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Informationen zum Autor 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. Klappentext 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. Zusammenfassung Applied mathematics and computational science play a fundamental role in new discoveries in the sciences and engineering. Inhaltsverzeichnis 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 2.2.1 Ginzburg-Landau energy 21 2.2.2 Symmetries of the equations 21 2.2.3 Quantization of flux 22 2.2.4 Homogeneous solutions 22 2.2.5 Type I and Type II superconductors 23 2.2.6 Self-dual case ¿=1/ ¿ 2 24 2.2.7 Critical magnetic fields 24 2.2.8 Time-dependent equations 25 2.3 Vortices 25 2.3.1 n-vortex solutions 25 2.3.2 Stability 26 2.4 Vortex Lattices 30 2.4.1 Abrikosov ...
