Probability distributions for the distance between adjacent center-of-mass beads of size for self-avoiding chains, parametrized by total chain length.
Cumulative distribution function for the coarse-grained bond angle, in a self-avoiding chain with and , as a function of , the “first” bond length forming the angle. The top, solid curve shows bond lengths less than the ideal value of for the freely jointed chain; the middle, dashed curve shows ; and the bottom, dash-dotted curve shows .
Estimate for the true interatomic potential used to improve the WAMC self-avoiding walk model. The potential is shown for coarse-grained beads representing 32 original beads of diameter 1. for the 32-mer.
Scaled probability distribution , illustrating the scaling of the distance away from the center of mass and scaling of the probability.
Dependence of overlap probability, on : overlap between 32-mers with test-volume size , , and as a function of the separation of centers of mass, as obtained via direct simulation [solid curves] and approximation (22), with given by (15) [dashed curves].
Scaled potential showing the dependence of the potential for two freely jointed chains of 32-mers in the limit using approximation (22).
Scaled potentials showing the dependence of the potential for overlap of two freely jointed chains of 32-mers determined by direct simulation.
Scaling of the two-body potential created by approximation (22), parametrized by increasing bond length ( is the bottom curve; is the top curve), demonstrating convergence towards a fixed curve as .
Scaling of the two-body potential created via direct simulation, parametrized by increasing bond length (, 64, and 128 from bottom to top, respectively).
The coarse-grained overlap potential for two self-avoiding chain segments of length 32, parametrized as a function of the test-volume size , demonstrating the dependence of as .
Collapse of coarse-grained overlap potential for two self-avoiding chains of lengths , 64, or 128, and test-volume size , showing an dependence for the range of the potential and an dependence on the magnitude.
Mean end-to-end distance of the pivot algorithm (circles) and of coarse-grained simulations based on bead sizes of 32 and 64 (triangles and squares, respectively).
Running time comparison for standard non-CG simulation (squares), optimized atomistic (non-CG) simulation (diamonds), and WAMC algorithm with (crosses) and (asterisks).
Mean bond length connecting 32-mers as a function of chain length.
Mean end-to-end distance for atomistic vs WAMC algorithms.
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