On the roots of Wiener polynomials of graphs

The Wiener polynomial of a connected graph $G$ is defined as $W(G;x)=\sum x^{d(u,v)}$, where $d(u,v)$ denotes the distance between $u$ and $v$, and the sum is taken over all unordered pairs of distinct vertices of $G$. We examine the nature and location of the roots of Wiener polynomials of graphs, and in particular trees. We show that while the maximum modulus among all roots of Wiener polynomials of graphs of order $n$ is $\left(\genfrac{}{}{0ex}{}{n}{2}\right)?1$, the maximum modulus among all roots of Wiener polynomials of trees of order $n$ grows linearly in $n$. We prove that the closure of the collection of real roots of Wiener polynomials of all graphs is precisely $(?\infty ,0]$, while in the case of trees, it contains $(?\infty ,?1]$. Finally, we demonstrate that the imaginary parts and (positive) real parts of roots of Wiener polynomials can be arbitrarily large.     

The semi-analytical method for time-dependent wave problems with uncertainties

This paper provides a constructive procedure for the computation of approximate solutions of random time-dependent hyperbolic mean square partial differential problems. Based on the theoretical representation of the solution as an infinite random improper integral, obtained via the random Fourier transform method, a double approximation process is implemented. Firstly, a random Gauss-Hermite quadrature is applied, and then, the evaluations at the nodes of the integrand are approximated by using a random Störmer numerical method. Numerical results are illustrated with examples.     

Transmission eigenvalues with artificial background for explicit material index identification

We are interested in the problem of retrieving information on the refractive index n of a penetrable inclusion embedded in a reference medium from farfield data associated with incident plane waves. Our approach relies on the use of transmission eigenvalues (TEs) that carry information on n and that can be determined from the knowledge of the farfield operator F. In this note, we explain how to modify F into a farfield operator $F^{\mathrm{art}}=F?\stackrel{?}{F}$, where $\stackrel{?}{F}$ is computed numerically, corresponding to well-chosen artificial background and for which the associated TEs provide more accessible information on n.     

Efficiency of a DC magnetic field used for braking the flow within a continuous casting mould

The continuous casting technology provides about 90 percent of the world steel production. The application of DC magnetic fields in form of so-called electromagnetic brakes is considered for an effective flow control with substantial capabilities to improve the product quality or to enhance the productivity of the process. The main effect of the DC magnetic field is supposed to result in a uniform reduction of the maximum velocities in the discharging jet from the submerged entry nozzle and to damp violent turbulent fluctuations. However, the electromagnetic braking of such highly turbulent and complex flows is complicated phenomenon and has not been understood fully until now. We present numerical and experimental investigations focusing on the fluid flow in the continuous casting mould under the influence of a transverse magnetic field. Numerical calculations were performed using the software package CFX with an implemented RANS-SST turbulence model. the non-isotropic nature of the MHD turbulence was taken into account by specific modifications of the turbulence model. Corresponding experimental investigations were carried out at the mock-up LIMMCAST at HZDR. The comparison between our numerical calculations and the experimental results display a very well agreement. An important outcome of this study is the feature that the magnetic field does not provide a continuous reduction of the velocity fluctuations at the nozzle port. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

N-Nitrosopiperazines form at high pH in post-combustion capture solutions containing piperazine: a low-energy collisional behaviour study

During the process of exploring aqueous piperazine chemistry under simulated flue‐gas scrubbing conditions, positive‐ion electrospray ionisation mass spectrometric (ESI‐MS) analyses of the resulting reaction mixtures in a triple quadrupole system revealed the presence of peaks at m/z 116 and 145, the putative N‐nitroso derivatives of piperazine. Confirmation of the presence of these species in the reaction mixtures was achieved using collision‐induced dissociation experiments. A purchased standard, together with in‐house synthesised N‐nitrosopiperazine standards (including N‐nitroso derivatives derived from deuterium‐labelled precursor materials), were used for this purpose. Across a small range of collision energies, large fluctuations in the abundance of the two major product ions of protonated N‐nitrosopiperazine, m/z 86 and 85, were observed. Using B3LYP/6‐311 + +G(d,p) computations, the potential energy surface was determined for loss of NO and [H,N,O]. At an activation energy slightly in excess of 1 eV, intramolecular isomerisation precedes loss of NO (m/z 86) via a 4,1 H‐shift, and at activation energies between 2.1–2.3 eV, consecutive loss of NO and atomic hydrogen competes with the direct loss of nitrosyl hydride (m/z 85). It is recommended that any multiple reaction monitoring method for quantifying N‐nitrosopiperazines at low collision energies use the sum of both transitions (m/z 116 ← 85, m/z 116 ← 86) to avoid errors that could be introduced by subtle changes in ES source conditions or collision voltages. This approach is adopted in an HPLC/MS/MS method used to monitor the degradation of N‐nitrosopiperazine exposed to (i) broad‐band UV light and (ii) heat typical of an amine regeneration (stripper) tower. The results reveal that aqueous N‐nitrosopiperazine is thermally stable at 150°C but will degrade slowly upon exposure to UV light. Copyright © 2010 John Wiley & Sons, Ltd.     

