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Demonstration that approximate solutions to certain classes of differential and difference equations can be expressed in form of finite state machines. Based on this result, a finite-state machine model of an adaptive gain changer in an aircraft stability augmentation system is developed. Results of simulated flights using the finite-state machine gain changer are presented.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photoelectron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
The theory of multiphoton ionization for an atomic system of arbitrary complexity is developed using a density matrix formalism. An expression is obtained which determines the differential N-photon ionization cross section as a function of the polarization states of the target atom and the incident radiation. The parameters which characterize the photo-electron angular distribution are related to the general reduced matrix elements for the N-photon transition. Two-photon ionization of unpolarized atoms is treated as an illustration of the use of the theory. The dependence of the multiphoton ionization cross section on the polarization state of the incident radiation, which has been observed in two- and three-photon ionization of Cs, is accounted for by the theory. Finally, the photoelectron spin polarization produced by the multiphoton ionization of unpolarized atoms, like the analogous polarization resulting from single-photon ionization, is found to depend on the circular polarization of the incident radiation.
The ionization structure of hydrogen and helium in dusty nebulae is discussed. The general equations for pure hydrogen nebulae are modified to include helium. An approximate analytic solution is presented for Stroemgren radii of hydrogen and helium in the absence of dust. It is shown that these results, with simple modifications, are also applicable to dusty nebulae where the effective absorption cross section of dust grains varies slowly with frequency in the 1000 to 200A range. No analytic solutions are possible if this cross section varies rapidly with frequency. In this case, however, simple coupled differential equations are derived. Approximate analytic expressions are presented for evaluation of the variation of the fraction of ionizing radiation absorbed by dust and the ratio of the volume emission measures of He II to H II regions with the spectrum of the ionizing source, helium abundance, and absorption properties of dust. The effects of dust on the He III zone are discussed. Results are restricted to spherically symmetric nebulae, but nonuniform gas and dust distributions and clumpiness can be taken into account.
A computational scheme is presented for the free vibration analysis of laminated composite elliptic plates. The scheme is based on Hamilton's principle, the Rayleigh-Ritz technique and symmetry considerations and is implemented with the aid of the MACSYMA symbolic manipulation system. The MACYSMA system, through differentiation, integration, and simplification of analytic expressions, produces highly-efficient FORTRAN code for the evaluation of the stiffness and mass coefficients. Multiple use is made of this code to obtain not only the frequencies and mode shapes of the plate, but also the derivatives of the frequencies with respect to various material and geometric parameters.
This paper presents a theoretical study of the response of filament wound composite shells under internal pressure. Each layer of the material is generally cylindrically anisotropic. By using cylindrically anisotropic elasticity field equations and Lekhnitskii's stress functions, a system of sixth-order ordinary differential equations is obtained. The general expressions for the stresses and displacements in the laminated composite shells under internal pressure are discussed. Two composite systems, graphite/epoxy and glass/epoxy, are selected to demonstrate the influence of degree of material anisotropy and fiber orientations on the axial and induced twisting deformation. Stress distributions of (45/-45)s symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratio.
Analytic elasticity solutions for laminated composite cylindrical shells under cylindrical bending are presented. The material of the shell is assumed to be general cylindrically anisotropic. Based on the theory of cylindrical anisotropic elasticity, coupled governing partial differential equations are developed. The general expressions for the stresses and displacements in the laminated composite cylinders are discussed. The closed form solutions based on Classical Shell Theory (CST) and Donnell's (1933) theory are also derived for comparison purposes. Three examples illustrate the effect of radius-to-thickness ratio, coupling and stacking sequence. The results show that, in general, CST yields poor stress and displacement distributions for thick-section composite shells, but converges to the exact elasticity solution as the radius-to-thickness ratio increases. It is also shown that Donnell's theory significantly underestimates the stress and displacement response.
Most methods of system identification of large flexible structures by far are based on the lumped parameter approach. Because of the considerable computational burden due to the large number of unknown parameters, distributed parameter approach, which greatly decreases the number of unknowns, has being investigated. In this paper a distributed parameter model for the estimation of modal characteristics of NASA Mini-Mast truss has been formulated. Both Bernoulli-Euler beam and Timoshenko beam equations are used to characterize the lateral bending vibrations of the truss. The measurement of the lateral displacement at the tip of the truss is provided to the maximum likelihood estimator. Closed-form solutions of the partial differential equations and closed-form expressions of the sensitivity functions are derived so that the estimation algorithm is highly efficient. The resulting estimates from test data by using Timoshenko beam model are found to be comparable to those derived from finite element analysis.
