553 research outputs found
Directed polymer in a random medium of dimension 1+1 and 1+3: weights statistics in the low-temperature phase
We consider the low-temperature disorder-dominated phase of the
directed polymer in a random potentiel in dimension 1+1 (where )
and 1+3 (where ). To characterize the localization properties of
the polymer of length , we analyse the statistics of the weights of the last monomer as follows. We numerically compute the probability
distributions of the maximal weight , the probability distribution of the parameter as well as the average values of the higher order
moments . We find that there exists a
temperature such that (i) for , the distributions
and present the characteristic Derrida-Flyvbjerg
singularities at and for . In particular, there
exists a temperature-dependent exponent that governs the main
singularities and as well as the power-law decay of the moments . The exponent grows from the value
up to . (ii) for , the
distribution vanishes at some value , and accordingly the
moments decay exponentially as in . The
histograms of spatial correlations also display Derrida-Flyvbjerg singularities
for . Both below and above , the study of typical and
averaged correlations is in full agreement with the droplet scaling theory.Comment: 13 pages, 29 figure
Lyapunov exponents as a dynamical indicator of a phase transition
We study analytically the behavior of the largest Lyapunov exponent
for a one-dimensional chain of coupled nonlinear oscillators, by
combining the transfer integral method and a Riemannian geometry approach. We
apply the results to a simple model, proposed for the DNA denaturation, which
emphasizes a first order-like or second order phase transition depending on the
ratio of two length scales: this is an excellent model to characterize
as a dynamical indicator close to a phase transition.Comment: 8 Pages, 3 Figure
Statistical physics of the melting of inhomogeneous DNA
We studied how the inhomogeneity of a sequence affects the phase transition
that takes place at DNA melting. Unlike previous works, which considered
thermodynamic quantities averaged over many different inhomogeneous sequences,
we focused on precise sequences and investigated the succession of local
openings that lead to their dissociation. For this purpose, we performed
Transfer Integral type calculations with two different dynamical models, namely
the heterogeneous Dauxois-Peyrard-Bishop model and the model based on finite
stacking enthalpies we recently proposed. It appears that, for both models, the
essential effect of heterogeneity is to let different portions of the
investigated sequences open at slightly different temperatures. Besides this
macroscopic effect, the local aperture of each portion indeed turns out to be
very similar to that of a homogeneous sequence with the same length. Rounding
of each local opening transition is therefore merely a size effect. For the
Dauxois-Peyrard-Bishop model, sequences with a few thousands base pairs are
still far from the thermodynamic limit, so that it is inappropriate, for this
model, to discuss the order of the transition associated with each local
opening. In contrast, sequences with several hundreds to a few thousands base
pairs are pretty close to the thermodynamic limit for the model we proposed.
The temperature interval where power laws holds is consequently broad enough to
enable the estimation of critical exponents. On the basis of the few examples
we investigated, it seems that, for our model, disorder does not necessarily
induce a decrease of the order of the transition
Statistics of first-passage times in disordered systems using backward master equations and their exact renormalization rules
We consider the non-equilibrium dynamics of disordered systems as defined by
a master equation involving transition rates between configurations (detailed
balance is not assumed). To compute the important dynamical time scales in
finite-size systems without simulating the actual time evolution which can be
extremely slow, we propose to focus on first-passage times that satisfy
'backward master equations'. Upon the iterative elimination of configurations,
we obtain the exact renormalization rules that can be followed numerically. To
test this approach, we study the statistics of some first-passage times for two
disordered models : (i) for the random walk in a two-dimensional self-affine
random potential of Hurst exponent , we focus on the first exit time from a
square of size if one starts at the square center. (ii) for the
dynamics of the ferromagnetic Sherrington-Kirkpatrick model of spins, we
consider the first passage time to zero-magnetization when starting from
a fully magnetized configuration. Besides the expected linear growth of the
averaged barrier , we find that the rescaled
distribution of the barrier decays as for large
with a tail exponent of order . This value can be simply
interpreted in terms of rare events if the sample-to-sample fluctuation
exponent for the barrier is .Comment: 8 pages, 4 figure
Single Chain Force Spectroscopy: Sequence Dependence
We study the elastic properties of a single A/B copolymer chain with a
specific sequence. We predict a rich structure in the force extension relations
which can be addressed to the sequence. The variational method is introduced to
probe local minima on the path of stretching and releasing. At given force, we
find multiple configurations which are separated by energy barriers. A
collapsed globular configuration consists of several domains which unravel
cooperatively. Upon stretching, unfolding path shows stepwise pattern
corresponding to the unfolding of each domain. While releasing, several cores
can be created simultaneously in the middle of the chain resulting in a
different path of collapse.Comment: 6 pages 3 figure
Bubble dynamics in DNA
The formation of local denaturation zones (bubbles) in double-stranded DNA is
an important example for conformational changes of biological macromolecules.
