Related papers: A simple method to construct exact density-potenti…
There is a growing interest in cylindrical structures of hard and soft particles. A promising new method to assemble such structures has recently been introduced by Lee et al. [T. Lee, K. Gizynski, and B. Grzybowski, Adv. Mater. 29, 1704274…
Pure power-law density profiles, $\rho(r)\propto r^{b-3}$, are classified in connection with the following reference cases: (i) isodensity, $b=3$, $\rho=$ const; (ii) isogravity, $b=2$, $g=$ const; (iii) isothermal, $b=1$,…
We present a detailed study of rotational asymmetry in galaxies for both morphological and physical diagnostic purposes. An unambiguous method for computing asymmetry is developed, robust for both distant and nearby galaxies. By degrading…
Axially symmetric equilibrium configurations of the conformally invariant Willmore energy are shown to satisfy an equation that is two orders lower in derivatives of the embedding functions than the equilibrium shape equation, not one as…
We describe a versatile mechanism that provides tight-binding models with an enriched, topologically nontrivial bandstructure. The mechanism is algebraic in nature, and leads to tight-binding models that can be interpreted as a non-trivial…
The Gauss-Bonnet density `a la Palatini' is not a total derivative in four dimensions. We study spherically symmetric fields for the torsion-free theory. The resulting equations are highly complicated but we show the existence of unexpected…
A formalism is developed which allows to determine the locations of all local symmetry axes of three-dimensional particles with overall icosahedral symmetry. It relies on the fact that the root system of the non-crystallographic Coxeter…
We study the stability of covers of simplicial complexes. Given a map $f:Y\to X$ that satisfies almost all of the local conditions of being a cover, is it close to being a genuine cover of $X$? Complexes $X$ for which this holds are called…
The positivity of the Bondi mass has been proven in 4 dimensions, but in higher dimensions the issue remains open. The formalism of the present paper has been developed to investigate this and is well suited to the higher dimensional case.…
We discuss asymptotic properties of a family of discrete probability measures which may be used to model particle configurations with a wall on a set of discrete nodes. The correlations are shown to be determinantal and are expressed in…
In this paper we construct an infinite family of homotopically rigid spaces. These examples are then used as building blocks to forge highly connected rational spaces with prescribed finite group of self-homotopy equivalences. They are also…
We present a new family of spherically symmetric models for the luminous components of elliptical and spiral galaxies and their dark matter haloes. Our starting point is a general expression for the logarithmic slope $\alpha(r) =…
We construct infinite families of abstract regular polytopes of type $\{4,p_1,\ldots,p_{n-1}\}$ from extensions of centrally symmetric spherical abstract regular $n$-polytopes. In addition, by applying the halving operation, we obtain…
Fully analytical dynamical models usually have an infinite extent, while real star clusters, galaxies, and dark matter haloes have a finite extent. The standard method for generating dynamical models with a finite extent consists of taking…
I shall describe a general model-theoretic task to construct expansions of pseudofinite structures and discuss several examples of particular relevance to computational complexity. Then I will present one specific situation where finding a…
In this paper we consider asymptotic expansions for a class of sequences of symmetric functions of many variables. Applications to classical and free probability theory are discussed.
This paper develops an explicit and implementable framework for constructing spherical designs by lifting point sets from tight fusion frames. By combining existing ingredients, we obtain, in every dimension, explicit spherical $5$-designs…
We derive a semi-analytical extension of the spherical collapse model of structure formation that takes account of the effects of deviations from spherical symmetry and shell crossing which are important in the non-linear regime. Our model…
The deprojection of axisymmetric density distributions is generally indeterminate to within the addition of certain axisymmetric distributions (konus densities) that are invisible in projection. The known class of konus densities is…
The asymptotic iteration method is used to find exact and approximate solutions of Schroedinger's equation for a number of one-dimensional trigonometric potentials (sine-squared, double-cosine, tangent-squared, and complex cotangent).…