Monomial integrals on the classical groups

This paper presents a powerfull method to integrate general monomials on the classical groups with respect to their invariant (Haar) measure. The method has first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)], and is here used to obtain similar integration formulas for the unitary and the unitary symplectic group. The integration formulas turn out to be of similar form. They are all recursive, where the recursion parameter is the number of column (row) vectors from which the elements in the monomial are taken. This is an important difference to other integration methods. The integration formulas are easily implemented in a computer algebra environment, which allows to obtain analytical expressions very efficiently. Those expressions contain the matrix dimension as a free parameter.Comment: 16 page

Analytical study of a free-wing/free-trimmer concept

The free-wing/free-trimmer is a NASA-Conceived extension of the free-wing concept intended to permit the use of high-lift flaps. Wing pitching moments are balanced by a smaller, external surface attached by a boom or equivalent structure. The external trimmer is, itself, a miniature free wing, and pitch control of the wing-trimmer assembly is effected through a trailing-edge control tab on the trimmer surface. The longitudinal behavior of representative small free-wing/free-trimmer aircraft was analyzed. Aft-mounted trimmer surfaces are found to be superior to forward trimmers, although the permissible trimmer moment arm is limited, in both cases, by adverse dynamic effects. Aft-trimmer configurations provide excellent gust alleviation and meet fundamental stick-fixed stability criteria while exceeding the lift capabilities of pure free-wing configurations

Non-linear rheology of active particle suspensions: Insights from an analytical approach

We consider active suspensions in the isotropic phase subjected to a shear flow. Using a set of extended hydrodynamic equations we derive a variety of {\em analytical} expressions for rheological quantities such as shear viscosity and normal stress differences. In agreement to full-blown numerical calculations and experiments we find a shear thickening or -thinning behaviour depending on whether the particles are contractile or extensile. Moreover, our analytical approach predicts that the normal stress differences can change their sign in contrast to passive suspensions.Comment: 11 pages, 10 figures, appear in PR

Ultrasonic Backscatter Rotation Scanner for Detection of Ply Bends and Fiber Wrinkles

Fiber wrinkles and ply bends in structures composed of laminated, fiber reinforced plastic materials are known to degrade performance under design load conditions. Such flaws can inadvertently be manufactured into structures, such as solid rocket motor (srm) cases and nozzles, and generally are difficult to detect. For structures such as nozzles, plies are not coplanar with the nozzle wall, but have an out-of-plane direction. Such materials offer an increased challenge for detection of ply bends and fiber wrinkles. Advanced nondestructive evaluation (NDE) methods are needed for detection of these flaws so that manufacturing processes can be characterized and improved and, also, to prevent the usage of defective materials. Ultrasonic backscatter-based methods have been demonstrated to be sensitive to fiber direction and to transverse cracks in composite laminate plates and test panels with plies lying in the plane of the plate or panel [1–5]. Backscatter methods, thus, provide a viable foundation for addressing the similar problem of ply bends and fiber wrinkles in composites with out-of-plane plies. This paper describes an improved ultrasonic backscatter method for detection of ply distortions in structures with out-of-plane ply orientations

Measurement of the mass of the τ lepton

The mass of the τ lepton has been measured at the Beijing Electron-Positron Collider using the Beijing Spectrometer. A search near threshold for e^+e^-→τ^+τ^- was performed. Candidate events were identified by requiring that one τ decay via τ→eνν¯, and the other via τ→μνν¯. The mass value, obtained from a fit to the energy dependence of the τ^+τ^- cross section, is m_τ=1776.9_(-0.5)^(+0.4)±0.2 MeV

Behavior of Braced Sheetpile Excavation in Detroit Clay

This paper presents the design criteria, finite element modeling and actual behavior of a braced sheetpile excavation in Detroit soft clay. Due to the close proximity of existing structures to the excavation, a detailed analysis was performed to design and construct an earth retention system to avoid damage to these structures. The excavation involved a 170 ft by 220 ft area. The maximum depth of excavation was 23.5 ft. The subsurface soil consists of soft to very soft Detroit clay from the excavation level to a depth of 80 ft and has an undrained shear strength as low as 360 psf

Performance of a Semi-Rigid Braced Excavation in Soft Clay

Construction of a 21-foot wide, 28-foot deep braced excavation in Detroit soft clays has been completed. In order to protect an existing 50-year old tunnel adjacent to the excavation, a semi-rigid, tangent wall earth retention system was constructed to minimize the soil movements. The tangent wall was formed by 118 drilled piers with 42-inch in diameter and 41-foot long. The maximum soil lateral and vertical movements adjacent to the excavation were controlled below a magnitude of 2.0 inches, while bottom of the excavation experienced about 3 inches of heave. This paper presents the design considerations and construction performance of the retention system based on geotechnical instrumentation data. Prediction of maximum soil lateral movement based on a finite element analysis and a semi-empirical method conformed well with field measurements. Experience learned from the design and construction will be valuable for future construction of braced excavation systems in similar soil conditions

Risk of cancer following primary total hip replacement or primary resurfacing arthroplasty of the hip : A retrospective cohort study in Scotland

Acknowledgements: We are grateful to Lee Barnsdale, Doug Clark, and Richard Dobbie for advice and assistance with data preparation before analysis, and to the three anonymous referees for their helpful comments and suggestions.Peer reviewedPublisher PD