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Entirely rigorous proofs of the symmetries induced by the phase matrix into the reflection and transmission operators used in the matrix operator theory are given. Results are obtained for multiple scattering in both homogeneous and inhomogeneous atmospheres. These results will be useful to researchers using the method since large savings in computer time and storage are obtainable.
Real time processing capabilities in the context of reconnaissance sensors, two dimensional beamforming, etc. are addressed. Matrix-matrix multiplier concepts using incoherent light are studied.
An indentation test technique for compressively loading the ends of individual fibers to produce debonding has been applied to metal, glass, and glass-ceramic matrix composites; bond strength values at debond initiation are calculated using a finite-element model. Results are correlated with composite longitudinal and interlaminar shear behavior for carbon and Nicalon fiber-reinforced glasses and glass-ceramics including the effects of matrix modifications, processing conditions, and high-temperature oxidation embrittlement. The data indicate that significant bonding to improve off-axis and shear properties can be tolerated before the longitudinal behavior becomes brittle. Residual stress and other mechanical bonding effects are important, but improved analyses and multiaxial interfacial failure criteria are needed to adequately interpret bond strength data in terms of composite performance.
The determination of the nature, distribution, and origin of organic material in carbonaceous chondrites is fundamental to understanding early solar nebular conditions and the origin of life. Using a variety of extraction techniques, followed by detailed chemical analysis, an extensive suite of organic compounds has been identified in carbonaceous chondrites. These data have provided key information on the diversity and isotopic composition of the organic component in chondrites. However, one disadvantage of extraction techniques is that all information regarding the spatial distribution of the organics on a fine scale is lost. This is especially important for the insoluble macromolecular carbon, which constitutes approximately 70% of the carbon in carbonaceous chondrites such as Murchison. The distribution and mineralogical associations may provide important constraints on the possible origins of the carbonaceous material. Our previous studies of the CV3 chondrites Allende and Vigarano have demonstrated that energy filtered transmission electron microscopy (EFTEM), combined with high resolution TEM (HRTEM) are powerful tools for the in situ characterization of insoluble organic matter in carbonaceous chondrites. In this study, we have used SEM and TEM techniques to characterize the matrix mineralogy of the CV3 chondrite ALH 84028 and examine the distribution and mineralogical associations of carbon. We are especially interested in establishing whether the occurrence of poorly graphitized carbon (PGC), observed in Allende matrix olivines, is common to all oxidized CV3 chondrites or is a unique feature of Allende.
We organized astrobiology lectures in the Eotvos Lorand University of Sciences and the Polaris Observatory in 2002. We present here the "Drake matrix" for the comparison of the astrobiological potential of different bodies [1], and astrobiology matrix for the visualization of the interdisciplinary connections between different fields of astrobiology. Conclusion: In Hungary it is difficult to integrate astrobiology in the education system but the great advantage is that it can connect different scientific fields and improve the view of students. We would like to get in contact with persons and organizations who already have experience in the education of astrobiology.
User manual for program language to execute numerical matrix operations with direct access time sharing computer systems
Reference manual for the programming language of Matrix Algebra Program /MAP/
An algorithm for spectral decomposition is presented which does not require knowledge of eigenvalues and eigenvectors. A set of eigenprojectors are defined which covers the entire spectrum of a matrix, and special attention is given to the projection on the zero eigenvalue. Some useful applications are discussed in the paper.
The mineralogy and mineral chemistry of the inclusion and meteorite matrices in the Allende CV3 chondrite are described, and the physical and chemical parameters of the conventional equilibrium condensation model of the origin of chondrite meteorites are evaluated. An alternative model of the origin of the mafic constituent of Allende inclusions is presented, on the basis of a new model of chondrule petrogenesis and the physical evolution of the primitive solar nebula. The model shows that the mineral chemistry of the olivine matrix in Allende CV3 seems to preserve a good record of nebular and planetary processes, including: (1) vapor-to-solid condensation under relatively oxidizing nonequilibrium conditions; (2) Fe/Mg equilibration in the meteorite parent body; and (3) recrystallization and incipient melting in the solar nebula.
Two specimen configuration of a (0/90)2s SCS-6/Ti-15-3 laminate were tested and analyzed: a center hole (CH) specimen and a double edge notch (DEN) specimen. The two specimen configurations failed at similar stress levels. Two analytical techniques, a 3-D finite-element analysis and a macro-micromechanical analysis were used to predict the overall stress-deformation behavior and the notch-tip fiber-matrix interface stresses in both configurations.
