A vector field method on the distorted Fourier side and decay for wave equations with potentials

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Verification of the Fourier-enhanced 3D finite element Poisson solver of the gyrokinetic full-f code PICLS

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We introduce and derive the Fourier -enhanced 3D electrostatic field solver of the gyrokinetic full -f PIC code PICLS. The solver makes use of a Fourier representation in one periodic direction of the domain to make the solving of the system easily paralle ...

Elsevier2024

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Buildings play a pivotal role in the ongoing worldwide energy transition, accounting for 30% of the global energy consumption. With traditional engineering solutions reaching their limits to tackle such large-scale problems, data-driven methods and Machine ...

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A Spectral Ansatz for The Long-Time Homogenization of The Wave Equation

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Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present wor ...

Ecole Polytechnique2024

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

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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 ...

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Electrical and Optical Manifestations of Flat Band Physics in Van der Waals Materials

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Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present wor ...

Ecole Polytechnique2024