Hopf hypersurfaces in pseudo-Riemannian complex and para-complex space forms

The study of real hypersurfaces in pseudo-Riemannian complex space forms and para-complex space forms, which are the pseudo-Riemannian generalizations of the complex space forms, is addressed. It is proved that there are no umbilic hypersurfaces, nor real hypersurfaces with parallel shape operator in such spaces. Denoting by J be the complex or para-complex structure of a pseudo-complex or para-complex space form respectively, a non-degenerate hypersurface of such space with unit normal vector field N is said to be Hopf if the tangent vector field JN is a principal direction. It is proved that if a hypersurface is Hopf, then the corresponding principal curvature (the Hopf curvature) is constant. It is also observed that in some cases a Hopf hypersurface must be, locally, a tube over a complex (or para-complex) submanifold, thus generalizing previous results of Cecil, Ryan and Montiel.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element/volume/difference methods, particularly when the long-time transient behaviour of a system is of interest. Since the exact solution is obtained at the grid collocation points superior accuracy can be achieved on modest grid resolution. Furthermore, the grid can be freely adapted with time and in space, to particular flow conditions or geometric variations. This is especially advantageous where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free sutface. The electromagnetic field then determines the instantaneous liquid volume shape and the liquid shape affects in turn the electromagnetic field. In AC applications a thin "skin effect" region results on the free surface that dominates grid requirements. Infinitesimally thin boundary cells can be introduced using Chebyshev polynomial expansions without detriment to the numerical accuracy. This paper presents a general methodology of the pseudo-spectral approach and outlines the solution procedures used. Several instructive example applications are given: the aluminium electrolysis MHD problem, induction melting and stirring and the dynamics of magnetically levitated droplets in AC and DC fields. Comparisons to available analytical solutions and to experimental measurements will be discussed.

Pseudo-spectral solutions for fluid flow and heat transfer in electro-metallurgical applications

The pseudo-spectral solution method offers a flexible and fast alternative to the more usual finite element and volume methods, particularly when the long-time transient behaviour of a system is of interest. The exact solution is obtained at grid collocation points leading to superior accuracy on modest grids. Furthermore, the grid can be freely adapted in time and space to particular flow conditions or geometric variations, especially useful where strongly coupled, time-dependent, multi-physics solutions are investigated. Examples include metallurgical applications involving the interaction of electromagnetic fields and conducting liquids with a free surface. The electromagnetic field determines the instantaneous liquid volume shape, which then affects the electromagnetic field. A general methodology of the pseudo-spectral approach is presented, with several instructive example applications: the aluminium electrolysis MHD problem, induction melting in a cold crucible and the dynamics of AC/DC magnetically levitated droplets. Finally, comparisons with available analytical solutions and to experimental measurements are discussed.

Comments On The Pseudo-Microfossil Linotolypen

Hollow, black reticulate ‘microfossils’ of unknown affinity found in Ordovician to late Cretaceous sediments from North America, Europe and Australia were given the name Linotolypa by Eisenack in 1962. In 1978, he recognised that they were pseudo-microfossils consisting of asphalt, and noted that their structure resembled that of soap bubbles formed in agitated suspensions. These objects are well known as a component of the particles caught from the air by pollen and spore traps at the present day. They are correctly termed ‘cenospheres’ and are formed from coal and possibly pitch and fuel oil by incomplete combustion. If their presence were to be confirmed in Palaeozoic sediments, this would provide important new evidence for the occurrence of fire in the geological record and of the history of levels of O2 in the atmosphere.

Validation of the detection of Pseudo-nitzschia spp. using specific RNA probes tested in a microarray format: Calibration of signal based on variability of RNA content with environmental conditions.

Harmful algal blooms (HAB) occur worldwide and cause health problems and economic damage to fisheries and tourism. Monitoring for toxic algae is therefore essential but is based primarily on light microscopy, which is time consuming and can be limited by insufficient morphological characters such that more time is needed to examine critical features with electron microscopy. Monitoring with molecular tools is done in only a few places world-wide. EU FP7 MIDTAL (Microarray Detection of Toxic Algae) used SSU and LSU rRNA genes as targets on microarrays to identify toxic species. In order to comply with current monitoring requirements to report cell numbers as the relevant threshold measurement to trigger closure of fisheries, it was necessary to calibrate our microarray to convert the hybridisation signal obtained to cell numbers. Calibration curves for two species of Pseudo-nitzschia for use with the MIDTAL microarray are presented to obtain cell numbers following hybridisation. It complements work presented by Barra et al. (2012b. Environ. Sci. Pollut. Res. doi: 10.1007/s11356-012-1330-1v) for two other Pseudo-nitzschia spp., Dittami and Edvardsen (2012a. J. Phycol. 48, 1050) for Pseudochatonella, Blanco et al. (2013. Harmful Algae 24, 80) for Heterosigma, McCoy et al. (2013. FEMS. doi: 10.1111/1574-6941.12277) for Prymnesium spp., Karlodinium veneficum, and cf. Chatonella spp. and Taylor et al. (2014. Harmful Algae, in press) for Alexandrium.

Kinetics of liquid phase semiconductor photoassisted reactions: Supporting observations for a pseudo-steady-state model

The kinetics of liquid phase semiconductor photocatalytic and photoassisted reactions are an area of some debate, reignited recently by an article by Ollis(1) in which he proposed a simple pseudo- steady- state model to interpret the Langmuir- Hinshelwood type kinetics, commonly observed in such systems. In the current article, support for this model, over other models, is provided by a reinterpretation of the results of a study, reported initially in 1999,2 of the photoassisted mineralization of 4- chlorophenol, 4-CP, by titania films and dispersions as a function of incident light intensity, I. On the basis of this model, these results indicate that 4- CP is adsorbed more strongly on P25 TiO2 when it is in a dispersed, rather than a film form, due to a higher rate constant for adsorption, k(1). In addition, the kinetics of 4- CP removal appear to depend on I-beta where, beta = 1 or 0.6 for when the TiO2 is in a film or a dispersed form, respectively. These findings are discussed both in terms of the pseudo- steady- state model and other popular kinetic models.