5 research outputs found
Coarse Grained Computations for a Micellar System
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
Coarse-Grained Kinetic Computations for Rare Events: Application to Micelle Formation
We discuss a coarse-grained approach to the computation of rare events in the
context of grand canonical Monte Carlo (GCMC) simulations of self-assembly of
surfactant molecules into micelles. The basic assumption is that the {\it
computational} system dynamics can be decomposed into two parts -- fast (noise)
and slow (reaction coordinates) dynamics, so that the system can be described
by an effective, coarse grained Fokker-Planck (FP) equation. While such an
assumption may be valid in many circumstances, an explicit form of FP equation
is not always available. In our computations we bypass the analytic derivation
of such an effective FP equation. The effective free energy gradient and the
state-dependent magnitude of the random noise, which are necessary to formulate
the effective Fokker-Planck equation, are obtained from ensembles of short
bursts of microscopic simulations {\it with judiciously chosen initial
conditions}. The reaction coordinate in our micelle formation problem is taken
to be the size of a cluster of surfactant molecules. We test the validity of
the effective FP description in this system and reconstruct a coarse-grained
free energy surface in good agreement with full-scale GCMC simulations. We also
show that, for very small clusters, the cluster size seizes to be a good
reaction coordinate for a one-dimensional effective description. We discuss
possible ways to improve the current model and to take higher-dimensional
coarse-grained dynamics into account