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This paper describes a tool for intersecting context-free grammars. Since this problem is undecidable the tool follows a refinement-based approach and implements a novel refinement which is complete for regularly separable grammars. We show its effectiveness for safety verification of recursive multi-threaded programs.
Multiband far-infrared (20-155 microns) observations of the large H II region/molecular cloud complex NGC 6334 are presented. The observations were performed simultaneously in four bands with effective wavelengths 21, 42, 71, and 134 microns. Eight far-infrared sources were detected which cover the range from sources with little of no continuum radio emission to well-developed H II regions. Maps of dust temperature and far-infrared optical depth of the complex are presented which reveal large-scale variations in the color temperature and optical depth. Star formation in the complex is discussed and it is concluded that a Rayleigh-Taylor instability generated by the gravitational attraction of the galactic plane can explain the regular separation of the far-IR sources.
A low-order panel code, VSAERO, was used to predict the aerodynamic characteristics of helicopter hub fairings. Since the simulation of this kind of bluff body by VSAERO was not documented before, the VSAERO solutions were correlated with experimental data to establish their validity. The validation process revealed that simulation of the aerodynamic environment around a hub fairing was sensitive to several modeling parameters. Some of these parameters are body and wake panels arrangement, streamwise and spanwise separation location, and the most prominent one-the wake modeling. Three wake models were used: regular wake, separated wake, and jet model. The regular wake is a wake with negligible thickness (thin wake). It is represented by a single vortex sheet. The separated wake and the jet model in the present application are wakes with finite thickness (thick wake). They consist of a vortex sheet enclosing a region of low-energy flow. The results obtained with the reqular wake were marginally acceptable for sharp-edged hub fairings. For all other cases under consideration, the jet model results correlated slightly better. The separated wake, which seemed to be the most appropriate model, caused the solution to diverge. While the regular wake was straight-forward to apply in simulations, the jet model was not. It requires the user to provide information about the doublet strength gradient on wake panels by guessing the efflux velocities at the wake shedding location. In summary, VSAERO neither predicts accurately the aerodynamic characteristics of helicopter hub fairings nor was cost effective.
Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.
Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for a number of separated flows and the accuracy of the method is verified.
A concise mathematical framework is constructed to study the topology of steady 3-D separated flows of an incompressible, or a compressible viscous fluid. Flow separation is defined by the existence of a stream surface which intersects with the body surface. The line of separation is itself a skin-friction line. Flow separation is classified as being either regular or singular, depending respectively on whether the line of separation contains only a finite number of singular points or is a singular line of the skin-friction field. The special cases of 2-D and axisymmetric flow separation are shown to be of singular type. In regular separation it is shown that a line of separation originates from a saddle point of separation of the skin-friction field and ends at nodal points of separation. Unsteady flow separation is defined relative to a coordinate system fixed to the body surface. It is shown that separation of an unsteady 3-D incompressible viscous flow at time t, when viewed from such a frame of reference, is topologically the same as that of the fictitious steady flow obtained by freezing the unsteady flow at the instant t. Examples are given showing effects of various forms of flow unsteadiness on flow separation.
Despite the obvious notion that the presence of hail or graupel is a good indication of convection, the model results show this does not provide an objective benchmark partly due to the unrealistic presence of small amounts of hail or graupel throughout the anvil in the model but mainly because of the significant amounts of hail or graupel, especially in the tropical TOGA COARE simulation, in the transition zone. Without use of a "transition" category, it is open to debate as how this region should best be defined, as stratiform or as convective. So, the presence of significant hail or graupel contents in this zone significantly degrades its use an objective benchmark for convection. The separation algorithm comparison was done in the context of a cloud-resolving model. These models are widely used and serve a variety of purposes especially with regard to retrieving information that cannot be directly measured by providing synthetic data sets that are consistent and complete. Separation algorithms are regularly applied in these models. However, as with any modeling system, these types 'of models are constantly being improved to overcome any known deficiencies and make them more accurate representations of observed systems. The presence of hail and graupel in the anvil and the bias towards heavy rainfall rates are two such examples of areas that need improvement. Since, both of these can effect the perceived performance of the separation algorithms, the Lang et al. (2003) study did not want to overstate the relative performance of any specific algorithms.
