Elegant Simulations From Simple Oscillators To Many Body Systems
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Elegant Simulations From Simple Oscillators To Many Body Systems
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Author : Julien Clinton Sprott
language : en
Publisher: World Scientific
Release Date : 2022-12-20
Elegant Simulations From Simple Oscillators To Many Body Systems written by Julien Clinton Sprott and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-12-20 with Science categories.
A recent development is the discovery that simple systems of equations can have chaotic solutions in which small changes in initial conditions have a large effect on the outcome, rendering the corresponding experiments effectively irreproducible and unpredictable. An earlier book in this sequence, Elegant Chaos: Algebraically Simple Chaotic Flows provided several hundred examples of such systems, nearly all of which are purely mathematical without any obvious connection with actual physical processes and with very limited discussion and analysis.In this book, we focus on a much smaller subset of such models, chosen because they simulate some common or important physical phenomenon, usually involving the motion of a limited number of point-like particles, and we discuss these models in much greater detail. As with the earlier book, the chosen models are the mathematically simplest formulations that exhibit the phenomena of interest, and thus they are what we consider 'elegant.'Elegant models, stripped of unnecessary detail while maximizing clarity, beauty, and simplicity, occupy common ground bordering both real-world modeling and aesthetic mathematical analyses. A computational search led one of us (JCS) to the same set of differential equations previously used by the other (WGH) to connect the classical dynamics of Newton and Hamilton to macroscopic thermodynamics. This joint book displays and explores dozens of such relatively simple models meeting the criteria of elegance, taste, and beauty in structure, style, and consequence.This book should be of interest to students and researchers who enjoy simulating and studying complex particle motions with unusual dynamical behaviors. The book assumes only an elementary knowledge of calculus. The systems are initial-value iterated maps and ordinary differential equations but they must be solved numerically. Thus for readers a formal differential equations course is not at all necessary, of little value and limited use.
Time Reversibility Computer Simulation Algorithms Chaos
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Author : William Graham Hoover
language : en
Publisher: World Scientific
Release Date : 2012
Time Reversibility Computer Simulation Algorithms Chaos written by William Graham Hoover and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
The book begins with a discussion, contrasting the idealized reversibility of basic physics against the pragmatic irreversibility of real life. Computer models, and simulation, are next discussed and illustrated. Simulations provide the means to assimilate concepts through worked-out examples. State-of-the-art analyses, from the point of view of dynamical systems, are applied to many-body examples from nonequilibrium molecular dynamics and to chaotic irreversible flows from finite-difference, finite-element, and particle-based continuum simulations. Two necessary concepts from dynamical-systems theory - fractals and Lyapunov instability - are fundamental to the approach. Undergraduate-level physics, calculus, and ordinary differential equations are sufficient background for a full appreciation of this book, which is intended for advanced undergraduates, graduates, and research workers.
Classical Mechanics Simulations
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Author : Bruce Hawkins
language : en
Publisher:
Release Date : 1995-03
Classical Mechanics Simulations written by Bruce Hawkins and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-03 with Science categories.
The Consortium for Upper Level Physics Software (CUPS) has developed a comprehensive series of Nine Book/Software packages that Wiley will publish in FY '95 and '96. CUPS is an international group of 27 physicists, all with extensive backgrounds in the research, teaching, and development of instructional software. The project is being supported by the National Science Foundation (PHY-9014548), and it has received other support from the IBM Corp., Apple Computer Corp., and George Mason University. The Simulations being developed are: Astrophysics, Classical Mechanics, Electricity & Magnetism, Modern Physics, Nuclear and Particle Physics, Quantum Mechanics, Solid State, Thermal and Statistical, and Waves and Optics.
Feedback Systems
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Author : Karl Johan Åström
language : en
Publisher: Princeton University Press
Release Date : 2021-02-02
Feedback Systems written by Karl Johan Åström and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-02-02 with Technology & Engineering categories.
