Kam Story The A Friendly Introduction To The Content History And Significance Of Classical Kolmogorov Arnold Moser Theory
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Kam Story The A Friendly Introduction To The Content History And Significance Of Classical Kolmogorov Arnold Moser Theory
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Author : H Scott Dumas
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-28
Kam Story The A Friendly Introduction To The Content History And Significance Of Classical Kolmogorov Arnold Moser Theory written by H Scott Dumas and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-28 with Mathematics categories.
This is a semi-popular mathematics book aimed at a broad readership of mathematically literate scientists, especially mathematicians and physicists who are not experts in classical mechanics or KAM theory, and scientific-minded readers. Parts of the book should also appeal to less mathematically trained readers with an interest in the history or philosophy of science.The scope of the book is broad: it not only describes KAM theory in some detail, but also presents its historical context (thus showing why it was a “breakthrough”). Also discussed are applications of KAM theory (especially to celestial mechanics and statistical mechanics) and the parts of mathematics and physics in which KAM theory resides (dynamical systems, classical mechanics, and Hamiltonian perturbation theory).Although a number of sources on KAM theory are now available for experts, this book attempts to fill a long-standing gap at a more descriptive level. It stands out very clearly from existing publications on KAM theory because it leads the reader through an accessible account of the theory and places it in its proper context in mathematics, physics, and the history of science.
Introduction To Arnold S Proof Of The Kolmogorov Arnold Moser Theorem
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Author : Achim Feldmeier
language : en
Publisher: CRC Press
Release Date : 2022-07-08
Introduction To Arnold S Proof Of The Kolmogorov Arnold Moser Theorem written by Achim Feldmeier and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-08 with Science categories.
INTRODUCTION TO ARNOLD’S PROOF OF THE KOLMOGOROV–ARNOLD–MOSER THEOREM This book provides an accessible step-by-step account of Arnold’s classical proof of the Kolmogorov–Arnold–Moser (KAM) Theorem. It begins with a general background of the theorem, proves the famous Liouville–Arnold theorem for integrable systems and introduces Kneser’s tori in four-dimensional phase space. It then introduces and discusses the ideas and techniques used in Arnold’s proof, before the second half of the book walks the reader through a detailed account of Arnold’s proof with all the required steps. It will be a useful guide for advanced students of mathematical physics, in addition to researchers and professionals. Features • Applies concepts and theorems from real and complex analysis (e.g., Fourier series and implicit function theorem) and topology in the framework of this key theorem from mathematical physics. • Covers all aspects of Arnold’s proof, including those often left out in more general or simplifi ed presentations. • Discusses in detail the ideas used in the proof of the KAM theorem and puts them in historical context (e.g., mapping degree from algebraic topology).
The Kam Story
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Author : H. Scott Dumas
language : en
Publisher:
Release Date : 2014
The Kam Story written by H. Scott Dumas and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Electronic books categories.
Introduction To Modern Dynamics
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Author : D. D. Nolte
language : en
Publisher:
Release Date : 2019
Introduction To Modern Dynamics written by D. D. Nolte and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Science categories.
Presents a unifying approach to the physics of chaos, nonlinear systems, dynamic networks, evolutionary dynamics, econophysics, and the theory of relativity. Each chapter has many worked examples and simple computer simulations that allow the student to explore the rich phenomena of nonlinear physics.
Molecular Dynamics Probability And Uncertainty
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Author : Peter V. Coveney
language : en
Publisher: Oxford University Press
Release Date : 2025-05-15
Molecular Dynamics Probability And Uncertainty written by Peter V. Coveney and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-15 with Science categories.
Embark on a fascinating exploration of molecular dynamics, which combines the authors' new probabilistic interpretation with cutting-edge simulations, some of which are performed on the largest supercomputers on our planet. From fundamental principles to innovative applications, this book covers the rich tapestry of molecular dynamics and its intersections with biological and medical sciences, materials science and engineering, and artificial intelligence, alongside uncertainty quantification. This enables the authors to highlight the critical role of molecular dynamics in delivering actionable outcomes for drug discovery, materials design and beyond. Beginning with a solid introduction to the intricate world of molecular dynamics, the book goes on to describe its modern probabilistic formulation. It investigates ensemble-based molecular dynamics simulations and free energies, uncovering both the way that ensemble techniques revolutionize simulation methodologies and how they empower researchers to generate new insights. Further, the book explores the exciting realm of simulations for advanced materials and discusses verification, validation and uncertainty quantification, illuminating the synergies between molecular dynamics and artificial intelligence and their potential for transformative breakthroughs. Whether you are a seasoned researcher seeking to expand your knowledge or a curious student eager to investigate the complexities of molecular dynamics, this book serves as an indispensable resource, challenging conventional approaches, offering fresh perspectives and unlocking new insights into real-world problems in this captivating field.
The Parameterization Method For Invariant Manifolds
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Author : Àlex Haro
language : en
Publisher: Springer
Release Date : 2016-04-18
The Parameterization Method For Invariant Manifolds written by Àlex Haro and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-18 with Mathematics categories.
This monograph presents some theoretical and computational aspects of the parameterization method for invariant manifolds, focusing on the following contexts: invariant manifolds associated with fixed points, invariant tori in quasi-periodically forced systems, invariant tori in Hamiltonian systems and normally hyperbolic invariant manifolds. This book provides algorithms of computation and some practical details of their implementation. The methodology is illustrated with 12 detailed examples, many of them well known in the literature of numerical computation in dynamical systems. A public version of the software used for some of the examples is available online. The book is aimed at mathematicians, scientists and engineers interested in the theory and applications of computational dynamical systems.
