SEARCH · Search NASA

Results for “MACROSCOPIC EQUATION”

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.

123 records · Page 7

All sources NASA NTRS DOE OSTI

NASA NTRS1980

Survey of the plasma electron environment of Jupiter: A view from Voyager

The plasma environment within Jupiter's bow shock is considered in terms of the in situ, calibrated electron plasma measurements made between 10 eV and 5.95 keV by the Voyager plasma science experiment (PLS). Measurements were analyzed and corrected for spacecraft potential variations; the data were reduced to nearly model independent macroscopic parameters of the local electron density and temperature. It is tentatively concluded that the radial temperature profile within the plasma sheet is caused by the intermixing of two different electron populations that probably have different temporal histories and spatial paths to their local observation. The cool plasma source of the plasma sheet and spikes is probably the Io plasma torus and arrives in the plasma sheet as a result of flux tube interchange motions or other generalized transport which can be accomplished without diverting the plasma from the centrifugal equator. The hot suprathermal populations in the plasma sheet have most recently come from the sparse, hot mid-latitude "bath" of electrons which were directly observed juxtaposed to the plasma sheet.

Scudder, J. D.↗

NASA NTRS1993

Particle injection and the structure of energetic-particle-modified shocks

A macroscopic 'self-consistent' nonlinear two-fluid model is developed for energetic-particle-modeled shocks. The model incorporates particle exchange between a thermal gas and an energetic population via a 'thermal leakage' mechanism. In the model, injection is regarded as a process whereby particles in the cooler thermal core of a total particle distribution are energized sufficiently to cross a 'momentum boundary' into the wings of the distribution. Particles in the wings are identified as 'energetic particles' or 'cosmic rays' and are assumed to propagate according to the diffusive transport equation of cosmic ray theory. Thermal particles are energized either as a result of adiabatic compression in a decelerating flow or directly via anomalous heating within a subshock. It is shown that the nature and model of particle injection directly affects the nature and dynamics of the shock, and hence the efficiency of particle acceleration, and that the shock itself regulates particle injection dynamically.

Zank, G. P.↗

NASA NTRS1990

A comparison of internal energy calculation methods for diatomic molecules

Various methods of calculating the internal energy of diatomic molecules are studied. An accurate and efficient method for computing the eigenvalues of the vibrational Schroedinger equation for an arbitrary potential is developed. The method is based on a finite-element discretization using the cubic Lobatto element. A combination of spectrum slicing and the Laguerre algorithm is used to solve for the eigenvalues. A simple method to compute the quasi-bound states is presented. For N2 molecules, all vibrational-rotational states of eleven available electronic potentials are computed, and summed to obtain the exact internal energy function with temperature. The total computation required 314 seconds of CPU-time on NASA's Cray 2 computer. Various approximate models are discussed and compared with the exact numerical simulation. It is shown that the splitting of the macroscopic internal energy into separate electronic, rotational, and vibrational energies is not justified at high temperatures.

Liu, Yen↗

NASA NTRS1994

Superconducting axisymmetric finite elements based on a gauged potential variational principle. Part 2: Solutions and numerical results

This paper discusses an incremental-iterative nonlinear solution technique for solving the nonlinear finite element equations of the superconducting state of a superconductor. The untreated equations are highly ill-conditioned and are impossible to solve within the typical 16-place double precision supplied by most computers. A combination of matrix scaling and mesh grading techniques is used to reduce the condition number of the tangent stiffness matrix and increase the accuracy of the current carrying boundary layer representation. Numerical results for a one-dimensional model of a time-independent superconductor treated by the Ginzburg-Landau model are presented and discussed. The computed solutions clearly display the Meissner effect of magnetic field expulsion from the central region of the superconductor. These results are compared to the physics of a low-viscosity fluid problem. From this analogy, a physical argument is advanced about the macroscopic behavior of superconductors.

Schuler, James J.↗

NASA NTRS1981

Zero-gravity aerosol behavior

The feasibility and scientific benefits of a zero gravity aerosol study in an orbiting laboratory were examined. A macroscopic model was devised to deal with the simultaneous effects of diffusion and coagulation of particles in the confined aerosol. An analytical solution was found by treating the particle coagulation and diffusion constants as ensemble parameters and employing a transformation of variables. The solution was used to carry out simulated zero gravity aerosol decay experiments in a compact cylindrical chamber. The results demonstrate that the limitations of physical space and time imposed by the orbital situation are not prohibitive in terms of observing the history of an aerosol confined under zero gravity conditions. While the absence of convective effects would be a definite benefit for the experiment, the mathematical complexity of the problem is not greatly reduced when the gravitational term drops out of the equation. Since the model does not deal directly with the evolution of the particle size distribution, it may be desirable to develop more detailed models before undertaking an orbital experiment.

