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Errors in interpolation and the choosing of the range of discreteness when making measurements in a hydrophysical field are discussed. Equations for optimum interpolating based on the theory of linear interpolation of stationary random sequences are presented; analogous equations are derived for the case of data collected at stations located at the apices of a right triangle.
The use of polymer adhesives for high reliability microcircuit applications is a radical deviation from past practices in electronic packaging. Bonding studies were performed using two gold-filled conductive adhesives, 10/90 tin/lead solder and Indalloy no. 7 solder. Various types of discrete components were mounted on ceramic substrates using both thick-film and thin-film metallization. Electrical and mechanical testing were performed on the samples before and after environmental exposure to MIL-STD-883 screening tests.
Film injection from discrete holes in a three row staggered array with 5-diameter spacing is studied. The boundary layer thickness-to-hole diameter ratio and Reynolds number are typical of gas turbine film cooling applications. Two different injection locations are studied to evaluate the effect of boundary layer thickness on film penetration and mixing. Detailed streaklines showing the turbulent motion of the injected air are obtained by photographing neutrally buoyant helium filled soap bubbles which follow the flow field. The bubble streaklines passing downstream injection locations are clearly identifiable and can be traced back to their origin. Visualization of surface temperature patterns obtained from infrared photographs of a similar film cooled surface are also included.
This modelization starts from the following hypotheses: pilot's behavior is a time discrete process, he can perform only one task at a time and his operating mode depends on the considered flight subphase. Pilot's behavior was observed using an electro oculometer and a simulator cockpit. A FORTRAN program has been elaborated using two strategies. The first one is a Markovian process in which the successive instrument readings are governed by a matrix of conditional probabilities. In the second one, strategy is an heuristic process and the concepts of mental load and performance are described. The results of the two aspects have been compared with simulation data.
A series of discrete maneuver tasks were used to evaluate the effects of steering gain and directional mode dynamic parameters on driver/vehicle responses. The importance and ranking of these parameters were evaluated through changes in subjective driver ratings and performance measures obtained from transient maneuvers such as a double lane change, an emergency lane change, and an unexpected obstacle. The unexpected obstacle maneuver proved more sensitive to individual driver differences than to vehicle differences. Results were based on full scale tests with an experienced test driver evaluating many different dynamic configurations plus seventeen ordinary drivers evaluating six key configurations.
Measurements are presented of the discrete vortex noise emitted by a thin airfoil. These measurements were made in a new wind tunnel designed specifically for aerodynamic noise measurements. The tunnel is an indraft type with a 25- by 35- by 100-cm testing section and a sonic-throat noise suppressor just downstream of the test section. Directivity and standing wave patterns are presented and compared with theoretical predictions. Frequency scaling criteria are developed and compared with other investigations.
The results are summarized of an investigation of discrete component bonding reliability and a fundamental study of new thick film resistor materials. The component bonding study examined several types of solder bonded components with some processing variable studies to determine their influence upon bonding reliability. The bonding reliability was assessed using the thermal cycle: 15 minutes at room temperature, 15 minutes at +125 C 15 minutes at room temperature, and 15 minutes at -55 C. The thick film resistor materials examined were of the transition metal oxide-phosphate glass family with several elemental metal additions of the same transition metal. These studies were conducted by preparing a paste of the subject composition, printing, drying, and firing using both air and reducing atmospheres. The resulting resistors were examined for adherence, resistance, thermal coefficient of resistance, and voltage coefficient of resistance.
Film injection from three rows of discrete holes angled 30 deg to the surface in line with mainstream flow and spaced 5 diameters apart in a staggered array was visualized by using helium bubbles as tracer particles. Both the main stream and the film injectant were ambient air. Detailed streaklines showing the turbulent motion of the film mixing with the main stream were obtained by photographing small, neutrally buoyant helium-filled soap bubbles which followed the flow field. The ratio of boundary layer thickness to hole diameter and the Reynolds number were typical of gas turbine film cooling applications. The results showed the behavior of the film and its interaction with the main stream for a range of blowing rates and two initial boundary layer thicknesses.
Film injection from discrete holes in a three-row, staggered array with five-diameter spacing was studied for three hole angles: (1) normal, (2) slanted 30 deg to the surface in the direction of the main stream, and (3) slanted 30 deg to the surface and 45 deg laterally to the main stream. The ratio of the boundary layer thickness-to-hole diameter and Reynolds number were typical of gas-turbine film-cooling applications. Detailed streaklines showing the turbulent motion of the injected air were obtained by photographing very small neutrally buoyant, helium-filled soap bubbles which follow the flow field.
A method is proposed for obtaining the time-weighted quadratic sum for linear discrete systems. The formula of the weighted quadratic sum is obtained from matrix z-transform formulation. In addition, it is shown that this quadratic sum can be derived in a recursive form for several useful weighted functions. The discussion presented parallels that of MacFarlane (1963) for weighted quadratic integral for linear continuous systems.
