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This thesis consists of two parts. The first part is about a variant of Banach's fixed point theorem and its applications to several partial differential equations (PDE's), abstractly of the form [ \mathcal Lu + \mathcal Q(u) = f.] The main result of thi ...
EPFL2015
In this paper, a time dependent one-dimensional linear advection-diffusion equation with Dirichlet homogeneous boundary conditions and an initial sine function is solved analytically by separation of variables and numerically by the finite element method. ...
Foundations of signal processing are heavily based on Shannon's sampling theorem for acquisition, representation and reconstruction. This theorem states that signals should not contain frequency components higher than the Nyquist rate, which is half of the ...
We investigate smooth approximations of functions, with prescribed gradient behavior on a distinguished stratified subset of the domain. As an application, we outline how our results yield important consequences for a recently introduced class of stochasti ...
Using the recently developed multiregion, relaxed MHD (MRxMHD) theory, which bridges the gap between Taylor's relaxation theory and ideal MHD, we provide a thorough analytical and numerical proof of the formation of singular currents at rational surfaces i ...
Multipactor is a resonant vacuum discharge occurring in microwave components of satellite systems as well as in particle accelerators. Due to its undesirable effects, multipactor analysis constitutes a mandatory step in the design of modern satellite compo ...
We complete the picture of sharp eigenvalue estimates for the -Laplacian on a compact manifold by providing sharp estimates on the first nonzero eigenvalue of the nonlinear operator when the Ricci curvature is bounded from below by a negative constant. We ...
We present a high precision particle-by-particle 3D reconstruction of granular systems composed of monodispersed spheres (sphere packings); the experimental approach is based on magnetic resonance imaging techniques. Our measurements revealed a strong corr ...
This work focuses on Green Functions (GFs) of planar multilayered structures that may include arbitrary number of conductive sheets. The spectral domain GFs are derived through an automatized strategy based on the propagator matrix technique, while the spa ...
In this paper we propose a local orthogonal decomposition method (LOD) for elliptic partial differential equations with inhomogeneous Dirichlet and Neumann boundary conditions. For this purpose, we present new boundary correctors which preserve the common ...
