Event info

Date: Thursday, 19 March 2026

Zoom: Online via Zoom

Speaker: Dr Olga Aryasova (Friedrich Schiller University, Jena, Germany)

Title: The hard membrane process and transport barriers of turbulent flows

Abstract: In confined fusion plasma devices such as tokamaks, turbulence is always present to some degree, and it has the undesirable effect of dispersing heat and particles from the central very hot and dense region to the boundary, and then to the surrounding areas and walls. Sometimes barriers arise in intermediate regions that reduce this dispersion. These barriers, also called zonal flows, are thin layers of plasma in which the fluid velocity is not turbulent, as it is elsewhere, but rather ordered, roughly laminar, and directed perpendicularly to the direction of dispersion.

There is still active research aimed at understanding how these barriers arise, whether they can be triggered, how they evolve, and what their precise links are with other plasma dynamical features and parameters. Our aim here is to rigorously define a mathematical model of a sharp heat-diffusion barrier. In a scaling limit of the turbulence model with separation of scales, we obtain a heat equation with a space-dependent diffusion coefficient that diffuses poorly near the barrier. We then investigate the scaling limit in which the diffused barrier converges to a sharp separating surface, and describe the limit by means of the stochastic process known as Brownian motion with a hard membrane.

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This seminar series is a valuable opportunity for graduate students to get acquainted with the work of more experienced researchers in various mathematical fields. Undergraduate students are also welcome to join, as the talks are intended for non-experts, too. Regardless of your area of research, you can attend the seminar to expand your knowledge and get in touch with the latest developments in mathematics for industry.
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