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NASA NTRS1990

Fourier analysis of finite element preconditioned collocation schemes

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Deville, Michel O.↗

NASA NTRS1993

An efficient model for coupling structural vibrations with acoustic radiation

The scattering of an incident wave by a flexible panel is studied. The panel vibration is governed by the nonlinear plate equations while the loading on the panel, which is the pressure difference across the panel, depends on the reflected and transmitted waves. Two models are used to calculate this structural-acoustic interaction problem. One solves the three dimensional nonlinear Euler equations for the flow-field coupled with the plate equations (the fully coupled model). The second uses the linear wave equation for the acoustic field and expresses the load as a double integral involving the panel oscillation (the decoupled model). The panel oscillation governed by a system of integro-differential equations is solved numerically and the acoustic field is then defined by an explicit formula. Numerical results are obtained using the two models for linear and nonlinear panel vibrations. The predictions given by these two models are in good agreement but the computational time needed for the 'fully coupled model' is 60 times longer than that for 'the decoupled model'.

Frendi, Abdelkader↗

NASA NTRS1997

Time Evolution of Modeled Reynolds Stresses in Planar Homogeneous Flows

The analytic expression of the time evolution of the Reynolds stress anisotropy tensor in all planar homogeneous flows is obtained by exact integration of the modeled differential Reynolds stress equations. The procedure is based on results of tensor representation theory, is applicable for general pressure-strain correlation tensors, and can account for any additional turbulence anisotropy effects included in the closure. An explicit solution of the resulting system of scalar ordinary differential equations is obtained for the case of a linear pressure-strain correlation tensor. The properties of this solution are discussed, and the dynamic behavior of the Reynolds stresses is studied, including limit cycles and sensitivity to initial anisotropies.

Jongen, T.↗

NASA NTRS2002

Tissue engineering skeletal muscle for orthopaedic applications

With current technology, tissue-engineered skeletal muscle analogues (bioartificial muscles) generate too little active force to be clinically useful in orthopaedic applications. They have been engineered genetically with numerous transgenes (growth hormone, insulinlike growth factor-1, erythropoietin, vascular endothelial growth factor), and have been shown to deliver these therapeutic proteins either locally or systemically for months in vivo. Bone morphogenetic proteins belonging to the transforming growth factor-beta superfamily are osteoinductive molecules that drive the differentiation pathway of mesenchymal cells toward the chondroblastic or osteoblastic lineage, and stimulate bone formation in vivo. To determine whether skeletal muscle cells endogenously expressing bone morphogenetic proteins might serve as a vehicle for systemic bone morphogenetic protein delivery in vivo, proliferating skeletal myoblasts (C2C12) were transduced with a replication defective retrovirus containing the gene for recombinant human bone morphogenetic protein-6 (C2BMP-6). The C2BMP-6 cells constitutively expressed recombinant human bone morphogenetic protein-6 and synthesized bioactive recombinant human bone morphogenetic protein-6, based on increased alkaline phosphatase activity in coincubated mesenchymal cells. C2BMP-6 cells did not secrete soluble, bioactive recombinant human bone morphogenetic protein-6, but retained the bioactivity in the cell layer. Therefore, genetically-engineered skeletal muscle cells might serve as a platform for long-term delivery of osteoinductive bone morphogenetic proteins locally.

Review↗

NASA NTRS2004

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition: Inclusion of Exchange - 2

The development of a practical method of accurately calculating the full scattering amplitude, without making a partial wave decomposition is continued. The method is developed in the context of electron-hydrogen scattering, and here exchange is dealt with by considering e-H scattering in the static exchange approximation. The Schroedinger equation in this approximation can be simplified to a set of coupled integro-differential equations. The equations are solved numerically for the full scattering wave function. The scattering amplitude can most accurately be calculated from an integral expression for the amplitude; that integral can be formally simplified, and then evaluated using the numerically determined wave function. The results are essentially identical to converged partial wave results.

