Mean Field Dynamos with Algebraic and Dynamic alpha-Quenchings

Calculations for mean field dynamo models (in both full spheres and spherical shells), with both algebraic and dynamic $\alpha$--quenchings, show qualitative as well as quantitative differences and similarities in the dynamical behaviour of these models. We summarise and enhance recent results with extra examples. Overall, the effect of using a dynamic $\alpha$ appears to be complicated and is affected by the region of parameter space examined.Comment: 6 pages, 2 postscript figures, also available at http://www.maths.qmw.ac.uk/~eo

Effects of boundary conditions on the dynamics of the solar convection zone

Recent analyses of the helioseismic data have produced evidence for a variety of interesting dynamical behaviour associated with torsional oscillations. What is not so far clear is whether these oscillations extend all the way to the bottom of the convection zone and, if so, whether the oscillatory behaviour at the top and the bottom of the convection zone is different. Attempts have been made to understand such modes of behaviour within the framework of nonlinear dynamo models which include the nonlinear action of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity. One aspect of these models that remains uncertain is the nature of the boundary conditions on the magnetic field. Here by employing a range of physically plausible boundary conditions, we show that for near-critical and moderately supercritical dynamo regimes, the oscillations extend all the way down to the bottom of the convection zone. Thus, such penetration is an extremely robust feature of the models considered. We also find parameter ranges for which the supercritical models show spatiotemporal fragmentation for a range of choices of boundary conditions. Given their observational importance, we also make a comparative study of the amplitude of torsional oscillations as a function of the boundary conditions

Turkey after the start of negotiations with the European Union - foreign relations and the domestic situation, Part II. OSW Report, July 2008

The Centre for Eastern Studies has decided to embark on the project entitled 'Turkey after the start of negotiations with the European Union - foreign relations and the domestic situation' for two major reasons: the start of the accession negotiations between Ankara and the European Union in October 2005, and the significant part which Turkey plays in western Eurasia (the Caucasus, the countries in the basins of the Black and Caspian Seas, the Middle East and the Balkans) which We wish to present our readers our second report discussing Turkey's relations with Central Asia, the Caucasus and Russia, the aspect of Turkish foreign policy regarding the Black Sea, and the role of Turkey as a transit country for oil and gas from the Middle East and the Caspian regions. The evaluation of Turkey's standpoint and potential regarding the aforementioned issues is especially important, considering the tensions existing in Turkey's relations with the EU and the USA, as well as the West's increasing engagement in the Caucasus, Central Asia and Black Sea regions. In this process, Ankara may play the role of a significant ally for the West. However, it may just as readily play the role of its rival, who could co-operate with other countries and may seriously frustrate the implementation of the EU and US' goals. The Report was developed between autumn 2006 and autumn 2007, over which time the project participants searched for publicly available documents in Poland, Turkey, EU countries and the USA, and went on five research trips to Central Asia, Russia, Turkey and Caucasus, where they met local analysts, officials and researchers

Dynamical variations of the differential rotation in the solar convection zone

Recent analyses of helioseismological observations seem to suggest the presence of two new phenomena connected with the dynamics of the solar convective zone. Firstly, there are present torsional oscillations with periods of about 11 years, which penetrate significantly into the solar convection zone and secondly, oscillatory regimes exist near the base of the convection which are markedly different from those observed near the top, having either significantly reduced periods or being non-periodic. Recently spatiotemporal fragmentation/bifurcation has been proposed as a possible dynamical mechanism to account for such observed multi-mode behaviours in different parts of the solar convection zone. Evidence for this scenario was produced in the context of an axisymmetric mean field dynamo model operating in a spherical shell, with a semi-open outer boundary condition and a zero order angular velocity obtained by the inversion of the MDI data, in which the only nonlinearity was the action of the Lorentz force of the dynamo generated magnetic field on the solar angular velocity. Here we make a detailed study of the robustness of this model with respect to plausible changes to its main ingredients, including changes to the alpha and eta profiles as well as the inclusion of a nonlinear alpha quenching. We find that spatiotemporal fragmentation is present in this model for different choices of the rotation data and as the details of the model are varied. Taken together, these results give strong support to the idea that spatiotemporal fragmentation is likely to occur in general dynamo settings.Comment: 14 pages, 30 figures, submitted to Astronomy and Astrophysics, also available at http://www.eurico.web.co

In--out intermittency in PDE and ODE models

We find concrete evidence for a recently discovered form of intermittency, referred to as in--out intermittency, in both PDE and ODE models of mean field dynamos. This type of intermittency (introduced in Ashwin et al 1999) occurs in systems with invariant submanifolds and, as opposed to on--off intermittency which can also occur in skew product systems, it requires an absence of skew product structure. By this we mean that the dynamics on the attractor intermittent to the invariant manifold cannot be expressed simply as the dynamics on the invariant subspace forcing the transverse dynamics; the transverse dynamics will alter that tangential to the invariant subspace when one is far enough away from the invariant manifold. Since general systems with invariant submanifolds are not likely to have skew product structure, this type of behaviour may be of physical relevance in a variety of dynamical settings. The models employed here to demonstrate in--out intermittency are axisymmetric mean--field dynamo models which are often used to study the observed large scale magnetic variability in the Sun and solar-type stars. The occurrence of this type of intermittency in such models may be of interest in understanding some aspects of such variabilities.Comment: To be published in Chaos, June 2001, also available at http://www.eurico.web.co