378 research outputs found
On the Use of Optimized Monte Carlo Methods for Studying Spin Glasses
We start from recently published numerical data by Hatano and Gubernatis
cond-mat/0008115 to discuss properties of convergence to equilibrium of
optimized Monte Carlo methods (bivariate multi canonical and parallel
tempering). We show that these data are not thermalized, and they lead to an
erroneous physical picture. We shed some light on why the bivariate multi
canonical Monte Carlo method can fail.Comment: 6 pages, 5 eps figures include
Simulation of Lattice Polymers with Multi-Self-Overlap Ensemble
A novel family of dynamical Monte Carlo algorithms for lattice polymers is
proposed. Our central idea is to simulate an extended ensemble in which the
self-avoiding condition is systematically weakened. The degree of the
self-overlap is controlled in a similar manner as the multicanonical ensemble.
As a consequence, the ensemble --the multi-self-overlap ensemble-- contains
adequate portions of self-overlapping conformations as well as higher energy
ones. It is shown that the multi-self-overlap ensemble algorithm reproduce
correctly the canonical averages at finite temperatures of the HP model of
lattice proteins. Moreover, it outperforms massively a standard multicanonical
algorithm for a difficult example of a polymer with 8-stickers. Alternative
algorithm based on exchange Monte Carlo method is also discussed.Comment: 5 Pages, 4 Postscript figures, uses epsf.st
Peculiar scaling of self-avoiding walk contacts
The nearest neighbor contacts between the two halves of an N-site lattice
self-avoiding walk offer an unusual example of scaling random geometry: for N
going to infinity they are strictly finite in number but their radius of
gyration Rc is power law distributed, ~ Rc^{-\tau}, where \tau>1 is a novel
exponent characterizing universal behavior. A continuum of diverging lengths
scales is associated to the Rc distribution. A possibly super-universal \tau=2
is also expected for the contacts of a self-avoiding or random walk with a
confining wall.Comment: 4 pages, 5 Postscript figures, uses psfig.sty; some sentences
clarifie
On the size of knots in ring polymers
We give two different, statistically consistent definitions of the length l
of a prime knot tied into a polymer ring. In the good solvent regime the
polymer is modelled by a self avoiding polygon of N steps on cubic lattice and
l is the number of steps over which the knot ``spreads'' in a given
configuration. An analysis of extensive Monte Carlo data in equilibrium shows
that the probability distribution of l as a function of N obeys a scaling of
the form p(l,N) ~ l^(-c) f(l/N^D), with c ~ 1.25 and D ~ 1. Both D and c could
be independent of knot type. As a consequence, the knot is weakly localized,
i.e. ~ N^t, with t=2-c ~ 0.75. For a ring with fixed knot type, weak
localization implies the existence of a peculiar characteristic length l^(nu) ~
N^(t nu). In the scaling ~ N^(nu) (nu ~0.58) of the radius of gyration of the
whole ring, this length determines a leading power law correction which is much
stronger than that found in the case of unrestricted topology. The existence of
such correction is confirmed by an analysis of extensive Monte Carlo data for
the radius of gyration. The collapsed regime is studied by introducing in the
model sufficiently strong attractive interactions for nearest neighbor sites
visited by the self-avoiding polygon. In this regime knot length determinations
can be based on the entropic competition between two knotted loops separated by
a slip link. These measurements enable us to conclude that each knot is
delocalized (t ~ 1).Comment: 29 pages, 14 figure
Roles of stiffness and excluded volume in DNA denaturation
The nature and the universal properties of DNA thermal denaturation are
investigated by Monte Carlo simulations. For suitable lattice models we
determine the exponent c describing the decay of the probability distribution
of denaturated loops of length l, . If excluded volume effects
are fully taken into account, c= 2.10(4) is consistent with a first order
transition. The stiffness of the double stranded chain has the effect of
sharpening the transition, if it is continuous, but not of changing its order
and the value of the exponent c, which is also robust with respect to inclusion
of specific base-pair sequence heterogeneities.Comment: RevTeX 4 Pages and 4 PostScript figures included. Final version as
publishe
Lattice Knots in a Slab
In this paper the number and lengths of minimal length lattice knots confined
to slabs of width , is determined. Our data on minimal length verify the
results by Sharein et.al. (2011) for the similar problem, expect in a single
case, where an improvement is found. From our data we construct two models of
grafted knotted ring polymers squeezed between hard walls, or by an external
force. In each model, we determine the entropic forces arising when the lattice
polygon is squeezed by externally applied forces. The profile of forces and
compressibility of several knot types are presented and compared, and in
addition, the total work done on the lattice knots when it is squeezed to a
minimal state is determined
Numerical study of linear and circular model DNA chains confined in a slit: metric and topological properties
Advanced Monte Carlo simulations are used to study the effect of nano-slit
confinement on metric and topological properties of model DNA chains. We
consider both linear and circularised chains with contour lengths in the
1.2--4.8 m range and slits widths spanning continuously the 50--1250nm
range. The metric scaling predicted by de Gennes' blob model is shown to hold
for both linear and circularised DNA up to the strongest levels of confinement.
More notably, the topological properties of the circularised DNA molecules have
two major differences compared to three-dimensional confinement. First, the
overall knotting probability is non-monotonic for increasing confinement and
can be largely enhanced or suppressed compared to the bulk case by simply
varying the slit width. Secondly, the knot population consists of knots that
are far simpler than for three-dimensional confinement. The results suggest
that nano-slits could be used in nano-fluidic setups to produce DNA rings
having simple topologies (including the unknot) or to separate heterogeneous
ensembles of DNA rings by knot type.Comment: 12 pages, 10 figure
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