232 research outputs found
Statistical Mechanics of Elastica on Plane as a Model of Supercoiled DNA-Origin of the MKdV hierarchy-
In this article, I have investigated statistical mechanics of a non-stretched
elastica in two dimensional space using path integral method. In the
calculation, the MKdV hierarchy naturally appeared as the equations including
the temperature fluctuation.I have classified the moduli of the closed elastica
in heat bath and summed the Boltzmann weight with the thermalfluctuation over
the moduli. Due to the bilinearity of the energy functional,I have obtained its
exact partition function.By investigation of the system,I conjectured that an
expectation value at a critical point of this system obeys the Painlev\'e
equation of the first kind and its related equations extended by the KdV
hierarchy.Furthermore I also commented onthe relation between the MKdV
hierarchy and BRS transformationin this system.Comment: AMS-Tex Us
Radial distribution function of semiflexible polymers
We calculate the distribution function of the end--to--end distance of a
semiflexible polymer with large bending rigidity. This quantity is directly
observable in experiments on single semiflexible polymers (e.g., DNA, actin)
and relevant to their interpretation. It is also an important starting point
for analyzing the behavior of more complex systems such as networks and
solutions of semiflexible polymers. To estimate the validity of the obtained
analytical expressions, we also determine the distribution function numerically
using Monte Carlo simulation and find good quantitative agreement.Comment: RevTeX, 4 pages, 1 figure. Also available at
http://www.cip.physik.tu-muenchen.de/tumphy/d/T34/Mitarbeiter/frey.htm
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