Related papers: Spheroidal harmonics for generalizing the morpholo…
Second-order self-force calculations will be critical for modelling extreme-mass-ratio inspirals, and they are now known to have high accuracy even for binaries with mass ratios $\sim 1:10$. Many of the challenges facing these calculations…
A sphere is a fundamental geometric object widely used in (computer aided) geometric design. It possesses rational parameterizations but no parametric polynomial parameterization exists. The present study provides an approach to the optimal…
It is commonplace in cosmology to analyze fields projected onto the celestial sphere, and in particular density fields that are defined by a set of points e.g. galaxies. When performing an harmonic-space analysis of such data (e.g. an…
The calculation of potential energy surfaces for quantum dynamics can be a time consuming task -- especially when a high level of theory for the electronic structure calculation is required. We propose an adaptive interpolation algorithm…
Harmonic analysis is a tool to infer cosmic topology from the measured astrophysical cosmic microwave background CMB radiation. For overall positive curvature, Platonic spherical manifolds are candidates for this analysis. We combine the…
The application of orthonormal basis functions such as Prolate Spheroidal Wave Functions (PSWF) for accurate source modeling in radio astronomy has been comprehensively studied. They are of great importance for high fidelity, high dynamic…
We propose the Particle Swarm Optimization (PSO) as an alternative method for locating periodic orbits in a three--dimensional (3D) model of barred galaxies. We develop an appropriate scheme that transforms the problem of finding periodic…
The problem of scattering of harmonic plane acoustic waves by fluid spheroids (prolate and oblate) is addressed from an analytical approach. Mathematically, it consists in solving the Helmholtz equation in an unbounded domain with…
In two previous papers (Price & Monaghan 2004a,b) (papers I,II) we have described an algorithm for solving the equations of Magnetohydrodynamics (MHD) using the Smoothed Particle Hydrodynamics (SPH) method. The algorithm uses dissipative…
Classical periodic orbits responsible for emergence of the superdeformed shell structures for single-particle motions in spheroidal cavities are identified and their relative contributions to the shell structures are evaluated. Both prolate…
This work presents a theoretical formalism and the corresponding numerical techniques to obtain the approximation of fractional-order operators over a 1D domain via the smoothed particle hydrodynamics (SPH) method. The method is presented…
We provide a detailed user guide for SMARTIES, a suite of Matlab codes for the calculation of the optical properties of oblate and prolate spheroidal particles, with comparable capabilities and ease-of-use as Mie theory for spheres.…
We here calculate the series expansion of the T-matrix for a spheroidal particle in the small-size/long-wavelength limit, up to third lowest order with respect to the size parameter, X, which we will define rigorously for a non-spherical…
Fluid-Structure Interaction (FSI) is a crucial problem in ocean engineering. The smoothed particle hydrodynamics (SPH) method has been employed recently for FSI problems in light of its Lagrangian nature and its advantage in handling…
We develop an efficient numerical method for calculating the image stress field induced by spherical voids in materials. The method is applied to dislocation-void interactions in dislocation dynamics simulations. We obtain a complete set of…
This paper develops an arbitrary-positioned buffer for the smoothed particle hydrodynamics (SPH) method, whose generality and high efficiency are achieved through two techniques. First, with the local coordinate system established at each…
We construct bases of polynomials for the spaces of square-integrable harmonic functions which are orthogonal to the monogenic and antimonogenic $\mathbb{R}^3$-valued functions defined in a prolate or oblate spheroid.
In this work we study orbit recovery over $SO(3)$, where the goal is to recover a function on the sphere from noisy, randomly rotated copies of it. We assume that the function is a linear combination of low-degree spherical harmonics. This…
Comparison of stellar catalogues with position and proper motion components using a decomposition on a set of orthogonal vector spherical harmonics. We show the theoretical and practical advantages of this technique as a result of…
I present a review of Smoothed Particle Hydrodynamics (SPH), with the aim of providing a mathematically rigorous, clear derivation of the algorithms from first principles. The method of discretising a continuous field into particles using a…