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In this report, spectroscopy was used to track the energy of different states in a LiHoF4 sample around its critical temperature. The experimental setup consist of a Cooper cavity with the sample, an antenna and a resonator inside. This cavity is attached ...
The thesis is dedicated to the study of two main partial differential equations (PDEs) in fluid dynamics: the Navier-Stokes equations, which describe the motion of incompressible fluids, and the transport equation with divergence-free velocity fields, whic ...
We introduce a classification of the radial spin textures in momentum space that emerge at the high-symmetry points in crystals characterized by nonpolar chiral point groups (D2, D3, D4, D6, T, O). Based on the symmetry constraints imposed by these point g ...
To enforce the conservation of mass principle, a pressure Poisson equation arises in the numerical solution of incompressible fluid flow using the pressure-based segregated algorithms such as projection methods. For unsteady flows, the pressure Poisson equ ...
Cavitating tip-leakage vortices appear in several hydrodynamic flows such as marine propellers or Kaplan turbines. Cavitating computations are a challenging topic since several keys issues are an ongoing work such as the definition of a universal mass sour ...
Given the contact forms f and g, and the 1-form h, we discuss the existence of a vector field u verifying L-u(f)= d(u (right perpendicular) f)+ u (right perpendicular) df = h. This is closely related to the pullback equation, where we seek for a diffeomorp ...
In this thesis, we study two distinct problems.
The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...
The aim of this short note is twofold. First, we give a sketch of the proof of a recent result proved by the authors in the paper [7] concerning existence and uniqueness of renormalized solutions of continuity equations with unbounded damping coefficient. ...
We propose new regularization models to solve inverse problems encountered in biomedical imaging applications. In formulating mathematical schemes, we base our approach on the sparse signal processing principles that have emerged as a central paradigm in t ...
We investigate the question of how plasma currents circulate and close in the scrape-off-layer (SOL) of convection-limited tokamak plasmas. A simplified two-fluid model describes how currents must evacuate charge at the sheaths due to cross-field currents ...
