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The Effect of Knotting on the Shape of Polymers Eric J. Rawdon

Summary: The Effect of Knotting on the Shape of Polymers
Eric J. Rawdon
John C. Kern
Michael Piatek
Patrick Plunkett§
Andrzej Stasiak¶
Kenneth C. Millett
August 13, 2008
Momentary configurations of long polymers at thermal equilibrium
usually deviate from spherical symmetry and can be better described, on
average, by a prolate ellipsoid. The asphericity and nature of aspheric-
ity (or prolateness) that describe these momentary ellipsoidal shapes of a
polymer are determined by specific expressions involving the three princi-
pal moments of inertia calculated for configurations of the polymer. Ear-
lier theoretical studies and numerical simulations have established that as
the length of the polymer increases, the average shape for the statistical
ensemble of random configurations asymptotically approaches a charac-
teristic universal shape that depends on the solvent quality. It has been
established, however, that these universal shapes differ for linear, circular,


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics