Related papers: Sizes of Pentagonal Clusters in Fullerenes
The problem of cluster formation and growth in first-order quark-hadron phase transition in heavy-ion collisions is considered. Behaving as Brownian particles, the clusters carry out random walks and can encounter one another, leading to…
The formation and evolution mechanism of fullerenes in the planetary nebula or in the interstellar medium are still not understood. Here we present the study on the cluster formation and the relative reactivity of fullerene cations (from…
Polyominoes are a subset of polygons which can be constructed from integer-length squares fused at their edges. A system of polygons P is interlocked if no subset of the polygons in P can be removed arbitrarily far away from the rest. It is…
After Curl, Kroto and Smalley were awarded 1996 the Nobel Prize in chemistry, fullerenes have been subject of much research. One part of that research is the prediction of a fullerene's stability using topological descriptors. It was mainly…
We prove the following generalised empty pentagon theorem: for every integer $\ell \geq 2$, every sufficiently large set of points in the plane contains $\ell$ collinear points or an empty pentagon. As an application, we settle the next…
Design of monomeric unit, by using sequences of map operations, and the growing process in the building of a double-shell multi torus with all-pentagonal faces, is presented. It is shown that the monomer and some small intermediates, as…
Non-equilibrium cluster-cluster aggregation of particles diffusing in or at the cell membrane has been hypothesized to lead to domains of finite size in different biological contexts such as lipid rafts, cell adhesion complexes, or…
We study $\alpha$-cluster structure based on the geometric configurations with a microscopic framework, which takes full account of the Pauli principle, and which also employs an effective inter-nucleon force including finite-range…
A set of $n$-lattice points in the plane, no three on a line and no four on a circle, such that all pairwise distances and all coordinates are integral is called an $n$-cluster (in $\mathbb{R}^2$). We determine the smallest existent…
A (4,5,6)-fullerene is a plane cubic graph whose faces are only quadrilaterals, pentagons and hexagons, which includes all (4,6)- and (5,6)-fullerenes. A connected graph $G$ with at least $2k+2$ vertices is $k$-extendable if $G$ has perfect…
A fullerene graph is a planar cubic 3-connected graph with only pentagonal and hexagonal faces. We show that fullerene graphs have exponentially many perfect matchings.
A polygonal complex in euclidean 3-space is a discrete polyhedron-like structure with finite or infinite polygons as faces and finite graphs as vertex-figures, such that a fixed number r of faces surround each edge. It is said to be regular…
We present the detection of fullerenes C60 and C70 in the star-forming region IC 348 of the Perseus molecular cloud. Mid-IR vibrational transitions of C60 and C70 in emission are found in Spitzer IRS spectra of individual stars (LRLL 1, 2,…
We have used the ESO Nearby Abell Cluster Survey (ENACS) in combination with the Cosmos Galaxy Catalogue, to investigate the existence of a Fundamental Plane (FP) for rich clusters of galaxies. The 20 clusters with the most regular…
We report a computational study of the stability and infrared (IR) vibrational spectra of neutral and singly ionised fullerene cages containing between 44 and 70 carbon atoms. The stability is characterised in terms of the standard enthalpy…
A simple cut-and-patch method is presented for the construction and classification for fullerenes belonging to the octahedral point groups, $O$ or $O_h$. In order to satisfy the symmetry requirement of the octahedral group, suitable numbers…
A fullerene graph is a cubic bridgeless plane graph with only pentagonal and hexagonal faces. We exhibit an infinite family of fullerene graphs of diameter $\sqrt{4n/3}$, where $n$ is the number of vertices. This disproves a conjecture of…
The most distant Kuiper belt objects exhibit the clustering in their orbits, and this anomalous architecture could be caused by Planet 9 with large eccentricity and high inclination. We then suppose that the orbital clustering of minor…
Periodic orbits in chaotic systems form clusters, whose elements traverse approximately the same points of the phase space. The distribution of cluster sizes depends on the length n of orbits and the parameter p which controls closeness of…
The problem of hadronic cluster production in heavy-ion collisions is studied in search for an observable signature of first-order quark-hadron phase transition. The study is carried out by cellular automata in a two-dimensional model of…