SEARCH · Engineering Papers

Results for “Expression”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 721 records · Page 40

All sources NASA NTRS DOE OSTI

NASA NTRS1979

Metastable sound speed in gas-liquid mixtures

A new method of calculating speed of sound for two-phase flow is presented. The new equation assumes no phase change during the propagation of an acoustic disturbance and assumes that only the total entropy of the mixture remains constant during the process. The new equation predicts single-phase values for the speed of sound in the limit of all gas or all liquid and agrees with available two-phase, air-water sound speed data. Other expressions used in the two-phase flow literature for calculating two-phase, metastable sound speed are reviewed and discussed. Comparisons are made between the new expression and several of the previous expressions -- most notably a triply isentropic equation as used, a triply isentropic equation as used, among others, by Karplus and by Wallis. Appropriate differences are pointed out and a thermodynamic criterion is derived which must be satisfied in order for the triply isentropic expression to be thermodynamically consistent. This criterion is not satisfied for the cases examined, which included two-phase nitrogen, air-water, two-phase parahydrogen, and steam-water. Consequently, the new equation derived is found to be superior to the other equations reviewed.

Bursik, J. W.↗

NASA NTRS1981

Synchrotron emissivity from mildly relativistic particles

Approximate analytic expressions are presented for evaluation of the frequency and angular dependence of synchrotron emissivity from mildly relativistic particles with arbitrary energy spectrum and pitch angle distribution in a given magnetic field. Results agree with previous expressions for a nonrelativistic Maxwellian particle distribution, and when extrapolated to nonrelativistic and extreme relativistic regimes, they also agree with the previous expressions obtained under those limiting conditions. The results from the analytic expression are compared with results from detailed numerical evaluations. Excellent agreement is found not only at frequencies large compared to the gyro-frequency but also at lower frequencies, in fact, all the way down to the gyro-frequency, where the analytic approximations are expected to be less accurate.

Petrosian, V.↗

NASA NTRS1982

Finite amplitude Alfven waves in a multi-ion plasma - Propagation, acceleration, and heating

An expression is derived for the wave action flux of finite-amplitude Alfven waves in a multi-ion plasma. The expression is valid in the presence of dissipative forces and permits an arbitrary angle between the average magnetic field and the wave vector. Applying the conservation of wave action and the first law of thermodynamics yields, for a multi-ion plasma, an expression for the spatial evolution of Alfven wave amplitude in the absence of dissipation. It also gives the relationship between the wave amplitude and the dissipative heating, as well as an expression for the acceleration of an ion species by finite-amplitude Alfven waves. It is pointed out that the acceleration comprises a nondissipative wave pressure that is identical to that derived previously under more restrictive conditions and a new term giving the acceleration that must accompany dissipative heating. The results are discussed in the context of the observations of heavy ions in the solar wind.

Isenberg, P. A.↗

NASA NTRS1985

A study of the applicability of nucleation theory to quasi-thermodynamic transitions of second and higher Ehrenfest-order

The applicability of classical nucleation theory to second (and higher) order thermodynamic transitions in the Ehrenfest sense has been investigated and expressions have been derived upon which the qualitative and quantitative success of the basic approach must ultimately depend. The expressions describe the effect of temperature undercooling, hydrostatic pressure, and tensile stress upon the critical parameters, the critical nucleus size, and critical free energy barrier, for nucleation in a thermodynamic transition of any general order. These expressions are then specialized for the case of first and second order transitions. The expressions for the case of undercooling are then used in conjunction with literature data to estimate values for the critical quantities in a system undergoing a pseudo-second order transition (the glass transition in polystyrene). Methods of estimating the interfacial energy gamma in systems undergoing a first and second order transition are also discussed.

