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Volumn 186, Issue 2, 2003, Pages 426-456

Energy, ropelength, and other physical aspects of equilateral knots

Author keywords

Equilateral knots; Knot energy; Knot space; Polygonal knots; Ropelength; Thickness

Indexed keywords

NUMERICAL METHODS; SPATIAL VARIABLES MEASUREMENT;

EID: 0037431127     PISSN: 00219991     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0021-9991(03)00026-3     Document Type: Article
Times cited : (33)

References (62)
  • 1
    • 0001972054 scopus 로고
    • Self linking numbers of space polygons
    • T. Banchoff, Self linking numbers of space polygons, Indiana Univ. Math. J. 25 (12) (1976) 1171-1188.
    • (1976) Indiana Univ. Math. J. , vol.25 , Issue.12 , pp. 1171-1188
    • Banchoff, T.1
  • 2
    • 0032546348 scopus 로고    scopus 로고
    • Four-thirds power law for knots and links
    • Scientific Correspondence
    • G. Buck, Four-thirds power law for knots and links, Nature 392 (1998) 238-239, Scientific Correspondence.
    • (1998) Nature , vol.392 , pp. 238-239
    • Buck, G.1
  • 3
    • 15944372663 scopus 로고    scopus 로고
    • Thickness and crossing number of knots
    • G. Buck, J. Simon, Thickness and crossing number of knots, Topol. Appl. 91 (3) (1999) 245-257.
    • (1999) Topol. Appl. , vol.91 , Issue.3 , pp. 245-257
    • Buck, G.1    Simon, J.2
  • 4
    • 0003782883 scopus 로고    scopus 로고
    • Geometric knot theory: The classification of spatial polygons with a small number of edges
    • Ph.D. thesis, University of California, Santa Barbara
    • J.A. Calvo, Geometric knot theory: the classification of spatial polygons with a small number of edges, Ph.D. thesis, University of California, Santa Barbara, 1998.
    • (1998)
    • Calvo, J.A.1
  • 5
    • 0009909312 scopus 로고    scopus 로고
    • Minimal edge piecewise linear knots
    • World Scientific, River Edge, NJ
    • J.A. Calvo, K.C. Millett, Minimal edge piecewise linear knots, in: Ideal Knots, World Scientific, River Edge, NJ, 1998, pp. 107-128.
    • (1998) Ideal Knots , pp. 107-128
    • Calvo, J.A.1    Millett, K.C.2
  • 6
    • 0344237819 scopus 로고    scopus 로고
    • The embedding space of hexagonal knots
    • J.A. Calvo, The embedding space of hexagonal knots, Topol. Appl. 112 (2) (2001) 137-174.
    • (2001) Topol. Appl. , vol.112 , Issue.2 , pp. 137-174
    • Calvo, J.A.1
  • 7
    • 0035590594 scopus 로고    scopus 로고
    • Geometric knot spaces and polygonal isotopy
    • Knots in Hellas '98, vol. 2 (Delphi)
    • J.A. Calvo, Geometric knot spaces and polygonal isotopy, J. Knot Theory Ramifications 10 (2) (2001) 245-267, Knots in Hellas '98, vol. 2 (Delphi).
    • (2001) J. Knot Theory Ramifications , vol.10 , Issue.2 , pp. 245-267
    • Calvo, J.A.1
  • 8
    • 1542575510 scopus 로고    scopus 로고
    • Nontrivial embeddings of polygonal intervals and unknots in 3-space
    • J. Cantarella, H. Johnston, Nontrivial embeddings of polygonal intervals and unknots in 3-space, J. Knot Theory Ramifications 7 (8) (1998) 1027-1039.
    • (1998) J. Knot Theory Ramifications , vol.7 , Issue.8 , pp. 1027-1039
    • Cantarella, J.1    Johnston, H.2
  • 9
    • 0028151069 scopus 로고
    • Processive recombination by wild-type Gin and an enhancer-independent mutant. Insight into the mechanisms of recombination selectivity and strand exchange
    • N.J. Crisona, R. Kanaar, T.N. Gonzalez, E.L. Zecheidrich, A. Klippel, N.R. Cozzarelli, Processive recombination by wild-type Gin and an enhancer-independent mutant. Insight into the mechanisms of recombination selectivity and strand exchange, J. Mol. Biol. 243 (3) (1994) 437-457.
