Publications associées à Champ solénoïdal

Anomalous dissipation and other non-smooth phenomena in fluids

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 ...

EPFL2024

Diversity of radial spin textures in chiral materials

Oleg Yazyev, Daniel Gosalbez Martinez, Alberto Crepaldi

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 ...

Amer Physical Soc2023

A Fast Hybrid Pressure-Correction Algorithm for Simulating Incompressible Flows by Projection Methods

Jiannong Fang

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 ...

2023

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

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- ...

EPFL2018

Some Remarks on the Lie Derivative and the Pullback Equation for Contact Forms

Bernard Dacorogna, Olivier Kneuss

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 ...

Walter De Gruyter Gmbh2017

Scrape-off-layer current loops and floating potential in limited tokamak plasmas

Paolo Ricci, Joaquim Loizu Cisquella, Paola Paruta, Federico David Halpern

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 ...

Cambridge University Press2017

Sparsity-Based Data Reconstruction Models for Biomedical Imaging

Emrah Bostan

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 ...

EPFL2016

Divergence-Free Wavelet Frames

Michaël Unser, Emrah Bostan, John Paul Ward

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

IEEE Institute of Electrical and Electronics Engineers2015

Electrical Neuroimaging with Irrotational Sources

This paper discusses theoretical aspects of the modeling of the sources of the EEG (i.e., the bioelectromagnetic inverse problem or source localization problem). Using theHelmholtz decomposition (HD) of the current density vector (CDV) of the primary curre ...

Hindawi Publishing Corporation2015

Variational Decomposition of Vector Fields in the Presence of Noise

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

We present a variational framework, and an algorithm based on the alternating method of multipliers (ADMM), for the problem of decomposing a vector field into its curl- and divergence-free components (Helmholtz decomposition) in the presence of noise. We p ...

IEEE2013