Related papers: On the Use of Vector Spherical Harmonics
The vector transform operators are investigated; these operators are used at the solution of boundary value problems in piecewise homogeneous spherically symmetric areas. In particular, examples of transformation operators for vector…
Star glyphs are a well-researched visualization technique to represent multi-dimensional data. They are often used in small multiple settings for a visual comparison of many data points. However, their overall visual appearance is strongly…
Retrieval of classical behaviour in quantum cosmology is usually discussed in the framework of minisuperspace models in the presence of scalar fields together with the inhomogeneous modes either of the gravitational or of the scalar fields.…
We apply Velocity Channel Gradients (VChGs) and Reduced Velocity Centroids Gradients (RVCGs) to H I data (the LAB survey), obtaining the plane-of-sky component (POS) of the magnetic field as a function of the relative velocity. Assuming a…
Astronomical observations, physical experiments as well as computer simulations often involve discrete data sets supposed to represent a fair sample of an underlying smooth and continuous field. Reconstructing the underlying fields from a…
Stars on the lower main sequence (F-type through M-type) have substantial convective envelopes beneath their stellar photospheres. Convection in these regions can couple with rotation to build global-scale structures that may be observable…
Weak gravitational lensing provides a unique method to map directly the distribution of dark matter in the universe and to measure cosmological parameters. This cosmic-shear technique is based on the measurement of the weak distortions that…
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…
Machine learning methods based on statistical principles have proven highly successful in dealing with a wide variety of data analysis and analytics tasks. Traditional data models are mostly concerned with independent identically…
Graph vertex ordering is widely employed in spatial data analysis, especially in urban analytics, where street graphs serve as spatial discretization for modeling and simulation. It is also crucial for visualization, as many methods require…
We develop a systematic framework for constructing spherical harmonics on the two-dimensional unit sphere as superpositions of Gaussian beams whose poles form well-separated point configurations. The distributional and analytic properties…
Gravitational waves perturb the paths of photons, impacting both the time-of-flight and the arrival direction of light from stars. Pulsar timing arrays can detect gravitational waves by measuring the variations in the time of flight of…
We re-examine the effects of redshift space distortion in all-sky galaxy redshift surveys in the formalism of spherical harmonics. Within this framework we show how one can treat both the large-scale linear effects, and the small-scale…
Sky surveys represent a fundamental data basis for astronomy. We use them to map in a systematic way the universe and its constituents, and to discover new types of objects or phenomena. We review the subject, with an emphasis on the…
Astronomical images are of crucial importance for astronomers since they contain a lot of information about celestial bodies that can not be directly accessible. Most of the information available for the analysis of these objects starts…
We generalize the definition of convolution of vectors and tensors on the 2-sphere, and prove that it commutes with differential operators. Moreover, vectors and tensors that are normal/tangent to the spherical surface remain so after the…
Like every other field of intellectual endeavor, astronomy is being revolutionised by the advances in information technology. There is an ongoing exponential growth in the volume, quality, and complexity of astronomical data sets, mainly…
We analyze a technique of obtaining turbulence power spectrum using spectral line data along the velocity coordinate, which we refer to as Velocity Coordinate Spectrum (VCS). We formalize geometrical aspects of observation through a single…
The Cartesian coordinate system is the most commonly used system in computer visualization. This is due to its ease of use and processing speed. However, it is not always suitable for a given problem. Angular measures often allow us to…
We present a review of data types and statistical methods often encountered in astronomy. The aim is to provide an introduction to statistical applications in astronomy for statisticians and computer scientists. We highlight the complex,…