    • (1994) J. Mol. Biol. , vol.243 , Issue.3 , pp. 437-457
    • Crisona, N.J.1    Kanaar, R.2    Gonzalez, T.N.3    Zecheidrich, E.L.4    Klippel, A.5    Cozzarelli, N.R.6
  • 14
    • 0344669267 scopus 로고    scopus 로고
    • Computational algorithms and the complexity of link polynomials
    • Hermann, Paris
    • B. Ewing, K.C. Millett, Computational algorithms and the complexity of link polynomials, in: Progress in Knot Theory and Related Topics, Hermann, Paris, 1997, pp. 51-68.
    • (1997) Progress in Knot Theory and Related Topics , pp. 51-68
    • Ewing, B.1    Millett, K.C.2
  • 15
    • 0000235632 scopus 로고
    • Uber Krummung und Windung Geschlossener Raumkurvern
    • W. Fenchel, Uber Krummung und Windung Geschlossener Raumkurvern, Ann. Math. 101 (1929) 238-252.
    • (1929) Ann. Math. , vol.101 , pp. 238-252
    • Fenchel, W.1
  • 16
    • 0001931601 scopus 로고
    • Möbius energy of knots and unknots
    • M.H. Freedman, Z.-X. He, Z. Wang, Möbius energy of knots and unknots, Ann. Math. (2) 139 (1) (1994) 1-50.
    • (1994) Ann. Math. , vol.139 , Issue.1-2 , pp. 1-50
    • Freedman, M.H.1    He, Z.-X.2    Wang, Z.3
  • 18
    • 0002629314 scopus 로고
    • Energy of a knot
    • Academic Press, Boston, MA
    • S. Fukuhara, Energy of a knot, in: A fête of Topology, Academic Press, Boston, MA, 1988, pp. 443-451.
    • (1988) A Fête of Topology , pp. 443-451
    • Fukuhara, S.1
  • 19
    • 0033608997 scopus 로고    scopus 로고
    • Global curvature, thickness, and the ideal shapes of knots
    • (electronic)
    • O. Gonzalez, J.H. Maddocks, Global curvature, thickness, and the ideal shapes of knots, Proc. Natl. Acad. Sci. USA 96 (9) (1999) 4769-4773 (electronic).
    • (1999) Proc. Natl. Acad. Sci. USA , vol.96 , Issue.9 , pp. 4769-4773
    • Gonzalez, O.1    Maddocks, J.H.2
  • 20
    • 85189847946 scopus 로고    scopus 로고
    • personal communication
    • J. Hoste, 2000, personal communication.
    • (2000)
    • Hoste, J.1
  • 22
  • 23
    • 0025376429 scopus 로고
    • Processive recombinations by the phage Mu Gin system: Implications for the mechanisms of DNA strand exchange, DNA site alignment and enhancer action
    • R. Kanaar, A. Klippel, E. Shekhtman, J.M. Dungan, R. Kahmann, N.R. Cozzarelli, Processive recombinations by the phage Mu Gin system: implications for the mechanisms of DNA strand exchange, DNA site alignment and enhancer action, Cell 62 (2) (1990) 353-366.
    • (1990) Cell , vol.62 , Issue.2 , pp. 353-366
    • Kanaar, R.1    Klippel, A.2    Shekhtman, E.3    Dungan, J.M.4    Kahmann, R.5    Cozzarelli, N.R.6
  • 27
    • 0000799989 scopus 로고    scopus 로고
    • Möbius energies for knots and links, surfaces and submanifolds
    • (Athens. GA. 1993), American Mathematical Society, Providence, RI
    • R.B. Kusner, J.M. Sullivan, Möbius energies for knots and links, surfaces and submanifolds, in: Geometric Topology (Athens. GA. 1993), American Mathematical Society, Providence, RI, 1997, pp. 570-604.
