Adaptive finite element simulation of three-dimensional surface tension dominated free-surface flow problems

An arbitrary Lagrangian--Eulerian finite element method is described for the solution of time-dependent, three-dimensional, free-surface flow problems. Many flows of practical significance involve contact lines, where the free surface meets a solid boundary. This contact line may be pinned to a particular part of the solid but is more typically free to slide in a manner that is characterised by the dynamic contact angle formed by the fluid. We focus on the latter case and use a model that admits spatial variation of the contact angle: thus permitting variable wetting properties to be simulated. The problems are driven by the motion of the fluid free surface (under the action of surface tension and external forces such as gravity) hence the geometry evolves as part of the solution, and mesh adaptivity is required to maintain the quality of the computational mesh for the physical domain. Continuous mesh adaptivity, in the form of a pseudo-elastic mesh movement scheme, is used to move the interior mesh nodes in response to the motion of the fluid's free surface. Periodic, discrete remeshing stages are also used for cases in which the fluid volume has grown, or is sufficiently distorted, by the free-surface motion. Examples are given of a droplet sliding on an inclined uniform plane and of a droplet spreading on a surface with variable wetting properties

Progress in Absorber R&D for Muon Cooling

A stored-muon-beam neutrino factory may require transverse ionization cooling of the muon beam. We describe recent progress in research and development on energy absorbers for muon-beam cooling carried out by a collaboration of university and laboratory groups.Comment: 7 pages, 1 figure, presented at the 3rd International Workshop on Neutrino Factory Based on Muon Storage Rings (NuFACT'01), May 24-30, 2001, Tsukuba, Japa

Warped Convolutions, Rieffel Deformations and the Construction of Quantum Field Theories

Warped convolutions of operators were recently introduced in the algebraic framework of quantum physics as a new constructive tool. It is shown here that these convolutions provide isometric representations of Rieffel's strict deformations of C*-dynamical systems with automorphic actions of R^n, whenever the latter are presented in a covariant representation. Moreover, the device can be used for the deformation of relativistic quantum field theories by adjusting the convolutions to the geometry of Minkowski space. The resulting deformed theories still comply with pertinent physical principles and their Tomita-Takesaki modular data coincide with those of the undeformed theory; but they are in general inequivalent to the undeformed theory and exhibit different physical interpretations.Comment: 34 page

Haag duality and the distal split property for cones in the toric code

We prove that Haag duality holds for cones in the toric code model. That is, for a cone Lambda, the algebra R_Lambda of observables localized in Lambda and the algebra R_{Lambda^c} of observables localized in the complement Lambda^c generate each other's commutant as von Neumann algebras. Moreover, we show that the distal split property holds: if Lambda_1 \subset Lambda_2 are two cones whose boundaries are well separated, there is a Type I factor N such that R_{Lambda_1} \subset N \subset R_{Lambda_2}. We demonstrate this by explicitly constructing N.Comment: 15 pages, 2 figures, v2: extended introductio

Finite element simulation of three-dimensional free-surface flow problems

An adaptive finite element algorithm is described for the stable solution of three-dimensional free-surface-flow problems based primarily on the use of node movement. The algorithm also includes a discrete remeshing procedure which enhances its accuracy and robustness. The spatial discretisation allows an isoparametric piecewise-quadratic approximation of the domain geometry for accurate resolution of the curved free surface. The technique is illustrated through an implementation for surface-tension-dominated viscous flows modelled in terms of the Stokes equations with suitable boundary conditions on the deforming free surface. Two three-dimensional test problems are used to demonstrate the performance of the method: a liquid bridge problem and the formation of a fluid droplet

String-localized Quantum Fields and Modular Localization

We study free, covariant, quantum (Bose) fields that are associated with irreducible representations of the Poincar\'e group and localized in semi-infinite strings extending to spacelike infinity. Among these are fields that generate the irreducible representations of mass zero and infinite spin that are known to be incompatible with point-like localized fields. For the massive representation and the massless representations of finite helicity, all string-localized free fields can be written as an integral, along the string, of point-localized tensor or spinor fields. As a special case we discuss the string-localized vector fields associated with the point-like electromagnetic field and their relation to the axial gauge condition in the usual setting.Comment: minor correction

Determination of Turbine Blade Life from Engine Field Data

It is probable that no two engine companies determine the life of their engines or their components in the same way or apply the same experience and safety factors to their designs. Knowing the failure mode that is most likely to occur minimizes the amount of uncertainty and simplifies failure and life analysis. Available data regarding failure mode for aircraft engine blades, while favoring low-cycle, thermal mechanical fatigue as the controlling mode of failure, are not definitive. Sixteen high-pressure turbine (HPT) T-1 blade sets were removed from commercial aircraft engines that had been commercially flown by a single airline and inspected for damage. Each set contained 82 blades. The damage was cataloged into three categories related to their mode of failure: (1) Thermal-mechanical fatigue, (2) Oxidation/Erosion, and (3) "Other." From these field data, the turbine blade life was determined as well as the lives related to individual blade failure modes using Johnson-Weibull analysis. A simplified formula for calculating turbine blade life and reliability was formulated. The L(sub 10) blade life was calculated to be 2427 cycles (11 077 hr). The resulting blade life attributed to oxidation/erosion equaled that attributed to thermal-mechanical fatigue. The category that contributed most to blade failure was Other. If there were there no blade failures attributed to oxidation/erosion and thermal-mechanical fatigue, the overall blade L(sub 10) life would increase approximately 11 to 17 percent

High-gradient normal-conducting RF structures for muon cooling channels

We present a status report on the research and development of high-gradient normal-conducting RF structures for the ionization cooling of muons in a neutrino factory or muon collider. High-gradient RF structures are required in regions enclosed in strong focusing solenoidal magnets, precluding the application of superconducting RF technology [1]. We propose using linear accelerating structures, with individual cells electromagnetically isolated, to achieve the required gradients of over 15 MV/m at 201 MHz and 30 MV/m at 805 MHz. Each cell will be powered independently, and cell length and drive phase adjusted to optimize shunt impedance of the assembled structure. This efficient design allows for relatively small field enhancement on the structure walls, and an accelerating field approximately 1.7 times greater than the peak surface field. The electromagnetic boundary of each cell may be provided by a thin Be sheet, or an assembly of thin-walled metal tubes. Use of thin, low-Z materials will allow passage of the muon beams without significant deterioration in beam quality due to scattering. R and D in design and analysis of robust structures that will operate under large electric and magnetic fields and RF current heating are discussed, including the experimental program based in a high-power test laboratory developed for this purpose