Related papers: Sizes of Pentagonal Clusters in Fullerenes
Probability of coincidental clustering among the orbits of comets, asteroids and meteoroids depends on many factors like: the size of the orbital sample searched for clusters or the size of the identified group, it is different for groups…
There are four characteristic circles for each triangle on a plane. All for are tangential to the three straight lines containing the triangles' three sides. Three are exterior circles, the fourth is the in-circle. When the triangle is…
This paper completes the classification of maximal unrefinable partitions, extending a previous work of Aragona et al. devoted only to the case of triangular numbers. We show that the number of maximal unrefinable partitions of an integer…
Interstellar molecules are thought to build up in the shielded environment of molecular clouds or in the envelope of evolved stars. This follows many sequential reaction steps of atoms and simple molecules in the gas phase and/or on (icy)…
The Clar number of a fullerene is the maximum number of independent resonant hexagons in the fullerene. It is known that the Clar number of a fullerene with n vertices is bounded above by [n/6]-2. We find that there are no fullerenes whose…
The determination of the densest packings of regular tetrahedra (one of the five Platonic solids) is attracting great attention as evidenced by the rapid pace at which packing records are being broken and the fascinating packing structures…
Recent analyses have shown that distant orbits within the scattered disk population of the Kuiper belt exhibit an unexpected clustering in their respective arguments of perihelion. While several hypotheses have been put forward to explain…
Stars in an open cluster are assumed to have formed from a broadly homogeneous distribution of gas, implying that they should be chemically homogeneous. Quantifying the level to which open clusters are chemically homogeneous can therefore…
We show that every packing of congruent regular pentagons in the Euclidean plane has density at most $(5-\sqrt5)/3$, which is about 0.92. More specifically, this article proves the pentagonal ice-ray conjecture of Henley (1986), and…
We argue that all transient searches for planets in globular clusters have a very low detection probability. Planets of low metallicity stars typically do not reside at small orbital separations. The dependance of planetary system…
Motivated by nucleation and molecular aggregation in physical, chemical and biological settings, we present an extension to a thorough analysis of the stochastic self-assembly of a fixed number of identical particles in a finite volume. We…
For finite-dimensional bipartite quantum systems, we find the exact size of the largest balls, in spectral $l_p$ norms for $1 \le p \le \infty$, of separable (unentangled) matrices around the identity matrix. This implies a simple and…
We identify least-perimeter unit-area tilings of the plane by convex pentagons, namely tilings by Cairo and Prismatic pentagons, find infinitely many, and prove that they minimize perimeter among tilings by convex polygons with at most five…
The formation of spherical polaron clusters is studied within the Fr$\ddot{o}$hlich polaron theory. In a dilute polaron gas, using the non-local statistical approach and the polaron pair interaction obtained within the Pekar strong coupling…
We simulate open clusters containing up to 182 stars initially in the form of singles, binaries and triples. Due to the high interaction rate a large number of stable quadruples, quintuples, sextuples, and higher-order hierarchies form…
We show the existence of generalized clusters of a finite or even infinite number of sets, with minimal total perimeter and given total masses, in metric measure spaces homogeneous with respect to a group acting by measure preserving…
We study the packing of a large number of congruent and non--overlapping circles inside a regular polygon. We have devised efficient algorithms that allow one to generate configurations of $N$ densely packed circles inside a regular polygon…
We consider hard-disc mixtures with disc sizes within ratio $\sqrt{2}-1$, that is, the small disc exactly fits in the hole between four large discs. For each prescribed stoichiometry of large and small discs, the densest packings are…
New results on pentagonal geometries PENT(k,r) with block sizes k = 3 or k = 4 are given. In particular we completely determine the existence spectra for PENT(3,r) systems with the maximum number of opposite line pairs as well as those…
A comprehensive study on the relative structural stability of various nanostructures of carbon clusters (including fullerenes, cages, onions, icosahedral clusters, bucky-diamond clusters, spherically bulk terminated clusters, and clusters…