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Kravchuk orthogonal functions - Kravchuk polynomials multiplied by the square root of the weight function - simplify the inversion algorithm for the analysis of discrete, finite signals in harmonic oscillator components. They can be regarded as the best approximation set. As the number of sampling points increases, the Kravchuk expansion becomes the standard oscillator expansion.
An analysis has been made of the characteristics of several cooling cycles suitable for cockpit cooling of supersonic aircraft. All the cycles considered utilize the difference between dynamic and ambient static pressure to actuate the cooling system and require no additional power source. The results of the study indicate that as flight speeds become greater, increasingly complex systems are required to reduce the altitudes above approximately 35,000 feet, a system composed of an externally loaded expansion turbine in conjunction with a supersonic diffuser would maintain tolerable ventilating air temperature, at least up to a flight Mach number of 2. The most complex system considered,composed of compressor, intercooler, and expansion turbine with the intercooler cooling air decreased in temperature by expansion through an auxiliary turbine is capable of maintaining a ventilation air temperature less than ambient temperature up to a flight Mach number of 3.7.
The skin temperature and surface pressure were measured on a large-scale, highly polished nose having a relatively sharp-tipped 100 deg total-angle cone followed by a conical flare section of 10 deg half-angle. The measurements were obtained in flight from a rocket-propelled model up to a peak Mach number of 4.08 and a peak Reynolds number of 22 x 10(exp 6) per foot. Temperature distributions indicated that the heating on the forward 3.5 inches of the 100 deg cone was lower than the heating on the rearward portion. Likewise, measured temperatures on the flare portion of the test nose were generally lower than the temperatures on the 100 deg cone portion. The data indicated that the local Reynolds numbers of transition, based on calculated boundary-layer momentum thicknesses, ranged from 530 to 940 for a Mach number range from 2.72 to 3.75. Comparison of measured cone pressures with theory for a sharp cone showed that theory overestimates the cone pressures. Pressure measurements on the flare portion of the nose showed that in the lower speed range the flow expands below atmospheric pressure in going from the cone to the flare; however, as the speed increased, the expansion diminished and for speeds greater than a Mach number of approximately 3.0 the flare pressure coefficients were at or near a value of zero.
An all-solid-state diffusion bonding process that exploits the eutectoid reaction between molybdenum and titanium has been developed for use in fabricating thermoelectric devices based on skutterudite compounds. In essence, the process is one of heating a flat piece of pure titanium in contact with a flat piece of pure molybdenum to a temperature of about 700 C while pushing the pieces together with a slight pressure [a few psi (of the order of 10 kPa)]. The process exploits the energy of mixing of these two metals to form a strong bond between them. These two metals were selected partly because the bonds formed between them are free of brittle intermetallic phases and are mechanically and chemically stable at high temperatures. The process is a solution of the problem of bonding hot-side metallic interconnections (denoted hot shoes in thermoelectric jargon) to titanium-terminated skutterudite n and p legs during the course of fabrication of a unicouple, which is the basic unit cell of a thermoelectric device (see figure). The hot-side operating temperature required for a skutterudite thermoelectric device is 700 C. This temperature precludes the use of brazing to attach the hot shoe; because brazing compounds melt at lower temperatures, the hot shoe would become detached during operation. Moreover, the decomposition temperature of one of the skutterudite compounds is 762 C; this places an upper limit on the temperature used in bonding the hot shoe. Molybdenum was selected as the interconnection metal because the eutectoid reaction between it and the titanium at the ends of the p and n legs has characteristics that are well suited for this application. In addition to being suitable for use in the present bonding process, molybdenum has high electrical and thermal conductivity and excellent thermal stability - characteristics that are desired for hot shoes of thermoelectric devices. The process takes advantage of the chemical potential energy of mixing between molybdenum and titanium. These metals have a strong affinity for each other. They are almost completely soluble in each other and remain in the solid state at temperatures above the eutectoid temperature of 695 C. As a result, bonds formed by interdiffusion of molybdenum and titanium are mechanically stable at and well above the original bonding temperature of about 700 C. Inasmuch as the bonds are made at approximately the operating temperature, thermomechanical stresses associated with differences in thermal expansion are minimized.
