Advanced search
Publication Cover
Experimental Mathematics Volume 20, 2011 - Issue 1
Submit an article Journal homepage
223
Views
46
CrossRef citations to date
0
Altmetric
Original Articles

Knot Tightening by Constrained Gradient Descent

Ted Ashton Linthicum Heights, MD, 21090
,
Jason Cantarella Department of Mathematics, University of Georgia, Athens, GA, 30602
,
Michael Piatek Department of Computer Science, University of Washington, Seattle, WA, 98195
&
Eric J. Rawdon Department of Mathematics, University of St. Thomas, St. Paul, MN
Pages 57-90 | Received 05 Feb 2010, Accepted 19 Apr 2010, Published online: 11 May 2011

Citations (46)

Keep up to date with the latest research on this topic with citation updates for this article.

Subscribe to citation updates

Read on this site (2)

Thomas D. Eddy & Clayton Shonkwiler. (2022) New Stick Number Bounds from Random Sampling of Confined Polygons. Experimental Mathematics 31:4, pages 1373-1395.
Read now
Yuanan Diao, Claus Ernst, Eric J. Rawdon & Uta Ziegler. (2018) Relative Frequencies of Alternating and Nonalternating Prime Knots and Composite Knots in Random Knot Spaces. Experimental Mathematics 27:4, pages 454-471.
Read now

Articles from other publishers (44)

