Discrete adjoint approximations with shocks

This paper is concerned with the formulation and discretisation of adjoint equations when there are shocks in the underlying solution to the original nonlinear hyperbolic p.d.e. For the model problem of a scalar unsteady one-dimensional p.d.e. with a convex flux function, it is shown that the analytic formulation of the adjoint equations requires the imposition of an interior boundary condition along any shock. A 'discrete adjoint' discretisation is defined by requiring the adjoint equations to give the same value for the linearised functional as a linearisation of the original nonlinear discretisation. It is demonstrated that convergence requires increasing numerical smoothing of any shocks. Without this, any consistent discretisation of the adjoint equations without the inclusion of the shock boundary condition may yield incorrect values for the adjoint solution

Benthic foraminifera show some resilience to ocean acidification in the northern Gulf of California, Mexico.

The version on PEARL: Corrected proofs are Articles in Press that contain the authors' corrections. Final citation details, e.g., volume/issue number, publication year and page numbers, still need to be added and the text might change before final publication. Although corrected proofs do not have all bibliographic details available yet, they can already be cited using the year of online publication and the DOI , as follows: author(s), article title, journal (year), DOIExtensive CO2 vents have been discovered in the Wagner Basin, northern Gulf of California, where they create large areas with lowered seawater pH. Such areas are suitable for investigations of long-term biological effects of ocean acidification and effects of CO2 leakage from subsea carbon capture storage. Here, we show responses of benthic foraminifera to seawater pH gradients at 74-207m water depth. Living (rose Bengal stained) benthic foraminifera included Nonionella basispinata, Epistominella bradyana and Bulimina marginata. Studies on foraminifera at CO2 vents in the Mediterranean and off Papua New Guinea have shown dramatic long-term effects of acidified seawater. We found living calcareous benthic foraminifera in low pH conditions in the northern Gulf of California, although there was an impoverished species assemblage and evidence of post-mortem test dissolution

Coherent states for compact Lie groups and their large-N limits

The first two parts of this article surveys results related to the heat-kernel coherent states for a compact Lie group K. I begin by reviewing the definition of the coherent states, their resolution of the identity, and the associated Segal-Bargmann transform. I then describe related results including connections to geometric quantization and (1+1)-dimensional Yang--Mills theory, the associated coherent states on spheres, and applications to quantum gravity. The third part of this article summarizes recent work of mine with Driver and Kemp on the large-N limit of the Segal--Bargmann transform for the unitary group U(N). A key result is the identification of the leading-order large-N behavior of the Laplacian on "trace polynomials."Comment: Submitted to the proceeding of the CIRM conference, "Coherent states and their applications: A contemporary panorama.

Fretting of CoCrMo and Ti6Al4V Alloys in Modular Prostheses

Implantation of a total hip replacements (THR) is an effective intervention in the management of arthritis. Modularity at the taper junction of THR was introduced in order to improve the ease with which the surgeon could modify the length of the taper section and the overall length of the replacement. Cobalt chromium (Co–28Cr–6Mo) and titanium (Ti–6Al–4V) alloys are the most commonly used materials for the device. This study investigates the fretting behaviour of both CoCr–CoCr and CoCr–Ti couplings and analyses their damage mechanisms. A reciprocating tribometer ball on plate fretting contact was instrumented with in situ electrochemistry to characterise the damage inflicted by tribocorrosion on the two couplings. Fretting displacements amplitudes of 10, 25 and 50 mm at an initial contact pressure of 1 GPa were assessed. The results reveal larger metallic volume loss from the CoCr–CoCr alloy compared to the CoCr–Ti alloy, and the open circuit potential indicates a depassivation of the protective oxide layer at displacement amplitudes .25 mm. In conclusion, the damage mechanisms of CoCr–CoCr and CoCr–Ti fretting contacts were identified to be wear and fatigue dominated mechanisms respectively

Minimal flavour violation extensions of the seesaw

We analyze the most natural formulations of the minimal lepton flavour violation hypothesis compatible with a type-I seesaw structure with three heavy singlet neutrinos N, and satisfying the requirement of being predictive, in the sense that all LFV effects can be expressed in terms of low energy observables. We find a new interesting realization based on the flavour group $SU(3)_e\times SU(3)_{\ell+N}$ (being $e$ and $\ell$ respectively the SU(2) singlet and doublet leptons). An intriguing feature of this realization is that, in the normal hierarchy scenario for neutrino masses, it allows for sizeable enhancements of $\mu \to e$ transitions with respect to LFV processes involving the $\tau$ lepton. We also discuss how the symmetries of the type-I seesaw allow for a strong suppression of the N mass scale with respect to the scale of lepton number breaking, without implying a similar suppression for possible mechanisms of N productionComment: 14 pages, 6 figure