189 research outputs found
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
Mitogenomic diversity and stable isotopes provide insights into the maternal genetic history, mobility patterns, and diet of early medieval individuals from the Eastern Italian Alps
Fractal geometry of spin-glass models
Stability and diversity are two key properties that living entities share
with spin glasses, where they are manifested through the breaking of the phase
space into many valleys or local minima connected by saddle points. The
topology of the phase space can be conveniently condensed into a tree
structure, akin to the biological phylogenetic trees, whose tips are the local
minima and internal nodes are the lowest-energy saddles connecting those
minima. For the infinite-range Ising spin glass with p-spin interactions, we
show that the average size-frequency distribution of saddles obeys a power law
, where w=w(s) is the number of minima that can be
connected through saddle s, and D is the fractal dimension of the phase space
Growth of non-infinitesimal perturbations in turbulence
We discuss the effects of finite perturbations in fully developed turbulence
by introducing a measure of the chaoticity degree associated to a given scale
of the velocity field. This allows one to determine the predictability time for
non-infinitesimal perturbations, generalizing the usual concept of maximum
Lyapunov exponent. We also determine the scaling law for our indicator in the
framework of the multifractal approach. We find that the scaling exponent is
not sensitive to intermittency corrections, but is an invariant of the
multifractal models. A numerical test of the results is performed in the shell
model for the turbulent energy cascade.Comment: 4 pages, 2 Postscript figures (included), RevTeX 3.0, files packed
with uufile
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
Order in glassy systems
A directly measurable correlation length may be defined for systems having a
two-step relaxation, based on the geometric properties of density profile that
remains after averaging out the fast motion. We argue that the length diverges
if and when the slow timescale diverges, whatever the microscopic mechanism at
the origin of the slowing down. Measuring the length amounts to determining
explicitly the complexity from the observed particle configurations. One may
compute in the same way the Renyi complexities K_q, their relative behavior for
different q characterizes the mechanism underlying the transition. In
particular, the 'Random First Order' scenario predicts that in the glass phase
K_q=0 for q>x, and K_q>0 for q<x, with x the Parisi parameter. The hypothesis
of a nonequilibrium effective temperature may also be directly tested directly
from configurations.Comment: Typos corrected, clarifications adde
Roundoff-induced Coalescence of Chaotic Trajectories
Numerical experiments recently discussed in the literature show that
identical nonlinear chaotic systems linked by a common noise term (or signal)
may synchronize after a finite time. We study the process of synchronization as
function of precision of calculations. Two generic behaviors of the average
coalescence time are identified: exponential or linear. In both cases no
synchronization occurs if iterations are done with {\em infinite} precision.Comment: 6 pages, 3 postscript figures, to be published in Phys. Rev.
Chaos vs. Linear Instability in the Vlasov Equation: A Fractal Analysis Characterization
In this work we discuss the most recent results concerning the Vlasov
dynamics inside the spinodal region. The chaotic behaviour which follows an
initial regular evolution is characterized through the calculation of the
fractal dimension of the distribution of the final modes excited. The ambiguous
role of the largest Lyapunov exponent for unstable systems is also critically
reviewed.Comment: 10 pages, RevTeX, 4 figures not included but available upon reques
Analytical method for parameterizing the random profile components of nanosurfaces imaged by atomic force microscopy
The functional properties of many technological surfaces in biotechnology,
electronics, and mechanical engineering depend to a large degree on the
individual features of their nanoscale surface texture, which in turn are a
function of the surface manufacturing process. Among these features, the
surface irregularities and self-similarity structures at different spatial
scales, especially in the range of 1 to 100 nm, are of high importance because
they greatly affect the surface interaction forces acting at a nanoscale
distance. An analytical method for parameterizing the surface irregularities
and their correlations in nanosurfaces imaged by atomic force microscopy (AFM)
is proposed. In this method, flicker noise spectroscopy - a statistical physics
approach - is used to develop six nanometrological parameters characterizing
the high-frequency contributions of jump- and spike-like irregularities into
the surface texture. These contributions reflect the stochastic processes of
anomalous diffusion and inertial effects, respectively, in the process of
surface manufacturing. The AFM images of the texture of corrosion-resistant
magnetite coatings formed on low-carbon steel in hot nitrate solutions with
coating growth promoters at different temperatures are analyzed. It is shown
that the parameters characterizing surface spikiness are able to quantify the
effect of process temperature on the corrosion resistance of the coatings. It
is suggested that these parameters can be used for predicting and
characterizing the corrosion-resistant properties of magnetite coatings.Comment: 7 pages, 3 figures, 2 tables; to be published in Analys
Constrained spin dynamics description of random walks on hierarchical scale-free networks
We study a random walk problem on the hierarchical network which is a
scale-free network grown deterministically. The random walk problem is mapped
onto a dynamical Ising spin chain system in one dimension with a nonlocal spin
update rule, which allows an analytic approach. We show analytically that the
characteristic relaxation time scale grows algebraically with the total number
of nodes as . From a scaling argument, we also show the
power-law decay of the autocorrelation function C_{\bfsigma}(t)\sim
t^{-\alpha}, which is the probability to find the Ising spins in the initial
state {\bfsigma} after time steps, with the state-dependent non-universal
exponent . It turns out that the power-law scaling behavior has its
origin in an quasi-ultrametric structure of the configuration space.Comment: 9 pages, 6 figure
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