    • (1997) Geometric Topology , pp. 570-604
    • Kusner, R.B.1    Sullivan, J.M.2
  • 28
    • 0002796757 scopus 로고    scopus 로고
    • On distortion and thickness of knots
    • (Minneapolis, MN, 1996), Springer, New York
    • R.B. Kusner, J.M. Sullivan, On distortion and thickness of knots, in: Topology and Geometry in Polymer Science (Minneapolis, MN, 1996), Springer, New York, 1998, pp. 67-78.
    • (1998) Topology and Geometry in Polymer Science , pp. 67-78
    • Kusner, R.B.1    Sullivan, J.M.2
  • 29
    • 0018989998 scopus 로고
    • Monte Carlo computation of the supercoiling energy, the sedimentation constant, and the radius of gyration of unknotted and knotted circular DNA
    • M. Le Bret, Monte Carlo computation of the supercoiling energy, the sedimentation constant, and the radius of gyration of unknotted and knotted circular DNA, Biopolymers 19 (3) (1980) 619-637.
    • (1980) Biopolymers , vol.19 , Issue.3 , pp. 619-637
    • Le Bret, M.1
  • 30
    • 0000452761 scopus 로고
    • A polynomial invariant of oriented links
    • W.B.R. Lickorish, K.C. Millett, A polynomial invariant of oriented links, Topology 26 (1) (1987) 107-141.
    • (1987) Topology , vol.26 , Issue.1 , pp. 107-141
    • Lickorish, W.B.R.1    Millett, K.C.2
  • 33
    • 0003515412 scopus 로고
    • World Scientific, River Edge, NJ, 1994, Papers from the AMS Special Session held in Vancouver, BC, August 15-19
    • K.C. Millett, D.W. Sumners (Eds.), Random Knotting and Linking, World Scientific, River Edge, NJ, 1994, Papers from the AMS Special Session held in Vancouver, BC, August 15-19, 1993.
    • (1993) Random Knotting and Linking
    • Millett, K.C.1    Sumners, D.W.2
  • 34
    • 0006258094 scopus 로고
    • Knotting of regular polygons in 3-space
    • (Vancouver, DC, 1993), World Scientific, River Edge, NJ
    • K.C. Millett, Knotting of regular polygons in 3-space, in: Random Knotting and Linking (Vancouver, DC, 1993), World Scientific, River Edge, NJ, 1994, pp. 31-46.
    • (1994) Random Knotting and Linking , pp. 31-46
    • Millett, K.C.1
  • 35
    • 0345100051 scopus 로고    scopus 로고
    • Monte Carlo explorations of polygonal knot spaces
    • Knots in Hellas '98 (Delphi), of Ser. Knots Everything, World Scientific, River Edge, NJ
    • K.C. Millett, Monte Carlo explorations of polygonal knot spaces, in: Knots in Hellas '98 (Delphi), volume 24 of Ser. Knots Everything, World Scientific, River Edge, NJ, 2000, pp. 306-334.
    • (2000) , vol.24 , pp. 306-334
    • Millett, K.C.1
  • 36
    • 0001761212 scopus 로고
    • On the total curvature of knots
    • J.W. Milnor, On the total curvature of knots, Ann. Math. (2) 52 (1950) 248 257.
    • (1950) Ann. Math. , vol.52 , Issue.2 , pp. 248-257
    • Milnor, J.W.1
  • 37
    • 84973959796 scopus 로고
    • e-codimension and the vanishing topology of parametrized curve singularities
    • e-codimension and the vanishing topology of parametrized curve singularities, Math. Proc. Cambridge Philos. Soc. 117 (2) (1995) 213-222.
    • (1995) Math. Proc. Cambridge Philos. Soc. , vol.117 , Issue.2 , pp. 213-222
    • Mond, D.1
  • 38
    • 0001424089 scopus 로고
    • Closed curves with no quadrisecants
    • H.R. Morton, D.M.Q. Mond, Closed curves with no quadrisecants, Topology 21 (3) (1982) 235-243.
    • (1982) Topology , vol.21 , Issue.3 , pp. 235-243
    • Morton, H.R.1    Mond, D.M.Q.2
  • 39
    • 0000269247 scopus 로고
    • Energy of a knot
    • J. O'Hara, Energy of a knot, Topology 30 (2) (1991) 241-247.
