Publications related to Linearization

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

Stability: a search for structure

Wouter Jongeneel

In this thesis we study stability from several viewpoints. After covering the practical importance, the rich history and the ever-growing list of manifestations of stability, we study the following. (i) (Statistical identification of stable dynamical syste ...

EPFL2024

Stability of a liquid layer draining around a horizontal cylinder: Interplay of capillary and gravity forces

François Gallaire, Shahab Eghbali, Simeon Vladimirov Djambov

We study the drainage of a viscous liquid film coating the outside of a solid horizontal cylinder, where gravity acts vertically. We focus on the limit of large Ohnesorge numbers Oh, where inertia is negligible compared to viscous effects. We first study t ...

Amer Physical Soc2024

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

Liquid film instability of an internally coated horizontal tube

François Gallaire, Edouard Boujo, Yves-Marie François Ducimetière, Shahab Eghbali

We study numerically and theoretically the gravity-driven flow of a viscous liquid film coating the inner side of a horizontal cylindrical tube and surrounding a shear-free dynamically inert gaseous core. The liquid-gas interface is prone to the Rayleigh-P ...

AMER PHYSICAL SOC2023

Gyrokinetic simulation of short wavelength ion temperature gradient instabilities in the ADITYA-U tokamak

Laurent Villard, Emmanuel Lanti

In this work, linear and nonlinear collisionless electrostatic simulation studies of the standard and short wavelength ion temperature gradient mode (SWITG) for experimental profiles and parameters of ADITYA-U tokamak are performed using the linear global ...

IOP Publishing Ltd2023

Exploration of the parameter space for the excitation and saturation of Edge Harmonic Oscillations

Guillermo Bustos Ramirez

This thesis presents advancements in the understanding of the plasma conditions leading to the excitation and saturation of the Edge Harmonic Oscillations (EHOs) observed during QH-mode operation in tokamak plasmas. Such operations represent a safer altern ...

EPFL2023

Numerical and experimental investigation of spiral-grooved gas journal bearings

Elia Iseli

Small-scale turbomachinery is increasingly used in carbon-free energy conversion systems, such as commercial or domestic scale heat pumps, fuels cells for transportation and waste heat recovery. The usage of aerodynamic bearings allows the design of compac ...

EPFL2022

Non-Linear Behaviors In The Dynamics Of Complex Systems Through A Multifractal Hydrodynamic Model

Maria-Alexandra Paun

Some non-linear behaviors in the dynamics of complex systems using the Scale Relativity Theory in the form of Multifractal Hydrodynamic Model are analyzed. By assimilating any complex system to a mathematical multifractal-type object, it is shown that the ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2022

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

Collective behavior and emerging patterns in dense dry aligning active matter

Elena Sesé Sansa

In this thesis, we study systems of active particles interacting via generic torques of different nature. We analyze the phase behavior of these systems, which results from the interplay between self-propulsion, excluded-volume and torques. We tackle the p ...

EPFL2022

Chance-Constrained Trajectory Planning With Multimodal Environmental Uncertainty

Maryam Kamgarpour, Kai Ren

We tackle safe trajectory planning under Gaussian mixture model (GMM) uncertainty. Specifically, we use a GMM to model the multimodal behaviors of obstacles' uncertain states. Then, we develop a mixed-integer conic approximation to the chance-constrained t ...

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC2022

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

Sara Bonetti, Shashank Kumar Anand

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

Whirling instability of an eccentric coated fibre

François Gallaire, Edouard Boujo, Shahab Eghbali, Ludovic Pierre Gustave Keiser

We study a gravity-driven viscous flow coating a vertical cylindrical fibre. The destabilisation of a draining liquid column into a downward moving train of beads has been linked to the conjunction of the Rayleigh-Plateau and Kapitza instabilities in the l ...

Cambridge University Press2022

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

Non-Linear Behaviors Of Airy Type On Scales Space From A Fractal Perspective

Maria-Alexandra Paun

Several non-linear behaviors in scales space, in the framework of Scale Relativity Theory, are highlighted. All these are possible through the employment of fractal-type Airy functions, which allow a revaluation of the wave/corpuscle duality, from the pers ...

UNIV POLITEHNICA BUCHAREST, SCI BULL2021

On the optimal controllability time for linear hyperbolic systems with time-dependent coefficients

Hoài-Minh Nguyên

The optimal time for the controllability of linear hyperbolic systems in one dimensional space with one-side controls has been obtained recently for time-independent coefficients in our previous works. In this paper, we consider linear hyperbolic systems w ...

2021

Stabilization of the linearized water tank system

Shengquan Xiang

In this article we study the so-called water tank system. In this system, the behavior of water contained in a 1-D tank is modelled by Saint-Venant equations, with a scalar distributed control. It is well-known that the linearized systems around uniform st ...

2022

Efficient Learning of a Linear Dynamical System with Stability Guarantees

Daniel Kuhn, Tobias Sutter, Wouter Jongeneel

We propose a principled method for projecting an arbitrary square matrix to the non- convex set of asymptotically stable matrices. Leveraging ideas from large deviations theory, we show that this projection is optimal in an information-theoretic sense and ...

2023

The effects of Prandtl number on the nonlinear dynamics of Kelvin-Helmholtz instability in two dimensions

Jeremy Peter Parker

It is known that the pitchfork bifurcation of Kelvin-Helmholtz instability occurring at minimum gradient Richardson number Ri(m) similar or equal to 1/4 in viscous stratified shear flows can be subcritical or supercritical depending on the value of the Pra ...

Cambridge University Press2021