Outside the Wall: Hydrodynamics of Type I Supernovae Interacting with a Partially Swept-Up Circumstellar Medium

Explaining the observed diversity of supernovae (SNe) and the physics of explosion requires knowledge of their progenitor stars, which can be obtained by constraining the circumstellar medium (CSM). Models of the SN ejecta colliding with CSM are necessary to infer the structure of the CSM and tie it back to a progenitor model. Recent SNe I revealed CSM concentrated at a distance $r\sim10^16$ cm, for which models of SN interaction are extremely limited. In this paper, we assume the concentrated region is a "wall" representing swept-up material, and unswept material lies outside the wall. We simulate one-dimensional hydrodynamics of SNe Ia & Ib impacting 300 unique CSM configurations using RT1D, which captures the Rayleigh-Taylor instability. We find that the density ratio between the wall and ejecta -- denoted $A_0$ or "wall height" -- is key, and higher walls deviate more from self-similar evolution. Functional fits accounting for $A_0$ are presented for the forward shock radius evolution. We show that higher walls have more degeneracy between CSM properties in the deceleration parameter, slower shocks, deeper-probing reverse shocks, slower shocked ejecta, less ejecta mass than CSM in the shock, and more mixing of ejecta into the CSM at early times. We analyze observations of SN 2014C (Type Ib) and suggest that it had a moderately high wall ($10 < A_0 < 200$) and wind-like outer CSM. We also postulate an alternate interpretation for the radio data of SN 2014C, that the radio rise occurs in the wind rather than the wall. Finally, we find that hydrodynamic measurements at very late times cannot distinguish the presence of a wall, except perhaps as an anomalously wide shock region.Comment: 17 pages, 13 figures, accepted to Ap

Case notes and clinicians : Galen's commentary on the Hippocratic epidemics in the Arabic tradition

Galen’s Commentaries on the Hippocratic Epidemics constitute one of the most detailed studies of Hippocratic medicine from Antiquity. The Arabic translation of the Commentaries by Ḥunayn ibn Isḥāq (d. c. 873) is of crucial importance because it preserves large sections now lost in Greek, and because it helped to establish an Arabic clinical literature. The present contribution investigate the translation of this seminal work into Syriac and Arabic. It provides a first survey of the manuscript tradition, and explores how physicians in the medieval Muslim world drew on it both to teach medicine to students, and to develop a framework for their own clinical research

Differential Renormalization of the Wess-Zumino Model

We apply the recently developed method of differential renormalization to the Wess-Zumino model. From the explicit calculation of a finite, renormalized effective action, the $\beta$-function is computed to three loops and is found to agree with previous existing results. As a further, nontrivial check of the method, the Callan-Symanzik equations are also verified to that loop order. Finally, we argue that differential renormalization presents advantages over other superspace renormalization methods, in that it avoids both the ambiguities inherent to supersymmetric regularization by dimensional reduction (SRDR), and the complications of virtually all other supersymmetric regulators.Comment: 10 page

Commentary on "The use of cognitive behaviour therapy to treat depression in people with learning disabilities: a systematic review"

Purpose – The purpose of this paper is to provide a commentary on “The use of cognitive-behaviour therapy to treat depression in people with learning disabilities: a systematic review”. Design/methodology/approach – Drawing on the literature, as well as both clinical and research experience, some reasons are outlined for the lack of attention given to psychological therapies to treat depression amongst people with intellectual disabilities (IDs). Findings – More research is needed, but existing evidence is promising regarding the effectiveness of adapted cognitive-behaviour therapy for depression amongst people with IDs. Originality/value – The commentary draws attention to the scope for developing a range of effective cognitive, behavioural and cognitive-behavioural treatments

Discrete Nodal Domain Theorems

We give a detailed proof for two discrete analogues of Courant's Nodal Domain Theorem