NF Spectrum Research Articles

Direct nonlinear Fourier transform algorithms for the computation of solitonic spectra in focusing nonlinear Schrödinger equation

Starting from a comparison of some established numerical algorithms for the computation of the eigenvalues (discrete or solitonic spectrum) of the non-Hermitian version of the Zakharov–Shabat spectral problem, this article delivers new algorithms that combine the best features of the existing ones and thereby allays their relative weaknesses. Our algorithm is modelled within the remit of the so-called direct nonlinear Fourier transform (NFT) associated with the focusing nonlinear Schrödinger equation. First, we present the data for the calibration of existing methods comparing the relative errors associated with the computation of the continuous NF spectrum. Then each method is paired with different numerical algorithms for finding zeros of a complex-valued function to obtain the eigenvalues. Next we describe a new class of methods based on the contour integrals evaluation for the efficient search of eigenvalues. After that we introduce a new hybrid method, one of our main results: the method combines the advances of contour integral approach and makes use of the iterative algorithms at its second stage for the refined eigenvalues search. The veracity of our new hybrid algorithm is established by estimating the convergence speed and accuracy across three independent test profiles. Along with the development of a new approach for the computation of the eigenvalues, our study also addresses the problem of computation of the so-called norming constants associated with the eigenvalues. We show that our formalism effectively amounts to accurate and fast enough computation of residues of the reflection coefficient in the upper complex half-plane of the spectral parameter.

Pilot Electromagnetic Field Measurements in Certain Areas in Greece

This paper reports preliminary electromagnetic field measurements conducted indoors in selected locations in Greece. The paper focuses on the electromagnetic radiation (EMR) of the extremely low-frequency (ELF) and radiofrequency (RF) frequency bands because these bands are considered as possible human carcinogens according to the Scientific Committee on Emerging and Newly Identified Health Risks (SCENIHR). ELF electric and magnetic fields and RF electric fields were measured indoors in several locations in urban, suburban and rural areas of the Zakynthos and Lesvos islands, suburban houses of Ileia Prefecture (Peloponnisos) and urban dwellings of Attica. A total number of 4816 measurements were taken in Zakynthos (276), Lesvos (964), Ileia (29) and Attica (3547) in the frequency range 50 Hz–2500 MHz. Measurements were conducted with NARDA EMR-300 RF survey meter (3935), Aaronia HF and NF spectrum analyzers (795), HI 3604 Holaday ELF survey meter (48) and ANTENNESSA EME SPY (38). The maximum electric field strengths were in most cases below 5 V/m. Strength of electric fields up to 3000 V/m were addressed near high voltage power transmission lines. Stronger average electric fields were measured in urban areas. The strengths of the magnetic field were in most cases lower than 1000 nTesla (1 μTesla), but values up to 6000 nTesla (6 μTesla) were observed near high voltage power transmission lines. The results indicated that the EMR strength values varied but were all below domestic and international established limits.

Full characterization of the signal and idler noise figure spectra in single-pumped fiber optical parametric amplifiers

For the first time, four different noise sources, which are amplified quantum noise, Raman phonon seeded excess noise, pump transferred noise (PTN), and pump residual noise, are considered simultaneously to model the wavelength-dependent noise figure in a single-pumped fiber optical parametric amplifier. An asymmetric signal NF spectrum induced by both Raman phonon seeded excess noise and Raman gain modified PTN is measured in the electrical domain. Theoretical results agree very well with the experimental data. The idler NF spectrum is also analyzed and measured, which shows a more symmetric profile.

An active catalyst system for proton reduction composed of a bipyridyl platinum complex and a polymer membrane

Electrocatalysis for the H+ reduction with bis(2,2′-bipyridyl) Pt complex (Pt(bpy)22+) incorporated in a polymer matrix was studied. When the cyclic voltammogram (CV) was measured at a basal-plane pyrolytic graphite (BPG) electrode coated with a Nafion® (Nf) membrane incorporating Pt(bpy)22+ (denoted as BPG/Nf[Pt(bpy)22+]), a remarkable growth of the cathodic current due to H+ reduction was observed below –0.4 V (vs. Ag/AgCl) in a repeated scanning. A much higher amount of H2 was obtained with the system BPG/Nf[Pt(bpy)22+] than by the conventional Pt-black. The XPS spectrum of Nf[Pt(bpy)22+] showed the formation of zero-valent Pt after the electrochemical process, indicating that H+ reduction begins to take place after formation of the catalytically active species. This work shows that a highly active catalyst system for H+ reduction can be fabricated from a noble metal complex and a polymer matrix.

