Related papers: Coherent Structures in Flame Fronts
We propose a novel method for establishing the convergence rates of solutions to reaction-diffusion equations to traveling waves. The analysis is based on the study of the traveling wave shape defect function introduced in [2]. It turns out…
The contact process is a stochastic process which exhibits a continuous, absorbing-state phase transition in the Directed Percolation (DP) universality class. In this work, we consider a contact process with a bias in conjunction with an…
We study an integro-differential equation that describes the slow erosion of granular flow. The equation is a first order non-linear conservation law where the flux function includes an integral term. We show that there exist unique…
In this study, we investigate the dynamics of moving fronts in three-dimensional spaces, which form as a result of in-situ combustion during oil production. This phenomenon is also observed in other contexts, such as various autowave models…
A new premixed turbulent combustion model is proposed. It is based on one-dimensional (1D) filtering of density times progress variable and of the reaction source term of laminar premixed flame profiles using a filter kernel which reflects…
We briefly report on a recent proposal (Fiore in J Phys A Math Theor 51:085203, 2018) for simplifying the equations of motion of charged particles in an electromagnetic (EM) field $F^{\mu\nu}$ that is the sum of a plane travelling wave…
In combustion theory, flames are usually described in terms of the dynamics of iso-surfaces of a specific scalar. The flame displacement speed is then introduced as a local variable quantifying the progression of these iso-surfaces relative…
We formulate a kinetic theory of quantum information scrambling in the context of a paradigmatic model of interacting electrons in the vicinity of a superconducting phase transition. We carefully derive a set of coupled partial differential…
A modification of the parabolic Allen-Cahn equation, determined by the substitution of Fick's diffusion law with a relaxation relation of Cattaneo-Maxwell type, is considered. The analysis concentrates on traveling fronts connecting the two…
We describe various types of traveling fronts of bistable reaction-diffusion cellular automata. These dynamical systems with discrete time, space, and state spaces can be seen as fully discrete versions of widely studied bistable…
We investigate traveling wave solutions for a nonlinear system of two coupled reaction-diffusion equations characterized by double degenerate diffusivity: \[n_t= -f(n,b), \quad b_t=[g(n)h(b)b_x]_x+f(n,b).\] These systems mainly appear in…
Generally, the normal displacement-based formation control has a sensing mode that requires the agent not only to have certain knowledge of its direction, but also to gather its local information characterized by nonnegative coupling…
Using the method of sub-super-solution, we construct a solution of $(-\Delta)^su-cu_z-f(u)=0$ on $\R^3$ of pyramidal shape. Here $(-\Delta)^s$ is the fractional Laplacian of sub-critical order $1/2<s<1$ and $f$ is a bistable nonlinearity.…
We investigate a coordinate-free model of flame fronts introduced by Frankel and Sivashinsky; this model has a parameter $\alpha$ which relates to how unstable the front might be. We first prove short-time well-posedness of the…
The spatial and temporal persistence, or first-return distributions are measured for slow combustion fronts in paper. The stationary temporal and (perhaps less convincingly) spatial persistence exponents agree with the predictions based on…
The profile of a nonlinear stationary thermomagnetic wave in the resistive state of superconductors is studied at different transport currents. It is proved that the thermomagnetic wave has an oscillating profile at relatively high values…
We study the equation $u_t +uu_x +u-K*u=0$ in the case of an arbitrary $K \geq 0$, which is a generalization of a model for radiating gas, in which $K(y)={1/2}e^{-|y|}$. Using a monotone iteration scheme argument we establish the existence…
We analyse a novel mathematical model of malignant invasion which takes the form of a two-phase moving boundary problem describing the invasion of a population of malignant cells into a population of background tissue, such as skin. Cells…
The known exact solutions of Einstein's vacuum field equations modeling the gravitational fields of pure gravitational radiation involve wave fronts which are either planar or roughly spherical. We describe a scheme designed to check…
Previous numerical investigations of the stability and bifurcation properties of different nonlinear combination structures of spiral vortices in a counterrotating Taylor-Couette system that were done for fixed axial wavelengths are…