Shertzer, Janine↗

NASA NTRS1996

The regulation and regulatory role of collagenase in bone

Interstitial collagenase plays an important role in both the normal and pathological remodeling of collagenous extracellular matrices, including skeletal tissues. The enzyme is a member of the family of matrix metalloproteinases. Only one rodent interstitial collagenase has been found but there are two human enzymes, human collagenase-1 and -3, the latter being the homologue of the rat enzyme. In developing rat and mouse bone, collagenase is expressed by hypertrophic chondrocytes, osteoblasts, and osteocytes, a situation that is replicated in a fracture callus. Cultured osteoblasts derived from neonatal rat calvariae show greater amounts of collagenase transcripts late in differentiation. These levels can be regulated by parathyroid hormone (PTH), retinoic acid, and insulin-like growth factors, as well as the degree of matrix mineralization. Much of the work on collagenase in bone has been derived from studies on the rat osteosarcoma cell line, UMR 106-01. All bone-resorbing agents stimulate these cells to produce collagenase mRNA and protein, with PTH being the most potent stimulator. Determination of secreted levels of collagenase has been difficult because UMR cells, normal rat osteoblasts, and rat fibroblasts possess a scavenger receptor that removes the enzyme from the extracellular space, internalizes and degrades it, thus imposing another level of control. PTH can also regulate the abundance of the receptor as well as the expression and synthesis of the enzyme. Regulation of the collagenase gene by PTH appears to involve the cAMP pathway as well as a primary response gene, possibly Fos, which then contributes to induction of the collagenase gene. The rat collagenase gene contains an activator protein-1 sequence that is necessary for basal expression, but other promoter regions may also participate in PTH regulation. Thus, there are many levels of regulation of collagenase in bone perhaps constraining what would otherwise be a rampant enzyme.

NASA Discipline Musculoskeletal↗

NASA NTRS1982

A theoretical study of a two-wavelength lidar technique for the measurement of atmospheric temperature profiles

The theory of differential absorption lidar measurements for lines with a Voigt profile is given and applied to a two-wavelength technique for measuring the atmospheric temperature profile using a high J line in the oxygen A band. Explicit expressions for the temperature and pressure dependence of the absorption coefficient are developed for lines with a Voigt profile. An iteration procedure for calculating the temperature for narrow laser bandwidths is described which has an accuracy better than 0.2 K for bandwidths less than 0.01/cm. To reduce the errors in lidar measurements due to uncertainties in pressure, a method for estimating the pressure from the temperature profile is described. A procedure for extending the differential absorption technique to the case of finite laser bandwidth with good accuracy is also described. Simulation results show that a knowledge of the laser frequency is needed to 0.005/cm for accurate temperature measurements. Evaluation of the sensitivity for both ground- and Shuttle-based measurements shows accuracies generally better than 1 K. This technique allows up to an order of magnitude improvement in sensitivity compared to other differential absorption lidar techniques.

Korb, C. L.↗

NASA NTRS1979

Note on the practical significance of the Drazin inverse

The solution of the differential system Bx = Ax + f where A and B are n x n matrices, and A - Lambda B is not a singular pencil, may be expressed in terms of the Drazin inverse. It is shown that there is a simple reduced form for the pencil A - Lambda B which is adequate for the determination of the general solution and that although the Drazin inverse could be determined efficiently from this reduced form it is inadvisable to do so.

Wilkinson, J. H.↗

NASA NTRS2005

Lunar and Planetary Science XXXVI, Part 17

The following topics were discussed: A Model for the Formation of Paterae on Io; LIBS-based Detection of As, Br, C, Cl, P, and S in the VUV Spectral Region in a Mars Atmosphere; Mass Independent Sulfur in Achondrites: Possible Evidence of Photochemistry in the Solar Nebula; Grain Size-dependent Viscosity and Oceans in Icy Satellites; Claritas Paleolake Studied from the MEX HRSC Data; Mars Express HRSC Colors of White Rock, Arabia, Mars; Lava and Flows of the Arcadia Region of Mars; Isotopic Composition of Lunar Soils and the Early Differentiation of the Moon; Trace Element Analysis of Lunar Soils by ICP-MS; Highly Siderophile Elements and Osmium Isotope Systematics in Ureilites: Are the Carbonaceous Veins Primary Components?; Evaporative Evolution of Martian Brines Based on Halogens in Nakhlites and MER Samples; Io from High-Resolution Galileo PPR Data Taken Simultaneously with SSI or NIMS Observations; Loki, Io: Groundbased Observations and a Model for Periodic Overturn; Deconstructing a Few Myths in the Interpretation of Satellite-Altitude Crustal Magnetic Field: Examples from Mars Global Surveyor; Semi-Autonomous Rover Operations: A Mars Technology Program Demonstration; Rotational Studies of Asteroids with Small Telescopes; Mineralogy and Temperature-induced Spectral Investigations of A-type Asteroids 246 Asporina and 446 Aeternitas; and Thermal History Calculations Versus Full Convection Models: Application to the Thermal Evolution of Mercury. Recent Solar-Proton Fluxes