Edwards, H. W.↗

NASA NTRS1994

Photometric diversity of terrains on Triton

Voyager disk-resolved images of Triton in the violet (0.41 micrometers) and green (0.56 micrometer wavelengths have been analyzed to derive the photometric characteristics of terrains on Triton. Similar conclusions are found using two distinct but related definitions of photometric units, one based on color ratio and albedo properties (A. S. McEwen, 1990), the other on albedo and brightness ratios at different phase angles (P. Lee et al., 1992). A significant diversity of photometric behavior, much broader than that discovered so far on any other icy satellite, occurs among Triton's terrains. Remarkably, differences in photometric behavior do not correlate well with geologic terrain boundaries defined on the basis of surface morphology. This suggests that in most cases photometric properties on Triton are controlled by thin deposits superposed on underlying geologic units. Single scattering albedos are 0.98 or higher and asymmetry factors range from -0.35 to -0.45 for most units. The most distinct scattering behavior is exhibited by the reddish northern units already identified as the Anomalously Scattering Region (ASR), which scatters light almost isotropically with g = -0.04. In part due to the effects of Triton's clouds and haze, it is difficult to constrain the value of bar-theta, Hapke's macroscopic roughness parameter, precisely for Triton or to map differences in bar-theta among the different photometric terrains. However, our study shows that Triton must be relatively smooth, with bar-theta less than 15-20 degs and suggests that a value of 14 degs is appropriate. The differences in photometric characteristics lead to significantly different phase angle behavior for the various terrains. For example, a terrain (e.g., the ASR) that appears dark relative to another at low phase angles will reverse its contrast (become relatively brighter) at larger phase angles. The photometric parameters have been used to calculate hemispherical albedos for the units and to infer likely surface temperatures. Based on these results, we determine that all but the most southerly regions (i.e., mostly south of the equator) of the reddish northern terrains are likely to have been covered with deposits of nitrogen frost at the time of the Voyager flyby, in agreement with the suggestion from the photometry that these units are overlain by a thin veneer of material.

Hillier, J.↗

NASA NTRS2000

Hierarchical Statistical 3D ' Atomistic' Simulation of Decanano MOSFETs: Drift-Diffusion, Hydrodynamic and Quantum Mechanical Approaches

When MOSFETs are scaled to deep submicron dimensions the discreteness and randomness of the dopant charges in the channel region introduces significant fluctuations in the device characteristics. This effect, predicted 20 year ago, has been confirmed experimentally and in simulation studies. The impact of the fluctuations on the functionality, yield, and reliability of the corresponding systems shifts the paradigm of the numerical device simulation. It becomes insufficient to simulate only one device representing one macroscopical design in a continuous charge approximation. An ensemble of macroscopically identical but microscopically different devices has to be characterized by simulation of statistically significant samples. The aims of the numerical simulations shift from predicting the characteristics of a single device with continuous doping towards estimating the mean values and the standard deviations of basic design parameters such as threshold voltage, subthreshold slope, transconductance, drive current, etc. for the whole ensemble of 'atomistically' different devices in the system. It has to be pointed out that even the mean values obtained from 'atomistic' simulations are not identical to the values obtained from continuous doping simulations. In this paper we present a hierarchical approach to the 'atomistic' simulation of aggressively scaled decanano MOSFETs. A full scale 3D drift-diffusion'atomostic' simulation approach is first described and used for verification of the more economical, but also more restricted, options. To reduce the processor time and memory requirements at high drain voltage we have developed a self-consistent option based on a thin slab solution of the current continuity equation only in the channel region. This is coupled to the Poisson's equation solution in the whole simulation domain in the Gummel iteration cycles. The accuracy of this approach is investigated in comparison with the full self-consistent solution. At low drain voltage only single solution of the nonlinear Poisson equation is sufficient to extract the current with satisfactory accuracy. A pilot version of a hydrodynamic 'atomistic' simulator has been developed in order to study the effect of the nonequilibrium, non local transport in decanano MOSFETs on the random dopant induced current fluctuations. For the first time we have also applied the density gradient approach in 3D to investigate the effect of the quantum confinement on the threshold voltage fluctuations. The developed 'atomistic' simulation techniques have been applied to study various fluctuation resistant MOSFET architectures including epitaxial and delta doped devices.

