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© 2015

Molecular Dynamics

With Deterministic and Stochastic Numerical Methods

  • 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

Textbook

Part of the Interdisciplinary Applied Mathematics book series (IAM, volume 39)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Ben Leimkuhler, Charles Matthews
    Pages 1-51
  3. Ben Leimkuhler, Charles Matthews
    Pages 53-96
  4. Ben Leimkuhler, Charles Matthews
    Pages 97-138
  5. Ben Leimkuhler, Charles Matthews
    Pages 139-177
  6. Ben Leimkuhler, Charles Matthews
    Pages 179-210
  7. Ben Leimkuhler, Charles Matthews
    Pages 211-260
  8. Ben Leimkuhler, Charles Matthews
    Pages 261-328
  9. Ben Leimkuhler, Charles Matthews
    Pages 329-401
  10. Back Matter
    Pages 403-443

About this book

Introduction

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. 

Keywords

65C20,65P10,65Z05,82C31,82C05,82B80 biomolecular simulation computational physics materials modelling molecular dynamics theoretical chemistry

Authors and affiliations

  1. 1.University of Edinburgh School of MathematicsEdinburghUnited Kingdom
  2. 2.Gordon Center for Integrative ScienceUniversity of ChicagoChicagoUSA

About the authors

Benedict Leimkuhler has worked extensively for more than two decades on the study of molecular dynamics algorithms. He is the author of research publications on constrained molecular dynamics, temperature controls, stochastic molecular dynamics methods, quantum methods, and advanced integration strategies (multiple time-stepping, adaptive methods).  He currently holds the Chair of Applied Mathematics at the University of Edinburgh, is a Fellow of the Royal Society of Edinburgh and a Fellow of the Institute of Mathematics and Its Applications, and is on the editorial boards of four journals.

Charles Matthews obtained his PhD in applied mathematics from the University of Edinburgh, working in the area of numerical methods for stochastic differential equations. He has published research in both chemical physics and mathematics journals on discretization problems in molecular dynamics. He currently is a research staff member in the Department of Statistics at the University of Chicago, investigating sampling methodologies for molecular simulation and the modelling of power networks.

Bibliographic information

  • Book Title Molecular Dynamics
  • Book Subtitle With Deterministic and Stochastic Numerical Methods
  • Authors Ben Leimkuhler
    Charles Matthews
  • Series Title Interdisciplinary Applied Mathematics
  • Series Abbreviated Title Interdisciplin. Appl. Math.
  • DOI https://doi.org/10.1007/978-3-319-16375-8
  • Copyright Information Springer International Publishing Switzerland 2015
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-16374-1
  • Softcover ISBN 978-3-319-35324-1
  • eBook ISBN 978-3-319-16375-8
  • Series ISSN 0939-6047
  • Series E-ISSN 2196-9973
  • Edition Number 1
  • Number of Pages XXII, 443
  • Number of Illustrations 24 b/w illustrations, 71 illustrations in colour
  • Topics Applications of Mathematics
    Mathematical and Computational Biology
  • Buy this book on publisher's site

Reviews

“This book is strongly recommended both for individual study and as the basis of a graduate course in computational MD that covers current research topics; for an audience of mathematics students, who may feel uneasy with the rather pragmatic presentation that mixes analytical arguments, numerical demonstrations, and heuristics … . Researchers in the field ought to find the book to be worth occupying a spot in their bookshelves.” (Carsten Hartmann, SIAM Review, Vol. 57 (3), September, 2015)