Long-term Nonlinear Behaviour of the Magnetorotational Instability in a Localised Model of an Accretion Disc

For more than a decade, the so-called shearing box model has been used to study the fundamental local dynamics of accretion discs. This approach has proved to be very useful because it allows high resolution and long term studies to be carried out, studies that would not be possible for a global disc. Localised disc studies have largely focused on examining the rate of enhanced transport of angular momentum, essentially a sum of the Reynolds and Maxwell stresses. The dominant radial-azimuthal component of this stress tensor is, in the classic Shakura-Sunayaev model, expressed as a constant alpha times the pressure. Previous studies have estimated alpha based on a modest number of orbital times. Here we use much longer baselines, and perform a cumulative average for alpha. Great care must be exercised when trying to extract numerical alpha values from simulations: dissipation scales, computational box aspect ratio, and even numerical algorithms all affect the result. This study suggests that estimating alpha becomes more, not less, difficult as computational power increases.Comment: 10 pages, 10 figures, 2 tables, accepted by MNRA

The Need for Greater Support in Academic Writing for PhD Students in Mathematics and Related Subjects

Within the United Kingdom (UK), the graduate student population in mathematics departments seeking to obtain the higher degree of Doctor of Philosophy (PhD) has become increasingly diverse as a result of a number of factors. This student body faces a variety of challenges that raise questions about what provisions universities should provide in order to give these students the greatest chance of a successful completion of their PhD programme. In this article I argue that universities should increase their provision for the development of the writing skills of PhD students and especially for those in mathematics and related disciplines. This is partially motivated by the new diversity of the graduate student body but also by the fact that undergraduate degrees in mathematics in the UK provide few opportunities for students to develop their writing skills. I argue for a centralized provision of support, either at the department or university level, to move the development of a student’s writing away from their PhD supervisor, which is not ideal

Play at Your Own Risk: Sport, the Injury Epidemic, and ACL Injury Prevention in Female Athletes

This article focuses on describing anterior cruciate ligament (ACL) injury in athletes and the efficacy of implementing a neuromuscular and proprioceptive sports-specific training program to reduce the incidence of ACL ligament injuries. This article will discuss the role of the ACL, epidemiology and etiology, and the four categorical risk factors for incurring an ACL injury: anatomical, environmental, hormonal, and biomechanical. In addition, this article will discuss the mechanisms ACL injuries, as well as a comprehensive review of all of the literature that has been published with regard to the prevention or reduction of ACL injury. The article concludes that a neuromuscular training program might have a direct benefit in decreasing the number of ACL injuries in athletes

Is There a Pink Slip in Your Genes?

On the insurance company side, it\u27s clear that insurance companies are not well loved by folks. They\u27re not even supposed to do that. At one point after a company had approached QualChoice and told us not to tell the enrollees something that, in fact, had been a policy decision by the company, I was suggesting that perhaps we should change the name to the company to the Scapegoat Insurance Company, since that really was what we were being paid for, and I think in this argument that may be part of the issue here

Is There a Pink Slip in Your Genes?

On the insurance company side, it\u27s clear that insurance companies are not well loved by folks. They\u27re not even supposed to do that. At one point after a company had approached QualChoice and told us not to tell the enrollees something that, in fact, had been a policy decision by the company, I was suggesting that perhaps we should change the name to the company to the Scapegoat Insurance Company, since that really was what we were being paid for, and I think in this argument that may be part of the issue here

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 Alfvén 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