Gradient discretization of Hybrid Dimensional Darcy Flows in Fractured Porous Media with discontinuous pressures at the matrix fracture interfaces

We investigate the discretization of Darcy flow through fractured porous media on general meshes. We consider a hybrid dimensional model, invoking a complex network of planar fractures. The model accounts for matrix-fracture interactions and fractures acting either as drains or as barriers, i.e. we have to deal with pressure discontinuities at matrix-fracture interfaces. The numerical analysis is performed in the general framework of gradient discretizations which is extended to the model under consideration. Two families of schemes namely the Vertex Approximate Gradient scheme (VAG) and the Hybrid Finite Volume scheme (HFV) are detailed and shown to satisfy the gradient scheme framework, which yields, in particular, convergence. Numerical tests confirm the theoretical results. Gradient Discretization; Darcy Flow, Discrete Fracture Networks, Finite Volum

Courts, care proceedings and outcomes uncertainty: the challenges of achieving and assessing ‘good outcomes’ for children after child protection proceedings

The professed aim of any social welfare or legal intervention in family life is often to bring about ‘better outcomes for the children’. But there is considerable ambiguity about ‘outcomes’, and the term is far too often used in far too simplistic a way. This paper draws on empirical research into the outcomes of care proceedings for a randomly selected sample of 616 children in England and Wales, about half starting proceedings in 2009-10, and the others in 2014-15. The paper considers the challenges of achieving and assessing ‘good outcomes’ for the children. Outcomes are complex and fluid for all children, whatever the court order. One has to assess the progress of the children in the light of their individual needs and in the context of ‘normal’ child development; and in terms of the legal provisions and policy expectations. A core paradox is that some of the most uncertain outcomes are for children who remain with or return to their parents; yet law and policy require that first consideration is given to this option. Greater transparency about the uncertainty of outcomes is a necessary step towards better understanding the risks and potential benefits of care proceedings

Nonlinear Preconditioning: How to use a Nonlinear Schwarz Method to Precondition Newton's Method

For linear problems, domain decomposition methods can be used directly as iterative solvers, but also as preconditioners for Krylov methods. In practice, Krylov acceleration is almost always used, since the Krylov method finds a much better residual polynomial than the stationary iteration, and thus converges much faster. We show in this paper that also for non-linear problems, domain decomposition methods can either be used directly as iterative solvers, or one can use them as preconditioners for Newton's method. For the concrete case of the parallel Schwarz method, we show that we obtain a preconditioner we call RASPEN (Restricted Additive Schwarz Preconditioned Exact Newton) which is similar to ASPIN (Additive Schwarz Preconditioned Inexact Newton), but with all components directly defined by the iterative method. This has the advantage that RASPEN already converges when used as an iterative solver, in contrast to ASPIN, and we thus get a substantially better preconditioner for Newton's method. The iterative construction also allows us to naturally define a coarse correction using the multigrid full approximation scheme, which leads to a convergent two level non-linear iterative domain decomposition method and a two level RASPEN non-linear preconditioner. We illustrate our findings with numerical results on the Forchheimer equation and a non-linear diffusion problem

Attitudes towards mental illness in Malawi: a cross-sectional survey

<p><b>Background:</b> Stigma and discrimination associated with mental illness are strongly linked to suffering, disability and poverty. In order to protect the rights of those with mental disorders and to sensitively develop services, it is vital to gain a more accurate understanding of the frequency and nature of stigma against people with mental illness. Little research about this issue has been conducted in sub Saharan Africa. Our study aimed to describe levels of stigma in Malawi.</p> <p><b>Method:</b> A cross-sectional survey of patients and relatives attending mental health and non-mental health related clinics in a general hospital in Blantyre, Malawi. Subjects were interviewed using an adapted version of the questionnaire developed for the World Psychiatric Association Program to Reduce Stigma and Discrimination Because of Schizophrenia.</p> <p><b>Results:</b> 210 subjects participated in our study. Most attributed mental disorder to alcohol and illicit drug abuse (95%). This was closely followed by brain disease (92.8%), spirit possession (82.8%) and then psychological trauma (76.1%). There were some associations found between demographic variables and single question responses, however no consistent trends were observed in stigmatising beliefs. These results should be interpreted with caution and in the context of existing research. Contrary to the international literature, having direct personal experience of mental illness seemed to have no positive effect on stigmatising beliefs in our sample.</p> <p><b>Conclusions:</b> Our study contributes to an emerging picture that individuals in sub Saharan Africa most commonly attribute mental illness to alcohol/ illicit drug use and spiritual causes. Our work adds weight to the argument that stigma towards mental illness is an important global health and human rights issue.</p&gt

Examples of derivation-based differential calculi related to noncommutative gauge theories

Some derivation-based differential calculi which have been used to construct models of noncommutative gauge theories are presented and commented. Some comparisons between them are made.Comment: 22 pages, conference given at the "International Workshop in honour of Michel Dubois-Violette, Differential Geometry, Noncommutative Geometry, Homology and Fundamental Interactions". To appear in a special issue of International Journal of Geometric Methods in Modern Physic

Modeling electricity loads in California: a continuous-time approach

In this paper we address the issue of modeling electricity loads and prices with diffusion processes. More specifically, we study models which belong to the class of generalized Ornstein-Uhlenbeck processes. After comparing properties of simulated paths with those of deseasonalized data from the California power market and performing out-of-sample forecasts we conclude that, despite certain advantages, the analyzed continuous-time processes are not adequate models of electricity load and price dynamics.Comment: To be published in Physica A (2001): Proceedings of the NATO ARW on Application of Physics in Economic Modelling, Prague, Feb. 8-10, 200

Synchronous Behavior of Two Coupled Electronic Neurons

We report on experimental studies of synchronization phenomena in a pair of analog electronic neurons (ENs). The ENs were designed to reproduce the observed membrane voltage oscillations of isolated biological neurons from the stomatogastric ganglion of the California spiny lobster Panulirus interruptus. The ENs are simple analog circuits which integrate four dimensional differential equations representing fast and slow subcellular mechanisms that produce the characteristic regular/chaotic spiking-bursting behavior of these cells. In this paper we study their dynamical behavior as we couple them in the same configurations as we have done for their counterpart biological neurons. The interconnections we use for these neural oscillators are both direct electrical connections and excitatory and inhibitory chemical connections: each realized by analog circuitry and suggested by biological examples. We provide here quantitative evidence that the ENs and the biological neurons behave similarly when coupled in the same manner. They each display well defined bifurcations in their mutual synchronization and regularization. We report briefly on an experiment on coupled biological neurons and four dimensional ENs which provides further ground for testing the validity of our numerical and electronic models of individual neural behavior. Our experiments as a whole present interesting new examples of regularization and synchronization in coupled nonlinear oscillators.Comment: 26 pages, 10 figure