1.

Record Nr.

UNINA9910140649403321

Titolo

Mathematical and computational modeling : with applications in natural and social sciences, engineering, and the arts / / edited by Roderick Melnik

Pubbl/distr/stampa

Hoboken, New Jersey : , : Wiley, , 2015

©2015

ISBN

1-118-85385-7

1-118-85388-1

Descrizione fisica

1 online resource (336 p.)

Collana

Pure and Applied Mathematics : A Wiley Series of Texts, Monographs and Tracts

Disciplina

511/.8

Soggetti

Mathematical models

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references at the end of each chapters and index.

Nota di contenuto

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 Extensively Drug-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

Sommario/riassunto

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,