Sustainable land management, including protected areas, is integral to conserving tropical ecosystems and reducing carbon emissions in the Brazilian Amazon. In disturbed Amazon landscapes fire is commonly used to clear land or old fields for agriculture or pastureland. Human-set fires are the most common driver of deforestation and carbon emissions in Amazonia. Evidence suggests that indigenous groups have also used fire for land management since Pre-Columbian times. However, when used unsustainably, fires in this biome can result in degradation of forest ecosystems, decreased ability to store carbon, and health impacts resulting from smoke and particulate matter. Due to the uptick in fire occurrences in 2019, more restrictions on fire use were implemented in 2019 and 2020. Presidential decrees 9.992/2019 and 10.424/2020 banned fire use completely for periods of 60 and 120 days respectively, except by indigenous communities or authorities. Despite these bans, fire use remained high in both years. In the state of Mato Grosso, agricultural activity and expansion influences the anthropogenic fire regime. Indigenous and protected areas cover approximately 25% of its land area.
The asymptotic behavior, for large time, of the quasi-linear diabatic solutions and their local approximations is considered. A time averaging procedure is introduced which yields the averages of these solutions over time intervals which contain only large time values. A discussion of the quasi-linear diabatic solutions which is limited to those solutions that are bounded from below as functions of time is given. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity the time averaged quasi-linear diabatic solutions must approach isotropy (mu-independence). The first derivative with respect to mu of these solutions is also considered. This discussion is limited to first derivatives which are bounded functions of time. It is shown that as the upper limit of the time averaging interval is allowed to approach infinity, the time averaged first derivative must approach zero everywhere in mu except at mu = 0 where it must approach a large value which is calculated. The impact of this large derivative on the quasi-linear expansion scheme is discussed. An H-theorem for the first local approximation to the quasi-linear diabatic solutions is constructed. Without time averaging, the H-theorem is used to determine sufficient conditions for the first local approximate solutions to asymptote, with increasing time, to exactly the same final state which the time averaged quasi-linear diabatic solutions must approach as discussed above.
A first-order optical potential is used to calculate the total and absorption cross sections for nucleus-nucleus scattering. The differential cross section is calculated by using a partial-wave expansion of the Lippmann-Schwinger equation in momentum space. The results are compared with solutions in the Eikonal approximation for the equivalent potential and with experimental data in the energy range from 25A to 1000A MeV.
This report is intended for the demonstration of function approximation concepts and their applicability in reliability analysis and design. Particularly, approximations in the calculation of the safety index, failure probability and structural optimization (modification of design variables) are developed. With this scope in mind, extensive details on probability theory are avoided. Definitions relevant to the stated objectives have been taken from standard text books. The idea of function approximations is to minimize the repetitive use of computationally intensive calculations by replacing them with simpler closed-form equations, which could be nonlinear. Typically, the approximations provide good accuracy around the points where they are constructed, and they need to be periodically updated to extend their utility. There are approximations in calculating the failure probability of a limit state function. The first one, which is most commonly discussed, is how the limit state is approximated at the design point. Most of the time this could be a first-order Taylor series expansion, also known as the First Order Reliability Method (FORM), or a second-order Taylor series expansion (paraboloid), also known as the Second Order Reliability Method (SORM). From the computational procedure point of view, this step comes after the design point identification; however, the order of approximation for the probability of failure calculation is discussed first, and it is denoted by either FORM or SORM. The other approximation of interest is how the design point, or the most probable failure point (MPP), is identified. For iteratively finding this point, again the limit state is approximated. The accuracy and efficiency of the approximations make the search process quite practical for analysis intensive approaches such as the finite element methods; therefore, the crux of this research is to develop excellent approximations for MPP identification and also different approximations including the higher-order reliability methods (HORM) for representing the failure surface. This report is divided into several parts to emphasize different segments of the structural reliability analysis and design. Broadly, it consists of mathematical foundations, methods and applications. Chapter I discusses the fundamental definitions of the probability theory, which are mostly available in standard text books. Probability density function descriptions relevant to this work are addressed. In Chapter 2, the concept and utility of function approximation are discussed for a general application in engineering analysis. Various forms of function representations and the latest developments in nonlinear adaptive approximations are presented with comparison studies. Research work accomplished in reliability analysis is presented in Chapter 3. First, the definition of safety index and most probable point of failure are introduced. Efficient ways of computing the safety index with a fewer number of iterations is emphasized. In chapter 4, the probability of failure prediction is presented using first-order, second-order and higher-order methods. System reliability methods are discussed in chapter 5. Chapter 6 presents optimization techniques for the modification and redistribution of structural sizes for improving the structural reliability. The report also contains several appendices on probability parameters.
