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Conservative Potentials for a Lattice-Mapped, Coarse-Grain Scheme with Fuzzy Switching Functions
1Department of Chemistry, University of British Columbia, Vancouver V6T 1Z1, Canada.
The Journal of Physical Chemistry. A
|June 29, 2022
Summary
This study introduces fuzzy boundaries for coarse-grain (CG) mapping, enabling a smooth transition from atomistic to continuum descriptions. Overlap degree controls mass distribution and correlations, informing when continuum theory is applicable.
Area of Science:
- Computational Chemistry
- Materials Science
- Statistical Mechanics
Background:
- Previous work established conservative potentials for lattice-like coarse-grain (CG) mapping.
- Sharply defined boundaries in CG models can be limiting for complex systems.
Purpose of the Study:
- To extend CG mapping schemes to systems with fuzzy, interpenetrating spatial regions.
- To investigate the impact of fuzzy boundaries on system properties and the applicability of continuum theory.
Main Methods:
- Utilized fuzzy switching functions to create overlapping subcells with fractional particle occupations.
- Calculated the full mass matrix, including off-diagonal elements, for fuzzy systems.
- Analyzed mass distribution transitions and correlations among CG variables as a function of overlap.
Main Results:
- Observed a transition in mass distribution from discrete to continuous (Gaussian-like) with increasing overlap, indicating suitability for continuum theory.
- Calculated CG correlations dependent on overlap degree, revealing trade-offs between interaction complexity and fuzziness.
- Found CG potentials approximated by generalized quadratic functions for large particle numbers and moderate overlap.
Conclusions:
- Demonstrated a quantitative method to bridge atomistic and continuum resolutions in CG models.
- Highlighted the importance of fuzzy boundaries in designing CG schemes with mixed resolution character.
- Provided insights into the relationship between spatial overlap, system dynamics, and theoretical descriptions.
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