Related papers: Do All Spherical Viruses Have Icosahedral Symmetry…
A reflection-asymmetric triaxial particle rotor model with three quasiparticles and a reflection-asymmetric triaxial rotor is developed, and applied to investigate the observed multiple chiral doublets (M\c{hi}D) candidates with octupole…
It is shown that tiling in icosahedral quasicrystals can also be properly described by cyclic twinning at the unit cell level. The twinning operation is applied on the primitive prolate golden rhombohedra, which can be considered a result…
We present a systematic analysis of scale-dependent properties of filamentary structures in seven nearby molecular clouds $-$ Taurus, Ophiuchus, Perseus, Orion A, California, IC 5146, Vela C $-$ using the multiscale extraction method…
We have attempted to find the global minima of clusters containing between 20 and 80 atoms bound by the Morse potential as a function of the range of the interatomic force. The effect of decreasing the range is to destabilize strained…
Every regular map on a closed surface gives rise to generally six regular maps, its "Petrie relatives", that are obtained through iteration of the duality and Petrie operations (taking duals and Petrie-duals). It is shown that the skeletal…
Brehm and K\"uhnel (1992) constructed three 15-vertex combinatorial 8-manifolds `like the quaternionic projective plane' with symmetry groups $\mathrm{A}_5$, $\mathrm{A}_4$, and $\mathrm{S}_3$, respectively. Gorodkov (2016) proved that…
We present a generalized Landau-Brazovskii free energy for the solidification of chiral molecules on a spherical surface in the context of the assembly of viral shells. We encounter two types of icosahedral solidification transitions. The…
Complex tetrahedral surface $\mathcal{T}$ is a non planar projective surface that is generated by four intersecting complex projective planes $CP^{2}$. In this paper, we study the family $\{\mathcal{T}_{m}\} $ of blow ups of $\mathcal{T}$…
We apply here the principle of affine symmetry to the nested fullerene cages (carbon onions) that arise in the context of carbon chemistry. Previous work on affine extensions of the icosahedral group has revealed a new organisational…
We parametrized the total structure of the Galaxy in cylindrical coordinates by radial and vertical exponentials up to z=10 kpc, covering thin disc, thick disc, and the inner spheroid. However, we let the scaleheight and scalelength to be a…
Stability and chemistry, both exohedral and endohedral, of fullerenes are critically dependent on the distribution of their obligatory 12 pentagonal faces. It is well known that there are infinitely many IPR-fullerenes and that the…
We present a map of the spiral structure of the Galaxy, as traced by molecular CS emission associated with IRAS sources which are believed to be compact HII regions. The CS line velocities are used to determine the kinematic distances of…
The ground state structures of small silicon clusters are determined through exhaustive tight-binding molecular dynamics simulation studies. These simulations revealed that \Si{11} is an icosahedron with one missing cap, \Si{12} is a…
Structural studies on the icosahedral quasicrystals in Zn-Mg-Sc, Cu-Ga-Mg-Sc, and Zn-Mg-Ti alloys as well as their corresponding 1/1 cubic approximants, have revealed that these quasicrystals belong to a new structural group similar to…
We develop equilibrium and kinetic theories that describe the assembly of viral capsid proteins on a charged central core, as seen in recent experiments in which brome mosaic virus (BMV) capsids assemble around nanoparticles functionalized…
We have examined the hypothesis by Bijker and Iachello who asserted that 12C has an internal structure with three alpha particles arranged in a triangular shape, leading to the formation of the ground rotational band consisting of 0+, 2+,…
Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it…
Can N-body simulations reliably determine the structural properties of dark matter halos? Focussing on a Virgo-sized galaxy cluster, we increase the resolution of current ``high resolution simulations'' by almost an order of magnitude to…
The algebraic cluster model is is applied to study cluster states in the nuclei 12C and 16O. The observed level sequences can be understood in terms of the underlying discrete symmetry that characterizes the geometrical configuration of the…
It is important to map the large-scale matter distribution in the local Universe for cosmological studies, such as the tracing of the large-scale peculiar velocity flow, the characterisation of the environment for different astronomical…