Source record↗

NASA NTRS2010

Response of Staphylococcus Aureus to a Spaceflight Analogue

The decreased gravity of the spaceflight environment creates quiescent, low fluid shear conditions. This environment can impart considerable effects on the physiology of microorganisms as well as their interactions with potential hosts. Using the rotating wall vessel (RWV), as a spaceflight analogue, the consequence of low fluid shear culture on microbial pathogenesis has provided a better understanding of the risks to the astronaut crew from infectious microorganisms. While the outcome of low fluid shear culture has been investigated for several bacterial pathogens, little has been done to understand how this environmental factor affects Staphylococcus aureus. S. aureus is an opportunistic human pathogen which presents a high level of infection risk to the crew, as it has been isolated from both the space shuttle and International Space Station. Given that approximately forty percent of the population are carriers of the bacteria, eradication of this organism from in flight environments is impractical. These reasons have lead to us to assess the response of S. aureus to a reduced fluid shear environment. Culture in the RWV demonstrated that S. aureus grown under the low-shear condition had lower cell concentrations after 10 hours when compared to the control culture. Furthermore, the low-shear cultured bacteria displayed a reduction in carotenoid production, pigments responsible for their yellow/gold coloration. When exposed to various environmental stressors, post low-shear culture, a decrease in the ability to survive oxidative assault was observed compared to control cultures. The low fluid shear environment also resulted in a decrease in hemolysin secretion, a staphylococcal toxin responsible for red blood cell lysis. When challenged by the immune components present in human whole blood, low-shear cultured S. aureus demonstrated significantly reduced survival rates as compared to the control culture. Assays to determine the duration of these alterations demonstrated that the low-shear response could be lost in as few as 2.5 hours. These changes in phenotypic properties prompted investigation into variations occurring at the genetic level. Microarray analysis of low-shear cultured S. aureus revealed the differential regulation of genes involved in metabolism, stress response, and phosphate transfer. Additional genetic analysis with quantitative real-time PCR revealed alterations in the expression of Hfq, the conserved RNA chaperone protein involved in global gene regulation. Hfq has been connected to the regulation of a spaceflight microgravity response in S. typhimurium. These findings in S. aureus suggest an evolutionary conserved response to spaceflight conditions among structurally-diverse microorganisms. Furthermore, the reduction in pigmentation, hemolysin secretion, and survival against oxidative stress and immunologically active whole blood demonstrate an overall decrease in the virulence factors of S. aureus in response to spaceflight-like conditions.

Castro, S. L.↗

NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗

NASA NTRS1992

Identification of a mouse B-type cyclin which exhibits developmentally regulated expression in the germ line

To begin to examine the function of cyclins in mammalian germ cells, we have screened an adult mouse testis cDNA library for the presence of B-type cyclins. We have isolated cDNAs that encode a murine B-type cyclin, which has been designated cycB1. cycB1 was shown to be expressed in several adult tissues and in the midgestation mouse embryo. In the adult tissues, the highest levels of cycB1 transcripts were seen in the testis and ovary, which contain germ cells at various stages of differentiation. The major transcripts corresponding to cycB1 are 1.7 and 2.5 kb, with the 1.7 kb species being the predominant testicular transcript and the 2.5 kb species more abundant in the ovary. Examination of cDNAs corresponding to the 2.5 kb and 1.7 kb mRNAs revealed that these transcripts encode identical proteins, differing only in the polyadenylation signal used and therefore in the length of their 3' untranslated regions. Northern blot and in situ hybridization analyses revealed that the predominant sites of cycB1 expression in the testis and ovary were in the germinal compartment, particularly in early round spermatids in the testis and growing oocytes in the ovary. Thus cycB1 is expressed in both meiotic and postmeiotic cells. This pattern of cycB1 expression further suggests that cycB1 may have different functions in the two cell types, only one of which correlates with progression of the cell cycle.

