24 research outputs found
Fronts dynamics in the presence of spatio-temporal structured noises
Front dynamics modeled by a reaction-diffusion equation are studied under the
influence of spatio-temporal structured noises. An effective deterministic
model is analytical derived where the noise parameters, intensity, correlation
time and correlation length appear explicitely. The different effects of these
parameters are discussed for the Ginzburg-Landau and Schl\"ogl models. We
obtain an analytical expression for the front velocity as a function of the
noise parameters. Numerical simulations results are in a good agreement with
the theoretical predictions.Comment: 11 pages, 6 figures; REVTEX; to be published in Phys.Rev.E, july 200
New methods to measure phase transition strength
A recently developed technique to determine the order and strength of phase
transitions by extracting the density of partition function zeroes (a
continuous function) from finite-size systems (a discrete data set) is
generalized to systems for which (i) some or all of the zeroes occur in
degenerate sets and/or (ii) they are not confined to a singular line in the
complex plane. The technique is demonstrated by application to the case of free
Wilson fermions.Comment: 3 pages, 2 figures, Lattice2002(spin
ERROR PROPAGATION IN EXTENDED CHAOTIC SYSTEMS
A strong analogy is found between the evolution of localized disturbances in
extended chaotic systems and the propagation of fronts separating different
phases. A condition for the evolution to be controlled by nonlinear mechanisms
is derived on the basis of this relationship. An approximate expression for the
nonlinear velocity is also determined by extending the concept of Lyapunov
exponent to growth rate of finite perturbations.Comment: Tex file without figures- Figures and text in post-script available
via anonymous ftp at ftp://wpts0.physik.uni-wuppertal.de/pub/torcini/jpa_le
Stochastic differential equations for non-linear hydrodynamics
We formulate the stochastic differential equations for non-linear
hydrodynamic fluctuations. The equations incorporate the random forces through
a random stress tensor and random heat flux as in the Landau and Lifshitz
theory. However, the equations are non-linear and the random forces are
non-Gaussian. We provide explicit expressions for these random quantities in
terms of the well-defined increments of the Wienner process.Comment: 11 pages, submitted to Phys. Rev.
Domain Walls in Non-Equilibrium Systems and the Emergence of Persistent Patterns
Domain walls in equilibrium phase transitions propagate in a preferred
direction so as to minimize the free energy of the system. As a result, initial
spatio-temporal patterns ultimately decay toward uniform states. The absence of
a variational principle far from equilibrium allows the coexistence of domain
walls propagating in any direction. As a consequence, *persistent* patterns may
emerge. We study this mechanism of pattern formation using a non-variational
extension of Landau's model for second order phase transitions. PACS numbers:
05.70.Fh, 42.65.Pc, 47.20.Ky, 82.20MjComment: 12 pages LaTeX, 5 postscript figures To appear in Phys. Rev.
Phase Transition Strength through Densities of General Distributions of Zeroes
A recently developed technique for the determination of the density of
partition function zeroes using data coming from finite-size systems is
extended to deal with cases where the zeroes are not restricted to a curve in
the complex plane and/or come in degenerate sets. The efficacy of the approach
is demonstrated by application to a number of models for which these features
are manifest and the zeroes are readily calculable.Comment: 16 pages, 12 figure
The Julia sets and complex singularities in hierarchical Ising models
We study the analytical continuation in the complex plane of free energy of
the Ising model on diamond-like hierarchical lattices. It is known that the
singularities of free energy of this model lie on the Julia set of some
rational endomorphism related to the action of the Migdal-Kadanoff
renorm-group. We study the asymptotics of free energy when temperature goes
along hyperbolic geodesics to the boundary of an attractive basin of . We
prove that for almost all (with respect to the harmonic measure) geodesics the
complex critical exponent is common, and compute it
The diffusion coefficient of propagating fronts with multiplicative noise
Recent studies have shown that in the presence of noise, both fronts propagating into a metastable state and so-called pushed fronts propagating into an unstable state, exhibit diffusive wandering about the average position. In this paper, we derive an expression for the effective diffusion coefficient of such fronts, which was motivated before on the basis of a multiple scale ansatz. Our systematic derivation is based on the decomposition of the fluctuating front into a suitably positioned average profile plus fluctuating eigenmodes of the stability operator. While the fluctuations of the front position in this particular decomposition are a Wiener process on all time scales, the fluctuations about the time-averaged front profile relax exponentially