728 research outputs found
Structural and ultrametric properties of twenty(L-alanine)
We study local energy minima of twenty(L-alanine). The minima are generated
using high-temperature Molecular Dynamics and Chain-Growth Monte Carlo
simulations, with subsequent minimization. We find that the lower-energy
configurations are -helices for a wide range of dielectric constant
values and that there is no noticeable difference
between the distribution of energy minima in space for different
values of Ultrametricity tests show that lower-energy -helical) configurations form a set which is ultrametric to a
certain degree, providing evidence for the presence of fine structure among
those minima. We put forward a heuristic argument for this fine structure. We
also find evidence for ultrametricity of a different kind among and energy minima. We analyze the distribution of lengths of
-helical portions among the minimized configurations and find a
persistence phenomenon for the ones, in qualitative agreement
with previous studies of critical lengths. Email contact:
[email protected]: Saclay-T93/025 Email: [email protected]
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
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
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
Statistics of low energy excitations for the directed polymer in a random medium ()
We consider a directed polymer of length in a random medium of space
dimension . The statistics of low energy excitations as a function of
their size is numerically evaluated. These excitations can be divided into
bulk and boundary excitations, with respective densities
and . We find that both densities follow the scaling
behavior , where is the exponent governing the
energy fluctuations at zero temperature (with the well-known exact value
in one dimension). In the limit , both scaling
functions and behave as , leading to the droplet power law
in the regime . Beyond their common singularity near , the two scaling functions
are very different : whereas decays
monotonically for , the function first decays for
, then grows for , and finally presents a power law
singularity near . The density
of excitations of length accordingly decays as
where
. We obtain , and , suggesting the possible relation
.Comment: 15 pages, 25 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
Random wetting transition on the Cayley tree : a disordered first-order transition with two correlation length exponents
We consider the random wetting transition on the Cayley tree, i.e. the
problem of a directed polymer on the Cayley tree in the presence of random
energies along the left-most bonds. In the pure case, there exists a
first-order transition between a localized phase and a delocalized phase, with
a correlation length exponent . In the disordered case, we find
that the transition remains first-order, but that there exists two diverging
length scales in the critical region : the typical correlation length diverges
with the exponent , whereas the averaged correlation length
diverges with the bigger exponent and governs the finite-size
scaling properties. We describe the relations with previously studied models
that are governed by the same "Infinite Disorder Fixed Point". For the present
model, where the order parameter is the contact density
(defined as the ratio of the number of contacts over the total length
), the notion of "infinite disorder fixed point" means that the thermal
fluctuations of within a given sample, become negligeable at large
scale with respect to sample-to-sample fluctuations. We characterize the
statistics over the samples of the free-energy and of the contact density. In
particular, exactly at criticality, we obtain that the contact density is not
self-averaging but remains distributed over the samples in the thermodynamic
limit, with the distribution .Comment: 15 pages, 1 figur
Anderson localization transition with long-ranged hoppings : analysis of the strong multifractality regime in terms of weighted Levy sums
For Anderson tight-binding models in dimension with random on-site
energies and critical long-ranged hoppings decaying
typically as , we show that the strong multifractality
regime corresponding to small can be studied via the standard perturbation
theory for eigenvectors in quantum mechanics. The Inverse Participation Ratios
, which are the order parameters of Anderson transitions, can be
written in terms of weighted L\'evy sums of broadly distributed variables (as a
consequence of the presence of on-site random energies in the denominators of
the perturbation theory). We compute at leading order the typical and
disorder-averaged multifractal spectra and as a
function of . For , we obtain the non-vanishing limiting spectrum
as . For , this method
yields the same disorder-averaged spectrum of order as
obtained previously via the Levitov renormalization method by Mirlin and Evers
[Phys. Rev. B 62, 7920 (2000)]. In addition, it allows to compute explicitly
the typical spectrum, also of order , but with a different -dependence
for all . As a consequence, we find
that the corresponding singularity spectra and
differ even in the positive region , and vanish at
different values , in contrast to the standard
picture. We also obtain that the saddle value of the Legendre
transform reaches the termination point where
only in the limit .Comment: 13 pages, 2 figures, v2=final versio
Numerical evidence for relevance of disorder in a Poland-Scheraga DNA denaturation model with self-avoidance: Scaling behavior of average quantities
We study numerically the effect of sequence heterogeneity on the
thermodynamic properties of a Poland-Scheraga model for DNA denaturation taking
into account self-avoidance, i.e. with exponent c_p=2.15 for the loop length
probability distribution. In complement to previous on-lattice Monte Carlo like
studies, we consider here off-lattice numerical calculations for large sequence
lengths, relying on efficient algorithmic methods. We investigate finite size
effects with the definition of an appropriate intrinsic length scale x,
depending on the parameters of the model. Based on the occurrence of large
enough rare regions, for a given sequence length N, this study provides a
qualitative picture for the finite size behavior, suggesting that the effect of
disorder could be sensed only with sequence lengths diverging exponentially
with x. We further look in detail at average quantities for the particular case
x=1.3, ensuring through this parameter choice the correspondence between the
off-lattice and the on-lattice studies. Taken together, the various results can
be cast in a coherent picture with a crossover between a nearly pure system
like behavior for small sizes N < 1000, as observed in the on-lattice
simulations, and the apparent asymptotic behavior indicative of disorder
relevance, with an (average) correlation length exponent \nu_r >= 2/d (=2).Comment: Latex, 33 pages with 15 postscript 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
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