Collapse of an initially spherical vapour cavity in the neighbourhood of a solid boundary

Vapour bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)^½ where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For Δp/ρ=10^6cm^2/sec^2 ≈ 1 atm/density of water the jet had a speed of about 130m/sec in the first case and 170m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapour are not important

Collapse of an initially spherical vapor cavity in the neighborhood of a solid boundary

Vapor bubble collapse problems lacking spherical symmetry are solved here using a numerical method designed especially for these problems. Viscosity and compressibility in the liquid are neglected. The method uses finite time steps and features an iterative technique for applying the boundary conditions at infinity directly to the liquid at a finite distance from the free surface. Two specific cases of initially spherical bubbles collapsing near a plane solid wall were simulated: a bubble initially in contact with the wall, and a bubble initially half its radius from the wall at the closest point. It is shown that the bubble develops a jet directed towards the wall rather early in the collapse history. Free surface shapes and velocities are presented at various stages in the collapse. Velocities are scaled like (Δp/ρ)^1/2 where ρ is the density of the liquid and Δp is the constant difference between the ambient liquid pressure and the pressure in the cavity. For Δp/ρ = 10^6 (cm/sec)^2 ~ 1 atm./density of water the jet had a speed of about 130 m/sec in the first case and 170 m/sec in the second when it struck the opposite side of the bubble. Such jet velocities are of a magnitude which can explain cavitation damage. The jet develops so early in the bubble collapse history that compressibility effects in the liquid and the vapor are not important

Data visualization within urban models

Models of urban environments have many uses for town planning, pre-visualization of new building work and utility service planning. Many of these models are three-dimensional, and increasingly there is a move towards real-time presentation of such large models. In this paper we present an algorithm for generating consistent 3D models from a combination of data sources, including Ordnance Survey ground plans, aerial photography and laser height data. Although there have been several demonstrations of automatic generation of building models from 2D vector map data, in this paper we present a very robust solution that generates models that are suitable for real-time presentation. We then demonstrate a novel pollution visualization that uses these models

On the Temperature Dependence of the Casimir Effect

The temperature dependence of the Casimir force between a real metallic plate and a metallic sphere is analyzed on the basis of optical data concerning the dispersion relation of metals such as gold and copper. Realistic permittivities imply, together with basic thermodynamic considerations, that the transverse electric zero mode does not contribute. This results in observable differences with the conventional prediction, which does not take this physical requirement into account. The results are shown to be consistent with the third law of thermodynamics, as well as being consistent with current experiments. However, the predicted temperature dependence should be detectable in future experiments. The inadequacies of approaches based on {\it ad hoc} assumptions, such as the plasma dispersion relation and the use of surface impedance without transverse momentum dependence, are discussed.Comment: 14 pages, 3 eps figures, revtex4. New version includes clarifications and new reference. Accepted for publication in Phys. Rev.

What is the Temperature Dependence of the Casimir Effect?

There has been recent criticism of our approach to the Casimir force between real metallic surfaces at finite temperature, saying it is in conflict with the third law of thermodynamics and in contradiction with experiment. We show that these claims are unwarranted, and that our approach has strong theoretical support, while the experimental situation is still unclear.Comment: 6 pages, REVTeX, final revision includes two new references and related discussio

Calculation of the Casimir Force between Similar and Dissimilar Metal Plates at Finite Temperature

The Casimir pressure is calculated between parallel metal plates, containing the materials Au, Cu, or Al. Our motivation for making this calculation is the need of comparing theoretical predictions, based on the Lifshitz formula, with experiments that are becoming gradually more accurate. In particular, the finite temperature correction is considered, in view of the recent discussion in the literature on this point. A special attention is given to the case where the difference between the Casimir pressures at two different temperatures, T=300 K and T=350 K, is involved. This seems to be a case that will be experimentally attainable in the near future, and it will be a critical test of the temperature correction.Comment: 23 latex pages, 12 figures. Introductory section expanded, 4 new references. To appear in J. Phys. A: Math. Ge

Surface Divergences and Boundary Energies in the Casimir Effect

Although Casimir, or quantum vacuum, forces between distinct bodies, or self-stresses of individual bodies, have been calculated by a variety of different methods since 1948, they have always been plagued by divergences. Some of these divergences are associated with the volume, and so may be more or less unambiguously removed, while other divergences are associated with the surface. The interpretation of these has been quite controversial. Particularly mysterious is the contradiction between finite total self-energies and surface divergences in the local energy density. In this paper we clarify the role of surface divergences.Comment: 8 pages, 1 figure, submitted to proceedings of QFEXT0

Devolution and the regional health divide: a longitudinal ecological study of 14 countries in Europe.

Greater regional devolution can reduce economic inequalities between regions; however, the impact on health inequalities is not clear. We investigated the association between changes over time in the level of devolution in European countries and regional economic and health inequalities. We used the proportion of government expenditure controlled by subnational levels of government as our measure of devolution in 14 European countries between 1995 and 2011. Fixed effects linear regression models were used to analyse trends in the level of devolution, trends in regional economic inequalities (Gini-coefficient) and trends in regional health inequalities (slope index) in life expectancy. Each additional percentage of government expenditure managed at subnational level reduced the Gini-coefficient of regional GDP by -0.17 points (95% CI: -0.33 to -0.01; P = 0.04). However, it increased the slope index of regional life expectancy by 23 days (95% CI: -2 to 48; P = 0.07). When trends in regional economic inequalities were controlled for, as a potential mediator-increased devolution-was significantly associated with an increase in health inequalities between regions (P = 0.01). Increased devolution does not appear to reduce regional health inequalities-even when it reduces regional economic inequalities-and it could be associated with increased health inequalities