This page discusses the physics of knots, generally, not just inside a physics simulator.
My main interest is in the shape of tightened dressed knots. However, any information that could help with doing numerical simulation of physical knots will be included here.
specific papers
- [2012] The Shapes of Tight Composite Knots (J. Cantarella, Al LaPointe, E. Rawdon) Journal of Physics A: Mathematical and Theoretical
[citation]
- [2011] Simplified Cosserat Rod for Interactive Suture Modeling (Sukitti Punak, Sergei Kurenov) Stud Health Technol Inform
[GScholar]
- [2008] CORDE: Cosserat Rod Elements for the Animation of Interacting Elastic Rods (Jonas Spillmann) dissertation, University of Freiburg
[GScholar]
- [2008] An Adaptive Contact Model for the Robust Simulation of Knots (Jonas Spillmann, Matthias Teschner) Eurographics 2008
[GScholar]
[video]
- [2008] Discrete elastic rods. (Bergou, M., Wardetzky, M., Robinson, S., Audoly, B., & Grinspun, E.) ACM Transactions on Graphics
[GScholar]
- [2007] A robust method for real-time thread simulation (Blazej Kubiak, Nico Pietroni, Fabio Ganovelli, Marco Fratarcangeli) Proceedings of the 2007 ACM symposium on Virtual reality software and technology
[video]
[GScholar]
- [2005] Visualizing the tightening of knots (Jason Cantarella, Michael Piatek, Eric Rawdon) Proceedings of the conference on Visualization 2005
[GScholar]
- [2005] An Introduction to the Theory of Hitches and Knots (Jeremy Stolarz) self published
- [2005] The Mathematical Theory of Hitches (Matt Krauel)
[citation]
[mirror]
- [2004] Real-time Knot-tying Simulation (J Brown, JC Latombe, K Montgomery), The Visual Computer
[GScholar]
- [2002] STRANDS: Interactive Simulation of Thin Solids using Cosserat Models (Dinesh Pai) Eurographics 2002
[GScholar]
- [2002] A Computational Simulation of the Untying of Knots (Joshua S. Martin)
- [2002] On the Minimum Ropelength of Knots and Links (J Cantarella , R Kusner, J Sullivan) Inventiones Mathematicae
[permalink]
- [2001] Localization of breakage points in knotted strings (P. Pieranski, S. Kasas, G. Dietler) New Journal of Physics
[citation]
- [1999] Thickness of Knots (R A Litherland, J Simon), Topology and its Applications
[GScholar]
- [1987] Ropes in Equilibrium, (Maddocks, J.H. and Keller, J. B.), SIAM Journal on Applied Mathematics
[citation]
[GScholar]
- [1977] Theory of hitches (B. Bayman) American Journal of Physics
[citation]
[mirror]
[GScholar]
Proposed energy functions:
Node shape:
Random knot-generation:
specific people
- Eric J. Rawdon
[GoogleScholar]
[homepage]
- Jonas Spillmann
Cool guy. He continued his research after the dissertation, and is currently employed at a commercial firm exploring it further. He also does mountain climbing. :)
specific algorithms
specific books
- [2005] "Physical and Numerical Models in Knot Theory", Jorge. A Calvo, ISBN 9-812-70346-2
preface
On the Theory of Solid Knots (Otto Krotenheerdt & Sigrid Veit)
A Tutorial on Knot Energies (E J J van Rensburg)
Universal Energy Spectrum of Tight Knots and Links in Physics (R V Buniy & T W Kephart)
Knot Dynamics in a Driven Hanging Chain: Experimental Results (A. Belmonte)
Biarcs, Global Radius of Curvature, and the Computation of Ideal Knot Shapes (4 Color Plates) (M Carlen et al.)
Knotted Umbilical Cords (2 Color Plates) (A Goriely)
Modelling DNA as a Thick Polymer: Application to DNA Elasticity and Packaging Thermodynamics (C. Micheletti & D. Marenduzzo)
Monte-Carlo Simulations of Gel-Electrophoresis of DNA Knots (C Weber et al.)
