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Dimensional analysis simplifies complex physical problems and guides experimental investigations, but it does not provide complete solutions. It identifies the dimensionless groups that influence a phenomenon, but experimental data is needed to establish the specific relationships and validate theoretical predictions.
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Analytic expressions for correlations in coarse-grained simple fluids.

Siwei Luo1, Mark Thachuk1

  • 1Department of Chemistry, University of British Columbia, Vancouver, British Columbia V6T 1Z1, Canada.

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This study develops an analytical method for coarse-graining fluid simulations, simplifying potential calculations for homogeneous fluids. The new approach offers a foundation for large-scale simulations and studying atomic versus continuum fluid models.

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Area of Science:

  • Computational physics
  • Statistical mechanics
  • Fluid dynamics

Background:

  • Coarse-graining of fluids is complex due to particle diffusion.
  • Existing methods group particles into regions, with potentials depending on statistical properties.
  • Previous work identified a generalized quadratic form for these potentials.

Purpose of the Study:

  • To derive analytic expressions for coarse-graining potential parameters using statistical mechanics.
  • To enable a priori calculation of potentials for homogeneous, simple fluids.
  • To provide a quantitative framework for exploring the discrete-continuum boundary in fluid modeling.

Main Methods:

  • Utilizing statistical mechanics to derive analytic expressions for potential parameters.
  • Employing fluid properties, including pair distribution functions.
  • Comparing derived expressions with simulation-obtained values.

Main Results:

  • Analytic expressions for coarse-graining potential parameters were successfully derived.
  • Derived expressions showed good agreement with simulation-based values.
  • The method allows for a priori potential calculation without fitting.

Conclusions:

  • The derived analytic expressions simplify the coarse-graining scheme for homogeneous fluids.
  • This work lays the foundation for large-scale, bottom-up fluid simulations.
  • The approach offers quantitative insights into the transition from atomic to continuum fluid descriptions.