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Interdisciplinary Applied Mathematics

Molecular Dynamics

With Deterministic and Stochastic Numerical Methods

Authors: Leimkuhler, Ben, Matthews, Charles

  • 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
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eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-319-16375-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-319-16374-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-319-35324-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
About this Textbook

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. 

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.

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)


Table of contents (8 chapters)

  • Introduction

    Leimkuhler, Ben (et al.)

    Pages 1-51

    Preview Buy Chapter 30,19 €
  • Numerical Integrators

    Leimkuhler, Ben (et al.)

    Pages 53-96

    Preview Buy Chapter 30,19 €
  • Analyzing Geometric Integrators

    Leimkuhler, Ben (et al.)

    Pages 97-138

    Preview Buy Chapter 30,19 €
  • The Stability Threshold

    Leimkuhler, Ben (et al.)

    Pages 139-177

    Preview Buy Chapter 30,19 €
  • Phase Space Distributions and Microcanonical Averages

    Leimkuhler, Ben (et al.)

    Pages 179-210

    Preview Buy Chapter 30,19 €

Buy this book

eBook 51,16 €
price for Spain (gross)
  • ISBN 978-3-319-16375-8
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-319-16374-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 62,39 €
price for Spain (gross)
  • ISBN 978-3-319-35324-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Molecular Dynamics
Book Subtitle
With Deterministic and Stochastic Numerical Methods
Authors
Series Title
Interdisciplinary Applied Mathematics
Series Volume
39
Copyright
2015
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-16375-8
DOI
10.1007/978-3-319-16375-8
Hardcover ISBN
978-3-319-16374-1
Softcover ISBN
978-3-319-35324-1
Series ISSN
0939-6047
Edition Number
1
Number of Pages
XXII, 443
Number of Illustrations and Tables
24 b/w illustrations, 71 illustrations in colour
Topics