Jointly radial and translation homothetic preferences: generalized constant risk aversion

The paper identifies the structural restrictions on preferences required for them to exhibit both translation homotheticity in particular direction and radial homotheticity. The results are illustrated by an application to an asset allocation problem in the absence of riskless asset.

Diabetes, my constant companion

Forty-five years as a doctor with diabetes has given Alan Stocks personal insight into how to manage life and practice when living with a chronic illness. Diabetes has proved beneficial to his career, rather than a disadvantage.

Van der Waals-corrected density functional theory: benchmarking for hydrogen-nanotube and nanotube-nanotube interactions

Density functional theory (DFT) is a powerful approach to electronic structure calculations in extended systems, but suffers currently from inadequate incorporation of long-range dispersion, or Van der Waals (VdW) interactions. VdW-corrected DFT is tested for interactions involving molecular hydrogen, graphite, single-walled carbon nanotubes (SWCNTs), and SWCNT bundles. The energy correction, based on an empirical London dispersion term with a damping function at short range, allows a reasonable physisorption energy and equilibrium distance to be obtained for H-2 on a model graphite surface. The VdW-corrected DFT calculation for an (8, 8) nanotube bundle reproduces accurately the experimental lattice constant. For H-2 inside or outside an (8, 8) SWCNT, we find the binding energies are respectively higher and lower than that on a graphite surface, correctly predicting the well known curvature effect. We conclude that the VdW correction is a very effective method for implementing DFT calculations, allowing a reliable description of both short-range chemical bonding and long-range dispersive interactions. The method will find powerful applications in areas of SWCNT research where empirical potential functions either have not been developed, or do not capture the necessary range of both dispersion and bonding interactions.

Pore size characterization of mesoporous materials by a thermodynamic approach: A curvature-dependent solid-fluid potential

A thermodynamic analysis of nitrogen adsorption in cylindrical pores of MCM-41 and SBA-15 samples at 77 K is presented within the framework of the Broekhoff and de Boer (BdB) theory. We accounted for the effect of the solid surface curvature on the potential exerted by the pore walls. The developed model is in quantitative agreement with the non-local density functional theory (NLDFT) for pores larger than 2 tun. This modified BdB theory accounting for the Curvature Dependent Potential (CDP-BdB) was applied to determine the pore size distribution (PSD) of a number of MCM-41 and SBA-15 samples on the basis of matching the equilibrium theoretical isotherm against the adsorption branch of the experimental isotherm. In all cases investigated the PSDs determined with the new approach are very similar to those determined with the non-local density functional theory also using the same basis of matching of theoretical isotherm against the experimental adsorption branch. The developed continuum theory is very simple in its utilization, suggesting that CDP-BdB could be used as an alternative tool to obtain PSD for mesoporous solids from the analysis of adsorption branch of adsorption isotherms of any sub-critical fluids.

A Bayesian approach to imposing curvature on distance functions

The estimated parameters of output distance functions frequently violate the monotonicity, quasi-convexity and convexity constraints implied by economic theory, leading to estimated elasticities and shadow prices that are incorrectly signed, and ultimately to perverse conclusions concerning the effects of input and output changes on productivity growth and relative efficiency levels. We show how a Bayesian approach can be used to impose these constraints on the parameters of a translog output distance function. Implementing the approach involves the use of a Gibbs sampler with data augmentation. A Metropolis-Hastings algorithm is also used within the Gibbs to simulate observations from truncated pdfs. Our methods are developed for the case where panel data is available and technical inefficiency effects are assumed to be time-invariant. Two models-a fixed effects model and a random effects model-are developed and applied to panel data on 17 European railways. We observe significant changes in estimated elasticities and shadow price ratios when regularity restrictions are imposed. (c) 2004 Elsevier B.V. All rights reserved.

