Massive spinor fields in flat spacetimes with non-trivial topology

The vacuum expectation value of the stress-energy tensor is calculated for spin $1\over 2$ massive fields in several multiply connected flat spacetimes. We examine the physical effects of topology on manifolds such as $R^3 \times S^1$, $R^2\times T^2$, $R^1 \times T^3$, the Mobius strip and the Klein bottle. We find that the spinor vacuum stress tensor has the opposite sign to, and twice the magnitude of, the scalar tensor in orientable manifolds. Extending the above considerations to the case of Misner spacetime, we calculate the vacuum expectation value of spinor stress-energy tensor in this space and discuss its implications for the chronology protection conjecture.Comment: 18 pages, Some of the equations in section VI as well as typographical errors corrected, 5 figures, Revtex

Oxidation of Zr-2.5 Nb Nuclear Reactor Pressure Tubes A New Model

The corrosion and associated deuterium (D) uptake of Zr alloy nuclear reactor pressure tubes have been studied for over 40 years. Zircaloy tubes exhibit rapid D ingress after a period of in-reactor exposure, and have been replaced with tubes fabricated from the more resistant Zr-2.5 wt % Nb alloy. Recently, however, a small percentage of Zr-2.5 Nb tubes have been found to contain high D contents. There is currently no clear understanding of the mechanism for this increased D uptake, and concern exists that an increasing number of high-D tubes will develop with time. A new model for Zr-2.5 Nb corrosion is presented in this paper. The rate of corrosion is shown to be dependent on the rate of transformation of the protective inner oxide layer (closer to the metal) to a porous outer layer. The mechanism of this transformation is not known and should be the subject of future investigations. It is assumed in the model that zirconia chemically dissolves into the solution at the pore bottom. The rate of this dissolution reaction depends on the local pH, which increases if there is a buildup of deuteroxyl ions generated in the cathodic part of the Zr corrosion reaction. A mathematical description of this model, containing several parameters with unknown values, is presented. Assigning certain values to these parameters results in predictions of oxide formation (and thus D buildup) that correspond well with observations.Support of this work by the Atomic Energy Control Board under AECB project no. 2.349.1 is gratefully acknowledged

Electromagnetic wormholes and virtual magnetic monopoles

We describe new configurations of electromagnetic (EM) material parameters, the electric permittivity $\epsilon$ and magnetic permeability $\mu$, that allow one to construct from metamaterials objects that function as invisible tunnels. These allow EM wave propagation between two points, but the tunnels and the regions they enclose are not detectable to EM observations. Such devices function as wormholes with respect to Maxwell's equations and effectively change the topology of space vis-a-vis EM wave propagation. We suggest several applications, including devices behaving as virtual magnetic monopoles.Comment: 4 pages, 3 figure

Pitting in Aluminum Thin Films Supersaturation and Effects of Dichromate Ions

The growth of pits in 209 nm thick Al films in chloride solutions with and without dichromate ions was examined using image analysis of the growing pits to determine pit current density. In pure chloride solutions, the pit current density decreased at high potentials after reaching a maximum value, and then was almost independent of applied potential. A hysteresis in the pit current density-potential behavior was observed during downward stepping of the potential from high values. This is a result of a combination of supersaturation of the pit electrolyte followed by salt film formation, and changes in mass transport from hydrogen bubbles that increase convection and lift the remnant passive film away from the dissolving surface. In solutions containing dichromate ions, the corrosion and repassivation potentials shifted in the noble direction, and rather large metastable pits formed at the open circuit. A large concentration of dichromate ions was needed to inhibit pit growth. In dichromate solutions, subsequent pit growth at higher potentials often initiated at the edge of the open-circuit pits. The rate of pit growth was lower for these pits because the remnant passive film layer was not easily lifted up at these sites, and thus created a barrier for mass transport away from the dissolving pit edge.This work was supported by Major H. DeLong at the United States Air Force Office of Scientific Research under contract F49620-96-0042

"Marginal pinching" in soap films

We discuss the behaviour of a thin soap film facing a frame element: the pressure in the Plateau border around the frame is lower than the film pressure, and the film thins out over a certain distance lambda(t), due to the formation of a well-localized pinched region of thickness h(t) and extension w(t). We construct a hydrodynamic theory for this thinning process, assuming a constant surface tension: Marangoni effects are probably important only at late stages, where instabilitites set in. We find lambda(t) ~ t^{1/4}, and for the pinch dimensions h(t) ~ t^{-1/2}$ and w(t) ~ t^{-1/4}. These results may play a useful role for the discussion of later instabilitites leading to a global film thinning and drainage, as first discussed by K. Mysels under the name ``marginal regeneration''.Comment: 7 pages, 2 figure

Pit Growth Study in Al Alloys by the Foil Penetration Technique

The foil penetration technique was used to study pit growth in AA1100-O and AA2024-T3. Preliminary work on AA1100-O foils of different thicknesses indicated that the pit growth rate increased with increasing applied potential, suggesting that pit growth was not under transport control. Foil penetration experiments were also carried out on AA2024-T3 foils of a given thickness, at open circuit as well as anodic potentials. Dichromate ions and other oxidizing agents were added to some test solutions. Dichromate ions were shown to have little influence on the pit growth rate at controlled anodic potentials, even when added in large concentrations. However, dichromate ions effectively inhibited pitting at open circuit when present in very small amounts. Polarization curves of AA2024-T3 in 1 M NaCl with various additives show a large effect of dichromate ions in the cathodic region and no effect in the anodic region. These observations suggest that chromate (or its reduction product) acts as a cathodic inhibitor. Examination of penetrated samples was performed by optical and scanning electron microscopies, as well as by microradiography.This work was supported by Major H. DeLong at the Air Force Office of Scientific Research, under contract F49620-96-0042

A Morse-theoretical analysis of gravitational lensing by a Kerr-Newman black hole

Consider, in the domain of outer communication of a Kerr-Newman black hole, a point (observation event) and a timelike curve (worldline of light source). Assume that the worldline of the source (i) has no past end-point, (ii) does not intersect the caustic of the past light-cone of the observation event, and (iii) goes neither to the horizon nor to infinity in the past. We prove that then for infinitely many positive integers k there is a past-pointing lightlike geodesic of (Morse) index k from the observation event to the worldline of the source, hence an observer at the observation event sees infinitely many images of the source. Moreover, we demonstrate that all lightlike geodesics from an event to a timelike curve in the domain of outer communication are confined to a certain spherical shell. Our characterization of this spherical shell shows that in the Kerr-Newman spacetime the occurrence of infinitely many images is intimately related to the occurrence of centrifugal-plus-Coriolis force reversal.Comment: 14 pages, 2 figures; REVTEX; submitted to J. Math. Phy

Taylor dispersion of gyrotactic swimming micro-organisms in a linear flow

The theory of generalized Taylor dispersion for suspensions of Brownian particles is developed to study the dispersion of gyrotactic swimming micro-organisms in a linear shear flow. Such creatures are bottom-heavy and experience a gravitational torque which acts to right them when they are tipped away from the vertical. They also suffer a net viscous torque in the presence of a local vorticity field. The orientation of the cells is intrinsically random but the balance of the two torques results in a bias toward a preferred swimming direction. The micro-organisms are sufficiently large that Brownian motion is negligible but their random swimming across streamlines results in a mean velocity together with diffusion. As an example, we consider the case of vertical shear flow and calculate the diffusion coefficients for a suspension of the alga <i>Chlamydomonas nivalis</i>. This rational derivation is compared with earlier approximations for the diffusivity