Related papers: Cosmic crystallography: the hyperbolic isometries
We examine a simple hard disc fluid with no long range interactions on the two dimensional space of constant negative Gaussian curvature, the hyperbolic plane. This geometry provides a natural mechanism by which global crystalline order is…
Isotropic cosmology built in the Riemann-Cartan spacetime is investigated. Properties of homogeneous isotropic cosmological models filled with usual gravitating matter and scalar fields are studied in the beginning of cosmological expansion…
The currently released datasets of the observational surveys reveal the redshift dependence of the physical features of cosmic voids. We study the void induced hyperbolicity, that is the deviation of the photon beams propagating the voids,…
The polarization of the CMBR represents a powerful test for modern cosmology. It allows to break the degeneracy of fundamental cosmological parameters, and also to observe the contribution of gravitational waves background to the CMBR…
We revisit the classification of polarization observables of the cosmic microwave background. There exists a unified approach to the $3 \times 3$ density matrix by which intensity, linear and circular polarization are treated on an equal…
Learning good image representations that are beneficial to downstream tasks is a challenging task in computer vision. As such, a wide variety of self-supervised learning approaches have been proposed. Among them, contrastive learning has…
Special relativity corresponds to hyperbolic geometry at constant velocity while the so-called general relativity corresponds to hyperbolic geometry of uniformly accelerated systems. Generalized expressions for angular momentum, centrifugal…
Observational Cosmology has indeed made very rapid progress in recent years. The ability to quantify the universe has largely improved due to observational constraints coming from structure formation Measurements of CMB anisotropy and, more…
The interaction between combinatorics and algebraic and differential geometry is very strong. While researching a problem of Hessian topology, we came across a series of identities of binomial coefficients, which are useful for proving a…
Isomerization, i.e. the rearrangement between distinct molecular configurations, is a fundamental process in chemistry. Here we demonstrate that two-dimensional Coulomb crystals can emulate molecular isomerization and be used to…
The measurements of CMB anisotropy have opened up a window for probing the global topology of the universe on length scales comparable to and beyond the Hubble radius. We have developed a new method for calculating the CMB anisotropy in…
We describe local similarities and global differences between minimal surfaces in Euclidean 3-space and constant mean curvature 1 surfaces in hyperbolic 3-space. We also describe how to solve global period problems for constant mean…
We classify isoparametric hypersurfaces in complex hyperbolic spaces.
Crochet models of a hyperbolic plane is a popular educational tool as they help to visualize complicated objets in hyperbolic geometry. We present another way how to make crochet models when we view them as a part of a triangulated…
We describe the needs and opportunities for preserving cosmology datasets and simulations, and facilitating their joint analysis beyond the lifetime of individual projects. We recommend that DOE fund a new cosmology data archive center to…
We study the growth of hyperbolic type distances in starlike domains. We derive estimates for various hyperbolic type distances and consider the asymptotic sharpness of the estimates.
This article provides a simple pictorial introduction to universal hyperbolic geometry. We explain how to understand the subject using only elementary projective geometry, augmented by a distinguished circle. This provides a completely…
We have presented computer simulations of conoscopic patterns occurring in optically uniaxial gyrotropic crystals in the vicinity of isotropic point for a number of sets of crystal parameters and orientations. The appearance of special…
The study of the properties of cosmic structures in the universe is one of the most fascinating subject of the modern cosmology research. Far from being predicted, the large scale structure of the matter distribution is a very recent…
Hypercontractive inequalities are a useful tool in dealing with extremal questions in the geometry of high-dimensional discrete and continuous spaces. In this survey we trace a few connections between different manifestations of…