Publications related to Equations of motion

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

. 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

Efficient Temporally-Aware DeepFake Detection using H.264 Motion Vectors

Sabine Süsstrunk, Yufan Ren, Peter Arpad Grönquist, Alessio Verardo, Qingyi He

Video DeepFakes are fake media created with Deep Learning (DL) that manipulate a person’s expression or identity. Most current DeepFake detection methods analyze each frame independently, ignoring inconsistencies and unnatural movements between frames. Som ...

2024

Non-normal forms

Yves-Marie François Ducimetière

In this thesis, we propose to formally derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they respond to harmonic or stochastic forcing, or to an initial condition. This approach reconciles the non-mo ...

EPFL2024

Parametric Reduced Order Model of a Gas Bearings Supported Rotor

Fabio Nobile, Jürg Alexander Schiffmann, Dimitri Maurice Goutaudier

Gas bearings use pressurized gas as a lubricant to support and guide rotating machinery. These bearings have a number of advantages over traditional lubricated bearings, including higher efficiency in a variety of applications and reduced maintenance requi ...

2024

Weakly nonlinear versus semi-linear models of the nonlinear evolution of the centrifugal instability

François Gallaire, Eunok Yim

We carry out a weakly nonlinear analysis of the centrifugal instability for a columnar vortex in a rotating fluid, and compare the results to those of the semi-linear model derived empirically by Yim et al. (J. Fluid Mech., vol. 897, 2020, A34). The asympt ...

CAMBRIDGE UNIV PRESS2023

Mean flow modeling in high-order nonlinear Schrodinger equations

Debbie Eeltink

The evaluation and consideration of the mean flow in wave evolution equations are necessary for the accurate prediction of fluid particle trajectories under wave groups, with relevant implications in several domains, from the transport of pollutants in the ...

2023

Rapid motion estimation and correction using self-encoded FID navigators in 3D radial MRI

Tobias Kober, Davide Piccini

Purpose: To develop a self-navigated motion compensation strategy for 3D radial MRI that can compensate for continuous head motion by measuring rigid body motion parameters with high temporal resolution from the central k-space acquisition point (self-enco ...

Hoboken2023

Bimanual dynamic grabbing and tossing of objects onto a moving target

Aude Billard, Michael Bosongo Bombile

Bimanual grabbing and tossing of packages onto trays or conveyor belts remains a human activity in the industry. For robots, such a dynamic task requires coordination between two arms and fast adaptation abilities when the tossing target is moving and subj ...

2023

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Hoài-Minh Nguyên, Jean Louis-Alexandre Fornerod

The transmission eigenvalue problem is a system of two second-order elliptic equations of two unknowns equipped with the Cauchy data on the boundary. In this work, we establish the Weyl law for the eigenvalues and the completeness of the generalized eigenf ...

Philadelphia2023

Equations of motion

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WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Efficient Temporally-Aware DeepFake Detection using H.264 Motion Vectors

Non-normal forms

Parametric Reduced Order Model of a Gas Bearings Supported Rotor

Weakly nonlinear versus semi-linear models of the nonlinear evolution of the centrifugal instability

Mean flow modeling in high-order nonlinear Schrodinger equations

Rapid motion estimation and correction using self-encoded FID navigators in 3D radial MRI

Bimanual dynamic grabbing and tossing of objects onto a moving target

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Leveraging Continuous Time to Understand Momentum When Training Diagonal Linear Networks

Rapid motion estimation and correction using self-encoded FID navigators in 3D radial MRI

THE WEYL LAW OF TRANSMISSION EIGENVALUES AND THE COMPLETENESS OF GENERALIZED TRANSMISSION EIGENFUNCTIONS WITHOUT COMPLEMENTING CONDITIONS

Non-normal forms

WILD SOLUTIONS TO SCALAR EULER-LAGRANGE EQUATIONS

Mean flow modeling in high-order nonlinear Schrodinger equations

Parametric Reduced Order Model of a Gas Bearings Supported Rotor

Bimanual dynamic grabbing and tossing of objects onto a moving target

Weakly nonlinear versus semi-linear models of the nonlinear evolution of the centrifugal instability

Efficient Temporally-Aware DeepFake Detection using H.264 Motion Vectors