Publications related to Helmholtz decomposition

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

ALMOST EVERYWHERE NONUNIQUENESS OF INTEGRAL CURVES FOR DIVERGENCE-FREE SOBOLEV VECTOR FIELDS

Massimo Sorella

We construct divergence-free Sobolev vector fields in C([0,1];W-1,W-r(T-d;Rd)) with r < d and d\geq 2 which simultaneously admit any finite number of distinct positive solutions to the continuity equation. These vector fields are then shown to have at leas ...

Siam Publications2023

On the commutativity of flows of rough vector fields

Maria Colombo, Riccardo Tione

In the class of Sobolev vector fields in R-n of bounded divergence, for which the theory of DiPerna and Lions provides a well defined notion of flow, we characterize the vector fields whose flow commutes in terms of the Lie bracket and of a regularity cond ...

ELSEVIER2022

Homogenization of Multiscale Eddy Current Problem by Localized Orthogonal Decomposition Method

Xiaotao Ren

A homogenization approach for the solution of multiscale eddy current problem is proposed. The method is based on the subspace decomposition and it involves a coarse space and a nested fine space. The homogenized problem is posed in the coarse space with t ...

Institute of Electrical and Electronics Engineers2019

Helical equilibrium magnetohydrodynamic flow effects on the stability properties of low-n ideal external-infernal modes in weak shear tokamak configurations

Wilfred Anthony Cooper, Jonathan Graves, Patrycja Nowak-Sliwinska, Daniele Brunetti, Alberto Mariani

The impact of equilibrium helical flows on the stability properties of low shear tokamak plasmas is assessed. The corrections due to such helical flow to the equilibrium profiles (mass density, pressure, Shafranov shift, magnetic fluxes) are computed by mi ...

IOP PUBLISHING LTD2019

LTCC magnetic sensors at EPFL and TCV: Lessons learnt for ITER

Duccio Testa, Xavier Llobet, Pierre Lavanchy, Matthieu Toussaint, Ugo Siravo, Frédéric Dolizy, Jonathan Bryan Lister, Thomas Maeder, Steve Couturier, Philippe Marmillod, Severino Antonioni, Caroline Jacq, Christian Moura, Blaise Marlétaz, Aylwin Iantchenko, Lorenzo Stipani, Adrien Aymeric Thibault Corne, Matthias Garcin

Innovative 3D high-frequency magnetic sensors have been designed and manufactured in-house for installation on the Tokamak a Configuration Variable (TCV), and are currently routinely operational. These sensors combine the Low Temperature Co-fired Ceramic ( ...

2019

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

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associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

Limiting absorption principle and well-posedness for the Helmholtz equation with sign changing coefficients

Hoài-Minh Nguyên

In this paper, we investigate the limiting absorption principle associated to and the well-posedness of the Helmholtz equations with sign changing coefficients which are used to model negative index materials. Using the reflecting technique introduced in [ ...

Elsevier2016

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

Approximate Sparsity Pattern Recovery: Information-Theoretic Lower Bounds

Michael Christoph Gastpar

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear mea- surements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown that if the m ...

Institute of Electrical and Electronics Engineers2013

A Dual Algorithm for $ L _{ 1 } $ -Regularized Reconstruction of Vector Fields

Michaël Unser, Emrah Bostan, Pouya Dehghani Tafti

Recent advances in vector-field imaging have brought to the forefront the need for efficient denoising and reconstruction algorithms that take the physical properties of vector fields into account and can be applied to large volumes of data. With these req ...

IEEE2012

The Sampling Rate-Distortion Tradeoff for Sparsity Pattern Recovery in Compressed Sensing

Michael Christoph Gastpar

Recovery of the sparsity pattern (or support) of an unknown sparse vector from a limited number of noisy linear measurements is an important problem in compressed sensing. In the high-dimensional setting, it is known that recovery with a vanishing fraction ...

Institute of Electrical and Electronics Engineers2012

Continuous interpolation between the fully frustrated Ising and quantum dimer models

We propose a quantum model interpolating between the fully frustrated spin-1/2 Ising model in a transverse field and a dimer model. This model contains a resonating-valence-bond phase, including a line with an exactly solvable ground state of Rokhsar-Kivel ...

2011

On Regularized Reconstruction of Vector Fields

Michaël Unser, Pouya Dehghani Tafti

In this paper, we give a general characterization of regularization functionals for vector field reconstruction, based on the requirement that the said functionals satisfy certain geometric invariance properties with respect to transformations of the coord ...

IEEE2011

Investigation on the Three-Dimensional Flow Mechanisms in Annular Axial Compressor Cascades for Aero Engines with Flow Control by Aspiration on the Hub and on the Blades

Elia Colombo

The axial compressor is an essential component of aero-engines and gas turbines. This work investigates how flow control by aspiration applied to the hub and to the blades of axial compressor wheels can improve the static pressure rise by preventing detrim ...

EPFL2011

Fractional Brownian Vector Fields

Michaël Unser, Pouya Dehghani Tafti

This work puts forward an extended definition of vector fractional Brownian motion (fBm) using a distribution theoretic formulation in the spirit of Gel′fand and Vilenkin's stochastic analysis. We introduce random vector fields that share the statistical i ...

SIAM2010

Experimental Evidence of Momentum Transport Induced by an Up-Down Asymmetric Magnetic Equilibrium in Toroidal Plasmas

Olivier Sauter, Basil Duval, Alexander Karpushov, Yann Camenen, Alessandro Bortolon, Lucia Isabel Federspiel, Francesco Piras

The first experimental evidence of parallel momentum transport generated by the up-down asymmetry of a toroidal plasma is reported. The experiments, conducted in the Tokamak a` Configuration Variable, were motivated by the recent theoretical discovery of i ...

2010

Some linear and nonlinear problems involving differential forms

Saugata Bandyopadhyay

In this thesis, we study some linear and nonlinear problems involving differential forms. We begin by studying the problem of pullbacks which asks the following question: for two given differential forms, if one is the pullback of the other via a diffeomor ...

EPFL2007