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.     

Thermally stimulated depolarization current spectra of cross-linked polyethylene and the influence of cross-linking byproducts

Cross-linked polyethylene (XLPE) is notable for its use as power cable insulation. Its longevity is limited by space charge buildup linked to impurities such as the byproducts left behind by the cross-linking agent dicumyl peroxide (DCP). The goal of this work is to determine the impacts of these byproducts on charge trapping and detrapping in XLPE using the thermally stimulated depolarization current technique. XLPE with byproducts has one source of trapped charge, which originates from the byproducts. XLPE that was thermally treated via degassing exhibits two other sources of trapped charge, which are charge injection and dipolar relaxations. Oxidation from degassing was shown to control the trapping from these sources, which is useful knowledge for processing this material prior to its use. Reintroducing acetophenone, one of the major byproducts of DCP, suppresses those two peaks once more, showing that it controls the overall space charge buildup characteristics in XLPE.     

Density Functional Study of Tetraphenylporphyrin Long-Range Exciton Coupling

The performance of time-dependent density functional theory (TDDFT) for calculations of long-range exciton circular dichroism (CD) is investigated. Tetraphenylporphyrin (TPP) is used as a representative of a class of strongly absorbing chromophores for which exciton CD with chromophore separations of 50 Å and even beyond has been observed experimentally. A dimer model for TPP is set up to reproduce long-range exciton CD previously observed for a brevetoxin derivative. The calculated CD intensity is consistent with TPP separations of over 40 Å. It is found that a hybrid functional with fully long-range corrected range-separated exchange performs best for full TDDFT calculations of the dimer. The range-separation parameter is optimally tuned for TPP, resulting in a good quality TPP absorption spectrum and small DFT delocalization error (measured by the curvature of the energy calculated as a function of fractional electron numbers). Calculated TDDFT data for the absorption spectra of TPP are also used as input for a ‘matrix method’ (MM) model of the exciton CD. For long-range exciton CD, comparison of MM spectra with full TDDFT CD spectra for the dimer shows that the matrix method is capable of producing very accurate results. A MM spectrum obtained from TPP absorption data calculated with the nonhybrid Becke88–Perdew86 (BP) functional is shown to match the experimental brevetoxin spectrum ‘best’, but for the wrong reasons.     

Acoustic emission from composite-reinforced metals

Acoustic-emission (AE) count rates are presented for tensile loading of unidirectional boron-epoxy and for aluminum sheets reinforced with unidirectional boron-epoxy. It is shown that different prepreg materials have different characteristic AE patterns. Results from composite-reinforced metal specimens show that early failures are accompanied by a sharp increase in AE count rate at the knee of the bilinear stress-strain diagram. It is further shown that the count rates are a function of specimen fabrication and that higher total counts do not necessarily correspond to early failures.     

Ricci curvature and monotonicity for harmonic functions

In this paper we generalize the monotonicity formulas of “Colding (Acta Math 209:229–263, 2012)” for manifolds with nonnegative Ricci curvature. Monotone quantities play a key role in analysis and geometry; see, e.g., “Almgren (Preprint)”, “Colding and Minicozzi II (PNAS, 2012)”, “Garofalo and Lin (Indiana Univ Math 35:245–267, 1986)” for applications of monotonicity to uniqueness. Among the applications here is that level sets of Green’s function on open manifolds with nonnegative Ricci curvature are asymptotically umbilic.     

Efficient Preparation of ((3‐Chloro‐2‐fluoro‐phenyl)‐[7‐methoxy‐8‐(3‐morpholin‐4‐yl‐propoxy)‐10,11‐dihydro‐5‐oxa‐2,4,11‐triaza‐dibenzo(a,d)cyclohepten‐1‐yl]‐amine) for In‐Vivo Study

An improved route for the preparation of highly functionalized 5,6‐dihydro‐pyrimido[4,5‐b][1,4]oxazepine 1a in multigram quantities was developed. This new methodology was highlighted by the proper methoxy disposition via a regioselective methylation of 2,4,5‐trihydroxy‐benzaldehyde followed by a magnesium sulfate–promoted cyclization.