Coarse Grained Computations for a Micellar System

TL;DR

This paper introduces an equation-free, coarse-grained computational framework that connects atomistic simulations of micelle formation with continuum numerical algorithms, enabling efficient analysis of system-level behavior without explicit macroscopic equations.

Contribution

It develops a novel equation-free approach that uses short atomistic simulations to estimate coarse-grained dynamics, bridging microscopic models and macroscopic analysis.

Findings

Successfully estimates coarse-grained dynamics from atomistic simulations.

Accelerates convergence to system equilibrium using traditional numerical methods.

Provides a computational method to analyze micellar systems without explicit macroscopic equations.

Abstract

We establish, through coarse-grained computation, a connection between traditional, continuum numerical algorithms (initial value problems as well as fixed point algorithms) and atomistic simulations of the Larson model of micelle formation. The procedure hinges on the (expected) evolution of a few slow, coarse-grained mesoscopic observables of the MC simulation, and on (computational) time scale separation between these and the remaining "slaved", fast variables. Short bursts of appropriately initialized atomistic simulation are used to estimate the (coarse-grained, deterministic) local dynamics of the evolution of the observables. These estimates are then in turn used to accelerate the evolution to computational stationarity through traditional continuum algorithms (forward Euler integration, Newton-Raphson fixed point computation). This "equation-free" framework, bypassing the derivation of explicit, closed equations for the observables (e.g. equations of state) may provide a computational bridge between direct atomistic / stochastic simulation and the analysis of its macroscopic, system-level consequences.