Simulating Hamiltonian Dynamics
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Simulating Hamiltonian Dynamics
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Author : Benedict Leimkuhler
language : en
Publisher: Cambridge University Press
Release Date : 2004
Simulating Hamiltonian Dynamics written by Benedict Leimkuhler 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 2004 with Mathematics categories.
Geometric integrators are time-stepping methods, designed such that they exactly satisfy conservation laws, symmetries or symplectic properties of a system of differential equations. In this book the authors outline the principles of geometric integration and demonstrate how they can be applied to provide efficient numerical methods for simulating conservative models. Beginning from basic principles and continuing with discussions regarding the advantageous properties of such schemes, the book introduces methods for the N-body problem, systems with holonomic constraints, and rigid bodies. More advanced topics treated include high-order and variable stepsize methods, schemes for treating problems involving multiple time-scales, and applications to molecular dynamics and partial differential equations. The emphasis is on providing a unified theoretical framework as well as a practical guide for users. The inclusion of examples, background material and exercises enhance the usefulness of the book for self-instruction or as a text for a graduate course on the subject.
Simulating Hamiltonian Dynamics
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Author : B. Leimkuhler
language : en
Publisher:
Release Date : 2004
Simulating Hamiltonian Dynamics written by B. Leimkuhler and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Hamiltonian systems categories.
The Genesis Of Simulation In Dynamics
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Author : Thomas P. Weissert
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Genesis Of Simulation In Dynamics written by Thomas P. Weissert and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
An introduction to certain aspects of developments in the modern theory of dynamics and simulation for a wide audience of scientifically literate readers. Unlike general texts on chaos theory and dynamical systems theory, this book follows the work on a specific problem at the very beginning of the modern era of dynamics, from its inception in 1954 through the early 1970s. It discusses such problems as the nonlinear oscillator simulation, the seminal discoveries at MIT in the early 1950s, the mathematical rediscovery of solitons in the late 1950s and the general problems of computability. In following these developments, the initial development of many of the now standard techniques of nonlinear modelling and numerical simulation are seen. No other text focuses so tightly and covers so completely one specific, pernicious problem at the heart of dynamics.
Microscopic And Macroscopic Simulation Techniques Kharagpur Lectures
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Author : Hoover William Graham
language : en
Publisher: World Scientific
Release Date : 2018-03-13
Microscopic And Macroscopic Simulation Techniques Kharagpur Lectures written by Hoover William Graham and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-03-13 with Science categories.
This book aims to provide an example-based education in numerical methods for atomistic and continuum simulations of systems at and away from equilibrium. The focus is on nonequilibrium systems, stressing the use of tools from dynamical systems theory for their analysis. Lyapunov instability and fractal dimensionality are introduced and algorithms for their analysis are detailed. The book is intended to be self-contained and accessible to students who are comfortable with calculus and differential equations. The wide range of topics covered will provide students, researchers and academics with effective tools for formulating and solving interesting problems, both atomistic and continuum. The detailed description of the use of thermostats to control nonequilibrium systems will help readers in writing their own programs rather than being saddled with packaged software. Contents: Mechanics, Molecular Dynamics, and Gibbs' Statistical Mechanics Numerical Integration and Error Analysis Molecular Dynamics with Thermostats Simple Systems with Thermal Constraints Ergodicity and Its Importance in Small Systems Equilibrium Thermodynamics + Nonequilibrium Hydrodynamics Statistical Mechanics of Small Systems Microscopic Reversibility, Macroscopic Irreversibility Lyapunov Instability, Fractals, and Chaos I Lyapunov Instability, Fractals, and Chaos II Smooth-Particle Continuum Mechanics Epilogue Readership: Undergraduate, graduate students, researchers focusing on statistical mechanics and numerical simulation. Keywords: Numerical Methods;Simulation;Nonequilibrium;Molecular Dynamics;Continuum Mechanics;Statistical Mechanics;Chaos;Lyapunov Instability;Hydrodynamics;ThermodynamicsReview: Key Features: Three useful areas covered — treatment of control variables such as thermostats and ergostats, dynamical system analysis and the use of smooth particle techniques for analyzing molecular dynamics, and the solution of continuum problems
Essentials Of Hamiltonian Dynamics
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Author : John H. Lowenstein
language : en
Publisher: Cambridge University Press
Release Date : 2012-01-19
Essentials Of Hamiltonian Dynamics written by John H. Lowenstein 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 2012-01-19 with Mathematics categories.
