Line shape analysis of two-colour photoassociation spectra on the example of the Cs ground state

Two-photon photoassociation spectra in a Λ-type excitation scheme are analysed under the systematically varied experimental conditions of frequency detunings and laser intensities. Line shape fits are presented as well as the investigation of intensity and detuning dependent line shifts. From both we determine the attained spectroscopic precision, that is corrected for a systematic line shift due to the thermal distribution of atoms in the trap. An energy correction for this effect is given. Information about the feasibility of generating translationally cold molecules in a well defined rotational and vibrational level by the photoassociation process is derived from the analysis. Received 21 May 2002 Published online 15 October 2002 RID="a" ID="a"Current address e-mail: christian.lisdat@ptb.de RID="b" ID="b"e-mail: pierre.pillet@lac.u-psud.fr     

Neighboring extremals of dynamic optimization problems with path equality constraints

Neighboring extremals of dynamic optimization problems with path equality constraints and with an unknown parameter vector are considered in this paper. With some simplifications, the problem is reduced to solving a linear, time-varying two-point boundary-value problem with integral path equality constraints. A modified backward sweep method is used to solve this problem. Two example problems are solved to illustrate the validity and usefulness of the solution technique. This research was supported in part by the National Aeronautics and Space Administration under NASA Grant No. NCC-2-106. The author is indebted to Professor A. E. Bryson, Jr., Department of Aeronautics and Astronautics, Stanford University, for many stimulating discussions.     

Energy Conservation with Non-Symplectic Methods: Examples and Counter-Examples

Energy conservation of numerical integrators is well understood for symplectic one-step methods. This article provides new insight into energy conservation with non-symplectic methods. Sufficient conditions and counter-examples are presented. AMS subject classification (2000) 65L06, 65P10, 37J99.Submitted June 2004. Accepted October 2004. Communicated by Syvert Nørsett.     

On the Convergence Behaviour of Variable Stepsize Multistep Methods for Singularly Perturbed Problems

In this note, we investigate the convergence behaviour of linear multistep discretizations for singularly perturbed systems, emphasising the features of variable stepsizes. We derive a convergence result for A()-stable linear multistep methods and specify a refined error estimate for backward differentiation formulas. Important ingredients in our convergence analysis are stability bounds for non-autonomous linear problems that are obtained by perturbation techniques.     

In-plane bistatic backward scattering from seabottom with randomly inhomogeneous sediment and rough interface

1 Introduction Backward scattering of sound due to sediment is the main source of shallow waterreverberation. In order to predict the reverberation or detect sediment properties frommeasured reverberation data, a reasonable in-plane bistatic backward scattering (BBS)model is essential. The scattering can be caused by the roughness of water-sediment in-terface or by inhomogeneities within the volume of sediment. A great deal of researchhas been done on sediment backscattering, most of which h…     

On perturbations of the group of shifts on the line by unitary cocycles

It is shown that the class of perturbations of the semigroup of shifts on by unitary cocycles with the property (where is the Hilbert-Schmidt class) contains strongly continuous semigroups of isometric operators, whose unitary parts possess spectral decompositions with the measure being singular with respect to the Lebesgue measure. Thus, we describe also the subclass of strongly continuous groups of unitary operators that are perturbations of the group of shifts on by Markovian cocycles with the property .

     

A Note on a Paper by P. Amodio and F. Mazzia

In 1999 Amodio and Mazzia presented a new backward error analysis for LU factorization and introduced a new growth factor _n . Their very interesting approach allowed them to obtain sharp error bounds. In particular, they derive nice results assuming that partial pivoting is used. However, the forward error bound for the solution of a linear system whose coefficient matrix A is an M-atrix given in Theorem 4.1 of that paper is not correct. They first obtain a bound for the condition number (U) assuming that one has the LU factorization of an M-matrix and then they apply the bounds obtained when partial pivoting is used. But if P is the permutation associated with partial pivoting then PA = LU can fail to be an M-atrix and the bound for (U) can be false, as shown in our Example 1.1. We also prove that, for a pivoting strategy presented in the paper, the growth factor of an M-matrix A is _n(A) = 1 and (U) (A), where U is the upper triangular matrix obtained after applying such a pivoting strategy.This revised version was published online in October 2005 with corrections to the Cover Date.     

A formula for -hyponormality of backstep extensions of subnormal weighted shifts

Let be a weight sequence of positive real numbers and let be a subnormal weighted shift with a weight sequence . Consider an extended weight sequence with and let 0: W_{\alpha (x)} \text{is} k \text{-hyponormal}\}$">for , where is the set of natural numbers. We obtain a formula to find the interval , which provides several examples to distinguish the classes of -hyponormal operators from one another.

     

High resolution polarization spectroscopy and laser induced fluorescence of CO<Subscript>2</Subscript> around 2μm

High resolution Infrared Polarisation Spectroscopy (IRPS) and Infrared Laser Induced Fluorescence (IRLIF) techniques were used to probe CO₂/N₂ binary gas mixture at atmospheric pressure and ambient temperature. The probed CO₂ molecules were prepared by laser excitation to an overtone and combination ro-vibrational state (12⁰1, J=15) of CO₂, centred at 4988.6612 cm^-1. IRPS and IRLIF line profiles were recorded for several CO₂/N₂ binary mixtures. The observed IRLIF line shapes have the expected Lorentzian form while the observed IRPS line shapes are narrower by a factor of two than those recorded with the IRLIF and appear to have a Lorentzian-cubed profile. The recorded line profiles provide measurements of the pressure-broadening coefficient directly at atmospheric pressure. The Full-Width-Half-Maxima (FWHM) pressure broadening coefficients are measured, based on IRLIF, to be 0.2174±0.0092 cm^-1atm^-1 and 0.1327 ±0.0077 cm^-1atm^-1 for self- and N₂ collision broadening, respectively. The broadening coefficients obtained based on IRPS were measured to be ~8% larger than those obtained with IRLIF.     

CO2-broadened water in the pure rotation and ν2 fundamental regions

The CO₂-broadened water coefficients (half-widths, line shifts, and temperature dependence of the widths) are predicted using a fully complex Robert-Bonamy formulation for the 937 allowed and forbidden perpendicular type transitions of (000)-(000) between 200 and 900 cm⁻¹ in order to facilitate atmospheric remote sensing of Mars and Venus. In addition, empirical Lorentz line widths and pressure-induced frequency-shifts of CO₂-broadened H₂¹⁶O are obtained at room temperature for 257 perpendicular transitions of the (010)-(000) fundamental. For this, calibrated spectra recorded at 0.0054 cm⁻¹ resolution are measured assuming Voigt line shapes. For transitions between 1287 and 1988 cm⁻¹ with rotational quanta up to J = 13 and K_a = 6, the widths vary from 0.045 to 0.212 cm⁻¹ atm⁻¹ at 300 K; the pressure-shifts are quite large and range from −0.0386 to +0.0436 cm⁻¹ atm⁻¹. For the (010)-(000) band, the RMS and mean observed and calculated differences for CO₂-broadened H₂O half-widths are 12% and −1.9%, respectively, while the RMS and mean ratios of the observed and calculated pressure-induced shift coefficients are 1.6 and 0.79, respectively. For pairs of transitions involving K_a = 0 and 1, such as 2_0 2 ← 3_1 3 and 3_1 3 ← 2_0 2, both the calculated and observed pressure induced shifts in positions are opposite in sign and often similar in magnitude. The data are too limited to characterize vibrational dependencies of the widths, however.