Vibrational Population of Hydrogen Molecules Excited by an RF Discharge in an Expanding Thermal Arc Plasma as Determined by Emission Spectroscopy

This work is devoted to the determination of the vibrational population of hydrogen molecules in the ground and excited electronic states from the analysis of visible spectra of the H₂ molecules excited by an RF discharge in an expanding thermal arc plasma. Comparison of the experimental results on relative electron-impact excitation cross sections for the transition H₂(X¹Σ, υ⁰ = 0)→ H₂(d³II_u, υ′) with other experiments, and with calculations based on the Franck-Condon principle, shows good agreement. This means, that for plasma under investigation: 1) in the ground electronic state H₂(d³II_u,υ′), only the lowest vibrational level with υ⁰ = 0 is significantly populated, and 2) direct electron exictation of H₂(d³II_u, υ′, υ′) state from the ground state H₂(X¹Σ, υ⁰ = 0) dominates.     

CW diode pumping and FM mode locking of a Nd: KGW laser

We have demonstrated cw diode end pumping of Nd: KGW, a novel solid-state gain medium, with up to 30% conversion efficiency into near-TEM₀₀ (M² < 1.05) output at = 1.067 µm for a pump level of 2.7 W. The slope efficiency was limited by intracavity reflections to 36%; however, direct comparison to a similar Nd:YAG laser indicates the same intrinsic slope efficiency of 60%. FM mode locking of this laser at 200 MHz has produced 12 ps pulses (compared to 16 ps for Nd: YAG), although an intracavity etalon was required. Considerable reduction in pulse width is possible (the line width limit is 0.5 ps) but different techniques may be necessary. Spatial hole burning was evident in both the 120 GHz free-running spectrum and the etalon-limited mode-locked spectrum.     

Time-resolved fluorescence relaxation of 3-methyllumiflavin in polar solution

We have studied the fluorescent properties of a well-defined model flavin compound (3-methyllumiflavin) in a relatively polar solvent like propylene glycol or ethanol. Inhomogeneous spectral broadening effects were directly time-resolved by detection at the extreme blue and red edges of the fluorescence band of 3-methyllumiflavin using excitation in the main absorption band. At the high-energy side of the emission band a rapid decay component (tens of picoseconds) was resolved indicative for the disappearance of the initially prepared, nonequilibrium state with a characteristic dipolar relaxation time. At the low-energy side the rise of a solvent relaxed fluorescent species could be time-resolved. The wavelength-dependent effects on the dipolar relaxation were abolished when excitation was at the low-energy side of the absorption band. The experimental decays of the flavin solvate at different energies of fluorescence and excitation are presented as they represent an easy diagnosis for energy dependent solvation dynamics. Wavelength dependent rotation of 3-methyllumiflavin, examined by fluorescence anisotropy decay, turned out to be absent for 3-methyllumiflavin in propylene glycol between 263 and 293 K, probably because of the small change in dipole moment upon flavin excitation.     

Generalized hypergeometric functions and rational curves on Calabi-Yau complete intersections in toric varieties

We formulate general conjectures about the relationship between the A-model connection on the cohomology of ad-dimensional Calabi-Yau complete intersectionV ofr hypersurfacesV ₁ ,...,V _r in a toric varietyP and the system of differential operators annihilating the special generalized hypergeometric series ⁰ constructed from the fan . Using this generalized hypergeometric series, we propose conjectural mirrorsV ofV and the canonicalq-coordinates on the moduli spaces of Calabi-Yau manifolds.In the second part of the paper we consider some examples of Calabi-Yau 3-folds having Picard number >1 in products of projective spaces. For conjectural mirrors, using the recurrent relation among coefficients of the restriction of the hypergeometric function ⁰ on a special line in the moduli space, we determine the Picard-Fuchs equation satisfied by periods of this special one-parameter subfamily. This allows to obtain some sequences of integers which can be conjecturally interpreted in terms of Gromov-Witten invariants. Using standard techniques from enumerative geometry, first terms of these sequence of integers are checked to coincide with numbers of rational curves on Calabi-Yau 3-folds.     

Close coupling results for inelastic collisions of NH3 and Ar. A stringent test of a spectroscopic potential

We have calculated state-to-state total cross sections for rotational excitation and inversion of NH3 by collisions with Ar using the close coupling method. The Ar-NH3 interaction potential has been obtained from a fit to the spectrum of this van der Waals molecule. The calculated cross sections agree to within about 30% with the measured values; the estimated error in the latter is 10% to 20%.     

Dynamic structure factor in a random diffusion model

Let {X _t:0} denote random walk in the random waiting time model, i.e., simple random walk with jump ratew ^–1(X _t), where {w(x):x^d} is an i.i.d. random field. We show that (under some mild conditions) theintermediate scattering function F(q,t)=E ₀ (q^d) is completely monotonic int (E ₀ denotes double expectation w.r.t. walk and field). We also show that thedynamic structure factor S(q, w)=2 ₀ cos(t)F(q, t) exists for 0 and is strictly positive. Ind=1, 2 it diverges as 1/||^1/2, resp. –ln(||), in the limit 0; ind3 its limit value is strictly larger than expected from hydrodynamics. This and further results support the conclusion that the hydrodynamic region is limited to smallq and small such that ||D |q|², whereD is the diffusion constant.     

On three conjectures by K. E. Shuler

Some fifteen years ago, Shuler formulated three conjectures relating to the large-time asymptotic properties of a nearest-neighbor random walk on ² that is allowed to make horizontal steps everywhere but vertical steps only on a random fraction of the columns. We give a proof of his conjectures for the situation where the column distribution is stationary and satisfies a certain mixing codition. We also prove a strong form of scaling to anisotropic Brownian motion as well as a local limit theorem. The main ingredient of the proofs is a large-deviation estimate for the number of visits to a random set made by a simple random walk on . We briefly discuss extensions to higher dimension and to other types of random walk.Dedicated to Prof. K. E. Shuler on the occasion of his 70th birthday, celebrated at a Symposium in his honor on July 13, 1992, at the University of California at San Diego, La Jolla, California.