Related papers: Energy Propagation in Scattering Convolution Netwo…
In this paper, we consider the scattering theory for acoustic-type equations on non-compact manifolds with a single flat end. Our main purpose is to show an existence result of non-scattering energies. Precisely, we show a Weyl-type lower…
A grand challenge in fundamental physics and practical applications is overcoming wave diffusion to deposit energy into a target region deep inside a diffusive system. While it is known that coherently controlling the incident wavefront…
In this paper, we study the asymptotic decay properties for defocusing semilinear wave equations in $\mathbb{R}^{1+2}$ with pure power nonlinearity. By applying new vector fields to null hyperplane, we derive improved time decay of the…
In this work we analytically calculate the time-averaged electromagnetic energy stored inside a nondispersive magnetic isotropic cylinder which is obliquely irradiated by an electromagnetic plane wave. An expression for the…
Deep convolutional neural networks have led to breakthrough results in numerous practical machine learning tasks such as classification of images in the ImageNet data set, control-policy-learning to play Atari games or the board game Go,…
We prove decay with respect to some Lebesgue norms for a class of Schr\"odinger equations with non-local nonlinearities by showing new Morawetz inequalities and estimates. As a byproduct, we obtain large-data scattering in the energy space…
Energy detection is a reliable non-coherent signal processing technology of spectrum sensing of cognitive radio networks, which thanks to its low complexity, no requirement of priori received information and fast sensing ability etc. Since…
Motivated by numerically modeling surface waves for inviscid Euler equations, we analyze linear models for damped water waves and establish decay properties for the energy for sufficiently regular initial configurations. Our findings give…
We study the defocusing energy-critical nonlinear wave equation in four dimensions. Our main result proves the stability of the scattering mechanism under random pertubations of the initial data. The random pertubation is defined through a…
Dynamic modulation of material properties in space and time enables powerful control over wave propagation, yet existing theories largely rely on idealized, nondispersive models. In realistic media, frequency dispersion can strongly reshape…
We have studied the times delay of slow electrons scattered by a spherically symmetric rectangular potential well as functions of the well parameters. We have shown that the electron interaction with the scattering center qualitatively…
Inspired by edge detection based on the decay behavior of wavelet coefficients, we introduce a (near) linear-time algorithm for detecting the local regularity in non-uniformly sampled multivariate signals. Our approach quantifies regularity…
The presence of a scattering medium in the imaging path between an object and an observer is known to severely limit the visual acuity of the imaging system. We present an approach to circumvent the deleterious effects of scattering, by…
The constant center frequency to bandwidth ratio (Q-factor) of wavelet transforms provides a very natural representation for audio data. However, invertible wavelet transforms have either required non-uniform decimation -- leading to…
We investigate scattering, localization and dispersive time-decay properties for the one-dimensional Schr\"odinger equation with a rapidly oscillating and spatially localized potential, $q_\epsilon=q(x,x/\epsilon)$, where $q(x,y)$ is…
The topic of this paper is a semi-linear, defocusing wave equation $u_{t t}-\Delta u=-|u|^{p-1} u$ in sub-conformal case in the higher dimensional space whose initial data are radical and come with a finite energy. We prove some decay…
We consider Morawetz estimates for weighted energy decay of solutions to the wave equation on scattering manifolds (i.e., those with large conic ends). We show that a Morawetz estimate persists for solutions that are localized at low…
We study the influence on diffusion in one dimension of a potential energy perturbation varying as a power in space and time. We concentrate on the case of a parabolic perturbation in space decaying as $t^{-\omega}$ which shows a rich…
The energy extinction cross section of a concentrically layered sphere varies with velocity as the Doppler shift moves the spectral content of the incident signal in the sphere's co-moving inertial reference frame toward or away from…
The performance of communication systems is fundamentally limited by the loss of energy through propagation and circuit inefficiencies. In this article, we show that it is possible to achieve ultra low energy communications at the…