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NASA NTRS1985

Implicit flux-split schemes for the Euler equations

Recent progress in the development of implicit algorithms for the Euler equations using the flux-vector splitting method is described. Comparisons of the relative efficiency of relaxation and spatially-split approximately factored methods on a vector processor for two-dimensional flows are made. For transonic flows, the higher convergence rate per iteration of the Gauss-Seidel relaxation algorithms, which are only partially vectorizable, is amply compensated for by the faster computational rate per iteration of the approximately factored algorithm. For supersonic flows, the fully-upwind line-relaxation method is more efficient since the numerical domain of dependence is more closely matched to the physical domain of dependence. A hybrid three-dimensional algorithm using relaxation in one coordinate direction and approximate factorization in the cross-flow plane is developed and applied to a forebody shape at supersonic speeds and a swept, tapered wing at transonic speeds.

Thomas, J. L.↗
NASA NTRS1986

Theoretical studies of Resonance Enhanced Stimulated Raman Scattering (RESRS) of frequency doubled Alexandrite laser wavelengths in cesium vapor

This work focused on understanding the effects of arbitrary transverse and longitudinal relaxation rates on the susceptibilities of coherently driven three-level systems. The approximation of a single relaxation rate often made in previous work is strongly invalidated by the variation in the spontaneous emission lifetime between various atomic level pairs in systems such as cesium. It is of great importance to the problem of nonlinear infrared generation to determine the dependence of both real and imaginary susceptibility on relaxation rates. The imaginary susceptibility on the pump transition determines the absorption of pump photons and the imaginary susceptibility on the laser transition determines the spectral dependence of the gain. This is of particular importance for pure Raman emission (i.e., absorption at linecenter of the gain transition) as it determines the tunability characteristics we are aiming to predict. The real susceptibility is important when cavities are used at the signal field as this will determine the loaded resonance of the Raman oscillator. Researchers show that in some cases which result from having different relaxation rates mode splitting may result, allowing more than one frequency to have the same Raman wavelength, possibly resulting in a temporal instability.

Lawandy, N. M.↗
NASA NTRS1986

Group-kinetic theory of turbulence

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Tchen, C. M.↗
NASA NTRS1987

Gaussian maximum likelihood and contextual classification algorithms for multicrop classification

The paper reviews some of the ways in which context has been handled in the remote-sensing literature, and additional possibilities are introduced. The problem of computing exhaustive and normalized class-membership probabilities from the likelihoods provided by the Gaussian maximum likelihood classifier (to be used as initial probability estimates to start relaxation) is discussed. An efficient implementation of probabilistic relaxation is proposed, suiting the needs of actual remote-sensing applications. A modified fuzzy-relaxation algorithm using generalized operations between fuzzy sets is presented. Combined use of the two relaxation algorithms is proposed to exploit context in multispectral classification of remotely sensed data. Results on both one artificially created image and one MSS data set are reported.

Di Zenzo, Silvano↗
NASA NTRS1988

The rate parameters for coupled vibration-dissociation in a generalized SSH approximation

A theoretical study of vibrational excitations and dissociations of nitrogen undergoing a nonequilibrium relaxation process upon heating and cooling is reported. The rate coefficients for collisional induced vibrational transitions and transitions from a bound vibrational state into a dissociative state have been calculated using an extension of the theory originally proposed by Schwarz (SSH) et al. (1952). High-lying vibrational states and dissociative states were explicitly included but rotational energy transfer was neglected. The transition probabilities calculated from the SSH theory were fed into the master equation, which was integrated numerically to determine the population distribution of the vibrational states as well as bulk thermodynamic properties. The results show that: (1) the transition rates have a minimum near the middle of the bound vibrational levels, causing a bottleneck in the vibrational relaxation and dissociation rates; (2) high vibrational states are always in equilibrium with the dissociative state; (3) for the heating case, only the low vibrational states relax according to the Landau-Teller theory; (4) for the cooling case, vibrational relaxation cannot be described by a rate equation; (5) Park's (1985, 1988) two-temperature model is approximately valid; and (6) the average vibrational energy removed in dissociation is about 30 percent of the dissociation energy.

