Bulk Upload 01 Dec 2008 (192/192) - LectureNotesMATH2009.pdf

Lecture notes for MATH2009, Vector Calculus and Applications (discontinued after 2007?). These are based on the notes of Bob Craine, typed up by Ian Hawke.

A review of the theoretical basis for bulk mass flux convective parameterization

Most parameterizations for precipitating convection in use today are bulk schemes, in which an ensemble of cumulus elements with different properties is modelled as a single, representative entraining-detraining plume. We review the underpinning mathematical model for such parameterizations, in particular by comparing it with spectral models in which elements are not combined into the representative plume. The chief merit of a bulk model is that the representative plume can be described by an equation set with the same structure as that which describes each element in a spectral model. The equivalence relies on an ansatz for detrained condensate introduced by Yanai et al. (1973) and on a simplified microphysics. There are also conceptual differences in the closure of bulk and spectral parameterizations. In particular, we show that the convective quasi-equilibrium closure of Arakawa and Schubert (1974) for spectral parameterizations cannot be carried over to a bulk parameterization in a straightforward way. Quasi-equilibrium of the cloud work function assumes a timescale separation between a slow forcing process and a rapid convective response. But, for the natural bulk analogue to the cloud-work function (the dilute CAPE), the relevant forcing is characterised by a different timescale, and so its quasi-equilibrium entails a different physical constraint. Closures of bulk parameterization that use the non-entraining parcel value of CAPE do not suffer from this timescale issue. However, the Yanai et al. (1973) ansatz must be invoked as a necessary ingredient of those closures.

Effects of copper on the antioxidant activity of olive polyphenols in bulk oil and oil-in-water emulsions

The antioxidant activity and interactions with copper of four olive oil phenolic compounds, namely oleuropein, hydroxytyrosol, 3,4- dihydroxyphenylethanol- elenolic acid ( 1), and 3,4- dihydroxyphenyl-ethanolelenolic acid dialdehyde ( 2), in olive oil and oil- in- water emulsions stored at 60 degrees C were studied. All four phenolic compounds significantly extended the induction time of lipid oxidation in olive oil with the order of activity being hydroxytyrosol > compound 1 > compound 2 > oleuropein > alpha- tocopherol; but in the presence of Cu( II), the stability of oil samples containing phenolic compounds decreased by at least 90%, and the antioxidant activity of hydroxytyrosol and compounds 1 and 2 became similar. In oil- in- water emulsions prepared from olive oil stripped of tocopherols, hydroxytyrosol enhanced the prooxidant effect of copper at pH 5.5 but not at pH 7.4. The stability of samples containing copper at pH 5.5 was not significantly different if oleuropein was present from that of the control. Oleuropein at pH 7.4, and compounds 1 and 2 at both pH values tested, reduced the prooxidant effect of copper. The lower stability and the higher reducing capacity of all compounds at pH 7.4 could not explain the higher stability of emulsions containing phenolic compounds at this pH value. However, mixtures containing hydroxytyrosol or oleuropein with copper showed higher 1,1-diphenyl- 2- picrylhydrazyl radical scavenging activity at pH 7.4 than at pH 5.5. Moreover, the compound 2- copper complex showed higher radical scavenging activity then the uncomplexed compound at pH 5.5. It can be concluded that the formation of a copper complex with radical scavenging activity is a key step in the antioxidant action of the olive oil phenolic compounds in an emulsion containing copper ions.

High signal to noise ratio THz spectroscopy with ASOPS and signal processing schemes for mapping and controlling molecular and bulk relaxation processes

Asynchronous Optical Sampling has the potential to improve signal to noise ratio in THz transient sperctrometry. The design of an inexpensive control scheme for synchronising two femtosecond pulse frequency comb generators at an offset frequency of 20 kHz is discussed. The suitability of a range of signal processing schemes adopted from the Systems Identification and Control Theory community for further processing recorded THz transients in the time and frequency domain are outlined. Finally, possibilities for femtosecond pulse shaping using genetic algorithms are mentioned.