Geometric phases for corotating elliptical vortex patches

We describe a geometric phase that arises when two elliptical vortex patches corotate. Using the Hamiltonian moment model of Melander, Zabusky, and Styczek [J. Fluid Mech. 167, 95–115 (1986)] we consider two corotating uniform elliptical patches evolving according to the second order truncated equations of the model. The phase is computed in the adiabatic setting of a slowly varying Hamiltonian as in the work of Hannay [J. Phys. A 18, 221–230 (1985)] and Berry [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We also discuss the geometry of the symplectic phase space of the model in the context of nonadiabatic phases. The adiabatic phase appears in the orientation angle of each patch—it is similiar in form and is calculated using a multiscale perturbation procedure as in the point vortex configuration of Newton [Physica D 79, 416–423 (1994)] and Shashikanth and Newton [J. Nonlinear Sci. 8, 183–214 (1998)], however, an extra factor due to the internal stucture of the patch is present. The final result depends on the initial orientation of the patches unlike the phases in the works of Hannay and Berry [J. Phys. A 18, 221–230 (1985)]; [Proc. R. Soc. London, Ser. A 392, 45–57 (1984)]. We then show that the adiabatic phase can be interpreted as the holonomy of a connection on the trivial principal fiber bundle pi:T2×S1-->S1, where T2 is identified with the product of the momentum level sets of two Kirchhoff vortex patches and S1 is diffeomorphic to the momentum level set of two point vortex motion. This two point vortex motion is the motion that the patch centroids approach in the adiabatic limit

Introduction to Q-tensor theory

This paper aims to provide an introduction to a basic form of the ${\bf Q}$-tensor approach to modelling liquid crystals, which has seen increased interest in recent years. The increase in interest in this type of modelling approach has been driven by investigations into the fundamental nature of defects and new applications of liquid crystals such as bistable displays and colloidal systems for which a description of defects and disorder is essential. The work in this paper is not new research, rather it is an introductory guide for anyone wishing to model a system using such a theory. A more complete mathematical description of this theory, including a description of flow effects, can be found in numerous sources but the books by Virga and Sonnet and Virga are recommended. More information can be obtained from the plethora of papers using such approaches, although a general introduction for the novice is lacking. The first few sections of this paper will detail the development of the ${\bf Q}$-tensor approach for nematic liquid crystalline systems and construct the free energy and governing equations for the mesoscopic dependent variables. A number of device surface treatments are considered and theoretical boundary conditions are specified for each instance. Finally, an example of a real device is demonstrated

Stellarator bootstrap current and plasma flow velocity at low collisionality

The bootstrap current and flow velocity of a low-collisionality stellarator plasma are calculated. As far as possible, the analysis is carried out in a uniform way across all low-collisionality regimes in general stellarator geometry, assuming only that the confinement is good enough that the plasma is approximately in local thermodynamic equilibrium. It is found that conventional expressions for the ion flow speed and bootstrap current in the low-collisionality limit are accurate only in the $1/\nu$-collisionality regime and need to be modified in the $\sqrt{\nu}$-regime. The correction due to finite collisionality is also discussed and is found to scale as $\nu^{2/5}$

Astrotech 21: A technology program for future astrophysics missions

The Astrotech 21 technology program is being formulated to enable a program of advanced astrophysical observatories in the first decade of the 21st century. This paper describes the objectives of Astrotech 21 and the process that NASA is using to plan and implement it. It also describes the future astrophysical mission concepts that have been defined for the twenty-first century and discusses some of the requirements that they will impose on information systems for space astrophysics

An operational system for subject switching between controlled vocabularies: A computational linguistics approach

The NASA Lexical Dictionary (NLD), a system that automatically translates input subject terms to those of NASA, was developed in four phases. Phase One provided Phrase Matching, a context sensitive word-matching process that matches input phrase words with any NASA Thesaurus posting (i.e., index) term or Use reference. Other Use references have been added to enable the matching of synonyms, variant spellings, and some words with the same root. Phase Two provided the capability of translating any individual DTIC term to one or more NASA terms having the same meaning. Phase Three provided NASA terms having equivalent concepts for two or more DTIC terms, i.e., coordinations of DTIC terms. Phase Four was concerned with indexer feedback and maintenance. Although the original NLD construction involved much manual data entry, ways were found to automate nearly all but the intellectual decision-making processes. In addition to finding improved ways to construct a lexical dictionary, applications for the NLD have been found and are being developed

A simple derivation of Kepler's laws without solving differential equations

Proceeding like Newton with a discrete time approach of motion and a geometrical representation of velocity and acceleration, we obtain Kepler's laws without solving differential equations. The difficult part of Newton's work, when it calls for non trivial properties of ellipses, is avoided by the introduction of polar coordinates. Then a simple reconsideration of Newton's figure naturally leads to en explicit expression of the velocity and to the equation of the trajectory. This derivation, which can be fully apprehended by beginners at university (or even before) can be considered as a first application of mechanical concepts to a physical problem of great historical and pedagogical interest

Proteomics of Carbon Fixation Energy Sources in Halothiobacillus neapolitanus

Through the use of proteomics, it was uncovered that the autotrophic, aerobic purple sulfur bacterium Halothiobacillus neapolitanus displays changes in cellular levels of portions of its carbon dioxide uptake and fixation mechanisms upon switch from bicarbonate to CO2(g) as carbon source. This includes an increase in level of a heterodimeric bicarbonate transporter along with a potential switch between form I and form II of RubisCO. Additional changes are seen in several sulfur oxidation pathways, which may indicate a link between sulfur oxidation pathways as an energy source and carbon uptake/fixation mechanisms

Dada, Expressionism, and Some Modern Modes

Paper by Robert P. Newton, Assistant Professor of German at the University of Pennsylvani

Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.Comment: Updated version. Contains some minor corrections compared to the published versio