The essential introduction to the principles and applications of feedback systems—now fully revised and expanded This textbook covers the mathematics needed to model, analyze, and design feedback systems. Now more user-friendly than ever, this revised and expanded edition of Feedback Systems is a one-volume resource for students and researchers in mathematics and engineering. It has applications across a range of disciplines that utilize feedback in physical, biological, information, and economic systems. Karl Åström and Richard Murray use techniques from physics, computer science, and operations research to introduce control-oriented modeling. They begin with state space tools for analysis and design, including stability of solutions, Lyapunov functions, reachability, state feedback observability, and estimators. The matrix exponential plays a central role in the analysis of linear control systems, allowing a concise development of many of the key concepts for this class of models. Åström and Murray then develop and explain tools in the frequency domain, including transfer functions, Nyquist analysis, PID control, frequency domain design, and robustness. Features a new chapter on design principles and tools, illustrating the types of problems that can be solved using feedback Includes a new chapter on fundamental limits and new material on the Routh-Hurwitz criterion and root locus plots Provides exercises at the end of every chapter Comes with an electronic solutions manual An ideal textbook for undergraduate and graduate students Indispensable for researchers seeking a self-contained resource on control theory
Biological Clocks Rhythms And Oscillations
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Author : Daniel B. Forger
language : en
Publisher: MIT Press
Release Date : 2017-11-16
Biological Clocks Rhythms And Oscillations written by Daniel B. Forger and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Science categories.
An introduction to the mathematical, computational, and analytical techniques used for modeling biological rhythms, presenting tools from many disciplines and example applications. All areas of biology and medicine contain rhythms, and these behaviors are best understood through mathematical tools and techniques. This book offers a survey of mathematical, computational, and analytical techniques used for modeling biological rhythms, gathering these methods for the first time in one volume. Drawing on material from such disciplines as mathematical biology, nonlinear dynamics, physics, statistics, and engineering, it presents practical advice and techniques for studying biological rhythms, with a common language. The chapters proceed with increasing mathematical abstraction. Part I, on models, highlights the implicit assumptions and common pitfalls of modeling, and is accessible to readers with basic knowledge of differential equations and linear algebra. Part II, on behaviors, focuses on simpler models, describing common properties of biological rhythms that range from the firing properties of squid giant axon to human circadian rhythms. Part III, on mathematical techniques, guides readers who have specific models or goals in mind. Sections on “frontiers” present the latest research; “theory” sections present interesting mathematical results using more accessible approaches than can be found elsewhere. Each chapter offers exercises. Commented MATLAB code is provided to help readers get practical experience. The book, by an expert in the field, can be used as a textbook for undergraduate courses in mathematical biology or graduate courses in modeling biological rhythms and as a reference for researchers.
Elegant Chaos
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Author :
language : en
Publisher:
Release Date :
Elegant Chaos written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
The Neuroscience Of Sleep And Dreams
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Author : Patrick McNamara
language : en
Publisher: Cambridge University Press
Release Date : 2019-02-28
The Neuroscience Of Sleep And Dreams written by Patrick McNamara 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 2019-02-28 with Health & Fitness categories.
Introduces the neuroscience of sleep and dreams, including an investigation into their potential evolutionary and social functions.
Biorheology
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Author :
language : en
Publisher:
Release Date : 1990
Biorheology written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Biophysics categories.
Condensed Matter Field Theory
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Author : Alexander Altland
language : en
Publisher: Cambridge University Press
Release Date : 2010-03-11
Condensed Matter Field Theory written by Alexander Altland 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 2010-03-11 with Science categories.
This primer is aimed at elevating graduate students of condensed matter theory to a level where they can engage in independent research. Topics covered include second quantisation, path and functional field integration, mean-field theory and collective phenomena.
Dissertation Abstracts International
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Author :
language : en
Publisher:
Release Date : 1992-04
Dissertation Abstracts International written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04 with Dissertations, Academic categories.