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Topological coarse graining of polymer chains using wavelet-accelerated Monte Carlo. I. Freely jointed chains
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Image of FIG. 1.
FIG. 1.

Coarse graining of a 16-site random walk in two dimensions using “center-of-mass aggregation” of adjacent points along the chain, as suggested by the wavelet transform method. The four sites which would be created after another iteration of this method are indicated on the graph; note that each is at a quarter-integer lattice point.

Image of FIG. 2.
FIG. 2.

Coarse graining of a three-dimensional walk on a cubic lattice using the wavelet transform. (a) A 512-step self-avoiding random walk. (b)–(d) The same walk, after one, two, and three iterations of the Haar transform defined by (6) and (7).

Image of FIG. 3.
FIG. 3.

Comparison of the probability distributions for the coarse-grained bond length (distance between adjacent center-of-mass beads) for freely jointed chains for different chain lengths, with each coarse-grained bead representing 32 beads on the original chain.

Image of FIG. 4.
FIG. 4.

Ideal and observed coarse-grained cumulative distribution functions for a coarse-grained Gaussian random walk divided into segments of 32 beads each (c=4).

Image of FIG. 5.
FIG. 5.

Cumulative distribution function for the coarse-grained bond angle, in a freely jointed 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 Gaussian value of ; the middle, dashed curve shows ; and the bottom, dash-dotted curve shows .

Image of FIG. 6.
FIG. 6.

Probability distribution function for the torsion angle of a freely jointed chain of length considered as four beads of effective size .

Image of FIG. 7.
FIG. 7.

The mean-square radius of gyration as a function of bead size for both the detailed and WAMC representations of the freely jointed chain.


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Table I.

Mean coarse-grained bond lengths between beads representing 32-mers.

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Table II.

Mean-square radius of gyration using bond-angle and torsion-angle distributions


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Topological coarse graining of polymer chains using wavelet-accelerated Monte Carlo. I. Freely jointed chains