Project title: Coarse-grained molecular dynamics.

Supervisors: Prof Matthew Foulkes, Prof Dimitri Vvedensky and Dr Paul Tangney                                                                                 

Project description:

The idea behind coarse-graining of classical molecular dynamics is to derive a reduced set of equations of motion on a finite-element mesh from an atomistic molecular dynamics Hamiltonian. When the mesh nodes and the atomic sites are identical, the coarse-grained equations of motion are exact. As the mesh size increases, shorter wavelength modes are eliminated, and their effect on the remaining modes is included through thermodynamic averaging. The proposed research aims to examine coarse-graining approaches based on the functional integral representation of the dynamics of a system, rather than focusing on the equilibrium properties through the partition function. This could shed light on the relationship between molecular dynamics and the quasicontinuum method, as well as providing new avenues of investigation for the structural dynamics of nanostructures. In regions of nearly ideal crystal, it may be possible to apply similar coarse-graining ideas to the quantum mechanical density matrix, by writing it as a smoothly varying “envelope” transform of the density matrix of the perfect crystal and deriving equations of motion for the envelope. If this proves practical, it will allow the embedding of time-consuming quantum simulations of, for example, point defects, into effectively infinite solids at reasonable costs.

Research highlights:

  • Talk at NPL: “Coarse-Grained Molecular Dynamics” (December 2010)
  • Talk at CMTH Informal Seminar: “Coarse-Grained Molecular Dynamics” (June 2011)