7 citations · 7 across the 12 of their papers we have counts for
13 papers
Sparse power spectrum for passive scalars under Pierrehumbert flow
Alex Blumenthal, William Cooperman
We study the long-time Fourier distribution of driven passive scalars transported by an incompressible alternating shear flow (the Pierrehumbert flow) subjected to IID random phase…
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^…
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 …
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 ψ^ν|^2(k) \appro…
Exponential scalar mixing for the 2D Navier-Stokes equations with degenerate stochastic forcing
William Cooperman, Keefer Rowan
We show exponential mixing of passive scalars advected by a solution to the stochastic Navier-Stokes equations with finitely many (e.g. four) forced modes satisfying a hypoelliptic…
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…
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…
Rigidity of harmonic functions on the supercritical percolation cluster
Ahmed Bou-Rabee, William Cooperman, Paul Dario
We use ideas from quantitative homogenization to show that nonconstant harmonic functions on the percolation cluster cannot satisfy certain structural constraints, for example, a L…
Slow periodic homogenization for Hamilton-Jacobi equations
William Cooperman
Capuzzo-Dolcetta and Ishii proved that the rate of periodic homogenization for coercive Hamilton-Jacobi equations is . We complement this result by constructi…
Exponential mixing by shear flows
William Cooperman
We prove a version of Bressan's mixing conjecture where the advecting field is constrained to be a shear at each time. Also, inspired by recent work of Blumenthal, Coti Zelati and…
On the random G equation with nonzero divergence
William Cooperman
We prove a quantitative rate of homogenization for the G equation in a random setting with finite range of dependence and nonzero divergence, with explicit dependence of the consta…
Quantitative stochastic homogenization of the G equation
William Cooperman
We prove a quantitative rate of homogenization for the G equation in a random environment with finite range of dependence. Using ideas from percolation theory, the proof bootstraps…
A near-optimal rate of periodic homogenization for convex Hamilton-Jacobi equations
William Cooperman
We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control the…