Discriminantal arrangement, 3 × 3 minors of Plücker matrix and hypersurfaces in Grassmannian Gr(3,n)

We show that points in specific degree-2 hypersurfaces in the Grassmannian $Gr(3,n)$ correspond to generic arrangements of n hyperplanes in ${\mathbb{C}}^3$ with associated discriminantal arrangement having intersections of multiplicity three in codimension two.     

An explicit algebraic Reynolds stress and heat flux model for incompressible turbulence: Part I Non-isothermal flow

Tensor representation theory is used to derive an explicit algebraic model that consists of an explicit algebraic stress model (EASM) and an explicit algebraic heat flux model (EAHFM) for two-dimensional (2-D) incompressible non-isothermal turbulent flows. The representation methodology used for the heat flux vector is adapted from that used for the polynomial representation of the Reynolds stress anisotropy tensor. Since the methodology is based on the formation of invariants from either vector or tensor basis sets, it is possible to derive explicit polynomial vector expansions for the heat flux vector. The resulting EAHFM is necessarily coupled with the turbulent velocity field through an EASM for the Reynolds stress anisotropy. An EASM has previously been derived by Jongen and Gatski [10]. Therefore, it is used in conjunction with the derived EAHFM to form the explicit algebraic model for incompressible 2-D flows. This explicit algebraic model is analyzed and compared with previous formulations including its ability to approximate the commonly accepted value for the turbulent Prandtl number. The effect of pressure-scrambling vector model calibration on predictive performance is also assessed. Finally, the explicit algebraic model is validated against a 2-D homogeneous shear flow with a variety of thermal gradients. Dedicated to the memory of the late Professor Charles G. Speziale of Boston University     

Diffuser stall and rotating zones of separated boundary layer

Unsteady flows and rotating stall in vaneless diffusers were investigated by measuring both the wall fluctuating pressures and the unsteady velocity field using hot-wires and laser Doppler anemometers. Experiments were carried out with a fixed impeller and fixed diffuser inlet and outlet radii. However, the diffuser width was varied so that its effect on rotating stall could be examined. Results show that the variation of _r with b/r _i is in qualitative agreement with the prediction of Senoo et al. (1977). Therefore, the onset of stall is delayed as diffuser width is decreased. For diffusers with small width, stall emerges first with one stall cell and then develops into 2 and 4 stall cells as the mass flow rate is decreased. On the other hand, for the diffuser with the largest width tested, stall emerges with one stall cell and quickly develops into 3 stall cells. The ratio of the speed of rotation of the stall cell to impeller speed is independent of diffuser width, but decreases slightly as the number of stall cells increases. Finally, rotating stall is associated with reversed flow originating from the hub side rather than from the shroud side.     

Secondary cells and separation in developing laminar curved-pipe flows

Laminar flows through 180° curved bends of circular cross section are investigated numerically. For small curvature ratio, , defined as pipe radius over mean bend radius, the governing equations could be parabolized. The equations are solved for an range of from 0.04 to 0.143, a Dean number (De) range of from 277.5 to 1360, and for a uniform flow, a potential vortex, and a parabolic flow inlet condition. In all these studies a zero cross-stream flow at the inlet is assumed. A detailed study of the effects of , De, and inlet condition on the secondary flow pattern is carried out. Within the range of parameters investigated, up to three secondary cells are found in the cross-stream half-plane of a curved pipe. They are the Dean-type secondary cell, a secondary separation cell near the inner bend (closest to the center of curvature of the bend), and a third cell near the pipe center. The number of secondary cells in the cross-stream half-plane is greatly influenced by the inlet flow, and to a much lesser extent by and De. For example, only the Dean cell is found in a curved-pipe flow where and De are small and the inlet flow is either uniform or a potential vortex. When the inlet condition of the same case is changed to a parabolic flow, a three-cell structure results. Furthermore, as De increases to 1180, incipient axial flow separation begins at around 23° downstream of the curved-pipe entrance. The formation and extent of the separation and third cells are investigated together with their dependence on the parameters studied. This investigation further shows that, within the range of parameters examined, there is no secondary cell occurring near the outer bend, contrary to some earlier findings on fully developed curved-pipe flows.This work was supported by the Office of Naval Research under Grant No. N0014-81-K-0428 and by DTRC, Annapolis, Maryland, under Contract No. N00167-86-K-0075. Also, support in the form of an IPA awarded to RMCS during his sabbatical leave at DTRC, Annapolis, Maryland, in the spring of 1990 is gratefully acknowledged.     

