Schematic representation of a reference coarse cell (dark shade) surrounded by a local environment shell (light shade).
Excess free energy change for particle insertion computed for the LJ potential for argon at T* = 1.2 as a function of cell and environment densities. The coarse cell length, L, was chosen to be 3σ, while the environment shell thickness is 1.5σ. Symbols correspond to Widom insertion simulation results, shaded surface represents polynomial interpolation (3rd-order in each dimension).
Schematic representation of a one-dimensional system with a concentration gradient. (a) Full-resolution MMC representation and (b) CG-MMC representation in which the gray shade denotes qualitatively the occupancy in each cell.
One-dimensional projection of particle density distribution with (a) CG-MMC and (b) NECG-MMC. Symbols – coarse-grained simulations after 2 × 108 moves, thick solid line – Gaussian fits to simulation, and thin dashed line – initial condition (Eq. (26) ).
One-dimensional projection of ideal-gas particle density distribution with CG-MMC (squares) and NECG-MMC (circles) after 2 × 108 moves in an external potential. Solid line – initial condition (Eq. (26) ).
Simulation “time” as a function of NECG-MMC steps extracted from Gaussian fits of the particle distribution for ideal gas diffusion without drift.
One-dimensional projection of LJ-argon particle density distribution with CG-MMC (squares) and NECG-MMC (circles) after 1 × 108 moves in an external potential. Solid line – initial condition (Eq. (25) ).
One-dimensional density distribution profiles obtained by NECG-MMC simulation after varying numbers of steps at different coarse-graining levels. The number of steps required at each coarse-graining level was chosen to map all curves onto the reference case – 5 × 107 steps with L cell = 1 (black circles). Other cases are: 3.2 × 107 steps, L cell = 1.25 (red diamonds); 1.8 × 107 steps, L cell = 1.67 (blue squares), and 0.8 × 107, L cell = 2.5 (green deltas). Solid line – Gaussian fit to all data; dashed line – initial condition (Eq. (26) ).
Equivalence of simulation time at different CG-MMC steps corresponding to different coarse-graining levels.
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