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Random Knotting: Theorems, Simulations and Applications

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Lectures on Topological Fluid Mechanics

Part of the book series: Lecture Notes in Mathematics ((LNMCIME,volume 1973))

Abstract

This article describes some of the theoretical and simulation results on random entanglement, and give a few scientific applications. I will prove that, on the simple cubic lattice Z3, the probability that a randomly chosen n-edge polygon in Z3 is knotted goes to one exponentially rapidly with length n (Murphy’s Law of entanglement); in other words, all but exponentially few polygons of length n in Z3 are knotted. Measures of entanglement complexity of random knots and random arcs are discussed as well as application of random knotting to viral DNA packing.

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  1. Department of Mathematics, Florida State University, 32303-4510, Tallahassee, FL, USA

    De Witt Sumners

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    Renzo L. Ricca

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Sumners, D. (2009). Random Knotting: Theorems, Simulations and Applications. In: Ricca, R. (eds) Lectures on Topological Fluid Mechanics. Lecture Notes in Mathematics(), vol 1973. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00837-5_7

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