Barker, R. E., Jr.↗

NASA NTRS1986

Viscosity and the Chew-Goldberger-Low equations in the solar corona

A general discussion of the dominant terms in the stress tensor in a magnetized plasma such as the solar corona is presented. The importance of dissipative terms such as electrical resistivity, heat conduction, and interspecies collisions is assessed. For average coronal conditions, the proton stress tensor is found to reduce to the dominant terms in the classical expression for the viscous stress. The classical expression can fail in the transition region, however. In the diffusion region of reconnection, classical viscosity will be appropriate if the resistivity is very large, so that the diffusion region is broad, but in that case the viscous heating is small compared to the resistive heating. On the other hand, the more general expression for the stress tensor is required if the diffusion region is thin; the stress tensor will be important in this case. The electron stress tensor is also considered, and it is shown how the classical expression for electron viscosity can fail in the transition region and lower corona.

Hollweg, J. V.↗

NASA NTRS1987

Slew maneuver dynamics of the Spacecraft Control Laboratory experiment

Mathematical expressions for slew maneuver dynamics are presented. The total kinetic energy expression of the system is given as T = T(0) + T(1) + T(2), where T(0), T(1), and T(2) refer to the kinetic energies of the shuttle, the flexible beam, and the tip mass (the reflector), respectively. The specific equations for each of these are defined and integrated into the total energy expression. Using the chain rule in the Lagrange equations and an expression allowing the transformation of the orbiter angular velocity from the inertial frame to the body-fixed frame, the rotational equations are obtained. Finally, the vibration equations for the beam are derived, again using the Lagrange equations.

Kakad, Y. P.↗

NASA NTRS1986

Analytic evaluation of two-center molecular integrals

By using the Fourier-transform technique, the explicit expressions for the one-electron - two-center overlap integrals of Slater-type atomic orbitals up to 3d are derived. The final expressions are analytic, simple, and independent of local coordinates. Furthermore, they do not contain the nonclosed-form of exponential integrals which were presented in expressions given in earlier work. It is shown that the two-electron - two-center Coulomb integrals, as well as the hybrid integrals, can simply be expressed in terms of these integrals. The numerical instability arising from the situation in which the exponents of the two orbitals are almost equal is discussed, and a solution for this problem based on a Taylor-series expansion of the integral is suggested.

Tai, H.↗

NASA NTRS1989

Kinetic effects of Alfven wave nonlinearity. I - Ponderomotive density fluctuations

The Vlasov theory is used to study kinetic corrections to fluid descriptions of Alfven wave nonlinearity. The method is to obtain an expression for the second-order perturbed distribution function produced by a nonlinear Alfven wave. From this distribution function a kinetically correct expression is obtained for the plasma density perturbation associated with an envelope-modulated Alfven wave. This kinetic theory result differs substantially from the fluid expression when the plasma beta is greater than about 1, and the electron and ion temperatures are approximately equal. This result is of interest because density fluctuations are an observationally accessible indicator of wave nonlinearity in solar system Alfven waves. It also will assist in the determination of properties of Alfven waves in the interstellar medium. Finally, this analysis also yields a kinetically correct expression for u, the magnetic field-aligned component of the plasma fluid velocity.

Spangler, Steven R.↗

NASA NTRS1991

Maximum-entropy probability distributions under Lp-norm constraints

Continuous probability density functions and discrete probability mass functions are tabulated which maximize the differential entropy or absolute entropy, respectively, among all probability distributions with a given L sub p norm (i.e., a given pth absolute moment when p is a finite integer) and unconstrained or constrained value set. Expressions for the maximum entropy are evaluated as functions of the L sub p norm. The most interesting results are obtained and plotted for unconstrained (real valued) continuous random variables and for integer valued discrete random variables. The maximum entropy expressions are obtained in closed form for unconstrained continuous random variables, and in this case there is a simple straight line relationship between the maximum differential entropy and the logarithm of the L sub p norm. Corresponding expressions for arbitrary discrete and constrained continuous random variables are given parametrically; closed form expressions are available only for special cases. However, simpler alternative bounds on the maximum entropy of integer valued discrete random variables are obtained by applying the differential entropy results to continuous random variables which approximate the integer valued random variables in a natural manner. All the results are presented in an integrated framework that includes continuous and discrete random variables, constraints on the permissible value set, and all possible values of p. Understanding such as this is useful in evaluating the performance of data compression schemes.