Numerical solutions of the laminar, incompressible boundary-layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified, and the pressure is deduced from the solution. A stream function/vorticity formulation of the boundary-layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite-difference equations, in which the flow direction is taken into account, are obtained by a successive column iteration scheme. Results are compared with Klineberg and Steger's (1974) separated boundary-layer calculations, and with Briley's (1971) solution of the Navier-Stokes equations for a separated region.
Numerical solutions of the laminar, incompressible boundary layer equations are presented for flows involving separation and reattachment. Regular solutions are obtained with an inverse approach in which either the displacement thickness or the skin friction is specified; the pressure is deduced from the solution. A vorticity-stream-function formulation of the boundary layer equations is used to eliminate the unknown pressure. Solutions of the resulting finite difference equations, in which the flow direction is taken into account, are obtained by several global iteration schemes which are stable and have unconditional diagonal dominance. Results are compared with Klineberg and Steger's separated boundary layer calculations, and with Briley's solution of Navier-Stokes equations for a separated region. In addition, an approximate technique is presented in which the streamwise convection of vorticity is set equal to zero in the reversed flow region; such a technique results in a quick forward marching procedure for separated flows.
Results are presented for the vibration response of a spacecraft shroud to a range of in-flight fluctuation pressures. An Atlas-Agena 15 degree cone-cylinder shroud was analyzed during the present study, and three critical flight Mach numbers were considered. At transonic Mach numbers, the aerodynamic flow over the shroud is complex, involving zones of regular attached flow, separated flow, shock wave oscillation, and modified attached flows induced by local thickening of the boundary layer. The overall shroud vibration levels for a particular Mach number were determined by initially calculating the mean square acceleration levels induced by the fluctuating pressures distributed over an individual zone, and then summing mean square acceleration levels in one-third octave bands over all zones.
An incompressible, two-dimensional, thin separation bubble is treated as an obstacle to the potential flow that perturbs and adjusts the original inviscid flow. The knowledge of the perturbed velocity allows a complete flow description in vicinity of the bubble. Suitable differential equations and boundary conditions are developed for three distinct regions, namely, a potential region, a parabolic viscous layer, and a viscous, slow recirculating region. With modified boundary conditions the boundary layer equations are regularly integrated through the separation region. Conclusions are also made on the wall stress and the position of zero velocity and zero vorticity lines.
Data from X-ray diffraction studies of the poly(carbon monofluoride) with empirical formula CF(1.09-1.15) are reported, and possible intercalation arrangements for the substance are discussed. The data do not conform to true hexagonal symmetry, indicating that the carbon atoms are not coplanar. Each bond angle of carbon is 118.8 deg, and the carbon-carbon distance is 1.47 A. The interlayer distance is 5.76 A. A total absence of (hkl) reflections in the X-ray pattern shows that the separate CF layers are not regularly arranged with respect to one another.
Power spectra of magnetic pulsations observed at synchronous orbit by the ATS 6 satellite often show several spectral peaks simultaneously. Such pulsations, called harmonic events because of the nearly constant separation between successive peaks, are continuously observed in the dayside in the Pc 3-4 frequency range (6.6-100 mHz). The harmonic events are seen clearly only in the east-west magnetic field component. The spectral peaks are regularly spaced with a typical minimum separation of 14 mHz in the morning gradually decreasing to 10 mHz in the afternoon. In the dynamic spectra of harmonic events, the fundamental mode is usually absent. In addition, the relative amplitudes of the higher harmonics depend on the magnetic latitude. These observed features can be explained by a standing Alfven wave consisting of many discrete harmonic frequencies. A statistical analysis of power spectra demonstrates that at least 10-30% of Pc 3 pulsations can be classified as harmonic events. For a selected event on August 7, 1975, the plasma mass density at the synchronous orbit is estimated to be 3-8 hydrogen mass/cu cm.
