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NASA NTRS2000

Inertial Effects in Suspension Dynamics

The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.

J. F. Brady↗

NASA NTRS2022

Whistler Waves Generated by Nongyrotropic and Gyrotropic Electron Beams During Asymmetric Guide Field Reconnection

Using a two-dimensional particle-in-cell simulation of asymmetric reconnection with a guide field whose strength is 0.3 times the reconnecting magnetic field, we study electron distribution functions and wave intensities in the diffusion region, focusing on the electron diffusion region (EDR). Wave activities with frequencies below the electron cyclotron frequency are observed, and these are whistler waves propagating almost anti-parallel to the magnetic field. The waves are concentrated near the magnetospheric separatrix away from the X line, but the wave activity also spreads through the EDR near the X line. The reconnection outflows are asymmetric in the outflow direction in the magnetospheric side, and the wave intensity is stronger in the side of the faster electron outflow. We study the whistler waves using the fast Fourier transform, analyses of electron velocity distribution functions, and the dispersion solver calculation. Along the magnetospheric separatrix in the stronger outflow side, highly anisotropic electron beams exist with super-Alfvénic drift speeds. The dispersion analysis shows that there are two modes: a temperature anisotropy mode and a beam mode. Outside the EDR, the whistler wave intensity is highest near the separatrix, but the wave intensity decreases if we move away from the separatrix toward the magnetic neutral line because of the increase in the electron population near zero parallel velocity. In the EDR, in the velocity plane perpendicular to the magnetic field, ring/crescent electron distribution functions are observed. Near the X-line, the wave power is enhanced where nongyrotropic electrons contribute to increase the perpendicular temperature anisotropy.

magnetic reconnection↗

NASA NTRS1978

The velocity distribution of interstellar gas observed in strong UV absorption lines

Observations of three strong interstellar UV absorption lines of N I (1199 A), N II (1083 A), and Si III (1206 A) in 47 stars of widely varying distance and a variety of spectral types are analyzed to obtain a velocity distribution function for the interstellar gas. A technique based on the maximum and minimum velocities observed along a line of sight is adopted because of heavy line blending, and results are discussed for both power-law and exponential distribution functions. The expected distribution of radiative-phase supernova remnants (SNRs) in the interstellar medium is calculated as a function of SNR birthrate and of the interstellar density in which they evolve. The results are combined with observed distance estimates, and it is shown that an interstellar density in excess of 0.1 per cu cm would be required to keep the SNRs sufficiently confined so that their cross sections are consistent with the observed number of components. The alternative possibility is considered that SNRs do not enter the radiative phase before escaping from the Galaxy or colliding with neighboring remnants.

Cowie, L. L.↗

NASA NTRS1992

Bivariate extreme value distributions

In certain engineering applications, such as those occurring in the analyses of ascent structural loads for the Space Transportation System (STS), some of the load variables have a lower bound of zero. Thus, the need for practical models of bivariate extreme value probability distribution functions with lower limits was identified. We discuss the Gumbel models and present practical forms of bivariate extreme probability distributions of Weibull and Frechet types with two parameters. Bivariate extreme value probability distribution functions can be expressed in terms of the marginal extremel distributions and a 'dependence' function subject to certain analytical conditions. Properties of such bivariate extreme distributions, sums and differences of paired extremals, as well as the corresponding forms of conditional distributions, are discussed. Practical estimation techniques are also given.

Elshamy, M.↗

NASA NTRS1968

Application of a truncated normal failure distribution in reliability testing

Statistical truncated normal distribution function is applied as a time-to-failure distribution function in equipment reliability estimations. Age-dependent characteristics of the truncated function provide a basis for formulating a system of high-reliability testing that effectively merges statistical, engineering, and cost considerations.

Groves, C., Jr.↗

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 NTRS2016

Coupled Retrieval of Aerosol Properties and Surface Reflection Using the Airborne Multi-Angle SpectroPolarimetric Imager (AirMSPI)