Fragmentation of the valence electronic states of NF 3+ studied by threshold photoelectron–photoion coincidence spectroscopy

The valence threshold photoelectron spectrum of NF 3 is reported for the first time in the literature, and threshold photoelectron–photoion coincidence (TPEPICO) spectroscopy has measured, state-selectively, the decay dynamics of the valence states of NF 3 + in the range 13–23 eV. Vacuum–UV radiation from the Daresbury synchrotron source dispersed by a 1 m Seya-Namioka monochromator photoionises the parent molecules. Electrons and ions are detected by threshold electron analysis and time-of-flight mass spectrometry, respectively. TPEPICO spectra are recorded continuously as a function of photon energy, allowing coincidence ion yields of the fragment ions and the breakdown diagram to be obtained. A comparison of the integrated threshold photoelectron and the total ion signals as a function of energy suggests that, in the range 16–19 eV, autoionisation via Rydberg states of NF 3 makes a significant contribution to the production of threshold electrons. The 50% crossover energy for production of NF 2 + from NF 3 + is determined to be 14.10±0.05 eV. The first onsets for NF 2 + and NF + production are 13.95±0.05 and 17.6±0.1 eV, respectively. The majority of the Franck–Condon region of the X ̃ 2 A 1 ground state of NF 3 + is stable with respect to dissociation to NF 2 +, whereas the unresolved A ̃ 2 E / B ̃ 2 A 2 states and most of the C ̃ 2 E state dissociate exclusively to NF 2 +. The D ̃ 2 A 1 and E ̃ 2 E states dissociate to NF +. Translational kinetic energy releases have been measured in NF 2 + and NF + at the energies of the Franck–Condon maxima of the valence states of NF 3 +. The results are compared with models assuming statistical and impulsive dissociation. The Ã/B̃ states of NF 3 + dissociate directly from the excited-state potential energy surface to NF 2 +, whereas the higher-lying C̃ state probably dissociates off the ground-state surface following rapid internal conversion. It is not possible to correlate unambiguously the formation of NF + with either F 2 or 2F, although on energetic grounds the latter products are more likely. Assuming that the neutral products are 2F, no information is obtained whether the two N–F bonds break simultaneously or sequentially.

Cataclysmic Variables and a Candidate Helium White Dwarf in the Globular Cluster NGC 6397

We have used the Hubble Space Telescope (HST ) and the Faint Object Spectrograph (FOS) to study faint UV stars in the core of the nearby globular cluster NGC 6397. We con—rm the presence of a fourth cataclysmic variable (CV) in NGC 6397 (hereafter CV 4), and we use the photometry of Cool et al. to present evidence that CVs 1¨4 all have faint disks and probably low accretion rates. By combining these results with new UV spectra of CV 1 and the published spectra of Grindlay et al., we present new evi- dence that CVs 1¨3 may be DQ Her systems, as originally suggested by Grindlay et al., and we show that CV 4 may either be a dwarf nova or another magnetic system. Another possibility is that the CVs could be old novae in hibernation between nova eruptions. We also present the —rst spectrum of a member of a new class of UV bright stars in NGC 6397. These faint, hot stars do not vary, unlike the CVs, and are thus denoted as ii non—ickerers ˇˇ (NFs). Like the CVs, their spatial concentration is strongly concentrated toward the cluster center. Using detailed comparisons with stellar atmosphere models, we have determined log g 6.25 ^ 1.0 and K for this NF. Using these line parameters T eff 17,500 ^ 5,000 and the luminosity of the NF, we show that the NF spectrum is consistent with a helium WD having a mass of D0.25 and an age between 0.1 and 0.5 Gyr (depending on the models used). The NF spec- M _ trum appears to be signi—cantly Doppler shifted from the expected wavelength, suggesting the presence of a dark, massive companion, probably a carbon-oxygen (CO) WD. Subject headings: globular clusters: individual (NGC 6397) ¨ novae, cataclysmic variables

