Applied And Computational Measurable Dynamics
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Applied And Computational Measurable Dynamics
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Author : Erik M. Bollt
language : en
Publisher: SIAM
Release Date : 2013-12-03
Applied And Computational Measurable Dynamics written by Erik M. Bollt and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-03 with Mathematics categories.
Until recently, measurable dynamics has been held as a highly theoretical 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.
Applied And Computational Measurable Dynamics
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Author : Erik M. Bollt
language : en
Publisher: SIAM
Release Date : 2013-12-03
Applied And Computational Measurable Dynamics written by Erik M. Bollt and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-03 with Mathematics categories.
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.
Pde Dynamics
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Author : Christian Kuehn
language : en
Publisher: SIAM
Release Date : 2019-04-10
Pde Dynamics written by Christian Kuehn and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-10 with Mathematics categories.
This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Differential Dynamical Systems Revised Edition
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Author : James D. Meiss
language : en
Publisher: SIAM
Release Date : 2017-01-24
Differential Dynamical Systems Revised Edition written by James D. Meiss and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-24 with Mathematics categories.
Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.
Implicit Explicit Methods For Evolutionary Partial Differential Equations
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Author : Sebastiano Boscarino
language : en
Publisher: SIAM
Release Date : 2024-12-12
Implicit Explicit Methods For Evolutionary Partial Differential Equations written by Sebastiano Boscarino and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-12-12 with Mathematics categories.
Implicit-explicit (IMEX) time discretization methods have proven to be highly effective for the numerical solution of a wide class of evolutionary partial differential equations (PDEs) across various contexts. These methods have become mainstream for solving evolutionary PDEs, particularly in the fields of hyperbolic and kinetic equations. The first book on the subject, Implicit-Explicit Methods for Evolutionary Partial Differential Equations provides an in-depth yet accessible approach. The authors summarize and illustrate the construction, analysis, and application of IMEX methods using examples, test cases, and implementation details; guide readers through the various methods and teach them how to select and use the one most appropriate for their needs; and demonstrate how to identify stiff terms and effectively implement high-order methods in time for a variety of systems of PDEs. Readers interested in learning modern techniques for the effective numerical solution of evolutionary PDEs with multiple time scales will find in this book a unified, compact, and accessible treatment. This book is intended for applied mathematicians, scientists, and engineers who use or are interested in learning about IMEX schemes. Readers should have some background in numerical methods for ODE systems and basic finite difference and finite volume discretization of evolutionary PDEs, along with a basic understanding of the relevant mathematical models. The book is suitable for students who have had a basic course in numerical analysis and are familiar with partial differential equations.
Model Emergent Dynamics In Complex Systems
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Author : A. J. Roberts
language : en
Publisher: SIAM
Release Date : 2014-12-18
Model Emergent Dynamics In Complex Systems written by A. J. Roberts and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-18 with Mathematics categories.
Arising out of the growing interest in and applications of modern dynamical systems theory, this book explores how to derive relatively simple dynamical equations that model complex physical interactions. The author?s objectives are to use sound theory to explore algebraic techniques, develop interesting applications, and discover general modeling principles. Model Emergent Dynamics in Complex Systems unifies into one powerful and coherent approach the many varied extant methods for mathematical model reduction and approximation. Using mathematical models at various levels of resolution and complexity, the book establishes the relationships between such multiscale models and clarifying difficulties and apparent paradoxes and addresses model reduction for systems, resolves initial conditions, and illuminates control and uncertainty. The basis for the author?s methodology is the theory and the geometric picture of both coordinate transforms and invariant manifolds in dynamical systems; in particular, center and slow manifolds are heavily used. The wonderful aspect of this approach is the range of geometric interpretations of the modeling process that it produces?simple geometric pictures inspire sound methods of analysis and construction. Further, pictures drawn of state spaces also provide a route to better assess a model?s limitations and strengths. Geometry and algebra form a powerful partnership and coordinate transforms and manifolds provide a powerfully enhanced and unified view of a swathe of other complex system modeling methodologies such as averaging, homogenization, multiple scales, singular perturbations, two timing, and WKB theory.
Barriers And Transport In Unsteady Flows
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Author : Sanjeeva Balasuriya
language : en
Publisher: SIAM
Release Date : 2016-12-08
Barriers And Transport In Unsteady Flows written by Sanjeeva Balasuriya and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-12-08 with Mathematics categories.
?Fluids that mix at geophysical or microscales tend to form well-mixed areas and regions of coherent blobs. The Antarctic circumpolar vortex, which mostly retains its structure while moving unsteadily in the atmosphere, is an example of a coherent structure. How do such structures exchange fluid with their surroundings? What is the impact on global mixing? What is the "boundary" of the structure, and how does it move? Can these questions be answered from time-varying observational data?? This book addresses these issues from the perspective of the differential equations that must be obeyed by fluid particles. In these terms, identification of the boundaries of coherent structures (i.e., "flow barriers"), quantification of transport across them, control of the locations of these barriers, and optimization of transport across them are developed using a rigorous mathematical framework. The concepts are illustrated with an array of theoretical and applied examples that arise from oceanography and microfluidics.? Barriers and Transport in Unsteady Flows: A Melnikov Approach?provides an extensive introduction and bibliography, specifically elucidating the difficulties arising when flows are unsteady and highlighting relevance in geophysics and microfluidics; careful and rigorous development of the mathematical theory of unsteady flow barriers within the context of nonautonomous stable and unstable manifolds, richly complemented with examples; and chapters on exciting new research in the control of flow barriers and the optimization of transport across them.
Advances On Nonlinear Dynamics Of Electronic Systems
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Author : Arturo Buscarino
language : en
Publisher: World Scientific
Release Date : 2019-01-08
Advances On Nonlinear Dynamics Of Electronic Systems written by Arturo Buscarino and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-01-08 with Technology & Engineering categories.
This book comprises the most recent advanced results on nonlinear electronic circuits, and the contents range from networks, synchronization, memristors to several other topics. Both theory and advanced timely results are included. It provides an overview of popular themes in the field of nonlinear dynamics of electronic circuits with contributions from outstanding scientists.
Climate Modeling For Scientists And Engineers
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Author : John B. Drake
language : en
Publisher: SIAM
Release Date : 2014-08-26
Climate Modeling For Scientists And Engineers written by John B. Drake and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-26 with Mathematics categories.
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, covers numerical methods for geophysical flows in more detail than many other texts, discusses parallel algorithms and the role of high-performance computing used in the simulation of weather and climate, and provides over 100 pages of supplemental lectures and MATLAB? exercises on an associated web page. 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.
Transport Barriers And Coherent Structures In Flow Data
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Author : George Haller
language : en
Publisher: Cambridge University Press
Release Date : 2023-03-16
Transport Barriers And Coherent Structures In Flow Data written by George Haller and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-16 with Science categories.
Transport barriers are observed inhibitors of the spread of substances in flows. The collection of such barriers offers a powerful geometric template that frames the main pathways, or lack thereof, in any transport process. This book surveys effective and mathematically grounded methods for defining, locating and leveraging transport barriers in numerical simulations, laboratory experiments, technological processes and nature. It provides a unified treatment of material developed over the past two decades, focusing on the methods that have a solid foundation and broad applicability to data sets beyond simple model flows. The intended audience ranges from advanced undergraduates to researchers in the areas of turbulence, geophysical flows, aerodynamics, chemical engineering, environmental engineering, flow visualization, computational mathematics and dynamical systems. Detailed open-source implementations of the numerical methods are provided in an accompanying collection of Jupyter notebooks linked from the electronic version of the book.