Fluid Flows of Mixed Regimes in Porous Media

In porous media, there are three known regimes of fluid flows, namely, pre-Darcy, Darcy and post-Darcy. Because of their different natures, these are usually treated separately in literature. To study complex flows when all three regimes may be present in different portions of a same domain, we use a single equation of motion to unify them. Several scenarios and models are then considered for slightly compressible fluids. A nonlinear parabolic equation for the pressure is derived, which is degenerate when the pressure gradient is either small or large. We estimate the pressure and its gradient for all time in terms of initial and boundary data. We also obtain their particular bounds for large time which depend on the asymptotic behavior of the boundary data but not on the initial one. Moreover, the continuous dependence of the solutions on initial and boundary data, and the structural stability for the equation are established.Comment: 33 page

Variational bound on energy dissipation in plane Couette flow

We present numerical solutions to the extended Doering-Constantin variational principle for upper bounds on the energy dissipation rate in turbulent plane Couette flow. Using the compound matrix technique in order to reformulate this principle's spectral constraint, we derive a system of equations that is amenable to numerical treatment in the entire range from low to asymptotically high Reynolds numbers. Our variational bound exhibits a minimum at intermediate Reynolds numbers, and reproduces the Busse bound in the asymptotic regime. As a consequence of a bifurcation of the minimizing wavenumbers, there exist two length scales that determine the optimal upper bound: the effective width of the variational profile's boundary segments, and the extension of their flat interior part.Comment: 22 pages, RevTeX, 11 postscript figures are available as one uuencoded .tar.gz file from [email protected]

Finding a moral homeground: appropriately critical religious education and transmission of spiritual values

Values-inspired issues remain an important part of the British school curriculum. Avoiding moral relativism while fostering enthusiasm for spiritual values and applying them to non-curricular learning such as school ethos or children's home lives are challenges where spiritual, moral, social and cultural (SMSC) development might benefit from leadership by critical religious education (RE). Whether the school's model of spirituality is that of an individual spiritual tradition (schools of a particular religious character) or universal pluralistic religiosity (schools of plural religious character), the pedagogy of RE thought capable of leading SMSC development would be the dialogical approach with examples of successful implementation described by Gates, Ipgrave and Skeie. Marton's phenomenography, is thought to provide a valuable framework to allow the teacher to be appropriately critical in the transmission of spiritual values in schools of a particular religious character as evidenced by Hella's work in Lutheran schools

Solving Nonlinear Parabolic Equations by a Strongly Implicit Finite-Difference Scheme

We discuss the numerical solution of nonlinear parabolic partial differential equations, exhibiting finite speed of propagation, via a strongly implicit finite-difference scheme with formal truncation error $\mathcal{O}\left[(\Delta x)^2 + (\Delta t)^2 \right]$. Our application of interest is the spreading of viscous gravity currents in the study of which these type of differential equations arise. Viscous gravity currents are low Reynolds number (viscous forces dominate inertial forces) flow phenomena in which a dense, viscous fluid displaces a lighter (usually immiscible) fluid. The fluids may be confined by the sidewalls of a channel or propagate in an unconfined two-dimensional (or axisymmetric three-dimensional) geometry. Under the lubrication approximation, the mathematical description of the spreading of these fluids reduces to solving the so-called thin-film equation for the current's shape $h(x,t)$. To solve such nonlinear parabolic equations we propose a finite-difference scheme based on the Crank--Nicolson idea. We implement the scheme for problems involving a single spatial coordinate (i.e., two-dimensional, axisymmetric or spherically-symmetric three-dimensional currents) on an equispaced but staggered grid. We benchmark the scheme against analytical solutions and highlight its strong numerical stability by specifically considering the spreading of non-Newtonian power-law fluids in a variable-width confined channel-like geometry (a "Hele-Shaw cell") subject to a given mass conservation/balance constraint. We show that this constraint can be implemented by re-expressing it as nonlinear flux boundary conditions on the domain's endpoints. Then, we show numerically that the scheme achieves its full second-order accuracy in space and time. We also highlight through numerical simulations how the proposed scheme accurately respects the mass conservation/balance constraint.Comment: 36 pages, 9 figures, Springer book class; v2 includes improvements and corrections; to appear as a contribution in "Applied Wave Mathematics II

Numerical study of radiative Maxwell viscoelastic magnetized flow from a stretching permeable sheet with the Cattaneo–Christov heat flux model

