Convexity-Increasing Morphs of Planar Graphs

We study the problem of convexifying drawings of planar graphs. Given any planar straight-line drawing of an internally 3-connected graph, we show how to morph the drawing to one with strictly convex faces while maintaining planarity at all times. Our morph is convexity-increasing, meaning that once an angle is convex, it remains convex. We give an efficient algorithm that constructs such a morph as a composition of a linear number of steps where each step either moves vertices along horizontal lines or moves vertices along vertical lines. Moreover, we show that a linear number of steps is worst-case optimal. To obtain our result, we use a well-known technique by Hong and Nagamochi for finding redrawings with convex faces while preserving y-coordinates. Using a variant of Tutte's graph drawing algorithm, we obtain a new proof of Hong and Nagamochi's result which comes with a better running time. This is of independent interest, as Hong and Nagamochi's technique serves as a building block in existing morphing algorithms.Comment: Preliminary version in Proc. WG 201

Entanglement in helium

Using a configuration-interaction variational method, we accurately compute the reduced, single-electron von Neumann entropy for several low-energy, singlet and triplet eigenstates of helium atom. We estimate the amount of electron-electron orbital entanglement for such eigenstates and show that it decays with energy.Comment: 5 pages, 2 figures, added references and discussio

Fluctuations in the spectra of open few-body systems

We investigate simple open few-body systems, the spectra of which exhibit fluctuating patterns, and review the conditions for the existence of an Ericson regime in deterministic, open quantum systems. A widely used criterion, the Lorentzian shape of the autocorrelation function of the spectrum, is shown to be insufficient for the occurrence of Ericson fluctuations: integrable systems or open systems that are not in the Ericson regime might display such an autocorrelation function. We also investigate the sensitivity of Ericson fluctuations on simplified models of realistic systems. In particular, we show that a simplified hydrogenic model for alkali atoms in crossed magnetic and electric fields does not yield Ericson fluctuations for a choice of the energy and field parameters where the realistic system is in the Ericson regime

Anwendung der NMR-Spektroskopie chiraler Assoziate 15: Flüssigkeits-Chromatographie an Triacetylcellulose 10: The enantiomers of N,N-dimethylthiobenzamides: Chromatographic behaviour and rotational barriers

N,N-Dimethylthiobenzamides bearing hydrogen atoms in both orthopositions were shown by 1H NMR in the presence of an optically active alcohol to have non-coplanar π-systems. The barrier to rotation about the C(sp2-C(sp2) bond amounts to 43 ± 2 kJ/mol. Liquid chromatography on triacetylcellulose served for the enrichment of enantiomers of 2-substituted thiobenzamides. In several cases considerable enantioselectivity (relative retention up to 8.7) was observed. The barriers to enantiomerization (Tables 3, 4 and 5), determined by thermal racemization, were discussed in terms of non-bonding interactions, electrostatic repulsions and buttressing effects in the transition state of rotation

Flüssigkeits-Chromatographie an Triacetylcellulose 4. Determination of enantiomeric purity in spite of incomplete chromatographic separation

A novel procedure for the measurement of enantiomeric purity P is derived, whereby the mixture to be analyzed is subjected to liquid chromatography (LC) on an optically active sorbent. Extensive peak overlap does not prohibit the application of the method, whereas the complete absence of separation does. In addition, the mixture is subjected to LC on an achiral sorbent. The same photometer and polarimeter detections are used for both experiments. At the same time, an x/y recorder plots the rotation angle α versus the absorbance A, thus generating the slopes Cm and C+ in Fig. 1 which result in P = Cm/C+. – Optically active samples of 1, 2, 3, and 4 were analyzed for P. The findings agree satisfactorily with the results of other methods

S-wave scattering of a polarizable atom by an absorbing nanowire

We study the scattering of a polarizable atom by a conducting cylindrical wire with incoming boundary conditions, that is, total absorption, near the surface of the wire. Based on the explicit expression given recently [C. Eberlein and R. Zietal, Phys. Rev. A75, 032516 (2007)] for the nonretarded atom-wire potential, we formulate a hierarchy of approximations that enables the numerical determination of this potential to any desired accuracy as economically as possible. We calculate the complex s-wave scattering length for the effectively two-dimensional atom-wire scattering problem. The scattering length a depends on the radius R of the wire and a characteristic length beta related to the polarizability of the atom via a simple scaling relation, a = R (a) over tilde(beta/R). The "scaled scattering length" (a) over tilde tends to unity in the thick-wire limit beta/R -> 0, and it grows almost proportional to 1/R in the opposite thin-wire limit

Chiroptical Detection after Liquid Chromatography 1: Chiroptical detection. Novel possibilities of its application to enantiomers

Polarimetric and/or circular dichroic detection of enantiomers after liquid chromatography on optically active sorberts has been used for the following purposes: determination of enantiomeric purity in spite of peak overlap, investigation of enantiomerization during chromatography, monitoring of racemizations and recording of circular dichrograms without preparative enrichment of enantiomers. Novel examples for all applications are give. The general prospects for chiroptical detection are discussed

Upward Planarity Testing of Embedded Mixed Graphs

A mixed graph has both directed and undirected edges. We study an upward planarity testing problem for embedded mixed graphs and solve it using Integer Linear Programming. Experiments show the efficiency of our technique