Publications related to Inductive dimension

From thin plates to Ahmed bodies: linear and weakly nonlinear stability of rectangular prisms

Edouard Boujo, Giuseppe Antonio Zampogna

We study the stability of laminar wakes past three-dimensional rectangular prisms. The width-to-height ratio is set to W/H = 1.2, while the length-to-height ratio 1/6 < L/H < 3 covers a wide range of geometries from thin plates to elongated Ahmed bodies. F ...

Cambridge University Press2023

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Linearization and Identification of Multiple-Attractor Dynamical Systems through Laplacian Eigenmaps

Aude Billard, Bernardo Fichera

Dynamical Systems (DS) are fundamental to the modeling and understanding time evolving phenomena, and have application in physics, biology and control. As determining an analytical description of the dynamics is often difficult, data-driven approaches are ...

Microtome Publishing2022

Bootstrapping mixed correlators in N=4 super Yang-Mills

Andrea Manenti, Alessandro Vichi

We perform a numerical bootstrap study of the mixed correlator system containing the half-BPS operators of dimension two and three in N = 4 Super Yang-Mills. This setup improves on previous works in the literature that only considered single correlators of ...

Springer Nature2021

A Computational Comparison Between Isogeometric Analysis and Spectral Element Methods: Accuracy and Spectral Properties

Alfio Quarteroni, Ondine Gabrielle Chanon

In this paper, we carry out a systematic comparison between the theoretical properties of Spectral Element Methods and NURBS-based Isogeometric Analysis in its basic form, that is in the framework of the Galerkin method, for the approximation of the Poisso ...

SPRINGER/PLENUM PUBLISHERS2020

On long time behavior of solutions to nonlinear dispersive equations

Stefano Francesco Burzio

In part I, we address the issue of existence of solutions for Cauchy problems involving nonlinear hyperbolic equations for initial data in Sobolev spaces with scaling subcritical regularity. In particular, we analyse nonlinear estimates for null-forms in t ...

EPFL2020

Type II blow up solutions with optimal stability properties for the critical focussing nonlinear wave equation on $\R^{3+1}$

Joachim Krieger, Stefano Francesco Burzio

We show that the finite time type II blow up solutions for the energy critical nonlinear wave equation [ \Box u = -u^5 ] on

\R^{3+1}

constructed in \cite{KST}, \cite{KS1} are stable along a co-dimension one Lipschitz manifold of data perturbations in a ...

2022

Stable high-order randomized cubature formulae in arbitrary dimension

Fabio Nobile, Giovanni Migliorati

We propose and analyse randomized cubature formulae for the numerical integration of functions with respect to a given probability measure μ defined on a domain Γ⊆ℝ^d, in any dimension d. Each cubature formula is conceived to be exact on a given finite dim ...

2022

Exact diagonalization of SU( N ) Heisenberg and Affleck-Kennedy-Lieb-Tasaki chains using the full SU( N ) symmetry

Frédéric Mila, Pierre Marcel Nataf, Kianna Wan

We present a method for the exact diagonalization of the SU(N) Heisenberg interaction Hamiltonian using Young tableaus to work directly in each irreducible representation of the global SU(N) group. This generalized scheme is applicable to chains consisting ...

2017

Methods and apparatuses for versatile beamforming

Paul Hurley, Matthieu Martin Jean-André Simeoni, Giovanni Cherubini

The present invention is directed to methods and apparatuses for beamforming signals or compute beamformed signals. The present approach is to determine a series of beams from or for a set of devices configured for receiving signals from and/or transmittin ...

2017

Eigenmaps Of Dynamic Functional Connectivity: Voxel-Level Dominant Patterns Through Eigenvector Centrality

Dimitri Nestor Alice Van De Ville, Maria Giulia Preti

Dynamic functional connectivity (dFC) based on resting-state functional magnetic resonance imaging (fMRI) explores the ongoing temporal configuration of brain networks. To reduce the large dimensionality of the data, conventional dFC analysis usually fores ...

IEEE2016

Dissipative Boundary Conditions for Nonlinear 1-D Hyperbolic Systems: Sharp Conditions Through an Approach via Time-Delay Systems

Hoài-Minh Nguyên

We analyze dissipative boundary conditions for nonlinear hyperbolic systems in one space dimension. We show that a known sufficient condition for exponential stability with respect to the H-2-norm is not sufficient for the exponential stability with respec ...

Society for Industrial and Applied Mathematics2015

A counterexample to well-posedness of entropy solutions to the compressible Euler system

Elisabetta Chiodaroli

We consider entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the spatially periodic case. In more than one space dimension, the methods developed by De Lellis-Szekelyhidi enable us to show here failure of uniquenes ...

World Scientific Publ Co Pte Ltd2014

Nondispersive solutions to the $L^2$-critical half-wave equation

Joachim Krieger

We consider the focusing

L^2

-critical half-wave equation in one space dimension

i \partial_t u = D u - |u|^2 u,

where

D

denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold

M_* > 0

such that all ...

Springer Verlag2013

treeKL: A distance between high dimension empirical distributions

François Fleuret

This paper offers a methodological contribution for computing the distance between two empirical distributions in an Euclidean space of very large dimension. We propose to use decision trees instead of relying on standard quantification of the feature spac ...

Elsevier Science Bv2013

On the number of lattice points in a small sphere and a recursive lattice decoding algorithm

Annika Meyer

Let L be a lattice in . This paper provides two methods to obtain upper bounds on the number of points of L contained in a small sphere centered anywhere in . The first method is based on the observation that if the sphere is sufficiently small then the la ...

Springer US2013

An adaptive finite-volume method for a model of two-phase pedestrian flow

Ricardo Esteban Ruiz Baier

A flow composed of two populations of pedestrians moving in different directions is modeled by a two-dimensional system of convection-diffusion equations. An efficient simulation of the two-dimensional model is obtained by a finite-volume scheme combined w ...

American Institute of Mathematical Sciences2011

A New Method to Explore Conformal Field Theories in Any Dimension

Alessandro Vichi

The thesis represents an investigation into Conformal Field Theories (CFT's) in arbitrary dimensions. We propose an innovative method to extract informations about CFT's in a quantitative way. Studying the crossing symmetry of the four point function of sc ...

EPFL2011

An X-ray computed tomography-based index to characterize the quality of cataclastic carbonate rock samples

Aurèle Parriaux, Pascal Turberg, Vincent Labiouse, Reto Meuli, Pierre Guillaume Christe

X-ray computed tomography (XRCT) can reconstruct, in a nondestructive way and in three-dimension, the distribution of densities within opaque materials. Consequently, it provides an effective possibility to characterize the inner content of rock core sampl ...

2011

Reduced Basis Approximation and A Posteriori Error Estimation for the Time- Dependent Viscous Burgers Equation

Gianluigi Rozza

In this paper we present rigorous a posteriori L2 error bounds for reduced basis approximations of the unsteady viscous Burgers equation in one space dimension. The key new ingredient is accurate solution-dependent (Online) calculation of the exponential-i ...

2009