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Conditions are developed under which exponential stability of a composite discrete system is implied by exponential stability of its subsystems and the nature of their interactions. Stability of the system is determined by testing positive definiteness property of a real symmetric matrix the dimension of which is equal to the number of subsystems.
Computer simulations of the concentration profiles of simple biprotic ampholytes with Delta pKs 1, 2, and 3, on immobilized pH gradients (IPG) at extreme pH values (pH 3-4 and pH 10-11) show markedly skewed steady-state profiles with increasing kurtosis at higher Delta pK values. Across neutrality, all the peaks are symmetric irrespective of their Delta pK values, but they show very high contribution to the conductivity of the background gel and significant alteration of the local buffering capacity. The problems of skewness, due to the exponential conductivity profiles at low and high pHs, and of gel burning due to a strong electroosmotic flow generated by the net charges in the gel matrix, also at low and high pHs, are solved by incorporating in the IPG gel a strong viscosity gradient. This is generated by a gradient of linear polyacrylamide which is trapped in the gel by the polymerization process.
In this report the problem we are going to study is the interpolation of a set of points in the plane with the use of control theory. We will discover how different systems generate different kinds of splines, cubic and exponential, and investigate the effect that the different systems have on the tracking problems. Actually we will see that the important parameters will be the two eigenvalues of the control matrix.
A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.
A sequential filtering algorithm is presented for attitude and attitude-rate estimation from Global Positioning System (GPS) differential carrier phase measurements. A third-order, minimal-parameter method for solving the attitude matrix kinematic equation is used to parameterize the filter's state, which renders the resulting estimator computationally efficient. Borrowing from tracking theory concepts, the angular acceleration is modeled as an exponentially autocorrelated stochastic process, thus avoiding the use of the uncertain spacecraft dynamic model. The new formulation facilitates the use of aiding vector observations in a unified filtering algorithm, which can enhance the method's robustness and accuracy. Numerical examples are used to demonstrate the performance of the method.
One dimensional integral formulas are derived for mutual impedance of arbitrary size, coplanar, parallel, and perpendicular surface monopoles. The integrals in formulas are expressed as exponential integrals where possible. The mutual impedance expression for parallel monopoles is a summation of exponential integrals and one-dimensional integrals. For perpendicular monopoles, the mutual impedance is in closed form, containing exponential integrals only. The final expressions are in a form suitable for numerical computation. Since the expressions contain at most one-dimensional integrals, they can be utilized to reduce the matrix filling time in the moment method formulations, especially when inhomogeneous sectioning is preferred. Additionally, they can be used in rectangular surface patch modeling of conducting surfaces with edges which are at an angle to the surface patches, providing the angle is small. To this end, the expressions were utilized in the moment method analysis of linearly tapered slot antennas. Very good accuracy was obtained with a reduction in computer time.
ATIC(Advanced Thin Ionization Calorimeter) is a balloon borne experiment designed to measure the cosmic ray composition for elements from hydrogen to iron and their energy spectra from approx.50 GeV to near 100 TeV. It consists of a Si-matrix detector to determine the charge of a CR particle, a scintillator hodoscope for tracking, carbon interaction targets and a fully active BGO calorimeter. ATIC had its first 16-day flight from McMurdo, Antarctica from 28/12/2000 to 13/01/2000. The ATIC flight collected approximately 25 million events. To measure charge of primary particle in presence of radiation scattered back from the interaction and subsequent shower development in the calorimeter a charge detector must be a mosaic of small detector pads so that the pad containing the signal from the incident particle has no additional signal from albedo particles. Therefore the silicon matrix was built of 4480 individual silicon pads each 2 cm x 1.5 cm. The matrix consists of four planes of detectors and the active detector area, in these planes are partially overlapped to completely cover the aperture. The lateral and amplitude distributions of albedo signals in Si-matrix are analyzed for different primary nuclei and different energy deposits in BGO calorimeter. The greater part of albedo signals has Q near 1, where Q = square root of Amplitude(MIP). The albedo distribution exponentially decreases up to Q near 8. These high values are produced by slow protons and plans. There are also a small number of signals of Q > 8, mainly for heavy nucleus primaries. These signals are apparently generated by neutrons. The comparison of the experimental data and simulations with GEANT 3-21 code using QGSM generator for nucleus-nucleus interactions is presented.
