1,195 research outputs found
Topologically Driven Swelling of a Polymer Loop
Numerical studies of the average size of trivially knotted polymer loops with
no excluded volume are undertaken. Topology is identified by Alexander and
Vassiliev degree 2 invariants. Probability of a trivial knot, average gyration
radius, and probability density distributions as functions of gyration radius
are generated for loops of up to N=3000 segments. Gyration radii of trivially
knotted loops are found to follow a power law similar to that of self avoiding
walks consistent with earlier theoretical predictions.Comment: 6 pages, 4 figures, submitted to PNAS (USA) in Feb 200
On practical applicability of the Jarzynski relation in statistical mechanics: a pedagogical example
We suggest and discuss a simple model of an ideal gas under the piston to
gain an insight into the workings of the Jarzynski identity connecting the
average exponential of the work over the non-equilibrium trajectories with the
equilibrium free energy. We show that the Jarzynski identity is valid for our
system due to the very rapid molecules belonging to the tail of the Maxwell
distribution. For the most interesting extreme, when the system volume is
large, while the piston is moving with large speed (compared to thermal
velocity) for a very short time, the necessary number of independent
experimental runs to obtain a reasonable approximation for the free energy from
averaging the non-equilibrium work grows exponentially with the system size.Comment: 15 pages, 7 figures, submitted to JP
Adsorption of a random heteropolymer at a potential well revisited: location of transition point and design of sequences
The adsorption of an ideal heteropolymer loop at a potential point well is
investigated within the frameworks of a standard random matrix theory. On the
basis of semi-analytical/semi-numerical approach the histogram of transition
points for the ensemble of quenched heteropolymer structures with bimodal
symmetric distribution of types of chain's links is constructed. It is shown
that the sequences having the transition points in the tail of the histogram
display the correlations between nearest-neighbor monomers.Comment: 11 pages (revtex), 3 figure
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