The formation mechanisms and optical properties of polycyclic aromatic hydrocarbons (PAH) isolated in argon and neon matrices were studied in a systematic manner in an attempt to provide spectroscopic data on PAH ions under conditions relevant to astrophysical applications. The results obtained indicate the strong influence of the matrix material on the competing radiative (fluorescence and phosphorescence) and nonradiative (internal conversion and intersystem crossing) relaxation processes of the trapped molecule.
Today, a major thrust for achieving engine components with improved thermal capability is the development of fiber-reinforced silicon-carbide (SiC) matrix composites. These materials are not only lighter and capable of higher use temperatures than state-of-the-art metallic alloys and oxide matrix composites (approx. 1100 C), but they can provide significantly better static and dynamic toughness than unreinforced silicon-based monolithic ceramics. However, for successful application in advanced engine systems, the SiC matrix composites should be able to withstand component service stresses and temperatures for the desired component lifetime. Since the high-temperature structural life of ceramic materials is typically controlled by creep-induced flaw growth, a key composite property requirement is the ability to display high creep resistance under these conditions. Also, because of the possibility of severe thermal gradients in the components, the composites should provide maximum thermal conductivity to minimize the development of thermal stresses. State-of-the-art SiC matrix composites are typically fabricated via a three-step process: (1) fabrication of a component-shaped architectural preform reinforced by high-performance fibers, (2) chemical vapor infiltration of a fiber coating material such as boron nitride (BN) into the preform, and (3) infiltration of a SiC matrix into the remaining porous areas in the preform. Generally, the highest performing composites have matrices fabricated by the CVI process, which produces a SiC matrix typically more thermally stable and denser than matrices formed by other approaches. As such, the CVI SiC matrix is able to provide better environmental protection to the coated fibers, plus provide the composite with better resistance to crack propagation. Also, the denser CVI SiC matrix should provide optimal creep resistance and thermal conductivity to the composite. However, for adequate preform infiltration, the CVI SiC matrix process typically has to be conducted at temperatures below 1100 C, which results in a SiC matrix that is fairly dense, but contains metastable atomic defects and is nonstoichiometric because of a small amount of excess silicon. Because these defects typically exist at the matrix grain boundaries, they can scatter thermal phonons and degrade matrix creep resistance by enhancing grain-boundary sliding. To eliminate these defects and improve the thermomechanical properties of ceramic composites with CVI SiC matrices, researchers at the NASA Glenn Research Center developed a high-temperature treatment process that can be used after the CVI SiC matrix is deposited into the fiber preform.
Micromechanical modeling via elastic-plastic finite element analyses were performed to investigate the effects that the residual stresses and the degree of matrix work hardening (i.e., cold-worked, annealed) have upon the behavior of a 9 vol percent, unidirectional W/Cu composite, undergoing tensile loading. The inclusion of the residual stress-containing state as well as the simulated matrix material conditions proved to be significant since the Cu matrix material exhibited plastic deformation, which affected the subsequent tensile response of the composite system. The stresses generated during cooldown to room temperature from the manufacturing temperature were more of a factor on the annealed-matrix composite, since they induced the softened matrix to plastically flow. This event limited the total load-carrying capacity of this matrix-dominated, ductile-ductile type material system. Plastic deformation of the hardened-matrix composite during the thermal cooldown stage was not considerable, therefore, the composite was able to sustain a higher stress before showing any appreciable matrix plasticity. The predicted room temperature, stress-strain response, and deformation stages under both material conditions represented upper and lower bounds characteristic of the composite's tensile behavior. The initial deformation stage for the hardened material condition showed negligible matrix plastic deformation while for the annealed state, its initial deformation stage showed extensive matrix plasticity. Both material conditions exhibited a final deformation stage where the fiber and matrix were straining plastically. The predicted stress-strain results were compared to the experimental, room temperature, tensile stress-strain curve generated from this particular composite system. The analyses indicated that the actual thermal-mechanical state of the composite's Cu matrix, represented by the experimental data, followed the annealed material condition.
