Related papers: Energy Propagation in Scattering Convolution Netwo…
A hallmark of integrable systems is the purely elastic scattering of their excitations. Such systems possess an extensive number of locally conserved charges, leading to the conservation of the number of scattered excitations, as well as…
Waves entering a spatially uniform lossy medium typically undergo exponential decay, arising from either the energy loss of the Beer-Lambert-Bouguer transmission law or the evanescent penetration during reflection. Recently, exceptional…
We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation…
Characterizing distinct electron wave packets is a basic task for solid-state electron quantum optics with applications in quantum metrology and sensing. A important circuit element for this task is a non-stationary potential barrier than…
Wavefront shaping enables targeted delivery of coherent light into random-scattering media, such as biological tissue, by constructive interference of scattered waves. However, broadband waves have short coherence times, weakening the…
We study the elastic scattering of slow electrons by two-atomic molecule in the frame of non-overlapping atomic potentials model. The molecular continuum wave function is represented as a combination of a plane wave and two spherical…
We introduce a two-layer wavelet scattering network, for object classification. This scattering transform computes a spatial wavelet transform on the first layer and a new joint wavelet transform along spatial, angular and scale variables…
This paper concerns the derivation of radiative transfer equations for acoustic waves propagating in a randomly fluctuating slab (between two parallel planes) in the weak-scattering regime, and the study of boundary effects through an…
We prove local and global energy decay for the asymptotically periodic damped wave equation on the Euclidean space. Since the behavior of high frequencies is already mostly understood, this paper is mainly about the contribution of low…
Conditions are established for the existence of a scattering length and an effective range in the low-energy expansion of the S-wave phase-shift of a central potential in two and three dimensions. The behavior of the phase-shift as a…
The diffusion model is used to calculate the time-averaged flow of particles in stochastic media and the propagation of waves averaged over ensembles of disordered static configurations. For classical waves exciting static disordered…
Previous theoretical studies have shown that attosecond electron dynamics can, in principle, be captured in electron momentum spectroscopy (EMS) using ultrashort electron pulses. By including further analytical considerations on the…
This work introduces a wavelet neural network to learn a filter-bank specialized to fit non-stationary signals and improve interpretability and performance for digital signal processing. The network uses a wavelet transform as the first…
An efficient numerical quadrature is proposed for the approximate calculation of the potential energy in the context of pseudo potential electronic structure calculations with Daubechies wavelet and scaling function basis sets. Our…
In this article, a numerical analysis of the asymptotic behavior of the discrete energy associated to a dissipative coupled wave system is conducted. The numerical approximation of the system is constructed using the P1 finite element…
In this paper we consider the local energy decay result for wave equations with a short-range potential. It is important to note that one never uses a finite speed of propagation property unlike the historical previous papers. The essential…
This paper focuses on improving the mathematical interpretability of convolutional neural networks (CNNs) in the context of image classification. Specifically, we tackle the instability issue arising in their first layer, which tends to…
Interaction of electromagnetic, acoustic and even gravitational waves with accelerating bodies forms a class of nonstationary time-variant processes. Scattered waves contain intrinsic signatures of motion, which manifest in a broad range of…
A wavelet transform spectrum analyzer operating in real time within the frequency range 3X10^(-5) - 1.3X10^5 Hz has been implemented on a low-cost Digital Signal Processing board operating at 150MHz. The wavelet decomposition of the signal…
We consider a beam and a wave equations coupled on an elastic beam through transmission conditions. The damping which is locally distributed acts through one of the two equations only; its effect is transmitted to the other equation through…