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A general result for the controllability of linear systems using positive controls was given by Saperstone and Yorke (1971). These results are applied to systems with nearly nonnegative matrices and a theorem is developed which delineates the geometry of the reachable set.
One hundred years have passed since the publication of Routh's fundamental work on determining the stability of constant linear systems. The paper presents an outline of the algorithm and considers such aspects of it as the distribution of zeros and applications of it that relate to the greatest common divisor, the abscissa of stability, continued fractions, canonical forms, the nonnegativity of polynomials and polynomial matrices, the absolute stability, optimality and passivity of dynamic systems, and the stability of two-dimensional circuits.
Matrix compositions of 32 of the approximately 40 known carbonaceous chondrites were analyzed using an electron probe defocussed-beam technique. Except in those chondrites that show evidence of metamorphism, matrices are compositionally similar and have correlation coefficients of +0.96 or greater. The implications of these analyses for the chemistry of individual matrix phases and for primitive solar system material are discussed.
Sympathetic variations in nickel and sulfur abundances, on a scale of micrometers, in Orgueil phyllosilicates apparently reproduce similar correlations among matrices of different carbonaceous chondrites. In Orgueil this effect probably results from aqueous alteration of a Ni-Si-bearing phase on the parent body.
Solid solutions of transition elements in copper, nickel, cobalt, iron, and aluminum matrices were analyzed by observing secondary ion emissions under bombardment with 6.2-keV argon ions. Enchancement of the production of solute-element ions was observed. An ion emission model is proposed according to which the ion yield is governed by the probability of an atom leaving the metal in a preionized state. The energy distribution of the valence electrons of the solute atoms is the bases of the probability calculation.
An extension of the Tridiagonal Reduction (FEER) method to complex eigenvalue analysis in NASTRAN is described. As in the case of real eigenvalue analysis, the eigensolutions closest to a selected point in the eigenspectrum are extracted from a reduced, symmetric, tridiagonal eigenmatrix whose order is much lower than that of the full size problem. The reduction process is effected automatically, and thus avoids the arbitrary lumping of masses and other physical quantities at selected grid points. The statement of the algebraic eigenvalue problem admits mass, damping and stiffness matrices which are unrestricted in character, i.e., they may be real, complex, symmetric or unsymmetric, singular or non-singular.
Prospective techniques for analyzing magnetic fields using NASTRAN are reviewed. A variational principle utilizing a vector potential function is presented which has as its Euler equations, the required field equations and boundary conditions for static magnetic fields including current sources. The need for an addition to this variational principle of a constraint condition is discussed. Some results using the Lagrange multiplier method to apply the constraint and CELAS2 elements to simulate the matrices are given. Practical considerations of using large numbers of CELAS2 elements are discussed.
A software program was developed and tested to process microwave radiometry data to be acquired by the microwave sensor (SSM/T) on the Defense Meteorological Satellite Program spacecraft. The SSM/T 7-channel microwave radiometer and systems data will be data-linked to Air Force Global Weather Central (AFGWC) where they will be merged with ephemeris data prior to product processing for use in the AFGWC upper air data base (UADB). The overall system utilizes an integrated design to provide atmospheric temperature soundings for global applications. The fully automated processing at AFGWC was accomplished by four related computer processor programs to produce compatible UADB soundings, evaluate system performance, and update the a priori developed inversion matrices. Tests with simulated data produced results significantly better than climatology.
Thermal effects on fracture strength and impact energy were studied in 50 volume percent unidirectional composites of 143 and 203 micron boron fibers in 6061 and 1100 aluminum matrices. For 6061 matrix composites, strength was maintained to approximately 400 C in the cyclic tests and higher than 400 C in the static tests. For the 1100 matrix composites, strength degradation appeared near 260 C after cycling and higher than 260 C in static heating. This composite strength degradation is explained by a fiber degradation mechanism resulting from a boron-aluminum interface reaction. The impact energy absorption degraded significantly only above 400 C for both matrix alloys. Thus, while impact loss for the 6061 composite correlates with the fiber strength loss, other energy absorption processes appear to extend the impact resistance of the 1100 matrix composites to temperatures beyond where its strength is degraded. Interrupted impact tests on as-received and thermally cycled composites define the range of load over which the fibers break in the impact event.
Self-cooled combustion chambers are chambers in which the chamber wall temperature is controlled by methods other than fluid flow within the chamber wall supplied from an external source. In such chambers, adiabatic wall temperature may be controlled by use of upstream fluid components such as the injector or a film-coolant ring, or by internal flow of self-contained materials; e.g. pyrolysis gas flow in charring ablators, and the flow of infiltrated liquid metals in porous matrices. Five types of self-cooled chambers are considered in this monograph. The name identifying the chamber is indicative of the method (mechanism) by which the chamber is cooled, as follows: ablative; radiation cooled; internally regenerative (Interegen); heat sink; adiabatic wall. Except for the Interegen and heat sink concepts, each chamber type is discussed separately. A separate and final section of the monograph deals with heat transfer to the chamber wall and treats Stanton number evaluation, film cooling, and film-coolant injection techniques, since these subjects are common to all chamber types. Techniques for analysis of gas film cooling and liquid film cooling are presented.