100 Years Of Math Milestones The Pi Mu Epsilon Centennial Collection
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Author : Stephan Ramon Garcia
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-06-13
100 Years Of Math Milestones The Pi Mu Epsilon Centennial Collection written by Stephan Ramon Garcia and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-06-13 with Mathematics categories.
This book is an outgrowth of a collection of 100 problems chosen to celebrate the 100th anniversary of the undergraduate math honor society Pi Mu Epsilon. Each chapter describes a problem or event, the progress made, and connections to entries from other years or other parts of mathematics. In places, some knowledge of analysis or algebra, number theory or probability will be helpful. Put together, these problems will be appealing and accessible to energetic and enthusiastic math majors and aficionados of all stripes. Stephan Ramon Garcia is WM Keck Distinguished Service Professor and professor of mathematics at Pomona College. He is the author of four books and over eighty research articles in operator theory, complex analysis, matrix analysis, number theory, discrete geometry, and other fields. He has coauthored dozens of articles with students, including one that appeared in The Best Writing on Mathematics: 2015. He is on the editorial boards of Notices of the AMS, Proceedings of the AMS, American Mathematical Monthly, Involve, and Annals of Functional Analysis. He received four NSF research grants as principal investigator and five teaching awards from three different institutions. He is a fellow of the American Mathematical Society and was the inaugural recipient of the Society's Dolciani Prize for Excellence in Research. Steven J. Miller is professor of mathematics at Williams College and a visiting assistant professor at Carnegie Mellon University. He has published five books and over one hundred research papers, most with students, in accounting, computer science, economics, geophysics, marketing, mathematics, operations research, physics, sabermetrics, and statistics. He has served on numerous editorial boards, including the Journal of Number Theory, Notices of the AMS, and the Pi Mu Epsilon Journal. He is active in enrichment and supplemental curricular initiatives for elementary and secondary mathematics, from the Teachers as Scholars Program and VCTAL (Value of Computational Thinking Across Grade Levels), to numerous math camps (the Eureka Program, HCSSiM, the Mathematics League International Summer Program, PROMYS, and the Ross Program). He is a fellow of the American Mathematical Society, an at-large senator for Phi Beta Kappa, and a member of the Mount Greylock Regional School Committee, where he sees firsthand the challenges of applying mathematics.
Galileo Unbound
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Author : David D. Nolte
language : en
Publisher: Oxford University Press
Release Date : 2018-07-12
Galileo Unbound written by David D. Nolte and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-12 with Science categories.
Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once -- setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.
Non Reciprocal Materials And Systems
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Author : Prabhakar Bandaru
language : en
Publisher: Elsevier
Release Date : 2024-01-22
Non Reciprocal Materials And Systems written by Prabhakar Bandaru and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-01-22 with Technology & Engineering categories.
Non-Reciprocal Materials and Systems: An Engineering Approach to the Control of Light, Sound, and Heat discusses the related concept of bound states which help confine sound and electromagnetic waves and can also lead to the control of thermal energy. The requirements for the formation of such bound states, their relationship to physical and topological characteristics of materials, and the possible application to new devices is considered. The book takes a unique approach to energy transfer in and between materials systems - considering dimensional effects, supersonic, transonic and subsonic wave motion, as well as the coupling of waves. This book is suitable for researchers in materials science, condensed matter physics, electrical, mechanical, and structural engineering, and technologists aiming for better control of non-electronic physical phenomena. - Provides information on how to use specific features in new and artificial materials for the control of sound, light and heat - Explores dimensional considerations such as surface material phenomena that can be decoupled from bulk materials or the inside of a material - Discusses new device concepts and related technologies such as energy sources, isolators, and diodes involving energy confinement
Phases Of Matter And Their Transitions
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Author : Gijsbertus de With
language : en
Publisher: John Wiley & Sons
Release Date : 2023-10-30
Phases Of Matter And Their Transitions written by Gijsbertus de With and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-30 with Science categories.
Phases of Matter and their Transitions An all-in-one, comprehensive take on matter and its phase properties In Phases of Matter and their Transitions, accomplished materials scientist Dr. Gijsbertus de With delivers an accessible textbook for advanced students in the molecular sciences. It offers a balanced and self-contained treatment of the thermodynamic and structural aspects of phases and the transitions between them, covering solids, liquids, gases, and their interfaces. The book lays the groundwork to describe particles and their interactions from the perspective of classical and quantum mechanics and compares phenomenological and statistical thermodynamics. It also examines materials with special properties, like glasses, liquid crystals, and ferroelectrics. The author has included an extensive appendix with a guide to the mathematics and theoretical models employed in this resource. Readers will also find: Thorough introductions to classical and quantum mechanics, intermolecular interactions, and continuum mechanics Comprehensive explorations of thermodynamics, gases, liquids, and solids Practical discussions of surfaces, including their general aspects for solids and liquids Fulsome treatments of discontinuous and continuous transitions, including discussions of irreversibility and the return to equilibrium Perfect for advanced students in chemistry and physics, Phases of Matter and their Transitions will also earn a place in the libraries of students of materials science.