Dipolar correlations and the dielectric permittivity of water

The static dielectric properties of liquid and solid water are investigated within linear response theory in the context of ab initio molecular dynamics. Using maximally localized Wannier functions to treat the macroscopic polarization we formulate a first-principles, parameter-free, generalization of Kirkwood's phenomenological theory. Our calculated static permittivity is in good agreement with experiment. Two effects of the hydrogen bonds, i.e., a significant increase of the average local moment and a local alignment of the molecular dipoles, contribute in almost equal measure to the unusually large dielectric constant of water.     

Water-walking devices

We report recent efforts in the design and construction of water-walking machines inspired by insects and spiders. The fundamental physical constraints on the size, proportion and dynamics of natural water-walkers are enumerated and used as design criteria for analogous mechanical devices. We report devices capable of rowing along the surface, leaping off the surface and climbing menisci by deforming the free surface. The most critical design constraint is that the devices be lightweight and non-wetting. Microscale manufacturing techniques and new man-made materials such as hydrophobic coatings and thermally actuated wires are implemented. Using high-speed cinematography and flow visualization, we compare the functionality and dynamics of our devices with those of their natural counterparts. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Strong Chromatic Index of Chordless Graphs

A strong edge coloring of a graph is an assignment of colors to the edges of the graph such that for every color, the set of edges that are given that color form an induced matching in the graph. The strong chromatic index of a graph G, denoted by , is the minimum number of colors needed in any strong edge coloring of G. A graph is said to be chordless if there is no cycle in the graph that has a chord. Faudree, Gyárfás, Schelp, and Tuza (The Strong Chromatic Index of Graphs, Ars Combin 29B (1990), 205–211) considered a particular subclass of chordless graphs, namely, the class of graphs in which all the cycle lengths are multiples of four, and asked whether the strong chromatic index of these graphs can be bounded by a linear function of the maximum degree. Chang and Narayanan (Strong Chromatic Index of 2‐degenerate Graphs, J Graph Theory, 73(2) (2013), 119–126) answered this question in the affirmative by proving that if G is a chordless graph with maximum degree Δ, then . We improve this result by showing that for every chordless graph G with maximum degree Δ, . This bound is tight up to an additive constant.     

Synthesis and thermal behavior of Janus dendrimers,part 1

Eight Janus-type dendrimers up to the second generation were synthesized, and their thermal properties were evaluated. Compounds consist of the dendritic bisMPA based polyester moieties, and either 3,4-dihexyloxybenzoic acid or 3,4-dihexadecyloxybenzoic acid moieties, attached to opposite sides of the pentaerythritol core. The structures of the molecules were verified with ¹H NMR, ¹³C NMR, ESI TOF mass spectrometry and elemental analysis. The thermal stability was evaluated by thermogravimetric analysis, displaying onset decomposition temperatures (T_d) ranging from 241 to 308 °C. Phase transitions were studied by differential scanning calorimetry. Based on the performed studies it was confirmed that OH terminated dendrimers 2, 4, 6 and 8 exhibited liquid crystalline phases. Also, the X-ray powder diffraction measurements were accomplished for the dendrimers having terminal hydroxyl groups.     

Photocatalytic synthesis of urea from in situ generated ammonia and carbon dioxide

TiO(2) and Fe-titanate (different wt%) supported on zeolite were prepared by sol-gel and solid-state dispersion methods. The photocatalysts prepared were characterized by X-ray diffraction, scanning electron microscopy and ultraviolet (UV)-visible diffuse reflectance spectroscopy techniques. Photocatalytic reduction of nitrate in water and isopropanol/oxalic acid as hole scavengers are investigated in a batch reactor under UV illumination. The yield of urea increased notably when the catalysts were supported on zeolite. The Fe-titanate supported catalyst promotes the charge separation that contributes to an increase in selective formation of urea. The product formation is because of the high adsorption of in situ generated CO(2) and NH(3) over shape-selective property of the zeolite in the composite photocatalyst. The maximum yield of urea is found to be 18 ppm while 1% isopropanol containing solution over 10 wt% Fe-titanate/HZSM-5 photocatalyst was used.     

