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.     

The Structurally Regular trans-1,4-Poly(chloroprene)

Radiation polymerization of large crystals of chloroprene formed within the temperature range -130 to -180°C has yielded the stereoregular trans-1,4-poly(2-chloro-1,3-butadiene). The monomer was found to have a glass transition temperature of ca. -180°C. Polymerization of monomer rapidly cooled to below -180°C was difficult and gave only structurally irregular polymer in low yield.     

Synthesis and tautomerism of spiro-pyrazolines

An experimental study on the synthesis, tautomerism, and acid promoted structural changes of spiro-pyrazolines is described. The target was achieved through a [3+2]-dipolar cycloaddition of an alkene with nitrile imines generated in situ and was isolated in high yield. The synthesized cycloadduct displayed a tendency to exhibit an imine–enamine type of tautomerism as evidenced by X-ray crystal and NMR studies. Furthermore, addition of an acid resulted in the transformation of an imine tautomer to an enamine. The current report constitutes a first formal observation of this kind of tautomerism observed in spiro-indoline pyrazolines.     

The structure and helicity of perfluorooctanonitrile, CF3–(CF2)6–CN

New molecular structural data is presented for a cyanide terminated oligomer of polytetrafluoroethene. The target molecule, CF₃–(CF₂)₆–CN, has been seeded within a pulsed supersonic expansion of argon. The result of this action is to cool the species to rotational temperatures below 4 K. Within this state, the pure rotational spectrum of the oligomer has been recorded using two types of Fourier transform microwave spectroscopy. A total of 111 transitions have been identified involving rotational J levels between 6 and 40. Only a- and b-type transitions were observed. The spectrum has been analyzed using a Hamiltonian containing all three rotational constants and one centrifugal distortion constant, D_J. The experimental spectroscopic constants have been used to develop an effective molecular structure by scaling the quantum chemical calculated structure. The data shows that the seven carbon perfluorinated chain for the isolated oligomer twists ≈104°. This compares well to the C₇F₁₃-twist of ≈97° anticipated from the X-ray structure of phase II polytetrafluoroethene.