A bounded operator A on a Hilbert space H was positive. These operators were symmetric, and as such constitute a natural generalization of nonnegative real diagonal matrices. The following result is thus both well known and not surprising: A positive operator has a unique positive square root (under operator composition).
The Green's function method and the computer program SOUSSA (Steady Oscillatory and Unsteady Subsonic and Supersonic Aerodynamics) are reviewed. The Green's function method is applied to the fully unsteady potential equation yielding an integro-differential-delay equation. This equation is approximated by a set of differential-delay equations in time using the finite element method. The Laplace transform is used to yield a matrix relating the velocity potential to the normal wash. The matrix of the generalized aerodynamic forces is obtained by premultiplying and postmultiplying the matrices relating generalized forces to the potential and the normal wash by the generalized coordinates. The program SOUSSA is compared with existing numerical results. Results indicate that the program is not only general, flexible, and easy to use, but also accurate and fast.
Commercially obtained PMR-15 polyimide prepregs with S-glass and graphite fiber reinforcements were evaluated along with in-house prepared glass and graphite cloth PMR 2 materials. A novel autoclave approach was conceived and used to demonstrate that both the PMR systems respond to 1.4 MPa (200 psi) autoclave pressures to produce void free composites equivalent to die molded laminates. Isothermal gravimetric analysis and subsequent mechanical property tests indicated that the PMR 2 system was significantly superior in thermo-oxidative stability, and that S-glass reinforcements may contribute to the accelerated degradation of composites at 316 C (600 F) when compared to graphite fiber reinforced composites. Fully reversed bending fatigue experiments were conducted with a type of fixture unused for organic matrix composites. These studies indicated that the graphite fiber composites were clearly superior in fatigue resistance to the glass fiber reinforced material and that PMR matrix composite systems yield performance of the same order as composite materials employing other families of matrices.
A series of approaches using airline-rated Boeing 737 pilots in an FAA qualified simulator was conducted. The test matrices include both manual and coupled approaches for VFR, Category 1 and Category 2 conditions. A nonintrusive oculometer system was used to track the pilot's eye-point-of-regard throughout the approach. The results indicate that, in general, the pilots use a different scan technique for the manual and coupled (auto-pilot with manual throttle) conditions. For the manual approach 73 percent of the time was spent on the Flight Director and 13 percent on airspeed as opposed to 50 percent on Flight Director and 23 percent on airspeed for the coupled approaches. For the visual portion of approach from less than 100m to touchdown or when the touchdown point came into view, the pilots tend to fixate on their aim or touchdown area until the flare initiation, at which time they let their eye-point-of-regard move up the runway to use the centerline lights for rollout guidance.
The fabrication of boron filaments and the production of composite materials consisting of boron filaments and organic or metallic matrices are discussed. Problem involving the use of tungsten substrates in the filament fabrication process, the protection of boron fibers with diffusion barrier cladings, and the application of alloy additives in the matrix to lessen the effects of diffusion are considered. Data on the kinetics of the boron fiber/matrix interaction at high temperatures, and the influence of the fiber/matrix interaction on the mechanical properties of the composite are presented.
A numerical method is reported which determines a value C for the degree of conditioning of a matrix. This value is C = 0 for a singular matrix and has progressively larger values for matrices which are increasingly well-conditioned. This value is C sub = C max sub max (C defined by the precision of the computer) when the matrix is perfectly well conditioned.
The far field diffraction pattern of a geometrically perfect corner reflector is examined analytically for normally incident monochromatic light. The states of polarization and the complex amplitudes of the emerging light are expressed through transformation matrices in terms of those of the original incident light for each sextant of the face in a single coordinate system. The analytic expression of the total diffraction pattern is obtained for a circular face. This expression consists of three component functions in addition to the basic Airy function. The coefficient of each function is expressed in terms of complex coefficients of reflectance of the reflecting surface. Some numerical results for different reflecting surfaces, including total internal reflection, are presented. The iso-intensity contours of the diffraction pattern evaluated from the analytical expressions for an uncoated solid corner reflector are also presented along with the photographs of the pattern.
The author has identified the following significant results. The probability of correct classification of various populations in data was defined as the primary performance index. The multispectral data being of multiclass nature as well, required a Bayes error estimation procedure that was dependent on a set of class statistics alone. The classification error was expressed in terms of an N dimensional integral, where N was the dimensionality of the feature space. The multispectral scanner spatial model was represented by a linear shift, invariant multiple, port system where the N spectral bands comprised the input processes. The scanner characteristic function, the relationship governing the transformation of the input spatial, and hence, spectral correlation matrices through the systems, was developed.