 Analysis of infrared brightness temperature satellite data for tropical dynamics -- 7.2.3.1 Dataset description -- 7.2.3.2 Modes recovered by NLSA -- 7.2.3.3 Reconstruction of the TOGA COARE MJOs -- 7.3 Conclusions, -- Acknowledgments -- References -- Chapter 8 On Smoothness Concepts in Regularization for Nonlinear Inverse Problems in Banach Spaces -- 8.1 Introduction -- 8.2 Model Assumptions, Existence, and Stability -- 8.3 Convergence of Regularized Solutions -- 8.4 A Powerful Tool for Obtaining Convergence Rates -- 8.5 How to Obtain Variational Inequalities? -- 8.5.1 Bregman distance as error measure: the benchmark case -- 8.5.2 Bregman distance as error measure: violating the benchmark -- 8.5.3 Norm distance as error measure: l1-regularization -- 8.6 Summary -- Acknowledgments -- References.
Chapter 9 Initial and Initial-Boundary Value Problems for First-Order Symmetric Hyperbolic Systems with Constraints -- 9.1 Introduction -- 9.2 FOSH Initial Value Problems with Constraints -- 9.2.1 FOSH initial value problems -- 9.2.2 Abstract formulation -- 9.2.3 FOSH initial value problems with constraints -- 9.3 FOSH Initial-Boundary Value Problems with Constraints -- 9.3.1 FOSH initial-boundary value problems -- 9.3.2 FOSH initial-boundary value problems with constraints -- 9.4 Applications -- 9.4.1 System of wave equations with constraints -- 9.4.2 Applications to Einstein's equations -- 9.4.2.1 Einstein-Christoffel formulation -- 9.4.2.2 Alekseenko-Arnold formulation -- Acknowledgments -- References -- Chapter 10 Information Integration, Organization, and Numerical Harmonic Analysis -- 10.1 Introduction -- 10.2 Empirical Intrinsic Geometry -- 10.2.1 Manifold formulation -- 10.2.2 Mahalanobis distance -- 10.3 Organization and Harmonic Analysis of Databases/Matrices -- 10.3.1 Haar bases -- 10.3.2 Coupled partition trees -- 10.4 Summary -- References -- Section 5 Mathematical Methods in Social Sciences and Arts -- Chapter 11 Satisfaction Approval Voting -- 11.1 Introduction -- 11.2 Satisfaction Approval Voting for Individual Candidates -- 11.3 The Game Theory Society Election -- 11.4 Voting for Multiple Candidates under SAV: A Decision-Theoretic Analysis -- 11.5 Voting for Political Parties -- 11.5.1 Bullet voting -- 11.5.2 Formalization -- 11.5.3 Multiple-party voting -- 11.6 Conclusions -- 11.7 Summary -- Acknowledgments -- References -- Chapter 12 Modeling Musical Rhythm Mutations with Geometric Quantization -- 12.1 Introduction -- 12.2 Rhythm Mutations -- 12.2.1 Musicological rhythm mutations -- 12.2.2 Geometric rhythm mutations -- 12.3 Similarity-Based Rhythm Mutations -- 12.3.1 Global rhythm similarity measures -- 12.4 Conclusion.
Acknowledgment -- References -- Index -- Series Page -- EULA.
Abstract:
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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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