Stabilization methods in relaxed micromagnetism

The magnetization of a ferromagnetic sample solves a non-convex variational problem, where its relaxation by convexifying the energy density resolves relevant macroscopic information. The numerical analysis of the relaxed model has to deal with a constrained convex but degenerated, nonlocal energy functional in mixed formulation for magnetic potential u and magnetization m. In [C. Carstensen and A. Prohl, Numer. Math. 90 (2001) 65–99], the conforming P1 - (P0)d-element in d=2,3 spatial dimensions is shown to lead to an ill-posed discrete problem in relaxed micromagnetism, and suboptimal convergence. This observation motivated a non-conforming finite element method which leads to a well-posed discrete problem, with solutions converging at optimal rate. In this work, we provide both an a priori and a posteriori error analysis for two stabilized conforming methods which account for inter-element jumps of the piecewise constant magnetization. Both methods converge at optimal rate; the new approach is applied to a macroscopic nonstationary ferromagnetic model [M. Kružík and A. Prohl, Adv. Math. Sci. Appl. 14 (2004) 665–681 – M. Kružík and T. Roubíček, Z. Angew. Math. Phys. 55 (2004) 159–182 ]

Plasminogen Activator Inhibitor-1 Promotes Neutrophil Infiltration and Tissue Injury on Ischemia–Reperfusion

Objective Ischemia-reperfusion (I/R) injury significantly contributes to organ dysfunction and failure after myocardial infarction, stroke, and transplantation. In addition to its established role in the fibrinolytic system, plasminogen activator inhibitor-1 has recently been implicated in the pathogenesis of I/R injury. The underlying mechanisms remain largely obscure. Approach and Results Using different in vivo microscopy techniques as well as ex vivo analyses and in vitro assays, we identified that plasminogen activator inhibitor-1 rapidly accumulates on microvascular endothelial cells on I/R enabling this protease inhibitor to exhibit previously unrecognized functional properties by inducing an increase in the affinity of 2 integrins in intravascularly rolling neutrophils. These events are mediated through low-density lipoprotein receptor-related protein-1 and mitogen-activated protein kinase-dependent signaling pathways that initiate intravascular adherence of these immune cells to the microvascular endothelium. Subsequent to this process, extravasating neutrophils disrupt endothelial junctions and promote the postischemic microvascular leakage. Conversely, deficiency of plasminogen activator inhibitor-1 effectively reversed leukocyte infiltration, microvascular dysfunction, and tissue injury on experimental I/R without exhibiting side effects on microvascular hemostasis. Conclusions Our experimental data provide novel insights into the nonfibrinolytic properties of the fibrinolytic system and emphasize plasminogen activator inhibitor-1 as a promising target for the prevention and treatment of I/R injury

Mediation in the Law Curriculum

Cited by Lord Neuberger in ‘Educating Future Mediators’ at the 4th Civil Mediation Council National Conference, May 201

Sprint start kinetics of amputee and non-amputee sprinters

The purpose of this study was to explore the relationship between the forces applied to the starting blocks and the start performances (SPs) of amputee sprinters (ASs) and non-amputee sprinters (NASs). SPs of 154 male and female NASs (100-m personal records [PRs], 9.58–14.00 s) and 7 male ASs (3 unilateral above knee, 3 unilateral below knee, 1 bilateral below knee; 100 m PRs, 11.70–12.70 s) with running specific prostheses (RSPs) were analysed during full-effort sprint starts using instrumented starting blocks that measured the applied forces in 3D. Using the NAS dataset and a combination of factor analysis and multiple regression techniques, we explored the relationship between force characteristics and SP (quantified by normalized average horizontal block power). Start kinetics were subsequently compared between ASs and NASs who were matched based on their absolute 100 m PR and their 100 m PR relative to the world record in their starting class. In NASs, 86% of the variance in SP was shared with five latent factors on which measured parameters related to force application to the rear and front blocks and the respective push-off directions in the sagittal plane of motion were loaded. Mediolateral force application had little influence on SP. The SP of ASs was significantly reduced compared to that of NASs matched on the basis of relative 100-m PR (−33.8%; d = 2.11, p < 0.001), while a non-significant performance reduction was observed when absolute 100-m PRs were used (−17.7%; d = 0.79, p = 0.09). These results are at least partially explained by the fact that force application to the rear block was clearly impaired in the affected legs of ASs

A Housing Affordability Standard for the UK

Since 1990 there has been extensive exploration of the meaning of housing affordability by members of the academic, professional and advocacy communities in Britain. These debates have revealed weaknesses in the traditional ratio standard of affordability and led to arguments in support of an alternative, residual income concept of affordability. However, so far there has been only limited success in operationalising and applying the residual income approach in the UK. In the US, by contrast, arguments in support of a residual income approach to housing affordability emerged in the late 1960s and early 1970s, culminating in the formulation of operational standards utilising normative family budgets. This paper draws upon the US experience to formulate a residual income housing affordability standard for the UK that utilises the non-shelter components of the Family Budget Unit (FBU) ‘Low Cost but Acceptable’ budgets as the normative standard for minimum adequate residual income. The paper concludes by suggesting how use of such a ‘shelter’ poverty standard to assess housing affordability problems and needs in the UK might yield results that differ from those based on the ratio standard

Hierarchical Basis Preconditioners for Coupled FEM-BEM Equations

this paper is to present a nearly optimal preconditioned iterative method to solve indefinite linear systems of equations arising from h-adaptive procedures for the symmetric coupling of Finite Elements and Boundary Elements. This solver is nearly optimal in the sense, that its convergence rate grows only logarithmically with the number of unknowns. The algorithm is based on the conjugate residual method with block-diagonal preconditioning, where no Schur complement construction is required. This method uses different hierarchical basis preconditioners for the positive semi--definite FEM block belonging to an interior Neumann problem and the negative definite boundary element block belonging to the single layer potential. The efficiency of the hierarchical basis solvers is underlined by a numerical experiment showing fast convergence