Related papers: Traveling waves and homogeneous fragmentation
The famous Fisher-KPP reaction diffusion model combines linear diffusion with the typical Fisher-KPP reaction term, and appears in a number of relevant applications. It is remarkable as a mathematical model since, in the case of linear…
In this Letter, we clarify the physical origin of effective transport in periodic and tilted periodic systems. When Brownian dynamics is examined on the scale of a single period, the particle displacement admits a natural separation into a…
In this note, we consider general growth-fragmentation equations from a probabilistic point of view. Using Foster-Lyapunov techniques, we study the recurrence of the associated Markov process depending on the growth and fragmentation rates.…
We describe and analyze the mean transport due to transient progressive waves, including breaking waves. The waves are packets and are generated with a boundary-forced air-water two-phase Navier Stokes solver. The analysis is done in the…
We consider a Fisher-KPP equation with nonlinear selection driven by a Poisson random measure. We prove that the equation admits a unique wave speed $ \mathfrak{s}> 0 $ given by $\frac{\mathfrak{s}^{2}}{2} = \int_{[0, 1]}\frac{ \log{(1 +…
Standard diffusion equation is based on Brownian motion of the dispersing species without considering persistence in the movement of the individuals. This description allows for the instantaneous spreading of the transported species over an…
In this paper we review recent developments in the statistical theory of weakly nonlinear dispersive waves, the subject known as Wave Turbulence (WT). We revise WT theory using a generalisation of the random phase approximation (RPA). This…
A new hidden variable theory is proposed, according to which particles follows definite trajectories, as in Bohmian Mechanics or Nelson's stochastic mechanics; in the new theory, however, the trajectories are classical, i.e. Newtonian. This…
We study the existence, regularity, and symmetry of periodic traveling solutions to a class of Gardner-Ostrovsky type equations, including the classical Gardner-Ostrovsky equation, the (modified) Ostrovsky, and the reduced (modified)…
We examine a general model for the Fisher-KPP (FKPP) equation with nonlocal advection. The main interpretation of this model is as describing a diffusing and logistically growing population that is also influenced by intraspecific…
Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation)…
We develop the idea of non-Markovian CTRW (continuous time random walk) approximation to the evolution of interacting particle systems, which leads to a general class of fractional kinetic measure-valued evolutions with variable order. We…
We investigate the linearized hydrodynamic equations of interacting self-propelled particles in two dimensional space. It is found that the small perturbations of density and polarization fields satisfy the hyperbolic partial differential…
Biological invasion, whereby populations of motile and proliferative individuals lead to moving fronts that invade into vacant regions, are routinely studied using partial differential equation (PDE) models based upon the classical…
We study travelling-wave spatially periodic solutions of a forced Cahn-Hilliard equation. This is a model for phase separation of a binary mixture, subject to external forcing. We look at arbitrary values of the mean mixture concentration,…
Some explicit traveling wave solutions to a Kolmogorov-Petrovskii-Piskunov equation are presented through two ans\"atze. By a Cole-Hopf transformation, this Kolmogorov-Petrovskii-Piskunov equation is also written as a bilinear equation and…
A non-Markovian counting process, the `generalized fractional Poisson process' (GFPP) introduced by Cahoy and Polito in 2013 is analyzed. The GFPP contains two index parameters $0<\beta\leq 1$, $\alpha >0$ and a time scale parameter.…
Continuing our previous study \cite{DJKZ} on the monostable reaction-diffusion-convection equation, we analyze the bistable case under weak regularity assumptions. Our approach applies monostable results on the subintervals where the…
We consider Smoluchowski's coagulation equation with kernels of homogeneity one of the form $K_{\varepsilon }(\xi,\eta) =\big( \xi^{1-\varepsilon }+\eta^{1-\varepsilon }\big)\big ( \xi\eta\big) ^{\frac{\varepsilon }{2}}$. Heuristically, in…
We present several families of nonlinear reaction diffusion equations with variable coefficients including Fisher-KPP and Burgers type equations. Special exact solutions such as traveling wave, rational, triangular wave and N-wave type…