相关论文: KPP Pulsating Front Speed-up by Flows
We consider the spreading dynamics of the Fisher-KPP equation in a shifting environment, by analyzing the limit of the rate function of the solutions. For environments with a weak monotone condition, it was demonstrated in a previous paper…
We investigate the sedimentation properties of quasi-neutrally buoyant inertial particles carried by incompressible zero-mean fluid flows. We obtain generic formulae for the terminal velocity in generic space-and-time periodic (or steady)…
We establish in this article spreading properties for the solutions of equations of the type $\partial$ t u -- a(x)$\partial$ xx u -- q(x)$\partial$ x u = f (x, u), where a, q, f are only assumed to be uniformly continuous and bounded in x,…
We consider spatially discrete bistable reaction-diffusion equations that admit wave front solutions. Depending on the parameters involved, such wave fronts appear to be pinned or to glide at a certain speed. We study the transition of…
Numerical solutions for: the integral curves of the velocity field (streamlines), the density contours, and the accretion rate of a steady-state flow of an ideal fluid with p=K n^(gamma) equation of state orbiting in a core-dipole-shell…
Rectification and diffusion of non-interacting self-propelled particles is numerically investigated in a two-dimensional corrugated channel. From numerical simulations, we obtain the average velocity and the effective diffusion coefficient.…
The solution of a boundary--value problem formulated for the Kretschmann configuration shows that the phase speed of a surface--plasmon--polariton (SPP) wave guided by the planar interface of a sufficiently thin metal film and a sculptured…
This paper presents results on the unboundedness and minimal speed of traveling wave solutions for a one-dimensional spatial reaction-diffusion equation with an asymptotically linear reaction term and a saturation parameter. By applying a…
A new diffuse interface model for a two-phase flow of two incompressible fluids with different densities is introduced using methods from rational continuum mechanics. The model fulfills local and global dissipation inequalities and is…
For a freely evolving granular fluid, the buildup of spatial correlations in density and flow field is described using fluctuating hydrodynamics. The theory for incompressible flows is extended to the general, compressible case, including…
Using dynamical density functional theory we calculate the speed of solidification fronts advancing into a quenched two-dimensional model fluid of soft-core particles. We find that solidification fronts can advance via two different…
We investigate the super-linear spreading in a reaction-diffusion model analogous to the Fisher-KPP equation, but in which the population is heterogeneous with respect to the dispersal ability of individuals, and the saturation factor is…
Starting with an integral formulation of mass flow rate through an ensemble of isotherms constituting a statistically planar, turbulent premixed flame, a scaling for the corresponding turbulent flame speed is derived without invoking…
We consider a run an tumble particle with two velocity states $\pm v_0$, in an inhomogeneous force field $f(x)$ in one dimension. We obtain exact formulae for its velocity $V_L$ and diffusion constant $D_L$ for arbitrary periodic $f(x)$ of…
The long-time behavior of a reaction-diffusion front between one static (e.g. porous solid) reactant A and one initially separated diffusing reactant B is analyzed for the mean-field reaction-rate density R(\rho_A,\rho_B) =…
This paper is concerned with the convergence rates of subsonic flows for airfoil problem and infinite long largely-open nozzle problem, which is an improvement of [7,11,15,20]. The maximum principle is applied to estimate the potential…
We consider a system of two reaction-diffusion-advection equations describing the one dimensional directed motion of particles with superimposed diffusion and mutual alignment. For this system we show the existence of traveling wave…
We examine the long-time behavior of solutions (and their derivatives) to the micropolar equations with nonlinear velocity damping. Additionally, we get a speed-up gain of $ t^{1/2} $ for the angular velocity, consistent with established…
We consider mixing by incompressible flows. In 2003, Bressan stated a conjecture concerning a bound on the mixing achieved by the flow in terms of an $L^1$ norm of the velocity field. Existing results in the literature use an $L^p$ norm…
We consider travelling wave solutions of the reaction diffusion equation with quintic nonlinearities $u_t = u_{xx} + \mu u (1 -u ) ( 1 +\alpha u + \beta u^2 +\gamma u^3)$. If the parameters $\alpha , \beta$ and $\gamma$ obey a special…