The equations for processing ground tracking data during a space shuttle ascent or entry, or any nonfree flight phase of a shuttle mission are given. The resulting computer program processes data from up to three stations simultaneously: C-band station number 1; C-band station number 2; and an S-band station. The C-band data consists of range, azimuth, and elevation angle measurements. The S-band data consists of range, two angles, and integrated Doppler data in the form of cycle counts. A nineteen element state vector is used in Kalman filter to process the measurements. The acceleration components of the shuttle are taken to be independent exponentially-correlated random variables. Nine elements of the state vector are the measurement bias errors associated with range and two angles for each tracking station. The biases are all modeled as exponentially-correlated random variables with a typical time constant of 108 seconds. All time constants are taken to be the same for all nine state variables. This simplifies the logic in propagating the state error covariance matrix ahead in time.
We present a multigrid solver for the exponential fitting method. The solver is applied to the current continuity equations of semiconductor device simulation in two dimensions. The exponential fitting method is based on a mixed finite element discretization using the lowest-order Raviart-Thomas triangular element. This discretization method yields a good approximation of front layers and guarantees current conservation. The corresponding stiffness matrix is an M-matrix. 'Standard' multigrid solvers, however, cannot be applied to the resulting system, as this is dominated by an unsymmetric part, which is due to the presence of strong convection in part of the domain. To overcome this difficulty, we explore the connection between Raviart-Thomas mixed methods and the nonconforming Crouzeix-Raviart finite element discretization. In this way we can construct nonstandard prolongation and restriction operators using easily computable weighted L(exp 2)-projections based on suitable quadrature rules and the upwind effects of the discretization. The resulting multigrid algorithm shows very good results, even for real-world problems and for locally refined grids.
The conventional Lorenz-Mie formalism is extended to the scattering process associated with a coated sphere embedded in an absorbing medium. It is shown that apparent and inherent scattering cross sections of a scattering particle, which are identical in the case of transparent host medium, are different if the host medium is absorptive. Here the inherent single-scattering properties are derived from the near-field information whereas the corresponding apparent counterparts are derived from the far-field asymptotic form of the scattered wave with scaling of host absorption that is assumed to be in an exponential form. The formality extinction and scattering efficiencies defined in the same manner as in the conventional sense can be unbounded. For a nonabsorptive particle embedded in an absorbing medium, the effect of host absorption on the phase matrix elements associated with polarization is significant. This effect, however, is largely reduced for strongly absorptive particles such as soot. For soot particles coated with water, the impurity can substantially reduce the single-scattering albedo of the particle if the size parameter is small. For water-coating soot and hollow ice spheres, it is shown that the phase matrix elements -P(sub 12)/P(sub 11) and P(sub 33)/P(sub 11) are unique if the shell is thin, as compared with the case for thick shell. Furthermore, the radiative transfer equation regarding a multidisperse particle system in an absorbing medium is discussed. It is illustrated that the conventional computation algorithms can be applied to solve the multiple scattering process if the scaled apparent single-scattering properties are applied.
A procedure is developed for the prediction of radiation transport events in the context of the entry heating environment. The equivalent-width and exponential approximations are employed to reduce the computational requirements of the governing equations. Novel features are introduced in the use of an Elsasser band model to estimate line overlapping events and in the formulation of the wall reflection events. A matrix of calculations is presented to allow an assessment of the trade-offs between accuracy and computational efforts. It is concluded that the equivalent width model allows significant savings in computational effort with only modest penalties in accuracy. Consequently, the model should be viewed as an attractive candidate for use in radiation-coupled flow field prediction procedures.
