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An overview of recent advances in the theory of critical phenomena in $d$-dimensional weakly anisotropic systems is given. On the basis of a generalized shear transformation between anisotropic and isotropic systems, exact and approximate…
The paper considers some class of dynamical systems that called density systems. For such systems the derivative of quadratic function depends on so-called density function. The density function is used to set the properties of phase space,…
We study the influence of surface anisotropy on the zero-temperature hysteretic properties of a small single-domain magnetic particle, and give an estimation of the anisotropy constant for which deviations from the Stoner-Wohlfarth model…
Self-similar solutions of the coherent diffusion equation are derived and measured. The set of real similarity solutions is generalized by the introduction of a nonuniform phase surface, based on the elegant Gaussian modes of optical…
The group of Conservative transformations is an enlargement of the group of diffeomorphisms which leads to a richer geometry than that of general relativity. The field variables of the theory are the usual orthonormal tetrads and also…
A rigorous homogenization theory is derived to describe the effective admittivity of cell suspensions. A new formula is reported for dilute cases that gives the frequency-dependent effective admittivity with respect to the membrane…
We prove a generalization of a so called "invariance principle" for partially hyperbolic diffeomorphisms: if an invariant probability measure has all its center Lyapunov exponents equal to zero then the measure admits a center…
Galactic nuclei, the densest stellar environments in the Universe, exhibit a complex geometrical structure. The stars orbiting the central supermassive black hole follow a mass segregated distribution both in the radial distance from the…
The relaxed distribution of stars around a massive black hole is known to follow a cusp profile $\rho(r)\propto r^{-\alpha}$ with characteristic slope $\alpha=7/4$. This follows from energy conservation and a scattering rate as given by two…
In this study we investigate potential large-angle anisotropies in the angular distribution of the cosmological parameters $H_0$ (the Hubble constant) and $\Omega_m$ (the matter density) in the flat-$\Lambda$CDM framework, using the…
We show that measuring the proper motion of ${{\sim 2000}}$ stars within a dwarf galaxy, with an uncertainty of 1 km/s at most, can establish whether the Dark Matter (DM) density profile of the dwarf has a central core or cusp. We derive…
To better understand the evolution of stars in binary systems as well as to constrain the formation of binary stars, it is important to know the binary mass-ratio distribution. However, in most cases, i.e. for single-lined spectroscopic…
We studied five methods to include anisotropy, or unequal stress distributions, in general relativistic matter configurations. We used nine acceptability conditions that the metric and physical variables must meet to determine if our models…
We develop the complete theory for the collective plasmon modes of an interacting electron system in the presence of explicit mass (or velocity) anisotropy in the corresponding non-interacting situation, with the effective Fermi velocity…
We study the dynamics of a collisionless kinetic gas whose particles follow future-directed timelike and spatially bound geodesics in the exterior of a sub-extremal Kerr black hole spacetime. Based on the use of generalized action-angle…
In materials science the phase field crystal approach has become popular to model crystallization processes. Phase field crystal models are in essence Landau-Ginzburg-type models, which should be derivable from the underlying microscopic…
Massive early-type galaxies are observed to lie on the Mass Plane (MP), a two-dimensional manifold in the space of effective radius R_e, projected mass M_p (measured via strong gravitational lensing) and projected velocity dispersion sigma…
Several general trends have been identified for equilibrated, self-gravitating collisionless systems, such as density or anisotropy profiles. These are integrated quantities which naturally depend on the underlying velocity distribution…
In the past two decades, it has been established by high-resolution observations of early-type galaxies that their nuclear surface brightness and corresponding stellar mass densities are characterized by cusps. In this paper, we present a…
The cosmological principle, as the cornerstone of the standard cosmological model, requires that the Universe be homogeneous and isotropic on large scales. As a fundamental assumption, it is constantly subjected to testing via various…