Related papers: Quantitative steepness, semi-FKPP reactions, and p…
We study the propagation of pulled fronts in the $A <-> \leftrightarrow A+A$ microscopic reaction-diffusion process using Monte Carlo (MC) simulations. In the mean field approximation the process is described by the deterministic…
Reaction-diffusion equations (RDEs) model the spatiotemporal evolution of a density field $u(\vec{x},t)$ according to diffusion and net local changes. Usually, the diffusivity is positive for all values of $u,$ which causes the density to…
We consider a class of Fokker--Planck equations with linear diffusion and superlinear drift enjoying a formal Wasserstein-like gradient flow structure with convex mobility function. In the drift-dominant regime, the equations have a finite…
Results of the idealized mode-coupling theory for the structural relaxation in suspensions of hard-sphere colloidal particles are presented and discussed with regard to recent light scattering experiments. The structural relaxation becomes…
Alternative approach for description of the non-equilibrium phenomena arising in solids at a severe external loading is analyzed. The approach is based on the new form of kinetic equations in terms of the internal and modified free energy.…
The probability density functions measured by Lewis and Swinney for turbulent Couette-Taylor flow, observed by Bodenschatz and co-workers in the Lagrangian measurement of particle accelerations and those obtained in the DNS by Gotoh et al.…
In this paper, a multi-dimensional fractional wave equation that describes propagation of the damped waves is introduced and analyzed. In contrast to the fractional diffusion-wave equation, the fractional wave equation contains fractional…
We consider a run-and-tumble particle (RTP) with stochastic resetting confined to the half line $[0,\infty)$ with a sticky boundary at $x=0$. In the bulk the RTP tumbles at a constant rate $\alpha>0$ between velocity states $\pm v$ with…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
The quantum wave-function of a massive particle with small initial uncertainties (consistent with the uncertainty relation) is believed to spread very slowly, so that the dynamics is deterministic. This assumes that the classical motions…
We report an experimental investigation of the statistical time dynamic of spatial Fourier modes in a fully developped turbulent jet flow. Measurements rely on an original acoustic scattering technique, allowing the direct and continuous…
We use a Fundamental-Measure density functional for hard board-like polydisperse particles, in the restricted-orientation approximation, to explain the phase behaviour of platelet colloidal suspensions studied in recent experiments. In…
The linear instability of Faraday waves in Hele-Shaw cells is investigated with consideration of the viscosity of fluids after gap-averaging the governing equations due to the damping from two lateral walls and the dynamic behavior of…
We classify the finite time blow-up profiles for the following reaction-diffusion equation with unbounded weight: $$ \partial_tu=\Delta u^m+|x|^{\sigma}u^p, $$ posed in any space dimension $x\in\mathbf{R}^N$, $t\geq0$ and with exponents…
We numerically examine the driven transport of an overdamped self-propelled particle through a two-dimensional array of circular obstacles. A detailed analysis of transport quantifiers (mobility and diffusivity) has been performed for two…
We consider a thin droplet that spreads over a flat, horizontal and chemically heterogeneous surface. The droplet is subjected to changes in its volume though a prescribed, arbitrary spatiotemporal function, which varies slowly and vanishes…
We present a perturbation theory by extending a prescription due to Feynman for computing the probability density function for the random flight motion. The method can be applied to a wide variety of otherwise difficult circumstances. The…
We introduce a novel numerical method for direct simulation of front propagation in the Fisher-KPP equation with a time-dependent parameter on an infinite domain. The method computes a time-dependent boundary condition that accurately…
We consider an extended Korteweg-de Vries (eKdV) equation, the usual Korteweg-de Vries equation with inclusion of an additional cubic nonlinearity. We investigate the statistical behaviour of flat-top solitary waves described by an eKdV…
We establish nonlinear stability of fronts that describe the creation of a periodic pattern through the invasion of an unstable state. Our results concern pushed fronts, that is, fronts whose propagation is driven by a localized mode at the…