Asenov, Asen↗

NASA NTRS2008

Analytical Model of the Nonlinear Dynamics of Cantilever Tip-Sample Surface Interactions for Various Acoustic-Atomic Force Microscopies

A comprehensive analytical model of the interaction of the cantilever tip of the atomic force microscope (AFM) with the sample surface is developed that accounts for the nonlinearity of the tip-surface interaction force. The interaction is modeled as a nonlinear spring coupled at opposite ends to linear springs representing cantilever and sample surface oscillators. The model leads to a pair of coupled nonlinear differential equations that are solved analytically using a standard iteration procedure. Solutions are obtained for the phase and amplitude signals generated by various acoustic-atomic force microscope (A-AFM) techniques including force modulation microscopy, atomic force acoustic microscopy, ultrasonic force microscopy, heterodyne force microscopy, resonant difference-frequency atomic force ultrasonic microscopy (RDF-AFUM), and the commonly used intermittent contact mode (TappingMode) generally available on AFMs. The solutions are used to obtain a quantitative measure of image contrast resulting from variations in the Young modulus of the sample for the amplitude and phase images generated by the A-AFM techniques. Application of the model to RDF-AFUM and intermittent soft contact phase images of LaRC-cp2 polyimide polymer is discussed. The model predicts variations in the Young modulus of the material of 24 percent from the RDF-AFUM image and 18 percent from the intermittent soft contact image. Both predictions are in good agreement with the literature value of 21 percent obtained from independent, macroscopic measurements of sheet polymer material.

Cantrell, John H., Jr.↗

NASA NTRS1994

On the Two-Dimensionalization of Homogeneous Rotating Turbulence

Large-eddy simulation of the incompressible Navier-Stokes equations has been used to examine the long-time development of initially isotropic turbulence subjected to solid-body rotation. The simulations were carried out using a pseudo-spectral method with 128 x 128 x 512 collocation points in a computational domain that is four times larger along the rotation axis than in the other directions; subgrid-scale motions were parameterized using a spectral eddy viscosity model modified for system rotation. Simulation results show that the correlation length along the rotation am's of velocities orthogonal to the rotation vector exhibits rapid growth while the integral length-scale of velocities aligned with the rotation axis is relatively unaffected by rotation. Examination of the energy spectrum of two-dimensional, two-component motions indicates the presence of an inverse cascade of energy. System rotation also causes an alignment of vorticity along the rotation axis with relatively stronger cyclonic vorticity than anticyclonic. The onset of anisotropic effects are well characterized by Rossby numbers defined in terms of both macroscopic and microscopic quantities.

Squires, K. D.↗

NASA NTRS2013

Advanced Colloids Experiment (ACE) Science Overview

The Advanced Colloids Experiment is being conducted on the International Space Station (ISS) using the Light Microscopy Module (LMM) in the Fluids Integrated Rack (FIR). Work to date will be discussed and future plans and opportunities will be highlighted. The LMM is a microscope facility designed to allow scientists to process, manipulate, and characterize colloidal samples in micro-gravity where the absence of gravitational settling and particle jamming enables scientists to study such things as:a.The role that disordered and ordered-packing of spheres play in the phase diagram and equation of state of hard sphere systems,b.crystal nucleation and growth, growth instabilities, and the glass transition, c.gelation and phase separation of colloid polymer mixtures,d.crystallization of colloidal binary alloys,e.competition between crystallization and phase separation,f.effects of anisotropy and specific interactions on packing, aggregation, frustration and crystallization,g.effects of specific reversible and irreversible interactions mediated in the first case by hybridization of complementary DNA strands attached to separate colloidal particles,h.Lock and key interactions between colloids with dimples and spheres which match the size and shape of the dimples,i.finding the phase diagrams of isotropic and interacting particles,j.new techniques for complex self-assembly including scenarios for self-replication, k.critical Casimir forces,l.biology (real and model systems) in microgravity,m.etc. By adding additional microscopy capabilities to the existing LMM, NASA will increase the tools available for scientists that fly experiments on the ISS enabling scientists to observe directly what is happening at the particle level. Presently, theories are needed to bridge the gap between what is being observed (at a macroscopic level when photographing samples) with what is happening at a particle (or microscopic) level. What is happening at a microscopic level will be directly accessible with the availability of the Light Microscopy Module (LMM) on ISS. To meet these goals, the ACE experiment is being built-up in stages, with the availability of confocal microscopy being the ultimate objective. Supported by NASAs Physical Sciences Research Program, ESAESTEC, and the authors respective governments.

