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

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

Solar Grand Minima and random fluctuations in dynamo parameters

We consider to what extent the long-term dynamics of cyclic solar activity in the form of Grand Minima can be associated with random fluctuations of the parameters governing the solar dynamo. We consider fluctuations of the alpha-coefficient in the conventional Parker migratory dynamo, and also in slightly more sophisticated dynamo models, and demonstrate that they can mimic the gross features of the phenomenon of the occurrence of Grand Minima over a suitable parameter range. The temporal distribution of these Grand Minima appears chaotic, with a more or less exponential waiting time distribution, typical of Poisson processes. In contrast however, the available reconstruction of Grand Minima statistics based on cosmogenic isotope data demonstrates substantial deviations from this exponential law. We were unable to reproduce the non-Poissonic tail of the waiting time distribution either in the framework of a simple alpha-quenched Parker model, or in its straightforward generalization, nor in simple models with feedback on the differential rotation. We suggest that the disagreement may only be apparent and is plausibly related to the limited observational data, and that the observations and results of numerical modeling can be consistent and represent physically similar dynamo regimes.Comment: Solar Physics, in prin

The model of dynamo with small number of modes and magnetic activity of T Tauri stars

The model that describes operation of dynamo in fully convective stars is presented. It is based on representation of stellar magnetic field as a superposition of finite number of poloidal and toroidal free damping modes. In the frame of adopted low of stellar differential rotation we estimated minimal value of dynamo number D, starting from which generation of cyclic magnetic field in stars without radiative core is possible. We also derived expression for period of the cycle. It was found that dynamo cycles of fully convective stars and stars with thin convective envelopes differ in a qualitative way: 1) distribution of spots over latitude during the cycle is different in these stars; 2) the model predicts that spot formation in fully convective stars should be strongly suppressed at some phases of the cycle. We have analyzed historical lightcurve of WTTS star V410 Tau and found that long term activity of the star is not periodic process. Rather one can speak about quasi cyclic activity with characteristic time of $\sim 4$ yr and chaotic component over imposed. We concluded also that redistribution of cool spots over longitude is the reason of long term variations of V410 Tau brightness. It means that one can not compare directly results of photometric observations with predictions of our axially symmetric (for simplicity) model which allows to investigate time evolution of spot's distribution over latitude. We then discuss what kind of observations and in which way could be used to check predictions of the dynamo theory.Comment: 18 pages, 5 figures, accepted to Astron. Let

Sensing and Integration of Erk and PI3K Signals by Myc

The transcription factor Myc plays a central role in regulating cell-fate decisions, including proliferation, growth, and apoptosis. To maintain a normal cell physiology, it is critical that the control of Myc dynamics is precisely orchestrated. Recent studies suggest that such control of Myc can be achieved at the post-translational level via protein stability modulation. Myc is regulated by two Ras effector pathways: the extracellular signal-regulated kinase (Erk) and phosphatidylinositol 3-kinase (PI3K) pathways. To gain quantitative insight into Myc dynamics, we have developed a mathematical model to analyze post-translational regulation of Myc via sequential phosphorylation by Erk and PI3K. Our results suggest that Myc integrates Erk and PI3K signals to result in various cellular responses by differential stability control of Myc protein isoforms. Such signal integration confers a flexible dynamic range for the system output, governed by stability change. In addition, signal integration may require saturation of the input signals, leading to sensitive signal integration to the temporal features of the input signals, insensitive response to their amplitudes, and resistance to input fluctuations. We further propose that these characteristics of the protein stability control module in Myc may be commonly utilized in various cell types and classes of proteins