Related papers: Analytical Potential-Density Pairs for Flat Rings …
Several conditions are given when a packing of equal disks in a torus is locally maximally dense, where the torus is defined as the quotient of the plane by a two-dimensional lattice. Conjectures are presented that claim that the density of…
We examine the integral cohomology rings of certain families of $2n$-dimensional orbifolds $X$ that are equipped with a well-behaved action of the $n$-dimensional real torus. These orbifolds arise from two distinct but closely related…
We establish stability and characteristics of two-dimensional (2D) vortex ring-shaped quantum droplets (QDs) formed by binary Bose-Einstein condensates (BECs). The system is modeled by the Gross-Pitaevskii (GP) equation with the cubic term…
We give a complete classification of torsion pairs in the cluster categories associated to tubes of finite rank. The classification is in terms of combinatorial objects called Ptolemy diagrams which already appeared in our earlier work on…
We find explicit formulas for the radii and locations of the circles in all the optimally dense packings of two, three or four equal circles on any flat torus, defined to be the quotient of the Euclidean plane by the lattice generated by…
Gravitational instabilities play an important role in structure formation of gas-rich high-redshift disc galaxies. In this paper, we revisit the axisymmetric perturbation theory and the resulting growth of structure by taking the realistic…
We investigate ground state configurations of atomic systems in two dimensions interacting via short range pair potentials. As the number of particles tends to infinity, we show that low-energy configurations converge to a macroscopic…
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
The structure, binding energy, magnetic moments and electronic structure of FemIrn clusters are investigated using state of the art density functional theory techniques. Fully unconstrained structural relaxations are undertaken by…
Density (or state) dependent pair potentials arise naturally from coarse-graining procedures in many areas of condensed matter science. However, correctly using them to calculate physical properties of interest is subtle and cannot be…
We present a simple method, based on the deformation of spherically symmetric potentials, to construct explicit axisymmetric and triaxial MOND density-potential pairs. General guidelines to the choice of suitable deformations, so that the…
I present a general family of dynamical models with simple analytical potential-density pairs suited to model galactic bulges and nuclei with double power-law radial density profiles and an optional central black hole. Analytical…
Attractive $p$-wave one-dimensional fermions are studied in the fermionic Tonks-Girardeau regime in which the diagonal properties are shared with those of an ideal Bose gas. We study the off-diagonal properties and present analytical…
An analytical description of polymer melts and their mixtures as liquids of interacting soft colloidal particles is obtained from liquid-state theory. The derived center-of-mass pair correlation functions with no adjustable parameters…
Polar ring galaxies are ideal objects with which to study the three-dimensional shapes of galactic gravitational potentials since two rotation curves can be measured in two perpendicular planes. Observational studies have uncovered…
We discuss integrable discretizations of 3-dimensional cyclic systems, that is, orthogonal coordinate systems with one family of circular coordinate lines. In particular, the underlying circle congruences are investigated in detail, and…
We systematically studied the validity and transferability of effective, coarse-grained, pair potentials in ultrasoft colloidal systems. We focused on amphiphilic dendrimers, macromolecules which can aggregate into clusters of overlapping…
The exact interaction energy of a many-electron system is determined by the electron pair density, which is not well-approximated in standard Kohn-Sham density functional models. Here we study the (complicated but well-defined) exact…
The series expansion formulae are established for the one- and two-center charge densities over complete orthonormal sets of exponential type orbitals introduced by the author. Three-center overlap integrals of appearing in these relations…
Dense packings of nonoverlapping bodies in three-dimensional Euclidean space are useful models of the structure of a variety of many-particle systems that arise in the physical and biological sciences. Here we investigate the packing…