Related papers: Physical geometry of the quasispherical Szekeres m…
This paper continues our study of quasicrystals initiated in Part I. We propose a general mechanism for constructing quasicrystals, existing globally in time, in spatially-extended systems (partial differential equations with Euclidean…
We investigate the asymptotic properties of axisymmetric inertial modes propagating in a spherical shell when viscosity tends to zero. We identify three kinds of eigenmodes whose eigenvalues follow very different laws as the Ekman number…
The quasispecies model introduced by Eigen in 1971 has close connections with the isometry group of the space of binary sequences relative to the Hamming distance metric. Generalizing this observation we introduce an abstract quasispecies…
The purpose of this article is to exploit the geometric structure of Quantum Mechanics and of statistical manifolds to study the qualitative effect that the quantum properties have in the statistical description of a system. We show that…
We use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation,…
A closed mathematical model of the statistical self-gravitating system of scalar charged particles for conformal invariant scalar interactions is constructed on the basis of relativistic kinetics and gravitation theory. Asymptotic…
We show that the Szekeres system with cosmological constant admits a sufficient number of conservation laws, which allow to claim the integrability of the system. The main novelty in this investigation is that we find that the unique…
We provide a comprehensive overview of metric-affine geometries with spherical symmetry, which may be used in order to solve the field equations for generic gravity theories which employ these geometries as their field variables. We discuss…
According to the socalled "quasi-metric" framework developed elsewhere, the cosmic expansion applies directly to gravitationally bound systems. This prediction has a number of observable consequences, none of which are in conflict with…
We present a class of exact solutions of Einstein's gravitational field equations describing spherically symmetric and static anisotropic stellar type configurations. The solutions are obtained by assuming a particular form of the…
With the era of precision cosmology upon us, and upcoming surveys expected to further improve the precision of our observations below the percent level, ensuring the accuracy of our theoretical cosmological model is of the utmost…
The Tolman~VII solution, an exact analytic solution to the spherically symmetric, static Einstein equations with a perfect fluid source, has many characteristics that make it interesting for modelling high density physical astronomical…
The existence of macroscopic shell structure of submicron metal clusters is known for several decades. Since the most studies provide theoretical analysis for clusters of spherical shape, the electron density inhomogeneities caused by shell…
We discuss Sasakian-Einstein geometry under a quasi-regularity assumption. It is shown that the space of all quasi-regular Sasakian-Einstein orbifolds has a natural multiplication on it. Furthermore, necessary and sufficient conditions are…
In this thesis we investigate cosmological models more general than the isotropic and homogeneous Friedmann-Lemaitre models. We focus on cosmologies with one spatial degree of freedom, whose matter content consists of a perfect fluid and…
The classical field equations of general relativity can be expressed as a single geodesic equation, describing the free fall of a point particle in superspace. Based on this formulation, a ``worldline'' quantization of gravity, analogous to…
Variables adapted to the quantum dynamics of spherically symmetric models are introduced, which further simplify the spherically symmetric volume operator and allow an explicit computation of all matrix elements of the Euclidean and…
Quasicrystals are characterized by quasi-periodic arrangements of atoms. The description of their mechanics involves deformation and a (so called phason) vector field accounting at macroscopic scale of local phase changes, due to atomic…
I give a brief overview of the mathematical theory of Noether symmetries of multifield cosmological models, which decompose naturally into visible and Hessian (a.k.a. 'hidden') symmetries. While visible symmetries correspond to those…
Applying the method of conformal metric to a given static axially symmetric vacuum solution of the Einstein equations, we have shown that there is no solution representing a cosmic ideal fluid which is asymtotically FLRW. Letting the cosmic…