Impact of surface imperfections on the Casimir force for lenses of centimeter-size curvature radii

The impact of imperfections, which are always present on surfaces of lenses with centimeter-size curvature radii, on the Casimir force in the lens-plate geometry is investigated. It is shown that the commonly used formulation of the proximity force approximation is inapplicable for spherical lenses with surface imperfections, such as bubbles and pits. More general expressions for the Casimir force are derived that take surface imperfections into account. Using these expressions we show that surface imperfections can both increase and decrease the magnitude of the Casimir force up to a few tens of percent when compared with the case of a perfectly spherical lens. We demonstrate that the Casimir force between a perfectly spherical lens and a plate described by the Drude model can be made approximately equal to the force between a sphere with some surface imperfection and a plate described by the plasma model, and vice versa. In the case of a metallic sphere and semiconductor plate, approximately the same Casimir forces are obtained for four different descriptions of charge carriers in the semiconductor if appropriate surface imperfections on the lens surface are present. The conclusion is made that there is a fundamental problem in the interpretation of measurement data for the Casimir force, obtained by using spherical lenses of centimeter-size radii, and their comparison with theory.Comment: 28 pages, 7 figures, 1 table. To appear in Phys. Rev.

Anomalous scaling in random shell models for passive scalars

A shell-model version of Kraichnan's (1994 {\it Phys. Rev. Lett. \bf 72}, 1016) passive scalar problem is introduced which is inspired from the model of Jensen, Paladin and Vulpiani (1992 {\it Phys. Rev. A\bf 45}, 7214). As in the original problem, the prescribed random velocity field is Gaussian, delta-correlated in time and has a power-law spectrum $\propto k_m^{-\xi}$, where $k_m$ is the wavenumber. Deterministic differential equations for second and fourth-order moments are obtained and then solved numerically. The second-order structure function of the passive scalar has normal scaling, while the fourth-order structure function has anomalous scaling. For $\xi = 2/3$ the anomalous scaling exponents $\zeta_p$ are determined for structure functions up to $p=16$ by Monte Carlo simulations of the random shell model, using a stochastic differential equation scheme, validated by comparison with the results obtained for the second and fourth-order structure functions.Comment: Plain LaTex, 15 pages, 4 figure available upon request to [email protected]

Dust in Spiral Galaxies: Comparing Emission and Absorption to Constrain Small-Scale and Very Cold Structures

The detailed distribution of dust in the disks of spiral galaxies is important to understanding the radiative transfer within disks, and to measuring overall dust masses if significant quantities of dust are either very opaque or very cold. We address this issue by comparing measures of dust absorption, using the galaxy-overlap technique in the optical, with measures of the dust grains' thermal emission from 50-2000 micron using ISOPHOT on board ISO and SCUBA at the JCMT. We examine three spiral galaxies projected partially in front of E/S0 galaxies --- AM1316-241, NGC 5545, and NGC 5091 (for NGC 5091 we have only optical and ISO data). Adopting an empirical exponential model for the dust distribution, we compare column densities and dust masses derived from the absorption and emission techniques. This comparison is sensitive to the amount of dust mass in small, opaque structures, which would not contribute strongly to area-weighted absorption measures, and to very cold dust, which would contribute to optical absorption but provide only a small fraction of the sub-mm emission. In AM1316-241, we find global dust masses of 2-5 x 10^7 M_solar, both techniques agreeing at the 50% level. NGC 5545 has about half this dust mass. The concordance of dust masses is well within the errors expected from our knowledge of the radial distribution of dust, and argues against any dominant part of the dust mass being so cold or opaque. The 50-2000 micron data are well fitted by modified Planck functions with an emissivity law beta=-2, at 21 +/- 2 K. We also present 12 micron ISOCAM observations of these pairs.Comparison of H-alpha and 12 micron images of NGC 5545 indicate that ISOCAM images are reliable tracers of star formation.Comment: 16 pages, 4 tables, 8 figures, in press for October Astronomical Journa

Rigorous Proof of a Liquid-Vapor Phase Transition in a Continuum Particle System

We consider particles in ${\Bbb R}^d, d \geq 2$, interacting via attractive pair and repulsive four-body potentials of the Kac type. Perturbing about mean field theory, valid when the interaction range becomes infinite, we prove rigorously the existence of a liquid-gas phase transition when the interaction range is finite but long compared to the interparticle spacing.Comment: 11 pages, in ReVTeX, e-mail addresses: [email protected], [email protected], [email protected]

