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We study the cluster structure of 20Ne and show that the available experimental data can be well described by a bi-pyramidal structure with D(3h) symmetry. Strong evidence for the occurrence of this symmetry comes from the observation of…
The exploration of the densest sphere packings is a fundamental problem in mathematics and a wide variety of sciences including materials science. We present our exhaustive computational exploration of the densest ternary sphere packings…
In this contribution, we present evidence for the occurrence of triangular symmetry in cluster nuclei. We discuss the structure of rotational bands for 3-alpha and 3-alpha+1 configurations with triangular D(3h) symmetry by exploiting the…
Vertices of the 4-dimensional semi-regular polytope, the \textit{grand antiprism} and its symmetry group of order 400 are represented in terms of quaternions with unit norm. It follows from the icosian representation of the \textbf{$E_{8}…
Ordered states on spheres require a minimum number of topological defects. For the case of crystalline order, triangular lattices must be interrupted by an array of at least 12 five-fold disclination defects, typically sitting at the…
Several $X$ and $Z_{cs}$ exotic hadrons were claimed in the LHCb's amplitude analysis on $B^+\to J/\psi \phi K^+$. The data shows that all the peaks and also dips in the spectra are located at thresholds of seemingly relevant meson-meson…
Generic polyhedra are interesting mathematical objects to study in their own right. In this paper, we initialize a systematic study of two-dimensional generic polyhedra with an eye towards applications to low-dimensional topology,…
Using density functional theory (DFT) and quantum Monte Carlo (QMC) calculations we show that the B12Hn and B12Fn (n = 0-4) quasi-planar structures are energetically more favorable than the corresponding icosahedral clusters. Moreover, we…
The smallest maximum kissing-number Voronoi polyhedron of 3d spheres is the icosahedron and the tetrahedron is the smallest volume that can show up in Delaunay tessalation. No periodic lattice is consistent with either and hence these dense…
Skeletal polyhedra and polygonal complexes in ordinary Euclidean 3-space are finite or infinite 3-periodic structures with interesting geometric, combinatorial, and algebraic properties. They can be viewed as finite or infinite 3-periodic…
Dense polyhedron packings are useful models of a variety of condensed matter and biological systems and have intrigued scientists mathematicians for centuries. Recently, organizing principles for the types of structures associated with the…
Galaxy clusters exhibit regular scaling relations among their bulk properties. These relations establish vital links between halo mass and cluster observables. Precision cosmology studies that depend on these links benefit from a better…
We present the observation and analysis of newly discovered coherent structures in the L1688 region of Ophiuchus and the B18 region of Taurus. Using data from the Green Bank Ammonia Survey (GAS), we identify regions of high density and…
The cellular uptake of nanoparticles or viruses requires that the gain of adhesion energy overcomes the cost of plasma membrane bending. It is well known that this leads to a minimal particle size for uptake. Using a simple deterministic…
We model the quasicrystal-related structure CaCd$_6$, a bcc packing of icosahedral clusters containing tetrahedra which undergo orientational orderings at T<100 K. We use general schemes to evaluate an effective Hamltonian for…
The continuous 1D defects of an isotropic homogeneous material in a flat 3D space are classified by the Volterra process construction method. We employ the same method to classify the continuous 2D defects of a vacuum in a 4D maximally…
The relation of s-convexity and sets modeling physical quasicrystals is explained for quasicrystals related to quadratic unitary Pisot numbers. We show that 1-dimensional model sets may be characterized by s-convexity for finite set of…
When the density parameter is close to unity, the universe has a large curvature radius independently of its being hyperbolic, flat, or spherical. Whatever the curvature, the universe may have either a simply connected or a multiply…
We study the possibility that the universe has compact topologies T^3, T^2 x R^1, or S^1 x R^2 using the seven-year WMAP data. The maximum likelihood 95% confidence intervals for the size L of the compact direction are 1.7 < L/L_0 < 2.1,…
We have obtained the radii and distances of 16 galactic Cepheids supposed to be members in open clusters or associations using the new optical and near-infrared calibrations of the surface brightness (Barnes-Evans) method given by Fouque &…