This paper describes efforts to locate the prewetting line in a binary liquid system (isopropanol-perfluoromethylcyclohexane) at the vapor-liquid interface. Tight upper bounds were placed on the temperature separation (0.2 K) between the prewetting line and the line of bulk liquid phase separation. The prewetting line in systems at equilibrium was not detected. Experimental signatures indicative of the prewetting line occurred only in nonequilibrium situations. Several theories predict that the adsorption of one of the components (the fluorocarbon, in this case) at the liquid-vapor interface should increase abruptly, at a temperature sightly above the temperature at which the mixture separates into two liquid phases. A regular solution calculation indicates that this prewetting line should have been easily detectable with the instruments used in this experiment. Significant features of the experiment are: (1) low-gradient thermostatting, (2) in situ stirring, (3) precision ellipsometry from the vapor-liquid interface, (4) high resolution differential index of refraction measurements using a novel cell design, and (5) computer control.
The radars utilized are meteor (2), medium frequency (2) and the new low frequency (1) systems: analysis techniques were exhaustively studied internally and comparatively and are not thought to affect the results. Emphasis is placed upon the new height-time contours of 24-, 12-h tidal amplitudes and phases, which best display height and seasonal structures; where possible high resolution (10 d) is used (Saskatoon), but all stations provide monthly mean resolution. At these latitudes the diurnal tide is generally smaller than the semidiurnal, and displays more variability. However, there is a tendency for vertical wavelengths and amplitudes to be larger during summer months. On occasions in winter and fall, wavelengths may be less than 50 km. The dominant semidiurnal tide shows significant regular season structure; wavelengths are generally small (about 50 km) in winter, large in summer (equal to or greater than 100 km), and these states are separated by rapid equinoctial transitions. There is some evidence for less regularity toward 40 deg. Coupling with mean winds is apparent. Data from earlier ATMAP campaigns are mentioned, and reasons for their inadequacies presented.
Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.
Although unsteady, high-Reynolds number, laminar boundary layers have conventionally been studied in terms of Eulerian coordinates, a Lagrangian approach may have significant analytical and computational advantages. In Lagrangian coordinates the classical boundary layer equations decouple into a momentum equation for the motion parallel to the boundary, and a hyperbolic continuity equation (essentially a conserved Jacobian) for the motion normal to the boundary. The momentum equations, plus the energy equation if the flow is compressible, can be solved independently of the continuity equation. Unsteady separation occurs when the continuity equation becomes singular as a result of touching characteristics, the condition for which can be expressed in terms of the solution of the momentum equations. The solutions to the momentum and energy equations remain regular. Asymptotic structures for a number of unsteady 3-D separating flows follow and depend on the symmetry properties of the flow. In the absence of any symmetry, the singularity structure just prior to separation is found to be quasi 2-D with a displacement thickness in the form of a crescent shaped ridge. Physically the singularities can be understood in terms of the behavior of a fluid element inside the boundary layer which contracts in a direction parallel to the boundary and expands normal to it, thus forcing the fluid above it to be ejected from the boundary layer.
The Moderate Resolution Imaging Spectroradiometer (MODIS) instruments on-board the Aqua and Terra space-craft have provided valuable science data for the last 18 and 20 years, respectively. Each instrument is equipped with 36 spectral bands, 20 of which are reflective solar bands (RSBs). These bands cover a wavelength range of 0.4 – 2.2μm and are calibrated on-orbit using several on-board calibrators (OBCs), such as a solar diffuser (SD)and a solar diffuser stability monitor (SDSM), along with regularly-scheduled lunar observations through the space view (SV) port. The gain (1/m1) and response-verses-scan angle (RVS) are updated on a near-monthly basis and act as the primary look-up-tables (LUTs) for the RSB calibration. A set of separate uncertainty LUTs for each of the RSBs are also delivered regularly and incorporated into the Level 1B (L1B) product to generate a pixel-level Uncertainty Index (UI). In addition to the gain, RVS and uncertainty, there are several other LUTs associated with the reflective bands that are either updated less frequently or remain static. The accuracy of both the forward-predicted and historical RSB LUTs, which are derived by the MODIS Characterization Sup-port Team (MCST), is important in maintaining the quality and accuracy of the L1B and science products.To ensure a timely and accurate LUT update, MCST has established a comprehensive set of procedures. This paper provides an overview of the calibration process, along with the current LUT delivery process for the RSB sin Collection 6 (C6) and Collection 6.1 (C6.1). Improvements to be implemented in future collections are also discussed.