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We describe a method for calculating directly the mean integrated intensity in an inhomogeneous Rayleigh scattering atmosphere using a combined variational and iterative technique. This method is particularly useful for computing dissociation rates in aeronomical problems. Simple semi-analytic expressions are derived.
Crop yield forecasting is performed monthly during the growing season by the United States Department of Agriculture’s National Agricultural Statistics Service. The underpinnings are long-established probability surveys reliant on farmers’ feedback in parallel with biophysical measurements. Over the last decade though, satellite imagery from the Moderate Resolution Imaging Spectroradiometer (MODIS) has been used to corroborate the survey information. This is facilitated through the Global Inventory Modeling and Mapping Studies/Global Agricultural Monitoring system, which provides open access to pertinent real-time normalized difference vegetation index (NDVI) data. Hence, two relatively straightforward MODIS-based modeling methods are employed operationally. The first model constitutes mid-season timing based on the maximum peak NDVI value, while the second is reflective of late-season timing by integrating accumulated NDVI over a threshold value. Corn model results nationally show the peak NDVI method provides a R^(2) of 0.88 and a coefficient of variation (CV) of 3.5%. The accumulated method, using an optimally derived 0.58 NDVI threshold, improves the performance to 0.93 and 2.7%, respectively. Both these models outperform simple trend analysis, which is 0.48 and 7.4%, correspondingly. For soybeans the R^(2) results of the peak NDVI model are 0.62, and 0.73 for the accumulated using a 0.56 threshold. CVs are 6.8% and 5.7%, respectively. Spring wheat’s R2performance with the accumulated NDVI model is 0.60 but just 0.40 with peak NDVI. The soybean and spring wheat models perform similarly to trend analysis. Winter wheat and upland cotton show poor model performance, regardless of method. Ultimately, corn yield forecasting derived from MODIS imagery is robust, and there are circumstances when forecasts for soybeans and spring wheat have merit too.
The time dependent solution of the magnetic field is introduced as a method for accounting for the variation, in time, of the machine parameters in predicting and analyzing the performance of the electrical machines. The method of time dependent finite element was used in combination with an also time dependent construction of a grid for the air gap region. The Maxwell stress tensor was used to calculate the airgap torque from the magnetic vector potential distribution. Incremental inductances were defined and calculated as functions of time, depending on eddy currents and saturation. The currents in all the machine circuits were calculated in the time domain based on these inductances, which were continuously updated. The method was applied to a chopper controlled DC series motor used for electric vehicle drive, and to a salient pole sychronous motor with damper bars. Simulation results were compared to experimentally obtained ones.
A method is described for interface shape control of Hg(1-x)Cd(x)Te alloys during Bridgman-type crystal growth. The authors have used this method for several years to obtain the flat or convex interface shapes required for simultaneously reducing radial compositional variations and crystal defects. The method turns to advantage the thick-walled, fused-silica ampules required for growing these alloys. A proper combination of furnace geometry (two isothermal zones separated by a thin barrier), upper- and lower-zone temperatures, and growth rate is required. Examples of results are reported.
The relativistic fluid equations may be completed in two physically distinct methods. One method assumes the mass, rho, (or particle number) is conserved, while the other method assumes an equation of state of the form P = P(rho). A variational principle for the mass conservation method both with and without an intrinsic spin for the fluid was constructed earlier (Ray and Smalley, 1982 and 1983). A variational principle for the fluid described by an equation of state both with and without spin is formulated. In all cases the variational principle is set in the Einstein-Cartan metric-torsion U4 geometry. The results for general relativity follow as a special case.
The performance of an optical system (for example, a telescope) is limited by the misalignments and manufacturing imperfections of the optical elements in the system. The impact of these misalignments and imperfections can be quantified by the phase variations imparted on light traveling through the system. Phase retrieval is a methodology for determining these variations. Phase retrieval uses images taken with the optical system and using a light source of known shape and characteristics. Unlike interferometric methods, which require an optical reference for comparison, and unlike Shack-Hartmann wavefront sensors that require special optical hardware at the optical system's exit pupil, phase retrieval is an in situ, image-based method for determining the phase variations of light at the system s exit pupil. Phase retrieval can be used both as an optical metrology tool (during fabrication of optical surfaces and assembly of optical systems) and as a sensor used in active, closed-loop control of an optical system, to optimize performance. One class of phase-retrieval algorithms is the iterative transform algorithm (ITA). ITAs estimate the phase variations by iteratively enforcing known constraints in the exit pupil and at the detector, determined from modeled or measured data. The Variable Sampling Mapping (VSM) technique is a new method for enforcing these constraints in ITAs. VSM is an open framework for addressing a wide range of issues that have previously been considered detrimental to high-accuracy phase retrieval, including undersampled images, broadband illumination, images taken at or near best focus, chromatic aberrations, jitter or vibration of the optical system or detector, and dead or noisy detector pixels. The VSM is a model-to-data mapping procedure. In VSM, fully sampled electric fields at multiple wavelengths are modeled inside the phase-retrieval algorithm, and then these fields are mapped to intensities on the light detector, using the properties of the detector and optical system, for comparison with measured data. Ultimately, this model-to-data mapping procedure enables a more robust and accurate way of incorporating the exit-pupil and image detector constraints, which are fundamental to the general class of ITA phase retrieval algorithms.
