An ergodic algorithm for generating knots with a prescribed injectivity radius

Chapman, Kyle

doi:10.1142/s0218216519500457

Cited by 1 publication

(1 citation statement)

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“…We will also examine how knot probabilities and knot sizes scale with the length N , as in Deguchi and Tsurusaki's work, and examining knot length as a function of walk thickness [9]. Beyond the realm of thick walks, another goal is to extend the similar results for rings to greater lengths, as well as simulations of polymer melts of thick chains and rings [3].…”

Section: Discussionmentioning

confidence: 94%

Off-Lattice Random Walks with Excluded Volume: A New Method of Generation, Proof of Ergodicity and Numerical Results

Plunkett,

Chapman

2017

Preprint

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We describe a new algorithm, the reflection method, to generate off-lattice random walks of specified, though arbitrarily large, thickness in R 3 and prove that our method is ergodic on the space of thick walks. The data resulting from our implementation of this method is consistent with the scaling of the squared radius of gyration of random walks, with no thickness constraint. Based on this, we use the data to describe the complex relationship between the presence and nature of knotting and size, thickness and shape of the random walk. We extend the current understanding of excluded volume by expanding the range of analysis of how the squared radius of gyration scales with length and thickness. We also examine the profound effect of thickness on knotting in open chains. We will quantify how thickness effects the size of thick open chains, calculating the growth exponent for squared radius of gyration as a function of thickness. We will also show that for radius r ≤ 0.4, increasing thickness by 0.1 decreases the probability of knot formation by 50% or more.

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Section: Discussionmentioning

confidence: 94%