Tunneling Assists the 1,2‐Hydrogen Shift in N‐Heterocyclic Carbenes

At room temperature, 1,2‐hydrogen‐transfer reactions of N‐heterocyclic carbenes, like the imidazol‐2‐ylidene to give imidazole is shown to occurr almost entirely (>90 %) by quantum mechanical tunneling (QMT). At 60 K in an Ar matrix, for the 2, 3‐dihydrothiazol‐2‐ylidene→thiazole transformation, QMT is shown to increase the rate about 10⁵ times. Calculations including small‐curvature tunneling show that the barrier for intermolecular 1,2‐hydrogen‐transfer reaction is small, and QMT leads to a reduced rate of the forward reaction because of nonclassical reflections even at room temperature. A small barrier also leads to smaller kinetic isotope effects because of efficient QMT by both H and D. QMT does not always lead to faster reactions or larger KIE values, particularly when the barrier is small.     

Intraband effects on ultrafast pulse propagation in semiconductor optical amplifier

High bit-rate (>10 Gb/s) signals are composed of very short pulses and propagation of such pulses through a semiconductor optical amplifier (SOA) requires consideration of intraband phenomena. Due to the intraband effects, the propagating pulse sees a fast recovering nonlinear gain which introduces less distortion in the pulse shape and spectrum of the output pulse but introduces a positive chirping at the trailing edge of the pulse.     

Construction of infinite unimodular sequences with zero autocorrelation

Unimodular waveforms x are constructed on the integers with the property that the autocorrelation of x is one at the origin and zero elsewhere. There are three different constructions: exponentials of the form e^{2 pi na q},e^{2 \pi i n^\alpha \theta}, sequences taken from roots of unity, and sequences constructed from the elements of real Hadamard matrices. The first is expected and elementary and the second is based on the construction of Wiener. The third is the most intricate and is really one of a family of distinct but structurally similar waveforms. A natural error estimate problem is posed for the last construction. The analytic solution is not as useful as the simulations because of the inherent counting problems in the construction.     

Spin-filter device based on the Rashba effect using a nonmagnetic resonant tunneling diode

We propose an electronic spin-filter device that uses a nonmagnetic triple barrier resonant tunneling diode (TB-RTD). This device combines the spin-split resonant tunneling levels induced by the Rashba spin-orbit interaction and the spin blockade phenomena between two regions separated by the middle barrier in the TB-RTD. Detailed calculations using the InAlAs/InGaAs material system reveal that a splitting of a peak should be observed in the I-V curve of this device as a result of the spin-filtering effect. The filtering efficiency exceeds 99.9% at the peak positions in the I-V curve.     

Error-systematics of determining elemental isotopic abundance ratios by the molecular ion beam method: a case study for the simultaneous isotopic analysis of lithium and boron as Li2BO2+

The simultaneous isotopic analysis of lithium and boron by the Li2BO2+ ion beam method involves measurements of two different molecular abundance ratios (say, Rj+/-delta(j) and Rk+/-delta(k)), and subsequently extensive calculations to arrive at the analyte isotopic ratios (say, L and Y). It is not presently known how the measurement errors (delta(j) and delta(k)) are transformed into the errors of analysis (deltaL and deltaY). This work addresses this question from fundamental considerations. In the literature, the calculations are sometimes simplified using Ri formulae based on Li2B16O2+ ions and then applying correction factors for the actual Li2BO2+ ions, but this procedure is not generally applicable. We show how equations based on true Li2BO2+ ions (with full isotopic variations of all the constituent elements) can be solved, and illustrate the procedure with several examples. These studies show that accuracy of analysis depends not only on the accuracies of measurements, delta(j) and delta(k), but also on the particular isotopic Li2BO2+ ion-pairs (j and k) used as the monitor pairs. Moreover, this dependence is shown to be different for the different isotopic ratios (L and Y) to be determined simultaneously. Therefore, proper selection of monitor molecular pairs is a requirement for avoiding larger (propagated) errors in the analysis. Similar arguments would, in fact, apply to any arbitrarily chosen case of determining two or an even greater number of isotopic abundance ratios (Ei's) by the molecular ion beam method, irrespective of whether the different analyte ratios, Ei's, relate to a single multi-isotopic element, or different elements.     

Effect of pH on the fluorescence and absorption spectra of hypericin in reverse micelles

The well-characterized, monodispersed nature of reverse micelles formed by sodium bis(2-ethylhexyl)sulfosuccinate/heptane and their usefulness in approximating a membrane-like environment have been exploited to investigate the effect of pH and water pool size on the photophysical properties of hypericin (Hyp). Our measurements reveal two titratable groups of pKa approximately 1.5 and approximately 12.5. These are assigned to the HypH+/Hyp equilibrium (the deprotonation of a carbonyl group) and the Hyp-/Hyp2- equilibrium (the deprotonation of a peri hydroxyl group). The low-energy absorbance maxima of HypH+, of Hyp and Hyp- and of Hyp2- are 583, 594 and 613 nm, respectively. Neither at pH 13 nor at 1 M HCl is the system entirely in the Hyp2- or the HypH+ forms. Ours is the first study of Hyp in reverse micelles as well as the first time-resolved study of Hyp as a function of pH.     

Singlet-Higgs-Boson signals at hadron colliders

Many extensions of the Standard Model includeSU(2) _L ×U(1) _Y singlet higgs bosons,h ⁰, and also vector-like fermions which couple to it. The production and detection possibilities of such singlet neutral scalars at hadron colliders are considered for different scenarios of vectorlike fermions. We find that for some values of masses and couplings, detection at the CERN large hadron collider (LHC) appears to be a distinct possibility, while at the Fermilab Tevatron upgrade theh ⁰ might be observed only in very favourable circumstances.     

Non-static electromagnetic fields in general relativity. IV

An investigation is made of Rainich's ‘already unified field theory’ from the standpoint of continuous groups of motions, and a solution is obtained for the case where the electromagnetic field is non-static and the space-time admits a three-parameter continuous group of motions whose minimum invariant varieties are three-dimensional spaces. There exists a divergence-free electromagnetic field for values of t at which the metric is not singular.     

Steady state thermal stresses in an elastic solid bounded by two cones

Zusammenfassung Es wird für das Problem der Wärmespannungen in einem kegelförmig begrenzten elastischen Körper eine Ähnlichkeitstransformation entwickelt. Ist die Temperatur an der freien Oberfläche als Potenz des Abstandes von der Spitze vorgeschrieben, so lässt sich ein Satz von Ähnlichkeitsvariablen angeben, welcher die thermoelastischen Beziehungen auf Legendre-Gleichungen reduziert und damit der Lösung leicht zugänglich macht. Die Rechnung ist für den Sonderfall konstant gehaltener Oberflächentemperatur im einzelnen durchgeführt.

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This work has been done at the Mathematics Research Center, University of Wisconsin, under the U.S. Army Contract DA-11-022-ORD-2059.