An investigation of the critical liquid-vapor properties of dilute KCl solutions

The three parameters that define the critical point, temperature, pressure, and volume have been experimentally determined by means of filling studies in a platinum-lined system for five KCl solutions ranging from 0.006 to 0.568m. The platinum-lined vessels were used to overcome the problems with corrosion experienced by earlier workers. The critical temperature (t _c), pressure (P _c), and volume (V _c) were found to fit the equations $\begin{gathered} {\text{t}}_c = 374.14{\text{ }} + {\text{ }}16.602\sqrt {\text{m}} {\text{ }} + {\text{ }}41.740{\text{m }} \pm 0.5^ \circ C \hfill \\ {\text{P}}_c = 220.9 {\text{ }} + {\text{ }}135.164{\text{m }} + {\text{ }}41.173{\text{m}}^{\text{2}} {\text{ }} \pm {\text{ }}0.5 bars \hfill \\ {\text{V}}_c = 3.155{\text{ }} - {\text{ }}1.373\sqrt m {\text{ }} + {\text{ }}0.507{\text{m }} \pm {\text{ }}0.008cm^3 - g^{ - 1} \hfill \\ \end{gathered} $ from infinite dilution to 1.0m.     

Variational derivation and extensions of distributed approximating functionals

Summary Extensions of the "Distributed Approximating Functional (DAF) approach to approximating functions and their derivatives are given. The method, although inherently approximate, can be made arbitrarily accurate, numerically stable, and computationally efficient by appropriate choice of parameters. It also provides approximate representations of quantum operators which are analytic and which can be accurate. Differences between the DAFs and more standard basis set approaches are discussed in order to clarify the properties of the DAFs. Some illustrative examples are given.Supported in part under National Science Foundation Grant CHE92-01967.The Ames Laboratory is operated for the Department of Energy by Iowa State University under Contract No 2-7405-ENG82.Supported under National Science Foundation Grants CHE-8907429 and CHE-9403416.Supported under R.A. Welch Foundation Grant E-0608.Supported under National Science Foundation Grants CHE-8907429 and CHE-9403416.     

Novel one pot synthesis of polysubstituted pyrazolo[1,5-a]- and imidazo[1,2-a]pyrimidines

We have described a convenient regioselective one-pot approach to pyrazolo[1,5-a]- and imidazo[1,2-a]pyrimidine derivatives from α,β-unsaturated imines generated in situ and amino heterocycles. Reaction is general with respect to all three components, namely (i) nitrile, (ii) aldehyde, and (iii) amino heterocycle reagents. Good yields (52-77%), convenient isolation of the targeted molecules are the distinct characteristics of the developed protocol.     

A molecule with small rotational constants containing an atom with a large nuclear quadrupole moment: The microwave spectrum of trans-1-iodoperfluoropropane

Using pulsed jet chirped-pulse, and cavity-based Fourier transform microwave spectroscopies over 900 transitions have been recorded for the title molecule in the 1–4 GHz and 8–18 GHz regions. The C₁,C₂ and C₃ carbon-13 species have been observed in natural abundance allowing a substitution structure for the CCC backbone to be determined. Nearly all the transitions observed were either a-type R branches or b-type Q branches. No c-type transitions were observed consistent with only the trans conformer being present under our experimental conditions. The χ_aa,χ_bb,χ_cc and χ_ab components of the iodine nuclear quadrupole coupling tensor have been determined. Of note, several forbidden, ΔJ±2 transitions, and one ΔJ±3 transition were observed with quite reasonable intensity. These observations have been rationalized through considerations of near degeneracies between energy levels connected via a large χ_ab value (≈1 GHz).     

On the Minimum Average Distance Spanning Tree of the Hypercube

Given an undirected and connected graph G, with a non-negative weight on each edge, the Minimum Average Distance (MAD) spanning tree problem is to find a spanning tree of G which minimizes the average distance between pairs of vertices. This network design problem is known to be NP-hard even when the edge-weights are equal. In this paper we make a step towards the proof of a conjecture stated by A.A. Dobrynin, R. Entringer and I. Gutman in 2001, and which says that the binomial tree B _n is a MAD spanning tree of the hypercube H _n . More precisely, we show that the binomial tree B _n is a local optimum with respect to the 1-move heuristic which, starting from a spanning tree T of the hypercube H _n , attempts to improve the average distance between pairs of vertices, by adding an edge e of H _n -T and removing an edge e′ from the unique cycle created by e. We also present a greedy algorithm which produces good solutions for the MAD spanning tree problem on regular graphs such as the hypercube and the torus.     