Tensile creep behavior of SiC/SiNC ceramic matrix composites at elevated temperatures and at various stress levels have been investigated for turbine engine applications. The objective of this research is to present creep behavior of SiC/SiCN composites at stress levels above and below the monotonic proportional limit strength and predict the life at creep rupture conditions. Tensile creep-rupture tests were performed on an Instron 8502 servohydraulic testing machine at constant load conditions up to a temperature limit of 1000 C. Individual creep curves indicate three stages such as primary, secondary, and tertiary. The creep rate increased linearly at an early stage and then gradually became exponential at higher strains. The stress exponent and activation energy were also obtained at 700 and 1000 C. The specimen lifetime was observed to be 55 hrs at 121 MPa and at 700 C. The life span reduced to 35 hrs at 143 MPa and at 1000 C. Scanning electron microscopy observations revealed significant changes in the crystalline phases and creep damage development. Creep failures were accompanied by extensive fiber pullout, matrix cracking, and debonding along with fiber fracture. The creep data was applied to Time-Temperature-Stress superposition model and the Manson-Haferd parametric model for long-time life prediction.
The Artemis Program is NASA’s campaign to explore the Moon and beyond. Artemis-1, the uncrewed exoLEO test flight of the Orion spacecraft, was completed in 2022. There were four navigation Extended Kalman Filters (EKFs) that are part of the Orion navigation system. The Atmospheric Extended Kalman Filter (ATMEKF) estimates the vehicle position, velocity, and attitude (referred to as the vehicle state) during the ascent and entry phases of flight. Once Orion is outside of Earths atmosphere, the Earth Orbit Extended Kalman Filter (EOEKF) and CisLunar Extended Kalman Filter (CLEKF) estimate the translational states, depending on the phase of flight, while the Attitude Extended Kalman Filter (ATTEKF) estimates the rotational state of the vehicle. The Kalman filters propagate the vehicle state forward in time using a combination of dynamics models and the output data from the Inertial Measurement Unit (IMU). The filters update the vehicle states and associated uncertainties, in the form of the covariance matrix, using pseudorange measurements from GPS (in ATMEKF/EOEKF), optical navigation measurements of the Earth or Moon (in CLEKF), and star tracker measurements (in ATTEKF). Simultaneously, the Kalman filters estimate error sources in the sensors, which are included in the state vectors as Exponentially Correlated Random Variables (ECRVs). This paper will summarize the performance of these filters during the Artemis-1 mission.
The Fadel (1990) two-point exponential approximation technique for rotorcraft airframe structural optimization is presently examined by comparing its results with the well established linear and hybrid first-order methods. Attention is given to both the elastic-line and FEM models of an AH-1G airframe. The Direct Matrix Abstraction Programming Language is used to compute sensitivity derivatives and motivate the CONMIN optimizer to produce the design change.
PURPOSE: To characterize the growth and maturation of nonimmortalized human lens epithelial (HLE) cells grown in vitro. METHODS: HLE cells, established from 18-week prenatal lenses, were maintained on bovine corneal endothelial (BCE) extracellular matrix (ECM) in medium supplemented with basic fibroblast growth factor (FGF-2). The identity, growth, and differentiation of the cultures were characterized by karyotyping, cell morphology, and growth kinetics studies, reverse transcription-polymerase chain reaction (RT-PCR), immunofluorescence, and Western blot analysis. RESULTS: HLE cells had a male, human diploid (2N = 46) karyotype. The population-doubling time of exponentially growing cells was 24 hours. After 15 days in culture, cell morphology changed, and lentoid formation was evident. Reverse transcription-polymerase chain reaction (RT-PCR) indicated expression of alphaA- and betaB2-crystallin, fibroblast growth factor receptor 1 (FGFR1), and major intrinsic protein (MIP26) in exponential growth. Western analyses of protein extracts show positive expression of three immunologically distinct classes of crystallin proteins (alphaA-, alphaB-, and betaB2-crystallin) with time in culture. By Western blot analysis, expression of p57(KIP2), a known marker of terminally differentiated fiber cells, was detectable in exponential cultures, and levels increased after confluence. MIP26 and gamma-crystallin protein expression was detected in confluent cultures, by using immunofluorescence, but not in exponentially growing cells. CONCLUSIONS: HLE cells can be maintained for up to 4 months on ECM derived from BCE cells in medium containing FGF-2. With time in culture, the cells demonstrate morphologic characteristics of, and express protein markers for, lens fiber cell differentiation. This in vitro model will be useful for investigations of radiation-induced cataractogenesis and other studies of lens toxicity.
