Knot probabilities in equilateral random polygons
| Autor: | S G Whittington, Alexander J. Taylor, Anda Xiong, Mark R. Dennis |
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| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
Statistical Mechanics (cond-mat.stat-mech) Monte Carlo method FOS: Physical sciences General Physics and Astronomy Geometric Topology (math.GT) Statistical and Nonlinear Physics Alexander polynomial Mathematical Physics (math-ph) Equilateral triangle Mathematics::Geometric Topology Power law Exponential function Combinatorics Mathematics - Geometric Topology Modeling and Simulation FOS: Mathematics Unknot Scaling Condensed Matter - Statistical Mechanics Mathematical Physics Mathematics Knot (mathematics) |
| Zdroj: | Journal of Physics A: Mathematical and Theoretical. 54:405001 |
| ISSN: | 1751-8121 1751-8113 |
| Popis: | We consider the probability of knotting in equilateral random polygons in Euclidean 3-dimensional space, which model, for instance, random polymers. Results from an extensive Monte Carlo dataset of random polygons indicate a universal scaling formula for the knotting probability with the number of edges. This scaling formula involves an exponential function, independent of knot type, with a power law factor that depends on the number of prime components of the knot. The unknot, appearing as a composite knot with zero components, scales with a small negative power law, contrasting with previous studies that indicated a purely exponential scaling. The methodology incorporates several improvements over previous investigations: our random polygon data set is generated using a fast, unbiased algorithm, and knotting is detected using an optimised set of knot invariants based on the Alexander polynomial. 24 pages, 8 figures |
| Databáze: | OpenAIRE |
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