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Introduction

  • Chapter
Molecular Dynamics

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

Abstract

Molecular dynamics is the study of how molecules move, deform and interact over time. Predicting or interpreting these changes is essential in chemistry, physics, biology, engineering and other fields. This book discusses the foundations of the numerical methods that are used for studying molecular dynamics.

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Notes

  1. 1.

    Building such a structure from microscopy data is complicated as one must first assemble the pentamer-hexamer frame and optimize the local hexamer and pentamer structural units (i.e. locate the atoms within the structure), using several levels of atomistic force fields (including also quantum-mechanical-molecular mechanical treatments). The last stage is a GPU-accelerated simulation involving 64M atoms for 200 ns using (a) r-RESPA multiple timestepping (See Chap. 4), and (b) constrained bonds to hydrogen atoms (Chap. 4), in (c) a constant temperature and pressure framework (see Chap. 8). (Details provided by one of the authors of the study, J. Perilla of the Theoretical and Computational Biophysics Group, University of Illinois.)

  2. 2.

    In fact, many results and estimates given in this book technically require greater smoothness, but in practice discontinuity in second or higher derivatives of the potential at a single point does not usually cause great difficulty.

  3. 3.

    We use roman (non-italic) letters for parameters that describe the thermodynamic state, e.g. number of degrees of freedom, the volume, the energy, the temperature or the pressure.

  4. 4.

    For readers conversant with concepts of statistical mechanics and in preparation for later discussions, we emphasize that the concept of mechanical equilibrium given in relation to the system of ordinary differential equation (1.6) is entirely different from the notion of statistical or thermal equilibrium of Chap. 6.

  5. 5.

    The Lennard-Jones Trimer is included as an example in the MD.M package, see http://MolecularDynamics.info

  6. 6.

    Note that in periodic boundary conditions the linear momentum would also be preserved, but the angular momentum is not.

  7. 7.

    The Anisotropic Oscillator is included as an example in the MD.M package, see http://MolecularDynamics.info

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Authors and Affiliations

  1. School of Mathematics, University of Edinburgh, Edinburgh, UK

    Ben Leimkuhler

  2. Gordon Center for Integrative Science, University of Chicago, Chicago, IL, USA

    Charles Matthews

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Leimkuhler, B., Matthews, C. (2015). Introduction. In: Molecular Dynamics. Interdisciplinary Applied Mathematics, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-16375-8_1

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