Numerical optimization design of advanced transonic wing configurations

A computationally efficient and versatile technique for use in the design of advanced transonic wing configurations has been developed. A reliable and fast transonic wing flow-field analysis program, TWING, has been coupled with a modified quasi-Newton method, unconstrained optimization algorithm, QNMDIF, to create a new design tool. Fully three-dimensional wing designs utilizing both specified wing pressure distributions and drag-to-lift ration minimization as design objectives are demonstrated. Because of the high computational efficiency of each of the components of the design code, in particular the vectorization of TWING and the high speed of the Cray X-MP vector computer, the computer time required for a typical wing design is reduced by approximately an order of magnitude over previous methods. In the results presented here, this computed wave drag has been used as the quantity to be optimized (minimized) with great success, yielding wing designs with nearly shock-free (zero wave drag) pressure distributions and very reasonable wing section shapes

Making Anti-de Sitter Black Holes

It is known from the work of Banados et al. that a space-time with event horizons (much like the Schwarzschild black hole) can be obtained from 2+1 dimensional anti-de Sitter space through a suitable identification of points. We point out that this can be done in 3+1 dimensions as well. In this way we obtain black holes with event horizons that are tori or Riemann surfaces of genus higher than one. They can have either one or two asymptotic regions. Locally, the space-time is isometric to anti-de Sitter space.Comment: LaTeX, 10 pages, 6 postscript figures, uses epsf.te

A modified time-of-flight method for precise determination of high speed ratios in molecular beams

Time-of-flight (TOF) is a standard experimental technique for determining, among others, the speed ratio S (velocity spread) of a molecular beam. The speed ratio is a measure for the monochromaticity of the beam and an accurate determination of S is crucial for various applications, for example, for characterising chromatic aberrations in focussing experiments related to helium microscopy or for precise measurements of surface phonons and surface structures in molecular beam scattering experiments. For both of these applications, it is desirable to have as high a speed ratio as possible. Molecular beam TOF measurements are typically performed by chopping the beam using a rotating chopper with one or more slit openings. The TOF spectra are evaluated using a standard deconvolution method. However, for higher speed ratios, this method is very sensitive to errors related to the determination of the slit width and the beam diameter. The exact sensitivity depends on the beam diameter, the number of slits, the chopper radius, and the chopper rotation frequency. We present a modified method suitable for the evaluation of TOF measurements of high speed ratio beams. The modified method is based on a systematic variation of the chopper convolution parameters so that a set of independent measurements that can be fitted with an appropriate function are obtained. We show that with this modified method, it is possible to reduce the error by typically one order of magnitude compared to the standard method

Alfvén Wave Turbulence as a Coronal Heating Mechanism: Simultaneously Predicting the Heating Rate and the Wave-induced Emission Line Broadening

We test the predictions of the Alfvén Wave Solar Model (AWSoM), a global wave-driven magnetohydrodynamic (MHD) model of the solar atmosphere, against high-resolution spectra emitted by the quiescent off-disk solar corona. AWSoM incorporates Alfvén wave propagation and dissipation in both closed and open magnetic field lines; turbulent dissipation is the only heating mechanism. We examine whether this mechanism is consistent with observations of coronal EUV emission by combining model results with the CHIANTI atomic database to create synthetic line-of-sight spectra, where spectral line widths depend on thermal and wave-related ion motions. This is the first time wave-induced line broadening is calculated from a global model with a realistic magnetic field. We used high-resolution SUMER observations above the solar west limb between 1.04 and 1.34 R o at the equator, taken in 1996 November. We obtained an AWSoM steady-state solution for the corresponding period using a synoptic magnetogram. The 3D solution revealed a pseudo-streamer structure transversing the SUMER line of sight, which contributes significantly to the emission; the modeled electron temperature and density in the pseudo-streamer are consistent with those observed. The synthetic line widths and the total line fluxes are consistent with the observations for five different ions. Further, line widths that include the contribution from the wave-induced ion motions improve the correspondence with observed spectra for all ions. We conclude that the turbulent dissipation assumed in the AWSoM model is a viable candidate for explaining coronal heating, as it is consistent with several independent measured quantities.National Science Foundation (U.S.) (Grant AGS-1322543

The Implementation of the Colored Abstract Simplicial Complex and its Application to Mesh Generation

We introduce CASC: a new, modern, and header-only C++ library which provides a data structure to represent arbitrary dimension abstract simplicial complexes (ASC) with user-defined classes stored directly on the simplices at each dimension. This is accomplished by using the latest C++ language features including variadic template parameters introduced in C++11 and automatic function return type deduction from C++14. Effectively CASC decouples the representation of the topology from the interactions of user data. We present the innovations and design principles of the data structure and related algorithms. This includes a metadata aware decimation algorithm which is general for collapsing simplices of any dimension. We also present an example application of this library to represent an orientable surface mesh.Comment: 24 pages, 6 figure

(2+1)-dimensional Einstein-Kepler problem in the centre-of-mass frame

We formulate and analyze the Hamiltonian dynamics of a pair of massive spinless point particles in (2+1)-dimensional Einstein gravity by anchoring the system to a conical infinity, isometric to the infinity generated by a single massive but possibly spinning particle. The reduced phase space \Gamma_{red} has dimension four and topology R^3 x S^1. \Gamma_{red} is analogous to the phase space of a Newtonian two-body system in the centre-of-mass frame, and we find on \Gamma_{red} a canonical chart that makes this analogue explicit and reduces to the Newtonian chart in the appropriate limit. Prospects for quantization are commented on.Comment: 38 pages, REVTeX v3.1 with amsfonts and epsf, 12 eps figures. (v2: Presentational improvement, references added, typos corrected.