Radio background and IGM heating due to Pop III supernovae explosions

We consider the synchrotron emission from high energy electrons accelerated in supernova explosions of massive Population III stars in high redshift minihaloes of mass $10^{5\hbox {--}7} \rm M_\odot$. We show the resulting intensity of radio background from this process can be substantial, which could potentially explain the recently reported EDGES result, if not for the associated heating of the IGM by CR protons which are also produced at the same time. The trade-off between the radio background and heating is such that the 21 cm brightness temperature cannot be larger than $\vert \Delta T_{21}\vert \sim 0.25$ K. The radio background and heating are both produced by energetic particles, although one by energetic electrons and the other by energetic protons. The two competing processes, production of radio background and heating of IGM by Pop III supernovae, determine the depth of the trough in the 21 cm brightness temperature which can be observed in future experiments and used as a test of this scenario.Comment: 6 pages, 2 figures, Accepted for publication in MNRA

A map and a pipe : a new approach to characterizing erosion-corrosion regimes of Fe in three dimensions using CFD modelling

In studies of erosion-corrosion, much work has been carried out in recent years to identify regimes of behaviour. Such regimes describe the transition between the erosion and corrosion dominated mechanisms. They can also be used, by assigning various criteria, to identify other regimes of behaviour such as extent of "synergy/antagonism" in the process, so-called "additive" behaviour and the extent of wastage. Despite this work, there has been very little effort to combine the two dimensional erosion-corrosion map with CFD modelling approaches, in which the characteristics of the fluid are accounted for in the regime description. This means that extrapolation of such maps in two dimensions to a three dimensional real surface presents some difficulties. However, it is these surfaces that corrosion engineers are required to tailor, either through modification of the material composition, the surface or the process parameters, for optimum erosion-corrosion resistance. In this paper, a methodology is generated to combine the concepts of CFD modelling, and the erosion-corrosion regime map for a specific geometry and for a range of pure metals in descending order in the Galvanic series. The changes in regimes are presented as a function of variation in the erosion and corrosion variables i.e. particle size, hardness and solution pH. Erosion-corrosion regimes are presented, based on the model results, showing the wide range of mechanistic and wastage mechanisms possible over the component surface

Bargaining in the Shadow of the Best-Interests Standard: The Close Connection Between Substance and Process in Resolving Divorce-Related Parenting Disputes

This essay, written for a Symposium celebrating the child custody scholarship of Professor Robert Mnookin, examines the close connection between changes in substantive child custody doctrine and changes in custody dispute resolution processes over the past 30 years. Part I of the article explores how the widespread adoption of an unmediated “best interest of the child” standard, and the ensuing rejection of the sole custody paradigm, precipitated a shift from adversarial to non-adversarial resolution of divorce-related parenting disputes. Part II of the essay reverses the direction of the analytic lens and considers how the shift from adversarial to non-adversarial dispute resolution has affected both the substantive legal norms that govern custody contests and the role of law and lawyers more generally in the custody decision-making process. The essay suggests that the shift from adjudication and adversary negotiation to mediation and collaboration as the preferred means of resolving divorce-related parenting disputes has delegalized custody decision-making -- initially by disaggregating the various components of child custody and ultimately by eroding the importance of custody as an essential legal concept in disputes between parents. The primary purpose of the analysis is not to evaluate the desirability of these changes, but to underscore the close connection between changes in substantive legal doctrine and changes in dispute resolution processes