{"title":"Barriers and transport in unsteady flows - a Melnikov approach","authors":"Sanjeeva Balasuriya","doi":"10.1137/1.9781611974584","DOIUrl":"https://doi.org/10.1137/1.9781611974584","url":null,"abstract":"","PeriodicalId":150595,"journal":{"name":"Mathematical modeling and computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2016-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124136477","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Climate modeling and simulation teach us about past, present, and future conditions of life on earth and help us understand observations about the changing atmosphere and ocean and terrestrial ecology. Focusing on high-end modeling and simulation of earth's climate, Climate Modeling for Scientists and Engineers presents observations about the general circulations of the earth and the partial differential equations used to model the dynamics of weather and climate and covers numerical methods for geophysical flows in more detail than many other texts. It also discusses parallel algorithms and the role of high-performance computing used in the simulation of weather and climate and provides supplemental lectures and MATLAB exercises on an associated Web page. Audience: This book is intended for graduate students in science and engineering. It is also useful for a broad spectrum of computational science and engineering researchers, especially those who want a brief introduction to the methods and capabilities of climate models and those who use climate model results in their investigations. Information on numerical methods used to solve the equations of motion and climate simulations using parallel algorithms on high-performance computers challenges researchers who aim to improve the prediction of climate on decadal to century time scales.
{"title":"Climate Modeling for Scientists and Engineers","authors":"J. Drake","doi":"10.1137/1.9781611973549","DOIUrl":"https://doi.org/10.1137/1.9781611973549","url":null,"abstract":"Climate modeling and simulation teach us about past, present, and future conditions of life on earth and help us understand observations about the changing atmosphere and ocean and terrestrial ecology. Focusing on high-end modeling and simulation of earth's climate, Climate Modeling for Scientists and Engineers presents observations about the general circulations of the earth and the partial differential equations used to model the dynamics of weather and climate and covers numerical methods for geophysical flows in more detail than many other texts. It also discusses parallel algorithms and the role of high-performance computing used in the simulation of weather and climate and provides supplemental lectures and MATLAB exercises on an associated Web page. Audience: This book is intended for graduate students in science and engineering. It is also useful for a broad spectrum of computational science and engineering researchers, especially those who want a brief introduction to the methods and capabilities of climate models and those who use climate model results in their investigations. Information on numerical methods used to solve the equations of motion and climate simulations using parallel algorithms on high-performance computers challenges researchers who aim to improve the prediction of climate on decadal to century time scales.","PeriodicalId":150595,"journal":{"name":"Mathematical modeling and computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2014-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131700458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Until recently, measurable dynamics has been held as a highly theoretcal mathematical topic with few generally known obvious links for practitioners in areas of applied mathematics. However, the advent of high-speed computers, rapidly developing algorithms, and new numerical methods has allowed for a tremendous amount of progress and sophistication in efforts to represent the notion of a transfer operator discretely but to high resolution. This book connects many concepts in dynamical systems with mathematical tools from areas such as graph theory and ergodic theory. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures, and transport problems. The new and fast-developing computational tools discussed throughout the book allow for detailed analysis of real-world problems that are simply beyond the reach of traditional methods. Audience: Applied and Computational Measurable Dynamics is intended for advanced undergraduate and graduate students and researchers in applied dynamical systems, computational ergodic theory, geosciences, and fluid dynamics. Contents Chapter 1: Dynamical Systems, Ensembles, and Transfer Operators; Chapter 2: Dynamical Systems Terminology and Definitions; Chapter 3: Frobenius-Perron Operator and Infintesimal Generator; Chapter 4: Graph Theoretic Methods and Markov Models of Dynamical Transport; Chapter 5: Graph Partition Methods and Their Relationship to Transport in Dynamical Systems; Chapter 6: The Topological Dynamics Perspective of Symbol Dynamics; Chapter 7: Transport Mechanism, Lobe Dynamics, Flux Rates, and Escape; Chapter 8: Finite Time Lyapunov Exponents; Chapter 9: Information Theory in Dynamical Systems; Appendix A: Computation, Codes, and Computational Complexity; Bibliography; Index
