Related papers: On the Use of Vector Spherical Harmonics
The analysis of vector fields is crucial for the understanding of several physical phenomena, such as natural events (e.g., analysis of waves), diffusive processes, electric and electromagnetic fields. While previous work has been focused…
Research on spatially-structured light has seen an explosion in activity over the past decades, powered by technological advances for generating such light, and driven by questions of fundamental science as well as engineering applications.…
Astronomical data does not always use Cartesian coordinates. Both all-sky observational data and simulations of rotationally symmetric systems, such as accretion and protoplanetary discs, may use spherical polar or other coordinate systems.…
Advances in optical astrometry allow us to infer the non-radial kinematic structure of the Universe directly from observations. Here I use a supervised machine learning neural network method to predict 1.57 million redshifts based on…
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 of gravitational or scalar fields. In this work we…
In this paper I shall consider various possible scalar-vector-tensor field theories which might be used to describe the Universe. After imposing numerous constraints of a physical and mathematical nature on the theories under consideration,…
We explore the scale and angular dependence of the cosmic shear three-point correlation function. The shear field is found to have a much more complex three-point function than the convergence field, but it also exhibits specific motifs…
In cosmological perturbation theory it is convenient to use the scalar, vector, tensor (SVT) basis as defined according to how these components transform under 3-dimensional rotations. In attempting to solve the fluctuation equations that…
We investigate the correlations in galaxy shapes between optical and radio wavelengths using archival observations of the COSMOS field. Cross-correlation studies between different wavebands will become increasingly important for precision…
Vectors fields defined on surfaces constitute relevant and useful representations but are rarely used. One reason might be that comparing vector fields across two surfaces of the same genus is not trivial: it requires to transport the…
While a large fraction of the stars are in multiple systems, our understanding of the processes leading to the formation of these systems is still inadequate. Given the large theoretical uncertainties, observation plays a basic role. Here…
Examples are presented for appearance of geometric symmetry in the shape of various astronomical objects and phenomena. Usage of these symmetries in astrophysical and extragalactic research is also discussed.
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…
Increasing the complexity of a light field through the advanced manipulation of its degrees of freedom (DoF) provides new opportunities for fundamental studies and technologies. Correlating polarization with the light's spatial or spectral…
When modeling global satellite data to recover a planetary magnetic or gravitational potential field and evaluate it elsewhere, the method of choice remains their analysis in terms of spherical harmonics. When only regional data are…
We study the optimal use of third order statistics in the analysis of weak lensing by large-scale structure. These higher order statistics have long been advocated as a powerful tool to break measured degeneracies between cosmological…
This article gives the construction and complete classification of all three-dimensional spherical manifolds, and orders them by decreasing volume, in the context of multiconnected universe models with positive spatial curvature. It…
Vector beams are often regarded as non-separable superpositions of spatial and polarization degrees of freedom that satisfy the wave equation. This interpretation ties their polarization structure to their spatial shape. Here, we introduce…
Context. Recently our ability to study stars using asteroseismic techniques has increased dramatically, largely through the use of space based photometric observations. Work has also been done using ground based spectroscopic observations…
The fields of cosmic ray astrophysics, gamma-ray astrophysics, and neutrino astrophysics have diverged somewhat. But for the air showers in the GeV and TeV energy ranges, the ground-based detector techniques have considerable overlaps. VHE…