Perfect Matchings in Total Domination Critical Graphs

A graph is total domination edge-critical if the addition of any edge decreases the total domination number, while a graph with minimum degree at least two is total domination vertex-critical if the removal of any vertex decreases the total domination number. A 3 _t EC graph is a total domination edge-critical graph with total domination number 3 and a 3 _t VC graph is a total domination vertex-critical graph with total domination number 3. A graph G is factor-critical if G − v has a perfect matching for every vertex v in G. In this paper, we show that every 3 _t EC graph of even order has a perfect matching, while every 3 _t EC graph of odd order with no cut-vertex is factor-critical. We also show that every 3 _t VC graph of even order that is K _1,7-free has a perfect matching, while every 3 _t VC graph of odd order that is K _1,6-free is factor-critical. We show that these results are tight in the sense that there exist 3 _t VC graphs of even order with no perfect matching that are K _1,8-free and 3 _t VC graphs of odd order that are K _1,7-free but not factor-critical.     

Hydrogen bonding in the hexagonal ice surface

A recently developed technique in sum frequency generation spectroscopy, polarization angle null (or PAN-SFG), is applied to two orientations of the prism face of hexagonal ice. It is found that the vibrational modes of the surface are similar in different faces. As in the basal face, the prism face of ice contains five dominant resonances: 3096, 3146, 3205, 3253, and 3386 cm(-1). On the basal face, the reddest resonance occurs at 3098 cm(-1); within the bandwidth, the same as the prism face. On both the prism and basal faces, this mode contains a significant quadrupole component and is assigned to the bilayer stitching hydrogen bonds. The bluest of the resonances, 3386 cm(-1), occurs slightly blue-shifted at 3393 cm(-1) in the basal face. The prism face has two orientations: one with the optic or c axis in the input plane (the plane formed by the surface normal and the interrogating beam propagation) and one with the c axis perpendicular to the input plane. The 3386 cm(-1) mode has significant intensity only with the c axis in the input plane. On the basis of these orientation characteristics, the 3386 cm(-1) mode is assigned to double-donor molecules in either the top half bilayer or in the lower half bilayer. On the basis of frequency considerations, it is assigned to double-donor molecules in the top half bilayer. These are water molecules containing a nonbonded lone pair. In addition to identification of the components of the broad hydrogen-bonded region, PAN-SFG measures the tangential vs longitudinal content of the vibrational modes. In accord with previous suggestions, the lower frequency modes are predominantly tangential, whereas the higher frequency modes are mainly longitudinal. On the prism face, the 3386 cm(-1) mode is entirely longitudinal.     

One-dimensional exciton diffusion in perylene bisimide aggregates

The dynamics and mobility of excitons in J-aggregates of perylene bisimides are investigated by transient absorption spectroscopy with a time resolution of 50 fs. The transient spectra are compatible with an exciton delocalization length of two monomers and indicate that vibrational and configurational relaxation processes are not relevant for the spectroscopic properties of the aggregates. Increasing the pump pulse energy and in that way the initial exciton density results in an accelerated signal decay and pronounced exciton-exciton annihilation dynamics. Modeling the data by assuming a diffusive exciton motion reveals that the excitons cannot migrate freely in all three directions of space but their mobility is restricted to one dimension. The observed anisotropy supports this picture and points against direct Fo?rster-transfer-mediated annihilation between the excitons. A diffusion constant of 1.29 nm(2)/ps is deduced from the fitting procedure that corresponds to a maximal exciton diffusion length of 96 nm for the measured exciton lifetime of 3.6 ns. The findings indicate that J-aggregates of perylene bisimides are promising building blocks to facilitate directed energy transport in optoelectronic organic devices or artificial light-harvesting systems.     

Spectroscopy of Dibenzorubicene: Experimental Data for a Search in Interstellar Spectra

We report on the characterization of dibenzo[cde,opq]rubicene (C₃₀H₁₄). The molecule was studied in solution at room temperature with absorption spectroscopy in the visible (vis) and ultraviolet (UV) wavelength ranges, and with emission spectroscopy. The infrared (IR), visible, ultraviolet, and vacuum ultraviolet (VUV) absorption spectra of a thin film were measured also at room temperature. In addition, the UV/vis absorption spectrum was measured at cryogenic temperatures using the matrix isolation spectroscopy technique. The interpretation of spectra was supported by theoretical calculations based on semiempirical and ab initio models, as well as on density functional theory. Finally, the results of the laboratory study were compared with interstellar spectra.     

A limit field for orthogonal range searches in two-dimensional random point search trees

We consider the cost of general orthogonal range queries in random quadtrees. The cost of a given query is encoded into a (random) function of four variables which characterize the coordinates of two opposite corners of the query rectangle. We prove that, when suitably shifted and rescaled, the random cost function converges uniformly in probability towards a random field that is characterized as the unique solution to a distributional fixed-point equation. We also state similar results for 2-d trees. Our results imply for instance that the worst case query satisfies the same asymptotic estimates as a typical query, and thereby resolve an open question of Chanzy et al. (2001).     

Correction to: Quasi-DNS Dataset of a Piloted Flame with Inhomogeneous Inlet Conditions

Flow, Turbulence and Combustion - The article Quasi-DNS Dataset of a Piloted Flame with Inhomogeneous Inlet Conditions written by Thorsten Zirwes, Feichi Zhang, Peter Habisreuther, Maximilian...