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Random Knotting: Theorems, Simulations and Applications

  • De Witt SumnersEmail author
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, 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.

Keywords

Viral Capsid Alexander Polynomial Seifert Surface Lattice Polygon Ball Pair 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  1. 1.Department of MathematicsFlorida State UniversityTallahasseeUSA

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