Publications related to Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author ha ...

Int Center Scientific Research & Studies2017

Discreteness of interior transmission eigenvalues revisited

Hoài-Minh Nguyên, Quoc Hung Nguyen

This paper is devoted to the discreteness of the transmission eigenvalue problems. It is known that this problem is not self-adjoint and a priori estimates are non-standard and do not hold in general. Two approaches are used. The first one is based on the ...

Springer Verlag2017

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

Nikola Besic, Urs Martin Germann, Daniele Nerini

In this paper we present a non-stationary stochastic generator for radar rainfall fields based on the short-space Fourier transform (SSFT). The statistical properties of rainfall fields often exhibit significant spatial heterogeneity due to variability in ...

Copernicus GmbH2017

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

Undecidability through Fourier series

In computability theory a variety of combinatorial systems are encountered (word problems, production systems) that exhibit undecidability properties. Here we seek such structures in the realm of Analysis, more specifically in the area of Fourier Analysis. ...

Elsevier Science Bv2016

A sparse reconstruction framework for Fourier-based plane wave imaging

Jean-Philippe Thiran, Yves Wiaux, Rafael Eduardo Carrillo Rangel, Adrien Georges Jean Besson, Olivier Bernard

Ultrafast imaging based on plane-wave (PW) insonification is an active area of research due to its capability of reaching high frame rates. Among PW imaging methods, Fourier-based approaches have demonstrated to be competitive compared to traditional delay ...

Ieee-Inst Electrical Electronics Engineers Inc2016

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model

Hoài-Minh Nguyên

This paper concerns approximate cloaking by mapping for a full, but scalar wave equation, when one allows for physically relevant frequency dependence of the material properties of the cloak. The paper is a natural continuation of [20], but here we employ ...

Elsevier2016

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

Matthieu Martin Jean-André Simeoni

The Square Kilometre Array (SKA) will form the largest radio telescope ever built, generating on the order of one terabyte of data per second. To reduce the data flow sent to the central processor, hierarchical designs have been proposed: the data is prima ...

2015

Divergence-Free Wavelet Frames

Michaël Unser, Emrah Bostan, John Paul Ward

We propose an efficient construction of wavelet frames in any number of dimensions that are divergence-free. Our approach is based on applying the Leray projector, which is scale-invariant, to a standard wavelet frame. We prove that the projected wavelets ...

Ieee-Inst Electrical Electronics Engineers Inc2015

Propagation of the Lower Hybrid wave in a density fluctuating SOL

Joan Decker

The perturbation of the lower hybrid wave (LH) power spectrum by fluctuations of the plasma in the vicinity of the antenna is investigated by solving the full wave equation in a slab geometry using COMSOL MultiphysicsÂ®. The numerical model whose generalit ...

2015

Stable Manifold for the Critical Non-Linear Wave Equation: A Fourier Theory Approach

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Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Discreteness of interior transmission eigenvalues revisited

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Undecidability through Fourier series

A sparse reconstruction framework for Fourier-based plane wave imaging

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

Divergence-Free Wavelet Frames

Propagation of the Lower Hybrid wave in a density fluctuating SOL

A non-stationary stochastic ensemble generator for radar rainfall fields based on the short-space Fourier transform

Undecidability through Fourier series

A sparse reconstruction framework for Fourier-based plane wave imaging

Towards More Accurate and Efficient Beamformed Radio Interferometry Imaging

Divergence-Free Wavelet Frames

Propagation of the Lower Hybrid wave in a density fluctuating SOL

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Discreteness of interior transmission eigenvalues revisited

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Approximate cloaking for the full wave equation via change of variables: The Drude-Lorentz model