The Airborne Multi-angle SpectroPolarimetric Imager (AirMSPI) has been flying aboard the NASA ER-2 high altitude aircraft since October 2010. In step-and-stare operation mode, AirMSPI acquires radiance and polarization data at 355, 380, 445, 470*, 555, 660*, 865*, and 935 nm (* denotes polarimetric bands). The imaged area covers about 10 km by 10 km and is observed from 9 view angles between ±67° off of nadir. We have developed an efficient and flexible code that uses the information content of AirMSPI data for a coupled retrieval of aerosol properties and surface reflection. The retrieval was built based on the multi-pixel optimization concept, with the use of a hybrid radiative transfer model that combines the Markov Chain and adding/doubling methods. The convergence and robustness of our algorithm is ensured by applying constraints on (a) the spectral variation of the Bidirectional Polarization Distribution Function (BPDF) and angular shape of the Bidirectional Reflectance Distribution Function (BRDF); (b) the spectral variation of aerosol optical properties; and (c) the spatial variation of aerosol parameters across neighboring image pixels. Our retrieval approach has been tested using over 20 AirMSPI datasets having low to moderately high aerosol loadings (~0.02<AOD550-nm<~0.45) and acquired during several field campaigns. Results are compared with AERONET aerosol reference data. We also explore the benefits of AirMSPI’s ultraviolet and polarimetric bands as well as the use of multiple view angles.

Xu, Feng↗

NASA NTRS1986

Low density gas dynamic wall boundary conditions

Low density nozzles or large expansion ratio nozzles used in space experience rarefaction effects near their exit in the form of velocity slip and temperature jump at the walls. In addition, the boundary layers become very thick and there is a very strong viscous/inviscid interaction. For these reasons no existing design technique has been found to accurately predict the nozzle flow properties up to the nozzle exit. The objective of this investigation was to examine the slip boundary conditions and formulate them in a form appropriate for use with a full Navier-Stokes numerical code. The viscous/inviscid interaction would automatically be accounted for by using a compressible Navier-Stokes code. Through examination of the interaction of molecules with solid surfaces, a model for the distribution function of the reflected molecules has been determined and this distribution function has been used to develop a new slip boundary condition that can be shown to yield more realistic surface boundary conditions.

Collins, F. G.↗

NASA NTRS1986

Analyses of convective flows and spatial gradients in energetic ion observations

Based on the measured anisotropy of three-dimensional energetic ion distributions obtained from the Medium Energy Particle Instrument experiment of the ISEE 1 spacecraft, bulk flow, epsilon x B convection, and pressure gradients in magnetospheric plasmas are measured with two techniques. In the first technique, using a Compton-Getting transform into the appropriate rest frame in an iterative fashion and converging to the unique velocity that removes the first-order anisotropy from the flux angular distribution, the actual measured angular distribution, and spectrum at each angle, are employed. The second technique uses a first moment of the distribution function in which the shift in velocity space of the distribution function is obtained at two phase space density values. The convection contribution to the velocity shift is assumed to be perpendicular to the pressure gradient contribution if an MHD generator condition is assumed, rendering the two shifts separable, and a gradient scale and a lower limit to the convection electric field are derived in one calculation.

Mitchell, D. G.↗

NASA NTRS1989

The distribution of solar magnetic fluxes and the nonlinearity of stellar flux-flux relations

Synoptic maps for the 1975-1984 period are used to determine the time-dependent distribution function of magnetic flux densities in the solar atmosphere. The distribution function depends only on the global level of magnetic activity, and it is used to study how relations between magnetic flux densities and radiative flux densities from different temperature regimes in the outer atmosphere (derived from spatially resolved solar observations) transform into relations between surface-averaged flux densities. It is found that the transformation to surface-averaged fluxes preserves the power-law character of relations between radiative and magnetic flux densities for spatially resolved data.

Schrijver, C. J.↗

NASA NTRS1985

Spline methods for approximating quantile functions and generating random samples

Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.

Schiess, J. R.↗

NASA NTRS1964

Symmetry relation in relaxation dispersions.

Symmetry relation between dispersion function of frequency variable and distribution function of relaxation time variable

RELAXATION TIME↗

NASA NTRS1986

Bidirectional reflectance modeling of non-homogeneous plant canopies

The objective of this research is to develop a 3-dimensional radiative transfer model for predicting the bidirectional reflectance distribution function (BRDF) for heterogeneous vegetation canopies. Leaf bidirectional reflectance and transmittance distribution functions were measured for corn and soybean leaves. The measurements clearly show that leaves are complex scatterers and considerable specular reflectance is possible. Because of the character of leaf reflectance, true leaf reflectance is larger than the nadir reflectances that are normally used to represent leaves. A 3-dimensional reflectance model, named BIGAR (Bidirectional General Array Model), was developed and compared with measurements from corn and soybean. The model is based on the concept that heterogeneous canopies can be described by a combination of many subcanopies, which contain all the foliage, and these subcanopy envelopes can be characterized by ellipsoids of various sizes and shapes. The model/measurement comparison results indicate that this relatively simple model captures the essential character of row crop BRDF's. Finally, two soil BDRF models were developed: one represents soil particles as rectangular blocks and the other represents soil particles as spheres. The sphere model was found to be superior.

