1 citations · 4 across the 10 of their papers we have counts for
10 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…
Existence of stationary measures for partially damped SDEs with generic, Euler-type nonlinearities
Jacob Bedrossian, Alex Blumenthal, Keagan Callis +1
We study nonlinear energy transfer and the existence of stationary measures in a class of degenerately forced SDEs on with a quadratic, conservative nonlinearity $B(x…
Norm Growth, Non-uniqueness, and Anomalous Dissipation in Passive Scalars
Tarek M. Elgindi, Kyle Liss
We construct a divergence-free velocity field satisfying such th…
Optimal enhanced dissipation and mixing for a time-periodic, Lipschitz velocity field on
Tarek M. Elgindi, Kyle Liss, Jonathan C. Mattingly
We consider the advection-diffusion equation on with a Lipschitz and time-periodic velocity field that alternates between two piecewise linear shear flows. We prove…
Stationary measures for stochastic differential equations with degenerate damping
Jacob Bedrossian, Kyle Liss
A variety of physical phenomena involve the nonlinear transfer of energy from weakly damped modes subjected to external forcing to other modes which are more heavily damped. In thi…
Quantitative spectral gaps and uniform lower bounds in the small noise limit for Markov semigroups generated by hypoelliptic stochastic differential equations
Jacob Bedrossian, Kyle Liss
We study the convergence rate to equilibrium for a family of Markov semigroups generated by a class of hypoelliptic stochastic differential equations o…
On the Sobolev stability threshold of 3D Couette flow in a homogeneous magnetic field
Kyle Liss
We study the stability of the Couette flow in the 3D incompressible magnetohydrodynamic (MHD) equations for a conducting fluid on $\mathbb{T} \times \mathbb{R} \times \…