Analysis and applications of the Voronoi Implicit Interface Method

We analyze a new mathematical and numerical framework, the " Voronoi Implicit Interface Method" (" VIIM" ), first introduced in Saye and Sethian (2011) [R.I. Saye, J.A. Sethian, The Voronoi Implicit Interface Method for computing multiphase physics, PNAS 108 (49) (2011) 19498-19503] for tracking multiple interacting and evolving regions (" phases" ) whose motion is determined by complex physics (fluids, mechanics, elasticity, etc.). From a mathematical point of view, the method provides a theoretical framework for moving interface problems that involve multiple junctions, defining the motion as the formal limit of a sequence of related problems. Discretizing this theoretical framework provides a numerical methodolology which automatically handles multiple junctions, triple points and quadruple points in two dimensions, as well as triple lines, etc. in higher dimensions. Topological changes in the system occur naturally, with no surgery required. In this paper, we present the method in detail, and demonstrate several new extensions of the method to different physical phenomena, including curvature flow with surface energy densities defined on a per-phase basis, as well as multiphase fluid flow in which density, viscosity and surface tension can be defined on a per-phase basis.We test this method in a variety of ways. We perform rigorous analysis and demonstrate convergence in both two and three dimensions for a variety of evolving interface problems, including verification of von Neumann-Mullins' law in two dimensions (and its analog in three dimensions), as well as normal driven flow and curvature flow with and without constraints, demonstrating topological change and the effects of different boundary conditions. We couple the method to a second order projection method solver for incompressible fluid flow, and study the effects of membrane permeability and impermeability, large shearing torsional forces, and the effects of varying density, viscosity and surface tension on a per-phase basis. Finally, we demonstrate convergence in both space and time of a topological change in a multiphase foam. © 2012 Elsevier Inc.

Twenty years on: lesbian, gay and bisexual police officers' experiences of workplace discrimination in England and Wales

Twenty years ago Mark Burke's pioneering research into homosexuality and policing evidenced widespread prejudice and hostility toward lesbian, gay and bisexual police officers in nine forces across England and Wales. These serving officers were felt to represent the most serious kind of contamination and threat to the integrity of the British Police Service by their heterosexual colleagues. Twenty years on this research, which represents one of the largest ever surveys of LGB police officers in England and Wales (N=836), evidences that just under one-fifth reported experiencing discrimination, with those in small and large forces, those in senior ranks and non-uniformed positions, and those who identify as gay male and Black, Minority Ethnic experiencing the highest levels of victimisation in training, deployment and promotion. Like Brown and Woolfenden, the authors conclude that a central aim of the diversity reform agenda must be a renegotiation of the psychological contract between staff and the organisation. A relational setup must be sought where mutual expectations of exchange are established and efforts are made to create a rich working environment that draws upon and invests in the subjective and intersubjective identity characteristics of LGB police officers