Local Well-Posedness And Blow-Up For The Half Ginzburg-Landau-Kuramoto Equation With Rough Coefficients And Potential

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On the density of the supremum of the solution to the linear stochastic heat equation

Robert Dalang, Fei Pu

We study the regularity of the probability density function of the supremum of the solution to the linear stochastic heat equation. Using a general criterion for the smoothness of densities for locally nondegenerate random variables, we establish the smoot ...

SPRINGER2020

Fast Least-Squares Padé approximation of problems with normal operators and meromorphic structure

Fabio Nobile, Davide Pradovera, Francesca Bonizzoni

In this work, we consider the approximation of Hilbert space-valued meromorphic functions that arise as solution maps of parametric PDEs whose operator is the shift of an operator with normal and compact resolvent, e.g., the Helmholtz equation. In this res ...

2020

Functional Inverse Problems on Spheres: Theory, Algorithms and Applications

Matthieu Martin Jean-André Simeoni

Many scientific inquiries in natural sciences involve approximating a spherical field -namely a scalar quantity defined over a continuum of directions- from generalised samples of the latter (e.g. directional samples, local averages, etc). Such an approxim ...

EPFL2020

Normal approximation of the solution to the stochastic heat equation with Levy noise

Carsten Hao Ye Chong

Given a sequence L & x2d9;epsilon of Levy noises, we derive necessary and sufficient conditions in terms of their variances sigma 2(epsilon) such that the solution to the stochastic heat equation with noise sigma(epsilon)-1L & x2d9;epsilon converges in law ...

SPRINGER2020

Novel corrector problems with exponential decay of the resonance error for numerical homogenization

Edoardo Paganoni

Multiscale problems, such as modelling flows through porous media or predicting the mechanical properties of composite materials, are of great interest in many scientific areas. Analytical models describing these phenomena are rarely available, and one mus ...

EPFL2020

Adaptive isogeometric analysis on two-dimensional trimmed domains based on a hierarchical approach

Annalisa Buffa, Pablo Antolin Sanchez, Rafael Vazquez Hernandez, Luca Coradello

The focus of this work is on the development of an error-driven isogeometric framework, capable of automatically performing an adaptive simulation in the context of second- and fourth-order, elliptic partial differential equations defined on two-dimensiona ...

2020

Linear Response Theory and Green-Kubo Relations for Active Matter

Demian Francisco Levis Sotomayor, Ignacio Pagonabarraga Mora

We address the question of how interacting active systems in a nonequilibrium steady state respond to an external perturbation. We establish an extended fluctuation-dissipation theorem for active Brownian particles (ABP), which highlights the role played b ...

2019

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

David Valentin Strütt

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

The role of the roughness spectral breadth in elastic contact of rough surfaces

Jean-François Molinari, Guillaume Anciaux, Vladislav Yastrebov

We study frictionless and non-adhesive contact between elastic half-spaces with self-affine surfaces. Using a recently suggested corrective technique, we ensure an unprecedented accuracy in computation of the true contact area evolution under increasing pr ...

2017

Equation of state of liquid mercury to 520 K and 7 GPa from acoustic velocity measurements

Livia Eleonora Bove Kado

Ultrafast acoustics measurements on liquid mercury have been performed at high pressure and temperature in a diamond anvil cell using picosecond acoustic interferometry. We extract the density of mercury from adiabatic sound velocities using a numerical it ...

American Institute of Physics2014

The Bounded Confidence Model Of Opinion Dynamics

Jean-Yves Le Boudec

The bounded confidence model of opinion dynamics, introduced by Deffuant et al, is a stochastic model for the evolution of continuous-valued opinions within a finite group of peers. We prove that, as time goes to infinity, the opinions evolve globally into ...

World Scientific Publishing2012