33 research outputs found
Monte Carlo results for three-dimensional self-avoiding walks
We discuss possible sources of systematic errors in the computation of critical exponents by renormalization-group methods, extrapolations from exact enumerations and Monte Carlo simulations. A careful Monte Carlo determination of the susceptibility exponent gamma for three-dimensional self-avoiding walks has been used to test the claimed accuracy of the various methods
Helicase on DNA: A Phase coexistence based mechanism
We propose a phase coexistence based mechanism for activity of helicases,
ubiquitous enzymes that unwind double stranded DNA. The helicase-DNA complex
constitutes a fixed-stretch ensemble that entails a coexistence of domains of
zipped and unzipped phases of DNA, separated by a domain wall. The motor action
of the helicase leads to a change in the position of the fixed constraint
thereby shifting the domain wall on dsDNA. We associate this off-equilibrium
domain wall motion with the unzipping activity of helicase. We show that this
proposal gives a clear and consistent explanation of the main observed features
of helicases.Comment: Revtex4. 5 pages. 4 figures. Published versio
A numerical approach to copolymers at selective interfaces
We consider a model of a random copolymer at a selective interface which
undergoes a localization/delocalization transition. In spite of the several
rigorous results available for this model, the theoretical characterization of
the phase transition has remained elusive and there is still no agreement about
several important issues, for example the behavior of the polymer near the
phase transition line. From a rigorous viewpoint non coinciding upper and lower
bounds on the critical line are known.
In this paper we combine numerical computations with rigorous arguments to
get to a better understanding of the phase diagram. Our main results include:
- Various numerical observations that suggest that the critical line lies
strictly in between the two bounds.
- A rigorous statistical test based on concentration inequalities and
super-additivity, for determining whether a given point of the phase diagram is
in the localized phase. This is applied in particular to show that, with a very
low level of error, the lower bound does not coincide with the critical line.
- An analysis of the precise asymptotic behavior of the partition function in
the delocalized phase, with particular attention to the effect of rare atypical
stretches in the disorder sequence and on whether or not in the delocalized
regime the polymer path has a Brownian scaling.
- A new proof of the lower bound on the critical line. This proof relies on a
characterization of the localized regime which is more appealing for
interpreting the numerical data.Comment: accepted for publication on J. Stat. Phy
Why is the DNA Denaturation Transition First Order?
We study a model for the denaturation transition of DNA in which the
molecules are considered as composed of a sequence of alternating bound
segments and denaturated loops. We take into account the excluded-volume
interactions between denaturated loops and the rest of the chain by exploiting
recent results on scaling properties of polymer networks of arbitrary topology.
The phase transition is found to be first order in d=2 dimensions and above, in
agreement with experiments and at variance with previous theoretical results,
in which only excluded-volume interactions within denaturated loops were taken
into account. Our results agree with recent numerical simulations.Comment: Revised version. To appear in Phys. Rev. Let
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
Scaling of Star Polymers with one to 80 Arms
We present large statistics simulations of 3-dimensional star polymers with
up to arms, and with up to 4000 monomers per arm for small values of
. They were done for the Domb-Joyce model on the simple cubic lattice. This
is a model with soft core exclusion which allows multiple occupancy of sites
but punishes each same-site pair of monomers with a Boltzmann factor . We
use this to allow all arms to be attached at the central site, and we use the
`magic' value to minimize corrections to scaling. The simulations are
made with a very efficient chain growth algorithm with resampling, PERM,
modified to allow simultaneous growth of all arms. This allows us to measure
not only the swelling (as observed from the center-to-end distances), but also
the partition sum. The latter gives very precise estimates of the critical
exponents . For completeness we made also extensive simulations of
linear (unbranched) polymers which give the best estimates for the exponent
.Comment: 7 pages, 7 figure
A class of nonlinear wave equations containing the continuous Toda case
We consider a nonlinear field equation which can be derived from a binomial
lattice as a continuous limit. This equation, containing a perturbative
friction-like term and a free parameter , reproduces the Toda case (in
absence of the friction-like term) and other equations of physical interest, by
choosing particular values of . We apply the symmetry and the
approximate symmetry approach, and the prolongation technique. Our main purpose
is to check the limits of validity of different analytical methods in the study
of nonlinear field equations. We show that the equation under investigation
with the friction-like term is characterized by a finite-dimensional Lie
algebra admitting a realization in terms of boson annhilation and creation
operators. In absence of the friction-like term, the equation is linearized and
connected with equations of the Bessel type. Examples of exact solutions are
displayed, and the algebraic structure of the equation is discussed.Comment: Latex file + [equations.sty], 22 p
Reunion of random walkers with a long range interaction: applications to polymers and quantum mechanics
We use renormalization group to calculate the reunion and survival exponents
of a set of random walkers interacting with a long range and a short
range interaction. These exponents are used to study the binding-unbinding
transition of polymers and the behavior of several quantum problems.Comment: Revtex 3.1, 9 pages (two-column format), 3 figures. Published version
(PRE 63, 051103 (2001)). Reference corrections incorporated (PRE 64, 059902
(2001) (E
A Simple Model for the DNA Denaturation Transition
We study pairs of interacting self-avoiding walks on the 3d simple cubic
lattice. They have a common origin and are allowed to overlap only at the same
monomer position along the chain. The latter overlaps are indeed favored by an
energetic gain.
This is inspired by a model introduced long ago by Poland and Sheraga [J.
Chem. Phys. {\bf 45}, 1464 (1966)] for the denaturation transition in DNA
where, however, self avoidance was not fully taken into account. For both
models, there exists a temperature T_m above which the entropic advantage to
open up overcomes the energy gained by forming tightly bound two-stranded
structures.
Numerical simulations of our model indicate that the transition is of first
order (the energy density is discontinuous), but the analog of the surface
tension vanishes and the scaling laws near the transition point are exactly
those of a second order transition with crossover exponent \phi=1. Numerical
and exact analytic results show that the transition is second order in modified
models where the self-avoidance is partially or completely neglected.Comment: 29 pages, LaTeX, 20 postscript figure
Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice
We present a high-statistics Monte Carlo determination of the exponent gamma
for self-avoiding walks on a Manhattan lattice in two dimensions. A
conservative estimate is \gamma \gtapprox 1.3425(3), in agreement with the
universal value 43/32 on regular lattices, but in conflict with predictions
from conformal field theory and with a recent estimate from exact enumerations.
We find strong corrections to scaling that seem to indicate the presence of a
non-analytic exponent Delta < 1. If we assume Delta = 11/16 we find gamma =
1.3436(3), where the error is purely statistical.Comment: 24 pages, LaTeX2e, 4 figure