We study the dynamics of bubble formation in terms of a Fokker-Planck equation
for the probability density to find a bubble of size n base pairs at time t, on
the basis of the free energy in the Poland-Scheraga model. Characteristic
bubble closing and opening times can be determined from the corresponding first
passage time problem, and are sensitive to the specific parameters entering the
model. A multistate unzipping model with constant rates recently applied to DNA
breathing dynamics [G. Altan-Bonnet et al, Phys. Rev. Lett. 90, 138101 (2003)]
emerges as a limiting case.Comment: 9 pages, 2 figure
THERMODYNAMICS OF A BROWNIAN BRIDGE POLYMER MODEL IN A RANDOM ENVIRONMENT
We consider a directed random walk making either 0 or moves and a
Brownian bridge, independent of the walk, conditioned to arrive at point on
time . The Hamiltonian is defined as the sum of the square of increments of
the bridge between the moments of jump of the random walk and interpreted as an
energy function over the bridge connfiguration; the random walk acts as the
random environment. This model provides a continuum version of a model with
some relevance to protein conformation. The thermodynamic limit of the specific
free energy is shown to exist and to be self-averaging, i.e. it is equal to a
trivial --- explicitly computed --- random variable. An estimate of the
asymptotic behaviour of the ground state energy is also obtained.Comment: 20 pages, uuencoded postscrip
To maximize or not to maximize the free energy of glassy systems, !=?
The static free energy of glassy systems can be expressed in terms of the
Parisi order parameter function. When this function has a discontinuity, the
location of the step is determined by maximizing the free energy. In dynamics a
transition is found at larger temperature, while the location of the step
satisfies a marginality criterion. It is shown here that in a replica
calculation this criterion minimizes the free energy. This leads to first order
phase transitions at the dynamic transition point. Though the order parameter
function is the same as in the long-time limit of a dynamical analysis,
thermodynamics is different.Comment: 4 pages PostScript, one figur
The SPHINX cosmological simulations of the first billion years: The impact of binary stars on reionization
We present the SPHINX suite of cosmological adaptive mesh refinement
simulations, the first radiation-hydrodynamical simulations to simultaneously
capture large-scale reionization and the escape of ionizing radiation from
thousands of resolved galaxies. Our and co-moving Mpc volumes resolve
haloes down to the atomic cooling limit and model the inter-stellar medium with
better than pc resolution. The project has numerous goals in
improving our understanding of reionization and making predictions for future
observations. In this first paper we study how the inclusion of binary stars in
computing stellar luminosities impacts reionization, compared to a model that
includes only single stars. Owing to the suppression of galaxy growth via
strong feedback, our galaxies are in good agreement with observational
estimates of the galaxy luminosity function. We find that binaries have a
significant impact on the timing of reionization: with binaries, our boxes are
percent ionized by volume at , while without them our
volumes fail to reionize by . These results are robust to changes in
volume size, resolution, and feedback efficiency. The escape of ionizing
radiation from individual galaxies varies strongly and frequently. On average,
binaries lead to escape fractions of percent, about times
higher than with single stars only. The higher escape fraction is a result of a
shallower decline in ionizing luminosity with age, and is the primary reason
for earlier reionization, although the higher integrated luminosity with
binaries also plays a sub-dominant role
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
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