Related papers: Spheroidal harmonics for generalizing the morpholo…
The use of adaptive spatial resolution to simulate flows of practical interest using Smoothed Particle Hydrodynamics (SPH) is of considerable importance. Recently, Muta and Ramachandran [1] have proposed an efficient adaptive SPH method…
The objective of polarization rendering is to simulate the interaction of light with materials exhibiting polarization-dependent behavior. However, integrating polarization into rendering is challenging and increases computational costs…
In this paper we develop a dual-support smoothed particle hydrodynamics (DS-SPH) that naturally satisfies the conservation of momentum, angular momentum and energy when the varying smoothing length is utilized. The DS-SPH is based on the…
Electromagnetic interaction between a sub-wavelength particle (the `probe') and a material surface (the `sample') is studied theoretically. The interaction is shown to be governed by a series of resonances corresponding to surface polariton…
In the last decade diffusion MRI has become a powerful tool to non-invasively study white-matter integrity in the brain. Recently many research groups have focused their attention on multi-shell spherical acquisitions with the aim of…
Satellites mapping the spatial variations of the gravitational or magnetic fields of the Earth or other planets ideally fly on polar orbits, uniformly covering the entire globe. Thus, potential fields on the sphere are usually expressed in…
The shapelets method for image analysis is based upon the decomposition of localised objects into a series of orthogonal components with convenient mathematical properties. We extend the "Cartesian shapelet" formalism from earlier work, and…
Recent work by McClarren & Hauck [29] suggests that the filtered spherical harmonics method represents an efficient, robust, and accurate method for radiation transport, at least in the two-dimensional (2D) case. We extend their work to the…
Smoothed Particle Hydrodynamics (SPH) is a Lagrangian method for solving the fluid equations that is commonplace in astrophysics, prized for its natural adaptivity and stability. The choice of variable to smooth in SPH has been the topic of…
We introduce adaptive particle refinement for compressible smoothed particle hydrodynamics (SPH). SPH calculations have the natural advantage that resolution follows mass, but this is not always optimal. Our implementation allows the user…
The numerical calculation of optical properties (extinction, absorption, scattering and polarisation efficiencies) is often time-consuming for non-spherical and inhomogeneous particles. Where possible analytical methods are therefore to be…
Series representations consisting of spherical harmonics are obtained for characteristic exponents and probability density functions of multivariate stable distributions under various conditions. A esult potentially applicable in a…
We show that generalized spherical harmonics are well suited for representing the space and orientation molecular density in the resolution of the molecular density functional theory. We consider the common system made of a rigid solute of…
We analyze one particle, two-center quantum problems which admit separation of variables in prolate spheroidal coordinates, a natural restriction satisfied by the H$_2^+$ molecular ion. The symmetry operator is constructed explicitly. We…
In many astronomical works, the structure of vector fields is analyzed, such as the differences in the celestial object coordinates in catalogs or the celestial object velocities, by decomposition into vector spherical harmonics (VSH). This…
This paper presents a spline-based parameterisation framework for plane graphs. The plane graph is characterised by a collection of curves forming closed loops that fence-off planar faces which have to be parameterised individually. Hereby,…
The transport of charged particles or photons in a scattering medium can be modelled with a Boltzmann equation. The mathematical treatment for scattering in such scenarios is often simplified if evaluated in a frame where the scattering…
Micromagnetic tomography aims at reconstructing large numbers of individual magnetizations of magnetic particles from combining high-resolution magnetic scanning techniques with micro X-ray computed tomography (microCT). Previous work…
Confocal microscopy of fluorescent labeled particles has been used to study the dynamical and structural properties of colloidal and granular matter in real space. Localization algorithms allow for a fully automatized determination of the…
We propose a sampling scheme on the sphere and develop a corresponding spherical harmonic transform (SHT) for the accurate reconstruction of the diffusion signal in diffusion magnetic resonance imaging (dMRI). By exploiting the antipodal…