Publications associées à The radial wave operator in similarity coordinates

A Spectral Ansatz for The Long-Time Homogenization of The Wave Equation

Consider the wave equation with heterogeneous coefficients in the homogenization regime. At large times, the wave interacts in a nontrivial way with the heterogeneities, giving rise to effective dispersive effects. The main achievement of the present wor ...

Ecole Polytechnique2024

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

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

Self-sustained dynamics and forced resonant oscillations in flows: cross-junction jets and sloshing liquids

Alessandro Bongarzone

In engineering, oscillatory instabilities and resonances are often considered undesirable flow features and measures are taken to avoid them. This may include avoiding certain parametric regions or implementing control and mitigation strategies. However, t ...

EPFL2023

Stochastic particle transport by deep-water irregular breaking waves

Debbie Eeltink

Correct prediction of particle transport by surface waves is crucial in many practical applications such as search and rescue or salvage operations and pollution tracking and clean-up efforts. Recent results by Deike et al. (J. Fluid Mech., vol. 829, 2017, ...

Cambridge University Press2023

Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to a-synuclein spreading in Parkinson's disease

Alfio Quarteroni, Francesca Bonizzoni

This spreading of prion proteins is at the basis of brain neurodegeneration. This paper deals with the numerical modelling of the misfolding process of a-synuclein in Parkinson's disease. We introduce and analyse a discontinuous Galerkin method for the sem ...

Elsevier Science Sa2023

On a Finite-Size Neuronal Population Equation

Valentin Marc Schmutz, Tilo Schwalger, Eva Löcherbach

Population equations for infinitely large networks of spiking neurons have a long tradition in theoret-ical neuroscience. In this work, we analyze a recent generalization of these equations to populations of finite size, which takes the form of a nonlinear ...

SIAM PUBLICATIONS2023

Microscopic field theory for structure formation in systems of self-propelled particles with generic torques

Ignacio Pagonabarraga Mora, Elena Sesé Sansa

We derive a dynamical field theory for self-propelled particles subjected to generic torques and forces by explicitly coarse-graining their microscopic dynamics, described by a many-body Fokker-Planck equation. The model includes both intrinsic torques ind ...

AIP Publishing2022

Inception of Regular Valley Spacing in Fluvial Landscapes: A Linear Stability Analysis

Shashank Kumar Anand, Sara Bonetti

Incipient valley formation in mountainous landscapes is often associated with their presence at a regular spacing under diverse hydroclimatic forcings. Here we provide a formal linear stability theory for a landscape evolution model (LEM) representing the ...

2022

Buoyancy-driven convection of droplets on hot nonwetting surfaces

François Gallaire, Eunok Yim

The global linear stability of a water drop on hot nonwetting surfaces is studied. The droplet is assumed to have a static shape and the surface tension gradient is neglected. First, the nonlinear steady Boussinesq equation is solved to obtain the axisymme ...

AMER PHYSICAL SOC2021

Ill-posedness of the quasilinear wave equation in the space 𝐻7/4(ln𝐻)−𝛽in ℝ2+1

Gaspard Ohlmann

We are interested in the well posedness of quasilinear partial differential equations of order two. Motivated by the study of the Einstein equation in relativity theory, there are a number of works dedicated to the local well-posedness issue for the quasil ...

EPFL2021

Nonlinear Transient Stability Analysis of Phased-Locked Loop Based Grid-Following Voltage Source Converters Using Lyapunov’s Direct Method

Alireza Karimi, Behrooz Bahrani

In this paper, using Lyapunov’s stability theorem, the transient stability conditions for a grid-following Voltage Source Converter (VSC) are found. These conditions take into account both the grid specifications and the VSC’s dynamics. The derived conditi ...

2021

Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

2020

Direct FEM-Domain Decomposition Using Convex-to-Concave Spherical Ports for Space Applications

Juan Ramon Mosig, Javier Rubio, Pedro Robustillo Bayon

This letter proposes the application of a hybrid numerical technique to two cases of interest in the space business: the reallocation of radiators and scatters on satellite platforms; and the analysis of antennas for mobile communications. It is based on t ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2020

A hierarchical preconditioner for wave problems in quasilinear complexity

Jan Sickmann Hesthaven, Boris Bonev

The paper introduces a novel, hierarchical preconditioner based on nested dissection and hierarchical matrix compression. The preconditioner is intended for continuous and discontinuous Galerkin formulations of elliptic problems. We exploit the property th ...

2022

Analogue computing with metamaterials

Romain Christophe Rémy Fleury, Farzad Zangeneh Nejad

Despite their widespread use for performing advanced computational tasks, digital signal processors suffer from several restrictions, including low speed, high power consumption and complexity, caused by costly analogue-to-digital converters. For this reas ...

2021

A Note on BIBO Stability

Michaël Unser

The statements on the BIBO stability of continuoustime convolution systems found in engineering textbooks are often either too vague (because of lack of hypotheses) or mathematically incorrect. What is more troubling is that they usually exclude the identi ...

2020

Stability of standing waves for a nonlinear Klein-Gordon equation with delta potentials

François Samer Genoud

In this paper, we study local well-posedness and orbital stability of standing waves for a singularly perturbed one-dimensional nonlinear Klein-Gordon equation. We first establish local well-posedness of the Cauchy problem by a fixed point argument. Unlike ...

2019

Time and space adaptivity of the wave equation discretized in time by a second-order scheme

Marco Picasso, Olga Gorynina

The aim of this paper is to obtain a posteriori error bounds of optimal order in time and space for the linear second-order wave equation discretized by the Newmark scheme in time and the finite element method in space. An error estimate is derived in the ...

2019

An Easily Computable Error Estimator In Space And Time For The Wave Equation

Marco Picasso, Olga Gorynina

We propose a cheaper version of a posteriori error estimator from Gorynina et al. (Namer. Anal. (2017)) for the linear second-order wave equation discretized by the Newmark scheme in time and by the finite element method in space. The new estimator preserv ...

EDP Sciences2019