Share This Author
Transport equations for elastic and other waves in random media
Quenching of flames by fluid advection
We consider a simple scalar reaction‐advection‐diffusion equation with ignition‐type nonlinearity and discuss the following question: What kinds of velocity profiles are capable of quenching any…
Bulk Burning Rate in¶Passive–Reactive Diffusion
AbstractWe consider a passive scalar that is advected by a prescribed mean zero divergence-free velocity field, diffuses, and reacts according to a KPP-type nonlinear reaction. We introduce a…
SELF-AVERAGING IN TIME REVERSAL FOR THE PARABOLIC WAVE EQUATION
We analyze the self-averaging properties of time-reversed solutions of the paraxial wave equation with random coefficients, which we take to be Markovian in the direction of propagation. This allows…
Transport theory for acoustic waves with reflection and transmission at interfaces
Enhancement of the traveling front speeds in reaction-diffusion equations with advection
Statistical Stability in Time Reversal
The refocusing resolution in a high frequency remote-sensing regime is analyzed and it is shown that, because of multiple scattering in an inhomogeneous or random medium, it can improve beyond the diffraction limit.
Diffusion Approximation of Radiative Transfer Problems with Interfaces
Using interface layer analysis, it is proved that the transport solution can be approximated by a diffusion term plus an interface layer which decays exponentially fast.
Wave-like Solutions for Nonlocal Reaction-diffusion Equations: a Toy Model
Traveling waves for the nonlocal Fisher Equation can exhibit much more complex behaviours than for the usual Fisher equation. A striking numerical observation is that a traveling wave with minimal…