Related papers: Cosmic crystallography: the hyperbolic isometries
Diffuse and translucent molecular clouds fill a vast majority of the interstellar space in the galactic disk being thus the most typical objects of the Interstellar Medium (ISM). Recent advances in observational techniques of modern optical…
The thermodynamic interpretation of the Stephani Universes is studied in detail. The general expression of the speed of sound and of the thermodynamic schemes associated with a thermodynamic solution is obtained. The constraints imposed on…
The assumption that a complete description of an early state of the universe does not privilege any position or direction in space leads to a unified account of probability in cosmology, macroscopic physics, and quantum mechanics. Such a…
We explore the possibility that the entire departure of galactic rotational velocities from their luminous Newtonian expectation be cosmological in origin, and show that within the framework of conformal gravity (but not Einstein gravity…
Deconstruction provides a novel way of dealing with the notoriously difficult ultraviolet problems of four-dimensional gravity. This approach also naturally leads to a new perspective on the holographic principle, tying it to the…
Density profiles of cosmological virialized systems, or dark halos, have recently attracted much attention. I first present a brief historical review of numerical simulations to quantify the halo density profiles. Then I describe the latest…
Smectic liquid crystals vividly illustrate the subtle interplay of broken translational and orientational symmetries, by exhibiting defect structures forming geometrically perfect confocal ellipses and hyperbolas. Here, we develop and…
Starting from the (apparently) elementary problem of deciding how many different topological spaces can be obtained by gluing together in pairs the faces of an octahedron, we will describe the central role played by hyperbolic geometry…
Using the method of C. V\"or\"os, we establish results on hyperbolic plane geometry, related to triangles. In this note we investigate the orthocenter, the concept of isogonal conjugate and some further center as of the symmedian of a…
The Cosmological Principle states that the universe is both homogeneous and isotropic. This, alone, is not enough to specify the global geometry of the spacetime. If we were able to measure both the Hubble constant and the energy density we…
The recent high-quality measurements of the Cosmic Microwave Background anisotropies have presented cosmologists with the possibility of studying the large scale properties of our universe with unprecedented precision. Here I review the…
The concept of cross density of states characterizes the intrinsic spatial coherence of complex photonic or plasmonic systems, independently on the illumination conditions. Using this tool and the associated intrinsic coherence length, we…
We investigate what supersymmetry says about the geometry of the moduli space of hyperbolic monopoles. We construct a three-dimensional supersymmetric Yang-Mills-Higgs theory on hyperbolic space whose half-BPS configurations coincide with…
Probabilistic cross-identification has been successfully applied to a number of problems in astronomy from matching simple point sources to associating stars with unknown proper motions and even radio observations with realistic morphology.…
The polarization of the cosmic microwave background radiation will have a distribution of singularities and anti-singularities, points where the polarization vanishes for topological reasons. The statistics of polarization singularities…
One of the basic problems in discrete geometry is to determine the most efficient packing of congruent replicas of a given convex set $K$ in the plane or in space. The most commonly used measure of efficiency is density. Several types of…
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.
We consider hyperbolic projections of orbits of holomorphic self-maps of the unit disc, onto curves landing on the unit circle with a given angle. We show that under certain, necessary, assumptions, the projections exhibit monotonicity…
We compute boundary correlation functions for scalar fields on tessellations of two- and three-dimensional hyperbolic geometries. We present evidence that the continuum relation between the scalar bulk mass and the scaling dimension…
When flat or on a firm mechanical substrate, the atomic composition and atomistic structure of two-dimensional crystals dictate their chemical, electronic, optical, and mechanical properties. These properties change when the two-dimensional…