5 papers
Residual Diffusivity for Expanding Bernoulli Maps
William Cooperman, Gautam Iyer, James Nolen
Consider a discrete time Markov process on that makes a deterministic jump based on its current location, and then takes a small Gaussian step of variance $ε^…
Unique continuation on planar graphs
Ahmed Bou-Rabee, William Cooperman, Shirshendu Ganguly
We show that a discrete harmonic function which is bounded on a large portion of a periodic planar graph is constant. A key ingredient is a new unique continuation result for the w…
Exponentially mixing flows with slow enhanced dissipation
William Cooperman, Gautam Iyer, Keefer Rowan +1
Consider a passive scalar which is advected by an incompressible flow and has small molecular diffusivity . Previous results show that if is exponentially mixing and $C…
Fourier mass lower bounds for Batchelor-regime passive scalars
William Cooperman, Keefer Rowan
Batchelor predicted that a passive scalar with diffusivity , advected by a smooth fluid velocity, should typically have Fourier mass distributed as $|\hat Ï^ν|^2(k) \…
A Harris theorem for enhanced dissipation, and an example of Pierrehumbert
William Cooperman, Gautam Iyer, Seungjae Son
In many situations, the combined effect of advection and diffusion greatly increases the rate of convergence to equilibrium -- a phenomenon known as enhanced dissipation. Here we s…