Related papers: Front propagation in random media: From extremal t…
We study the speed of propagation of fronts for the scalar reaction-diffusion equation $u_t = u_{xx} + f(u)$\, with $f(0) = f(1) = 0$. We give a new integral variational principle for the speed of the fronts joining the state $u=1$ to…
We study the energy distribution function $\rho (E)$ for interfaces in a random field environment at zero temperature by summing the leading terms in the perturbation expansion of $\rho (E)$ in powers of the disorder strength, and by taking…
We have studied the dispersive behaviour of imbibition fronts in a porous medium by X-ray tomography. Injection velocities were varied and the porous medium was initially prewetted or not. At low velocity in the prewetted medium, the…
Out-of-equilibrium systems, inherently complex and challenging to understand, are prevalent across various disciplines, including physics where they arise in contexts such as fluid dynamics. In particular, critical out-of-equilibrium…
We study the slow stochastic dynamics near the depinning threshold of an elastic interface in a random medium by solving a particularly suited model of hopping interacting particles that belongs to the quenched-Edwards-Wilkinson depinning…
We built a model of the daily temperature based on a diffusion process and address to extreme values not taken into account in the literature on this kind of models. We first study, using non parametric tools, the trends on mean and…
We derive exact predictions for universal scaling exponents and scaling functions associated with the statistics of maximum velocities vm during avalanches described by the mean field theory of the interface depinning transition. In…
The propagation of (planar) cracks in a heterogeneous brittle material characterized by a random field of toughness is considered, taking into account explicitly the effect of the crack front roughness on the local stress intensity factor.…
One-dimensional free fermions are studied with emphasis on propagating fronts emerging from a step initial condition. The probability distribution of the number of particles at the edge of the front is determined exactly. It is found that…
We show that propagation speeds in invasion processes modeled by reaction-diffusion systems are determined by marginal spectral stability conditions, as predicted by the marginal stability conjecture. This conjecture was recently settled in…
We introduce a speed selection mechanism for front propagation in reaction-diffusion systems with multiple fields. This mechanism applies to pulled and pushed fronts alike, and operates by restricting the fields to large "finite" intervals…
In order to study the dependence of the coercive force of sintered magnets on temperature, nucleation and domain wall propagation at the grain boundary are studied as rate-determining processes of the magnetization reversal phenomena in…
In a recent letter [Europhys. Lett. 97, 34002 (2012)], random matrix theory is introduced for long-range acoustic propagation in the ocean. The theory is expressed in terms of unitary propagation matrices that represent the scattering…
Nonlinear waves are a robust phenomenon observed in complex systems ranging from mechanics to ecology. Fronts are fundamental due to their robustness against perturbations and capacity to propagate one state over another. Controlling and…
Information diffusion on social networks has been described as a collective outcome of threshold behaviors in the framework of threshold models. However, since the existing models do not take into account individuals' optimization problem,…
We describe the resulting spatiotemporal dynamics when a homogeneous equilibrium loses stability in a spatially extended system. More precisely, we consider reaction-diffusion systems, assuming only that the reaction kinetics undergo a…
The dynamics of flame propagation in systems with infinite Lewis number and spatially discretized sources of heat release is examined, which is applicable to the combustion of suspensions of fuel particles in air. The system is analyzed…
We consider a two-species reaction-diffusion system in one space dimension that is derived from an epidemiological model in a spatially periodic environment with two types of pathogens: the wild type and the mutant. The system is of a…
Classical diffusion in a random medium involves an exponential functional of Brownian motion. This functional also appears in the study of Brownian diffusion on a Riemann surface of constant negative curvature. We analyse in detail this…
We investigate experimentally and theoretically the dynamics of a crack front during the micro-instabilities taking place in heterogeneous materials between two successive equilibrium positions. We focus specifically on the spatio-temporal…