In this article, the Cattaneo-Christov heat flux model is implemented to study non-Fourier heat and mass transfer in the magnetohydrodynamic (MHD) flow of an upper convected Maxwell (UCM) fluid over a permeable stretching sheet under a transverse constant magnetic field. Thermal radiation and chemical reaction effects are also considered. The nonlinear partial differential conservation equations for mass, momentum, energy and species conservation are transformed with appropriate similarity variables into a system of coupled, highly nonlinear ordinary differential equations with appropriate boundary conditions. Numerical solutions have been presented for the influence of elasticity parameter (), magnetic parameter (M2), suction/injection parameter (λ), Prandtl number (Pr), conduction-radiation parameter (Rd), sheet stretching parameter (A), Schmidt number (Sc), chemical reaction parameter (γ_c), modified Deborah number with respect to relaxation time of heat flux (i.e. non-Fourier Deborah number) on velocity components, temperature and concentration profiles using the successive Taylor series linearization method (STSLM) utilizing Chebyshev interpolating polynomials and Gauss-Lobatto collocation. The effects of selected parameters on skin friction coefficient, Nusselt number and Sherwood number are also presented with the help of tables. Verification of the STSLM solutions is achieved with existing published results demonstrating close agreement. Further validation of skin friction coefficient, Nusselt number and Sherwood number values computed with STSLM is included using Mathematica software shooting quadrature

Compensatory shifts in visual perception are associated with hallucinations in Lewy body disorders

Abstract Visual hallucinations are a common, distressing, and disabling symptom of Lewy body and other diseases. Current models suggest that interactions in internal cognitive processes generate hallucinations. However, these neglect external factors. Pareidolic illusions are an experimental analogue of hallucinations. They are easily induced in Lewy body disease, have similar content to spontaneous hallucinations, and respond to cholinesterase inhibitors in the same way. We used a primed pareidolia task with hallucinating participants with Lewy body disorders (n = 16), non-hallucinating participants with Lewy body disorders (n = 19), and healthy controls (n = 20). Participants were presented with visual “noise” that sometimes contained degraded visual objects and were required to indicate what they saw. Some perceptions were cued in advance by a visual prime. Results showed that hallucinating participants were impaired in discerning visual signals from noise, with a relaxed criterion threshold for perception compared to both other groups. After the presentation of a visual prime, the criterion was comparable to the other groups. The results suggest that participants with hallucinations compensate for perceptual deficits by relaxing perceptual criteria, at a cost of seeing things that are not there, and that visual cues regularize perception. This latter finding may provide a mechanism for understanding the interaction between environments and hallucinations

Practitioner insights as a means of setting a context for conservation

A key obstacle to conservation success is the tendency of conservation professionals to tackle each challenge individually rather than collectively and in context. We sought to prioritize barriers to conservation previously described in the conservation literature. We undertook an online survey of 154 practitioners from over 70 countries to ascertain the most important barriers to conservation they faced. We used statistical analyses to identify the key impediments to conservation success and to examine whether these were affected by organizational attributes. Twenty‐one barriers were identified. The importance ascribed to those was influenced by continent of operation and organization size, but not by organization age or autonomy (from larger parent organizations). We found the most important barriers to consider when undertaking conservation action were wider issues (e.g., population growth, consumerism, favoring development, and industrial‐scale activity), operating environment (e.g., lack of political will, ineffective law enforcement, weak governments, corruption, safety and security), community attributes (e.g., dynamics, conflicts, and education levels), and the way conservation is undertaken (overconfidence, lack of funding, and externally set agendas). However, we advise against applying a one‐size‐fits‐all approach. We propose that conservationists account for the complex socioecological systems they operate in if they are to achieve success

The Three Rs: The Way Forward

This is the report of the eleventh of a series of workshops organised by the European Centre for the Validation of Alternative Methods (ECVAM), which was established in 1991 by the European Commission. ECVAM\u27s main goal, as defined in 1993 by its Scientific Advisory Committee, is to promote the scientific and regulatory acceptance of alternative methods which are of importance to the biosciences and which reduce, refine or replace the use of laboratory animals. One of the first priorities set by ECVAM was the implementation of procedures which would enable it to become well-informed about the state-of-the-art of non-animal test development and validation. and the potential for the possible incorporation of replacement alternative tests into regulatory procedures. It was decided that this would be best achieved by the organisation of ECVAM workshops on specific topics, at which small groups of invited experts would review the current status of various types of in vitro tests and their potential uses, and make recommendations about the best ways forward

The food superstore revolution: changing times, changing research agendas in the UK

This paper considers the changing scope of research into UK food superstores over a 30-year period. Rather than catalogue changing market shares by format, we seek instead to show how change links to national policy agendas. Academic research has evolved to address the growing complexities of the social, technological, economic and political impacts of the superstore format. We exemplify this by tracing the progression of retail change in Portsmouth, Hampshire, over 30 years. We discover that academic research can conflict with the preconceptions of some public policymakers. The position is exacerbated by a progressive decline in public information – and a commensurate rise in factual data held by commercial data companies – that leaves policymakers with a choice of which data to believe. This casts a shadow over the objectivity of macro-policy as currently formulated. Concerns currently arise because the UK Competition Commission (2008 but ongoing) starts each inquiry afresh with a search for recent data. Furthermore, it has recently called for changes to retail planning – the very arena in which UK superstore research commenced