On the vanishing viscosity limit in a disk

We say that the solution u to the Navier-Stokes equations converges to a solution v to the Euler equations in the vanishing viscosity limit if u converges to v in the energy norm uniformly over a finite time interval. Working specifically in the unit disk, we show that a necessary and sufficient condition for the vanishing viscosity limit to hold is the vanishing with the viscosity of the time-space average of the energy of u in a boundary layer of width proportional to the viscosity due to modes (eigenfunctions of the Stokes operator) whose frequencies in the radial or the tangential direction lie between L and M. Here, L must be of order less than 1/(viscosity) and M must be of order greater than 1/(viscosity)

A New Method for Laminar Boundary Layer Transition Visualization in Flight: Color Changes in Liquid Crystal Coatings

The visualization of laminar to turbulent boundary layer transition plays an important role in flight and wind tunnel aerodynamic testing of aircraft wing and body surfaces. Visualization can help provide a more complete understanding of both transition location as well as transition modes; without visualization, the transition process can be very difficult to understand. In the past, the most valuable transition visualization methods for fight applications included sublimating chemicals and oil flows. Each method has advantages and limitations. In particular, sublimating chemicals are impractical to use in subsonic applications much above 20,000 feet because of the greatly reduced rates of sublimation at lower temperatures (less than -4 degrees Fahrenheit). Both oil flow and sublimating chemicals have the disadvantage of providing only one good data point per flight. Thus, for many important flight conditions, transition visualization has not been readily available. This paper discusses a new method for visualizing transition in fight by the use of liquid crystals. The new method overcomes the limitations of past techniques, and provides transition visualization capability throughout almost the entire altitude and speed ranges of virtually all subsonic aircraft flight envelopes. The method also has wide applicability for supersonic transition visualization in flight and for general use in wind tunnel research over wide subsonic and supersonic speed ranges

On the flow map for 2D Euler equations with unbounded vorticity

In Part I, we construct a class of examples of initial velocities for which the unique solution to the Euler equations in the plane has an associated flow map that lies in no Holder space of positive exponent for any positive time. In Part II, we explore inverse problems that arise in attempting to construct an example of an initial velocity producing an arbitrarily poor modulus of continuity of the flow map.Comment: http://iopscience.iop.org/0951-7715/24/9/013/ for published versio

Setting up tracking tools for NuFact bowtie decay ring studies

This paper describes the setting up of ray-tracing tools, and preliminary beam dynamics studies concerning the NuFact bowtie decay ring

Amplitude dependent orbital period in alternating gradient accelerators

Orbital period in a ring accelerator and time of flight in a linear accelerator depend on the amplitude of betatron oscillations. The variation is negligible in ordinary particle accelerators with relatively small beam emittance. In an accelerator for large emittance beams like muons and unstable nuclei, however, this effect cannot be ignored. We measured orbital period in a linear non-scaling fixed field alternating gradient (FFAG) accelerator, which is a candidate for muon acceleration, and compared with the theoretical prediction. The good agreement between them gives important ground for the design of particle accelerators for a new generation of particle and nuclear physics experiments.Comment: 9 pages, 3 figure

Pamela: development of the RF system for a non-relativistic non-scaling FFAG

The PAMELA project(Particle Accelerator For MEdical Applications) currently consists of the design of a particle therapy facility. The project, which is in the design phase, contains Non-Scaling FFAG, particle accelerator capable of rapid beam acceleration, giving a pulse repetition rate of 1kHz, far beyond that of a conventional synchrotron. To realise the repetition rate, a key component of the accelerator is the rf accelerating system. The combination of a high energy gain per turn and a high repetition rate is a significant challenge. In this paper, options for the rf system of the proton ring and the status of development are presented

Wave energy transmission apparatus for high-temperature environments

A wave energy transmission apparatus has a conduit made from a refractory oxide. A transparent, refractory ceramic window is coupled to the conduit. Wave energy passing through the window enters the conduit

Viscous-Inviscid Interactions in a Boundary-Layer Flow Induced by a Vortex Array

In this paper we investigate the asymptotic validity of boundary layer theory. For a flow induced by a periodic row of point-vortices, we compare Prandtl's solution to Navier-Stokes solutions at different $Re$ numbers. We show how Prandtl's solution develops a finite time separation singularity. On the other hand Navier-Stokes solution is characterized by the presence of two kinds of viscous-inviscid interactions between the boundary layer and the outer flow. These interactions can be detected by the analysis of the enstrophy and of the pressure gradient on the wall. Moreover we apply the complex singularity tracking method to Prandtl and Navier-Stokes solutions and analyze the previous interactions from a different perspective

Working time flexibility components and working time regimes in Europe: using company-level data across 21 countries

Working time ?exibility comprises a wide variety of arrangements, from part-time, overtime, to long-term leaves. Theoretical approaches to grouping these arrangements have been developed, but empirical underpinnings are rare. This article investigates the bundles that can be found for various ?exible working time arrangements, using the Establishment Survey on Working Time and Work–Life Balance, 2004/2005, covering 21 EU member states and 13 industries. The results from the factor analyses con?rmed that working time arrangements can be grouped into two bundles, one for the employee-centred arrangements and second for the employer-centred arrangements, and that these two bundles are separate dimensions.Wealso tested the stability of the factor analysisoutcome, showing that although we ?nd some deviations from the pan-Europe and pan-industry outcome, the naming of the components as ?exibility for employees and ?exibility for employers can be considered rather stable. Lastly, we ?nd three country clusters for the 21 European countries using the bundle approach. The ?rst group includes the Northern European countries along side Poland and Czech Republic, the second group the continental European countries with UK and Ireland, and lastly, the southern European countries with Hungary and Slovenia