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At least 307 records · Page 17

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.↗

An implicit time-marching method for studying unsteady flow with massive separation

A fully implicit time-marching method is developed such that all spatial derivatives are approximated using central differences, but no use is made of any artificial dissipation. The numerical method solves the discretized equations using Alternating Direction Implicit-Block Gaussian Elimination technique. The method is implemented in the unsteady analysis, which solves the incompressible Navier-Stokes equations in terms of vorticity and stream function in generalized orthogonal coordinates. A clustered conformal C-grid is employed, and every effort is made to resolve the various length scales in the flow problem. The metric discontinuity at the branch-cut is treated appropriately using analytic continuation. Introduction of the BGE reordering permits implicit treatment of the branch cut in the numerical method. The vorticity singularity at the cusped trailing edge is also appropriately treated. This accurate and efficient implicit method is used to study flow at Re = 1000, past a 12-percent thick symmetric Joukowski airfoil at high angle of attack 30 and 53 deg.

Osswald, G. A.↗

Developing aqueous solubilizing agents as an alternative to solvent extraction

Here, advancing separations science is important for the entire field of chemistry. One partitioning technique that would benefit from improvement is solvent extraction. Despite its effective and widespread use, the method suffers from some problems: generation of flammable organic waste, lengthy process times, and safety concerns associated with contacting organic solvents with acidic aqueous solutions. We developed an alternative separation method inspired by solvent extraction that side-steps those issues. Toward this end, we identified that the functionality of an extractant (an agent used in solvent extraction to pull analytes from the aqueous phase into the organic phase) would change if it was modified for water solubility. In this alternative scenario, the extractant transforms into an “aqueous solubilizing agent.” We discovered that adding this aqueous solubilizing agent alongside a precipitating agent caused the contaminants to precipitate, but not the analyte. This separation concept was demonstrated within the bounds of one of the most difficult partitioning problems, separating minor actinides (Am 3+ ) from lanthanides (Ln 3+ ). We discovered that the (HSO 3 Ph) 4 BTP (aq) aqueous solubilizing agent prevented Am 3+ (aq) from precipitating with Ln 3+ (aq) when f-element precipitating agents (NaF (aq) or HF (aq) ) were added. This separation boasts impressive Am 3+ (aq) recovery yield (90 ± 2 %), near quantitative Ln 3+ (aq) removal, and high separation factors [>3000, Am 3+ (aq) vs. Nd 3+ (aq) ]. It seems likely – given the large number of candidate extractants that could be modified for aqueous solubility and the numerous combinations of existing solubilizing and precipitating agents – that this alternative approach could be used broadly in place of solvent extraction and solve other important separation problems.

(HSO3Ph)4BTP(aq)↗

On differential transformations between Cartesian and curvilinear (geodetic) coordinates

Differential transformations are developed between Cartesian and curvilinear orthogonal coordinates. Only matrix algebra is used for the presentation of the basic concepts. After defining the reference systems used the rotation (R), metric (H), and Jacobian (J) matrices of the transformations between cartesian and curvilinear coordinate systems are introduced. A value of R as a function of H and J is presented. Likewise an analytical expression for J(-1) as a function of H(-2) and R is obtained. Emphasis is placed on showing that differential equations are equivalent to conventional similarity transformations. Scaling methods are discussed along with ellipsoidal coordinates. Differential transformations between elipsoidal and geodetic coordinates are established.

Soler, T.↗

General design method for three-dimensional potential flow fields. 1: Theory

A general design method was developed for steady, three dimensional, potential, incompressible or subsonic-compressible flow. In this design method, the flow field, including the shape of its boundary, was determined for arbitrarily specified, continuous distributions of velocity as a function of arc length along the boundary streamlines. The method applied to the design of both internal and external flow fields, including, in both cases, fields with planar symmetry. The analytic problems associated with stagnation points, closure of bodies in external flow fields, and prediction of turning angles in three dimensional ducts were reviewed.

Stanitz, J. D.↗

Stochastic treatment of electron multiplication without scattering in dielectrics

By treating the emission of optical phonons as a Markov process, a simple analytic method is developed for calculating the electronic ionization rate per unit length for dielectrics. The effects of scattering from acoustic and optical phonons are neglected. The treatment obtains universal functions in recursive form, the theory depending on only two dimensionless energy ratios. A comparison of the present work with other numerical approaches indicates that the effect of scattering becomes important only when the electric potential energy drop in a mean free path for optical-phonon emission is less than about 25% of the ionization potential. A comparison with Monte Carlo results is also given for Teflon.

Lin, D. L.↗

Stress and Damage in Polymer Matrix Composite Materials Due to Material Degradation at High Temperatures

This report describes analytical methods for calculating stresses and damage caused by degradation of the matrix constituent in polymer matrix composite materials. Laminate geometry, material properties, and matrix degradation states are specified as functions of position and time. Matrix shrinkage and property changes are modeled as functions of the degradation states. The model is incorporated into an existing composite mechanics computer code. Stresses, strains, and deformations at the laminate, ply, and micro levels are calculated, and from these calculations it is determined if there is failure of any kind. The rationale for the model (based on published experimental work) is presented, its integration into the laminate analysis code is outlined, and example results are given, with comparisons to existing material and structural data. The mechanisms behind the changes in properties and in surface cracking during long-term aging of polyimide matrix composites are clarified. High-temperature-material test methods are also evaluated.

McManus, Hugh L.↗

Ground Test of the Urine Processing Assembly for Accelerations and Transfer Functions

This viewgraph presentation gives an overview of the ground test of the urine processing assembly for accelerations and transfer functions. Details are given on the test setup, test data, data analysis, analytical results, and microgravity assessment. The conclusions of the tests include the following: (1) the single input/multiple output method is useful if the data is acquired by tri-axial accelerometers and inputs can be considered uncorrelated; (2) tying coherence with the matrix yields higher confidence in results; (3) the WRS#2 rack ORUs need to be isolated; (4) and future work includes a plan for characterizing performance of isolation materials.

