Publications associées à A stability theory beyond the co-rotational setting for critical wave maps blow up

Wave-momentum shaping for moving objects in heterogeneous and dynamic media

Romain Christophe Rémy Fleury, Bakhtiyar Orazbayev, Matthieu Francis Malléjac, Stefan Rotter

Light and sound waves can move objects through the transfer of linear or angular momentum, which has led to the development of optical and acoustic tweezers, with applications ranging from biomedical engineering to quantum optics. Although impressive manip ...

2024

Design of a Flexure-Based Flywheel for the Storage of Angular Momentum and Kinetic Energy

Simon Nessim Henein, Florent Cosandier, Hubert Pierre-Marie Benoît Schneegans, Patrick Robert Flückiger

The flywheel is a widespread mechanical component used for the storage of kinetic energy and angular momentum. It typically consists of cylindrical inertia rotating about its axis on rolling bearings, which involves undesired friction, lubrication, and wea ...

2024

Experimental observation of topological transition in linear and nonlinear parametric oscillators

Romain Christophe Rémy Fleury, Benjamin Apffel

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is perturbed by a continuo ...

2024

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

This paper deals with the initial value problem for a semilinear wave equation on a bounded domain and solutions are required to vanish on the boundary of this domain. The essential feature of the situation considered here is that the ellipticity of the sp ...

2024

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Carl Johan Peter Johansson

. We study very weak solutions to scalar Euler-Lagrange equations associated with quadratic convex functionals. We investigate whether W1,1 solutions are necessarily W 1,2 Nash and Schauder applicable. We answer this question positively for a suitable clas ...

Amer Mathematical Soc2024

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Nicolas Henri Bernard Flammarion, Hristo Georgiev Papazov, Scott William Pesme

In this work, we investigate the effect of momentum on the optimisation trajectory of gradient descent. We leverage a continuous-time approach in the analysis of momentum gradient descent with step size

\gamma

and momentum parameter

\beta

that allows u ...

2024

On the Generalization of Stochastic Gradient Descent with Momentum

Volkan Cevher, Kimon Antonakopoulos

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we first show that th ...

Brookline2024

Rotating spokes, potential hump and modulated ionization in radio frequency magnetron discharges

Haomin Sun, Liang Xu

In this work, the transition from the gradient drift instability (GDI) into an m = 1 rotating spoke in the radio frequency magnetron discharge was studied by means of the two-dimensional axial-azimuthal (z - y) particle-in-cell/Monte Carlo collision method ...

Bristol2023

Robust Collaborative Learning with Linear Gradient Overhead

Rachid Guerraoui, John Stephan, Sadegh Farhadkhani, Le Nguyen Hoang, Nirupam Gupta, Rafaël Benjamin Pinot

Collaborative learning algorithms, such as distributed SGD (or D-SGD), are prone to faulty machines that may deviate from their prescribed algorithm because of software or hardware bugs, poisoned data or malicious behaviors. While many solutions have been ...

PLMR2023

Single-shot Kramers-Kronig complex orbital angular momentum spectrum retrieval

Camille Sophie Brès, Jianqi Hu, Yujie Chen

Orbital angular momentum (OAM) spectrum diagnosis is a fundamental building block for diverse OAM-based systems. Among others, the simple on-axis interferometric measurement can retrieve the amplitude and phase information of complex OAM spectra in a few s ...

SPIE-SOC PHOTO-OPTICAL INSTRUMENTATION ENGINEERS2023

A stability theory beyond the co-rotational setting for critical wave maps blow up

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Wave-momentum shaping for moving objects in heterogeneous and dynamic media

Design of a Flexure-Based Flywheel for the Storage of Angular Momentum and Kinetic Energy

Experimental observation of topological transition in linear and nonlinear parametric oscillators

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

On the Generalization of Stochastic Gradient Descent with Momentum

Rotating spokes, potential hump and modulated ionization in radio frequency magnetron discharges

Robust Collaborative Learning with Linear Gradient Overhead

Single-shot Kramers-Kronig complex orbital angular momentum spectrum retrieval

Wave-momentum shaping for moving objects in heterogeneous and dynamic media

Experimental observation of topological transition in linear and nonlinear parametric oscillators

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Design of a Flexure-Based Flywheel for the Storage of Angular Momentum and Kinetic Energy

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Critical degeneracy in a nonlinear hyperbolic equation can produce atypical instability

On the Generalization of Stochastic Gradient Descent with Momentum

Robust Collaborative Learning with Linear Gradient Overhead

Single-shot Kramers-Kronig complex orbital angular momentum spectrum retrieval

Rotating spokes, potential hump and modulated ionization in radio frequency magnetron discharges