Non-conservation of dimension in divergence-free solutions of passive and active scalar systems

For any $h\in(1,2]$, we give an explicit construction of a compactly supported, uniformly continuous, and (weakly) divergence-free velocity field in $\mathbb{R}^2$ that weakly advects a measure whose support is initially the origin but for positive times has Hausdorff dimension $h$. These velocities are uniformly continuous in space-time and compactly supported, locally Lipschitz except at one point and satisfy the conditions for the existence and uniqueness of a Regular Lagrangian Flow in the sense of Di Perna and Lions theory. We then construct active scalar systems in $\mathbb{R}^2$ and $\mathbb{R}^3$ with measure-valued solutions whose initial support has co-dimension 2 but such that at positive times it only has co-dimension 1. The associated velocities are divergence free, compactly supported, continuous, and sufficiently regular to admit unique Regular Lagrangian Flows. This is in part motivated by the investigation of dimension conservation for the support of measure-valued solutions to active scalar systems. This question occurs in the study of vortex filaments in the three-dimensional Euler equations.Comment: 32 pages, 3 figures. This preprint has not undergone peer review (when applicable) or any post-submission improvements or corrections. The Version of Record of this article is published in Arch Rational Mech Anal, and is available online at https://doi.org/10.1007/s00205-021-01708-

Youth and Local Community Engagement in Devon in the 1960s: Voluntary Sector or State Control after the Albemarle Report?

Between the publication of the Albemarle Report on the Youth Service in 1960 and the findings of the Youth and Community Work in the 70s: the Fairbairn-Milson Report in 1969, local authorities in England attempted to rationalize services for young people in line with State directives. The decade began optimistically with policies that aimed to engineer an expansion of the State's role in influencing after-school activities. However, throughout the period progress was uneven and this study focuses on Devon to shed light on the effectiveness of the State ideology in the 1960 directive and its impact on the voluntary organisations that determined local strategies for engaging young people. History from below has a valuable contribution to make to national studies of the Youth Service, and this is enriched by the oral contributions and primary sources that help to develop an understanding of how local authorities responded to the young people in their area, the challenges they faced in improving services, and how far their relationship with the voluntary sector changed as a result of the 1960 Albemarle Report

How rapidly do neutron stars spin at birth? Constaints from archival X-ray observations of extragalactic supernovae

Traditionally, studies aimed at inferring the distribution of birth periods of neutron stars are based on radio surveys. Here we propose an independent method to constrain the pulsar spin periods at birth based on their X-ray luminosities. In particular, the observed luminosity distribution of supernovae (SNe) poses a constraint on the initial rotational energy of the embedded pulsars, via the correlation found for radio pulsars, and under the assumption that this relation continues to hold beyond the observed range. We have extracted X-ray luminosities (or limits) for a large sample of historical SNe observed with Chandra, XMM and Swift, which have been firmly classified as core-collapse SNe. We have then compared these observational limits with the results of Monte Carlo simulations of the pulsar X-ray luminosity distribution for a range of values of the birth parameters. We find that a pulsar population dominated by millisecond periods at birth is ruled out by the data

Maternal inbreeding reduces parental care in the zebra finch, <i>Taeniopygia guttata</i>

Increased embryo mortality is the most commonly cited cause of reduced fitness in inbred organisms. Reduced embryo survival may be the result of reduced parental expenditure by inbred individuals and here we tested the hypothesis that inbreeding results in impaired incubation behaviour in captive zebra finches. We compared incubation attentiveness of inbred female zebra finches (derived from full-sibling mating) with that of control females (derived from unrelated parents) and found a statistically significant inbreeding depression of 17% in incubation attentiveness. This shows that inbreeding can significantly influence parental behaviour. Despite a reduction in the amount of time inbred females spent incubating, their partners were able to compensate for the reduced incubation attentiveness. Incubation temperature also did not differ between inbred and control females. To test for the effect of incubation behaviour, we fostered eggs laid by control females to either inbred or control females at the end of laying. Eggs that were incubated by inbred females had an 8.5% lower hatching success than eggs incubated by control females and, although based on a relatively small sample and not statistically significant, the magnitude of the difference was consistent with differences in hatching success observed in the wild under relatively benign environmental conditions. Thus, under more challenging environmental conditions usually encountered in the wild, the reduced incubation attentiveness of inbred females could provide one proximate explanation for the consistent finding of decreased hatching success with increasing maternal inbreeding in birds

A calibration of the stellar mass fundamental plane at z ~ 0.5 using the micro-lensing induced flux ratio anomalies of macro-lensed quasars

We measure the stellar mass surface densities of early type galaxies by observing the micro-lensing of macro-lensed quasars caused by individual stars, including stellar remnants, brown dwarfs and red dwarfs too faint to produce photometric or spectroscopic signatures. Instead of observing multiple micro-lensing events in a single system, we combine single epoch X-ray snapshots of ten quadruple systems, and compare the measured relative magnifications for the images with those computed from macro-models. We use these to normalize a stellar mass fundamental plane constructed using a Salpeter IMF with a low mass cutoff of 0.1 solar mass and treat the zeropoint of the surface mass density as a free parameter. Our method measures the graininess of the gravitational potential produced by individual stars, in contrast to methods that decompose a smooth total gravitational potential into two smooth components, one stellar and one dark. We find the median likelihood value for the normalization factor F by which the Salpeter stellar masses must be multiplied is 1.23, with a one sigma confidence range, dominated by small number statistics, of 0.77 < F < 2.10Comment: Revised in response to referee's suggestions and re-submitted to ApJ; changes to the adopted effective radii propagate to a new value of the factor F (by which Salpeter stellar masses must be multiplied) of 1.2

Extended X-ray Emission From a Quasar-Driven Superbubble

We present observations of extended, 20-kpc scale soft X-ray gas around a luminous obscured quasar hosted by an ultra-luminous infrared galaxy caught in the midst of a major merger. The extended X-ray emission is well fit as a thermal gas with a temperature of kT ~ 280 eV and a luminosity of L_X ~ 10^42 erg/s and is spatially coincident with a known ionized gas outflow. Based on the X-ray luminosity, a factor of ~10 fainter than the [OIII] emission, we conclude that the X-ray emission is either dominated by photoionization, or by shocked emission from cloud surfaces in a hot quasar-driven wind.Comment: Accepted for publication in ApJ, 6 pages, 2 figure