Drop Behavior in Uniform DC Electric Field

Drop deformation in uniform electric fields is a classic problem. The pioneering work of G.I.Taylor demonstrated that for weakly conducting media, the drop fluid undergoes a toroidal flow and the drop adopts a prolate or oblate spheroidal shape, the flow and shape being axisymmetrically aligned with the applied field. However, recent studies have revealed a nonaxisymmetric rotational mode for drops of lower conductivity than the surrounding medium, similar to the rotation of solid dielectric particles observed by Quincke in the 19th century. This fluid dynamics video demonstrates three behavioral modes. I) toroidal recirculation inside the drop in weak fields II) nonaxisymmetric fluid rotation in strong fields and III) drop breakup in strong fields.Comment: APS DFD Gallery of Fluid Motion 200

Rayleigh-Benard Convection with a Radial Ramp in Plate Separation

Pattern formation in Rayleigh-Benard convection in a large-aspect-ratio cylinder with a radial ramp in the plate separation is studied analytically and numerically by performing numerical simulations of the Boussinesq equations. A horizontal mean flow and a vertical large scale counterflow are quantified and used to understand the pattern wavenumber. Our results suggest that the mean flow, generated by amplitude gradients, plays an important role in the roll compression observed as the control parameter is increased. Near threshold the mean flow has a quadrupole dependence with a single vortex in each quadrant while away from threshold the mean flow exhibits an octupole dependence with a counter-rotating pair of vortices in each quadrant. This is confirmed analytically using the amplitude equation and Cross-Newell mean flow equation. By performing numerical experiments the large scale counterflow is also found to aid in the roll compression away from threshold but to a much lesser degree. Our results yield an understanding of the pattern wavenumbers observed in experiment away from threshold and suggest that near threshold the mean flow and large scale counterflow are not responsible for the observed shift to smaller than critical wavenumbers.Comment: 10 pages, 13 figure

Roughening and preroughening in the six vertex model with an extended range of interaction

We study the phase diagram of the BCSOS model with an extended interaction range using transfer matrix techniques, pertaining to the (100) surface of single component fcc and bcc crystals. The model shows a 2x2 reconstructed phase and a disordered flat phase. The deconstruction transition between these phases merges with a Kosterlitz-Thouless line, showing an interplay of Ising and Gaussian degrees of freedom. As in studies of the fully frustrated XY model, exponents deviating from Ising are found. We conjecture that tri-critical Ising behavior may be a possible explanation for the non-Ising exponents found in those models.Comment: 25 pages in RevTeX 3.0, seven uuencoded postscript figures, REPLACED because of submission error (figures were not included

Quantal Andreev billiards: Semiclassical approach to mesoscale oscillations in the density of states

Andreev billiards are finite, arbitrarily-shaped, normal-state regions, surrounded by superconductor. At energies below the superconducting gap, single-quasiparticle excitations are confined to the normal region and its vicinity, the essential mechanism for this confinement being Andreev reflection. This Paper develops and implements a theoretical framework for the investigation of the short-wave quantal properties of these single-quasiparticle excitations. The focus is primarily on the relationship between the quasiparticle energy eigenvalue spectrum and the geometrical shape of the normal-state region, i.e., the question of spectral geometry in the novel setting of excitations confined by a superconducting pair-potential. Among the central results of this investigation are two semiclassical trace formulas for the density of states. The first, a lower-resolution formula, corresponds to the well-known quasiclassical approximation, conventionally invoked in settings involving superconductivity. The second, a higher-resolution formula, allows the density of states to be expressed in terms of: (i) An explicit formula for the level density, valid in the short-wave limit, for billiards of arbitrary shape and dimensionality. This level density depends on the billiard shape only through the set of stationary-length chords of the billiard and the curvature of the boundary at the endpoints of these chords; and (ii) Higher-resolution corrections to the level density, expressed as a sum over periodic orbits that creep around the billiard boundary. Owing to the fact that these creeping orbits are much longer than the stationary chords, one can, inter alia, hear the stationary chords of Andreev billiards.Comment: 52 pages, 15 figures, 1 table, RevTe

Coronagraphic phase diversity: performance study and laboratory demonstration

The final performance of current and future instruments dedicated to exoplanet detection and characterization (such as SPHERE on the European Very Large Telescope, GPI on Gemini North, or future instruments on Extremely Large Telescopes) is limited by uncorrected quasi-static aberrations. These aberrations create long-lived speckles in the scientific image plane, which can easily be mistaken for planets. Common adaptive optics systems require dedicated components to perform wave-front analysis. The ultimate wave-front measurement performance is thus limited by the unavoidable differential aberrations between the wavefront sensor and the scientific camera. To reach the level of detectivity required by high-contrast imaging, these differential aberrations must be estimated and compensated for. In this paper, we characterize and experimentally validate a wave-front sensing method that relies on focal-plane data. Our method, called COFFEE (for COronagraphic Focal-plane wave-Front Estimation for Exoplanet detection), is based on a Bayesian approach, and it consists in an extension of phase diversity to high-contrast imaging. It estimates the differential aberrations using only two focal-plane coronagraphic images recorded from the scientific camera itself. In this paper, we first present a thorough characterization of COFFEE's performance by means of numerical simulations. This characterization is then compared with an experimental validation of COFFEE using an in-house adaptive optics bench and an apodized Roddier & Roddier phase mask coronagraph. An excellent match between experimental results and the theoretical study is found. Lastly, we present a preliminary validation of COFFEE's ability to compensate for the aberrations upstream of a coronagraph.Comment: A&A accepte

Macroeconomic Implications of Alternative Exchange Rate Models

In this paper we estimate and compare several alternative exchange rate models that have received wide attention, but little comparison, during the 1970s. In order to compare purchasing power parity (PPP), nominal interest rate parity, real interest rate parity, and portfolio balance models, we first strip each down to its essential core and undertake comparable single-equation tests of both 'hard' and 'easy' (more and less constrained) versions of each model. We then embed each of the 'hard' versions in a new macroeconomic model of Canada, and assess their implications for the impacts of monetary and fiscal shocks. Using annual Canadian data from the 1950s and 1970s, all of the models have single-equation errors of about 3%, except for the 'hard' versions of PPP and real interest parity, which are heavily rejected by the data. In a macroeconomic context, the models have modestly different implications for the effects of fiscal shocks, and diverge more widely under monetary shocks.