Dolinar, S.↗

NASA NTRS1993

Kinematics and constraints associated with swashplate blade pitch control

An important class of techniques to reduce helicopter vibration is based on using a Higher Harmonic controller to optimally define the Higher Harmonic blade pitch. These techniques typically require solution of a general optimization problem requiring the determination of a control vector which minimizes a performance index where functions of the control vector are subject to inequality constraints. Six possible constraint functions associated with swashplate blade pitch control were identified and defined. These functions constrain: (1) blade pitch Fourier Coefficients expressed in the Rotating System, (2) blade pitch Fourier Coefficients expressed in the Nonrotating System, (3) stroke of the individual actuators expressed in the Nonrotating System, (4) blade pitch expressed as a function of blade azimuth and actuator stroke, (5) time rate-of-change of the aforementioned parameters, and (6) required actuator power. The aforementioned constraints and the associated kinematics of swashplate blade pitch control by means of the strokes of the individual actuators are documented.

Leyland, Jane A.↗

NASA NTRS1995

A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence: An analytical theory

The mathematical consequences of a few simple scaling assumptions about the effects of compressibility are explored using a simple singular perturbation idea and the methods of statistical fluid mechanics. Representations for the pressure-dilation and dilatational dissipation covariances appearing in single-point moment closures for compressible turbulence are obtained. While the results are expressed in the context of a second-order statistical closure they provide some interesting and very clear physical metaphors for the effects of compressibility that have not been seen using more traditional linear stability methods. In the limit of homogeneous turbulence with quasi-normal large-scales the expressions derived are - in the low turbulent Mach number limit - asymptotically exact. The expressions obtained are functions of the rate of change of the turbulence energy, its correlation length scale, and the relative time scale of the cascade rate. The expressions for the dilatational covariances contain constants which have a precise and definite physical significance; they are related to various integrals of the longitudinal velocity correlation. The pressure-dilation covariance is found to be a nonequilibrium phenomena related to the time rate of change of the internal energy and the kinetic energy of the turbulence. Also of interest is the fact that the representation for the dilatational dissipation in turbulence, with or without shear, features a dependence on the Reynolds number. This article is a documentation of an analytical investigation of the implications of a pseudo-sound theory for the effects of compressibility.

Ristorcelli, J. R.↗

NASA NTRS1996

A Potato cDNA Encoding a Homologue of Mammalian Multidrug Resistant P-Glycoprotein

A homologue of the multidrug resistance (MDR) gene was obtained while screening a potato stolon tip cDNA expression library with S-15-labeled calmodulin. The mammalian MDR gene codes for a membrane-bound P-glycoprotein (170-180 kDa) which imparts multidrug resistance to cancerous cells. The potato cDNA (PMDR1) codes for a polypeptide of 1313 amino acid residues (ca. 144 kDa) and its structural features are very similar to the MDR P-glycoprotein. The N-terminal half of the PMDR1-encoded protein shares striking homology with its C-terminal half, and each half contains a conserved ATP-binding site and six putative transmembrane domains. Southern blot analysis indicated that potato has one or two MDR-like genes. PMDR1 mRNA is constitutively expressed in all organs studied with higher expression in the stem and stolon tip. The PMDR1 expression was highest during tuber initiation and decreased during tuber development.

Wang, W.↗

NASA NTRS1996

Calcium-Dependent Protein Kinase Genes in Corn Roots

Two cDNAs encoding Ca-2(+) - Dependent Protein Kinases (CDPKs), Corn Root Protein Kinase 1 and 2 (CRPK 1, CRPK 2) were isolated from the root tip library of corn (Zea mays L., cv. Merit) and their nucleotide sequences were determined. Deduced amino acid sequences of both the clones have features characteristic of plant CDPKS, including all 11 conserved serine/threonine kinase subdomains, a junction domain and a calmodulin-like domain with four Ca-2(+), -binding sites. Northern analysis revealed that CRPKI mRNA is preferentially expressed in roots, especially in the root tip; whereas, the expression of CRPK2 mRNA was very low in all the tissues tested. In situ hybridization experiments revealed that CRPKI mRNA is highly expressed in the root apex, as compared to other parts of the root. Partially purified CDPK from the root tip phosphorylates syntide-2, a common peptide substrate for plant CDPKs, and the phosphorylation was stimulated 7-fold by the addition of Ca-2(+). Our results show that two CDPK isoforms are expressed in corn roots and they may be involved in the Ca-2(+)-dependent signal transduction process.

