797 research outputs found
A finite-difference solution of solute transport through a membrane bioreactor
The current paper presents a theoretical analysis of the transport of solutes through a fixed-film membrane bioreactor (MBR), immobilised with an active biocatalyst. The dimensionless convection-diffusion equation with variable coefficients was solved analytically and numerically for concentration profiles of the solutes through the MBR. The analytical solution makes use of regular perturbation and accounts for radial convective flow as well as axial diffusion of the substrate species. The Michaelis-Menten (or Monod) rate equation was assumed for the sink term, and the perturbation was extended up to second-order. In the analytical solution only the first-order limit of the Michaelis-Menten equation was considered; hence the linearized equation was solved. In the numerical solution, however, this restriction was lifted. The solution of the nonlinear, elliptic, partial differential equation was based on an implicit finite-difference method (FDM). An upwind scheme was employed for numerical stability. The resulting algebraic equations were solved simultaneously using the multivariate Newton-Raphson iteration method. The solution allows for the evaluation of the effect on the concentration profiles of (i) the radial and axial convective velocity, (ii) the convective mass transfer rates, (iii) the reaction rates, (iv) the fraction retentate, and (v) the aspect ratio
A Solution to the Graceful Exit Problem in Pre-Big Bang Cosmology
We examine the string cosmology equations with a dilaton potential in the
context of the Pre-Big Bang Scenario with the desired scale factor duality, and
give a generic algorithm for obtaining solutions with appropriate evolutionary
properties. This enables us to find pre-big bang type solutions with suitable
dilaton behaviour that are regular at , thereby solving the graceful exit
problem. However to avoid fine tuning of initial data, an `exotic' equation of
state is needed that relates the fluid properties to the dilaton field. We
discuss why such an equation of state should be required for reliable dilaton
behaviour at late times.Comment: 16 pages LaTeX, 5 figures. To appear in Physical Review
Bounce Conditions in f(R) Cosmologies
We investigate the conditions for a bounce to occur in
Friedmann-Robertson-Walker cosmologies for the class of fourth order gravity
theories. The general bounce criterion is determined and constraints on the
parameters of three specific models are given in order to obtain bounces
solutions. It is found that unlike the case of General Relativity, a bounce
appears to be possible in open and flat cosmologies.Comment: 11 pages LaTe
Caustics of Compensated Spherical Lens Models
We consider compensated spherical lens models and the caustic surfaces they
create in the past light cone. Examination of cusp and crossover angles
associated with particular source and lens redshifts gives explicit lensing
models that confirm previous claims that area distances can differ by
substantial factors from angular diameter distances even when averaged over
large angular scales. `Shrinking' in apparent sizes occurs, typically by a
factor of 3 for a single spherical lens, on the scale of the cusp caused by the
lens; summing over many lenses will still leave a residual effect.Comment: 21 pages, 5 ps figures, eps
Brane Dynamics in the Randall-Sundrum model, Inflation and Graceful Exit
We study the averaged action of the Randall-Sundrum model with a time
dependent metric ansatz. It can be reformulated in terms of a Brans-Dicke
action with time dependent Newton's constant. We show that the physics of early
universe, particularly inflation, is governed by the Brans-Dicke theory. The
Brans-Dicke scalar, however, quickly settles to its equilibrium value and
decouples from the post-inflationary cosmology. The deceleration parameter is
negative to start with but changes sign before the Brans-Dicke scalar settles
to its equilibrium value. Consequently, the brane metric smoothly exits
inflation. We have also studied the slow-roll inflation in our model and
investigated the spectra of the density perturbation generated by the radion
field and find them consistent with the current observations.Comment: Revised version, Accepted in Class. Quant. Gravit
Bounce behaviour in Kantowski-Sachs and Bianchi Cosmologies
Many cosmological scenarios envisage either a bounce of the universe at early
times, or collapse of matter locally to form a black hole which re-expands into
a new expanding universe region. Energy conditions preclude this happening for
ordinary matter in general relativistic universes, but scalar or dilatonic
fields can violate some of these conditions, and so could possibly provide
bounce behaviour. In this paper we show that such bounces cannot occur in
Kantowski-Sachs models without violating the {\it reality condition}
. This also holds true for other isotropic spatially
homogenous Bianchi models, with the exception of closed
Friedmann-Robertson-Walker and Bianchi IX models; bounce behaviour violates the
{\em weak energy condition} and . We turn to the
Randall-Sundrum type braneworld scenario for a possible resolution of this
problem.Comment: Matches published versio
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Supervision, scheduling, satisfaction and shared working: how experiences of junior doctors relate to excess mortality within the NHS.
BACKGROUND: We sought to explore associations between trainee doctor perception and excess patient mortality. METHODS: Data from two publicly available databases reflecting mortality and components of trainee satisfaction within 81 NHS healthcare institutions between the years 2012 and 2019 were analysed. Pearson's correlation coefficients were calculated. RESULTS: All domains of trainee perception were correlated with excess mortality. Clinical supervision out of hours (R=-0.44; p<0.0001), teamwork (R=-0.36; p<0.0001) and clinical supervision at any time (R=-0.35; p<0.0001) were most strongly correlated. Most associations remained consistent year on year. CONCLUSION: Trainee doctor perceptions of clinical supervision, rota design and teamwork within the NHS are consistently correlated with excess patient mortality. Further exploration of these associations could identify opportunities for interventions to reduce excess patient mortality. Given the clinical significance of our findings, organisations should consider rapid implementation of evidence-based interventions where they exist
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