Application of a generalized thermodynamic approach to characterize mesoporous materials

Equilibrium adsorption and desorption in mesoporous adsorbents is considered on the basis of rigorous thermodynamic analysis, in which the curvature-dependent solid-fluid potential and the compressibility of the adsorbed phase are accounted for. The compressibility of the adsorbed phase is considered for the first time in the literature in the framework of a rigorous thermodynamic approach. Our model is a further development of continuum thermodynamic approaches proposed by Derjaguin and Broekhoff and de Boer, and it is based on a reference isotherm of a non-porous material having the same chemical structure as that of the pore wall. In this improved thermodynamic model, we incorporated a prescription for transforming the solid-fluid potential exerted by the flat reference surface to the potential inside cylindrical and spherical pores. We relax the assumption that the adsorbed film density is constant and equal to that of the saturated liquid. Instead, the density of the adsorbed fluid is allowed to vary over the adsorbed film thickness and is calculated by an equation of state. As a result, the model is capable to describe the adsorption-desorption reversibility in cylindrical pores having diameter less than 2 nm. The generalized thermodynamic model may be applied to the pore size characterization of mesoporous materials instead of much more time-consuming molecular approaches. (c) 2005 Elsevier B.V. All rights reserved.

Hypoxic/ischemic models in newborn piglet: Comparison of constant FiO(2) versus variable FiO(2) delivery

A comparison of a constant (continuous delivery of 4% FiO(2)) and a variable (initial 5% FiO(2) with adjustments to induce low amplitude EEG (LAEEG) and hypotension) hypoxic/ischemic insult was performed to determine which insult was more effective in producing a consistent degree of survivable neuropathological damage in a newborn piglet model of perinatal asphyxia. We also examined which physiological responses contributed to this outcome. Thirty-nine 1-day-old piglets were subjected to either a constant hypoxic/ischemic insult of 30- to 37-min duration or a variable hypoxic/ischemic insult of 30-min low peak amplitude EEG (LAEEG < 5 mu V) including 10 min of low mean arterial blood pressure (MABP < 70% of baseline). Control animals (n = 6) received 21% FiO(2) for the duration of the experiment. At 72 h, the piglets were euthanased, their brains removed and fixed in 4% paraformaldehyde and assessed for hypoxic/ischemic injury by histological analysis. Based on neuropathology scores, piglets were grouped as undamaged or damaged; piglets that did not survive to 72 h were grouped separately as dead. The variable insult resulted in a greater number of piglets with neuropathological damage (undamaged = 12.5%, damaged = 68.75%, dead = 18.75%) while the constant insult resulted in a large proportion of undamaged piglets (undamaged = 50%, damaged = 22.2%, dead = 27.8%). A hypoxic insult varied to maintain peak amplitude EEG < 5 mu V results in a greater number of survivors with a consistent degree of neuropathological damage than a constant hypoxic insult. Physiological variables MABP, LAEEG, pH and arterial base excess were found to be significantly associated with neuropathological outcome. (c) 2006 Elsevier B.V. All rights reserved.

Positive solutions of a Neumann problem with competing critical nonlinearities

We present existence results for a Neumann problem involving critical Sobolev nonlinearities both on the right hand side of the equation and at the boundary condition.. Positive solutions are obtained through constrained minimization on the Nehari manifold. Our approach is based on the concentration 'compactness principle of P. L. Lions and M. Struwe.

Muscle metabolism during constant- and alternating-intensity exercise around critical power

Few studies have focused on the metabolic responses to alternating high- and low-intensity exercise and, specifically, compared these responses to those seen during constant-load exercise performed at the same average power output. This study compared muscle metabolic responses between two patterns of exercise during which the intensity was either constant and just below critical power (CP) or that oscillated above and below CP. Six trained males (mean +/- SD age 23.6 +/- 2.6 y) completed two 30-minute bouts of cycling (alternating and constant) at an average intensity equal to 90% of CR The intensity during alternating exercise varied between 158% CP and 73% CP. Biopsy samples from the vastus lateralis muscle were taken before (PRE), at the midpoint and end (POST) of exercise and analysed for glycogen, lactate, PCr and pH. Although these metabolic variables in muscle changed significantly during both patterns of exercise, there were no significant differences (p > 0.05) between constant and alternating exercise for glycogen (PRE: 418.8 +/- 85 vs. 444.3 +/- 70; POST: 220.5 +/- 59 vs. 259.5 +/- 126mmol.kg(-1) dw), lactate (PRE: 8.5 +/- 7.7 vs. 8.5 +/- 8.3; POST: 49.9 +/- 19.0 vs. 42.6 +/- 26.6 mmol.kg(-1)dw), phosphocreatine (PRE: 77.9 +/- 11.6 vs. 75.7 +/- 16.9; POST: 65.8 +/- 12.1 vs. 61.2 +/- 12.7mmol.kg(-1)dw) or pH (PRE: 6.99 +/- 0.12 vs. 6.99 +/- 0.08; POST: 6.86 +/- 0.13 vs. 6.85 +/- 0.06), respectively. There were also no significant differences in blood lactate responses to the two patterns of exercise. These data suggest that, when the average power output is similar, large variations in exercise intensity exert no significant effect on muscle metabolism.

