787 research outputs found
Delocalization transition of the selective interface model: distribution of pseudo-critical temperatures
According to recent progress in the finite size scaling theory of critical
disordered systems, the nature of the phase transition is reflected in the
distribution of pseudo-critical temperatures over the ensemble of
samples of size . In this paper, we apply this analysis to the
delocalization transition of an heteropolymeric chain at a selective
fluid-fluid interface. The width and the shift
are found to decay with the same exponent
, where . The distribution of
pseudo-critical temperatures is clearly asymmetric, and is well
fitted by a generalized Gumbel distribution of parameter . We also
consider the free energy distribution, which can also be fitted by a
generalized Gumbel distribution with a temperature dependent parameter, of
order in the critical region. Finally, the disorder averaged
number of contacts with the interface scales at like with
.Comment: 9 pages,6 figure
Lyman Alpha and MgII as Probes of Galaxies and their Environments
Ly{\alpha} emission, Ly{\alpha} absorption and MgII absorption are powerful
tracers of neutral hydrogen. Hydrogen is the most abundant element in the
universe and plays a central role in galaxy formation via gas accretion and
outflows, as well as being the precursor to molecular clouds, the sites of star
formation. Since 21cm emission from neutral hydrogen can only be directly
observed in the local universe, we rely on Ly{\alpha} emission, and Ly{\alpha}
and MgII absorption to probe the physics that drives galaxy evolution at higher
redshifts. Furthermore, these tracers are sensitive to a range of hydrogen
densities that cover the interstellar medium, the circumgalactic medium and the
intergalactic medium, providing an invaluable means of studying gas physics in
regimes where it is poorly understood. At high redshift, Ly{\alpha} emission
line searches have discovered thousands of star-forming galaxies out to z = 7.
The large Ly{\alpha} scattering cross-section makes observations of this line
sensitive to even very diffuse gas outside of galaxies. Several thousand more
high-redshift galaxies are known from damped Ly{\alpha} absorption lines and
absorption by the MgII doublet in quasar and GRB spectra. MgII, in particular,
probes metal-enriched neutral gas inside galaxy haloes in a wide range of
environments and redshifts (0.1 < z < 6.3), including the so-called redshift
desert. Here we review what observations and theoretical models of Ly{\alpha}
emission, Ly{\alpha} and MgII absorption have told us about the interstellar,
circumgalactic and intergalactic medium in the context of galaxy formation and
evolution.Comment: 59 Pages, 19 Figures, 1 Table. Accepted for publication in
Publications of the Astronomical Society of the Pacifi
Smoothening of Depinning Transitions for Directed Polymers with Quenched Disorder
We consider disordered models of pinning of directed polymers on a defect
line, including (1+1)-dimensional interface wetting models, disordered
Poland--Scheraga models of DNA denaturation and other (1+d)-dimensional
polymers in interaction with columnar defects. We consider also random
copolymers at a selective interface. These models are known to have a
(de)pinning transition at some critical line in the phase diagram. In this work
we prove that, as soon as disorder is present, the transition is at least of
second order: the free energy is differentiable at the critical line, and the
order parameter (contact fraction) vanishes continuously at the transition. On
the other hand, it is known that the corresponding non-disordered models can
have a first order (de)pinning transition, with a jump in the order parameter.
Our results confirm predictions based on the Harris criterion.Comment: 4 pages, 1 figure. Version 2: references added, minor changes made.
