Publications associées à Long-range order in the Bose-Einstein condensation of polaritons

Modeling friction and wear using an adaptive discrete-continuum coupling

When two objects slide against each other, wear and friction occur at their interface. The accumulation of wear forms what is commonly referred to as a ``third-body''. Understanding third-body evolution has significant applications in industry, where contr ...

EPFL2024

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

On the fast assemblage of finite element matrices with application to nonlinear heat transfer problems

Yannis Dirk Voet

The finite element method is a well-established method for the numerical solution of partial differential equations (PDEs), both linear and nonlinear. However, the repeated re -assemblage of finite element matrices for nonlinear PDEs is frequently pointed ...

ELSEVIER SCIENCE INC2023

Dynamical low rank approximation for uncertainty quantification of time-dependent problems

Eva Vidlicková

The quantification of uncertainties can be particularly challenging for problems requiring long-time integration as the structure of the random solution might considerably change over time. In this respect, dynamical low-rank approximation (DLRA) is very a ...

EPFL2022

Finite element modeling of dynamic frictional rupture with rate and state friction

Jean-François Molinari, Fabian Barras, Roozbeh Rezakhani, Michael Ludovic Brun

Numerous laboratory experiments have demonstrated the dependence of the friction coefficient on the interfacial slip rate and the contact history, a behavior generically called rate and state friction. Although numerical models have been widely used for an ...

PERGAMON-ELSEVIER SCIENCE LTD2020

On arithmetic progressions in symmetric sets in finite field model

Jan Hazla

We consider two problems regarding arithmetic progressions in symmetric sets in the finite field (product space) model. ...

ELECTRONIC JOURNAL OF COMBINATORICS2020

Fast assembly of Galerkin matrices for 3D solid laminated composites using finite element and isogeometric discretizations

Pablo Antolin Sanchez

This work presents a novel methodology for speeding up the assembly of stiffness matrices for laminate composite 3D structures in the context of isogeometric and finite element discretizations. By splitting the involved terms into their in-plane and out-of ...

2020

Dynamical collapse of cylindrical symmetric Dipolar Bose-Einstein condensates

Luigi Forcella

We study the formation of singularities for cylindrical symmetric solutions to the Gross-Pitaevskii equation describing a Dipolar Bose-Einstein condensate. We prove that solutions arising from initial data with energy below the energy of the Ground State a ...

2021

Modeling spatially dependent functional data via regression with differential regularization

Fabio Nobile, Eleonora Arnone

We propose a method for modelling spatially dependent functional data, based on regression with differential regularization. The regularizing term enables to include problem-specific information about the spatio-temporal variation of phenomenon under study ...

2019

The time-dependent expected reward and deviation matrix of a finite QBD process

Sophie Myriam Hautphenne

Deriving the time-dependent expected reward function associated with a continuous-time Markov chain involves the computation of its transient deviation matrix. In this paper we focus on the special case of a finite quasi-birth-and-death (QBD) process, moti ...

ELSEVIER SCIENCE INC2019

Coupling non-conforming discretizations of PDEs by spectral approximation of the Lagrange multiplier space

Simone Deparis, Luca Pegolotti, Antonio Iubatti

This work focuses on the development of a non-conforming method for the coupling of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a finite number of Lagrange multipliers defined over the interfac ...

2019

MATHICSE Technical Report: A posteriori error estimation for the stochastic collocation finite element approximation of the heat equation with random coefficients

Fabio Nobile, Eva Vidlicková

In this work we present a residual based a posteriori error estimation for a heat equation with a random forcing term and a random diffusion coefficient which is assumed to depend affinely on a finite number of independent random variables. The problem is ...

MATHICSE2019

On quadratic matrix equations with infinite size coefficients encountered in QBD stochastic processes

Stefano Massei

Matrix equations of the kind A(1)X(2)+A(0)X+A(-1)=X, where both the matrix coefficients and the unknown are semi-infinite matrices belonging to a Banach algebra, are considered. These equations, where coefficients are quasi-Toeplitz matrices, are encounter ...

WILEY2018

Correspondence functors and finiteness conditions

Jacques Thévenaz, Serge Bouc

We investigate the representation theory of finite sets. The correspondence functors are the functors from the category of finite sets and correspondences to the category of k-modules, where k is a commutative ring. They have various specific properties wh ...

2018

Light refocusing with up-scalable resonant waveguide gratings in confocal prolate spheroid arrangements

Olivier Martin, Benjamin Gallinet, Guillaume Basset, Zdenek Benes, Giorgio Quaranta

Resonant waveguide gratings (RWGs) are thin-film structures, where coupled modesinterfere with the diffracted incoming wave and produce strong angular and spectral filtering. The combination of two finite-length and impedance matched RWGs allows the creati ...

2018

Development of a monolithic near-field optomechanical system

Ryan Daniel Schilling

In the same year as Einstein's annus mirabilis, English engineer and physicist John Flemming patented the first rectifying diode, which he called the "Flemming valve". Einstein's work on the photoelectric effect would change our understanding of the nature ...

EPFL2018

Isogeometric Analysis And Proper Orthogonal Decomposition For The Acoustic Wave Equation

Alfio Quarteroni, Shengfeng Zhu

Discretization methods such as finite differences or finite elements were usually employed to provide high fidelity solution approximations for reduced order modeling of parameterized partial differential equations. In this paper, a novel discretization te ...

Edp Sciences S A2017

Patching And Weak Approximation In Isometry Groups

Eva Bayer Fluckiger

Let R be a semilocal principal ideal domain. Two algebraic objects over R in which scalar extension makes sense (e.g. quadratic spaces) are said to be of the same genus if they become isomorphic after extending scalars to all completions of R and its fract ...

Amer Mathematical Soc2017

Level crossings induced by a longitudinal coupling in the transverse field Ising chain

Frédéric Mila, Grégoire Vionnet

We study the effect of antiferromagnetic longitudinal coupling on the one-dimensional transverse field Ising model with nearest-neighbor couplings. In the topological phase where, in the thermodynamic limit, the ground state is twofold degenerate, we show ...

2017