Related papers: Sizes of Pentagonal Clusters in Fullerenes
The rich diversity of multi-planetary systems and their architectures is greatly contrasted by the uniformity exhibited within many of these systems. Previous studies have shown that compact Kepler systems tend to exhibit a peas-in-a-pod…
Since fullerene formation occurs under conditions where direct observation of atomic-scale reactions is not possible, modeling is the only way to reveal atomistic mechanisms which can lead to selection of abundant fullerene isomers (like…
Particle rafts floating at an air-liquid interface exhibit a variety of behaviors when interfacial flow is introduced. Motivated by previous experimental observations, the failure pattern of particle rafts under uniform radial expansion is…
We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent…
[Abridged] Fullerenes have been recently detected in various circumstellar and interstellar environments, raising the question of their formation pathway. It has been proposed that they can form by the photo-chemical processing of large…
Mutually repelling particles form spontaneously ordered clusters when forced into confinement. The clusters may adopt similar spatial arrangements even if the underlying particle interactions are contrastingly different. Here we demonstrate…
$\renewcommand{\Re}{\mathbb{R}}$Given a set $P$ of $n$ points in $\Re^d$, consider the problem of computing $k$ subsets of $P$ that form clusters that are well-separated from each other, and each of them is large (cardinality wise). We…
A $(3, 6)$-fullerene is a cubic planar graph whose faces all have 3 or 6 sides. We give an exact enumeration of $(3, 6)$-fullerenes with $V$ vertices. We also enumerate $(3, 6)$-fullerenes with mirror symmetry, with 3-fold rotational…
The existence of minimizers in the fractional isoperimetric problem with multiple volume constraints is proved, together with a partial regularity result.
We prove that every homogeneous convex polyhedron with only one unstable equilibrium (known as a mono-unstable convex polyhedron) has at least $7$ vertices. Although it has been long known that no mono-unstable tetrahedra exist, and…
Ordered graphene has been extensively studied. In this paper we undertake a first density functional study of it topologically disordered analogues of graphene, in the form of a random network, consisting predominantly of hexagonal rings,…
We present a detailed investigation of static dipole polarizability of lithium clusters containing up to 22 atoms. We first build a database of lithium clusters by optimizing several candidate structures for the ground state geometry for…
In this paper, we investigate a problem concerning quartets, which are a particular type of tree on four leaves. Loosely speaking, a set of quartets is said to be `definitive' if it completely encapsulates the structure of some larger tree,…
We present an infinite series of operations on fullerenes generalizing the Endo-Kroto operation, such that each combinatorial fullerene is obtained from the dodecahedron by a sequence of such operations. We prove that these operations are…
Instabilities in planetary systems can result in the ejection of planets from their host system, resulting in free-floating planets (FFPs). If this occurs in a star cluster, the FFP may remain bound to the star cluster for some time and…
Unlike atoms, colloidal particles are not identical, but can only be synthesised within a finite size tolerance. Colloids are therefore polydisperse, i.e. mixtures of infinitely many components with sizes drawn from a continuous…
Cluster of galaxies are the largest concentrations of visible mass in the Universe and therefore a fundamental topic of cosmology and astrophysics. Recent radio, EUV, and X-ray observations suggest that clusters contain large populations of…
Some scenarios for planetesimal formation go through a phase of collapse of gravitationally bound clouds of mm-cm-sized pebbles. Such clouds can form for example through the streaming instability in protoplanetary disks. We model the…
Using a global optimization approach that directly searches for the composition of greatest stability, we have been able to find the particularly stable structures for binary Lennard-Jones clusters with up to 100 atoms for a range of…
The metal content of clusters of galaxies and its relation to their stellar content is revisited making use of a cluster sample for which all four basic parameters are homogeneously measured within consistent radii, namely core-excised…