Consideration of dissipative processes in anisotropic homogeneous world models, showing that dissipation reduces the anisotropy. The viscosity approximation and its range of applicability is discussed. Examples are presented which have been calculated by the use of a simple approximation to the collision-time method, using the cross section appropriate to weak interaction neutrino scattering. It is found that such dissipation is quite effective except for one particular cosmological model which is axisymmetric and in which the entire expansion of the model is taken up by expansion along the axis. A detailed multicomponent model is developed for dissipative processes in Euclidean homogeneous cosmological models. These processes involve neutrinos which might have long mean free times in interaction with other constituents which are thermalized by electromagnetic interactions, and whose weak interactions produce thermal neutrinos.
We consider the solution of scattering problems for the wave equation using approximate boundary conditions at artificial boundaries. These conditions are explicitly viewed as approximations to an exact boundary condition satisfied by the solution on the unbounded domain. We study the short and long term behavior of the error. It is provided that, in two space dimensions, no local in time, constant coefficient boundary operator can lead to accurate results uniformly in time for the class of problems we consider. A variable coefficient operator is developed which attains better accuracy (uniformly in time) than is possible with constant coefficient approximations. The theory is illustrated by numerical examples. We also analyze the proposed boundary conditions using energy methods, leading to asymptotically correct error bounds.
The recent development of a high-resolution submillimeter-wave heterodyne radiometer has made possible the first measurements of H2O molecule rotational line excitation temperatures and detailed profiles in supersonic flow. Absorption signals were measured across the flow for the 2/11/ from 2//02/ (752 GHz) para-H2O rotational transition against a hot background. These signals decrease downstream owing to the volume expansion of the gas away from the sonic nozle exit in the high-vacuum chamber. Radiative transfer calculations based on the large-velocity-gradient approximation and multilevel statistical equilibrium agree with these results and with the measured spectral line shapes. The data reveal nearly isentropic gas expansion and cooling. These studies have shown that submillimeter-wave heterodyne radiometry can be useful for remote sensing of supersonic flow with low mass flux, provided the signal transmission is through a dry or thin atmosphere.
A primary factor governing hypersonic flowfield characteristics of blunt vehicles entering planetary atmospheres is the normal shock density ratio. Hence, a means of duplicating or simulating the high density ratios experienced during planetary entry is needed. One facility having the capability of generating a range of hypersonic-hypervelocity flow conditions in arbitrary test gases is the expansion tube. Preliminary shock shape results obtained in the Langley 6-in. expansion tube at hypersonic conditions are presented. Normal shock density ratios from approximately 4 to 19 were generated using helium, air, and CO2 test gases at freestream velocities from 5 to 7 km/sec. Test models were a flat-faced cylinder and the Viking aeroshell.