Cell adhesion molecules (CAMs) are proteins which anchor cells to each other and to the extracellular matrix (ECM), but whose functions also include signal transduction, differentiation, and apoptosis. We are testing a hypothesis that particle radiations modulate CAM expression and this contributes to radiation-induced lens opacification. We observed dose-dependent changes in the expression of beta 1-integrin and ICAM-1 in exponentially-growing and confluent cells of a differentiating human lens epithelial cell model after exposure to particle beams. Human lens epithelial (HLE) cells, less than 10 passages after their initial culture from fetal tissue, were grown on bovine corneal endothelial cell-derived ECM in medium containing 15% fetal bovine serum and supplemented with 5 ng/ml basic fibroblast growth factor (FGF-2). Multiple cell populations at three different stages of differentiation were prepared for experiment: cells in exponential growth, and cells at 5 and 10 days post-confluence. The differentiation status of cells was characterized morphologically by digital image analysis, and biochemically by Western blotting using lens epithelial and fiber cell-specific markers. Cultures were irradiated with single doses (4, 8 or 12 Gy) of 55 MeV protons and, along with unirradiated control samples, were fixed using -20 degrees C methanol at 6 hours after exposure. Replicate experiments and similar experiments with helium ions are in progress. The intracellular localization of beta 1-integrin and ICAM-1 was detected by immunofluorescence using monoclonal antibodies specific for each CAM. Cells known to express each CAM were also processed as positive controls. Both exponentially-growing and confluent, differentiating cells demonstrated a dramatic proton-dose-dependent modulation (upregulation for exponential cells, downregulation for confluent cells) and a change in the intracellular distribution of the beta 1-integrin, compared to unirradiated controls. In contrast, there was a dose-dependent increase in ICAM-1 immunofluorescence in confluent, but not exponentially-growing cells. These results suggest that proton irradiation downregulates beta 1-integrin and upregulates ICAM-1, potentially contributing to cell death or to aberrant differentiation via modulation of anchorage and/or signal transduction functions. Quantification of the expression levels of the CAMs by Western analysis is in progress.
It is the purpose of this work to gain knowledge of the glassy materials used as matrices in composites and to study the homogeneity resulting from the curing process. An attempt is made to link the glass transition quantitatively with the presence of a given material. Expoxy resins containing various amounts of hardener (TGDDM/DDS system) were cured in a muffle furnace at 473 K for seven hours. The glass transition temperature, T sub g versus weight minus percent of hardener in the epoxy resin were measured. A limit was rapidly reached in T sub g at only two percent hardener. Thus, the glass transition of the fully cured epoxy-amine matrix seems not much different from the epoxide-epoxide cure. The T sub g versus cure-time for the epoxide-epoxide reaction was also studied. My 720 was cured by itself in an oil bath at 473 K for different lengths of time. The T sub g was found to increase exponentially with the cure time, and a maximum T sub g of about 450 K was reached after eleven hours. The reaction was found to be inhibited by running the sample under argon.
A code has been developed to investigate the kinematic properties of stellar populations of the Galaxy by modeling the distributions of proper motion and line-of-sight velocity. The coordinate frames of reference are discussed in detail and the general matrix transformations valid beyond the solar neighborhood are given. As a first application, the kinematic properties of the magnitude-selected sample of 3993 stars in the Bright Star Catalogue with V less than 6.0 and (B-V) greater than 0 are selected. The observed kinematic distributions are compared with a conventional model that has an exponential disk with scale heights, components of velocity dispersion ellipsoid, and asymmetric drift taken from the literature and defined as functions of spectral type. The comparisons suggest that a significant fraction of the Bright Star Catalogue belongs to a relatively young population that is not properly represented in the model.