NASA Discipline Developmental Biology↗

NASA NTRSDate not supplied

A Temporal Differential Dynamic Logic Formal Embedding

Differential dynamic logic is a formal framework to specify and reason about hybrid programs (HPs). The core of dL is a proof calculus that contains a collection of axioms and rules for the rigorous verification of properties of HPs. Recently, dL has been embedded within the theorem prover Prototype Verification System (PVS) resulting in the tool Plaidypvs2. The integration of dL into PVS expands its expressive power; user defined functions, such as trigonometric and other transcendental functions, can be used inside the dL framework, and meta-reasoning about HPs can be performed, including reasoning about entire classes of HPs, specified using dependent types in PVS. The differential temporal dynamic logic (dTL2) extends dL with temporal logic operators to reason about all the states reachable during the execution of an HP. This paper presents a work in progress focusing on embedding dTL2 in PVS as an extension of Plaidypvs. Plaidypvs is expanded with the formalization of a trace semantics for HPs, the definition of the LTL temporal operators eventually and globally, and the implementation of the proof calculus for dTL2. This new embedding has the same capabilties as Plaidypvs, which allows user defined functions and meta-reasoning of properties of HPs. To the best of the authors’ knowledge this is the first implementation of dTL2.

differential dynamic logic↗

NASA NTRS1974

A theory of wave scatter from an inhomogeneous medium with a slightly rough boundary and its application to sea ice

An analytical theory of electromagnetic wave scattering from an inhomogeneous medium with a slightly rough boundary surface is formulated. The inhomogeneity in the medium is assumed to vary continuously in the vertical direction and to have a small random variation in the horizontal direction. The medium is assumed to consist of two layers. Maxwell's equations are solved by using the small perturbation method together with Fourier transform technique. The resulting differential equations are solved by using WKB and variation of parameter methods. Field amplitudes in each medium are determined by taking boundary conditions into account. The expressions for first order polarized radar backscatter cross-section are obtained. An attempt is made to apply the developed theory to compute sea ice scatter. Numerical calculations are performed for polarized radar backscatter cross-section at two frequencies, 13.3 GHz and 400 MHz. It is shown that WKB method is applicable at both of these frequencies. Theoretical results are compared with the experimental results obtained from NASA Earth Resources Program mission 126. Theoretical results and experimental results are in good agreement.

Parashar, S. K.↗

NASA NTRS1979

Development of analytical orbit propagation technique with drag

Two orbit computation methods were used: (1) numerical method- The solution to the satellite differential equations were solved in a step-by-step manner, using a mathematical algorithm taken from numerical analysis; and (2) analytical method - The solution was expressed by explicit functions of the independent variable. Analytical drag modules, tesseral terms initialization module, second order and long period terms module, and verification testing of the ASOP program were also considered.

Source record↗

NASA NTRS1975

Propagation of high amplitude higher order sounds in slightly soft rectangular ducts, carrying mean flow

The resonance expansion method, developed to study the propagation of sound in rigid rectangular ducts is applied to the case of slightly soft ducts. Expressions for the generation and decay of various harmonics are obtained. The effect of wall admittance is seen through a dissipation function in the system of nonlinear differential equations, governing the generation of harmonics. As the wall admittance increases, the resonance is reduced. For a given wall admittance this phenomenon is stronger at higher input intensities. Both the first and second order solutions are obtained and the results are extended to the case of ducts having mean flow.

Wang, K. S.↗

NASA NTRS1977

Computer transformation of partial differential equations into any coordinate system

The use of tensors to provide a compact way of writing partial differential equations in a form valid in all coordinate systems is discussed. In order to find solutions to the equations with their boundary conditions they must be expressed in terms of the coordinate system under consideration. The process of arriving at these expressions from the tensor formulation was automated by a software system, TENSR. An allied system that analyzes the resulting expressions term by term and drops those that are negligible is also described.

Sullivan, R. D.↗

NASA NTRS1988

Estimates of green tensors for certain boundary value problems

Consider the first boundary value problem for a stationary Navier-Stokes system in a bounded three-dimensional region Omega with the boundary S: delta v = grad p+f, div v=0, v/s=0. Odqvist (1930) developed the potential theory and formulated the Green tensor for the above problem. The basic singular solution used by Odqvist to express the Green tensor is given. A theorem generalizing his results is presented along with four associated theorems. A specific problem associated with the study of the differential properties of the solution of stationary problems of magnetohydrodynamics is examined.

Solonnikov, V.↗