Drop formation and breakup of low viscosity elastic fluids: Effects of molecular weight and concentration

The dynamics of drop formation and pinch-off have been investigated for a series of low viscosity elastic fluids possessing similar shear viscosities, but differing substantially in elastic properties. On initial approach to the pinch region, the viscoelastic fluids all exhibit the same global necking behavior that is observed for a Newtonian fluid of equivalent shear viscosity. For these low viscosity dilute polymer solutions, inertial and capillary forces form the dominant balance in this potential flow regime, with the viscous force being negligible. The approach to the pinch point, which corresponds to the point of rupture for a Newtonian fluid, is extremely rapid in such solutions, with the sudden increase in curvature producing very large extension rates at this location. In this region the polymer molecules are significantly extended, causing a localized increase in the elastic stresses, which grow to balance the capillary pressure. This prevents the necked fluid from breaking off, as would occur in the equivalent Newtonian fluid. Alternatively, a cylindrical filament forms in which elastic stresses and capillary pressure balance, and the radius decreases exponentially with time. A (0+1)-dimensional finitely extensible nonlinear elastic dumbbell theory incorporating inertial, capillary, and elastic stresses is able to capture the basic features of the experimental observations. Before the critical "pinch time" t(p), an inertial-capillary balance leads to the expected 2/3-power scaling of the minimum radius with time: R-min similar to(t(p)-t)(2/3). However, the diverging deformation rate results in large molecular deformations and rapid crossover to an elastocapillary balance for times t>t(p). In this region, the filament radius decreases exponentially with time R-min similar to exp[(t(p)-t)/lambda(1)], where lambda(1) is the characteristic time constant of the polymer molecules. Measurements of the relaxation times of polyethylene oxide solutions of varying concentrations and molecular weights obtained from high speed imaging of the rate of change of filament radius are significantly higher than the relaxation times estimated from Rouse-Zimm theory, even though the solutions are within the dilute concentration region as determined using intrinsic viscosity measurements. The effective relaxation times exhibit the expected scaling with molecular weight but with an additional dependence on the concentration of the polymer in solution. This is consistent with the expectation that the polymer molecules are in fact highly extended during the approach to the pinch region (i.e., prior to the elastocapillary filament thinning regime) and subsequently as the filament is formed they are further extended by filament stretching at a constant rate until full extension of the polymer coil is achieved. In this highly extended state, intermolecular interactions become significant, producing relaxation times far above theoretical predictions for dilute polymer solutions under equilibrium conditions. (C) 2006 American Institute of Physics

A Constant Torque Micro-Viscometer

We present a technique to measure the viscosity of microscopic volumes of liquid using rotating optical tweezers. The technique can be used when only microlitre (or less) sample volumes are available, for example biological or medical samples, or to make local measurements in complicated micro-structures such as cells. The rotation of the optical tweezers is achieved using the polarisation of the trapping light to rotate a trapped birefringent spherical crystal, called vaterite. Transfer of angular momentum from a circularly polarised beam to the particle causes the rotation. The transmitted light can then be analysed to determine the applied torque to the particle and its rotation rate. The applied torque is determined from the change in the circular polarisation of the beam caused by the vaterite and the rotation rate is used to find the viscous drag on the rotating spherical particle. The viscosity of the surrounding liquid can then be determined. Using this technique we measured the viscosity of liquids at room temperature, which agree well with tabulated values. We also study the local heating effects due to absorption of the trapping laser beam. We report heating of 50-70 K/W in the region of liquid surrounding the particle.