Natural convection in a shallow cavity with differentially heated end walls. Part 2. Numerical solutions

Numerical solutions of the full Navier-Stokes equations are obtained for the problem of natural convection in closed cavities of small aspect ratio with differentially heated end walls. These solutions cover the parameter range Pr = 6.983, 10 ≤ Gr ≤ 2x10^4 and 0.05 ≤ A ≤ 1. A comparison with the asymptotic theory of part 1 shows excellent agreement between the analytical and numerical solutions provided that A ≾ 0.1 and Gr^2A^3Pr^2 ≾ l0^5. In addition, the numerical solutions demonstrate the transition between the shallow-cavity limit of part 1 and the boundary-layer limit; A fixed, Gr → ∞

Natural convection in a shallow cavity with differentially heated end walls. Part 1. Asymptotic theory

The problem of natural convection in a cavity of small aspect ratio with differentially heated end walls is considered. It is shown by use of matched asymptotic expansions that the flow consists of two distinct regimes : a parallel flow in the core region and a second, non-parallel flow near the ends of the cavity. A solution valid at all orders in the aspect ratio A is found for the core region, while the first several terms of the appropriate asymptotic expansion are obtained for the end regions. Parametric limits of validity for the parallel flow structure are discussed. Asymptotic expressions for the Nusselt number and the single free parameter of the parallel flow solution, valid in the limit as A → 0, are derived

The martyrdom effect : when pain and effort increase prosocial contributions

Most theories of motivation and behavior (and lay intuitions alike) consider pain and effort to be deterrents. In contrast to this widely held view, we provide evidence that the prospect of enduring pain and exerting effort for a prosocial cause can promote contributions to the cause. Specifically, we show that willingness to contribute to a charitable or collective cause increases when the contribution process is expected to be painful and effortful rather than easy and enjoyable. Across five experiments, we document this “martyrdom effect,” show that the observed patterns defy standard economic and psychological accounts, and identify a mediator and moderator of the effect. Experiment 1 showed that people are willing to donate more to charity when they anticipate having to suffer to raise money. Experiment 2 extended these findings to a non-charity laboratory context that involved real money and actual pain. Experiment 3 demonstrated that the martyrdom effect is not the result of an attribute substitution strategy (whereby people use the amount of pain and effort involved in fundraising to determine donation worthiness). Experiment 4 showed that perceptions of meaningfulness partially mediate the martyrdom effect. Finally, Experiment 5 demonstrated that the nature of the prosocial cause moderates the martyrdom effect: the effect is strongest for causes associated with human suffering. We propose that anticipated pain and effort lead people to ascribe greater meaning to their contributions and to the experience of contributing, thereby motivating higher prosocial contributions. We conclude by considering some implications of this puzzling phenomenon. Copyright © 2011 John Wiley & Sons, Ltd

Does ohmic heating influence the flow field in thin-layer electrodeposition?

In thin-layer electrodeposition the dissipated electrical energy leads to a substantial heating of the ion solution. We measured the resulting temperature field by means of an infrared camera. The properties of the temperature field correspond closely with the development of the concentration field. In particular we find, that the thermal gradients at the electrodes act like a weak additional driving force to the convection rolls driven by concentration gradients.Comment: minor changes: correct estimation of concentration at the anode, added Journal-re

Experimental investigation of the initial regime in fingering electrodeposition: dispersion relation and velocity measurements

Recently a fingering morphology, resembling the hydrodynamic Saffman-Taylor instability, was identified in the quasi-two-dimensional electrodeposition of copper. We present here measurements of the dispersion relation of the growing front. The instability is accompanied by gravity-driven convection rolls at the electrodes, which are examined using particle image velocimetry. While at the anode the theory presented by Chazalviel et al. describes the convection roll, the flow field at the cathode is more complicated because of the growing deposit. In particular, the analysis of the orientation of the velocity vectors reveals some lag of the development of the convection roll compared to the finger envelope.Comment: 11 pages, 15 figures, REVTEX 4; reference adde

Coronary computed tomography angiography compared with single photon emission computed tomography myocardial perfusion imaging as a guide to optimal medical therapy in patients presenting with stable angina: The RESCUE trial

Background The RESCUE (Randomized Evaluation of Patients with Stable Angina Comparing Utilization of Noninvasive Examinations) trial was a randomized, controlled, multicenter, comparative efficacy outcomes trial designed to assess whether initial testing with coronary computed tomographic angiography (CCTA) is noninferior to single photon emission computed tomography (SPECT) myocardial perfusion imaging in directing patients with stable angina to optimal medical therapy alone or optimal medical therapy with revascularization. Methods and Results The end point was first major adverse cardiovascular event (MACE) (cardiac death or myocardial infarction), or revascularization. Noninferiority margin for CCTA was set a priori as a hazard ratio (HR) of 1.3 (95% CI=0, 1.605). One thousand fifty participants from 44 sites were randomized to CCTA (n=518) or SPECT (n=532). Mean follow-up time was 16.2 (SD 7.9) months. There were no cardiac-related deaths. In patients with a negative CCTA there was 1 acute myocardial infarction; in patients with a negative SPECT examination there were 2 acute myocardial infarctions; and for positive CCTA and SPECT, 1 acute myocardial infarction each. Participants in the CCTA arm had a similar rate of MACE or revascularization compared with those in the SPECT myocardial perfusion imaging arm, (HR, 1.03; 95% CI=0.61-1.75)

