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

Self-Similar Vector Fields

Pouya Dehghani Tafti

We propose statistically self-similar and rotation-invariant models for vector fields, study some of the more significant properties of these models, and suggest algorithms and methods for reconstructing vector fields from numerical observations, using the ...

EPFL2011

Singular Reduction Of Dirac Structures

Tudor Ratiu, Madeleine Jotz

The regular reduction of a Dirac manifold acted upon freely and properly by a Lie group is generalized to a nonfree action. For this, several facts about G-invariant vector fields and one-forms are shown. ...

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

Fractal Modelling And Analysis Of Flow-Field Images

Michaël Unser, Ricard Delgado Gonzalo, Pouya Dehghani Tafti

We introduce stochastic models for flow fields with parameters that dictate the scale-dependent (self-similar) character of the field and control the balance between its rotational vs compressive behaviour. The development of our models is motivated by the ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

On A Class Of Mean Field Solutions Of The Monge Problem For Perfect And Self-Interacting Systems

Philippe Choquard

The Monge problem (Monge 1781; Taton 1951), as reformulated by Kantorovich (2006a, 2006b) is that of the transportation at a minimum "cost" of a given mass distribution from an initial to a final position during a given time interval. It is an optimal tran ...

2010

Fractional Brownian Models For Vector Field Data

Michaël Unser, Pouya Dehghani Tafti

In this note we introduce a vector generalization of fractional Brownian motion. Our definition takes into account directional properties of vector fields-such as divergence, rotational behaviour, and interactions with coordinate transformations-that have ...

Ieee Service Center, 445 Hoes Lane, Po Box 1331, Piscataway, Nj 08855-1331 Usa2010

Constraints from F and D supersymmetry breaking in general supergravity theories

Claudio Scrucca

We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit vacua with spontaneously broken supersymmetry and realistic cosmological constant. We find that the existence of such viable vacua implies som ...

2008

Metastable supergravity vacua with F and D supersymmetry breaking

Claudio Scrucca

We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit viable metastable vacua with spontaneously broken supersymmetry and realistic cosmological constant. To do so, we impose that on the vacuum th ...

Springer Nature2007

Optimal control of geodesics in Riemannian manifolds

Roland Rozsnyo

The aim of this dissertation is to solve numerically the following problem, denoted by P : given a Riemannian manifold and two points a and b belonging to that manifold, find a tangent vector T at a, such that expa(T) = b, assuming that T exists. This prob ...

EPFL2007

Quotient Submanifolds for Static Feedback Linearization

Philippe Müllhaupt

A procedure for finding locally the linearizing output of a single input nonlinear affine system is proposed. It relies on successive integrations of one-dimensional distributions and projections along these submanifolds. The algorithm proceeds recursively ...

2006