The extended interior penalty function formulation is implemented. A rational method for determining the transition between the interior and extended parts is set forth. The formulation includes a straightforward method for avoiding design points with some negative components, which are physically meaningless in structural analysis. The technique, when extended to problems involving parametric constraints, can facilitate closed form integration of the penalty terms over the most important parts of the parameter interval. The method lends itself well to the use of approximation concepts, such as design variable linking, constraint deletion and Taylor series expansions of response quantities in terms of design variables. Examples demonstrating the algorithm, in the context of planar orthogonal frames subjected to ground motion, are included.
The note draws attention to a structural feature in the Orion nebula, consisting of a parachute-shaped object converging on 64 Orionis, noted on H alpha photographs of the Orion nebula taken with the 76-cm Allegheny refractor. The same feature shows up clearly on a photograph taken in 1909 with the Mount Wilson 152-cm reflector, and on a photograph taken with the Palomar 5-m reflector. Measurements made on these three plates indicate a possible expansion of the object of about 3.6 seconds of arc per century, corresponding to a tangential velocity of about 90 to 100 km/sec. If the expansion continued at a linear rate, an explosive event may have occurred approximately 900 years ago.
Particle observations from pairs of satellites (Ogo 5, Vela 4A and 5B, Imp 3) during the recovery of plasma sheet thickness late in substorms were examined. Six of the nine events occurred within about 5 min in locations near the estimated position of the neutral sheet, but over wide ranges of east-west and radial separations. The time of occurrence and spatial extent of the recovery were related to the onset (defined by ground Pi 2 pulsations) and approximate location (estimated from ground mid-latitude magnetic signatures) of substorm expansions. It was found that the plasma sheet recovery occurred 10 - 30 min after the last in a series of Pi bursts, which were interpreted to indicate that the recovery was not due directly to a late, high latitude substorm expansion. The recovery was also observed to occur after the substorm current wedge had moved into the evening sector and to extend far to the east of the center of the last preceding substorm expansion.
Effects of several geometric parameters on the internal performance of nonaxisymmetric convergent-divergent, single-ramp expansion, and wedge nozzles were investigated at nozzle pressure ratios up to approximately 10. In addition, two different thrust-vectoring schemes were investigated with the wedge nozzle. The results indicated that as with conventional round nozzles, peak nonaxisymmetric nozzle, internal performance occurred near the nozzle pressure ratio required for fully expanded exhaust flow. Nozzle sidewall length or area generally had little effect on the internal performance of the nozzles investigated.
It was shown experimentally that the Marangoni phenomenon is a primary mechanism for the movement of a gas bubble in a nonisothermal liquid in a low gravity environment. A mathematical model consisting of the Navier-Stokes and thermal energy equations, together with the appropriate boundary conditions for both media, is presented. Parameter perturbation theory is used to solve this boundary value problem; the expansion parameter is the Marangoni number. The zeroth, first, and second order approximations for the velocity, temperature and pressure distributions in the liquid and in the bubble, and the deformation and terminal velocity of the bubble are determined. Experimental zero gravity data for a nitrogen bubble in ethylene glycol, ethanol, and silicone oil subjected to a linear temperature gradient were obtained using the NASA Lewis zero gravity drop tower. Comparison of the zeroth order analytical results for the bubble terminal velocity showed good agreement with the experimental measurements. The first and second order solutions for the bubble deformation and bubble terminal velocity are valid for liquids having Prandtl numbers on the order of one, but there is a lack of appropriate data to test the theory fully.
A study of the effects of thermal environment and microcracking in graphite epoxy composites was made. Research indicates that microcracking does affect the thermal expansion of composite laminates. The amount of reduction in thermal expansion was a function of the crack density. A maximum reduction of approximately 25% occurred in a quasi-isotropic specimen with a crack density of 2.05 mm 1 in the 90 deg plies. Laminate analysis with appropriate reductions in E sub 2 and Alpha sub 2 of the damaged plies appears to be capable of modeling the observed