Weakly nonlinear evolution of stochastically driven non-normal systems
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We prove a sharp quantitative version of the Faber–Krahn inequality for the short-time Fourier transform (STFT). To do so, we consider a deficit which measures by how much the STFT of a function fails to be optimally concentrated on an arbitrary set of pos ...
Predicting the evolution of systems with spatio-temporal dynamics in response to external stimuli is essential for scientific progress. Traditional equations-based approaches leverage first principles through the numerical approximation of differential equ ...
In this thesis we will present two results on global existence for nonlinear dispersive equations with data at or below the scaling regularity. In chapter 1 we take a probabilistic perspective to study the energy-critical nonlinear Schrödinger equation in ...
A novel approach for linear parameter-varying (LPV) controller synthesis for adaptive rejection of time-varying sinusoidal disturbances is proposed. Only the frequency response data of a linear time-invariant (LTI) multiple-input multiple-output (MIMO) sys ...
We consider on the torus the scaling limit of stochastic 2D (inviscid) fluid dynamics equations with transport noise to deterministic viscous equations. Quantitative estimates on the convergence rates are provided by combining analytic and probabilistic ar ...
We propose a novel approach to evaluating the ionic Seebeck coefficient in electrolytes from relatively short equilibrium molecular dynamics simulations, based on the Green-Kubo theory of linear response and Bayesian regression analysis. By exploiting the ...
Situational awareness strategies are essential for the reliable and secure operation of the electric power grid which represents critical infrastructure in modern society. With the rise of converter-interfaced renewable generation and the consequent shift ...
Plasma turbulence plays a fundamental role in determining the performances of magnetic confinement fusion devices, such as tokamaks. Advances in computer science, combined with the development of efficient physical models, have significantly improved our u ...
Simulations of plasma turbulence in a linear plasma device configuration are presented. These simulations are based on a simplified version of the gyrokinetic (GK) model proposed by Frei et al. [J. Plasma Phys. 86, 905860205 (2020)], where the full-F distr ...
We study the problem of learning unknown parameters in stochastic interacting particle systems with polynomial drift, interaction, and diffusion functions from the path of one single particle in the system. Our estimator is obtained by solving a linear sys ...