State estimation techniques serve effectively to provide mean state estimates. However, the state error covariance matrices provided as part of these techniques suffer from some degree of lack of confidence in their ability to adequately describe the uncertainty in the estimated states. A specific problem with the traditional form of state error covariance matrices is that they represent only a mapping of the assumed observation error characteristics into the state space. Any errors that arise from other sources (environment modeling, precision, etc.) are not directly represented in a traditional, theoretical state error covariance matrix. Consider that an actual observation contains only measurement error and that an estimated observation contains all other errors, known and unknown. It then follows that a measurement residual (the difference between expected and observed measurements) contains all errors for that measurement. Therefore, a direct and appropriate inclusion of the actual measurement residuals in the state error covariance matrix will result in an empirical state error covariance matrix. This empirical state error covariance matrix will fully account for the error in the state estimate. By way of a literal reinterpretation of the equations involved in the weighted least squares estimation algorithm, it is possible to arrive at an appropriate, and formally correct, empirical state error covariance matrix. The first specific step of the method is to use the average form of the weighted measurement residual variance performance index rather than its usual total weighted residual form. Next it is helpful to interpret the solution to the normal equations as the average of a collection of sample vectors drawn from a hypothetical parent population. From here, using a standard statistical analysis approach, it directly follows as to how to determine the standard empirical state error covariance matrix. This matrix will contain the total uncertainty in the state estimate, regardless as to the source of the uncertainty. Also, in its most straight forward form, the technique only requires supplemental calculations to be added to existing batch algorithms. The generation of this direct, empirical form of the state error covariance matrix is independent of the dimensionality of the observations. Mixed degrees of freedom for an observation set are allowed. As is the case with any simple, empirical sample variance problems, the presented approach offers an opportunity (at least in the case of weighted least squares) to investigate confidence interval estimates for the error covariance matrix elements. The diagonal or variance terms of the error covariance matrix have a particularly simple form to associate with either a multiple degree of freedom chi-square distribution (more approximate) or with a gamma distribution (less approximate). The off diagonal or covariance terms of the matrix are less clear in their statistical behavior. However, the off diagonal covariance matrix elements still lend themselves to standard confidence interval error analysis. The distributional forms associated with the off diagonal terms are more varied and, perhaps, more approximate than those associated with the diagonal terms. Using a simple weighted least squares sample problem, results obtained through use of the proposed technique are presented. The example consists of a simple, two observer, triangulation problem with range only measurements. Variations of this problem reflect an ideal case (perfect knowledge of the range errors) and a mismodeled case (incorrect knowledge of the range errors).
Stress-controlled isothermal fatigue experiments were performed at room temperature (RT) and 548 C (in argon) on (0)8 SCS6/Ti 15-3 metal matrix composites (MMC's) with 15 and 41 volume percent SCS6 (SiC) fibers. The primary objectives were to evaluate the mechanical responses, and to obtain a clear understanding of the damage mechanisms leading to failure of the MMC's. The mechanical data indicated that strain ranges attained fairly constant values in the stress-controlled experiments at both RT and 538 C, and remained so for more than 85 percent of life. The fatigue data for MMC's with different volume fraction fibers showed that MMC life was controlled by the imposed strain range rather than the stress range. At RT, and at low and intermediate strain ranges, the dominant fatigue mechanism was matrix fatigue, and this was confirmed metallurgically from fractographic evidence as well as from observations of channel type dislocation structures in the matrix of fatigued MMC specimens. Reaction-zone cracks acted as important crack initiating sites at RT, with their role being to facilitate slip band formation and consequent matrix crack initiation through classical fatigue mechanisms. MMC life agreed with matrix life at the lower strain ranges, but was smaller than matrix life at higher strain ranges. Unlike the case of monotonic deformation, debonding damage was another major damage mechanism during fatigue at RT, and it increased for higher strain ranges. At high strain ranges at RT, fractography and metallography showed an absence of matrix cracks, but long lengths of debonds in the outer layers of the SCS6 fibers. Such debonding and consequent rubbing during fatigue is believed to have caused fiber damage and their failure at high strain ranges. Thus, whereas life was matrix dominated at low and intermediate strain ranges, it was fiber dominated at high strain ranges. At 538 C, the mean stain constantly increased (ratchetting) with the number of cycles. At high strain ranges, such ratchetting led to overload failure of the fibers, and debonding of the type at RT was very small. At intermediate strain ranges, fractography showed large areas of matrix cracks. However, in spite of this matrix dominated mechanism, the MMC life at elevated temperatures was significantly less than the matrix fatigue life at all strain ranges. The reason for this difference is still unclear, although metallographic and fractographic evidences suggest that internal crack initiation sites at Mo-ribbons and reaction-zone cracks may have played a critical role, with the former tending to dominate.