Using the complex polynomial method with Mathematica to model problems involving the Laplace and Poisson equations

The complex polynomial method variant of the well‐known complex variable boundary element method (CVBEM) is reexamined in its utility in solving Partial Differential Equations (PDE) of the Poisson and Laplace type. Because the CVBEM was recently extended to three and higher dimensions, the use of complex polynomials to solve higher dimension PDE becomes apparent and therefore the advantages afforded by the use of complex polynomials can be brought to focus on higher dimension problems. Because complex polynomials involve use of computational algorithms that require high accuracy in numerical precision, including the solution of fully populated nonsymmetric matrices, the computer program Mathematica is evaluated for use as the underlying computational engine. Furthermore, Mathematica is evaluated for its internal high‐accuracy computational features and algorithms, including ease of program setup. In this research, the new program is found to provide at least a 5‐fold increase in complex polynomial degree utilization (from degree 10 to degree 50), with computational speed less than was involved in the original degree 10 approximation of Hromadka and Guymon [ASCE J Hydraulic Eng 110 (1984), 329–339], and with exceptional computational accuracy and reporting features. The Mathematica program is quite small and is provided to the reader as freeware and can be obtained from the first author. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Modulational instability in the cubic-quintic nonlinear Schrödinger equation through the variational approach

The dynamics of nonlinear pulse propagation in an average dispersion-managed soliton system is governed by a constant coefficient nonlinear Schrödinger (NLS) equation. For a special set of parameters the constant coefficient NLS equation is completely integrable. The same constant coefficient NLS equation is also applicable to optical fiber systems with phase modulation or pulse compression. We also investigate MI arising in the cubic-quintic nonlinear Schrödinger equation for ultrashort pulse propagation. Within this framework, we derive ordinary differential equations (ODE’s) for the time evolution of the amplitude and phase of modulation perturbations. Analyzing the ensuing ODE’s, we derive the classical modulational instability criterion and identify it numerically. We show that the quintic nonlinearity can be essential for the stability of solutions. The evolutions of modulational instability are numerically investigated and the effects of the quintic nonlinearity on the evolutions are examined. Numerical simulations demonstrate the validity of the analytical predictions.     

Quantum fluctuations of the refractive index near the interface between a metal and a nonlinear dielectric

Zero-point fluctuations of surface plasmon modes near the interface between a metal and a nonlinear dielectric are shown to produce a thin layer of shifted fluctuating dielectric constant near the interface. The shift of the dielectric constant in this layer may be sufficiently large to produce multiple metastable states of the surface plasmon vacuum.     

Resolution enhancement of a surface immersion microscope near the plasmon resonance

Resolution of a surface immersion microscope has been studied as a function of surface-plasmon-polariton frequency. Enhancement of resolution near the surface-plasmon resonance has been observed. This effect may potentially be used in direct imaging of biological samples in liquid ambient.     

Supercooling molecular hydrogen down through the superfluid transition

Recent calculations by Vorobev and Malyshenko [JETP Lett. 71, 39 (2000)] show that molecular hydrogen may stay liquid and superfluid in strong electric fields of the order of 4x10(7) V/cm. I demonstrate that strong local electric fields of similar magnitude exist beneath a two-dimensional layer of electrons localized in the image potential above the surface of solid hydrogen. Even stronger local fields exist around charged particles (ions or electrons) if the surface or bulk of a solid hydrogen crystal is statically charged. Measurements of the frequency shift of the 1 --> 2 photoresonance transition in the spectrum of a two-dimensional layer of electrons above a positively or negatively charged solid hydrogen surface performed in the temperature range 7-13.8 K support the prediction of electric field induced surface melting. The range of surface charge density necessary to stabilize the liquid phase of molecular hydrogen at the temperature of superfluid transition is estimated.