Numerical solution of the 3D time dependent Schrödinger equation in spherical coordinates: Spectral basis and effects of split-operator technique

We study a numerical solution of the multi-dimensional time dependent Schrödinger equation using a split-operator technique for time stepping and a spectral approximation in the spatial coordinates. We are particularly interested in systems with near spherical symmetries. One expects these problems to be most efficiently computed in spherical coordinates as a coarse grain discretization should be sufficient in the angular directions. However, in this coordinate system the standard Fourier basis does not provide a good basis set in the radial direction. Here, we suggest an alternative basis set based on Chebyshev polynomials and a variable transformation.     

Solving stochastic complementarity problems in energy market modeling using scenario reduction

In this paper, we analyze market equilibrium models with random aspects that lead to stochastic complementarity problems. While the models presented depict energy markets, the results are believed to be applicable to more general stochastic complementarity problems. The contribution is the development of new heuristic, scenario reduction approaches that iteratively work towards solving the full, extensive form, stochastic market model. The methods are tested on three representative models and supporting numerical results are provided as well as derived mathematical bounds.     

An algebraic metric for phylogenetic trees

The definition of similarity measures for phylogenetic trees has been motivated by the computation of consensus trees, the search by similarity in databases, and the assessment of phylogenetic reconstruction methods. The transposition distance for fully resolved trees is a recent addition to the extensive collection of available metrics for comparing phylogenetic trees. In this work, we generalize the transposition metric from fully resolved to arbitrary phylogenetic trees, through a construction that involves an embedding of the set of phylogenetic trees (up to isomorphisms) with a fixed number of labeled leaves into a symmetric group. We also show that this transposition distance can be computed in linear time and we establish some of its basic properties.     

Electrostatic self-assembly of quaternized 2,(3)-tetra(oxo-pyridine) phthalocyaninato chloroindium(III) with a series of tetrasulfonated phthalocyanines

The self-assembly of oppositely charged phthalocyanines, fabricated using quaternized 2,(3)-tetra(oxo-pyridine) phthalocyaninato chloroindium (III) (QInPyPc) as the positively charge molecule and a series of tetrasulfonate phthalocyanine (MTSPc), M = 2H, Mn, Fe, Co and Ni as negatively charged molecules are reported. The self-assembly results in the formation of heteroaggregates. The metallated sulfonated phthalocyanines form nanorod and nanoleaf shaped structures as evidenced by transmission electron microscopy (TEM). The UV–Vis spectra showed blue shifted Q bands, suggesting that these structures were in a face-to-face arrangement. The Raman spectra of the heteroaggregates showed shifting compared to the spectra of the precursors.     

Comparative characterisation of zinc oxide thin films prepared from zinc acetate with or without water of hydration via the sol–gel method

Zinc oxide thin films were prepared using either zinc acetate dihydrate or anhydrous zinc acetate via the sol–gel method. Comparative characterisation of the crystallographical, morphological, optical/spectroscopical and electrical properties of the so-obtained films was performed. The idea of one- (in the case of the anhydrous precursor), and two- (in the other case) stage hydrolysis/condensation was postulated, which was supported by the characterisation results. The film prepared using the anhydrous precursor had a more pronounced c-axis crystal orientation preference, with a larger average crystallite size and more porous morphology. The transparency of this film was significantly lower over the UV/visible region due to its more porous morphology, which also resulted in lower intensity of the ‘near band edge emission’, and higher electrical resistivity. The overall results also suggested that anhydrous zinc acetate could be employed as a precursor for the sol–gel synthesis of zinc oxide thin films, which might have potential advantages in microelectronic and optoelectronic applications.     

X?X Through‐Cage Bonding in Cu,Ni, and Cr Complexes with M3X2 Cores (X=S,As)

Density functional calculations on trinuclear complexes bridged by two sulfur atoms, [(tmeda)₃Cu₃(μ‐S)₂]³⁺, [(tmeda)₃Ni₃(μ‐S)₂]²⁺, and [(tmeda)₃Ni₃(μ‐S₂)]⁴⁺, as well as on the formation of [(tmeda)₃Cu₃(μ‐S)₂]³⁺ from a dinuclear [(tmeda)₂Cu₂(μ‐S₂)]²⁺ complex and a mononuclear [(tmeda)Cu(η²‐S₂)]⁺ fragment, are reported. A qualitative orbital analysis of the M₃X₂ framework bonding is presented for the case in which each metal atom M has a square planar coordination sphere completed by one bidentate or two monodentate ligands (that is, [(L₂M)₃X₂] compounds). It is concluded that a framework electron count (FEC) of 12 corresponds to systems with six M? X bonds but no X? X bond through the cage, while an FEC of 10 favors the formation of an X? X bond. Framework electron counting rules are also presented for related M₃X₂ cores in [(L₅M)₃X₂] complexes, based on a qualitative molecular orbital (MO) analysis supported by DFT calculations on [(OC)₁₅Cr₃(μ‐As₂)].     

A hybrid stimulation strategy for suppression of spiral waves in cardiac tissue

Atrial fibrillation (AF) is the most common cardiac arrhythmia whose mechanisms are thought to be mainly due to the self perpetuation of spiral waves (SW). To date, available treatment strategies (antiarrhythmic drugs, radiofrequency ablation of the substrate, electrical cardioversion) to restore and to maintain a normal sinus rhythm have limitations and are associated with AF recurrences. The aim of this study was to assess a way of suppressing SW by applying multifocal electrical stimulations in a simulated cardiac tissue using a 2D FitzHugh-Nagumo model specially convenient for AF investigations. We identified stimulation parameters for successful termination of SW. However, SW reinduction, following the electrical stimuli, leads us to develop a hybrid strategy based on sodium channel modification for the simulated tissue.     

Solvable groups having only three rational classes of 2-elements

The main result of this paper is that a solvable group that has only three or fewer rational classes consisting of 2-elements has 2-length at most 1.