195 research outputs found
Beyond the Mean Field Approximation for Spin Glasses
We study the d-dimensional random Ising model using a Bethe-Peierls
approximation in the framework of the replica method. We take into account the
correct interaction only inside replicated clusters of spins. Our ansatz is
that the interaction of the borders of the clusters with the external world can
be described via an effective interaction among replicas. The Bethe-Peierls
model is mapped into a single Ising model with a random gaussian field, whose
strength (related to the effective coupling between two replicas) is determined
via a self-consistency equation. This allows us to obtain analytic estimates of
the internal energy and of the critical temperature in d dimensions.Comment: plane TeX file,19 pages. 3 figures may be requested to Paladin at
axscaq.aquila.infn.i
2d frustrated Ising model with four phases
In this paper we consider a 2d random Ising system on a square lattice with
nearest neighbour interactions. The disorder is short range correlated and
asymmetry between the vertical and the horizontal direction is admitted. More
precisely, the vertical bonds are supposed to be non random while the
horizontal bonds alternate: one row of all non random horizontal bonds is
followed by one row where they are independent dichotomic random variables. We
solve the model using an approximate approach that replace the quenched average
with an annealed average under the constraint that the number of frustrated
plaquettes is keep fixed and equals that of the true system. The surprising
fact is that for some choices of the parameters of the model there are three
second order phase transitions separating four different phases:
antiferromagnetic, glassy-like, ferromagnetic and paramagnetic.Comment: 17 pages, Plain TeX, uses Harvmac.tex, 4 ps figures, submitted to
Physical Review
Predictability in Systems with Many Characteristic Times: The Case of Turbulence
In chaotic dynamical systems, an infinitesimal perturbation is exponentially
amplified at a time-rate given by the inverse of the maximum Lyapunov exponent
. In fully developed turbulence, grows as a power of the
Reynolds number. This result could seem in contrast with phenomenological
arguments suggesting that, as a consequence of `physical' perturbations, the
predictability time is roughly given by the characteristic life-time of the
large scale structures, and hence independent of the Reynolds number. We show
that such a situation is present in generic systems with many degrees of
freedom, since the growth of a non-infinitesimal perturbation is determined by
cumulative effects of many different characteristic times and is unrelated to
the maximum Lyapunov exponent. Our results are illustrated in a chain of
coupled maps and in a shell model for the energy cascade in turbulence.Comment: 24 pages, 10 Postscript figures (included), RevTeX 3.0, files packed
with uufile
Bethe-Peierls Approximation for the 2D Random Ising Model
The partition function of the 2d Ising model with random nearest neighbor
coupling is expressed in the dual lattice made of square plaquettes. The dual
model is solved in the the mean field and in different types of Bethe-Peierls
approximations, using the replica method.Comment: Plane TeX file, 21 pages, 5 figures available under request to
[email protected]
Transition to Chaos in a Shell Model of Turbulence
We study a shell model for the energy cascade in three dimensional turbulence
at varying the coefficients of the non-linear terms in such a way that the
fundamental symmetries of Navier-Stokes are conserved. When a control parameter
related to the strength of backward energy transfer is enough small,
the dynamical system has a stable fixed point corresponding to the Kolmogorov
scaling. This point becomes unstable at where a stable
limit cycle appears via a Hopf bifurcation. By using the bi-orthogonal
decomposition, the transition to chaos is shown to follow the Ruelle-Takens
scenario. For the dynamical evolution is intermittent
with a positive Lyapunov exponent. In this regime, there exists a strange
attractor which remains close to the Kolmogorov (now unstable) fixed point, and
a local scaling invariance which can be described via a intermittent
one-dimensional map.Comment: 16 pages, Tex, 20 figures available as hard cop
The Viscous Lengths in Hydrodynamic Turbulence are Anomalous Scaling Functions
It is shown that the idea that scaling behavior in turbulence is limited by
one outer length and one inner length is untenable. Every n'th order
correlation function of velocity differences \bbox{\cal
F}_n(\B.R_1,\B.R_2,\dots) exhibits its own cross-over length to
