We prove existence, uniqueness, and stability of transition fronts (generalized traveling waves) for reaction-diffusion equations in cylindrical domains with general inhomogeneous ignition reactions. We also show uniform convergence of solutions with exponentially decaying initial data to time translates of the front. In the case of stationary ergodic reactions the fronts are proved to propagat...

The time-variable coastal upwelling during CODE 2 is simulated using a mixing-advection coupled model. The agreement between model results and observations is generally good. During periods of strong equatorward wind stress, shelf water is cold and weakly stratified, and a front moves offshore; during periods of wind relaxation, surface temperature rises markedly, but the subsurface front usual...

Advection is critical for efficient mass transport. For instance, bare diffusion cannot explain the spatial and temporal scales of some of the cellular processes. The regulation of intracellular functions is strongly influenced by the transport of mass at low Reynolds numbers where viscous drag dominates inertia. Mimicking the efficacy and specificity of the cellular machinery has been a long t...

The conventional thermal instability criterion can not be applied to the advectiondominated accretion disks around black holes where the radiative cooling is insufficient to balance the viscous heating. The surface density change associated with the temperature perturbations, which was usually neglected in deriving the conventional criterion, was recently shown to be much significant in the adv...

We consider the influence of a shifting environment and an advection on the spreading of an invasive species through a model given by the diffusive logistic equation with a free boundary. When the environment is shifting and without advection (β = 0), Du, Wei and Zhou in [16] showed that the species always dies out when the shifting speed c∗ ≥ C, and the long-time behavior of the species is det...

We present a comprehensive analysis of salt transport and overlimiting currents in a microchannel during concentration polarization. We have carried out full numerical simulations of the coupled Poisson-Nernst-Planck-Stokes problem governing the transport and rationalized the behavior of the system. A remarkable outcome of the investigations is the discovery of strong couplings between bulk adv...

A partitioned implicit-explicit orthogonal Runge-Kutta method (PIROCK) is proposed for the time integration of diffusion-advection-reaction problems with possibly severely stiff reaction terms and stiff stochastic terms. The diffusion terms are solved by the explicit second order orthogonal Chebyshev method (ROCK2), while the stiff reaction terms (solved implicitly) and the advection and noise ...

Limiting profiles of solutions to a 2×2 Lotka–Volterra competition-diffusion-advection system, when the strength of the advection tends to infinity, are determined. The two species, competing in a heterogeneous environment, are identical except for their dispersal strategies: one is just a random diffusion, while the other is “smarter”—a combination of random diffusion and a directed movement u...

We propose a new, black-box online stabilization strategy for reduced basis (RB) approximations of parameter-dependent advection-diffusion problems in the advection-dominated case. Our goal is to stabilize the RB problem irrespectively of the stabilization (if any) operated on the high-fidelity (e.g. finite element) approximation, provided a set of stable RB functions have been computed. Inspir...

Methodologies to improve disdrometer processing, loosely based on mathematical techniques common to the field of particle flow and fluid mechanics, are examined and tested. The inclusion of advection and vertical wind field estimates appears to produce significantly improved results in a Lagrangian hydrometeor trajectory model, in spite of very strict assumptions of noninteracting hydrometeors,...