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Experimental Mathematics Volume 12, 2003 - Issue 3
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Original Articles

Can Computers Discover Ideal Knots?

Eric J. Rawdon Duquesne University, Department of Mathematics and Computer Science, Pittsburgh, PA, 15282 E-mail: [email protected]
Pages 287-302 | Published online: 03 Apr 2012

Citations (20)

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Read on this site (1)

Ted Ashton, Jason Cantarella, Michael Piatek & EricJ. Rawdon. (2011) Knot Tightening by Constrained Gradient Descent. Experimental Mathematics 20:1, pages 57-90.
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Articles from other publishers (19)

Paul Johanns, Changyeob BaekPaul Grandgeorge, Samia GueridShawn A. Chester & Pedro M. Reis. (2023) The strength of surgical knots involves a critical interplay between friction and elastoplasticity. Science Advances 9:23.
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Myfanwy E. Evans, Vanessa Robins & Stephen T. Hyde. (2015) Ideal geometry of periodic entanglements. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471:2181, pages 20150254.
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Eric J. Rawdon, Kenneth C. Millett & Andrzej Stasiak. (2015) Subknots in ideal knots, random knots and knotted proteins. Scientific Reports 5:1.
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Youngsik Huh, Sungjong No, Seungsang Oh & Eric J Rawdon. (2015) Link lengths and their growth powers. Journal of Physics A: Mathematical and Theoretical 48:3, pages 035202.
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Sylwester Przybyl & Piotr Pieranski. (2014) High resolution portrait of the ideal trefoil knot. Journal of Physics A: Mathematical and Theoretical 47:28, pages 285201.
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Cédric Weber, Mathias Carlen, Giovanni Dietler, Eric J. Rawdon & Andrzej Stasiak. (2013) Sedimentation of macroscopic rigid knots and its relation to gel electrophoretic mobility of DNA knots. Scientific Reports 3:1.
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J. Piili, D. Marenduzzo, K. Kaski & R. P. Linna. (2013) Sedimentation of knotted polymers. Physical Review E 87:1.
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Yani Zhao & Franco Ferrari. (2012) A numerical technique for studying topological effects on the thermal properties of knotted polymer rings. Journal of Statistical Mechanics: Theory and Experiment 2012:11, pages P11022.
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Jason Cantarella, Al LaPointe & Eric J Rawdon. (2012) Shapes of tight composite knots. Journal of Physics A: Mathematical and Theoretical 45:22, pages 225202.
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Derek Harland, Martin Speight & Paul Sutcliffe. (2011) Hopf solitons and elastic rods. Physical Review D 83:6.
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ERIC J. RAWDON & JOSEPH WORTHINGTON. (2011) ERROR ANALYSIS OF THE MINIMUM DISTANCE ENERGY OF A POLYGONAL KNOT AND THE MÖBIUS ENERGY OF AN APPROXIMATING CURVE. Journal of Knot Theory and Its Ramifications 19:08, pages 975-1000.
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PH. CAUSSIGNAC. (2011) A 1D MODEL FOR A CLOSED RIGID FILAMENT IN STOKES FLOW. Mathematical Models and Methods in Applied Sciences 19:06, pages 911-937.
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J. Baranska, S. Przybyl & P. Pieranski. (2008) Curvature and torsion of the tight closed trefoil knot. The European Physical Journal B 66:4, pages 547-556.
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Eric RawdonAkos DobayJohn C. KernKenneth C. MillettMichael PiatekPatrick PlunkettAndrzej Stasiak. (2008) Scaling Behavior and Equilibrium Lengths of Knotted Polymers. Macromolecules 41:12, pages 4444-4451.
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KENNETH C. MILLETT, MICHAEL PIATEK & ERIC J. RAWDON. (2011) POLYGONAL KNOT SPACE NEAR ROPELENGTH-MINIMIZED KNOTS. Journal of Knot Theory and Its Ramifications 17:05, pages 601-631.
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Elizabeth Denne, Yuanan Diao & John M Sullivan. (2006) Quadrisecants give new lower bounds for the ropelength of a knot. Geometry & Topology 10:1, pages 1-26.
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J. Cantarella, M. Piatek & E. Rawdon. (2005) Visualizing the tightening of knots. Visualizing the tightening of knots.
Justyna Baranska, Piotr Pieranski, Sylwester Przybyl & Eric J. Rawdon. (2004) Length of the tightest trefoil knot. Physical Review E 70:5.
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Gregory Buck & Eric J. Rawdon. (2004) Role of flexibility in entanglement. Physical Review E 70:1.
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