Oliver Gross, Ulrich Pinkall & Peter Schröder. (2023) Plasma knots. Physics Letters A 480, pages 128986.
Crossref
Jan Knappmann, Henrik Schumacher, Daniel Steenebrügge & Heiko von der Mosel. (2023) A speed preserving Hilbert gradient flow for generalized integral Menger curvature. Advances in Calculus of Variations 16:3, pages 597-635.
Crossref
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.
Crossref
Halid Abdulrahim Kadi & Kasim Terzić. (2023) Data-Driven Robotic Manipulation of Cloth-like Deformable Objects: The Present, Challenges and Future Prospects. Sensors 23:5, pages 2389.
Crossref
Anna Lagemann & Heiko von der Mosel. (2023) Tangent-point energies and ropelength as Gamma-limits of discrete tangent-point energies on biarc curves. Advances in Continuous and Discrete Models 2023:1.
Crossref
Alexander R. Klotz. (2022) The tightest knot is not necessarily the smallest. Journal of Knot Theory and Its Ramifications 31:14.
Crossref
Alexander R Klotz & Matthew Maldonado. (2021) The ropelength of complex knots. Journal of Physics A: Mathematical and Theoretical 54:44, pages 445201.
Crossref
Youngsik Huh, Hyoungjun Kim & Seungsang Oh. (2021) Tight conformation of 2-bridge knots using superhelices. Journal of Mathematical Physics 62:11.
Crossref
H.K. Moffatt. (2021) Some topological aspects of fluid dynamics. Journal of Fluid Mechanics 914.
Crossref
Chris Yu, Henrik Schumacher & Keenan Crane. (2021) Repulsive Curves. ACM Transactions on Graphics 40:2, pages 1-21.
Crossref
W. A. Haney, A. J. Clark & T. A. Uyeno. (2019) Characterization of body knotting behavior used for escape in a diversity of hagfishes. Journal of Zoology 310:4, pages 261-272.
Crossref
Weifu Wang & Devin Balkcom. 2020. Algorithmic Foundations of Robotics XII. Algorithmic Foundations of Robotics XII 480 495 .
Daria W Atkinson, Christian D Santangelo & Gregory M Grason. (2019) Constant spacing in filament bundles. New Journal of Physics 21:6, pages 062001.
Crossref
Jack Binysh, Carl A. Whitfield & Gareth P. Alexander. (2019) Stable and unstable vortex knots in excitable media. Physical Review E 99:1.
Crossref
Youngsik Huh, Hyoungjun Kim & Seungsang Oh. (2018) Ropelength of superhelices and (2, n )-torus knots . Journal of Physics A: Mathematical and Theoretical 51:48, pages 485203.
Crossref
Yuanan Diao, Claus Ernst, Eric J. Rawdon & Uta Ziegler. (2018) Average crossing number and writhe of knotted random polygons in confinement. Reactive and Functional Polymers 131, pages 430-444.
Crossref
Weifu Wang & Devin Balkcom. (2018) Knot grasping, folding, and re-grasping. The International Journal of Robotics Research 37:2-3, pages 378-399.
Crossref
Fabian Maucher & Paul Sutcliffe. (2017) Length of excitable knots. Physical Review E 96:1.
Crossref
Antonio Šiber. (2016) Shapes of minimal-energy DNA ropes condensed in confinement. Scientific Reports 6:1.
Crossref
Weifu Wang & Devin Balkcom. (2016) Tying knot precisely. Tying knot precisely.
Shawn W. Walker. (2016) Shape optimization of self-avoiding curves. Journal of Computational Physics 311, pages 275-298.
Crossref
Weifu Wang, Matthew P. Bell & Devin Balkcom. (2015) Towards Arranging and Tightening Knots and Unknots With Fixtures. IEEE Transactions on Automation Science and Engineering 12:4, pages 1318-1331.
Crossref
David A B Hyde, Joshua Henrich, Eric J Rawdon & Kenneth C Millett. (2015) Knotting fingerprints resolve knot complexity and knotting pathways in ideal knots. Journal of Physics: Condensed Matter 27:35, pages 354112.
Crossref
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.
Crossref
Alexander Coward & Joel Hass. (2015) Topological and physical link theory are distinct. Pacific Journal of Mathematics 276:2, pages 387-400.
Crossref
Eric J. Rawdon, Kenneth C. Millett & Andrzej Stasiak. (2015) Subknots in ideal knots, random knots and knotted proteins. Scientific Reports 5:1.
Crossref
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.
Crossref
Weifu Wang, Matthew P. Bell & Devin Balkcom. 2015. Algorithmic Foundations of Robotics XI. Algorithmic Foundations of Robotics XI 677 694 .
Roman V Buniy, Jason Cantarella, Thomas W Kephart & Eric Rawdon. (2014) The spectrum of tightly knotted flux tubes in QCD. Journal of Physics: Conference Series 544, pages 012025.
Crossref
Simon Blatt & Philipp Reiter. (2014) How nice are critical knots? Regularity theory for knot energies. Journal of Physics: Conference Series 544, pages 012020.
Crossref
Sylwester Przybyl & Piotr Pieranski. (2014) High resolution portrait of the ideal trefoil knot. Journal of Physics A: Mathematical and Theoretical 47:28, pages 285201.
Crossref
Renzo L Ricca & Francesca Maggioni. (2014) On the groundstate energy spectrum of magnetic knots and links. Journal of Physics A: Mathematical and Theoretical 47:20, pages 205501.
Crossref
Roman V. Buniy, Jason Cantarella, Thomas W. Kephart & Eric J. Rawdon. (2014) Tight knot spectrum in QCD. Physical Review D 89:5.
Crossref
Jason Cantarella, Joseph H. G. Fu, Matt Mastin & Jennifer Ellis Royal. (2014) Symmetric criticality for tight knots. Journal of Knot Theory and Its Ramifications 23:02, pages 1450008.
Crossref
Paweł Strzelecki & Heiko von der Mosel. (2013) Menger curvature as a knot energy. Physics Reports 530:3, pages 257-290.
Crossref
Kasper W. Olsen & Jakob Bohr. (2013) A principle for ideal torus knots. EPL (Europhysics Letters) 103:3, pages 30002.
Crossref
Reuben BrasherRob G. Scharein & Mariel Vazquez. (2013) New biologically motivated knot table. Biochemical Society Transactions 41:2, pages 606-611.
Crossref
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.
Crossref
J. Piili, D. Marenduzzo, K. Kaski & R. P. Linna. (2013) Sedimentation of knotted polymers. Physical Review E 87:1.
Crossref
T. W. KEPHART, P. LESER & H. PÄS. (2012) KNOTTED STRINGS AND LEPTONIC FLAVOR STRUCTURE. Modern Physics Letters A 27:38, pages 1250224.
Crossref
Jason Cantarella, Al LaPointe & Eric J Rawdon. (2012) Shapes of tight composite knots. Journal of Physics A: Mathematical and Theoretical 45:22, pages 225202.
Crossref
Louis H. Kauffman. (2012) Following Knots down Their Energy Gradients. Symmetry 4:2, pages 276-284.
Crossref
M. CARLEN & H. GERLACH. (2012) FOURIER APPROXIMATION OF SYMMETRIC IDEAL KNOTS. Journal of Knot Theory and Its Ramifications 21:05, pages 1250057.
Crossref
PAWEŁ STRZELECKI & HEIKO VON DER MOSEL. (2012) TANGENT-POINT SELF-AVOIDANCE ENERGIES FOR CURVES. Journal of Knot Theory and Its Ramifications 21:05, pages 1250044.
Crossref

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.