There is a growing practical and theoretical interest in developing accurate macroscopic modelling for flows arising in chemical or physical vapor transport (VT) crystal growth experiments, including those conducted in reduced gravity environments. Rosner was the first person to point out that previously neglected rarefield gas dynamics phenomena (Stefan and bouyancy-driven flows) become rather important sources of convection. In particular, the combination of rarefaction and strong gradients of temperature (and/or concentration) tangential to the side-walls of the ampoule induces convective flows known as thermal (and concentration) 'creep' respectively. His order-of-magnitude estimates revealed that thermal creep effects can be non-negligible even at normal gravitational levels. On the macroscopic level, the bulk fluid mechanics can be adequately described by the familiar macroscopic equations as long as the boundary conditions are modified to account for the integrated effect of kinetic boundary layers adjacent to solid boundaries. Motivated by the growing importance of these phenomena, we have embarked on a series of computational studies to elucidate these fundamental creep-induced effects for a rarefied gas in simple, two-dimensional confined geometries. However, unlike previous related studies, we resort to a microscopic description of the gas, mathematically expressed by the Boltzmann integro-differential equation. We employ the direct simulation Monte Carlo (DSMC) method of Bird, the theoretical foundations and several practical applications. In the case of thermally induced flows, the no-time counter method of Bird is used, as implemented for a hard-sphere gas. The scheme has been also extended to account for realistic molecular interaction models, an extension necessary if the diffusion physics underlying concentration creep are to be captured.
Reactive programming, functional reactive programming, event-based programming, stream programming, and temporal logic all share an underlying commonality: values can vary over time. These languages differ in multiple ways, including the nature of time itself (e.g., continuous or discrete, dense or sparse, implicit or explicit), on how much of the past and future can be referenced, on the kinds of values that can be represented, as well as the mechanisms used to evaluate expressions or formulas. This paper presents a series of abstractions that capture the essence of different forms of time variance. By separating the aspects that differentiate each family of formalisms, we can better express the commonalities and differences between them. We demonstrate our work with a prototype in Haskell that allows us to write programs in terms of a generic interface that can be later instantiated to different abstractions depending on the desired target.
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.
The secretion of fibronectin by differentiating osteoblasts and its accumulation at sites of osteogenesis suggest that fibronectin participates in bone formation. To test this directly, we determined whether fibronectin-cell interactions regulate progressive differentiation of cultured fetal rat calvarial osteoblasts. Spatial distributions of alpha 5 integrin subunit, fibronectin, osteopontin (bone sialoprotein I) and osteocalcin (bone Gla-protein) were similar in fetal rat calvaria and mineralized, bone-like nodules formed by cultured osteoblasts. Addition of anti-fibronectin antibodies to cultures at confluence reduced subsequent formation of nodules to less than 10% of control values, showing that fibronectin is required for normal nodule morphogenesis. Anti-fibronectin antibodies selectively inhibited steady-state expression of mRNA for genes associated with osteoblast differentiation; mRNA levels for alkaline phosphatase and osteocalcin were suppressed, whereas fibronectin, type I collagen and osteopontin were unaffected. To identify functionally relevant domains of fibronectin, we treated cells with soluble fibronectin fragments and peptides. Cell-binding fibronectin fragments (type III repeats 6-10) containing the Arg-Gly-Asp (RGD) sequence blocked both nodule initiation and maturation, whether or not they contained a functional synergy site. In contrast, addition of the RGD-containing peptide GRGDSPK alone did not inhibit nodule initiation, although it did block nodule maturation. Thus, in addition to the RGD sequence, other features of the large cell-binding fragments contribute to the full osteogenic effects of fibronectin. Nodule formation and osteoblast differentiation resumed after anti-fibronectin antibodies or GRGDSPK peptides were omitted from the media, showing that the inhibition was reversible and the treatments were not cytotoxic. Outside the central cell-binding domain, peptides from the IIICS region and antibodies to the N terminus did not inhibit nodule formation. We conclude that osteoblasts interact with the central cell-binding domain of endogenously produced fibronectin during early stages of differentiation, and that these interactions regulate both normal morphogenesis and gene expression.
Localized synthesis of insulin-like growth factors (IGFs) has been broadly implicated in skeletal muscle growth, hypertrophy and regeneration. Virally delivered IGF-1 genes induce local skeletal muscle hypertrophy and attenuate age-related skeletal muscle atrophy, restoring and improving muscle mass and strength in mice. Here we show that the molecular pathways underlying the hypertrophic action of IGF-1 in skeletal muscle are similar to those responsible for cardiac hypertrophy. Transfected IGF-1 gene expression in postmitotic skeletal myocytes activates calcineurin-mediated calcium signalling by inducing calcineurin transcripts and nuclear localization of calcineurin protein. Expression of activated calcineurin mimics the effects of IGF-1, whereas expression of a dominant-negative calcineurin mutant or addition of cyclosporin, a calcineurin inhibitor, represses myocyte differentiation and hypertrophy. Either IGF-1 or activated calcineurin induces expression of the transcription factor GATA-2, which accumulates in a subset of myocyte nuclei, where it associates with calcineurin and a specific dephosphorylated isoform of the transcription factor NF-ATc1. Thus, IGF-1 induces calcineurin-mediated signalling and activation of GATA-2, a marker of skeletal muscle hypertrophy, which cooperates with selected NF-ATc isoforms to activate gene expression programs.