dissipative behavior as a function of, say, . This length depends on
{and on the remaining separations} . One result of this Letter
is that when all these separations are of the same order this length scales
like with
, with being
the scaling exponent of the 'th order structure function. We derive a class
of scaling relations including the ``bridge relation" for the scaling exponent
of dissipation fluctuations .Comment: PRL, Submitted. REVTeX, 4 pages, I fig. (not included) PS Source of
the paper with figure avalable at http://lvov.weizmann.ac.il/onlinelist.htm
MobiDB 3.0: more annotations for intrinsic disorder, conformational diversity and interactions in proteins
The MobiDB (URL: mobidb.bio.unipd.it) database of protein disorder and mobility annotations has been significantly updated and upgraded since its last major renewal in 2014. Several curated datasets for intrinsic disorder and folding upon binding have been integrated from specialized databases. The indirect evidence has also been expanded to better capture information available in the PDB, such as high temperature residues in X-ray structures and overall conformational diversity. Novel nuclear magnetic resonance chemical shift data provides an additional experimental information layer on conformational dynamics. Predictions have been expanded to provide new types of annotation on backbone rigidity, secondary structure preference and disordered binding regions. MobiDB 3.0 contains information for the complete UniProt protein set and synchronization has been improved by covering all UniParc sequences. An advanced search function allows the creation of a wide array of custom-made datasets for download and further analysis. A large amount of information and cross-links to more specialized databases are intended to make MobiDB the central resource for the scientific community working on protein intrinsic disorder and mobility
Lagrangian Velocity Statistics in Turbulent Flows: Effects of Dissipation
We use the multifractal formalism to describe the effects of dissipation on
Lagrangian velocity statistics in turbulent flows. We analyze high Reynolds
number experiments and direct numerical simulation (DNS) data. We show that
this approach reproduces the shape evolution of velocity increment probability
density functions (PDF) from Gaussian to stretched exponentials as the time lag
decreases from integral to dissipative time scales. A quantitative
understanding of the departure from scaling exhibited by the magnitude
cumulants, early in the inertial range, is obtained with a free parameter
function D(h) which plays the role of the singularity spectrum in the
asymptotic limit of infinite Reynolds number. We observe that numerical and
experimental data are accurately described by a unique quadratic D(h) spectrum
which is found to extend from to , as
the signature of the highly intermittent nature of Lagrangian velocity
fluctuations.Comment: 5 pages, 3 figures, to appear in PR
Integral correlation measures for multiparticle physics
We report on a considerable improvement in the technique of measuring
multiparticle correlations via integrals over correlation functions. A
modification of measures used in the characterization of chaotic dynamical
sytems permits fast and flexible calculation of factorial moments and cumulants
as well as their differential versions. Higher order correlation integral
measurements even of large multiplicity events such as encountered in heavy ion
collisons are now feasible. The change from ``ordinary'' to ``factorial''
powers may have important consequences in other fields such as the study of
galaxy correlations and Bose-Einstein interferometry.Comment: 23 pages, 6 tar-compressed uuencoded PostScript figures appended,
preprint TPR-92-4
Geometric dynamical observables in rare gas crystals
We present a detailed description of how a differential geometric approach to
Hamiltonian dynamics can be used for determining the existence of a crossover
between different dynamical regimes in a realistic system, a model of a rare
gas solid. Such a geometric approach allows to locate the energy threshold
between weakly and strongly chaotic regimes, and to estimate the largest
Lyapunov exponent. We show how standard mehods of classical statistical
mechanics, i.e. Monte Carlo simulations, can be used for our computational
purposes. Finally we consider a Lennard Jones crystal modeling solid Xenon. The
value of the energy threshold turns out to be in excellent agreement with the
numerical estimate based on the crossover between slow and fast relaxation to
equilibrium obtained in a previous work by molecular dynamics simulations.Comment: RevTeX, 19 pages, 6 PostScript figures, submitted to Phys. Rev.
- …