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Publications associées (12)

Fredholm transformation on Laplacian and rapid stabilization for the heat equation

We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Lapla ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Fredholm transformation on Laplacian and rapid stabilization for the heat equations

Shengquan Xiang

We revisit the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. We prove that, under some assumption on the control operator, two scalar controls are necessary and sufficient ...

2021

Frequency selection in a gravitationally stretched capillary jet in the jetting regime

François Gallaire, Isha Shukla

A capillary jet falling under the effect of gravity continuously stretches while thinning downstream. We report here the effect of external periodic forcing on such a spatially varying jet in the jetting regime. Surprisingly, the optimal forcing frequency ...

CAMBRIDGE UNIV PRESS2020

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

Fabio Nobile, Francesca Bonizzoni, Davide Pradovera

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

Self-consistent triple decomposition of the turbulent flow over a backward-facing step under finite amplitude harmonic forcing

François Gallaire, Eunok Yim, Philippe Meliga

We investigate the saturation of harmonically forced disturbances in the turbulent flow over a backward-facing step subjected to a finite amplitude forcing. The analysis relies on a triple decomposition of the unsteady flow into mean, coherent and incohere ...

ROYAL SOC2019

Response of noise-amplifier flows: From linear control to nonlinear jet breakup

Isha Shukla

Among hydrodynamically unstable flows, the amplifier-flows are characterized by their large amplification potential in presence of external noise. Since amplifiers do not have an intrinsic dynamics, a chosen forcing can be applied to eventually control the ...

EPFL2019

Generalized resolution matrix for neutron spin-echo three-axis spectrometers

Thomas Keller, Felix Groitl

This article describes the energy resolution of spin-echo three-axis spectrometers (SE-TASs) by a compact matrix formalism. SE-TASs allow one to measure the line widths of elementary excitations in crystals, such as phonons and magnons, with an energy reso ...

INT UNION CRYSTALLOGRAPHY2018

Exponential decay and Fredholm properties in second-order quasilinear elliptic systems

Charles Stuart, Hicham Georges Gebran

We consider second-order quasilinear elliptic systems on un-bounded domains in the setting of Sobolev spaces. We complete our earlier work on the Fredholm and properness properties of the associated differential operators by giving verifiable conditions fo ...

2010

Global continuation for ODE systems over the half-line and study of von Kármán's swirling flow problem

Gilles Evéquoz

This work is concerned with the global continuation for solutions (λ,u,ξ) ∈ R × C1{0}([0,∞), RN) × Rk of the following system of ordinary differential equations: where F: [0,∞) × RN × U × J → RN and φ: U × J → X1, for some open sets J ⊂ R and U ⊂ Rk, and w ...

EPFL2007

On spectral pollution in the finite element approximation of thin elastic ''membrane'' shells

Jacques Rappaz

The bending terms in a shell are small with respect to membrane ones as the thickness tends to zero. Consequently, the membrane approximation gives a good description of vibration properties of a thin shell. This vibration problem is associated with a non- ...

1997

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