Related papers: Spheroidal harmonics for generalizing the morpholo…
We discuss in some details a novel algorithm for performing partial-sky spherical harmonic transforms (SHT), building on the Fourier-sphere method of Reinecke et al (2023) handling efficiently high numbers of arbitrary locations on the…
Understanding the mechanisms and spatial correlations of crystallographic symmetry breaking in ferroelectric materials is essential to tuning their functional properties. While optical second harmonic generation (SHG) has long been utilized…
The standard algorithm for the numerical evaluation of the prolate spheroidal wave function $\mathsf{Ps}\hskip.05em{}_{n}(x;\gamma^2)$ of order $0$, bandlimit $\gamma > 0$ and characteristic exponent $n$ has running time which grows with…
We propose SHARC, a novel framework that synthesizes arbitrary, genus-agnostic shapes by means of a collection of Spherical Harmonic (SH) representations of distance fields. These distance fields are anchored at optimally placed reference…
As shown recently [Phys. Rev. E 95, 033307 (2017)], spheroidal harmonics expansions are well suited for the external solution of Laplace's equation for a point source outside a spherical object. Their intrinsic singularity matches the line…
Depolarization dyadics play a central role in theoretical studies involving scattering from small particles and homogenization of particulate composite materials. Closed-form expressions for depolarization dyadics have been developed for…
In this paper, we compare two optimization algorithms using full Hessian and approximation Hessian to obtain numerical spherical designs through their variational characterization. Based on the obtained spherical design point sets, we…
We present a wave generalization of the classic Schwarzschild method for constructing self-consistent halos -- such a halo consists of a suitable superposition of waves instead of particle orbits, chosen to yield a desired mean density…
We seek to accelerate and increase the size of simulations for fluid-structure interactions (FSI) by using multiple resolutions in the spatial discretization of the equations governing the time evolution of systems displaying two-way…
The spheroidal wave functions, which are the solutions to the Helmholtz equation in spheroidal coordinates, are notoriously difficult to compute. Because of this, practically no programming language comes equipped with the means to compute…
A new means of incorporating radiative transfer into smoothed particle hydrodynamics (SPH) is introduced, which builds on the success of two previous methods - the polytropic cooling approximation as devised by Stamatellos et al (2007), and…
This paper presents a new approach for the computation of eigenvalues of the generalized spheroidal wave equations. The novelty of the present method is in the use of the analytical derivatives of the eigenvalues to minimize losses in…
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\infty$) coefficients. Our method does not rely on concepts of ergodicity or…
Many standard structural quantities, such as order parameters and correlation functions, exist for common condensed matter systems, such as spherical and rod-like particles. However, these structural quantities are often insufficient for…
We numerically simulate the uniform athermal shearing of bidisperse, frictionless, two dimensional spherocylinders and three dimensional prolate ellipsoids. We focus on the orientational ordering of particles as an asphericity parameter…
When using a formulation of Smooth Particle Hydrodynamics (SPH) which conserves momentum exactly the motion of the particles is observed to be unstable to negative stress. It is also found that under normal circumstances a lattice of SPH…
We show how to develop an expansion of nearly oblate systems in terms of a set of potential-density pairs. A harmonic (multipole) structure is imposed on the potential set at infinity, and the density can be made everywhere regular. We…
Curvilinear coordinate systems distinct from the rectangular Cartesian coordinate system are particularly valuable in the field calculations as they facilitate the expression of boundary conditions of differential equations in a reasonably…
We present a class of general prolate and oblate spheroidal spacetimes for the description of cosmic structures in the Universe. They are exact geometries which represent, in an appropriated way, the imbedding of spheroidal matter-energy…
In this article, we present a $T$-matrix method for numerical computation of second-harmonic generation from clusters of arbitrarily distributed spherical particles made of centrosymmetric optical materials. The electromagnetic fields at…