Microgravity Biology Research↗

NASA NTRS2002

Efficient Reformulation of HOTFGM: Heat Conduction with Variable Thermal Conductivity

Functionally graded materials (FGMs) have become one of the major research topics in the mechanics of materials community during the past fifteen years. FGMs are heterogeneous materials, characterized by spatially variable microstructure, and thus spatially variable macroscopic properties, introduced to enhance material or structural performance. The spatially variable material properties make FGMs challenging to analyze. The review of the various techniques employed to analyze the thermodynamical response of FGMs reveals two distinct and fundamentally different computational strategies, called uncoupled macromechanical and coupled micromechanical approaches by some investigators. The uncoupled macromechanical approaches ignore the effect of microstructural gradation by employing specific spatial variations of material properties, which are either assumed or obtained by local homogenization, thereby resulting in erroneous results under certain circumstances. In contrast, the coupled approaches explicitly account for the micro-macrostructural interaction, albeit at a significantly higher computational cost. The higher-order theory for functionally graded materials (HOTFGM) developed by Aboudi et al. is representative of the coupled approach. However, despite its demonstrated utility in applications where micro-macrostructural coupling effects are important, the theory's full potential is yet to be realized because the original formulation of HOTFGM is computationally intensive. This, in turn, limits the size of problems that can be solved due to the large number of equations required to mimic realistic material microstructures. Therefore, a basis for an efficient reformulation of HOTFGM, referred to as user-friendly formulation, is developed herein, and subsequently employed in the construction of the efficient reformulation using the local/global conductivity matrix approach. In order to extend HOTFGM's range of applicability, spatially variable thermal conductivity capability at the local level is incorporated into the efficient reformulation. Analytical solutions to validate both the user-friendly and efficient reformulations am also developed. Volume discretization sensitivity and validation studies, as well as a practical application of the developed efficient reformulation are subsequently carried out. The presented results illustrate the accuracy and implementability of both the user-friendly formulation and the efficient reformulation of HOTFGM.

Zhong, Yi↗

NASA NTRS2000

Fatigue, Creep-Fatigue, and Thermomechanical Fatigue Life Testing of Alloys

The fatigue crack initiation resistance of an alloy is determined by conducting a series of tests over a range of values of stress amplitude or strain range. The observed number of cycles to failure is plotted against the stress amplitude or strain range to obtain a fatigue curve. The fatigue properties quoted for an alloy are typically the constants used in the equation(s) that describe the fatigue curve. Fatigue lives of interest may be as low as 10(exp 2) or higher than 10(exp 9) cycles. Because of the enormous scatter associated with fatigue, dozens of tests may be needed to confidently establish a fatigue curve, and the cost may run into several thousands of dollars. To further establish the effects on fatigue life of the test temperature, environment, alloy condition, mean stress effects, creep-fatigue effects, thermomechanical cycling, etc. requires an extraordinarily large and usually very costly test matrix. The total effort required to establish the fatigue resistance of an alloy should not be taken lightly. Fatigue crack initiation tests are conducted on relatively small and presumed to be initially crack-free, samples of an alloy that are intended to be representative of the alloy's metallurgical and physical condition. Generally, samples are smooth and have uniformly polished surfaces within the test section. Some may have intentionally machined notches of well-controlled geometry, but the surface at the root of the notch is usually not polished. The purpose of polishing is to attain a reproducible surface finish. This is to eliminate surface finish as an uncontrolled variable. Representative test specimen geometries will be discussed later. Test specimens are cyclically loaded until macroscopically observable cracks initiate and eventually grow to failure. Normally, the fatigue failure life of a specimen is defined as the number of cycles to separation of the specimen into two pieces. Alternative definitions are becoming more common, particularly for low-cycle fatigue testing, wherein some prescribed indication of impending failure due to cracking is adopted. Specific criteria will be described later. As a rule, cracks that develop during testing are not measured nor are the test parameters intentionally altered owing to the presence of cracking.

