Related papers: Analytical Potential-Density Pairs for Flat Rings …
The complex-shift method is applied to the Kuzmin-Toomre family of discs to generate a family of non-axisymmetric flat distributions of matter. These are then superposed to construct non-axisymmetric flat rings. We also consider triaxial…
Pairs potential-density in terms of elementary functions that represents flat rings structures are presented. We study structures representing one or several concentric flat rings. Also disks surrounded by concentric flat rings are…
Relativistic thick ring models are constructed using previously found analytical Newtonian potential-density pairs for flat rings and toroidal structures obtained from Kuzmin-Toomre family of discs. In particular, we present systems with…
We present a potential-density pair designed to model nearly isothermal star clusters (and similar self-gravitating systems) with a central core and an outer turnover radius, beyond which density falls off as $r^{-4}$. In the intermediate…
We start from a study of the density-potential relation for classical homeoids in terms of an asymptotic expansion for small deviations from spherical symmetry. We then show that such expansion is a useful device that allows us to construct…
We report a simple method to generate potential/surface density pairs in flat axially symmetric finite size disks. Potential/surface density pairs consist of a ``homogeneous'' pair (a closed form expression) corresponding to a uniform disk,…
A general method is presented for constructing distribution functions for flat systems whose surface density and Toomre's Q number profile is given. The purpose of these functions is to provide plausible galactic models and assess their…
Ring mass density and the corresponding circular velocity in thin disk model are known to be integral transforms of one another. But it may be less familiar that the transforms can be reduced to one-fold integrals with identical weight…
A class of complete potential-density basis sets in cylindrical (R,phi,z) coordinates is presented. This class is suitable for stability studies of galactic disks in three dimensions and includes basis sets tailored for disks with vertical…
An identity that relates multipolar solutions of the Einstein equations to Newtonian potentials of bars with linear densities proportional to Legendre polynomials is used to construct analytical potential-density pairs of infinitesimally…
We present a family of analytical potential-density pairs for barred discs, which can be combined to describe galactic bars in a realistic way, including boxy/peanut components. We illustrate this with two reasonable compound models.…
Exact analytical solutions are given for the three finite disks with surface density $\Sigma_n=\sigma_0 (1-R^2/\alpha^2)^{n-1/2} \textrm{with} n=0, 1, 2$. Closed-form solutions in cylindrical co-ordinates are given using only elementary…
A family of potential-density pairs that represent spherical shells with finite thickness is obtained from the superposition of spheres with finite radii. Other families of shells with infinite thickness with a central hole are obtained by…
A set of bi-orthogonal potential-density basis functions is introduced to model the density and its associated gravitational field of three dimensional stellar systems. Radial components of our basis functions are weighted integral forms of…
The two-nucleon density distributions in states with isospin $T=0$, spin $S$=1 and projection $M_S$=0 and $\pm$1 are studied in $^2$H, $^{3,4}$He, $^{6,7}$Li and $^{16}$O. The equidensity surfaces for $M_S$=0 distributions are found to be…
The size-dependent electronic, structural, magnetic and vibrational properties of small pure cop- per and silver clusters and their alloys with one and two palladium atoms are studied by using full-potential all-electron density functional…
We apply the theory of cotorsion pairs to study closure properties of classes of modules with finite projective dimension with respect to direct limit operations and to filtrations. We also prove that if the ring is an order in an…
We present several closed-form expressions of useful mass distributions. These include the potentials and accelerations of circular rings and arcs, the potentials of uniform density rings and arcs at arbitrary eccentricities, and the…
We studied the structural and the electronic properties of ionized and neutral small Au clusters via plane wave pseudopotential calculations. All except the anionic heptamer favor one-dimensional zigzag structures or two-dimensional…
We describe a family of circular, and elliptical, finite disks with a disk potential that is a power of the radius. These are all flattened ellipsoids, obtained by squashing finite spheres with a power-law density distribution, and cutoff…