The microwave spectrum of the NF radical in the second electronically excited (b 1Σ+) state: Potentials of three low-lying states (X 3Σ−,a 1Δ,b 1Σ+)

The pure rotational transition of the NF radical in the second electronically excited state, b 1Σ+, was detected by microwave spectroscopy. The NF radical was generated by dc-discharge through a mixture of NF3 and H2 at around 90 K. Six rotational transitions for v=0 and four for v=1 were observed in the 73–442 GHz region. In addition to the rotational and centrifugal distortion constants, the quadrupole coupling constant of the nitrogen nucleus of NF(b 1Σ+) was determined for the first time from the lowest two transitions of NF in the v=0 level. The spectrum of NF(a 1Δ) in the first vibrational excited state was also observed in order to derive highly accurate potential parameters for comparison with the data of NF(X 3Σ−,b 1Σ+).

ChemInform Abstract: The Microwave Spectrum of the NF Radical in the Metastable Electronic State (a 1δ).

AbstractThe microwave spectrum of NF (a 1Δ), generated in the dc discharge plasma of NF3 and H2, has been analyzed.

An ab initio calculation of the barrier to inversion in NF3+

Abstract It is shown that electron correlation is important in determining the inversion barrier in NF + 3 . Employing polarized basis sets, the barrier height has been calculated to be 10–11 and 14–17 kcal mol without and with correlation energies, respectively. The experimental value was estimated at 17.3 kcal mol from vibrational analysis of the first band in the photoelectron spectrum of NF 3 .

Far infrared laser magnetic resonance spectrum of NF(a 1Δ)

The NF radical in its a 1Δ metastable state has been detected by far infrared laser magnetic resonance spectroscopy at 513 μm. The spectrum arises from the J = 7→8 rotational transition, and yields an accurate measurement for this spacing of 19.55172 cm−1.

The Raman spectrum of NF3: Coriolis coupling and transition dipole interaction in the liquid

First order Coriolis coupling in an e-symmetry mode of a symmetric top and its consequences on the associated Raman line in the liquid are investigated for classical rotations and a classical harmonic vibration. Except for quantum asymmetries, the overall features of the Raman line are reproduced. The second and fourth classical moments of the e-symmetry Raman line are given together with an expression of the linewidth for Debye diffusion. The relevant autocorrelation function <Trβ (0) β (t) ≳ is obtained for free rotation and J rotational diffusion. The Raman spectrum of gaseous NF3 was recorded and the band contours of ν3(e) and ν4(e) were analyzed to determine the intensity ratio between the contributions of γ±1 and γ±2. The Raman profiles were studied in the plastic crystal and in the liquid between 60 and 185 K. The intense infrared lines ν1(a1) and ν3(e) show complex structures made up of two peaks at low temperature, similar to the LO-TO structures of the intense infrared lines of crystals and which are due to a particularly strong transition dipole coupling. The separation between peaks, which is proportional to the integrated infrared intensity of the lines, can be reasonably well predicted by the theory of cubic crystals. The isotropic part of ν1 looses its pseudo-LO-TO structure above 100 K and narrows as the temperature increases, due to rotational averaging of transition dipole coupling. The weak infrared lines ν2(a1) and ν4(e) have temperature-sensitive, symmetrical Raman spectra which were analyzed in terms of molecular rotations. The NF3 molecules rotate more easily about the main axis with a ratio between the mean angles Φ∥ and Φ⊥ of rotation about the main axis and the other axis, respectively, equal to ∼3 at 78 K. The Coriolis perturbation is found to reduce the contribution of the spinning motion to the linewidth of ν4, by a factor of 3 owing to the large value of the Coriolis constant ζ4=−0.895.

