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

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 University 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

Increasing the Energy Efficiency of Gas Boosters for Hydrogen Storage and for Refueling Stations

Alfred Rufer

A new electrically driven gas booster is described as an alternative to the classical air-driven gas boosters known for their poor energetic efficiency. These boosters are used in small scale Hydrogen storage facilities and in refueling stations for Hydrog ...

MDPI2023

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 ...

Wiley2023

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 ...

Elsevier2023

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 ...

Siam Publications2023

Dynamical Low-Rank Approximation for Stochastic Differential Equations

Fabio Nobile, Yoshihito Kazashi, Fabio Zoccolan

In this paper, we set the mathematical foundations of the Dynamical Low-Rank Approximation (DLRA) method for stochastic differential equations (SDEs). DLRA aims at approximating the solution as a linear combination of a small number of basis vectors with r ...

American Mathematical Society (AMS)2024

Long Term Motion Prediction Using Keyposes

Pascal Fua, Mathieu Salzmann, Wei Wang, Sena Kiciroglu

Long term human motion prediction is essential in safety-critical applications such as human-robot interaction and autonomous driving. In this paper we show that to achieve long term forecasting, predicting human pose at every time instant is unnecessary. ...

IEEE2022

Weakly-supervised Action Transition Learning for Stochastic Human Motion Prediction

Mathieu Salzmann, Wei Mao

We introduce the task of action-driven stochastic human motion prediction, which aims to predict multiple plausible future motions given a sequence of action labels and a short motion history. This differs from existing works, which predict motions that ei ...

IEEE COMPUTER SOC2022

Prospective motion correction in kidney MRI using FID navigators

Tobias Kober

Purpose Abdominal MRI scans may require breath-holding to prevent image quality degradation, which can be challenging for patients, especially children. In this study, we evaluate whether FID navigators can be used to measure and correct for motion prospec ...

WILEY2022

Controlling motion at the nanoscale with light

Mintae Chung

Optical manipulation at the micro- nano-scale is a fascinating topic due to its inherent non-invasive properties and multifaceted applications in various fields such as biology, sensing, micro-fluidics, and micro- nano-robotics. This thesis involves intens ...

EPFL2022

Scrutinizing thermally stimulated current transients originating from trapped charges in organic semiconductors: A drift-diffusion study

Frank Nüesch, Beat Ruhstaller

Thermally stimulated current (TSC) is a widely used technique to assess trap states and extract their density, energy, and capture rate using analytical expressions. In many cases, the latter are derived from physical models pertaining to inorganic semicon ...

AIP Publishing2022

Weak nonlinearity for strong non-normality

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière

We propose a theoretical approach to derive amplitude equations governing the weakly nonlinear evolution of non-normal dynamical systems, when they experience transient growth or respond to harmonic forcing. This approach reconciles the non-modal nature of ...

Cambridge University Press2022

State-to-state surface scattering of methane studied by bolometric infrared laser tagging detection

Bo-Jung Chen

State-to-state molecule/surface scattering experiments prepare the incident molecules in a specific quantum state and measure the quantum state distribution of the scattered molecules. The comparison of state resolved experiments with theory can serve as s ...

EPFL2022

Tree-cotree decomposition of isogeometric mortared spaces in H(curl) on multi-patch domains

Rafael Vazquez Hernandez, Bernard Kapidani

When applying isogeometric analysis to engineering problems, one often deals with multi-patch spline spaces that have incompatible discretisations, e.g. in the case of moving objects. In such cases mortaring has been shown to be advantageous. This contribu ...

2022

Analysis-aware defeaturing of complex geometries

Pablo Antolin Sanchez, Ondine Gabrielle Chanon

Local modifications of a computational domain are often performed in order to simplify the meshing process and to reduce computational costs and memory requirements. However, removing geometrical features of a domain often introduces a non-negligible error ...

2022