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

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

The legal framework for offshore wind farms: A critical analysis of the consents process

The impact of the legal framework for the consents process on the rate of development of offshore wind farms in England, and the achievement of targets for renewable electricity generation have been reviewed. From the literature and consulted stakeholders it was found that the complexity of the current consents process has adversely affected the rate of development and the achievement of renewable energy targets. Future projects will be subject to a different legal framework for consents, under the Planning Act 2008 and the Marine and Coastal Access Bill. From a comparison of process diagrams for the current and future consents processes, it is concluded that the future process should be an improvement. However, uncertainties remain about the detailed procedures and operation of the future consenting authorities. The capacity and capability of key stakeholders to meet their obligations have implications for the time frame for the processes of applying for, and the granting of, consents. Furthermore improved engagement from developers and clarity about the role of local authorities are essential if progress is to be made. The need for a holistic and strategic view of the industry, including associated development of the supply chain and the transmission grid, is also highlighted. (C) 2010 Elsevier Ltd. All rights reserved

The Elementary Divisors of the Incidence Matrix of Skew Lines in PG(3,q)

The elementary divisors of the incidence matrix of lines in PG(3,q) are computed, where two lines are incident if and only if they are skew.Comment: 13 pages. The results of this paper supersede those in the paper arXiv:math/1001.2551 V2. Minor correction