The Deuterium, Oxygen, and Nitrogen Abundance Toward LSE 44

We present measurements of the column densities of interstellar DI, OI, NI, and H2 made with FUSE, and of HI made with IUE toward the sdO star LSE 44, at a distance of 554+/-66 pc. This target is among the seven most distant Galactic sight lines for which these abundance ratios have been measured. The column densities were estimated by profile fitting and curve of growth analyses. We find D/H = (2.24 +1.39 -1.32)E-5, D/O = (1.99 +1.30 -0.67)E-2, D/N = (2.75 +1.19 -0.89)E-1, and O/H = (1.13 +0.96 -0.71)E-3 (2 sigma). Of the most distant Galactic sight lines for which the deuterium abundance has been measured LSE 44 is one of the few with D/H higher than the Local Bubble value, but D/O toward all these targets is below the Local Bubble value and more uniform than the D/H distribution. (Abstract abridged.)Comment: 20 pages, including 9 figures. Accepted for publication in Ap

Excitation and relaxation in atom-cluster collisions

Electronic and vibrational degrees of freedom in atom-cluster collisions are treated simultaneously and self-consistently by combining time-dependent density functional theory with classical molecular dynamics. The gradual change of the excitation mechanisms (electronic and vibrational) as well as the related relaxation phenomena (phase transitions and fragmentation) are studied in a common framework as a function of the impact energy (eV...MeV). Cluster "transparency" characterized by practically undisturbed atom-cluster penetration is predicted to be an important reaction mechanism within a particular window of impact energies.Comment: RevTeX (4 pages, 4 figures included with epsf

Diffractive Dissociation and Eikonalization in High Energy pp and p pˉ {\bar p} Collisions

We show that eikonal corrections imposed on diffraction dissociation processes calculated in the triple Regge limit, produce a radical change in the energy dependence of the predicted cross section. The induced correction is shown to be in general agreement with the new experimental data measured at the Tevatron.Comment: 11 pages LATEX, ( two figures not included obtainable from authors) (TAUP 2066-93 and FERMILAB PUB 93/ T

Husimi Transform of an Operator Product

It is shown that the series derived by Mizrahi, giving the Husimi transform (or covariant symbol) of an operator product, is absolutely convergent for a large class of operators. In particular, the generalized Liouville equation, describing the time evolution of the Husimi function, is absolutely convergent for a large class of Hamiltonians. By contrast, the series derived by Groenewold, giving the Weyl transform of an operator product, is often only asymptotic, or even undefined. The result is used to derive an alternative way of expressing expectation values in terms of the Husimi function. The advantage of this formula is that it applies in many of the cases where the anti-Husimi transform (or contravariant symbol) is so highly singular that it fails to exist as a tempered distribution.Comment: AMS-Latex, 13 page

Low-energy Pion-nucleon Scattering

This paper contains the results of an analysis of recent low-energy pion-nucleon scattering experiments. Obtained are phase shifts, the pion-nucleon coupling constant and an estimate of the Sigma term.Comment: 30 pages, 11 figures, LaTe

The large-scale ionised outflow of CH Cygni

HST and ground-based [OII} and [NII] images obtained from 1996 to 1999 reveal the existence of a ionised optical nebula around the symbiotic binary CH Cyg extending out to 5000 A.U. from the central stars. The observed velocity range of the nebula, derived from long-slit echelle spectra, is of 130 km/s. In spite of its complex appearence, the velocity data show that the basic morphology of the inner regions of the optical nebula is that of a bipolar (or conical) outflow extending nearly along the plane of the sky out to some 2000 A.U. from the centre. Even if the extension of this bipolar outflow and its position angle are consistent with those of the radio jet produced in 1984 (extrapolated to the time of our optical imagery), no obvious counterpart is visible of the original, dense radio bullets ejected by the system. We speculate that the optical bipolar outflow might be the remannt of the interaction of the bullets with a relatively dense circumstellar medium.Comment: 8 text pages + 3 figures (jpeg). ApJ in press. For a full PostScript version with figures inline see ftp://ftp.ll.iac.es/pub/research/preprints/PP252001.ps.g