IN SEARCH OF IDEAL KNOTS*
Department of Physics, Poznań University of Technology,
Institute of Molecular Physics, Polish Academy of Sciences
e-mail: pieransk@man.poznan.pl
DOI: 10.12921/cmst.1998.04.01.09-23
OAI: oai:lib.psnc.pl:488
Abstract:
A concise introduction to the mathematical theory of knots is presented. Definitions of basic notions are explained. Then, knots are considered as material objects and the question concerning their optimal conformations is posed. A numerical algorithm searching for the ideal knots is described. A few results obtained with its help are presented.
References:
[1] For an introduction to the theory of knots see e. g. The knot book, Collin. C. Adams,
W. H. Freemann and Company, New York 1994.
[2] J. H. Przytycki, Wiadomości matematyczne, XXXI, 1 (1995).
[3] Explanantion of the origin of the integral can be found in: H. K. Moffat and R. L. Ricca, Proc.
R. Soc. Lond., A439, 411 (1992).
[4] The term writhing number was introduced by F. B. Fuller, Proc. Nat. Acad. Sci. USA,
68, 815 (1971). See also Ref. 2.
[5] V. Katritch, J. Bednar, J. Michoud, R. G. Scherein, J. Dubochet and A. Stasiak, Nature,
384. 142 (1996).
[6] P. Pierański, Pro Dialog 5, 111 (1996).
[7] P. Pierański, In search of ideal knots, in IdeaI Knots, eds. A. Stasiak, V. Katritch
and L. H. Kauffman, World Scientific, Singapore 1998.
[8] H. K. Moffatt, Nature, 384, 114 (1996).
[9] V. Katritch, W. K. Olson, P. Pierański, J. Dubochet and A. Stasiak, Nature, 388, 148 (1997).
A concise introduction to the mathematical theory of knots is presented. Definitions of basic notions are explained. Then, knots are considered as material objects and the question concerning their optimal conformations is posed. A numerical algorithm searching for the ideal knots is described. A few results obtained with its help are presented.
[1] For an introduction to the theory of knots see e. g. The knot book, Collin. C. Adams,
W. H. Freemann and Company, New York 1994.
[2] J. H. Przytycki, Wiadomości matematyczne, XXXI, 1 (1995).
[3] Explanantion of the origin of the integral can be found in: H. K. Moffat and R. L. Ricca, Proc.
R. Soc. Lond., A439, 411 (1992).
[4] The term writhing number was introduced by F. B. Fuller, Proc. Nat. Acad. Sci. USA,
68, 815 (1971). See also Ref. 2.
[5] V. Katritch, J. Bednar, J. Michoud, R. G. Scherein, J. Dubochet and A. Stasiak, Nature,
384. 142 (1996).
[6] P. Pierański, Pro Dialog 5, 111 (1996).
[7] P. Pierański, In search of ideal knots, in IdeaI Knots, eds. A. Stasiak, V. Katritch
and L. H. Kauffman, World Scientific, Singapore 1998.
[8] H. K. Moffatt, Nature, 384, 114 (1996).
[9] V. Katritch, W. K. Olson, P. Pierański, J. Dubochet and A. Stasiak, Nature, 388, 148 (1997).
