A one-dimensional prescribed curvature equation modeling the corneal shape

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

A one-dimensional prescribed curvature equation modeling the corneal shape.

We prove existence, uniqueness, and stability of solutions of the prescribed curvature problem (u'/root 1 + u'(2))' = au - b/root 1 + u'(2) in [0, 1], u'(0) = u(1) = 0, for any given a > 0 and b > 0. We also develop a linear monotone iterative scheme for approximating the solution. This equation has been proposed as a model of the corneal shape in the recent paper (Okrasinski and Plociniczak in Nonlinear Anal., Real World Appl. 13:1498-1505, 2012), where a simplified version obtained by partial linearization has been investigated.

Positive Solutions of the Dirichlet Problem for the One-dimensional Minkowski-Curvature Equation

We discuss existence and multiplicity of positive solutions of the Dirichlet problem for the quasilinear ordinary differential equation-(u' / root 1 - u'(2))' = f(t, u). Depending on the behaviour of f = f(t, s) near s = 0, we prove the existence of either one, or two, or three, or infinitely many positive solutions. In general, the positivity of f is not required. All results are obtained by reduction to an equivalent non-singular problem to which variational or topological methods apply in a classical fashion.

Capillary bridging and long-range attractive forces in a mean-field approach

When a mixture is confined, one of the phases can condense out. This condensate, which is otherwise metastable in the bulk, is stabilized by the presence of surfaces. In a sphere-plane geometry, routinely used in atomic force microscope and surface force apparatus, it, can form a bridge connecting the surfaces. The pressure drop in the bridge gives rise to additional long-range attractive forces between them. By minimizing the free energy of a binary mixture we obtain the force-distance curves as well as the structural phase diagram of the configuration with the bridge. Numerical results predict a discontinuous transition between the states with and without the bridge and linear force-distance curves with hysteresis. We also show that similar phenomenon can be observed in a number of different systems, e.g., liquid crystals and polymer mixtures. (C). 2004 American Institute of Physics.

Positive radial solutions of the Dirichlet problem for the Minkowski-Curvature equation in a ball

We study the existence and multiplicity of positive radial solutions of the Dirichlet problem for the Minkowski-curvature equation { -div(del upsilon/root 1-vertical bar del upsilon vertical bar(2)) in B-R, upsilon=0 on partial derivative B-R,B- where B-R is a ball in R-N (N >= 2). According to the behaviour off = f (r, s) near s = 0, we prove the existence of either one, two or three positive solutions. All results are obtained by reduction to an equivalent non-singular one-dimensional problem, to which variational methods can be applied in a standard way.

Optimisation of exposure parameters for spinal curvature measurements in paediatric radiography

This review aims to identify strategies to optimise radiography practice using digital technologies, for full spine studies on paediatrics focusing particularly on methods used to diagnose and measure severity of spinal curvatures. The literature search was performed on different databases (PubMed, Google Scholar and ScienceDirect) and relevant websites (e.g., American College of Radiology and International Commission on Radiological Protection) to identify guidelines and recent studies focused on dose optimisation in paediatrics using digital technologies. Plain radiography was identified as the most accurate method. The American College of Radiology (ACR) and European Commission (EC) provided two guidelines that were identified as the most relevant to the subject. The ACR guidelines were updated in 2014; however these guidelines do not provide detailed guidance on technical exposure parameters. The EC guidelines are more complete but are dedicated to screen film systems. Other studies provided reviews on the several exposure parameters that should be included for optimisation, such as tube current, tube voltage and source-to-image distance; however, only explored few of these parameters and not all of them together. One publication explored all parameters together but this was for adults only. Due to lack of literature on exposure parameters for paediatrics, more research is required to guide and harmonise practice.

Optimisation of paediatrics computed radiography for full spine curvature measurements using a phantom: a pilot study

Aim: Optimise a set of exposure factors, with the lowest effective dose, to delineate spinal curvature with the modified Cobb method in a full spine using computed radiography (CR) for a 5-year-old paediatric anthropomorphic phantom. Methods: Images were acquired by varying a set of parameters: positions (antero-posterior (AP), posteroanterior (PA) and lateral), kilo-voltage peak (kVp) (66-90), source-to-image distance (SID) (150 to 200cm), broad focus and the use of a grid (grid in/out) to analyse the impact on E and image quality (IQ). IQ was analysed applying two approaches: objective [contrast-to-noise-ratio/(CNR] and perceptual, using 5 observers. Monte-Carlo modelling was used for dose estimation. Cohen’s Kappa coefficient was used to calculate inter-observer-variability. The angle was measured using Cobb’s method on lateral projections under different imaging conditions. Results: PA promoted the lowest effective dose (0.013 mSv) compared to AP (0.048 mSv) and lateral (0.025 mSv). The exposure parameters that allowed lower dose were 200cm SID, 90 kVp, broad focus and grid out for paediatrics using an Agfa CR system. Thirty-seven images were assessed for IQ and thirty-two were classified adequate. Cobb angle measurements varied between 16°±2.9 and 19.9°±0.9. Conclusion: Cobb angle measurements can be performed using the lowest dose with a low contrast-tonoise ratio. The variation on measurements for this was ±2.9° and this is within the range of acceptable clinical error without impact on clinical diagnosis. Further work is recommended on improvement to the sample size and a more robust perceptual IQ assessment protocol for observers.

Electric vehicles as a mean to reduce, energy, emissions and electricity costs

Electric vehicles (EVs) and plug-in hybrid electric vehicles (PHEVs), which obtain their fuel from the grid by charging a battery, are set to be introduced into the mass market and expected to contribute to oil consumption reduction. This research is concerned with studying the potential impacts on the electric utilities of large-scale adoption of plug-in electric vehicles from the perspective of electricity demand, fossil fuels use, CO2 emissions and energy costs. Simulations were applied to the Portuguese case study in order to analyze what would be the optimal recharge profile and EV penetration in an energy-oriented, an emissions-oriented and a cost-oriented objective. The objectives considered were: The leveling of load profiles, minimization of daily emissions and minimization of daily wholesale costs. Almost all solutions point to an off-peak recharge and a 50% reduction in daily wholesale costs can be verified from a peak recharge scenario to an off-peak recharge for a 2 million EVs in 2020. A 15% improvement in the daily total wholesale costs can be verified in the costs minimization objective when compared with the off-peak scenario result.

The electric vehicles as a mean to reduce Co2 emissions and energy costs in isolated regions: the São Miguel (Azores) case study

Most of small islands around the world today, are dependent on imported fossil fuels for the majority of their energy needs especially for transport activities and electricity production. The use of locally renewable energy resources and the implementation of energy efficiency measures could make a significant contribution to their economic development by reducing fossil fuel imports. An electrification of vehicles has been suggested as a way to both reduce pollutant emissions and increase security of supply of the transportation sector by reducing the dependence on oil products imports and facilitate the accommodation of renewable electricity generation, such as wind and, in the case of volcanic islands like Sao Miguel (Azores) of the geothermal energy whose penetration has been limited by the valley electricity consumption level. In this research, three scenarios of EV penetration were studied and it was verified that, for a 15% LD fleet replacement by EVs with 90% of all energy needs occurring during the night, the accommodation of 10 MW of new geothermal capacity becomes viable. Under this scenario, reductions of 8% in electricity costs, 14% in energy, 23% in fossil fuels use and CO2 emissions for the transportation and electricity production sectors could be expected.