Halford, Gary R.↗

NASA NTRS1995

Durability and life prediction modeling in polyimide composites

Sudden appearance of cracks on a macroscopically smooth surface of brittle materials due to cooling or drying shrinkage is a phenomenon related to many engineering problems. Although conventional strength theories can be used to predict the necessary condition for crack appearance, they are unable to predict crack spacing and depth. On the other hand, fracture mechanics theory can only study the behavior of existing cracks. The theory of crack initiation can be summarized into three conditions, which is a combination of a strength criterion and laws of energy conservation, the average crack spacing and depth can thus be determined. The problem of crack initiation from the surface of an elastic half plane is solved and compares quite well with available experimental evidence. The theory of crack initiation is also applied to concrete pavements. The influence of cracking is modeled by the additional compliance according to Okamura's method. The theoretical prediction by this structural mechanics type of model correlates very well with the field observation. The model may serve as a theoretical foundation for future pavement joint design. The initiation of interactive cracks of quasi-brittle material is studied based on a theory of cohesive crack model. These cracks may grow simultaneously, or some of them may close during certain stages. The concept of crack unloading of cohesive crack model is proposed. The critical behavior (crack bifurcation, maximum loads) of the cohesive crack model are characterized by rate equations. The post-critical behavior of crack initiation is also studied.

Binienda, Wieslaw K.↗

NASA NTRS1993

Feasibility study: Monodisperse polymer particles containing laser-excitable dyes

The optical properties associated with small particles, which include aerosols, hydrosols and solid microspheres have an impact on several areas of science and engineering. Since the advent of high-speed computers and lasers, the interaction of light with matter in the form of small particles with a discontinuous optical boundary relative to the surroundings has been much better understood. Various nonlinear optical effects have been observed involving interaction of a laser beam with both solid microspheres and liquid microdroplets. These include observation of second and third harmonic generation, four wave mixing, optical visibility, two photon absorption, observation of stimulated emission and lasing, and Stimulated Raman Scattering. Many of these effects are observed with laser intensities which are orders of magnitude less than that required by threshold condition for interactions in macroscopic bulk medium. The primary reason for this is twofold. The front surface of the microsphere acts as a thick lens to enhance the internal intensity of the input laser radiation, and the spherical shape of the droplet acts as an optical cavity to provide feedback at specific wavelengths corresponding to the whispering gallery modes or the morphology dependent resonances (MDR's). The most interesting and significant recent finding in this field is undoubtedly the existence of resonance peaks in linear and nonlinear optical spectra. Such resonance peaks are only dependent on the particle morphology, which means the size, shape and refractive index of the particle. Because of the simultaneous presence of these resonances, they have been referred to by many names, including structural resonances, whispering modes or whispering gallery modes, creeping waves, circumferential waves, surfaces modes, and virtual modes. All of these names refer to the same phenomena, i.e. morphology dependent resonances (MDR's) which has already been described and predicted precisely by electromagnetic theory and Loentz-Mie theory since 1908. MDR's can become important when the particle size (radius a) approaches and exceeds the wavelength of the electromagnetic wave (lambda) and the refractive index of the particle is greater than that of the surrounding medium. Such resonances are easiest to observe from a single particle with high symmetry, such as a sphere, spheroid, or cylinder. MDR's correspond to solutions of the characteristic equations of the electromagnetic fields in the presence of a sphere.

Venkateswarlu, Putcha↗

NASA NTRS1989

On the Nature of Navier-stokes Turbulence

Several turbulent and nonturbulent solutions of the Navier-Stokes equations are obtained. The unaveraged equations are used numerically in conjunction with tools and concepts from nonlinear dynamics, including time series, phase portraits, Poincare sections, largest Liapunov exponents, power spectra, and strange attractors. Initially neighboring solutions for a low-Reynolds-number fully developed turbulence are compared. The solutions, separate exponentially with time, having a positive Liapunov exponent. Thus the turbulence is characterized as chaotic. In a search for solutions which contrast with the turbulent ones, the Reynolds number is reduced. Several qualitatively different flows are noted. These are, fully chaotic, complex period, weakly chaotic, simple periodic, and fixed-point. Of these, only the fully chaotic flows are classified as turbulent. Those flows have both a positive Liapunov exponent and Poincare sections without pattern. By contrast, the weakly chaotic flows have some pattern in their Poincare sections. The fixed-point and periodic flows are nonturbulent, since turbulence, is both time-dependent and aperiodic. Turbulent solutions are obtained in which energy cascades from large to small-scale motions. In general, the spectral energy transfer takes place between wavenumber bands that are considerably separated. The special transfer can occur either as a result of nonlinear turbulence self-interaction or by interaction of turbulence with mean gradients. Turbulent systems are compared with those studied in kinetic theory. The two types of systems are fundamentally different (continuous and dissipative as opposed to discrete and conservative), but there are similarities. For instance, both are nonlinear and show sensitive dependence on initial conditions. Also, the turbulent and molecular stress tensors are identical if the macroscopic velocities for the turbulent stress are replaced by molecular velocities.

Deissler, Robert G.↗