Theory and observations of ice particle evolution in cirrus using Doppler radar: evidence for aggregation

Vertically pointing Doppler radar has been used to study the evolution of ice particles as they sediment through a cirrus cloud. The measured Doppler fall speeds, together with radar-derived estimates for the altitude of cloud top, are used to estimate a characteristic fall time tc for the `average' ice particle. The change in radar reflectivity Z is studied as a function of tc, and is found to increase exponentially with fall time. We use the idea of dynamically scaling particle size distributions to show that this behaviour implies exponential growth of the average particle size, and argue that this exponential growth is a signature of ice crystal aggregation.

Reconciling internalization theory and the eclectic paradigm

The eclectic paradigm of Dunning (1980) (with its OLI and four motives for FDI framework) can be reconciled with the firm and country matrix of Rugman (1981). However, the fit is not perfect. The main reason for misalignment is that Dunning is focused upon outward FDI into host economies, whereas Rugman’s matrix is for firm-level strategy covering MNE activity in both home and host countries.

The calculation of accurate normal coordinates I: general theory, and application to methane

The calculation of accurate and reliable vibrational potential functions and normal co-ordinates is discussed, for such simple polyatomic molecules as it may be possible. Such calculations should be corrected for the effects of anharmonicity and of resonance interactions between the vibrational states, and should be fitted to all the available information on all isotopic species: particularly the vibrational frequencies, Coriolis zeta constants and centrifugal distortion constants. The difficulties of making these corrections, and of making use of the observed data are reviewed. A programme for the Ferranti Mercury Computer is described by means of which harmonic vibration frequencies and normal co-ordinate vectors, zeta factors and centrifugal distortion constants can be calculated, from a given force field and from given G-matrix elements, etc. The programme has been used on up to 5 × 5 secular equations for which a single calculation and output of results takes approximately l min; it can readily be extended to larger determinants. The best methods of using such a programme and the possibility of reversing the direction of calculation are discussed. The methods are applied to calculating the best possible vibrational potential function for the methane molecule, making use of all the observed data.

Mapping and controlling molecular processes: The application of control theory and system identification algorithms to ASOPS and other fast pulse spectroscopies

Asynchronous Optical Sampling (ASOPS) [1,2] and frequency comb spectrometry [3] based on dual Ti:saphire resonators operated in a master/slave mode have the potential to improve signal to noise ratio in THz transient and IR sperctrometry. The multimode Brownian oscillator time-domain response function described by state-space models is a mathematically robust framework that can be used to describe the dispersive phenomena governed by Lorentzian, Debye and Drude responses. In addition, the optical properties of an arbitrary medium can be expressed as a linear combination of simple multimode Brownian oscillator functions. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing the recorded THz transients in the time or frequency domain will be outlined [4,5]. Since a femtosecond duration pulse is capable of persistent excitation of the medium within which it propagates, such approach is perfectly justifiable. Several de-noising routines based on system identification will be shown. Furthermore, specifically developed apodization structures will be discussed. These are necessary because due to dispersion issues, the time-domain background and sample interferograms are non-symmetrical [6-8]. These procedures can lead to a more precise estimation of the complex insertion loss function. The algorithms are applicable to femtosecond spectroscopies across the EM spectrum. Finally, a methodology for femtosecond pulse shaping using genetic algorithms aiming to map and control molecular relaxation processes will be mentioned.