Simulating Hamiltonian Dynamics

Author: Benedict Leimkuhler,Sebastian Reich

Publisher: Cambridge University Press

ISBN: 9780521772907

Category: Mathematics

Page: 379

View: 1531

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.

Global Formulations of Lagrangian and Hamiltonian Dynamics on Manifolds

A Geometric Approach to Modeling and Analysis

Author: Taeyoung Lee,Melvin Leok,N. Harris McClamroch

Publisher: Springer

ISBN: 3319569538

Category: Mathematics

Page: 539

View: 3243

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.

New Algorithms for Macromolecular Simulation

Author: Benedict Leimkuhler,Christophe Chipot,Ron Elber,Aatto Laaksonen,Alan Mark,Tamar Schlick,Christoph Schütte,Robert Skeel

Publisher: Springer Science & Business Media

ISBN: 3540316183

Category: Computers

Page: 367

View: 5336

Molecular simulation is a widely used tool in biology, chemistry, physics and engineering. This book contains a collection of articles by leading researchers who are developing new methods for molecular modelling and simulation. Topics addressed here include: multiscale formulations for biomolecular modelling, such as quantum-classical methods and advanced solvation techniques; protein folding methods and schemes for sampling complex landscapes; membrane simulations; free energy calculation; and techniques for improving ergodicity. The book is meant to be useful for practitioners in the simulation community and for those new to molecular simulation who require a broad introduction to the state of the art.

Computer Simulation of Liquids

Author: Michael P. Allen,Dominic J. Tildesley

Publisher: Oxford University Press

ISBN: 0198803192

Category: Computers

Page: 640

View: 5401

This book provides a practical guide to molecular dynamics and Monte Carlo simulation techniques used in the modelling of simple and complex liquids. Computer simulation is an essential tool in studying the chemistry and physics of condensed matter, complementing and reinforcing both experiment and theory. Simulations provide detailed information about structure and dynamics, essential to understand the many fluid systems that play a key role in our daily lives: polymers, gels, colloidal suspensions, liquid crystals, biological membranes, and glasses. The second edition of this pioneering book aims to explain how simulation programs work, how to use them, and how to interpret the results, with examples of the latest research in this rapidly evolving field. Accompanying programs in Fortran and Python provide practical, hands-on, illustrations of the ideas in the text.

Symplectic Geometric Algorithms for Hamiltonian Systems

Author: Kang Feng,Mengzhao Qin

Publisher: Springer Science & Business Media

ISBN: 3642017770

Category: Mathematics

Page: 676

View: 8586

"Symplectic Geometric Algorithms for Hamiltonian Systems" will be useful not only for numerical analysts, but also for those in theoretical physics, computational chemistry, celestial mechanics, etc. The book generalizes and develops the generating function and Hamilton-Jacobi equation theory from the perspective of the symplectic geometry and symplectic algebra. It will be a useful resource for engineers and scientists in the fields of quantum theory, astrophysics, atomic and molecular dynamics, climate prediction, oil exploration, etc. Therefore a systematic research and development of numerical methodology for Hamiltonian systems is well motivated. Were it successful, it would imply wide-ranging applications.

Thermal Analysis of Polymeric Materials

Author: Bernhard Wunderlich

Publisher: Springer Science & Business Media

ISBN: 9783540236290

Category: Science

Page: 894

View: 4950

"Thermal Analysis of Polymeric Materials" systematically treats macroscopic measurements by thermal analysis and the quantitative link to microscopic, molecular structure and mobility. Reversible and irreversible thermodynamics, kinetics, quantum mechanics, and statistical thermodynamics are the roots of the described thermal analysis. The book aims to broaden readers’ understanding of materials and the connection of flexible macromolecules (polymers) to small molecules and rigid macromolecules (minerals, salts, and metals). An effort is made to discover how the long, flexible molecules fit into their small phases which are characterized as microphases or nanophases. Their order ranges from amorphous to mesophase-like and crystalline. Ultimately, it is shown that the basic structure-property-processing triangle is connected to the better-known types of molecules and their common macroscopic phases.

