Truth and Probability

Contains two other essays as well: Further Considerations & Last Papers: Probability and Partial Belief.

Hall drift of axisymmetric magnetic fields in solid neutron-star matter

Hall drift, i. e., transport of magnetic flux by the moving electrons giving rise to the electrical current, may be the dominant effect causing the evolution of the magnetic field in the solid crust of neutron stars. It is a nonlinear process that, despite a number of efforts, is still not fully understood. We use the Hall induction equation in axial symmetry to obtain some general properties of nonevolving fields, as well as analyzing the evolution of purely toroidal fields, their poloidal perturbations, and current-free, purely poloidal fields. We also analyze energy conservation in Hall instabilities and write down a variational principle for Hall equilibria. We show that the evolution of any toroidal magnetic field can be described by Burgers' equation, as previously found in plane-parallel geometry. It leads to sharp current sheets that dissipate on the Hall time scale, yielding a stationary field configuration that depends on a single, suitably defined coordinate. This field, however, is unstable to poloidal perturbations, which grow as their field lines are stretched by the background electron flow, as in instabilities earlier found numerically. On the other hand, current-free poloidal configurations are stable and could represent a long-lived crustal field supported by currents in the fluid stellar core.Comment: 8 pages, 5 figure panels; new version with very small correction; accepted by Astronomy & Astrophysic

Search for Stable Magnetohydrodynamic Equilibria in Barotropic Stars

It is now believed that magnetohydrodynamic equilibria can exist in stably stratified stars due to the seminal works of Braithwaite & Spruit (2004) and Braithwaite & Nordlund (2006). What is still not known is whether magnetohydrodynamic equilibria can exist in a barotropic star, in which stable stratification is not present. It has been conjectured by Reisenegger (2009) that there will likely not exist any magnetohydrodynamical equilibria in barotropic stars. We aim to test this claim by presenting preliminary MHD simulations of barotropic stars using the three dimensional stagger code of Nordlund & Galsgaard (1995).Comment: 4 pages, 2 figures, to appear in the proceedings of IAUS 302: "Magnetic Fields Throughout Stellar Evolution

Hans Eysenck, education and the experimental approach: A meta-analysis of academic capabilities in university students

Hans Eysenck had a long-established interest in the influence of individual differences on educational attainment, noting that typically personality traits and cognitive abilities are ignored in debates regarding educational policy and practice. Eysenck's general scientific approach emphasized the importance of applying an experimental approach to answering social questions. Inspired by this perspective, in this article, we conducted a meta-analysis of the literature on (largely quasi) experimental intervention studies (N = 47, with 49 independent samples) aimed at enhancing mainly self-efficacy and self-confidence in order to influence a range of academic outcomes in university students (N = 5771). Results revealed small-to-moderate, but statistically significant, positive effects across all the outcome domains examined. There was little evidence for moderation of these effects, with quality of the study intervention the only one statistically significant (lower quality studies showing the largest effect sizes). Although our analysis shows the paucity of purely experimental studies in higher education research, the results are sufficiently clear to suggest that the study of individual differences variables are relevant in educational design and instruction. This is something Hans Eysenck told us to expect

Visualising gas heating from an RF plasma loudspeaker

In an electro-acoustic transduction mechanism, an ac modulation (here in the audio frequency range) of the electric field in an atmospheric pressure air plasma gives rise to a rapid increase in the gas temperature and dimensions of the gas volume. As in natural lightning, the rapid expansion in the ionised column though the air produces external pressure variations at the modulation frequency.  \ud Spatial and temporal measurement of the gas temperature can identify the nature of the thermal expansion and provide a direct approach to understanding its relationship to the sound pressure wave that is generated. However, the established method through spectroscopic measurement of rotational line emission from nitrogen molecules is limited to the main current channel where relaxation and subsequent optical emission of the excited nitrogen molecules occurs. The wider picture is revealed through the use of the Schlieren method where the refractive index gradients caused by gas heating in the plasma are imaged

Geographic patterns of diffusion in the 2011 London riots

Surprisingly little research has examined the localised diffusion of riots within cities. In this paper, we investigate such patterns during the 2011 London riots, and consider how they changed as police numbers increased. Understanding how offences spread in space and time can provide insights regarding the mechanisms of contagion, and of the risk of events spreading between contiguous areas. Using spatial–temporal grids of varying resolution, and a Monte Carlo simulation, we compare observed patterns with those expected assuming the timing and location of events are independent. In particular, we differentiate between four space–time signatures: “flashpoints” of disorder which appear out of nowhere, “containment” whereby already affected areas experience further events, “escalation” whereby rioting continues in affected areas and spreads to those nearby, and “relocation” whereby the disorder moves from one locality to those adjacent. During the first half of the disorder, fewer counts of relocation diffusion were observed than expected, but patterns of containment, escalation, and flashpoints were all more prominent. For the second half of the disorder, when police capacity increased roughly three-fold, observed patterns did not differ from expectation. Our results show support for theories of spatial contagion, and suggest that there was a degree of coordination amongst rioters. They also show that police activity did not just suppress rioting, but dampened the influence of contagion, without displacement

Magnetic confinement of the solar tachocline

We study the physics of the solar tachocline and related MHD instabilities. We have performed 3-D MHD simulations of the solar radiative interior to check whether a fossil magnetic field is able to prevent the spread of the tachocline. Starting with a purely poloidal magnetic field and a latitudinal shear meant to be imposed by the convection zone at the top of the radiation zone, we have investigated the interactions between magnetic fields, rotation and shear, using the spectral code ASH on massive parallel supercomputers. In all cases we have explored, the fossil field diffuses outward and ends up connecting with the convection zone, whose differential rotation is then imprinted at latitudes above 40 deg throughout the radiative interior, according to Ferraro's law of isorotation. Rotation remains uniform in the lower latitude region which is contained within closed field lines. We find that the meridional flow cannot stop the inward progression of the differential rotation. Further, we observe the development of non-axisymmetric magnetohydrodynamic instabilities, first due to the initial poloidal configuration of the fossil field, and later to the toroidal field produced by shearing the poloidal field through the differential rotation. We do not find dynamo action as such in the radiative interior, since the mean poloidal field is not regenerated. But the instability persists during the whole evolution, while slowly decaying with the mean poloidal field. According to our numerical simulations, a fossil magnetic field cannot prevent the radiative spread of the tachocline, and thus it is unable to enforce uniform rotation in the radiation zone. Neither can the observed thinness of that layer be invoked as a proof for such an internal fossil magnetic field.Comment: 12 pages, 8 color figures (low res), published in A&A, october 200