Anhydrous CeCl3 catalyzed C3-selective propargylation of indoles with tertiary alcohols

Anhydrous CeCl₃ was successfully used as catalyst for the synthesis of several 3-propargyl indoles in good yields through the reaction of indole with propargyl alcohols in nitromethane.     

High-pressure phase equilibria of binary and ternary mixtures of carbon dioxide,triglycerides and free fatty acids: Measurement and modeling with the GC-EOS

Vapor–liquid equilibria were measured for binary systems including carbon dioxide and free fatty acids such as oleic and linoleic acid, triglycerides as triolein or vegetable oils as sunflower oil, and modelled by the Group Contribution Equation of State (GC-EoS). Binary group parameters used in the calculation and prediction of CO₂–triglycerides systems were obtained from the literature but in the case of CO₂-free fatty acids, binary group parameters were adjusted through a parameterization strategy. At the end, a unique set of parameters could be established to model systems of vegetable oils at high pressures in the presence of CO₂. Moreover, a strategy to calculate the two-phase region in a ternary diagram was also studied. The good correspondence between theoretical and experimental results suggests that the strategy and the set of binary group parameters proposed in this work can be reliable predictive tools for using GC-EoS to describe systems involving vegetable oils with a composition based mainly in free fatty acids and triglycerides, such as those which can be encountered, for example, in oil deacidification processes using supercritical CO₂.     

Intermolecular potential parameters and combining rules determined from viscosity data

The law of corresponding states has been demonstrated for a number of pure substances and binary mixtures and provides evidence that the transport properties viscosity and diffusion can be determined from a molecular shape function, often taken to be a Lennard–Jones 12‐6 potential, that requires two scaling parameters: a well depth ε_ij and a collision diameter σ_ij, both of which depend on the interacting species i and j. We obtain estimates for ε_ij and σ_ij of interacting species by finding the values that provide the best fit to viscosity data for binary mixtures and compare these to calculated parameters using several “combining rules” that have been suggested for determining parameter values for binary collisions from parameter values that describe collisions of like molecules. Different combining rules give different values for σ_ij and ε_ij, and for some mixtures the differences between these values and the best‐fit parameter values are rather large. There is a curve in (ε_ij, σ_ij) space such that parameter values on the curve generate a calculated viscosity in good agreement with measurements for a pure gas or a binary mixture. The various combining rules produce couples of parameters ε_ij, σ_ij that lie close to the curve and, therefore, generate predicted mixture viscosities in satisfactory agreement with experiment. Although the combining rules were found to underpredict the viscosity in most of the cases, Kong's rule was found to work better than the others, but none of the combining rules consistently yields parameter values near the best‐fit values, suggesting that improved rules could be developed. © 2010 Wiley Periodicals, Inc. *

1 This article is a U.S. Government work and, as such, is in the public domain of the United States of America.

Int J Chem Kinet 42: 713–723, 2010     

Reaction of a phospholipid monolayer with gas-phase ozone at the air-water interface: measurement of surface excess and surface pressure in real time

The reaction between gas-phase ozone and monolayers of the unsaturated lipid 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine, POPC, on aqueous solutions has been studied in real time using neutron reflection and surface pressure measurements. The reaction between ozone and lung surfactant, which contains POPC, leads to decreased pulmonary function, but little is known about the changes that occur to the interfacial material as a result of oxidation. The results reveal that the initial reaction of ozone with POPC leads to a rapid increase in surface pressure followed by a slow decrease to very low values. The neutron reflection measurements, performed on an isotopologue of POPC with a selectively deuterated palmitoyl strand, reveal that the reaction leads to loss of this strand from the air-water interface, suggesting either solubilization of the product lipid or degradation of the palmitoyl strand by a reactive species. Reactions of (1)H-POPC on D(2)O reveal that the headgroup region of the lipids in aqueous solution is not dramatically perturbed by the reaction of POPC monolayers with ozone supporting degradation of the palmitoyl strand rather than solubilization. The results are consistent with the reaction of ozone with the oleoyl strand of POPC at the air-water interface leading to the formation of OH radicals. The highly reactive OH radicals produced can then go on to react with the saturated palmitoyl strands leading to the formation of oxidized lipids with shorter alkyl tails.