Publications associées à Lie bracket of vector fields

Probabilistic and Deterministic Wellposedness for Low Regularity Dispersive Equations

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 ...

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

Coarse graining and large-N behavior of the d-dimensional N-clock model

Matthias Ruf, Matthias Benjamin Ruf

We study the asymptotic behavior of the N-clock model, a nearest neighbors ferromagnetic spin model on the d-dimensional cubic epsilon-lattice in which the spin field is constrained to take values in a discretization S-N of the unit circle S-1 consisting o ...

2021

Bi-Jacobi Fields And Riemannian Cubics For Left-Invariant SO(3)

Tudor Ratiu

Bi-Jacobi fields are generalized Jacobi fields, and are used to efficiently compute approximations to Riemannian cubic splines in a Riemannian manifold M. Calculating bi-Jacobi fields is straightforward when M is a symmetric space such as bi-invariant SO(3 ...

Int Press Boston, Inc2016

Large Eddy Simulation of the Rotating Stall in a Pump-Turbine Operated in Pumping Mode at a Part-Load Condition

François Avellan, Olivier Pacot, Chisachi Kato

The investigation of the rotating stall phenomenon appearing in the HYDRODYNA pump-turbine reduced scale model is carried out by performing a large-scale large eddy simulation (LES) computation using a mesh featuring approximately 85 x 10(6) elements. The ...

American Society of Mechanical Engineers2016

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

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

Geodesic distance for right invariant Sobolev metrics of fractional order on the diffeomorphism group. II

Martins Bruveris, Martin Bauer

The geodesic distance vanishes on the group of compactly supported diffeomorphisms of a Riemannian manifold of bounded geometry, for the right invariant weak Riemannian metric which is induced by the Sobolev metric of order on the Lie algebra of vector fie ...

Springer Verlag2013

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