To appear on Phys. Rev. Let
Numerical study of the disordered Poland-Scheraga model of DNA denaturation
We numerically study the binary disordered Poland-Scheraga model of DNA
denaturation, in the regime where the pure model displays a first order
transition (loop exponent ). We use a Fixman-Freire scheme for the
entropy of loops and consider chain length up to , with
averages over samples. We present in parallel the results of various
observables for two boundary conditions, namely bound-bound (bb) and
bound-unbound (bu), because they present very different finite-size behaviors,
both in the pure case and in the disordered case. Our main conclusion is that
the transition remains first order in the disordered case: in the (bu) case,
the disorder averaged energy and contact densities present crossings for
different values of without rescaling. In addition, we obtain that these
disorder averaged observables do not satisfy finite size scaling, as a
consequence of strong sample to sample fluctuations of the pseudo-critical
temperature. For a given sample, we propose a procedure to identify its
pseudo-critical temperature, and show that this sample then obeys first order
transition finite size scaling behavior. Finally, we obtain that the disorder
averaged critical loop distribution is still governed by in
the regime , as in the pure case.Comment: 12 pages, 13 figures. Revised versio
Estimation and comparison of signed symmetric covariation coefficient and generalized association parameter for alpha-stable dependence modeling
Accepté à Communications in Statistics - Theory and methodsInternational audienceIn this paper we study the estimators of two measures of dependence: the signed symmetric covariation coefficient proposed by Garel and Kodia and the generalized association parameter put forward by Paulauskas. In the sub-Gaussian case, the signed symmetric covariation coefficient and the generalized association parameter coincide. The estimator of the signed symmetric covariation coefficient proposed here is based on fractional lower-order moments. The estimator of the generalized association parameter is based on estimation of a stable spectral measure. We investigate the relative performance of these estimators by comparing results from simulations
A simple model for DNA denaturation
Following Poland and Scheraga, we consider a simplified model for the
denaturation transition of DNA. The two strands are modeled as interacting
polymer chains. The attractive interactions, which mimic the pairing between
the four bases, are reduced to a single short range binding term. Furthermore,
base-pair misalignments are forbidden, implying that this binding term exists
only for corresponding (same curvilinear abscissae) monomers of the two chains.
We take into account the excluded volume repulsion between monomers of the two
chains, but neglect intra-chain repulsion. We find that the excluded volume
term generates an effective repulsive interaction between the chains, which
decays as . Due to this long-range repulsion between the chains, the
denaturation transition is first order in any dimension, in agreement with
previous studies.Comment: 10 page
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
On the multifractal statistics of the local order parameter at random critical points : application to wetting transitions with disorder
Disordered systems present multifractal properties at criticality. In
particular, as discovered by Ludwig (A.W.W. Ludwig, Nucl. Phys. B 330, 639
(1990)) on the case of diluted two-dimensional Potts model, the moments
of the local order parameter scale with a set
of non-trivial exponents . In this paper, we revisit
these ideas to incorporate more recent findings: (i) whenever a multifractal
measure normalized over space occurs in a random
system, it is crucial to distinguish between the typical values and the
disorder averaged values of the generalized moments , since
they may scale with different generalized dimensions and
(ii) as discovered by Wiseman and Domany (S. Wiseman and E. Domany, Phys Rev E
{\bf 52}, 3469 (1995)), the presence of an infinite correlation length induces
a lack of self-averaging at critical points for thermodynamic observables, in
particular for the order parameter. After this general discussion valid for any
random critical point, we apply these ideas to random polymer models that can
be studied numerically for large sizes and good statistics over the samples. We
study the bidimensional wetting or the Poland-Scheraga DNA model with loop
exponent (marginal disorder) and (relevant disorder). Finally,
we argue that the presence of finite Griffiths ordered clusters at criticality
determines the asymptotic value and the minimal value of the typical multifractal spectrum
.Comment: 17 pages, 20 figure
On Heteropolymer Shape Dynamics
We investigate the time evolution of the heteropolymer model introduced by
Iori, Marinari and Parisi to describe some of the features of protein folding
mechanisms. We study how the (folded) shape of the chain evolves in time. We
find that for short times the mean square distance (squared) between chain
configurations evolves according to a power law, . We discuss
the influence of the quenched disorder (represented by the randomness of the
coupling constants in the Lennard-Jones potential) on value of the critical
exponent. We find that decreases from to when
the strength of the quenched disorder increases.Comment: 12 pages, very simple LaTeX file, 6 figures not included, sorry. SCCS
33
Copolymer adsorption kinetics at a selective liquid-liquid interface: Scaling theory and computer experiment
We consider the adsorption kinetics of a regular block-copolymer of total
length and block size at a selective liquid-liquid interface in the
limit of strong localization. We propose a simple analytic theory based on
scaling considerations which describes the relaxation of the initial coil into
a flat-shaped layer. The characteristic times for attaining equilibrium values
of the gyration radius components perpendicular and parallel to the interface
are predicted to scale with chain length and block length as
(here is the Flory exponent)
and as , although initially the rate of coil
flattening is expected to decrease with block size as . Since
typically for multiblock copolymers, our results suggest that the
flattening dynamics proceeds faster perpendicular rather than parallel to the
interface. We also demonstrate that these scaling predictions agree well with
the results of extensive Monte Carlo simulations of the localization dynamics.Comment: 4 pages, 4 figures, submited to Europhys. Let
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