Sharma, Surendra P.↗
NASA NTRS1989

Conservation equations and physical models for hypersonic air flows over the aeroassist flight experiment vehicle

The code development and application program for the Langley Aerothermodynamic Upwind Relaxation Algorithm (LAURA), with emphasis directed toward support of the Aeroassist Flight Experiment (AFE) in the near term and Aeroassisted Space Transfer Vehicle (ASTV) design in the long term is reviewed. LAURA is an upwind-biased, point-implicit relaxation algorithm for obtaining the numerical solution to the governing equations for 3-D, viscous, hypersonic flows in chemical and thermal nonequilibrium. The algorithm is derived using a finite volume formulation in which the inviscid components of flux across cell walls are described with Roe's averaging and Harten's entropy fix with second-order corrections based on Yee's Symmetric Total Variation Diminishing scheme. Because of the point-implicit relaxation strategy, the algorithm remains stable at large Courant numbers without the necessity of solving large, block tri-diagonal systems. A single relaxation step depends only on information from nearest neighbors. Predictions for pressure distributions, surface heating, and aerodynamic coefficients compare well with experimental data for Mach 10 flow over an AFE wind tunnel model. Predictions for the hypersonic flow of air in chemical and thermal nonequilibrium over the full scale AFE configuration obtained on a multi-domain grid are discussed.

Gnoffo, Peter A.↗
NASA NTRS1990

Solar Response to Luminosity Variations

The connection between solar luminosity and magnetic fields is now well-established. Magnetic fields under the guise of sunspots and faculae enhance or suppress heat transfer through the solar surface, leading to changes in the total solar luminosity. This raises the question of the effect that such surface heat transfer perturbations have on the internal structure of the sun. The problem has been considered previously by Foukal and Spruit. Here, researchers generalize the calculation of Spruit, removing the assumption of a constant heat diffusivity coefficient by treating the full mixing length heat transfer expression. Further, they treat the surface conditions in a simpler manner, and show that the previous conclusions of Foukal and Spruit are unaffected by these modifications. The model shows that following the application of a step function emissivity change: a fraction 1 - D(sub 0) of the luminosity change relaxes away after approx. 50 days. This corresponds to the thermal diffusion time across the convection zone, adjusting to a value in correspondence with the surface change. In other words, the whole convection zone feels the perturbation on this timescale. The remaining fraction relaxes away on a timescale of 10 to the 5th power years, corresponding to the convective layer radiating away enough energy so that it can adjust to its new adiabat. These are the same results arrived at by Spruit and Foukal. For variations of sigma on timescales of 10 to 200 years, then, the only important relaxation is the 50 day one. If the amplitude of this relaxation is small, the luminosity follows the sigma variation.

Arendt, S.↗
NASA NTRS1991

Vibration-dissociation coupling in nonequilibrium flows

The purpose of the study is to evaluate all important physical phenomena contributing to the vibration-dissociation problem by developing a numerical technique for the simulation of the vibrational relaxation and dissociation/recombination of N(2) in an isothermal box. A set of coupled master equations representing each vibrational level of N(2) is solved, and both V-V and V-T exchanges between molecules and atoms are included, along with the effects of dissociation and recombustion from/to each level. It is observed that the inverse range parameter has a strong impact on the vibrational exchange rates and relaxation. In a heating case, the lower vibrational levels relax through a series of equilibrium distributions, while in a cooling case, a population inversion is formed in the upper levels. Other cases of heating and cooling will be simulated, and together with this work, used to develop a matrix of nonequilibrium relaxation runs.

Landrum, D. Brian↗
NASA NTRS1992

Analysis of sonic boom data to quantify distortions of shock profiles

Researchers at Penn State have been examining some sonic boom waveforms recorded during overflights by the Air Force which have become available to NASA and its contractors. The quality of the digitized data and the supporting meteorological data was such that one could test the applicability of molecular relaxation theories. In the late sixties, it had been supposed that the finite rise times in the absence of turbulence had neglected the vibrational relaxation of nitrogen molecules. Bass et al. have demonstrated that molecular relaxation definitely gives the correct order of magnitude of the observed rise times. However, the Air Force data in conjunction with the recent steady-state shock profile model theory of Kang and Pierce give the first opportunity to make a detailed quantitative assessment of the molecular relaxation hypothesis. Currently an investigation is ongoing to establish a method of quantifying the distortion of a sonic boom wave from a classic N-wave shape using the Air Force data taken at Edwards AFB in 1987. Using the premise that energy will be conserved approximately for a sonic boom wave both before and after the boom passes through the Earth's turbulent boundary layer, a classic undistorted waveform is constructed from the distorted signature received at the ground. A correlation between the mean-squared deviation of the distorted and undistorted waveforms and the distance the boom travels through the turbulence is sought.

