Related papers: The linear eigenvalue problem for barotropic selfg…

The paper concerns the discreteness of the eigenvalues and the solvability of the interior transmission problem for anisotropic media. Conditions for the ellipticity of the problem are written explicitly, and it is shown that they do not…

Gravitational waves from neutron-star and black-hole binaries carry valuable information on their physical properties and probe physics inaccessible to the laboratory. Although development of black-hole gravitational-wave templates in the…

We extensively develop a perturbation theory for nonlinear cosmological dynamics, based on the Lagrangian description of hydrodynamics. We solve hydrodynamic equations for a self-gravitating fluid with pressure, given by a polytropic…

In this paper we propose a new method for reconstructing the surface density of matter in flat disks of spiral galaxies. The surface density is expressed through observational rotation velocity curves of visible matter in the disks of…

We propose an explanation of features of spiral galaxies: spiral arms and observed flat rotation curves, without the presence of an exotic form of matter. The formalism is based on Boltzmanns transport equation for the collisional matter…

In this paper, we discuss numerical approximation of the eigenvalues of the one-dimensional radial Schr\"{o}dinger equation posed on a semi-infinite interval. The original problem is first transformed to one defined on a finite domain by…

In the density wave theory of spiral structure, the grand-design two-armed spiral pattern is taken to rotate rigidly in a galactic disc with a constant, definite pattern speed. The observational measurement of the pattern speed of the…

We study how well the complex gas velocity fields induced by massive spiral arms are modelled by the hydrodynamical simulations we used to constrain the dark matter fraction in nearby spiral galaxies (Kranz et al. 2001, 2003). More…

We consider a product of an arbitrary number of independent rectangular Gaussian random matrices. We derive the mean densities of its eigenvalues and singular values in the thermodynamic limit, eventually verified numerically. These…

Previously, we showed that surface density profiles of the form of a power-law times a Sersic function satisfy the hydrostatic Jeans equations, a variety of observational constraints, and the condition of a minimal radial entropy profile in…

I utilize the Petrov-Galerkin formulation and develop a new method for solving the unsteady collisionless Boltzmann equation in both the linear and nonlinear regimes. In the first order approximation, the method reduces to a linear…

We studied global nonaxisymmetric hydrodynamic instabilities in an extensive collection of hot, self-gravitating polytropic disk systems, systems that covered a wide expanse of the parameter space relevant to protostellar and protoplanetary…

The origin of magnetic fields in the universe still remains unknown and constitutes one of the most intriguing questions in astronomy and astrophysics. Their significance is enormous since they have a strong influence on many astrophysical…

By means of 3D hydrodynamical simulations, in a separate paper we have discussed the properties of non-axisymmetric density wave trains in the outermost regions of galaxy disks, based on the picture that self-excited global spiral modes in…

A dispersion relation for gravity waves in water covered by disk-like impurities embedded in a viscous matrix is derived. The macroscopic equations are obtained by ensemble-averaging the fluid equations at the disk scale in the asymptotic…

Rotating spiral waves organize spatial patterns in chemical, physical and biological excitable systems. Factors affecting their dynamics such as spatiotemporal drift are of great interest for par- ticular applications. Here, we propose a…

Three-dimensional geophysical fluids support both internal and boundary-trapped waves. To obtain the normal modes in such fluids we must solve a differential eigenvalue problem for the vertical structure (for simplicity, we only consider…

A thin gaseous disk has often been investigated in the context of various phenomena in galaxies, which point to the existence of starburst rings and dense circumnuclear molecular disks. The effect of self-gravity of the gas in the 2D disk…

We study a spherical, self-gravitating fluid model, which finds applications in cosmic structure formation. We argue that since the system features nonlinearity and gravity-induced dispersion, the emergence of solitons becomes possible. We…

Scattered light images of transition discs in the near-infrared often show non-axisymmetric structures in the form of wide-open spiral arms in addition to their characteristic low-opacity inner gap region. We study self-gravitating discs…