The Length Scale of 3-Space Knots, Ephemeral Knots, and Slipknots in Random Walks(Statistical Physics and Topology of Polymers with Ramifications to Structure and Function of DNA and Proteins)
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概要
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The probability that a random walk or polygon in the 3-space or in the simple cubic lattice contains a small knot, an ephemeral knot, or a slipknot goes to one as the length goes to infinity. The probability that a polygon or walk contains a "global" knot also goes to one as the length goes to infinity. What immerges is a highly complex picture of the length scale of knotting in polygons and walks. Here we study the average scale of knots, ephemeral knots, and slipknots in 3-space random walks, paying special attention to the probability of their occurance and to the growth of their average sizes as a function of the length of the walk.
- 2011-12-16
著者
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MILLETT Kenneth
Department of Mathematics, University of California
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Millett Kenneth
Department Of Mathematics University Of California Sanra Barbara
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Millett Kenneth
Department Of Mathematics University Of California
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MILLETT Kenneth
Department of Mathematics, University of California, Sanra Barbara
関連論文
- A Study of the Entanglement in Systems with Periodic Boundary Conditions(Statistical Physics and Topology of Polymers with Ramifications to Structure and Function of DNA and Proteins)
- Cumulative Shapes of Knotted Polymers(Statistical Physics and Topology of Polymers with Ramifications to Structure and Function of DNA and Proteins)
- The Length Scale of 3-Space Knots, Ephemeral Knots, and Slipknots in Random Walks(Statistical Physics and Topology of Polymers with Ramifications to Structure and Function of DNA and Proteins)