Intensities of binary overtone and combination bands in the i.r. spectrum of NF 3

The intensities of the binary overtone and combination bands in the i.r. spectrum of NF 3 have been measured in the gas phase and in liquid—argon solution. The observed intensities have been interpreted in terms of a simple model which ascribes all the intensity of the binary overtones and combinations to anharmonic coupling with the fundamentals; i.e., a model in which the second derivatives of the dipole moment with respect to the normal coordinates are assumed to be zero. The agreement between the observed intensities and the calculated ones is extremely good for the bending modes but less satisfactory for the stretching modes. The use of a polar-tensor model to predict the intensities of the vibrational fundamentals is also explored.

Infrared spectra of simple molecules in liquid-argon solution—II. NF 3 and N 2O

The i.r. spectrum of NF 3 has been measured in liquid-argon solution. Since the sample of NF 3 used for the experiments was contaminated with N 2O, it was also necessary to measure the spectrum of N 2O in liquid-argon solution so that the impurity bands could be identified unambiguously. In the observed spectrum of NF 3 it was possible to identify 29 overtone and combination bands in addition to the vibrational fundamentals. The measured wavenumbers of the NF 3 bands have been used to estimate the anharmonic coefficients x ss′, which are compared with the corresponding quantities determined from the gas-phase spectrum.

Microwave spectrum of NF 2

About 350 lines in the microwave spectrum of NF 2 have been measured in various ranges of frequency between 13.0 and 65.2 GHz by using two types of Zeeman effect spectrometers. Complete assignment of all lines has been achieved and, via the general microwave computer program SPINRO, the rotational constants, centrifugal distortion constants, dipole moment, electronic spin-rotation coupling constants, the constants for the coupling of the several nuclear spins with the electron spin and the nitrogen quadrupole coupling constants have all been obtained. By drawing upon the observed vibrational frequencies the average geometry of NF 2 has been evaluated. Force constants and Coriolis coupling constants have also been derived. The values of the spin coupling constants for N and for F indicate that NF 2 is a π-radical with the spin density mainly located on nitrogen. The multiplet patterns indicate that the ground electronic state wavefunction is antisymmetric to rotation about the molecular symmetry axis and so, for a π-radical, identifies the ground state as 2 B 1 as has previously been assumed for this molecule.

L-type resonance in an overtone band. The 2 ν4 spectrum of nitrogen trifluoride

l-type resonance in an overtone band is discussed. It is shown that if the anharmonic constant g ll is small the resonance effect may be as large as or even larger than, the corresponding fundamental. Intensity perturbation may be manifested by the appearance of forbidden lines. This analysis is applied to the high frequency portion of the 2 ν 4 spectrum of NF 3 and band constants are obtained.

Gas-phase electron paramagnetic resonance spectrum and dipole moment of NF( 1 ∆)

The gas-phase paramagnetic resonance spectrum of NF in the J = 2 rotational level of the 1 ∆ state has been studied, and the dipole moment in this state is found to be 0.37 ± 0.60D. The rotational constant previously determined from the electronic spectrum is shown to be consistent with the electron resonance results, and the 14 N quadrupole coupling constant e 2 qQ is 4.1 ± 0.2 MHz. The hyperfine coupling constants of the 14 N and 19 F nuclei are + 109.92 ± 0.14 and +758.06 ± 0.23 MHz respectively.

The electron paramagnetic resonance spectrum of NF( 1Δ) in the gas phase

EPR transitions of NF in its 3Σ − ground state and for the J = 2 level of its 1Δ first excited state have been detected in the reaction between hydrogen atoms and NF 2 in the gas phase. Second order effects have been detected in the nuclear hyperfine interaction; comparison of the hyperfine splittings is of some interest.

The absorption spectrum of NF 2

In the course of flash-photolysis kinetic-spectroscopy experiments on NF containing compounds, it was found necessary to examine the absorption of the NF 2 radical at 2600Å reproted by Johnson and Colburn. Johnson and Colburn, using a Beckman Model DK-1 recording spectrophotometer, were able to demonstrate that NF 2 is responsible for this absorption but limited their description of the spectrum to the statement that it was a “poorly structured band” with a “maximum at 260 mμ with a 20-mμ half-width”. Their primary use of this absorption has been to demonstrate the existence of the equilibrium N 2F 4 ⇄ 2 NF 2 and to measure the equilibrium constant as a function of temperature. This communication reports a study of this absorption at a higher dispersion than that used by these authors.