4 papers
Uniform-in-diffusivity mixing by shear flows: stochastic and dynamical perspectives
Kyle L. Liss, Kunhui Luan
We study passive scalar mixing by parallel shear flows in the presence of weak molecular diffusion. We recover the sharp uniform-in-diffusivity mixing rate for shear flows with fin…
The Batchelor spectrum for a deterministically driven passive scalar
Kyle L. Liss, Jonathan C. Mattingly
We study the long-time behavior of a passive scalar transported by an incompressible flow in the presence of smooth, deterministic forcing. For a specific spatially Lipschitz and t…
Quantitative positivity of transition densities for random perturbations of Hamiltonian systems
Shimaa Elesaely, David P. Herzog, Kyle L. Liss
We study a class of diffusion processes arising from random perturbations of conservative Hamiltonian systems. Under a set of abstract hypotheses -- including basic structural assu…
A pathwise approach to the enhanced dissipation of passive scalars advected by shear flows
Victor Gardner, Kyle L. Liss, Jonathan C. Mattingly
We develop a framework for studying the enhanced dissipation of passive scalars advected by shear flows based on analyzing the particle trajectories of the stochastic differential…