Cartan-Hannay-Berry Phases and Symmetry

We give a systematic treatment of the treatment of the classical Hannay-Berry phases for mechanical systems in terms of the holonomy of naturally constructed connections on bundles associated to the system. We make the costructions using symmetry and reduction and, for moving systems, we use the Cartan connection. These ideas are woven with the idea of Montgomery [1988] on the averaging of connections to produce the Hannay-Berry connection

Constraining the Surface Inhomogeneity and Settling Times of Metals on Accreting White Dwarfs

Due to the short settling times of metals in DA white dwarf atmospheres, any white dwarfs with photospheric metals must be actively accreting. It is therefore natural to expect that the metals may not be deposited uniformly on the surface of the star. We present calculations showing how the temperature variations associated with white dwarf pulsations lead to an observable diagnostic of the surface metal distribution, and we show what constraints current data sets are able to provide. We also investigate the effect that time-variable accretion has on the metal abundances of different species, and we show how this can lead to constraints on the gravitational settling times.Comment: 4 pages, 5 figures, accepted for publication in the Astrophysical Journal Letters, updated reference

Power dissipation in nanoscale conductors: classical, semi-classical and quantum dynamics

Modelling Joule heating is a difficult problem because of the need to introduce correct correlations between the motions of the ions and the electrons. In this paper we analyse three different models of current induced heating (a purely classical model, a fully quantum model and a hybrid model in which the electrons are treated quantum mechanically and the atoms are treated classically). We find that all three models allow for both heating and cooling processes in the presence of a current, and furthermore the purely classical and purely quantum models show remarkable agreement in the limit of high biases. However, the hybrid model in the Ehrenfest approximation tends to suppress heating. Analysis of the equations of motion reveals that this is a consequence of two things: the electrons are being treated as a continuous fluid and the atoms cannot undergo quantum fluctuations. A means for correcting this is suggested

Simple kinematic models for the environmental interaction of tropical cyclones in vertical wind shear

A major impediment to the intensity forecast of tropical cyclones (TCs) is believed to be associated with the interaction of TCs with dry environmental air. However, the conditions under which pronounced TC-environment interaction takes place are not well understood. As a step towards improving our understanding of this problem, we analyze here the flow topology of a TC immersed in an environment of vertical wind shear in an idealized, three-dimensional, convection-permitting numerical experiment. A set of distinct streamlines, the so-called manifolds, can be identified under the assumptions of steady and layer-wise horizontal flow. The manifolds are shown to divide the flow around the TC into distinct regions. <br></br> The manifold structure in our numerical experiment is more complex than the well-known manifold structure of a non-divergent point vortex in uniform background flow. In particular, one manifold spirals inwards and ends in a limit cycle, a meso-scale dividing streamline encompassing the eyewall above the layer of strong inflow associated with surface friction and below the outflow layer in the upper troposphere. From the perspective of a steady and layer-wise horizontal flow model, the eyewall is well protected from the intrusion of environmental air. In order for the environmental air to intrude into the inner-core convection, time-dependent and/or vertical motions, which are prevalent in the TC inner-core, are necessary. Air with the highest values of moist-entropy resides within the limit cycle. This "moist envelope" is distorted considerably by the imposed vertical wind shear, and the shape of the moist envelope is closely related to the shape of the limit cycle. In a first approximation, the distribution of high- and low-<i>θ</i><sub><i>e</i></sub> air around the TC at low to mid-levels is governed by the stirring of convectively modified air by the steady, horizontal flow. <br></br> Motivated by the results from the idealized numerical experiment, an analogue model based on a weakly divergent point vortex in background flow is formulated. The simple kinematic model captures the essence of many salient features of the manifold structure in the numerical experiment. A regime diagram representing realistic values of TC intensity and vertical wind shear can be constructed for the point-vortex model. The results indicate distinct scenarios of environmental interaction depending on the ratio of storm intensity and vertical-shear magnitude. Further implications of the new results derived from the manifold analysis for TCs in the real atmosphere are discussed

Spontaneous creation of non-zero angular momentum modes in tunnel-coupled two-dimensional degenerate Bose gases

We investigate the dynamics of two tunnel-coupled two-dimensional degenerate Bose gases. The reduced dimensionality of the clouds enables us to excite specific angular momentum modes by tuning the coupling strength, thereby creating striking patterns in the atom density profile. The extreme sensitivity of the system to the coupling and initial phase difference results in a rich variety of subsequent dynamics, including vortex production, complex oscillations in relative atom number and chiral symmetry breaking due to counter-rotation of the two clouds.Comment: 7 pages, 5 figure

Observed structure, evolution and potential intensity of category 5 hurricane Isabel

Mon. Wea. Rev., 136, pp. 2023-2046The article of record as published may be located at http://dx.doi.org/10.1175/2007MWR1858.

SCHEDULING INPUTS WITH PRODUCTION FUNCTIONS: OPTIMAL NITROGEN PROGRAMS FOR RICE

The problem of scheduling input applications can be examined by extending conventional production function analysis. Using appropriately designed agricultural experiments, it is possible to estimate production function parameters with alternative specifications for input timing (and amount). A study of nitrogen applications to rice is employed to illustrate scheduling via production functions. Alternative specifications and functional forms are simultaneously examined to determine the sensitivity of economic results to these factors. Sensitivity is found to be high, and this finding is hypothesized to be critical for other approaches to input scheduling as well.Crop Production/Industries,