Norman, John M.↗

NASA NTRS1997

Ponderomotive Force and Lower Hybrid Turbulence Effects in Space Plasmas Subjected to Large-Amplitude Low-Frequency Waves

In the auroral region, simultaneous occurrences of upward-flowing ions and field-aligned electrons have been observed by the Viking satellite. The occurrence is strongly correlated with large amplitude low frequency fluctuations of the electric field. Large-amplitude shear Alfven waves have also been observed by sounding rockets in the auroral ionosphere. When such LF waves are propagating in a plasma, a ponderomotive force and other types of waves are produced which may lead to significant effects on the plasma. This force is directed toward decreasing density, providing the electromagnetic lift of the background plasma and an increase of collisionless plasma expansion. We find that even for modest wave strengths, the influence on the outflowing oxygen ions can be dramatic, increasing the high-altitude density by orders of magnitude. It is also demonstrated that large-amplitude low-frequency waves (LFW) may generate lower hybrid waves (LHW) in the auroral zone. The excitation of LHW by a LF wave may lead to the appearance of an additional channel of energy transfer from, for example, Alfven or fast magnetosonic waves, to particles. This process then influences the formation of the plasma distribution function at the expense of acceleration in the tail of the distribution during the collapse of the LHW. The ion energization due to the LHW can be comparable with that produced by the ponderomotive force of the LFW. It is shown that the LH turbulence leads to equalization of the ponderomotive acceleration of the different ion species. The mechanism of LHW excitation due to the oxygen ion relative drift in a plasma subjected to low-frequency waves is used for analysis of Viking satellite data for events in the cusp/cleft region. It is found that, in some cases, such a mechanism leads to LHW energy densities and ion distribution functions close to those observed.

Khazanov, G. V.↗

NASA NTRS1991

Observations of ion-neutral collisional effects in the auroral E region

Thermal ion energy distribution functions and local electric and magnetic fields were directly measured for the first time in the ionospheric E region. Measured ion distribution functions were fitted to shifted Maxwellian distributions, and their resulting ion drift velocities were compared with E x B/B-squared velocities from the double-probe electric field observations. The results show that the ion drift direction rotates with respect to the local electric field direction and that the ratio of the magnitudes of the ion velocity to the E x B/B-squared velocity decreases with decreasing altitudes. Using these observations, the quiet time ion-neutral collison frequencies and neutral wind velocities were estimated and found to be consistent with theoretical estimates. However, significant discrepancies between observations and theory are found in the disturbed E region near auroral particle precipitation regions. These data indicate that the auroral atmosphere is significantly perturbed due to Joule as well as particle heating effects.

Watanabe, S.↗

NASA NTRS1984

Whistler mode turbulence generated by electron beams in earth's bow shock

The Landau and cyclotron growth rates of whistler mode waves in the earth's bow shock are calculated by using electron distribution functions obtained with the fast plasma experiment on ISEE 2. Three electron distribution functions measured within the transition region of the shock are analyzed. These functions spontaneously generate whistler mode waves with plasma rest frame frequencies between about 0.1 and 100 Hz. The wave normal angles of the generated whistlers range from 0 deg to the resonance cone angle. Electromagnetic Landau resonance and/or cyclotron resonance contribute to wave growth over the range of observed velocity distributions. Waves generated by the normal cyclotron resonance have wave vectors directed toward the solar wind, while those generated by the Landau and the anomalous cyclotron resonances have vectors directed toward the magnetosheath. The preditions of the study are in qualitative agreement with observations of whistler mode waves near the earth's bow shock.

Tokar, R. L.↗

NASA NTRS1984

Photon-photon absorption and the uniqueness of the spectra of active galactic nuclei

The effects of the feedback of e(+)-e(-) pair reinjection in a plasma due to photon-photon absorption of its own radiation was examined. Under the assumption of continuous electron injection with a power law spectrum E to the minus gamma power and Compton losses only, it is shown that for gamma 2 the steady state electron distribution function has a unique form independent of the primary injection spectrum. This electron distribution function can, by synchrotron emission, reproduce the general characteristics of the observed radio to optical active galactic nuclei spectra. Inverse Compton scattering of the synchrotron photons by the same electron distribution can account for their X-ray spectra, and also implies gamma ray emission from these objects. This result is invoked to account for the similarity of these spectra, and it is consistent with observations of the diffuse gamma ray background.

Kazanas, D.↗

NASA NTRS1984

Photon-photon absorption and the uniqueness of the spectra of active galactic nuclei

Kazanas, D.↗