Related papers: Analytical calculation of the solid angle subtende…
We derive analytical expressions for the solid angle subtended by a right finite circular cylinder at a point source with cosine angular distribution in the case where the source direction is parallel to the cylinder axis. As a subsidiary…
We derive analytical expressions for the solid angle subtended by a right circular cylinder at a point source with cosine angular distribution in the case where the source and the cylinder axes are mutually orthogonal.
The solid angle subtended by a right circular cylinder at a point source located at an arbitrary position generally consists of a sum of two terms: that defined by the cylindrical surface ($\Omega_{cyl}$) and the other by either of the end…
Closed form solutions for the computation of the solid angle from polygonal cross-sections are well known, however similar formulae for computation of projected solid angle are not generally available. Formulae for computing the projected…
We find, from our study of binary spiral galaxies in the Sloan Digital Sky Survey Data Release 6, that the relative orientation of disks in binary spiral galaxies is consistent with their being drawn from a random distribution of…
This paper addresses the computation of normalized solid angle measure of polyhedral cones. This is well understood in dimensions two and three. For higher dimensions, assuming that a positive-definite criterion is met, the measure can be…
Position angle measurements of Sloan Digital Sky Survey (SDSS) galaxies, as measured by the surface brightness profile fitting code of the SDSS photometric pipeline (Lupton 2001), are known to be strongly biased, especially in the case of…
We propose an analytical method to describe a matter density profile near a galaxy center. The description is based on the study of the distribution function of particles over possible trajectories. We establish a relation between the…
Motivated by models in engineering and also biology we determine in closed form the probability density function of the angle shaped by two random chords in a fixed disc. Our main result focus on the event in which the intersection locates…
Using smoothed particle hydrodynamics, we numerically simulate steady state accretion discs for Cataclysmic Variable Dwarf Novae systems that have a secondary-to-primary mass ratio (0.35 \le q \le 0.55). After these accretion discs have…
This paper presents formulae for calculation the solid angle of intersecting spherical caps, conical surfaces and polyhedral cones.
The fuzzy disc, introduced by the authors of Ref.[1], is a disc-shaped region in a noncommutative plane, and is a fuzzy approximation of a commutative disc. In this paper we show that one can introduce a concept of angles to the fuzzy disc,…
We give a new characterization of pseudoconvex point, and of finite type point, using analytic discs.
Observations of non-random distribution of galaxies with opposite spin directions have recently attracted considerable attention. Here, a method for identifying cosine-dependence in a dataset of galaxies annotated by their spin directions…
We propose and demonstrate a computational imaging technique that uses structured illumination based on a two-dimensional discrete cosine transform to perform imaging with a single-pixel detector. A scene is illuminated by a projector with…
Compton scattering by a locally plane parallel atmosphere is analyzed within the Kompaneets approximation. In contrast to almost all previous analytic calculations of inverse Compton scattering, we assume neither homogeneity nor isotropy of…
Emission from an accretion disc around compact objects, such as neutron stars and black holes, is expected to be significantly polarized. The polarization can be used to put constraints on geometrical and physical parameters of the compact…
Analytical solutions to acoustic scattering problems involving nonspherical shapes, such as spheroids and disks, have long been known and have many applications. However, these solutions require special functions that are not easily…
A new method to calculate the electric field inside a spherical shell with surface charge in terms of solid angle is presented. The integral can be readily carried out without invoking special functions typically used for this classical…
Analytical models of axially symmetric thin disks of finite extension in presence of magnetic field are presented based on the well-known Morgan-Morgan solutions. The source of the magnetic field is cons\-tructed separating the equation…