Geometry and Topology in Hamiltonian Dynamics and Statistical Mechanics

Author: Marco Pettini

Publisher: Springer Science & Business Media

ISBN: 0387499571

Category: Mathematics

Page: 456

View: 8961

This book covers a new explanation of the origin of Hamiltonian chaos and its quantitative characterization. The author focuses on two main areas: Riemannian formulation of Hamiltonian dynamics, providing an original viewpoint about the relationship between geodesic instability and curvature properties of the mechanical manifolds; and a topological theory of thermodynamic phase transitions, relating topology changes of microscopic configuration space with the generation of singularities of thermodynamic observables. The book contains numerous illustrations throughout and it will interest both mathematicians and physicists.

IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence

Proceedings of the IUTAM Symposium held in Moscow, 25-30 August, 2006

Author: Alexey V. Borisov,Valery V. Kozlov,Ivan S. Mamaev,Mikhail A. Sokolovskiy

Publisher: Springer Science & Business Media

ISBN: 1402067445

Category: Science

Page: 501

View: 9563

This work brings together previously unpublished notes contributed by participants of the IUTAM Symposium on Hamiltonian Dynamics, Vortex Structures, Turbulence (Moscow, 25-30 August 2006). The study of vortex motion is of great interest to fluid and gas dynamics: since all real flows are vortical in nature, applications of the vortex theory are extremely diverse, many of them (e.g. aircraft dynamics, atmospheric and ocean phenomena) being especially important.

Nonlinearity

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematical analysis

Page: N.A

View: 2623


Hamiltonian Dynamical Systems

History, Theory, and Applications

Author: H.S. Dumas,K.R. Meyer,D.S. Schmidt

Publisher: Springer Science & Business Media

ISBN: 9780387944371

Category: Mathematics

Page: 385

View: 7249

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.

Physical Review

Statistical physics, plasmas, fluids, and related interdisciplinary topics. E

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Fluids

Page: N.A

View: 4417


Lectures on Geophysical Fluid Dynamics

Author: Rick Salmon

Publisher: Oxford University Press

ISBN: 9780195355321

Category: Science

Page: 400

View: 4370

Lectures on Geophysical Fluid Dynamics offers an introduction to several topics in geophysical fluid dynamics, including the theory of large-scale ocean circulation, geostrophic turbulence, and Hamiltonian fluid dynamics. Since each chapter is a self-contained introduction to its particular topic, the book will be useful to students and researchers in diverse scientific fields.

The Genesis of Simulation in Dynamics

Pursuing the Fermi-Pasta-Ulam Problem

Author: Thomas P. Weissert

Publisher: Springer Science & Business Media

ISBN: 1461219566

Category: Science

Page: 176

View: 7645

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.

Probabilistic Forecasting and Bayesian Data Assimilation

Author: Sebastian Reich,Colin Cotter

Publisher: Cambridge University Press

ISBN: 1316299422

Category: Computers

Page: N.A

View: 9490

In this book the authors describe the principles and methods behind probabilistic forecasting and Bayesian data assimilation. Instead of focusing on particular application areas, the authors adopt a general dynamical systems approach, with a profusion of low-dimensional, discrete-time numerical examples designed to build intuition about the subject. Part I explains the mathematical framework of ensemble-based probabilistic forecasting and uncertainty quantification. Part II is devoted to Bayesian filtering algorithms, from classical data assimilation algorithms such as the Kalman filter, variational techniques, and sequential Monte Carlo methods, through to more recent developments such as the ensemble Kalman filter and ensemble transform filters. The McKean approach to sequential filtering in combination with coupling of measures serves as a unifying mathematical framework throughout Part II. Assuming only some basic familiarity with probability, this book is an ideal introduction for graduate students in applied mathematics, computer science, engineering, geoscience and other emerging application areas.

Vorticity, Statistical Mechanics, and Monte Carlo Simulation

Author: Chjan Lim,Joseph Nebus

Publisher: Springer Science & Business Media

ISBN: 0387494316

Category: Mathematics

Page: 290

View: 4436

This book is drawn from across many active fields of mathematics and physics. It has connections to atmospheric dynamics, spherical codes, graph theory, constrained optimization problems, Markov Chains, and Monte Carlo methods. It addresses how to access interesting, original, and publishable research in statistical modeling of large-scale flows and several related fields. The authors explicitly reach around the major branches of mathematics and physics, showing how the use of a few straightforward approaches can create a cornucopia of intriguing questions and the tools to answer them.