Concept

Équation de Laplace

Publications associées (70)

Blow-up, partial regularity and turbulence in incompressible fluid dynamics

Weak solutions arise naturally in the study of the Navier-Stokes and Euler equations both from an abstract regularity/blow-up perspective and from physical theories of turbulence. This thesis studies the structure and size of singular set of such weak solu ...

EPFL2022

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

Harmonic Power-Flow Study of Polyphase Grids with Converter-Interfaced Distributed Energy Resources, Part I: Modelling Framework and Algorithm

Mario Paolone, Lorenzo Enrique Reyes Chamorro, Andreas Martin Kettner, Johanna Kristin Maria Becker

Power distribution systems are experiencing a largescale integration of Converter-Interfaced Distributed Energy Resources (CIDERs). This complicates the analysis and mitigation of harmonics, whose creation and propagation are facilitated by the interaction ...

2021

MATHICSE Technical Report : Analysis-aware defeaturing: problem setting and a posteriori estimation

Annalisa Buffa, Rafael Vazquez Hernandez, Ondine Gabrielle Chanon

Defeaturing consists in simplifying geometrical models by removing the geometrical features that are considered not relevant for a given simulation. Feature removal and simplification of computer-aided design models enables faster simulations for engineeri ...

EPFL2021

Quantitative rapid and finite time stabilization of the heat equation

Shengquan Xiang

The null controllability of the heat equation is known for decades [21, 25, 34]. The finite time stabilizability of the one dimensional heat equation was proved by Coron-Nguyên [15], while the same question for high dimensional spaces remained widely open. ...

2020

Regularity In Time Of Holder Solutions Of Euler And Hypodissipative Navier-Stokes Equations

Maria Colombo, Luigi De Rosa

In this work we investigate some regularization properties of the incompressible Euler equations and of the fractional Navier-Stokes equations where the dissipative term is given by (-Delta)(alpha) for a suitable power alpha is an element of (0, 1/2) (the ...

SIAM PUBLICATIONS2020

Classical nucleation theory predicts the shape of the nucleus in homogeneous solidification

Michele Ceriotti, Bingqing Cheng, Gareth Aneurin Tribello

Macroscopic models of nucleation provide powerful tools for understanding activated phase transition processes. These models do not provide atomistic insights and can thus sometimes lack material-specific descriptions. Here, we provide a comprehensive fram ...

AMER INST PHYSICS2020

Stationary Structures near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

Klaus Martin Widmayer

We study the behavior of solutions to the incompressible 2d Euler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated Navier-Stokes problems. We exhibit a large family of ...

2020

On-the-fly ab initio semiclassical evaluation of third-order response functions for two-dimensional electronic spectroscopy

Jiri Vanicek, Tomislav Begusic

Ab initio computation of two-dimensional electronic spectra is an expanding field, whose goal is improving upon simple, few-dimensional models often employed to explain experiments. Here, we propose an accurate and computationally affordable approach, base ...

2020

Global Solutions To Stochastic Reaction-Diffusion Equations With Super-Linear Drift And Multiplicative Noise

Robert Dalang, Davar Khoshnevisan

Let xi(t, x) denote space-time white noise and consider a reaction-diffusion equation of the form (t, x) = 1/2u ''(t, x) + b(u(t, x)) + sigma(u(t,x))xi(t,x) on R+ x [0, 1], with homogeneous Dirichlet boundary conditions and suitable initial d ...

INST MATHEMATICAL STATISTICS2019

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