Takezawa, D.↗

NASA NTRS1996

Metastable Solution Thermodynamic Properties and Crystal Growth Kinetics

The crystal growth rates of NH4H2PO4, KH2PO4, (NH4)2SO4, KAl(SO4)2 central dot 12H2O, NaCl, and glycine and the nucleation rates of KBr, KCl, NaBr central dot 2H2O, (NH4)2Cl, and (NH4)2SO4 were expressed in terms of the fundamental driving force of crystallization calculated from the activity of supersaturated solutions. The kinetic parameters were compared with those from the commonly used kinetic expression based on the concentration difference. From the viewpoint of thermodynamics, rate expressions based on the chemical potential difference provide accurate kinetic representation over a broad range of supersaturation. The rates estimated using the expression based on the concentration difference coincide with the true rates of crystallization only in the concentration range of low supersaturation and deviate from the true kinetics as the supersaturation increases.

Kim, Soojin↗

NASA NTRS1995

Radiation Pressure, Poynting-Robertson Drag, and Solar Wind Drag in the Restricted Three-Body Problem

In this paper, we examine the effects of radiation pressure, Poynting-Robertson (PR) drag, and solar wind drag on dust grains trapped in mean motion resonances with the Sun and Jupiter in the restricted (negligible dust mass) three-body Problem. We especially examine the evolution of dust grains in the 1:1 resonance. As a first step, the Sun and Jupiter are idealized to both be in circular orbit about a common center of mass (circular restricted three-body problem). From the equation of motion of the dust particle in the rotating reference frame, the drag-induced time rate of change of its Jacobi "constant," C, is then derived and expressed in spherical coordinates. This new mathematical expression in spherical coordinates shows that C, in the 1:1 resonance, both oscillates and secularly increases with increasing time. The new expression gives rise to an easy understanding of how an orbit evolves when the radiation force and solar wind drag are included. All dust grain orbits are unstable in time when PR and solar wind drag are included in the Sun-Jupiter-dust system. Tadpole orbits evolve into horseshoe orbits; and these orbits continuously expand in size to lead to close encounters with Jupiter. Permanent trapping is impossible. Orbital evolutions of a dust grain trapped in the 1:1 resonance in the planar circular, an inclined case, an eccentric case, and the actual Sun-Jupiter case are numerically simulated and compared with each other and show grossly similar time behavior. Resonances other than 1:1 are also explored with the new expression. Stable exterior resonance trapping may be possible under certain conditions. One necessary condition for such a trap is derived. Trapping in interior resonances is shown to be always unstable.

Liou, Jer-Chyi↗

NASA NTRS1961

Applicability of Mixing Length Theory to a Turbulent Vortex System

The ability of mixing length theory to correlate vortex data is evaluated. Expressions are derived for eddy diffusivity by applying the techniques of von Karman and Prandtl which have been established for pipe flow. Total and static pressures were measured from the outer radius to the exhaust-nozzle radius of a vortex generator for a range of mass flows. These data are combined with Navier-Stokes solutions for this region of a compressible vortex to determine turbulent Reynolds numbers. The Reynolds number is related to Prandtl and Karman functions for various assumed boundary conditions, and the experimental data are used to determine the usefulness of these expressions. The following conclusions were reached: (1) Mixing length functions developed by applying von Karman's similarity hypothesis to vortex motion correlate the data better than do Prandtl functions obtained with the assumption that mixing length is proportional to radius. (2) Some of the expressions developed do not adequately represent the experimental data. (3) The data are correlated with acceptable scatter by evaluating the fluid radial inertia at the outer boundary and the shear stress at the inner boundary. The universal constant K was found to be 0.04 to 0.08, rather than the value of 0.4 which is accepted for rectilinear flow. (4) The data are best correlated by a modified Karman expression which includes an effect of radial inertia, as well as shear stress, on eddy diffusivity.