Dose ratio proton radiography using the proximal side of the Bragg peak

Purpose: In recent years there has been a movement towards single-detector proton radiography, due to its potential ease of implementation within the clinical environment. One such single-detector technique is the dose ratio method, in which the dose maps from two pristine Bragg peaks are recorded beyond the patient. To date, this has only been investigated on the distal side of the lower energy Bragg peak, due to the sharp fall-off. We investigate the limits and applicability of the dose ratio method on the proximal side of the lower energy Bragg peak, which has the potential to allow a much wider range of water-equivalent thicknesses (WET) to be imaged. Comparisons are made with the use of the distal side of the Bragg peak. Methods: Using the analytical approximation for the Bragg peak we generated theoretical dose ratio curves for a range of energy pairs, and then determined how an uncertainty in the dose ratio would translate to a spread in the WET estimate. By defining this spread as the accuracy one could achieve in the WET estimate, we were able to generate look-up graphs of the range on the proximal side of the Bragg peak that one could reliably use. These were dependent on the energy pair, noise level in the dose ratio image and the required accuracy in the WET. Using these look-up graphs we investigated the applicability of the technique for a range of patient treatment sites. We validated the theoretical approach with experimental measurements using a complementary metal oxide semiconductor active pixel sensor (CMOS APS), by imaging a small sapphire sphere in a high energy proton beam. Results: Provided the noise level in the dose ratio image was 1% or less, a larger spread of WETs could be imaged using the proximal side of the Bragg peak (max 5.31 cm) compared to the distal side (max 2.42 cm). In simulation it was found that, for a pediatric brain, it is possible to use the technique to image a region with a square field equivalent size of 7.6 cm2, for a required accuracy in the WET of 3 mm and a 1% noise level in the dose ratio image. The technique showed limited applicability for other patient sites. The CMOS APS demonstrated a good accuracy, with a root-mean-square-error of 1.6 mm WET. The noise in the measured images was found to be σ =1.2% (standard deviation) and theoretical predictions with a 1.96σ noise level showed good agreement with the measured errors. Conclusions: After validating the theoretical approach with measurements, we have shown that the use of the proximal side of the Bragg peak when performing dose ratio imaging is feasible, and allows for a wider dynamic range than when using the distal side. The dynamic range available increases as the demand on the accuracy of the WET decreases. The technique can only be applied to clinical sites with small maximum WETs such as for pediatric brains

Theory and practice: bulk synthesis of C3B and its H2- and Li-storage capacity.

Previous theoretical studies of C3B have suggested that boron-doped graphite is a promising H2- and Li-storage material, with large maximum capacities. These characteristics could lead to exciting applications as a lightweight H2-storage material for automotive engines and as an anode in a new generation of batteries. However, for these applications to be realized a synthetic route to bulk C3B must be developed. Here we show the thermolysis of a single-source precursor (1,3-(BBr2)2C6H4) to produce graphitic C3B, thus allowing the characteristics of this elusive material to be tested for the first time. C3B was found to be compositionally uniform but turbostratically disordered. Contrary to theoretical expectations, the H2- and Li-storage capacities are lower than anticipated, results that can partially be explained by the disordered nature of the material. This work suggests that to model the properties of graphitic materials more realistically, the possibility of disorder must be considered.We thank the ERC (Advance Investigator awards for D.S.W., C.P.G.), the EPSRC (T.C.K., P.D.M., H.G., J.C.), and the Spanish Ministerio de Economia y Competitividad (under grants ENE2011-24-412 and IPT-2011-1553-420000). We thank John Bulmer for Raman spectroscopy and Keith Parmenter for glass blowing. We thank the Schlumberger Gould Research Centre for XPS analysis.This is the author accepted manuscript. The final version is available from Wiley via http://dx.doi.org/10.1002/anie.20141220

Relative energetics and structural properties of zirconia using a self-consistent tight-binding model

We describe an empirical, self-consistent, orthogonal tight-binding model for zirconia, which allows for the polarizability of the anions at dipole and quadrupole levels and for crystal field splitting of the cation d orbitals. This is achieved by mixing the orbitals of different symmetry on a site with coupling coefficients driven by the Coulomb potentials up to octapole level. The additional forces on atoms due to the self-consistency and polarizabilities are exactly obtained by straightforward electrostatics, by analogy with the Hellmann-Feynman theorem as applied in first-principles calculations. The model correctly orders the zero temperature energies of all zirconia polymorphs. The Zr-O matrix elements of the Hamiltonian, which measure covalency, make a greater contribution than the polarizability to the energy differences between phases. Results for elastic constants of the cubic and tetragonal phases and phonon frequencies of the cubic phase are also presented and compared with some experimental data and first-principles calculations. We suggest that the model will be useful for studying finite temperature effects by means of molecular dynamics.Comment: to be published in Physical Review B (1 march 2000