Physical Knots: Knotting, Linking and Folding Geometric Objects in R 3 (Contemporary Mathematics)

Physical Knots: Knotting, Linking and Folding Geometric Objects in R 3 (Contemporary Mathematics)


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The properties of knotted and linked configurations in space have long been of interest to physicists and mathematicians. More recently and more widely, they have become important to biologists, chemists, computer scientists, and engineers. The depth and breadth of their applications are widely appreciated. Nevertheless, fundamental and challenging questions remain to be answered. Based on a Special Session at the AMS Sectional Meeting in Las Vegas (NV) in April 2001, this volume discusses critical questions and introduces new ideas that will stimulate multi-disciplinary applications.Some of the papers are primarily theoretical; others are experimental. Some are purely mathematical; others deal with applications of mathematics to theoretical computer science, engineering, physics, biology, or chemistry. Connections are made between classical knot theory and the physical world of macromolecules, such as DNA, geometric linkages, rope, and even cooked spaghetti. This book introduces the world of physical knot theory in all its manifestations and points the way for new research. It is suitable for a diverse audience of mathematicians, computer scientists, engineers, biologists, chemists, and physicists.


Physical knots by J. Simon The space of piecewise-linear knots by R. Randell Characterizing polygons in $\mathbb{R}^3$ by J. A. Calvo Upper bounds for equilateral stick numbers by E. J. Rawdon and R. G. Scharein An investigation of equilateral knot spaces and ideal physical knot configurations by K. C. Millett Topological effects on the average size of random knots by T. Deguchi and M. K. Shimamura Bringing an order into random knots by A. Dobay, P.-E. Sottas, J. Dubochet, and A. Stasiak The probability of knotting in lattice polygons by E. J. J. van Rensburg Knotting in adsorbing lattice polygons by E. J. J. van Rensburg In search of the ideal trefoil knot by P. Pieranski and S. Przybyl The crossing numbers of thick knots and links by Y. Diao and C. Ernst On thickness and packing density for knots and links by R. Kusner Approximating ropelength by energy functions by J. M. Sullivan Conformal geometric viewpoints for knots and links I by R. Langevin and J. O'Hara Curves, circles, and spheres by O. Gonzalez, J. H. Maddocks, and J. Smutny The rupture of knotted strings under tension by G. Dietler, P. Pieranski, S. Kasas, and A. Stasiak Classifying and applying rational knots and rational tangles by L. H. Kauffman and S. Lambropoulou Untangling some spheres in $\mathbb{R}^4$ by energy minimizing flow by D. Roseman Convexifying polygons in 3D: A survey by M. Soss and G. T. Toussaint Infinitesimally locked self-touching linkages with applications to locked trees by R. Connelly, E. D. Demaine, and G. Rote Biologic by L. H. Kauffman.

Product Details

  • ISBN13: 9780821832004
  • Format: Paperback
  • ID: 9780821832004
  • ISBN10: 082183200X

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