121716987
Instability of constant Yang-Mills fields
Both a constant (non-Abelian) electric field and a constant magnetic field are solutions to the sourceless Yang-Mills field equations in Minkowski space. We discuss the stability of these solutions under small fluctuations in the potentials. We conclude that a magnetic field B, which is constant over a region of size L, has instabilities which grow exponentially in time provided gBL/sup 2/ > or approx. = 1. A constant electric field is unstable. A fluctuation in such a field will accelerate continuously in the direction of the field.
6193348
How to distinguish a confining from a deconfining phase in gauge theories with fermions.
122529357
Momentum boundary conditions and Euclidean field theory
The authors discuss the effect of the imposition of momentum boundary conditions on the semiclassical approximation to Euclidean path integrals. For free field theories they derive an explicit simple expression for the resulting Euclidean path integral. As an example they discuss the relationship between the formulation of a massless scalar field theory in terms of a 2-form potential which is used in the context of wormholes and its usual formulation.
34427103
Cosmology with an extremely light scalar field.
A theory with a vanishing cosmological constant can have a nonzero effective cosmological constant of cosmological significance if the theory has a scalar field with a mass m of the order of the inverse age of the Universe (tau/similar to/10/sup 33/ eV/sup -1/) provided the field has a nonzero but evolving expectation value. We discuss the cosmological consequences of scalar fields with masses mapprox. <10/sup -28/ eV. The effect on the age of the Universe and on the growth of density perturbations is discussed in detail. For small masses (mapprox.
40079538
Consistency of Hamiltonian diagonalization for field theories in a Robertson-Walker background.
120480610
Screening Solutions to Classical Yang-Mills Theory
We present two new solutions to the classical Yang-Mills field equations in the presence of a localized external source. These solutions totally screen the charge of the source. They have lower energy than the corresponding Coulomb solution.
16284410
Differential rotation and convection in the Sun
We show that the differential rotation profile of the solar convection zone, apart from inner and outer boundary layers, can be reproduced with great accuracy if the isorotation contours correspond to characteristics of the thermal wind equation. This requires that there be a formal quantitative relationship involving the entropy and the angular velocity. Earlier work has suggested that this could arise from magnetohydrodynamic stability constraints; here, we argue that purely hydrodynamical processes could also lead to such a result. Of special importance to the hydrodynamical solution is the fact that the thermal wind equation is insensitive to radial entropy gradients. This allows a much more general class of solutions to fit the solar isorotation contours, beyond just those in which the entropy itself must be a function of the angular velocity. In particular, for this expanded class, the thermal wind solution of the solar rotation profile remains valid even when large radial entropy gradients are present. A clear and explicit example of this class of solution appears to be present in published numerical simulations of the solar convective zone. Though hydrodynamical in character, the theory is not sensitive to the presence of weak magnetic fields. Thus, the identification of solar isorotation contours with the characteristics of the thermal wind equation appears to be robust, accommodating, but by no means requiring, magnetic field dynamics.
53074129
Magnetic buoyancy instabilities in the presence of magnetic flux pumping at the base of the solar convection zone
We perform idealized numerical simulations of magnetic buoyancy instabilities in three dimensions, solving the equations of compressible magnetohydrodynamics in a model of the solar tachocline. In particular, we study the effects of including a highly simplified model of magnetic flux pumping in an upper layer (‘the convection zone’) on magnetic buoyancy instabilities in a lower layer (‘the upper parts of the radiative interior – including the tachocline’), to study these competing flux transport mechanisms at the base of the convection zone. The results of the inclusion of this effect in numerical simulations of the buoyancy instability of both a preconceived magnetic slab and a shear-generated magnetic layer are presented. In the former, we find that if we are in the regime that the downward pumping velocity is comparable with the Alfven speed of the magnetic layer, magnetic flux pumping is able to hold back the bulk of the magnetic field, with only small pockets of strong field able to rise into the upper layer. 
 
In simulations in which the magnetic layer is generated by shear, we find that the shear velocity is not necessarily required to exceed that of the pumping (therefore the kinetic energy of the shear is not required to exceed that of the overlying convection) for strong localized pockets of magnetic field to be produced which can rise into the upper layer. This is because magnetic flux pumping acts to store the field below the interface, allowing it to be amplified both by the shear and by vortical fluid motions, until pockets of field can achieve sufficient strength to rise into the upper layer. In addition, we find that the interface between the two layers is a natural location for the production of strong vertical gradients in the magnetic field. If these gradients are sufficiently strong to allow the development of magnetic buoyancy instabilities, strong shear is not necessarily required to drive them (cf. previous work by Vasil & Brummell). We find that the addition of magnetic flux pumping appears to be able to assist shear-driven magnetic buoyancy in producing strong flux concentrations that can rise up into the convection zone from the radiative interior.
7847831
FINE STRUCTURE IN SUNSPOTS
▪ Abstract Important physical processes on the Sun, and especially in sunspots, occur on spatial scales at or below the limiting resolution of current solar telescopes. Over the past decade, using ...
119300936
Differential rotation in fully convective stars
Under the assumption of thermal wind balance and effective entropy mixing in constant rotation surfaces, the isorotational contours of the solar convective zone may be reproduced with great fidelity. Even at this early stage of development, this helioseismology fit may be used to put a lower bound on the mid-latitude radial solar entropy gradient, which is in good accord with standard mixing length theory. In this paper, we generalize this solar calculation to fully convective stars (and potentially planets), retaining the assumptions of thermal wind balance and effective entropy mixing in isorotational surfaces. It is found that each isorotation contour is of the form R 2 = A + B� (r), where R is the radius from the rotation axis, � (r) is the (assumed spherical) gravitational potential, and A and B are constants along the contour. This result is applied to simple models of fully convective stars. Both solar-like surface rotation profiles (angular velocity decreasing toward the poles) as well as ‘antisolar’ profiles (angular velocity increasing toward the poles) are modelled; the latter bear some suggestive resemblance to numerical simulations. We also perform exploratory studies of zonal surface flows similar to those seen in Jupiter and Saturn. In addition to providing a practical framework for understanding the results of large-scale numerical simulations, our findings may also prove useful in dynamical calculations for which a simple but viable model for the background rotation profile in a convecting fluid is needed. Finally, our work bears directly on an important goal of the CoRoT programme: to elucidate the internal structure of rotating, convecting stars.