SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 46: Poster: Machine Learning and Data Analytics

DY 46.9: Poster

Donnerstag, 30. März 2023, 13:00–16:00, P1

Extreme Fluctuations of the Stochastic Nonlinear Schrödinger Equation via Large Deviation Theory — •Sumeja Bureković¹, Tobias Schäfer², and Rainer Grauer¹ — ¹Institute for Theoretical Physics I, Ruhr-University Bochum, Germany — ²Department of Mathematics, College of Staten Island, Staten Island, United States of America

Recently, the focusing nonlinear Schrödinger equation with additive noise has been proposed as a model for finite-time singularity mediated turbulence [1]. Among other findings, the authors of [1] show through direct numerical simulations that the statistics of quantities such as the energy dissipation rate and structure functions are intermittent. Here, in order to explain these observations and to quantify the effect of extreme fluctuations on the turbulence statistics, we employ methods from large deviation theory or instanton calculus [2]. In the first step, the probability density function or expectation for the quantities of interest is approximated by the Freidlin-Wentzell action of the large deviation minimizer or instanton. Additionally, our aim is to improve this approximation by taking into account Gaussian fluctuations around the instanton, harnessing the techniques of [3].

[1] Josserand, C., Pomeau, Y., & Rica, S. (2020). Phys. Rev. Fluid, 5(5), 054607. [2] Grafke, T., Grauer, R., & Schäfer, T. (2015). J. Phys. A Math. Theor., 48(33), 333001. [3] Schorlepp, T., Grafke, T., & Grauer, R. (2021). J. Phys. A Math. Theor., 54(23), 235003.