Unsteady forces on circular cylinders in a cross-flow

A three-axis piezoelectric load cell was used to measure the local unsteady forces induced on cylinders placed in a cross-flow. In conjunction with this, a single hot-wire was used to traverse the wake at a fixed distance behind the cylinder so that correlations between the induced forces on the cylinder and the wake velocity could be calculated to provide insight into the character of the flow-induced unsteady forces. Experiments were carried out on both two-dimensional and finite-span cylinders at a Reynolds number of 46,000. For the two-dimensional cylinder case, substantial evidence was obtained to demonstrate that the strength of the vortex roll-up along the span was quite uniform. Consequently, the lift-velocity correlation along the span remained unchanged. On the other hand, there was a total lack of correlation between the fluctuating drag and the wake velocity, thus indicating that the drag signal was not quite periodic. In the finite-span cylinder case, the separated flow from the top edge of the cylinder was found to suppress vortex shedding along the span of the cylinder, destroyed its coherence and caused the wake flow to oscillate in the stream direction. This oscillation induced a significant fluctuating drag on the cylinder. Consequently, the fluctuating drag far exceeded the fluctuating lift and the wake velocity was found to correlate well with the drag and not with the lift. This correlation remained intact along the span of the cylinder. Finally, the rms fluctuating lift and drag forces were found to vary along the cylinder span, with the lift increasing and the drag decreasing as the base of the cylinder is approached; thus suggesting that a submerged two-dimensional region exists near the base of the cylinder.List of symbols a span of active element on cylinder - C _D local rms drag coefficient, - C _L local rms lift coefficient, - C _D local mean drag coefficient - (C _D ) _2D spanwise-averaged mean drag coefficient for two dimensional cylinder - d diameter of cylinder (= 10.2 cm) - D fluctuating component of instantaneous drag - D local rms of fluctuating drag - E _D power spectrum of fluctuating drag, defined as - E _L power spectrum of fluctuating lift, defined as - E _U power spectrum of fluctuating streamwise velocity, defined as - f _L dominant frequency of lift spectrum - f _D dominant frequency of drag spectrum - f _u dominant frequency of velocity spectrum - h span of cylinder - H height of test section (= 30.5 cm) - L fluctuating component of instantaneous lift - L local rms of fluctuating lift - R _Du () cross-correlation function of streamwise velocity and local drag - R _Lu () cross-correlation function of streamwise velocity and local lift - Re Reynolds number, - S _L Strouhal number based on f _L , - S _D Strouhal number based on f _D , - S _U Strouhal number based on f _u , - t time - u fluctuating component of instantaneous streamwise velocity - u rms of streamwise fluctuating velocity - u rms of streamwise fluctuating velocity upstream of cylinder - U mean streamwise velocity - U mean stream velocity upstream of cylinder - x streamwise distance measured from axis of cylinder - y transverse distance measured from axis of cylinder - z spanwise distance measured from floor of test section - v kinematic viscosity of air - density of air - time lag in cross-correlation function - _D normalized spectrum of fluctuating drag - _L normalized spectrum of fluctuating lift - _U normalized spectrum of fluctuating streamwise velocity     

Direct analysis of herbal powders by pipette-tip electrospray ionization mass spectrometry

