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Inhomogeneous multiscale dynamics in harmonic lattices.

David Cubero1, Sophia N Yaliraki

  • 1Department of Chemistry, South Kensington Campus, Imperial College, London SW7 2AZ, United Kingdom.

The Journal of Chemical Physics
|March 3, 2005
PubMed
Summary

This study introduces a novel projection operator method for coarse-grained multiscale systems. It accurately recovers thermodynamic equilibrium and the fluctuation-dissipation theorem from simulations.

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Area of Science:

  • Multiscale modeling
  • Statistical mechanics
  • Computational physics

Background:

  • Coarse-grained models simplify complex systems by reducing degrees of freedom.
  • Existing methods often rely on thermodynamic averages, limiting applicability.
  • Harmonic systems present unique challenges in multiscale analysis.

Purpose of the Study:

  • To develop a projection operator approach for coarse-grained multiscale problems in harmonic systems.
  • To present stochastic equations of motion for coarse-grained variables with inhomogeneous coarse-graining.
  • To establish a framework that recovers thermodynamic equilibrium and the fluctuation-dissipation theorem.

Main Methods:

  • Utilizing projection operators and a physically motivated projection matrix.
  • Employing molecular dynamics simulations to compute system-specific information.
  • Analyzing the algebraic properties of the projection matrix for stability.

Main Results:

  • Thermodynamic equilibrium and the fluctuation-dissipation theorem are recovered a posteriori.
  • The approach extends existing methods like quasicontinuum and offers insights into dissipative particle dynamics.
  • Demonstrates that coarse-grained variables may not follow a Markovian process.

Conclusions:

  • The projection operator method provides a robust framework for multiscale analysis in harmonic systems.
  • Applicable to systems with linear coarse-grained regions, including mesoscopic particle dynamics.
  • Offers a new perspective on the nature of stochastic processes in coarse-grained models.

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