{"title":"Applied and Computational Measurable Dynamics","authors":"E. Bollt, N. Santitissadeekorn","doi":"10.1137/1.9781611972641","DOIUrl":"https://doi.org/10.1137/1.9781611972641","url":null,"abstract":"Until recently, measurable dynamics has been held as a highly theoretcal mathematical topic with few generally known obvious links for practitioners in areas of applied mathematics. However, the advent of high-speed computers, rapidly developing algorithms, and new numerical methods has allowed for a tremendous amount of progress and sophistication in efforts to represent the notion of a transfer operator discretely but to high resolution. This book connects many concepts in dynamical systems with mathematical tools from areas such as graph theory and ergodic theory. The authors introduce practical tools for applications related to measurable dynamical systems, coherent structures, and transport problems. The new and fast-developing computational tools discussed throughout the book allow for detailed analysis of real-world problems that are simply beyond the reach of traditional methods. Audience: Applied and Computational Measurable Dynamics is intended for advanced undergraduate and graduate students and researchers in applied dynamical systems, computational ergodic theory, geosciences, and fluid dynamics. Contents Chapter 1: Dynamical Systems, Ensembles, and Transfer Operators; Chapter 2: Dynamical Systems Terminology and Definitions; Chapter 3: Frobenius-Perron Operator and Infintesimal Generator; Chapter 4: Graph Theoretic Methods and Markov Models of Dynamical Transport; Chapter 5: Graph Partition Methods and Their Relationship to Transport in Dynamical Systems; Chapter 6: The Topological Dynamics Perspective of Symbol Dynamics; Chapter 7: Transport Mechanism, Lobe Dynamics, Flux Rates, and Escape; Chapter 8: Finite Time Lyapunov Exponents; Chapter 9: Information Theory in Dynamical Systems; Appendix A: Computation, Codes, and Computational Complexity; Bibliography; Index","PeriodicalId":150595,"journal":{"name":"Mathematical modeling and computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2013-12-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134556137","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Mathematical modeling—the ability to apply mathematical concepts and techniques to real-life systems—has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to extensively worked-out case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics.
{"title":"Continuum modeling in the physical sciences","authors":"Embrecht W. C. van Groesen, Jaap Molenaar","doi":"10.1137/1.9780898718249","DOIUrl":"https://doi.org/10.1137/1.9780898718249","url":null,"abstract":"Mathematical modeling—the ability to apply mathematical concepts and techniques to real-life systems—has expanded considerably over the last decades, making it impossible to cover all of its aspects in one course or textbook. Continuum Modeling in the Physical Sciences provides an extensive exposition of the general principles and methods of this growing field with a focus on applications in the natural sciences. The authors present a thorough treatment of mathematical modeling from the elementary level to more advanced concepts. Most of the chapters are devoted to a discussion of central issues such as dimensional analysis, conservation principles, balance laws, constitutive relations, stability, robustness, and variational methods, and are accompanied by numerous real-life examples. Readers will benefit from the exercises placed throughout the text and the Challenging Problems sections found at the ends of several chapters. The last chapter is devoted to extensively worked-out case studies in polymer dynamics, fiber spinning, water waves, and waveguide optics.","PeriodicalId":150595,"journal":{"name":"Mathematical modeling and computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2007-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124851625","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Preface List of figures List of tables 1. Introduction 2. Linear systems 3. Existence and uniqueness 4. Dynamical systems 5. Invariant manifolds 6. The phase plane 7. Chaotic dynamics 8. Bifurcation theory 9. Hamiltonian dynamics A. Mathematical software Bibliography Index.
{"title":"Differential dynamical systems","authors":"J. Meiss","doi":"10.1137/1.9780898718232","DOIUrl":"https://doi.org/10.1137/1.9780898718232","url":null,"abstract":"Preface List of figures List of tables 1. Introduction 2. Linear systems 3. Existence and uniqueness 4. Dynamical systems 5. Invariant manifolds 6. The phase plane 7. Chaotic dynamics 8. Bifurcation theory 9. Hamiltonian dynamics A. Mathematical software Bibliography Index.","PeriodicalId":150595,"journal":{"name":"Mathematical modeling and computation","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115614547","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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