Knot Tightening by Constrained Gradient Descent

DOI10.1080/10586458.2011.544581zbMath1261.49007arXiv1002.1723OpenAlexW2108273387MaRDI QIDQ4915374

Ted Ashton, Jason Cantarella, Michael Piatek, Eric J. Rawdon

Publication date: 10 April 2013

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1002.1723

zbMATH Keywords

ropelengthideal knotstight knotsconstrained gradient descentknot-tighteningsparse nonnegative least-squares problem

Mathematics Subject Classification ID

Related Items (19)

Shape optimization of self-avoiding curves ⋮ New Stick Number Bounds from Random Sampling of Confined Polygons ⋮ Following knots down their energy gradients ⋮ TANGENT-POINT SELF-AVOIDANCE ENERGIES FOR CURVES ⋮ FOURIER APPROXIMATION OF SYMMETRIC IDEAL KNOTS ⋮ Tangent-point energies and ropelength as gamma-limits of discrete tangent-point energies on biarc curves ⋮ Plasma knots ⋮ A descent scheme for thick elastic curves with self-contact and container constraints ⋮ A speed preserving Hilbert gradient flow for generalized integral Menger curvature ⋮ Ropelength of superhelices and (2, n)-torus knots ⋮ Relative Frequencies of Alternating and Nonalternating Prime Knots and Composite Knots in Random Knot Spaces ⋮ Menger curvature as a knot energy ⋮ KNOTTED STRINGS AND LEPTONIC FLAVOR STRUCTURE ⋮ Symmetric criticality for tight knots ⋮ Sobolev gradients for the Möbius energy ⋮ Some topological aspects of fluid dynamics ⋮ Tight conformation of 2-bridge knots using superhelices ⋮ The tightest knot is not necessarily the smallest ⋮ The ropelength of complex knots

Uses Software

• KnotPlot
• TAUCS
• TSNNLS

Cites Work

• Characterization of ideal knots
• On the non-existence of three-dimensional water waves with finite energy
• Criticality for the Gehring link problem
• Curvature and torsion of the tight closed trefoil knot
• Thickness of knots
• A simple energy function for knots
• Global curvature and self-contact of nonlinearly elastic curves and rods
• On the minimum ropelength of knots and links
• Local structure of ideal shapes of knots
• Quadrisecants give new lower bounds for the ropelength of a knot
• The Fritz John necessary optimality conditions in the presence of equality and inequality constraints
• Ropes in Equilibrium
• LSQR: An Algorithm for Sparse Linear Equations and Sparse Least Squares
• THE LOWER BOUNDS OF THE LENGTHS OF THICK KNOTS
• EXISTENCE OF IDEAL KNOTS
• APPROXIMATING SMOOTH THICKNESS
• Non‐recursive functions, knots “with thick ropes,” and self‐clenching “thick” hyperspheres
• Can Computers Discover Ideal Knots?
• Geometry and physics of knots
• Scaling behavior of random knots
• The Gradient Projection Method for Nonlinear Programming. Part II. Nonlinear Constraints
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