Conventional electrospray ionization mass spectrometry (ESI-MS) is widely used for analysis of solution samples. The development of solid-substrate ESI-MS allows direct ionization analysis of bulky solid samples. In this study, we developed pipette-tip ESI-MS, a technique that combines pipette tips with syringe and syringe pump, for direct analysis of herbal powders, another common form of samples. We demonstrated that various herbal powder samples, including herbal medicines and food samples, could be readily online extracted and analyzed using this technique. Various powder samples, such as Rhizoma coptidis, lotus plumule, great burdock achene, black pepper, Panax ginseng, roasted coffee beans, Fructus Schisandrae Chinensis and Fructus Schisandrae Sphenantherae, were analyzed using pipette-tip ESI-MS and quality mass spectra with stable and durable signals could be obtained. Both positive and negative ion modes were attempted and various compounds including amino acids, oligosaccharides, glycosides, alkaloids, organic acids, ginosensides, flavonoids and lignans could be detected. Principal component analysis (PCA) based on the acquired mass spectra allowed rapid differentiation of closely related herbal species.     

Electrospray ionization with aluminum foil: A versatile mass spectrometric technique

In this study, we developed a novel electrospray ionization (ESI) technique based on household aluminum foil (Al foil) and demonstated the desirable features and applications of this technique. Al foil can be readily cut and folded into desired configuration for effective ionization and for holding sample solution in bulk to allowing acquisition of durable ion signals. The present technique was demonstrated to be applicable in analysis of a wide variety of samples, ranging from pure chemical and biological compounds, e.g., organic compounds and proteins, to complex samples in liquid, semi-solid, and solid states, e.g., beverages, skincare cream, and herbal medicines. The inert, hydrophobic and impermeable surface of Al foil allows convenient and effective on-target extraction of solid samples and on-target sample clean-up, i.e., removal of salts and detergents from proteins and peptides, extending ESI device from usually only for sample loading and ionization to including sample processing. Moreover, Al foil is an excellent heat-conductor and highly heat-tolerant, permitting direct monitoring of thermal reactions, e.g., thermal denaturation of proteins. Overall, the present study showed that Al-foil ESI could be an economical and versatile method that allows a wide range of applications.     

When to rebuild or when to adjust scorecards

Data-based scorecards, such as those used in credit scoring, age with time and need to be rebuilt or readjusted. Unlike the huge literature on modelling the replacement and maintenance of equipment there have been hardly any models that deal with this problem for scorecards. This paper identifies an effective way of describing the predictive ability of the scorecard and from this describes a simple model for how its predictive ability will develop. Using a dynamic programming approach one is then able to find when it is optimal to rebuild and when to readjust a scorecard. Failing to readjust or rebuild a scorecard when they aged was one of the defects in credit scoring identified in the investigations into the sub-prime mortgage crisis.     

Photoinduced superoxide radical anion and singlet oxygen generation in the presence of novel selenadiazoloquinolones (an EPR Study)

Novel 7‐substituted 6‐oxo‐6,9‐dihydro[1,2,5]selenadiazolo[3,4‐h]quinoline ( SeQ(1–6) ) and 8‐substituted 9‐oxo‐6,9‐dihydro[1,2,5]selenadiazolo[3,4‐f ]quinoline derivatives ( SeQN(1–5) ) with R₇, R₈ = H, COOC₂H₅, COOCH₃, COOH, COCH₃ or CN were synthesized and their spectral characteristics were obtained by UV/Vis spectroscopy. Ultraviolet A photoexcitation of the selenadiazoloquinolones in dimethylsulfoxide or acetonitrile resulted in the formation of paramagnetic species coupled with molecular oxygen activation generating the superoxide radical anion or singlet oxygen, evidenced by electron paramagnetic resonance spectroscopy. The cytotoxic/photocytotoxic impact of selenadiazoloquinolones on murine and human cancer cell lines was demonstrated using the derivative SeQ5 (with R₇ = COCH₃).     

The synthesis of piperidine nucleoside analogs—a comparison of several methods to access the introduction of nucleobases

This work deals with the synthesis of piperidine and hydroxypiperidine analogs of nucleosides. Starting from commercially available 3-hydroxypiperidine, proline or 4-hydroxyproline, a series of piperidine derivatives of both purine and pyrimidine nucleobases was prepared. Various methods of nucleobase attachment were evaluated. The prepared compounds were tested for cytostatic, antibacterial, and antiviral properties but no significant activity was found.