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Aims. We consider the stability of simple hydrodynamic models of the solar tachocline. This study addresses only the non-magnetic instabilities. In our model there is a strong radial shear, which because of the rotation is coupled to a latitudinal temperature gradient. We also assume there is a strong stable stratification, appropriate for the slow tachocline.

A new general approach to the direct formation of bipolar devices from heterogeneous colloids is suggested. By using surface‐force theory and direct measurements, combinations of conductive device materials between which short‐range repulsive forces exist in the presence of an intervening liquid, and use these interactions to self‐form electrochemical junctions are identified. The inclusion of Lifshitz–van der Waals (LW) and acid–base (AB) interactions appears to be generally sufficient for the prediction of short‐range interactions. Device concepts using repulsive and attractive short‐range interactions to produce self‐organizing colloidal‐scale devices are proposed and demonstrated. A prototype self‐organizing lithium rechargeable battery is demonstrated using lithium cobalt oxide (LiCoO2) and graphite as the active electrode materials.

In this article I review the fundamentals of solar–dynamo theory. I describe both historical and contemporary observations of the solar magnetic field before outlining why it is believed that the solar field is maintained by a hydromagnetic dynamo. Having explained the basic dynamo process and applications of the theory to the Sun, I shall conclude by speculating on future directions for the theory.

The linear and nonlinear dynamo properties of a class of periodically forced flows is considered. The forcing functions are chosen to drive, in the absence of magnetic effects (kinematic regime), a time-dependent version of the ABC flow with A= B= C= 1. The time-dependence consists of a harmonic displacement of the origin along the line x= y= z= 1 with amplitude and frequency ?. The finite-time Lyapunov exponents are computed for several values of and ?. It is found that for values of these parameters near unity chaotic streamlines occupy most of the volume. In this parameter range, and for moderate kinetic and magnetic Reynolds numbers, the basic flow is both hydrodynamically and hydromagnetically unstable. However, the dynamo instability has a higher growth rate than the hydrodynamic one, so that the nonlinear regime can be reached with negligible departures from the basic ABC flow.

Stellar magnetic activity in slowly rotating stars is often cyclic, with the period of the magnetic cycle depending critically on the rotation rate and the convective turnover time of the star. Here we show that the interpretation of this law from dynamo models is not a simple task. It is demonstrated that the period is (unsurprisingly) sensitive to the precise type of non‐linearity employed. Moreover the calculation of the wave‐speed of plane‐wave solutions does not (as was previously supposed) give an indication of the magnetic period in a more realistic dynamo model, as the changes in length‐scale of solutions are not easily captured by this approach. Progress can be made, however, by considering a realistic two‐dimensional model, in which the radial length‐scale of waves is included. We show that it is possible in this case to derive a more robust relation between cycle period and dynamo number. For all the non‐linearities considered in the most realistic model, the magnetic cycle period is a decreasing function of |D| (the amplitude of the dynamo number). However, discriminating between different non‐linearities is difficult in this case and care must therefore be taken before advancing explanations for the magnetic periods of stars.

Stellar dynamos are governed by non‐linear partial differential equations (PDEs) which admit solutions with dipole, quadrupole or mixed symmetry (i.e. with different parities). These PDEs possess periodic solutions that describe magnetic cycles, and numerical studies reveal two different types of modulation. For modulations of Type 1 there are parity changes without significant changes of amplitude, while for Type 2 there are amplitude changes without significant changes in parity. In stars like the Sun, cyclic magnetic activity is interrupted by grand minima that correspond to Type 2 modulation. Although the Sun’s magnetic field has maintained dipole symmetry for almost 300 yr, there was a significant parity change at the end of the Maunder Minimum. We infer that the solar field may have flipped from dipole to quadrupole polarity (and back) after deep minima in the past and may do so again in the future. Other stars, with different masses or rotation rates, may exhibit cyclic activity with dipole, quadrupole or mixed parity. The origins of such behaviour can be understood by relating the PDE results to solutions of appropriate low‐order systems of ordinary differential equations (ODEs). Type 1 modulation is reproduced in a fourth‐order system while Type 2 modulation occurs in a third‐order system. Here we construct a new sixth‐order system that describes both types of modulation and clarifies the interactions between symmetry‐breaking and modulation of activity. Solutions of these non‐linear ODEs reproduce the qualitative behaviour found for the PDEs, including flipping of polarity after a prolonged grand minimum. Thus we can be confident that these patterns of behaviour are robust, and will apply to stars that are similar to the Sun.

Recent observations have revealed the interlocking-comb structure of the magnetic field in the outer penumbra of a sunspot. We have argued that this structure owes its origin in part to downward pumping of magnetic flux by vigorous granular convection in the region surrounding the spot. Here we stress the difference between the inner and outer penumbra, and correct some misleading assertions in a recent paper by Spruit & Scharmer.