Related papers: Certain upper bounds on the eigenvalues associated…
The Dirichlet problem for the wave equation is a classical example of a problem which is not well-posed. Nevertheless, it has been used to model internal waves oscillating sinusoidally in time, in various situations, standing internal waves…
In this paper we discuss a theoretical model for the interfacial profiles of progressive non-linear waves which result from introducing a triangular obstacle, of finite height, attached to the bottom below the flow of a stratified, ideal,…
In this paper, the asymptotic behavior of abstract strongly coupled hyperbolic equations with one infinite memory term is investigated, one specific case of which is the model for describing the dynamical behaviour of magnetic effected…
The one-dimensional PDE model of the wave equation with a state feedback controller at its boundary, which describes wave dynamics of a wide-range of controlled mechanical systems, has exponentially stable solutions. However, it is known…
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…
This paper describes a fast and accurate method for obtaining steerable principal components from a large dataset of images, assuming the images are well localized in space and frequency. The obtained steerable principal components are…
We consider the spectrum of a Schroedinger operator in a multi-dimensional cylinder perturbed by a shrinking potential. We study the phenomenon of a new eigenvalue emerging from the threshold of the essential spectrum and give the…
A high-performance shooting algorithm is developed to compute time-periodic solutions of the free-surface Euler equations with spectral accuracy in double and quadruple precision. The method is used to study resonance and its effect on…
Although methods for estimating the pose of objects in indoor scenes have achieved great success, the pose estimation of underwater objects remains challenging due to difficulties brought by the complex underwater environment, such as…
The paper investigates a variant of semi-implicit spectral deferred corrections (SISDC) in which the stiff, fast dynamics correspond to fast propagating waves ("fast-wave slow-wave problem"). We show that for a scalar test problem with two…
We discuss the solution of boundary value problems that arise after the separation of variables in the Schr\"odinger equation in oblate spheroidal coordinates. The specificity of these boundary value problems is that the singular points of…
Recently, Ferrulli-Laptev-Safronov (2016arXiv161205304F) obtained eigenvalue estimates for an operator associated to bilayer graphene in terms of $L^q$ norms of the (possibly non-selfadjoint) potential. They proved that for $1<q<4/3$ all…
A numerical model is proposed to compute the eigenmodes and the forced response of multilayered elastic spheres. The main idea is to describe analytically the problem along the angular coordinates with spherical harmonics and to discretize…
We describe a novel framework for estimating subsurface properties, such as rock permeability and porosity, from time-lapse observed seismic data by coupling full-waveform inversion, subsurface flow processes, and rock physics models. For…
In this paper, we describe Fourier-based Wave Front Sensors (WFS) as linear integral operators, characterized by their Kernel. In a first part, we derive the dependency of this quantity with respect to the WFS's optical parameters: pupil…
The Fourier transform truncated on [-c,c] is usually analyzed when acting on L^2(-1/b,1/b) and its right-singular vectors are the prolate spheroidal wave functions. This paper considers the operator acting on the larger space L^2(exp(b|.|))…
Motivated by a host of recent applications requiring some amount of redundancy, frames are becoming a standard tool in the signal processing toolbox. In this paper, we study a specific class of frames, known as discrete Fourier transform…
Large-amplitude Alfv\'en waves are subject to parametric decays which can have important consequences in space, astrophysical, and fusion plasmas. Though the Alfv\'en wave parametric decay instability was predicted decades ago,…
This paper addresses the problem of computing the eigenvalues lying in the gaps of the essential spectrum of a periodic Schrodinger operator perturbed by a fast decreasing potential. We use a recently developed technique, the so called…
To obtain a local description from highly accurate density functional theory codes that are based on modified plane wave bases, a transformation to a local orthonormal Wannier function basis is required. In order to do so while enforcing…