Concise and pedagogical textbook that covers all the topics necessary for a graduate-level course in dynamics based on Hamiltonian methods.
Complex Hamiltonian Dynamics
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Author : Tassos Bountis
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-04-03
Complex Hamiltonian Dynamics written by Tassos Bountis and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-04-03 with Science categories.
This book introduces and explores modern developments in the well established field of Hamiltonian dynamical systems. It focuses on high degree-of-freedom systems and the transitional regimes between regular and chaotic motion. The role of nonlinear normal modes is highlighted and the importance of low-dimensional tori in the resolution of the famous FPU paradox is emphasized. Novel powerful numerical methods are used to study localization phenomena and distinguish order from strongly and weakly chaotic regimes. The emerging hierarchy of complex structures in such regimes gives rise to particularly long-lived patterns and phenomena called quasi-stationary states, which are explored in particular in the concrete setting of one-dimensional Hamiltonian lattices and physical applications in condensed matter systems. The self-contained and pedagogical approach is blended with a unique balance between mathematical rigor, physics insights and concrete applications. End of chapter exercises and (more demanding) research oriented problems provide many opportunities to deepen the reader’s insights into specific aspects of the subject matter. Addressing a broad audience of graduate students, theoretical physicists and applied mathematicians, this text combines the benefits of a reference work with those of a self-study guide for newcomers to the field.
Hamiltonian Dynamics Theory And Applications
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Author : CIME-EMS Summer School (
language : en
Publisher: Springer Science & Business Media
Release Date : 2005
Hamiltonian Dynamics Theory And Applications written by CIME-EMS Summer School ( and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Hamiltonian systems categories.
Hamiltonian Dynamics
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Author : Gaetano Vilasi
language : en
Publisher: World Scientific
Release Date : 2001-03-09
Hamiltonian Dynamics written by Gaetano Vilasi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-03-09 with Science categories.
This is both a textbook and a monograph. It is partially based on a two-semester course, held by the author for third-year students in physics and mathematics at the University of Salerno, on analytical mechanics, differential geometry, symplectic manifolds and integrable systems.As a textbook, it provides a systematic and self-consistent formulation of Hamiltonian dynamics both in a rigorous coordinate language and in the modern language of differential geometry. It also presents powerful mathematical methods of theoretical physics, especially in gauge theories and general relativity.As a monograph, the book deals with the advanced research topic of completely integrable dynamics, with both finitely and infinitely many degrees of freedom, including geometrical structures of solitonic wave equations.
Hamiltonian Dynamical Systems
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Author : H.S. Dumas
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Hamiltonian Dynamical Systems written by H.S. Dumas and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.
Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds
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Author : Taeyoung Lee
language : en
Publisher: Springer
Release Date : 2017-08-14
Global Formulations Of Lagrangian And Hamiltonian Dynamics On Manifolds written by Taeyoung Lee and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-14 with Mathematics categories.
This book provides an accessible introduction to the variational formulation of Lagrangian and Hamiltonian mechanics, with a novel emphasis on global descriptions of the dynamics, which is a significant conceptual departure from more traditional approaches based on the use of local coordinates on the configuration manifold. In particular, we introduce a general methodology for obtaining globally valid equations of motion on configuration manifolds that are Lie groups, homogeneous spaces, and embedded manifolds, thereby avoiding the difficulties associated with coordinate singularities. The material is presented in an approachable fashion by considering concrete configuration manifolds of increasing complexity, which then motivates and naturally leads to the more general formulation that follows. Understanding of the material is enhanced by numerous in-depth examples throughout the book, culminating in non-trivial applications involving multi-body systems. This book is written for a general audience of mathematicians, engineers, and physicists with a basic knowledge of mechanics. Some basic background in differential geometry is helpful, but not essential, as the relevant concepts are introduced in the book, thereby making the material accessible to a broad audience, and suitable for either self-study or as the basis for a graduate course in applied mathematics, engineering, or physics.