We present a novel method that identifies the contributions of thermodynamic phase shifts and processes governing supercooled liquid and ice clouds to cloud optical depth variations with temperature using MODIS observations. Our findings suggest that thermodynamic phase shifts outweigh the net influence of processes governing supercooled liquid and ice clouds in causing increases in mid-latitudinal cold cloud optical depth with temperature. Cloud regime analysis suggests that dynamical conditions appear to have less influence on the contribution of thermodynamic phase shifts to cloud optical depth variations with temperature. Thermodynamic phase shifts also contribute more to increases in cloud optical depth during colder seasons due to the enhanced optical thickness contrast between liquid and ice clouds. The results of this study highlight the importance of thermodynamic phase shifts in explaining cold cloud optical depth increases with temperature in the current climate and may elucidate their role in the cloud optical depth feedback.
An analysis is presented on a method for varying rocket thrust by varying the bulk density of the propellants. This density variation was accomplished by uniformly dispersing an inert, insoluble gas in the liquid propellants. Only qualitative agreement with theory was obtained from preliminary experiments with a 1000-pound-thrust ammonia - nitric acid rocket engine; the required experimental gas-flow rates were two to six times greater than those predicted by theory. It was demonstrated, however, that this method of rocket-thrust variation is feasible.
Attitude control for earth satellite in elliptic orbit, linearization in attitude control, and computation of optimal controls by method based on second variations
Sinusoidal pulse test method to account for variation of shock spectra with damping
Relation between optimal control problem and Liapunov functions, and calculus of variations and maximum principle methods of solving synthesis problems
Spaced receiver method for measuring height variations in scintillating radio signals from artificial satellites
Peano-Baker method for integration of variational equations to produce partial derivatives used in satellite trajectory estimation
A numerical method is presented for calculating the incompressible boundary-induced interference in wind tunnels of rectangular cross section with slotted or perforated walls. The method includes a wall representation which is capable of satisfying a generalized homogeneous boundary condition including the effects of viscosity within the slots. The effects of viscosity in the slots are found to be very significant. The method allows for a variation in the boundary conditions along the tunnel walls. The model can be any configuration and can be located anywhere in the test section. The interference can be computed at any point in the test section.
Most of the data collected under conditions of high temperature and pressure have been determined using a thick-walled bomb of carefully measured and fixed volume which is externally heated by an electric furnace or a thermostatically controlled bath. There are numerous variations on the basic method depending on the pressure-temperature range of interest, and the particular gas or gas mixture being studied. The construction and calibration of the apparatus is discussed, giving attention to the pressure vessel, the volume of the bomb, the measurement of pressure, the control and measurement of temperature, and the measurement of the amount and composition of gas in the bomb.
An interesting variation on the familiar method of determining the earth's equatorial radius a sub e, from a knowledge of the earth's equatorial gravity is suggested. The value of equatorial radius thus found is 6378,142 + or - 5 meters. The associated parameters are GM = 3,986008 + or - 4 X 1014 cu cm/sec/sec which includes the relative mass of atmosphere approximately 0.000001 x GM, the equatorial gravity gamma sub e = 978,030.9 milligals (constrained in this solution by the Potsdam Correction of 13.67 milligals as the Potsdam Correction is more directly, or less indirectly, measurable than the equatorial gravity) and an ellipsoidal flattening of f = 1/298.255.
The fluidized bed technique was used to measure the relative thermal fatigue resistance of twenty-one superalloys. Among the thirty-six variations of composition, solidification method, and surface protection the cycles to cracking differed by two to three orders of magnitude. Some alloys suffered serious weight losses and oxidation. Thermal fatigue data, oxidation, and dimensional changes are reported. The types of superalloys are identified.
The fluidized bed technique was used to measure the relative thermal fatigue resistance of 21 superalloys: B1900, B1900 DID, IN-100, MAR-M 200, Udimet 700 wrought and cast, NX-188, WAZ-20, TAZ-8A, M22, IN 713C, IN 738, IN 162, MAR-M 509, Rene 80, RBH, NASA VI A, TD-NiCr, MAR-M 302, WI-52, and X-40. IN-100, MAR-M 200, NX-188, WAZ-20 and TAZ-8A were also tested in the directionally solidified form. B1900, B1900 DID, IN-100, MAR-M200, Udimet 700, NX-188, WAZ-20 and TAZ-8A were tested with surface protection. Among the 36 variations of composition, solidification method, and surface protection the cycles to cracking differed by 2 to 3 orders of magnitude. Some alloys suffered serious weight losses and oxidation. Previous fluidized bed thermal fatigue data on some of these alloys were reported in N71-10027. Thermal fatigue data, oxidation, and dimensional changes are reported in N73-30507. Metallographic and hardness data are given in this report.