The occurrence of matrix cracks in melt-infiltrated SiC/SiC composites with a 3D orthogonal architecture was determined at room temperature for specimens tested in tension oriented in the X-direction (parallel to Z-bundle weave direction) and Y-direction (perpendicular to Z-bundle weave direction) and Y-direction (perpendicular to Z-bundle weave direction). The fiber-types were Sylramic and Sylramic-IBN in the X and Y-directions and lower modulus ZMI, T300, and rayon in the Z-direction. Acoustic emission (AE) was used to monitor the matrix cracking activity. For Y-direction composites, the AE data was used to determine the exact (+/- 0.25 mm) location where matrix cracks occurred in the 3D orthogonal architecture. This enabled the determination of the stress-dependent matrix crack distributions for small but repeatable matrix rich 'unidirectional' and the matrix poor 'cross-ply' regions within the architecture. It was found that matrix cracking initiated at very low stresses (approx. 40 MPa) in the 'unidirectional' regions for the largest z-direction fiber tow composites. Decreasing the size of the z-fiber bundle, increased the stress for matrix cracking in the 'unidirectional' regions. Matrix cracking in the 'cross-ply' regions always occurred at higher stresses than in 'unidirectional' regions, and the stress-dependent matrix crack distribution of the 'cross-ply' regions was always over a wider stress-range than the 'unidirectional' regions. For composites tested in the X-direction, a lower elastic modulus and a narrower and lower stress-range for matrix cracking were observed compared to composites tested in the Y-direction.
Silicon carbide fiber reinforced, silicon carbide matrix composites are some of the most advanced composite systems for high-temperature, high-stress applications in oxidizing environments. A basic area that needs to be understood for the purpose of material behavior modeling and optimization is the architectural, constituent, and mechanistic factors that contribute to non-linear stress-strain behavior. The mechanism that causes non-linear stress-strain in dense-matrix composites is the formation and propagation of bridged matrix cracks. In addition, the occurrence and propagation of matrix cracks controls the time-dependent strength-properties of these materials in oxidizing environments at elevated temperatures. A modal acoustic emission technique has been used to monitor and estimate the stress-dependent matrix cracking. Two different SiC matrix systems, chemical vapor infiltrated (CVI) and melt-infiltrated (MI), with two different SiC fiber reinforcement, Hi-Nicalon (trademark) and Sylramic (trademark) were compared. Even though the averages of the range where matrix cracking occurred for the composites varied by more than 0.1% in strain and almost 200 MPa in stress, the range or distribution for matrix cracking could be reduced to a narrow band of stress for CVI SiC and MI SiC composites if it were assumed that all matrix cracks emanate outside of the load-bearing fiber, interphase, CVI preform minicomposite. A simple relationship was determined to describe stress-dependent matrix cracking which can then be used to estimate the onset of large, bridged matrix cracks or for material behavior models.
In an alternative approach to increasing the degrees of wetting and adhesion between the fiber and matrix components of organic-fiber/polymer matrix composite materials, the matrix resins are modified. Heretofore, it has been common practice to modify the fibers rather than the matrices: The fibers are modified by chemical and/or physical surface treatments prior to combining the fibers with matrix resins - an approach that entails considerable expense and usually results in degradation (typically, weakening) of fibers. The alternative approach of modifying the matrix resins does not entail degradation of fibers, and affords opportunities for improving the mechanical properties of the fiber composites. The alternative approach is more cost-effective, not only because it eliminates expensive fiber-surface treatments but also because it does not entail changes in procedures for manufacturing conventional composite-material structures. The alternative approach is best described by citing an example of its application to a composite of ultra-high-molecular- weight polyethylene (UHMWPE) fibers in an epoxy matrix. The epoxy matrix was modified to a chemically reactive, polarized epoxy nano-matrix to increase the degrees of wetting and adhesion between the fibers and the matrix. The modification was effected by incorporating a small proportion (0.3 weight percent) of reactive graphitic nanofibers produced from functionalized nanofibers into the epoxy matrix resin prior to combining the resin with the UHMWPE fibers. The resulting increase in fiber/matrix adhesion manifested itself in several test results, notably including an increase of 25 percent in the maximum fiber pullout force and an increase of 60-65 percent in fiber pullout energy. In addition, it was conjectured that the functionalized nanofibers became involved in the cross linking reaction of the epoxy resin, with resultant enhancement of the mechanical properties and lower viscosity of the matrix.