Related papers: Shaping wave patterns in reaction-diffusion system…
Reaction-diffusion equations are widely used as the governing evolution equations for modeling many physical, chemical, and biological processes. Here we derive reaction-diffusion equations to model transport with reactions on a…
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…
The ultrafast formation of strongly bound excitons in two-dimensional semiconductors provide a rich platform for studying fundamental physics as well as developing novel optoelectronic technologies. While extensive research has explored the…
Reaction-diffusion processes in two-dimensional percolating structures are investigated. Two different problems are addressed: reaction spreading on a percolating cluster and front propagation through a percolating channel. For reaction…
Reaction-diffusion (Turing) systems are fundamental to the formation of spatial patterns in nature and engineering. These systems are governed by a set of non-linear partial differential equations containing parameters that determine the…
In a companion paper, we established nonlinear stability with detailed diffusive rates of decay of spectrally stable periodic traveling-wave solutions of reaction diffusion systems under small perturbations consisting of a nonlocalized…
Reaction-diffusion waves in multiple spatial dimensions advance at a rate that strongly depends on the curvature of the wave fronts. These waves have important applications in many physical, ecological, and biological systems. In this work,…
The paper is devoted to a reaction-diffusion equation with doubly nonlocal nonlinearity arising in various applications in population dynamics. One of the integral terms corresponds to the nonlocal consumption of resources while another one…
We prove existence and uniqueness of travelling waves for a reaction-diffusion system coupling a classical reaction-diffusion equation in a strip with a diffusion equation on a line. To do this we use a continuation method which leads to…
We investigate Turing instability and pattern formation in two-dimensional domains for two reaction-diffusion models, obtained as diffusive limits of kinetic equations for mixtures of monatomic and polyatomic gases. The first model is of…
While controlling particle diffusion in a confined geometry is a popular approach taken by both natural and artificial systems, it has not been widely adopted for controlling light transport in random media, where wave interference effects…
A nonlinear PDE featuring flux limitation effects together with those of the porous media equation (nonlinear Fokker-Planck) is presented in this paper. We analyze the balance of such diverse effects through the study of the existence and…
This paper concerns wave propagation in a class of scalar reaction-diffusion-convection equations with $p$-Laplacian-type diffusion and monostable reaction. We introduce a new concept of a non-smooth traveling wave profile, which allows us…
The propagation of unstable interfaces is at the origin of remarkable patterns that are observed in various areas of science as chemical reactions, phase transitions, growth of bacterial colonies. Since a scalar equation generates usually…
Nonlinear waves are studied in a mixture of liquid and gas bubbles. Influence of viscosity and heat transfer is taken into consideration on propagation of the pressure waves. Nonlinear evolution equations of the second and the third order…
A set of traveling wave solution to convection-reaction-diffusion equation is studied by means of methods of local nonlinear analysis and numerical simulation. It is shown the existence of compactly supported solutions as well as solitary…
Light-matter interactions inside turbid medium can be controlled by tailoring the spatial distribution of energy density throughout the system. Wavefront shaping allows selective coupling of incident light to different transmission…
In this work an activator-depleted reaction-diffusion system is investigated on polar coordinates with the aim of exploring the relationship and the corresponding influence of domain size on the types of possible diffusion-driven…
We calculate the frequency-dispersed nonlinear transmission signal of a phase-shaped visible pulse to fourth order in the field. Two phase profiles, a phase-step and phase-pulse, are considered. Two dimensional signals obtained by varying…
In this article we propose a new design methodology allowing us to control both ampli- tude and phase of electromagnetic waves from a cylindrical incident wave. This results in isotropic materials and does not resort to transformation…