Samuel Punshon-Smith
Tulane University of Louisiana, LA·Mathematics & Statistics·Early-career
Stir cream into coffee and it blends; the same stirring, done slightly differently each time, can blend it faster or slower. Real flows are full of such unpredictable jiggles, from gusts in the atmosphere to eddies in the ocean, and those random pieces strongly shape how quickly a fluid mixes and how far it carries heat, salt or pollutants.
- Fields
Mathematics & Statistics
Physics
- Topics
stochastic partial differential equations
fluid dynamics
advection-diffusion
- Grants
- 1 known grant, through Aug 2030
What they work on
- Develop a microlocal framework, using pseudodifferential operators that track behavior across spatial scales, to analyze how randomly fluctuating velocity fields mix a substance in advection-diffusion and nonlinear fluid PDE models.
- Prove exponential lower bounds on mixing for advection-diffusion equations on compact domains, with quantitative dependence on the diffusivity, the parameter controlling how fast the substance spreads on its own.
- Advance techniques for Lyapunov exponents, which measure how fast nearby states separate, in infinite-dimensional stochastic systems by establishing existence of projective stationary measures and finiteness of the exponents.
- Characterize chaotic and unstable behavior in randomly forced infinite-dimensional fluid systems by combining tools from analysis, probability and dynamical systems.
More about the research
This project builds mathematical tools to say precisely what randomness does to mixing and to the onset of chaotic, turbulent behavior in fluids.
Why it matters
Mixing and transport set how heat, salt and pollutants spread in the ocean and atmosphere, and how chaotic a flow becomes. Rigorous bounds on these processes in randomly forced fluid models give a firmer footing for the approximations used in climate modeling, oceanography and engineering, and clarify when chaos in such systems can be quantified at all.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Adam Kanigowski
University of Maryland, MD·Mathematics & Statistics
Study how chaotic and statistical properties arise and interact in smooth dynamical systems where some, but not all, Lyapunov exponents (rates at which nearby paths spread apart) are zero.
Sandra Cerrai
University of Maryland, MD·Mathematics & Statistics
Prove that the Smoluchowski-Kramers small-mass limit holds for stochastic damped geometric wave equations, starting with one-dimensional stochastic wave maps.
Theodore Drivas
Stony Brook University, NY·Mathematics & Statistics·Early-career
Analyze the long-time behavior of the two-dimensional Euler equations to explain how ideal fluids form lasting, hurricane-like vortices through vortex merging and mixing.
The school
Tulane University of Louisiana: 17 labs on PI Pages, $276M a year on research, 187 research doctorates a year.
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