Gionfriddo, Thomas A.↗
NASA NTRS1993

Multigrid solution of the Navier-Stokes equations on highly stretched grids with defect correction

Relaxation-based multigrid solvers for the steady incompressible Navier-Stokes equations are examined to determine their computational speed and robustness. Four relaxation methods with a common discretization have been used as smoothers in a single tailored multigrid procedure. The equations are discretized on a staggered grid with first order upwind used for convection in the relaxation process on all grids and defect correction to second order central on the fine grid introduced once per multigrid cycle. A fixed W(1,1) cycle with full weighting of residuals is used in the FAS multigrid process. The resulting solvers have been applied to three 2D flow problems, over a range of Reynolds numbers, on both uniform and highly stretched grids. In all cases the L(sub 2) norm of the velocity changes is reduced to 10(exp -6) in a few 10's of fine grid sweeps. The results from this study are used to draw conclusions on the strengths and weaknesses of the individual relaxation schemes as well as those of the overall multigrid procedure when used as a solver on highly stretched grids.

Sockol, Peter M.↗
NASA NTRS1995

High Temperature Superconductivity in Praseodymium Doped (0%, 2%, 4%) in Melt-Textured Y(1-x)Pr(x)Ba2Cu3O(7-delta) Systems

A study of the magnetic and structural properties of the alloy Y(1-x)Pr(x)Ba2Cu3O(7-delta) of 0%, 2%, and 4% doping of praseodymium is presented. The resulting oxides of the alloy series are a high-temperature superconductor Y-Ba-Cu-O, which has an orthorhombic superconducting crystal-lattice. Magnetic relaxation studies have been performed on the Y-Pr-Ba-CuO bulk samples for field orientation parallel to the c-axis, using a vibrating sample magnetometer. Relaxation was measured at several temperatures to obtain the irreversible magnetization curves used for the Bean model. Magnetization current densities were derived from the relaxation data. Field and temperature dependence of the logarithmic flux-creep relaxation was measured in critical state. The data indicates that the effective activation energy U(eff) increases with increasing T between 77 K and 86 K. Also, the data shows that U(eff)(T) and superconducting transition temperature, Tc, decreased as the lattice parameters increased with increasing Pr ion concentration, x, for the corresponding Y(1-x)Pr(x)Ba(x)Cu3O(7-delta) oxides. One contribution to Tc decrease in this sampling is suspected to be due to the larger ionic radius of the Pr(3+) ion. The upper critical field (H(sub c2)) was measured in the presence of magnetic field parallel to the c axis. A linear temperature dependence with H(sub c2) was obtained.

James, Claudell↗
NASA NTRS1996

Electronic Characterization of Defects in Narrow Gap Semiconductors-Comparison of Electronic Energy Levels and Formation Energies in Mercury Cadmium Telluride, Mercury Zinc Telluride, and Mercury Zinc Selenide

We have used a Green's function technique to calculate the energy levels and formation energy of deep defects in the narrow gap semiconductors mercury cadmium telluride (MCT), mercury zinc telluride (MZT) and mercury zinc selenide (MZS). The formation energy is calculated from the difference between the total energy with an impurity cluster and the total energy for the perfect crystal. Substitutional (including antisite), interstitial (self and foreign), and vacancy deep defects are considered. Relaxation effects are calculated (with molecular dynamics). By use of a pseudopotential, we generalize the ideal vacancy model so as to be able to consider relaxation for vacancies. Different charge states are considered and the charged state energy shift (as computed by a modified Haldane-Anderson model) can be twice that due to relaxation. Different charged states for vacancies were not calculated to have much effect on the formation energy. For all cases we find deep defects in the energy gap only for cation site s-like orbitals or anion site p-like orbitals, and for the substitutional case only the latter are appreciably effected by relaxation. For most cases for MCT, MZT, MZS, we consider x (the concentration of Cd or Zn) in the range appropriate for a band gap of 0.1 eV. For defect energy levels, the absolute accuracy of our results is limited, but the precision is good, and hence chemical trends are accurately predicted. For the same reason, defect formation energies are more accurately predicted than energy level position. We attempt, in Appendix B, to calculate vacancy formation energies using relatively simple chemical bonding ideas due to Harrison. However, these results are only marginally accurate for estimating vacancy binding energies. Appendix C lists all written reports and publications produced for the grant. We include abstracts and a complete paper that summarizes our work which is not yet available.

