Related papers: Fluctuations and stability in front propagation
Single-point measurements of fluctuations in the scrape-off layer of magnetized plasmas are generally found to be dominated by large-amplitude bursts which are associated with radial motion of blob-like structures. A stochastic model for…
We propose a simple model for reaction-diffusion systems with orientational constraints on the reactivity of particles, and map it onto a field theory with upper critical dimension d_c=2. To two-loop level the long-time particle density…
A multiscale analysis of 1D stochastic bistable reaction-diffusion equations with additive noise is carried out w.r.t. travelling waves within the variational approach to stochastic partial differential equations. It is shown with explicit…
We study the reaction-fractional-diffusion equation $u_t+(-\Delta)^{s} u=f(u)$ with ignition and monostable reactions $f$, and $s\in(0,1)$. We obtain the first optimal bounds on the propagation of front-like solutions in the cases where no…
A stochastic version of the Brusselator model is proposed and studied via the system size expansion. The mean-field equations are derived and shown to yield to organized Turing patterns within a specific parameters region. When determining…
The problem of velocity selection of reaction-diffusion fronts has been widely investigated. While the mean field limit results are well known theoretically, there is a lack of analytic progress in those cases in which fluctuations are to…
Understanding anomalous transport and reaction kinetics due to microscopic physical and chemical disorder is a long-standing goal in many fields including geophysics, biology, and engineering. We consider reaction-diffusion characterized by…
Fluctuations may govern the fate of an interacting particle system even on the mean-field level. This is demonstrated via a three species cyclic trapping reaction with a large, yet finite number of particles, where the final number of…
A reaction-diffusion-advection predator-prey model with Holling type-II predator functional response is considered. We show the stability/instability of the positive steady state and the existence of a Hopf bifurcation when the diffusion…
The dynamics of dispersal-structured populations, consisting of competing individuals that are characterized by different diffusion coefficients but are otherwise identical, is investigated. Competition is taken into account through…
We analytically evaluate the large deviation function in a simple model of classical particle transfer between two reservoirs. We illustrate how the asymptotic large time regime is reached starting from a special propagating initial…
We study the influence of a dissipation process on diffusion dynamics triggered by fluctuations with long-range correlations. We make the assumption that the perturbation process involved is of the same kind as those recently studied…
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…
Localized wave fronts are a fundamental feature of biological systems from cell biology to ecology. Here, we study a broad class of bistable models subject to self-activation, degradation and spatially inhomogeneous activating agents. We…
This work is dedicated to the analysis of the delicate details of the effect of upstream velocity fluctuations on the flame propagation speed. The investigation was carried out using the Sivashinsky model of cellularisation of…
Spatio-temporal extensions of familiar compartment models for disease transmission incorporating diffusive behavior, or interactions between individuals at separate locations, are explored. The models considered have the character of…
We consider reaction-diffusion equations that are stochastically forced by a small multiplicative noise term. We show that spectrally stable travelling wave solutions to the deterministic system retain their orbital stability if the…
In various situations where wave transport is preeminent, like in wireless communication, a strong established transmission is present in a complex scattering environment. We develop a novel approach to describe emerging fluctuations, which…
We study a reaction diffusion system where we consider a non-gaussian process instead of a standard diffusion. If the process increments follow a probability distribution with tails approaching to zero faster than a power law, the usual…
Spontaneous pattern formation in living systems is driven by reaction-diffusion chemistry and active mechanics. The feedback between chemical and mechanical forces is often essential to robust pattern formation, yet it remains poorly…