Related papers: A Note on Spherical Needlets
Needlets have been recognized as state-of-the-art tools to tackle spherical data, due to their excellent localization properties in both spacial and frequency domains. This paper considers developing kernel methods associated with the…
In this paper, a selection of elegant, highly symmetric examples of three-periodic tangled nets and filaments are presented. They are constructed via familiar crystal nets using edges as geometric scaffolds for n-fold helical windings.…
Quantum entanglement occurs not just in discrete systems such as spins, but also in the spatial wave functions of systems with more than one degree of freedom. It is easy to introduce students to entangled wave functions at an early stage,…
Methods of preparation and analysis of structured waves of light, electrons, and atoms have been advancing rapidly. Despite the proven power of neutrons for material characterization and studies of fundamental physics, neutron science has…
The connection between spherical harmonics and symmetric tensors is explored. For each spherical harmonic, a corresponding traceless symmetric tensor is constructed. These tensors are then extended to include nonzero traces, providing an…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic…
The representation of the potential energy surfaces of atom molecule or molecular dimers interactions should account faithfully for the symmetry properties of the systems, preserving at the same time a compact analytical form. To this aim,…
While many geological and geophysical processes such as the melting of icecaps, the magnetic expression of bodies emplaced in the Earth's crust, or the surface displacement remaining after large earthquakes are spatially localized, many of…
We construct the spin flaglet transform, a wavelet transform to analyze spin signals in three dimensions. Spin flaglets can probe signal content localized simultaneously in space and frequency and, moreover, are separable so that their…
This paper is concerned with spherical harmonics, and two refinements thereof: complex harmonics and symplectic harmonics. The reproducing kernels of the spherical and complex harmonics are explicitly given in terms of Gegenbauer or Jacobi…
The amount of information propagated by an intermediate heavy particle exhibits characteristic features in inelastic scatterings with $n\geq 3$ final particles. As the total energy increases, the entanglement entropy, between its decay…
Spherical wave functions play an important role in the theoretical study of antenna. When they are used to investigate the stored energy outside the circumscribing sphere of the antenna, two different types of modal quality factors appear…
In this article, we investigate the application of wavelet packet transform as a novel spectrum sensing approach. The main attraction for wavelet packets is the tradeoffs they offer in terms of satisfying various performance metrics such as…
Spherical Harmonics, $Y_\ell^m(\theta,\phi)$, are derived and presented (in a Table) for half-odd-integer values of $\ell$ and $m$. These functions are eigenfunctions of $L^2$ and $L_z$ written as differential operators in the…
Symmetries are known to dictate important physical properties and can be used as a design principle in particular in wave physics, including wave structures and the resulting propagation dynamics. Local symmetries, in the sense of a…
A spectral technique is applied to evaluate the resonance frequencies of the full retarded scattering from spherical nanoparticles. This approach allows one to unambiguously identify the modes that are responsible of both the peaks and the…
Recent research on needle beams and space-time wavepackets (STWPs) is presented. Quasi-nondiffracting STWPs propagate at stable spatial and temporal localization over extended distances. In a simple model, STWPs are interpreted as being…
We construct a directional spin wavelet framework on the sphere by generalising the scalar scale-discretised wavelet transform to signals of arbitrary spin. The resulting framework is the only wavelet framework defined natively on the…
We develop a technique to directly study spinons (emergent spin S = 1/2 particles) in quantum spin models in any number of dimensions. The size of a spinon wave packet and of a bound pair (a triplon) are defined in terms of wave-function…