Mapping phosphorylation rate of fluoro-deoxy-glucose in rat brain by F chemical shift imaging

¹⁹F magnetic resonance spectroscopy (MRS) studies of 2-fluoro-2-deoxy-d-glucose (FDG) and 2-fluoro-2-deoxy-d-glucose-6-phosphate (FDG-6P) can be used for directly assessing total glucose metabolism in vivo. To date, ¹⁹F MRS measurements of FDG phosphorylation in the brain have either been achieved ex vivo from extracted tissue or in vivo by unusually long acquisition times. Electrophysiological and functional magnetic resonance imaging (fMRI) measurements indicate that FDG doses up to 500 mg/kg can be tolerated with minimal side effects on cerebral physiology and evoked fMRI-BOLD responses to forepaw stimulation. In halothane-anesthetized rats, we report localized in vivo detection and separation of FDG and FDG-6P MRS signals with ¹⁹F 2D chemical shift imaging (CSI) at 11.7 T. A metabolic model based on reversible transport between plasma and brain tissue, which included a non-saturable plasma to tissue component, was used to calculate spatial distribution of FDG and FDG-6P concentrations in rat brain. In addition, spatial distribution of rate constants and metabolic fluxes of FDG to FDG-6P conversion were estimated. Mapping the rate of FDG to FDG-6P conversion by ¹⁹F CSI provides an MR methodology that could impact other in vivo applications such as characterization of tumor pathophysiology.     

A note on acyclic edge coloring of complete bipartite graphs

An acyclic edge coloring of a graph is a proper edge coloring such that there are no bichromatic (2-colored) cycles. The acyclic chromatic index of a graph is the minimum number k such that there is an acyclic edge coloring using k colors and is denoted by a^′(G). Let Δ=Δ(G) denote the maximum degree of a vertex in a graph G. A complete bipartite graph with n vertices on each side is denoted by K_n,n. Alon, McDiarmid and Reed observed that a^′(K_p−1,p−1)=p for every prime p. In this paper we prove that a^′(K_p,p)≤p+2=Δ+2 when p is prime. Basavaraju, Chandran and Kummini proved that a^′(K_n,n)≥n+2=Δ+2 when n is odd, which combined with our result implies that a^′(K_p,p)=p+2=Δ+2 when p is an odd prime. Moreover we show that if we remove any edge from K_p,p, the resulting graph is acyclically Δ+1=p+1-edge-colorable.     

Effective operators and the truncation of shell model configuration space

An alternative derivation of the projection method for constructing effective operators in the truncated shell model space is presented. The results of explicit numerical calculations in three different nuclear regions are discussed. Non-hermiticity of the effective Hamiltonian and various hermitisation procedures are investigated in detail.     

Intermolecular dynamical charge fluctuations in water: a signature of the H-bond network

We report a simulation of deuterated water using a Car-Parrinello approach based on maximally localized Wannier functions. This provides local information on the dynamics of the hydrogen-bond network and on the origin of the low-frequency infrared activity. The oscillator strength of the translational modes, peaked around approximately 200 cm-1, is anisotropic and originates from intermolecular--not intramolecular--charge fluctuations. These fluctuations are a signature of a tetrahedral hydrogen-bonding environment.     

Comparative performance of INAA and other spectroscopy techniques in the elemental analysis of stainless steel materials

Samples of high alloy Stainless Steel SS 1 were analyzed by instrumental neutron activation analysis (INAA) at 5 research institutes in 4 European countries within the frame of an Inter-Laboratory Comparison (ILC) exercise aiming at checking if the results were independent of the standardization methods, and if INAA was accurate enough to contribute to certification. The mean element concentration values yielded by INAA were also compared with mean values obtained by atomic emission spectroscopy techniques at other laboratories that took part in the International Proficiency Testing organized by KIMAB Institute of Sweden, producer of the SS 1. The performances of the nuclear and atomic techniques were compared in terms of the z-score values calculated for 11 element concentrations evaluated by the two analytical ways. Finally, consideration is given to the ways in which highest accuracy and precision can be ensured for certifying stainless steels as CRMs.