At various time concerns have been expressed that rapid decompressions of compartments of gas pockets and thermal blankets during spacecraft launches may have caused pressure differentials across their walls sufficient to cause minor structural failures, separations of adhesively-joined parts, ballooning, and flapping of blankets. This paper presents a close form equation expressing the expected pressure differentials across the walls of a compartment as a function of the external to the volume pressure drops, the pressure at which the rates occur and the vent capability of the compartment. The pressure profiles measured inside the shrouds of several spacecraft propelled by several vehicles and some profiles obtained from ground vacuum systems have been included. The equation can be used to design the appropriate vent, which will preclude excessive pressure differentials. Precautions and needed approaches for the evaluations of the expected pressures have been indicated. Methods to make a rapid assessment of the response of the compartment to rapid external pressure drops have been discussed. These are based on the evaluation of the compartment vent flow conductance, the volume and the length of time during which the rapid pressure drop occurs.
Loss of weight bearing in the growing rat decreases bone formation, osteoblast numbers, and bone maturation in unloaded bones. These responses suggest an impairment of osteoblast proliferation and differentiation. To test this assumption, we assessed the effects of skeletal unloading using an in vitro model of osteoprogenitor cell differentiation. Rats were hindlimb elevated for 0 (control), 2, or 5 days, after which their tibial bone marrow stromal cells (BMSCs) were harvested and cultured. Five days of hindlimb elevation led to significant decreases in proliferation, alkaline phosphatase (AP) enzyme activity, and mineralization of BMSC cultures. Differentiation of BMSCs was analyzed by quantitative competitive polymerase chain reaction of cDNA after 10, 15, 20, and 28 days of culture. cDNA pools were analyzed for the expression of c-fos (an index of proliferation), AP (an index of early osteoblast differentiation), and osteocalcin (a marker of late differentiation). BMSCs from 5-day unloaded rats expressed 50% less c-fos, 61% more AP, and 35% less osteocalcin mRNA compared with controls. These data demonstrate that cultured osteoprogenitor cells retain a memory of their in vivo loading history and indicate that skeletal unloading inhibits proliferation and differentiation of osteoprogenitor cells in vitro.
Osteoblasts are highly coupled by gap junctions formed primarily by connexin43 (Cx43). We have shown that interference with Cx43 expression or function disrupts transcriptional regulation of osteoblast genes, and that deletion of Cx43 in the mouse causes skeletal malformations, delayed mineralization, and osteoblast dysfunction. Here, we studied the mechanisms by which genetic deficiency of Cx43 alters osteoblast development. While cell proliferation rates were similar in osteoblastic cells derived from calvaria of Cx43-null and wild type mice, camptothecin-induced apoptosis was 3-fold higher in mutant compared to wild type osteoblasts. When grown in mineralizing medium, Cx43-null cells were able to produce mineralized matrix but it took one week longer to reach the same mineralization levels as in normal cells. Likewise, expression of alkaline phosphatase activity per cell--a marker of osteoblast differentiation--was maximal only 2 weeks later in Cx43-null relative to wild-type cells. These observations suggest that Cx43 is important for a normal and timely development of the osteoblastic phenotype. Delayed differentiation and increase programmed cell death may explain the skeletal phenotype of Cx43-null mice.
Investigation of two cases of integrability of a second-order differential equation describing the projection of an axisymmetric satellite orbit on to a plane perpendicular to the rotation axis. It is demonstrated that for these two cases the integration can be carried out either by quadratures or reduced to a first-order differential equation. Analytical and physical properties are expressed, and it is shown that the equation can be derived from the classical plane eikonal equation of geometric optics.
A computer program is presented which achieves a numerical solution for the equations of motion of a noncontacting mechanical face seal. The flexibly-mounted primary seal ring motion is expressed by a set of second order differential equations for three degrees of freedom. These equations are reduced to a set of first order equations and the GEAR software package is used to solve the set of first order equations. Program input includes seal design parameters and seal operating conditions. Output from the program includes velocities and displacements of the seal ring about the axis of an inertial reference system. One example problem is described.