Atomic Force Microscopy of Complex DNA Knots (F. Valle, M. Favre, J. Roca, G. Dietler)
Protein Folds, Knots and Tangles (W R Taylor)
Tying Down Open Knots: A Statistical Method For Identifying Open Knots With Applications To Proteins (K. C. Millett & B. M. Sheldon)
Folding Complexity in a Random-Walk Copolymer Model (G A Arteca)
Universal Characteristics of Polygonal Knot Probabilities (K C Millett & E J Rawdon)
Ropelength of Tight Polygonal Knots (J Baranska et al.)
A Fast Octree-Based Algorithm for Computing Ropelength (T. Ashton & J. Cantarella)
Topological Entropic Force Between a Pair of Random Knots Forming a Fixed Link (T Deguchi)
Under-Knotted and Over-Knotted Polymers: 1. Unrestricted Loops (N. Moore, R. Lua, A. Grosberg)
Under-Knotted and Over-Knotted Polymers: 2. Compact Self-Avoiding Loops (N. Moore, R. Lua, A. Grosberg)
On the mean gyration radius and the radial distribution function of ring polymers with excluded volume under a topological constraint
Thermodynamics and topology of disordered knots : correlations in trivial lattice knot diagrams
Generating large random knot projections (Yuanan Diao, Claus Ernst, Uta Ziegler)
Minimal Flat Knotted Ribbons (L H Kauffman)
Quadrisecants of Knots with Small Crossing Number (G T Jin)
On the writhing number of a non-closed curve
On a mathematical model for thick surfaces
Some ropelength-critical clasps
Remarks on some hyperbolic invariants of 2-bridge knots
Conjectures on the Enumeration of Alternating Links (P Zinn-Justin)
- [2002] Physical Knots: Knotting, Linking and Folding Geometric Objects in R^{3}, Jorge Calvo
Physical knots (Jonathan Simon)
The space of piecewise-linear knots (Richard Randell)
Characterizing polygons in R^{3} (Jorge Alberto Calvo)
Upper bounds for equilateral stick numbers (Eric J. Rawdon, Robert G. Scharein)
An investigation of equilateral knot spaces and ideal physical knot configurations (Kenneth C. Millett)
Topological effects on the average size of random knots (Tetsuo Deguchi, Miyuki K. Shimamura)
Bringing an order into random knots (Akos Dobay, Pierre-Edouard Sottas, Jacques Dubochet, Andrzej Stasiak)
The probability of knotting in lattice polygons (E. J. Janse van Rensburg)
Knotting in adsorbing lattice polygons (E. J. Janse van Rensburg)
In search of the ideal trefoil knot (Piotr Pieranski, Sylwester Przybyl)
The crossing numbers of thick knots and links (Yuanan Diao, Claus Ernst)
On thickness and packing density for knots and links (Rob Kusner)
Approximating ropelength by energy functions (John M. Sullivan)
Conformal geometric viewpoints for knots and links I (R. Langevin, J. O'Hara)
Curves, circles, and spheres (Oscar Gonzalez, John H. Maddocks, Jana Smutny)
The rupture of knotted strings under tension (Giovanni Dietler, Piotr Pieranski, Sandor Kasas, Andrzej Stasiak)
Classifying and applying rational knots and rational tangles (Louis H. Kauffman, Sofia Lambropoulou)
Untangling some spheres in R^{4} by energy minimizing flow (Dennis Roseman)
Convexifying polygons in 3D: A survey (Michael Soss, Godfried T. Toussaint)
Infinitesimally locked self-touching linkages with applications to locked trees (Robert Connelly, Erik D. Demaine, Gunter Rote)
Biologic (Louis H. Kauffman)
- [2005] "Mathematical Models for Elastic Structures", Piero Villaggio, ISBN 0-521-57324-6
Ch. IV Theories of Cables
28. Equilibrium Equations
29. Classical Solutions for Linearly Elastic Strings
30. Influence of Friction
31. Equilibrium States for Nonlinear Elastic Strings
32. Inverse Problems in Strings
33. Unilateral Problems for Strings
34. Dynamical Problems for Strings
35. Peeling and Slipping