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 With Deterministic and Stochastic Numerical Methods (2015) - Ben Leimkuhler, Charles Matthews - Molecular Dynamics [ENG] [PDF] [LIBGEN]

With Deterministic and Stochastic Numerical Methods (2015) - Ben Leimkuhler, Charles Matthews - Molecular Dynamics [ENG] [PDF] [LIBGEN]
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Describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods
Provides precise statements regarding different numerical procedures which enables selection of the best method for a given problem
Although it is aimed at a broad audience and presumes only basic mathematical preparation, the book presents the relevant theory of Hamiltonian mechanics and stochastic differential equations
Coverage is provided of symplectic numerical methods, constraints and rigid bodies, Langevin dynamics, thermostats and barostats, multiple time-stepping, and the dissipative particle dynamics method


This book describes the mathematical underpinnings of algorithms used for molecular dynamics simulation, including both deterministic and stochastic numerical methods. Molecular dynamics is one of the most versatile and powerful methods of modern computational science and engineering and is used widely in chemistry, physics, materials science and biology. Understanding the foundations of numerical methods means knowing how to select the best one for a given problem (from the wide range of techniques on offer) and how to create new, efficient methods to address particular challenges as they arise in complex applications.

Aimed at a broad audience, this book presents the basic theory of Hamiltonian mechanics and stochastic differential equations, as well as topics including symplectic numerical methods, the handling of constraints and rigid bodies, the efficient treatment of Langevin dynamics, thermostats to control the molecular ensemble, multiple time-stepping, and the dissipative particle dynamics method.


Topics
Applications of Mathematics
Mathematical and Computational Biology
Table of contents :
Front Matter....Pages i-xxii
Introduction....Pages 1-51
Numerical Integrators....Pages 53-96
Analyzing Geometric Integrators....Pages 97-138
The Stability Threshold....Pages 139-177
Phase Space Distributions and Microcanonical Averages....Pages 179-210
The Canonical Distribution and Stochastic Differential Equations....Pages 211-260
Numerical Methods for Stochastic Molecular Dynamics....Pages 261-328
Extended Variable Methods....Pages 329-401
Back Matter....Pages 403-443
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