Patterson, James D.↗
NASA NTRS1996

Nonlinear Dynamics and Nucleation Kinetics in Near-Critical Liquids

The objective of our study is to model the nonlinear behavior of a near-critical liquid following a rapid change of the temperature and/or other thermodynamic parameters (pressure, external electric or gravitational field). The thermodynamic critical point is manifested by large, strongly correlated fluctuations of the order parameter (particle density in liquid-gas systems, concentration in binary solutions) in the critical range of scales. The largest critical length scale is the correlation radius r(sub c). According to the scaling theory, r(sub c) increases as r(sub c) = r(sub 0)epsilon(exp -alpha) when the nondimensional distance epsilon = (T - T(sub c))/T(sub c) to the critical point decreases. The normal gravity alters the nature of correlated long-range fluctuations when one reaches epsilon approximately equal to 10(exp -5), and correspondingly the relaxation time, tau(r(sub c)), is approximately equal to 10(exp -3) seconds; this time is short when compared to the typical experimental time. Close to the critical point, a rapid, relatively small temperature change may perturb the thermodynamic equilibrium on many scales. The critical fluctuations have a hierarchical structure, and the relaxation involves many length and time scales. Above the critical point, in the one-phase region, we consider the relaxation of the liquid following a sudden temperature change that simultaneously violates the equilibrium on many scales. Below T(sub c), a non-equilibrium state may include a distribution of small scale phase droplets; we consider the relaxation of such a droplet following a temperature change that has made the phase of the matrix stable.

Patashinski, Alexander Z.↗
NASA NTRS1996

Revenge of the Semicoarsening Frequency Decomposition Multigrid Method

The frequency decomposition multigrid method was previously considered and modified so as to obtain robustness for problems with discontinuous coefficients while retaining robustness for problems with anisotropic coefficients. The application of this modified method to a problem arising in global ocean modeling was also considered. For this problem it was shown that the discretization employed gives rise to an operator for which point relaxation is not robust. In fact, alternating line relaxation is required for robustness, negating the main advantage of the frequency decomposition method: robustness for anisotropic operators using only point relaxation. In this paper a semicoarsening variant, which requires line relaxation in one direction only is considered, and it is shown that this variant works well for the global ocean modeling problem.

Dendy, J. E., Jr.↗
NASA NTRS1999

Molecular Modeling of the Poling of Piezoelectric Polyimides

The computational method described in this paper allows the calculation of the dielectric relaxation strength of an amorphous polymer based solely upon its chemical structure. The 4,4' oxydiphthalic anhydride (ODPA) dianhydride and bis-aminophenoxybenzene (APB) diamine based polyimides, (beta-CN) APB-ODPA and APB-ODPA were studied. Amorphous cells were constructed and then poled using molecular dynamics. Dielectric relaxation strengths of Delta(epsilon) = 17.8 for (beta-CN) APB-ODPA and Delta(epsilon) = 7.7 for APB-ODPA were predicted. These values are in excellent agreement with the experimental values. It was found that both the pendant nitrile dipole and the backbone anhydride residue dipole make significant contributions to the polyimides dielectric response. Specifically, it was shown that the difference in the magnitude of the dielectric relaxations is directly attributable to the nitrile dipole. The size of the relaxations indicate an absence of cooperative dipolar motions, The model was used to explain these results in terms of the average orientation of the nitrile and anhydride dipoles to within 51 deg. and 63 deg., respectively, of the applied electric field.

