C Laing and D W Sumners 2006 J. Phys. A: Math. Gen. 39 3535 doi:10.1088/0305-4470/39/14/003
C Laing and D W Sumners
Show affiliationsGiven a polygonal closed curve on a lattice or space group, we describe a method for computing the writhe of the curve as the average of weighted projected writhing numbers of the polygon in a few directions. These directions are determined by the lattice geometry, the weights are determined by areas of regions on the unit 2-sphere, and the regions are formed by the tangent indicatrix to the polygonal curve. We give a new formula for the writhe of polygons on the face centred cubic lattice and prove that the writhe of polygons on the body centred cubic lattice, the hexagonal simple lattice, and the diamond space group is always a rational number, and discuss applications to ring polymers.
05.50.+q Lattice theory and statistics (Ising, Potts, etc.)
61.41.+e Polymers, elastomers, and plastics
61.50.Ah Theory of crystal structure, crystal symmetry; calculations and modeling
82B41 Random walks, random surfaces, lattice animals, etc. (See also 60G50, 82C41)
51E12 Generalized quadrangles, generalized polygons
82D25 Crystals (For crystallographic group theory, see 20H15)
82B20 Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs
Soft matter, liquids and polymers
Issue 14 (7 April 2006)
Received 9 November 2005, in final form 9 February 2006
Published 22 March 2006
C Laing and D W Sumners 2006 J. Phys. A: Math. Gen. 39 3535
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