Ragsdale, Robert G.↗

NASA NTRS1998

Applications of Anabolic Vitamin D Analogs as Countermeasures to Bone Loss

The experiments in Round 2 were designed to extend the results of our efforts in Round 1 which led us to hypothesize that the seco-steroid, 1,25-dihydroxyvitamin D3[1,25(OH)2D3], acts in synergy with parathyroid hormone (PTH) to regulate bone calcium homeostasis. Our work centered on one particular target of 1,25(OH)2D3 action, the voltage-sensitive calcium channels (VSCC's), which are activated acutely by this steroid within milliseconds of exposure . A second area of research focused on the effects of mechanical strain on VSCC expression in bone. These experiments were performed in collaboration with Dr. Steven Goldstein (Univ. Michigan), who generously provided RNA extracted from dog bones that had been exposed to mechanical strain in vivo. Our results suggest that mechanical loading elevated VSCC expression in the long bones from 3 of the 6 animals tested. A second line of experimentation, carried out in collaboration with Dr. Randall Duncan, a NASA-funded investigator in Indianapolis, centered on RT-PCR analysis of effects of mechanical strain on Ca2(+) channel expression in cultured bone cells. Compared to unstrained controls, the expression of vitamin-D-sensidve Ca2(+) channels is elevated 3- to 5-fold over a 24 hr period.

Karin, Norman J.↗

NASA NTRS1999

The Role of Calcium in the Response of Osteoblasts to Mechanical Stimulation

A major biomedical concern in the exploration and development of space is the rapid loss of bone associated with extended periods of spaceflight. Mineral content, bone formation, matrix protein production and total body calcium are all reduced during long-term periods of weightlessness. These effects of weightlessness appears to be due to decreases in the anabolic function of osteoblasts and osteocytes rather than changes in the resorptive activity of osteoclasts. Conversely, subjecting the skeleton to exogenous mechanical loading increases matrix protein synthesis and bone formation rate, a process which also appears mediated through osteogenic cells. Osteoblasts have been shown to respond to a number of types of mechanical stimulation. However recently we have demonstrated that osteoblasts respond to fluid shear, but not physiologic levels of mechanical strain, with increases in expression of the matrix protein, osteopontin. We have also shown similar responses in other markers for the anabolic response in bone. The expression of the early response gene, c-fos, and the inducible-isoform of the prostaglandin synthetic enzyme, cyclooygenase-2 (COX-2), both increase rapidly in response to fluid shear, but not strain. How osteoblasts and osteocytes perceive mechanical stimuli and convert this stimulus into a biochemical event within the cell is still unknown. However, examination of the cellular events following mechanical stimulation indicate that two of the earliest responses are a rapid increase in intracellular calcium ([Ca(2+)](sub i)) and a reorganization of the actin cytoskeleton. The increase in [Ca(2+)](sub i) is dependent on the presence of extracellular Ca(2+), suggesting the activation of membrane Ca(2+) channel. We have previously characterized a mechanosensitive, cation-selective channel (MSCC) in osteoblast-like clonal cells, which we postulate is important in this early response to mechanical loading. Using an antisense oligodeoxynucleotide strategy, we have tentatively identified this channel as an isoform of the alc subunit of the dihydropyridine-sensitive, voltage sensitive Ca(2+) channel (VSCC). However, a major component in this mechanically induced rise in [Ca(2+)](sub i) is the release of Ca(2+) from intracellular stores. The actin cytoskeleton also rapidly responds to fluid shear with an increase in stress fiber formation and a realignment of the cell parallel to the direction of flow. To ascertain whether these two observations are related and how they effect shear-induced gene expression, we examined the role of Ca(2+) channels and intracellular Ca(2+) release on cytoskeletal reorganization and the resultant increases in the expression and production of c-fos and COX-2 in response to fluid shear.

Duncan, R. L.↗