Related papers: Inferring a Cell Structure on the Space of Cyclooc…
We prove that octants are cover-decomposable, i.e., any 12-fold covering of any subset of the space with a finite number of translates of a given octant can be decomposed into two coverings. As a corollary, we obtain that any 12-fold…
We analyze the structure of two dimensional disordered cellular systems generated by extensive computer simulations. These cellular structures are studied as topological trees rooted on a central cell or as closed shells arranged…
We study a versatile structurally favorable periodic $sp^2$-bonded carbon atomic planar sheet with $C_{4v}$ symmetry by means of the first-principles calculations. This carbon allotrope is composed of carbon octagons and squares with two…
We report on various nanocarbons formed from a unique structural pattern containing two pentagons, three hexagons and two heptagons, resulting from local rearrange- ments around a divacancy in pristine graphene or nanotubes. This defect can…
Carbon allotropes built from rings of two-coordinate atoms, known as cyclo[n]carbons, have fascinated chemists for many years, but until now they could not be isolated or structurally characterized, due to their high reactivity. We…
We construct a class of periodic tilings of the plane, which corresponds to toroidal arrangements of trivalent atoms, with pentagonal, hexagonal and heptagonal rings. Each tiling is characterized by a set of four integers and determines a…
The primordial ingredient of cuprate superconductivity is the CuO2 unit cell. Here, theoretical attention usually concentrates on the intra-atom Coulombic interactions dominating the 3d^9 and 3d^10 configurations of each copper ion.…
We systematically investigate the relationships between structural and electronic effects of finite size zigzag or armchair carbon nanotubes of various diameters and lengths, starting from a molecular template of varying shape and diameter,…
We present first principles density functional calculations and downfolding studies of the electronic and magnetic properties of the layered quantum spin system TiOCl. We discuss explicitely the nature of the exchange pathes and attempt to…
The carbon atom provides the backbone for the complex organic chemistry composing the building blocks of life. The physics of the carbon nucleus in its predominant isotope, $^{12}$C, is similarly full of multifaceted complexity. Some…
We consider the cell decomposition of the moduli space of real genus two curves with a marked point on the only real oval. The cells are enumerated by certain graphs with their weights describing the complex structure on a curve. We show…
Topologically stable cellular partitions of D dimensional spaces are studied. A complete statistical description of the average structural properties of such partition is given in term of a sequence of D/2-1 (or (D-1)/2) variables for D…
The cycle-preserving symmetries for the nine two-dimensional real spaces of constant curvature are collectively obtained within a Cayley-Klein framework. This approach affords a unified and global study of the conformal structure of the…
Formation of the complex structure with 16 atoms in the orthorhombic cell, space group Cmca (Pearson symbol oC16) was experimentally found under high pressure in the alkali elements (K, Rb, Cs) and polyvalent elements of groups IV (Si, Ge)…
Spacetime is represented by ordered sequences of topologically closed Poincare sections of the primary space constructed of primary empty cells. These mappings are constrained to provide homeomorphic structures serving as frames of…
Structural organization and correlations are studied in very large packings of equally sized acrylic spheres, reconstructed in three-dimensions by means of X-ray computed tomography. A novel technique, devised to analyze correlations among…
Compliant environments can mediate interactions between mechanically active cells like fibroblasts. Starting with a phenomenological model for the behaviour of single cells, we use extensive Monte Carlo simulations to predict non-trivial…
Let $S$ be a closed oriented surface of genus $g\geq 2$. Fix an arbitrary non-elementary representation $\rho\colon\pi_1(S)\to {\rm SL}_2(\mathbb{C})$ and consider all marked (complex) projective structures on $S$ with holonomy $\rho$. We…
A class of Cantor-type spaces and related geometric structures are discussed.
A single-walled carbon nanotube presents a seamless cylindrical graphene surface and is thus an ideal adsorption substrate for investigating the physics of atoms and molecules in two dimensions and approaching the one-dimensional limit.…