An isolated line-shape model based on the Keilson and Storer function for velocity changes. I. Theoretical approaches

2009 ◽  
Vol 130 (9) ◽  
pp. 094301 ◽  
Author(s):  
H. Tran ◽  
J.-M. Hartmann
Keyword(s):  
Line Shape ◽  
Shape Model ◽  
Model Based ◽  
Theoretical Approaches ◽  
Velocity Changes

scholarly journals Pressure effects on water vapour lines: beyond the Voigt profile

2012 ◽  
Vol 370 (1968) ◽  
pp. 2495-2508 ◽  
Author(s):  
N. H. Ngo ◽  
H. Tran ◽  
R. R. Gamache ◽  
J. M. Hartmann
Keyword(s):  
Water Vapour ◽  
Line Shape ◽  
Pressure Effects ◽  
Shape Model ◽  
Line Shapes ◽  
Voigt Profile ◽  
Voigt Model ◽  
Velocity Changes ◽  
Dynamics Simulations ◽  
Induced Velocity

A short overview of recent results on the effects of pressure (collisions) regarding the shape of isolated infrared lines of water vapour is presented. The first part of this study considers the basic collisional quantities, which are the pressure-broadening and -shifting coefficients, central parameters of the Lorentzian (and Voigt) profile and thus of any sophisticated line-shape model. Through comparisons of measured values with semi-classical calculations, the influences of the molecular states (both rotational and vibrational) involved and of the temperature are analysed. This shows the relatively unusual behaviour of H 2 O broadening, with evidence of a significant vibrational dependence and the fact that the broadening coefficient (in cm −1 atm −1 ) of some lines increases with temperature. In the second part of this study, line shapes beyond the Voigt model are considered, thus now taking ‘velocity effects’ into account. These include both the influence of collisionally induced velocity changes that lead to the so-called Dicke narrowing and the influence of the dependence of collisional parameters on the speed of the radiating molecule. Experimental evidence of deviations from the Voigt shape is presented and analysed. The interest of classical molecular dynamics simulations, to model velocity changes, together with semi-classical calculations of the speed-dependent collisional parameters for line-shape predictions from ‘first principles’, are discussed.

A note on design-based versus model-based variance estimation in stereology

2002 ◽  
Vol 34 (03) ◽  
pp. 484-490 ◽  
Author(s):  
Asger Hobolth ◽  
Eva B. Vedel Jensen
Keyword(s):  
Mathematical Model ◽  
Original Problem ◽  
Variance Estimation ◽  
Point Of View ◽  
Systematic Sampling ◽  
Variance Estimator ◽  
Shape Model ◽  
Model Based ◽  
Versus Model ◽  
Special Case

Recently, systematic sampling on the circle and the sphere has been studied by Gual-Arnau and Cruz-Orive (2000) from a design-based point of view. In this note, it is shown that their mathematical model for the covariogram is, in a model-based statistical setting, a special case of the p-order shape model suggested by Hobolth, Pedersen and Jensen (2000) and Hobolth, Kent and Dryden (2002) for planar objects without landmarks. Benefits of this observation include an alternative variance estimator, applicable in the original problem of systematic sampling. In a wider perspective, the paper contributes to the discussion concerning design-based versus model-based stereology.

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