    • (1991) Topology , vol.30 , Issue.2 , pp. 241-247
    • O'Hara, J.1
  • 40
    • 0001083757 scopus 로고
    • Energy functionals of knots
    • (Honolulu, HI, 1990), World Scientific, River Edge, NJ
    • J. O'Hara, Energy functionals of knots, in: Topology Hawaii (Honolulu, HI, 1990), World Scientific, River Edge, NJ, 1992, pp. 201-214.
    • (1992) Topology Hawaii , pp. 201-214
    • O'Hara, J.1
  • 41
    • 38249010915 scopus 로고
    • Family of energy functionals of knots
    • J. O'Hara, Family of energy functionals of knots, Topol. Appl. 48 (2) (1992) 147-161.
    • (1992) Topol. Appl. , vol.48 , Issue.2 , pp. 147-161
    • O'Hara, J.1
  • 42
    • 38149146717 scopus 로고
    • Energy functionals of knots. II
    • J. O'Hara, Energy functionals of knots. II, Topol. Appl. 56 (1) (1994) 45-61.
    • (1994) Topol. Appl. , vol.56 , Issue.1 , pp. 45-61
    • O'Hara, J.1
  • 43
    • 84979310598 scopus 로고
    • Eine freie Abbildung der n-dimensionalen Sphäre in die Ebene
    • E. Pannwitz, Eine freie Abbildung der n-dimensionalen Sphäre in die Ebene, Math. Nachr. 7 (1952) 183-185.
    • (1952) Math. Nachr. , vol.7 , pp. 183-185
    • Pannwitz, E.1
  • 44
    • 0002828937 scopus 로고    scopus 로고
    • In search of ideal knots
    • World Scientific, River Edge, NJ
    • P. Pierański, In search of ideal knots, in: Ideal Knots, World Scientific, River Edge, NJ, 1998, pp. 20-41.
    • (1998) Ideal Knots , pp. 20-41
    • Pierański, P.1
  • 45
    • 0000019149 scopus 로고
    • Conformation spaces of molecular rings
    • R.C. Lacher (Ed.), Studies in Physical and Theoretical Chemistry, volume 54 of MATH/CHEM/COMP 1987, Elsevier Science, Amsterdam
    • R. Randell, Conformation spaces of molecular rings, in: R.C. Lacher (Ed.), Studies in Physical and Theoretical Chemistry, volume 54 of MATH/CHEM/COMP 1987, Elsevier Science, Amsterdam, 1988, pp. 141-156.
    • (1988) , pp. 141-156
    • Randell, R.1
  • 46
    • 0002576842 scopus 로고
    • A molecular conformation space
    • R.C. Lacher (Ed.), Studies in Physical and Theoretical Chemistry, volume 54 of MATH/CHEM/COMP 1987, Elsevier Science, Amsterdam
    • R. Randell, A molecular conformation space, in: R.C. Lacher (Ed.), Studies in Physical and Theoretical Chemistry, volume 54 of MATH/CHEM/COMP 1987, Elsevier Science, Amsterdam, 1988, pp. 125-140.
    • (1988) , pp. 125-140
    • Randell, R.1
  • 47
    • 85189849805 scopus 로고    scopus 로고
    • TOROS. Program for visualizing, manipulating, and thickness maximizing knots
    • E. Rawdon. TOROS. http://www.mathcs.duq.edu/~rawdon. Program for visualizing, manipulating, and thickness maximizing knots.
    • Rawdon, E.1
  • 48
    • 0345531516 scopus 로고    scopus 로고
    • The thickness of polygonal knots
    • Ph.D. thesis, University of Iowa
    • E. Rawdon, The thickness of polygonal knots, Ph.D. thesis, University of Iowa, 1997.
    • (1997)
    • Rawdon, E.1
  • 49
    • 85189849959 scopus 로고    scopus 로고
    • Polygonal approximation and energy of smooth knots
    • (preprint)
    • E. Rawdon, J. Simon, Polygonal approximation and energy of smooth knots, 2000 (preprint).
