94 research outputs found

### Slow regions percolate near glass transition

A nano-second scale in situ probe reveals that a bulk linear polymer
undergoes a sharp phase transition as a function of the degree of conversion,
as it nears the glass transition. The scaling behaviour is in the same
universality class as percolation. The exponents \gamma and \beta are found to
be 1.7 \pm .1 and 0.41\pm 0.01 in agreement with the best percolation results
in three dimensions.Comment: 7 pages, 3 figure

### Hamiltonian model for multidimensional epistasis

We propose and solve a Hamiltonian model for multidimensional epistastatic
interactions between beneficial mutations. The model is able to give rise
either to a phase transition between two equilibrium states, without any
coexistence, or exhibits a state where hybrid species can coexist, with gradual
passage from one wild type to another. The transition takes place as a function
of the "tolerance" of the environment, which we define as the amount of noise
in the system.Comment: 3 pages, 2 figures (in seperate files) spelling corrected and a
reference adde

### Analytical Solution of a Stochastic Content Based Network Model

We define and completely solve a content-based directed network whose nodes
consist of random words and an adjacency rule involving perfect or approximate
matches, for an alphabet with an arbitrary number of letters. The analytic
expression for the out-degree distribution shows a crossover from a leading
power law behavior to a log-periodic regime bounded by a different power law
decay. The leading exponents in the two regions have a weak dependence on the
mean word length, and an even weaker dependence on the alphabet size. The
in-degree distribution, on the other hand, is much narrower and does not show
scaling behavior. The results might be of interest for understanding the
emergence of genomic interaction networks, which rely, to a large extent, on
mechanisms based on sequence matching, and exhibit similar global features to
those found here.Comment: 13 pages, 5 figures. Rewrote conclusions regarding the relevance to
gene regulation networks, fixed minor errors and replaced fig. 4. Main body
of paper (model and calculations) remains unchanged. Submitted for
publicatio

### Continuous RSB mean-field solution of the Potts glass

We investigate the p-state mean-field model of the
Potts glass ($2\le p \le 4$) below the continuous phase transition to a
glassy phase. We find that apart from a solution with a first hierarchical
level of replica-symmetry breaking (1RSB), locally stable close to the
transition point, there is a continuous full replica-symmetry breaking (FRSB)
solution. The latter is marginally stable and has a higher free energy than the
former. We argue that the true equilibrium is reached only by FRSB, being
globally thermodynamically homogeneous, whereas 1RSB is only locally
homogeneous.Comment: REVTeX4.1, 4 pages, 1 figur

### Dynamical real-space renormalization group calculations with a new clustering scheme on random networks

We have defined a new type of clustering scheme preserving the connectivity
of the nodes in network ignored by the conventional Migdal-Kadanoff bond moving
process. Our new clustering scheme performs much better for correlation length
and dynamical critical exponents in high dimensions, where the conventional
Migdal-Kadanoff bond moving scheme breaks down. In two and three dimensions we
find the dynamical critical exponents for the kinetic Ising Model to be z=2.13
and z=2.09, respectively at pure Ising fixed point. These values are in very
good agreement with recent Monte Carlo results. We investigate the phase
diagram and the critical behaviour for randomly bond diluted lattices in d=2
and 3, in the light of this new transformation. We also provide exact
correlation exponent and dynamical critical exponent values on hierarchical
lattices with power-law degree distributions, both in the pure and random
cases.Comment: 8 figure

### Non-Parametric Analyses of Log-Periodic Precursors to Financial Crashes

We apply two non-parametric methods to test further the hypothesis that
log-periodicity characterizes the detrended price trajectory of large financial
indices prior to financial crashes or strong corrections. The analysis using
the so-called (H,q)-derivative is applied to seven time series ending with the
October 1987 crash, the October 1997 correction and the April 2000 crash of the
Dow Jones Industrial Average (DJIA), the Standard & Poor 500 and Nasdaq
indices. The Hilbert transform is applied to two detrended price time series in
terms of the ln(t_c-t) variable, where t_c is the time of the crash. Taking all
results together, we find strong evidence for a universal fundamental
log-frequency $f = 1.02 \pm 0.05$ corresponding to the scaling ratio $\lambda =
2.67 \pm 0.12$. These values are in very good agreement with those obtained in
past works with different parametric techniques.Comment: Latex document 13 pages + 58 eps figure

### Log-periodic route to fractal functions

Log-periodic oscillations have been found to decorate the usual power law
behavior found to describe the approach to a critical point, when the
continuous scale-invariance symmetry is partially broken into a discrete-scale
invariance (DSI) symmetry. We classify the `Weierstrass-type'' solutions of the
renormalization group equation F(x)= g(x)+(1/m)F(g x) into two classes
characterized by the amplitudes A(n) of the power law series expansion. These
two classes are separated by a novel ``critical'' point. Growth processes
(DLA), rupture, earthquake and financial crashes seem to be characterized by
oscillatory or bounded regular microscopic functions g(x) that lead to a slow
power law decay of A(n), giving strong log-periodic amplitudes. In contrast,
the regular function g(x) of statistical physics models with
``ferromagnetic''-type interactions at equibrium involves unbound logarithms of
polynomials of the control variable that lead to a fast exponential decay of
A(n) giving weak log-periodic amplitudes and smoothed observables. These two
classes of behavior can be traced back to the existence or abscence of
``antiferromagnetic'' or ``dipolar''-type interactions which, when present,
make the Green functions non-monotonous oscillatory and favor spatial modulated
patterns.Comment: Latex document of 29 pages + 20 ps figures, addition of a new
demonstration of the source of strong log-periodicity and of a justification
of the general offered classification, update of reference lis

### Critical Behavior of the Sandpile Model as a Self-Organized Branching Process

Kinetic equations, which explicitly take into account the branching nature of
sandpile avalanches, are derived. The dynamics of the sandpile model is
described by the generating functions of a branching process. Having used the
results obtained the renormalization group approach to the critical behavior of
the sandpile model is generalized in order to calculate both critical exponents
and height probabilities.Comment: REVTeX, twocolumn, 4 page

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