Phase field modelling of surfactants in multi-phase flow

A diffuse interface model for surfactants in multi-phase flow with three or more fluids is derived. A system of Cahn-Hilliard equations is coupled with a Navier-Stokes system and an advection-diffusion equation for the surfactant ensuring thermodynamic consistency. By an asymptotic analysis the model can be related to a moving boundary problem in the sharp interface limit, which is derived from first principles. Results from numerical simulations support the theoretical findings. The main novelties are centred around the conditions in the triple junctions where three fluids meet. Specifically the case of local chemical equilibrium with respect to the surfactant is considered, which allows for interfacial surfactant flow through the triple junctions

Compensation of relector antenna surface distortion using an array feed

The dimensional stability of the surface of a large reflector antenna is important when high gain or low sidelobe performance is desired. If the surface is distorted due to thermal or structural reasons, antenna performance can be improved through the use of an array feed. The design of the array feed and its relation to the surface distortion are examined. The sensitivity of antenna performance to changing surface parameters for fixed feed array geometries is also studied. This allows determination of the limits of usefulness for feed array compensation

Recovery of continuous wave squeezing at low frequencies

We propose and demonstrate a system that produces squeezed vacuum using a pair of optical parametric amplifiers. This scheme allows the production of phase sidebands on the squeezed vacuum which facilitate phase locking in downstream applications. We observe strong, stably locked, continuous wave vacuum squeezing at frequencies as low as 220 kHz. We propose an alternative resonator configuration to overcome low frequency squeezing degradation caused by the optical parametric amplifiers.Comment: 9 pages, 4 figure

Schubert Polynomials for the affine Grassmannian of the symplectic group

We study the Schubert calculus of the affine Grassmannian Gr of the symplectic group. The integral homology and cohomology rings of Gr are identified with dual Hopf algebras of symmetric functions, defined in terms of Schur's P and Q-functions. An explicit combinatorial description is obtained for the Schubert basis of the cohomology of Gr, and this is extended to a definition of the affine type C Stanley symmetric functions. A homology Pieri rule is also given for the product of a special Schubert class with an arbitrary one.Comment: 45 page

Isolating Geometry in Weak Lensing Measurements

Given a foreground galaxy-density field or shear field, its cross-correlation with the shear field from a background population of source galaxies scales with the source redshift in a way that is specific to lensing. Such a source-scaling can be exploited to effectively measure geometrical distances as a function of redshift and thereby constrain dark energy properties, free of any assumptions about the galaxy-mass/mass power spectrum (its shape, amplitude or growth). Such a geometrical method can yield a ~ 0.03 - 0.07 f_{sky}^{-1/2} measurement on the dark energy abundance and equation of state, for a photometric redshift accuracy of dz ~ 0.01 - 0.05 and a survey with median redshift of ~ 1. While these constraints are weaker than conventional weak lensing methods, they provide an important consistency check because the geometrical method carries less theoretical baggage: there is no need to assume any structure formation model (e.g. CDM). The geometrical method is at the most conservative end of a whole spectrum of methods which obtain smaller errorbars by making more restrictive assumptions -- we discuss some examples. Our geometrical approach differs from previous investigations along similar lines in three respects. First, the source-scaling we propose to use is less demanding on the photometric redshift accuracy. Second, the scaling works for both galaxy-shear and shear-shear correlations. Third, we find that previous studies underestimate the statistical errors associated with similar geometrical methods, the origin of which is discussed.Comment: 13 pages, 4 figures, submitted to Ap

Magneto-Seebeck effect in spin-valve with in-plane thermal gradient

We present measurements of magneto-Seebeck effect on a spin valve with in-plane thermal gradient. We measured open circuit voltage and short circuit current by applying a temperature gradient across a spin valve stack, where one of the ferromagnetic layers is pinned. We found a clear hysteresis in these two quantities as a function of magnetic field. From these measurements, the magneto-Seebeck effect was found to be 0.82%.Comment: 10 Pages, 7 figure

Weighing the Cosmological Energy Contents with Weak Gravitational Lensing

Bernardeau et al. (1997), using perturbation theory, showed that the skewness of the large-scale lensing-convergence, or projected mass density, could be used to constrain $\Omega_m$, the matter content of the universe. On the other hand, deep weak-lensing field surveys in the near future will likely measure the convergence on small angular scales (< 10 arcmin.), where the signal will be dominated by highly nonlinear fluctuations. We develop a method to compute the small-scale convergence skewness, using a prescription for the highly nonlinear three-point function developed by Scoccimarro and Frieman (1998). This method gives predictions that agree well with existing results from ray-tracing N-body simulations, but is significantly faster, allowing the exploration of a large number of models. We demonstrate that the small-scale convergence skewness is insensitive to the shape and normalization of the primordial (CDM-type) power spectrum, making it dependent almost entirely on the cosmological energy contents, through their influence on the global geometrical distances and fluctuation growth rate. Moreover, nonlinear clustering appears to enhance the differences between predictions of the convergence skewness for a range of models. Hence, in addition to constraining $\Omega_m$, the small-scale convergence skewness from future deep several- degree-wide surveys can be used to differentiate between curvature dominated and cosmological constant ($\Lambda$) dominated models, as well as to constrain the equation of state of a quintessence component, thereby distinguishing $\Lambda$ from quintessence as well. Finally, our method can be easily generalized to other measures such as aperture mass statistics.Comment: 13 pages, 2 ps figures, submitted to ApJ

A one-sided Prime Ideal Principle for noncommutative rings

Completely prime right ideals are introduced as a one-sided generalization of the concept of a prime ideal in a commutative ring. Some of their basic properties are investigated, pointing out both similarities and differences between these right ideals and their commutative counterparts. We prove the Completely Prime Ideal Principle, a theorem stating that right ideals that are maximal in a specific sense must be completely prime. We offer a number of applications of the Completely Prime Ideal Principle arising from many diverse concepts in rings and modules. These applications show how completely prime right ideals control the one-sided structure of a ring, and they recover earlier theorems stating that certain noncommutative rings are domains (namely, proper right PCI rings and rings with the right restricted minimum condition that are not right artinian). In order to provide a deeper understanding of the set of completely prime right ideals in a general ring, we study the special subset of comonoform right ideals.Comment: 38 page