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

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

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 $f$ 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 $f$. We prove that for almost all (with respect to the harmonic measure) geodesics the complex critical exponent is common, and compute it

Noise Induced Fronts

A simple model is introduced that exhibits a noise-induced front propagation and where the noise enters multiplicatively. The invasion of the unstable state is studied, both theoretically and numerically. A good agreement is obtained for the mean value of the order parameter and the mean front velocity using the analytical predictions of the linear marginal stability analysis

Metastability and front propagation in the first-order optical Fréedericksz transition

A general dynamical model for the first-order optical Fréedericksz transition incorporating spatial transverse inhomogeneities and hydrodynamic effects is discussed in the framework of a time-dependent Ginzburg-Landau model. The motion of an interface between two coexisting states with different director orientations is considered. A uniformly translating front solution of the dynamical equations for the motion of that interface is described

Reaction-diffusion fronts under stochastic advection

We study front propagation in stirred media using a simplified modelization of the turbulent flow. Computer simulations reveal the existence of the two limiting propagation modes observed in recent experiments with liquid phase isothermal reactions. These two modes respectively correspond to a wrinkled although sharp propagating interface and to a broadened one. Specific laws relative to the enhancement of the front velocity in each regime are confirmed by our simulations