The multipath channel for communication between an aerospace vehicle and a ground terminal is modeled by a multiplicative first-order Markov process. The multiplicative process is treated as a component of the message model and the discrete-time demodulation algorithms using the extended Kalman nonlinear estimation technique are developed for continuous-time angle-modulated signals. The equivalent baseband form of the demodulator structure is derived. Two examples of the message process are discussed for an FM system. The simulation results are presented for various values of the bandwidth expansion ratio and the additive SNR. The performance of the baseband algorithms is discussed.
The concept of a 'best approximating m-dimensional subspace' for a given set of vectors in n-dimensional whole space is introduced. Such a subspace is easily described in terms of the eigenvectors of an associated Gram matrix. This technique is used to approximate an achievable set for a discrete linear time-invariant dynamical system. This approximation characterizes the part of the state space that may be reached using modest levels of control. If the achievable set can be closely approximated by a proper subspace of the whole space then the system is 'essentially uncontrollable'. The notion finds application in studies of failure-tolerant systems, and in decoupling.
A method for designing discrete model reference adaptive control systems when one has access to only the plant's input and output signals is given. Controllers for single-input, single-output, nonlinear, nonautonomous plants are developed via Liapunov's second method. Anticipative values of the plant output are not required, but are replaced by signals easily obtained from a low-pass filter operating on the plant's output. The augmented error signal method is employed, ensuring finally that the normally used error signal also approaches zero asymptotically.
This paper presents particularly simple mathematical formulas for the calculation of force-free fields of constant alpha from the distribution of discrete sources on a flat surface. The advantage of these formulas lies in their physical simplicity and the fact that they can be easily used in practice to calculate the fields. The disadvantage is that they are limited to fields of 'sufficiently small alpha'. These formulas may be useful in the study of chromospheric magnetic fields by the comparison of high-resolution H-alpha photographs and photospheric magnetograms.
The equilibrium properties of a two-dimensional plasma are examined theoretically within the framework of the random-phase approximation. The guiding-center case is of most interest because of the formal equivalence to two-dimensional discrete-line vortex fluids and because of the formal admissibility of negative temperatures. Using a judicious treatment of the periodic boundary conditions, extensive thermodynamics for nonnegative temperatures and a new value for the energy at which the temperature becomes negative are found. An explicit form for the structure function is derived and compared with the result of a Monte Carlo calculation. Good agreement is found for the negative-temperature-threshold prediction and for the general shape of the structure function. An equilibrium energy spectrum is calculated, which for positive temperatures, is the Debye-Hueckel result; for negative temperatures, it predicts an enhanced excitation of the lowest mode, corresponding to macroscopic charge separation.
A method of discrete modeling is presented that effectively isolates steady state model accuracy from dynamic model accuracy. The steady state model may be generated from the engine design equations with any desired degree of accuracy. The dynamic model is generated by applying a step disturbance of a manipulated variable to an open loop engine simulation. The sampled response of the variable is combined with the steady state model's response to form a set of weighting factors. These weighting factors are then used to weight past values of the manipulated variable, thus forming the dynamic model. The method is used to estimate various TF30-P-3 engine variables. A dynamic trim function is developed to compensate for the dynamic nonlinearities of the variables as well as for inaccuracies in dynamic definition. The trim function is shown to be realted to the square root of the sum of the squares of the weighting factors obtained at various engine operating conditions. Finally, the estimation of variables without dynamic modeling is discussed.
The bonding reliability of discrete capacitor chips bonded with solders and conductive epoxies was examined along with the thick film resistor materials consisting of iron oxide phosphate and vanadium oxide phosphates. It was concluded from the bonding reliability studies that none of the wide range of types of solders examined is capable of resisting failure during thermal cycling while the conductive epoxy gives substantially lower failure rates. The thick film resistor studies proved the feasibility of iron oxide phosphate resistor systems although some environmental sensitivity problems remain. One of these resistor compositions has inadvertently proven to be a candidate for thermistor applications because of the excellent control achieved upon the temperature coefficient of resistance. One new and potentially damaging phenomenon observed was the degradation of thick film conductors during the course of thermal cycling.
Optimum estimates of nonobservable random variables or random processes which influence the rate functions of a discrete time jump process (DTJP) are obtained. The approach is based on the a posteriori probability of a nonobservable event expressed in terms of the a priori probability of that event and of the sample function probability of the DTJP. A general representation for optimum estimates and recursive equations for minimum mean squared error (MMSE) estimates are obtained. MMSE estimates are nonlinear functions of the observations. The problem of estimating the rate of a DTJP when the rate is a random variable with a probability density function of the form cx super K (l-x) super m and show that the MMSE estimates are linear in this case. This class of density functions explains why there are insignificant differences between optimum unconstrained and linear MMSE estimates in a variety of problems.