Criticality for the Gehring link problem

In 1974, Gehring posed the problem of minimizing the length of two linked curves separated by unit distance. This constraint can be viewed as a measure of thickness for links, and the ratio of length over thickness as the ropelength. In this paper we refine Gehring's problem to deal with links in a fixed link-homotopy class: we prove ropelength minimizers exist and introduce a theory of ropelength criticality. Our balance criterion is a set of necessary and sufficient conditions for criticality, based on a strengthened, infinite-dimensional version of the Kuhn--Tucker theorem. We use this to prove that every critical link is C^1 with finite total curvature. The balance criterion also allows us to explicitly describe critical configurations (and presumed minimizers) for many links including the Borromean rings. We also exhibit a surprising critical configuration for two clasped ropes: near their tips the curvature is unbounded and a small gap appears between the two components. These examples reveal the depth and richness hidden in Gehring's problem and our natural extension.Comment: This is the version published by Geometry & Topology on 14 November 200

Giant viscosity enhancement in a spin-polarized Fermi liquid

The viscosity is measured for a Fermi liquid, a dilute $^3$He-$^4$He mixture, under extremely high magnetic field/temperature conditions ($B \leq 14.8$ T, $T \geq 1.5$ mK). The spin splitting energy $\mu B$ is substantially greater than the Fermi energy $k_B T_F$; as a consequence the polarization tends to unity and s-wave quasiparticle scattering is suppressed for $T \ll T_F$. Using a novel composite vibrating-wire viscometer an enhancement of the viscosity is observed by a factor of more than 500 over its low-field value. Good agreement is found between the measured viscosity and theoretical predictions based upon a $t$-matrix formalism.Comment: 4 pages, 4 figure

Wind turbine generator rotor blade concepts with low cost potential

Four processed for producing blades are examined. Two use filament winding techniques and two involve filling a mold or form to produce all or part of a blade. The processes are described and a comparison is made of cost, material properties, design and free vibration characteristics. Conclusions are made regarding the feasibility of each process to produce low cost, structurally adequate blades

Large structures and tethers working group

The Large Structures and Tethers Working Group sought to clarify the meaning of large structures and tethers as they related to space systems. Large was assumed to mean that the characteristic length of the structure was greater than one of such relevant plasma characteristics as ion gyroradius or debey length. Typically, anything greater than or equal to the Shuttle dimensions was considered large. It was agreed that most large space systems that the tether could be better categorized as extended length, area, or volume structures. The key environmental interactions were then identified in terms of these three categories. In the following Working Group summary, these categories and the related interactions are defined in detail. The emphasis is on how increases in each of the three spatial dimensions uniquely determine the interactions with the near-Earth space environment. Interactions with the environments around the other planets and the solar wind were assumed to be similar or capable of being extrapolated from the near-Earth results. It should be remembered in the following that the effects on large systems do not just affect specific technologies but will quite likely impact whole missions. Finally, the possible effects of large systems on the plasma environment, although only briefly discussed, were felt to be of potentially great concern

Fabrication of glass gas cells for the HALOE and MAPS satellite experiments

The Halogen Occultation Experiment (HALOE) and the Measurement of Air Pollution from Satellites (MAPS) experiment are satellite-borne experiments which measure trace constituents in the Earth's atmosphere. The instruments which obtain the data for these experiments are based on the gas filter correlation radiometer measurement technique. In this technique, small samples of the gases of interest are encapsulated in glass cylinders, called gas cells, which act as very selective optical filters. This report describes the techniques employed in the fabrication of the gas cells for the HALOE and MAPS instruments. Details of the method used to fuse the sapphire windows (required for IR transmission) to the glass cell bodies are presented along with detailed descriptions of the jigs and fixtures used during the assembly process. The techniques and equipment used for window inspection and for pairing the HALOE windows are discussed. Cell body materials and the steps involved in preparing the cell bodies for the glass-to-sapphire fusion process are given

The learning experiences of health and social care paraprofessionals on a foundation degree

Foundation degrees have been developed in the UK as a means of meeting the learning needs of paraprofessionals in health and social care and the services within which they work in a cost-effective fashion. Workplace learning is an intrinsic component to these degrees. Taking a socio-cultural perspective, this paper examines how the students' workplaces, life circumstances and sense of career trajectory shaped their learning experience and motivation. A small-scale evaluation study, using semi-structured interviews, focused on the learning experiences of a group of paraprofessionals enrolled in a foundation degree in health and social care. Data revealed fragmented employment patterns, underpinned by consistent vocational drives. While the study resonated with vocation, participants were ambivalent or lacked information about career progression. Workplace conditions, relationships and limited time shaped learning and coping strategies. A strategic and focused approach to student learning is required and includes attention to career pathways, workforce development strategy, the requirements of a range of stakeholders, workplace supervision and support for learning

Aerothermal modeling program, phase 2

The main objectives of the Aerothermal Modeling Program, Phase 2 are: to develop an improved numerical scheme for incorporation in a 3-D combustor flow model; to conduct a benchmark quality experiment to study the interaction of a primary jet with a confined swirling crossflow and to assess current and advanced turbulence and scalar transport models; and to conduct experimental evaluation of the air swirler interaction with fuel injectors, assessments of current two-phase models, and verification the improved spray evaporation/dispersion models

The Richardson's Law in Large-Eddy Simulations of Boundary Layer flows

Relative dispersion in a neutrally stratified planetary boundary layer (PBL) is investigated by means of Large-Eddy Simulations (LES). Despite the small extension of the inertial range of scales in the simulated PBL, our Lagrangian statistics turns out to be compatible with the Richardson $t^3$ law for the average of square particle separation. This emerges from the application of nonstandard methods of analysis through which a precise measure of the Richardson constant was also possible. Its values is estimated as $C_2\sim 0.5$ in close agreement with recent experiments and three-dimensional direct numerical simulations.Comment: 15 LaTex pages, 4 PS figure

Measuring the quantum efficiency of single radiating dipoles using a scanning mirror

Using scanning probe techniques, we show the controlled manipulation of the radiation from single dipoles. In one experiment we study the modification of the fluorescence lifetime of a single molecular dipole in front of a movable silver mirror. A second experiment demonstrates the changing plasmon spectrum of a gold nanoparticle in front of a dielectric mirror. Comparison of our data with theoretical models allows determination of the quantum efficiency of each radiating dipole.Comment: 4 pages, 4 figure