Young, J. A.↗
NASA NTRS2003

Structural Fluctuation and Thermophysical Properties of Molten II-VI Compounds

The objectives of the project is to conduct ground-based experimental and theoretical research on the structural fluctuations and thermophysical properties of molten II-VI compounds to enhance the basic understanding of the existing flight experiments in microgravity materials science programs and to study the fundamental heterophase fluctuations phenomena in these melts by: 1) Conducting neutron scattering analysis and measuring quantitatively the relevant thermophysical properties of the II-VI melts such as viscosity, electrical conductivity, thermal diffusivity and density as well as the relaxation characteristics of these properties to advance the understanding of the structural properties and the relaxation phenomena in these melts and 2) Performing theoretical analyses on the melt systems to interpret the experimental results. All the facilities required for the experimental measurements have been procured, installed and tested. A relaxation phenomenon, which shows a slow drift of the measured thermal conductivity toward the equilibrium value after cooling of the sample, was observed for the first time. An apparatus based on the transient torque induced by a rotating magnetic field has been developed to determine the viscosity and electrical conductivity of semiconducting liquids. Viscosity measurements on molten tellurium showed similar relaxation behavior as the measured diffusivity. Neutron scattering experiments were performed on the HgTe and HgZnTe melts and the results on pair distribution showed better resolution than previous reported.

Source record↗
NASA NTRS1995

Noninvasive analysis of human neck muscle function

STUDY DESIGN. Muscle use evoked by exercise was determined by quantifying shifts in signal relaxation times of T2-weighted magnetic resonance images. Images were collected at rest and after exercise at each of two intensities (moderate and intense) for each of four head movements: 1) extension, 2) flexion, 3) rotation, and 4) lateral flexion. OBJECTIVE. This study examined the intensity and pattern of neck muscle use evoked by various movements of the head. The results will help elucidate the pathophysiology, and thus methods for treating disorders of the cervical musculoskeletal system. SUMMARY OF BACKGROUND DATA. Exercise-induced contrast shifts in T2 has been shown to indicate muscle use during the activity. The noninvasive nature of magnetic resonance imaging appears to make it an ideal approach for studying the function of the complex neuromuscular system of the neck. METHODS. The extent of T2 increase was examined to gauge how intensely nine different neck muscles or muscle pairs were used in seven subjects. The absolute and relative cross-sectional area of muscle showing a shift in signal relaxation was assessed to infer the pattern of use among and within individual neck muscles or muscle pairs. RESULTS. Signal relaxation increased with exercise intensity for each head movement. The absolute and relative cross-sectional area of muscle showing a shift in signal relaxation also increased with exercise load. Neck muscles or muscle pairs extensively used to perform each head movement were: extension--semispinalis capitis and cervicis and splenius capitis; flexion--sternocleidomastoid and longus capitis and colli; rotation--splenius capitis, levator scapulae, scalenus, semispinalis capitis ipsilateral to the rotation, and sternocleidomastoid contralateral; and lateral flexion--sternocleidomastoid CONCLUSION. The results of this study, in part, agree with the purported functions of neck muscles derived from anatomic location. This also was true for the few selected muscles that have been examined in human electromyographic studies. Neck muscle function and morphology can be studied at a detailed level using exercise-induced shifts in magnetic resonance images.

NASA Program Space Physiology and Countermeasures↗
NASA NTRS2003

Surface Segregation Energies of BCC Binaries from Ab Initio and Quantum Approximate Calculations

We compare dilute-limit segregation energies for selected BCC transition metal binaries computed using ab initio and quantum approximate energy method. Ab initio calculations are carried out using the CASTEP plane-wave pseudopotential computer code, while quantum approximate results are computed using the Bozzolo-Ferrante-Smith (BFS) method with the most recent parameterization. Quantum approximate segregation energies are computed with and without atomistic relaxation. The ab initio calculations are performed without relaxation for the most part, but predicted relaxations from quantum approximate calculations are used in selected cases to compute approximate relaxed ab initio segregation energies. Results are discussed within the context of segregation models driven by strain and bond-breaking effects. We compare our results with other quantum approximate and ab initio theoretical work, and available experimental results.

Good, Brian S.↗