    • (2000)
    • Rawdon, E.1    Simon, J.2
  • 50
    • 0012940634 scopus 로고    scopus 로고
    • Möbius energy of thick knots
    • E. Rawdon, J. Simon, Möbius energy of thick knots, Topol. Appl. 125 (1) (2002) 97-109.
    • (2002) Topol. Appl. , vol.125 , Issue.1 , pp. 97-109
    • Rawdon, E.1    Simon, J.2
  • 51
    • 0002148984 scopus 로고    scopus 로고
    • Approximating the thickness of a knot
    • World Scientific, River Edge, NJ
    • E.J. Rawdon, Approximating the thickness of a knot, in: Ideal Knots, World Scientific, River Edge, NJ, 1998, pp. 143-150.
    • (1998) Ideal Knots , pp. 143-150
    • Rawdon, E.J.1
  • 52
    • 0034420282 scopus 로고    scopus 로고
    • Approximating smooth thickness
    • E.J. Rawdon, Approximating smooth thickness, J. Knot Theory Ramifications 9 (1) (2000) 113-145.
    • (2000) J. Knot Theory Ramifications , vol.9 , Issue.1 , pp. 113-145
    • Rawdon, E.J.1
  • 53
    • 0030977220 scopus 로고    scopus 로고
    • The effect of ionic conditions on the conformations of supercoiled DNA. I. Sedimentation analysis
    • V.V. Rybenkov, A.V. Vologoskii, N.R. Cozarelli, The effect of ionic conditions on the conformations of supercoiled DNA. I. Sedimentation analysis, J. Mol. Biol. 267 (2) (1997) 299-311.
    • (1997) J. Mol. Biol. , vol.267 , Issue.2 , pp. 299-311
    • Rybenkov, V.V.1    Vologoskii, A.V.2    Cozarelli, N.R.3
  • 54
    • 84938580533 scopus 로고    scopus 로고
    • Program for drawing, visualizing, manipulating, and energy minimizing knots
    • Knotplot
    • R. Scharein. Knotplot. http://www.knotplot.com. Program for drawing, visualizing, manipulating, and energy minimizing knots.
    • Scharein, R.1
  • 55
    • 85189853262 scopus 로고    scopus 로고
    • personal communication
    • J. Simon, J. Tockle, 1999, personal communication.
    • (1999)
    • Simon, J.1    Tockle, J.2
  • 56
    • 0012944530 scopus 로고
    • Energy functions for polygonal knots
    • Random knotting and linking (Vancouver, BC, 1993)
    • J.K. Simon, Energy functions for polygonal knots, J. Knot Theory Ramifications 3 (3) (1994) 299-320, Random knotting and linking (Vancouver, BC, 1993).
    • (1994) J. Knot Theory Ramifications , vol.3 , Issue.3 , pp. 299-320
    • Simon, J.K.1
  • 59
    • 0000941036 scopus 로고    scopus 로고
    • Ideal knots and their relation to the physics of real knots
    • World Scientific, River Edge, NJ
    • A. Stasiak, J. Dubochet, V. Katritch, P. Pieranski, Ideal knots and their relation to the physics of real knots, in: Ideal Knots, World Scientific, River Edge, NJ, 1998, pp. 1-19.
    • (1998) Ideal Knots , pp. 1-19
    • Stasiak, A.1    Dubochet, J.2    Katritch, V.3    Pieranski, P.4
  • 61
    • 0001705405 scopus 로고
    • Elementary structure of real algebraic varieties
    • H. Whitney, Elementary structure of real algebraic varieties, Ann. Math. (2) 66 (1957) 545-556.
    • (1957) Ann. Math. , vol.66 , Issue.2 , pp. 545-556
    • Whitney, H.1
  • 62
    • 85031185369 scopus 로고    scopus 로고
    • Program for visualizing, manipulating, and energy minimizing polygonal knots
    • Ming
    • Y.-Q. Wu. Ming. http://www.math.uiowa.edu/~wu. Program for visualizing, manipulating, and energy minimizing polygonal knots.
    • Wu, Y.-Q.1


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