Houston, Janice↗

Curved Waveguide Based Nuclear Fission for Small, Lightweight Reactors

The focus of the presented work is on the creation of a system of grazing incidence, supermirror waveguides for the capture and reuse of fission sourced neutrons. Within research reactors, neutron guides are a well known tool for directing neutrons from the confined and hazardous central core to a more accessible testing or measurement location. Typical neutron guides have rectangular, hollow cross sections, which are crafted as thin, mirrored waveguides plated with metal (commonly nickel). Under glancing angles with incoming neutrons, these waveguides can achieve nearly lossless transport of neutrons to distant instruments. Furthermore, recent developments have created supermirror surfaces which can accommodate neutron grazing angles up to four times as steep as nickel. A completed system will form an enclosing ring or spherical resonator system to a coupled neutron source for the purpose of capturing and reusing free neutrons to sustain and/or accelerate fission. While grazing incidence mirrors are a known method of directing and safely using neutrons, no method has been disclosed for capture and reuse of neutrons or sustainment of fission using a circular waveguide structure. The presented work is in the process of fabricating a functional, highly curved, neutron supermirror using known methods of Ni-Ti layering capable of achieving incident reflection angles up to four times steeper than nickel alone. Parallel work is analytically investigating future geometries, mirror compositions, and sources for enabling sustained fission with applicability to the propulsion and energy goals of NASA and other agencies. Should research into this concept prove feasible, it would lead to development of a high energy density, low mass power source potentially capable of sustaining fission with a fraction of the standard critical mass for a given material and a broadening of feasible materials due to reduced rates of release, absorption, and non-fission for neutrons. This advance could be applied to direct propulsion through guided fission products or as a secondary energy source for high impulse electric propulsion. It would help meet national needs for highly efficient energy sources with limited dependence on fossil fuels or conflict materials, and it would improve the use of low grade fissile materials which would help reduce national stockpiles and waste.

Coker, Robert↗

On the Fast Evaluation Method of Temperature and Gas Mixing Ratio Weighting Functions for Remote Sensing of Planetary Atmospheres in Thermal IR and Microwave

Evaluation of weighting functions in the atmospheric remote sensing is usually the most computer-intensive part of the inversion algorithms. We present an analytic approach to computations of temperature and mixing ratio weighting functions that is based on our previous results but the resulting expressions use the intermediate variables that are generated in computations of observable radiances themselves. Upwelling radiances at the given level in the atmosphere and atmospheric transmittances from space to the given level are combined with local values of the total absorption coefficient and its components due to absorption of atmospheric constituents under study. This makes it possible to evaluate the temperature and mixing ratio weighting functions in parallel with evaluation of radiances. This substantially decreases the computer time required for evaluation of weighting functions. Implications for the nadir and limb viewing geometries are discussed.

Ustinov, E. A.↗

Inference of Ice Cloud Properties from High-spectral Resolution Infrared Observations

The theoretical basis is explored for inferring the microphysical properties of ice crystal from high-spectral resolution infrared observations. A radiative transfer model is employed to simulate spectral radiances to address relevant issues. The extinction and absorption efficiencies of individual ice crystals, assumed as hexagonal columns for large particles and droxtals for small particles, are computed from a combination of the finite- difference time-domain (FDTD) technique and a composite method. The corresponding phase functions are computed from a combination of FDTD and an improved geometric optics method (IGOM). Bulk scattering properties are derived by averaging the single- scattering properties of individual particles for 30 particle size distributions developed from in situ measurements and for additional four analytical Gamma size distributions for small particles. The non-sphericity of ice crystals is shown to have a significant impact on the radiative signatures in the infrared (IR) spectrum; the spherical particle approximation for inferring ice cloud properties may result in an overest&ation of the optical thickness and an inaccurate retrieval of effective particle size. Furthermore, we show that the error associated with the use of the Henyey-Greenstein phase function can be as larger as 1 K in terms of brightness temperature for larger particle effective size at some strong scattering wavenumbers. For small particles, the difference between the two phase functions is much less, with brightness temperatures generally differing by less than 0.4 K. The simulations undertaken in this study show that the slope of the IR brightness temperature spectrum between 790-960/cm is sensitive to the effective particle size. Furthermore, a strong sensitivity of IR brightness temperature to cloud optical thickness is noted within the l050-1250/cm region. Based on this spectral feature, a technique is presented for the simultaneous retrieval of the visible optical thickness and effective particle size from high spectral resolution infrared data under ice cloudy con&tion. The error analysis shows that the uncertainty of the retrieved optical thickness and effective particle size has a small range of variation. The error for retrieving particle size in conjunction with an uncertainty of 5 K in cloud'temperature, or a surface temperature uncertainty of 2.5 K, is less than 15%. The corresponding e m r in the uncertainty of optical thickness is within 5-2096, depending on the value of cloud optical thickness. The applicability of the technique is demonstrated using the aircraft-based High- resolution Interferometer Sounder (HIS) data from the Subsonic Aircraft: Contrail and Cloud Effects Special Study (SUCCESS) in 1996 and the First ISCCP Regional Experiment - Arctic Clouds Experiment (FIRE-ACE) in 1998.

Huang, Hung-Lung↗

Transfer function verification and block diagram simplification of a very high-order distributed pole closed-loop servo by means of non-linear time-response simulation

Linear frequency domain methods are inadequate in analyzing the 1975 Viking Orbiter (VO75) digital tape recorder servo due to dominant nonlinear effects such as servo signal limiting, unidirectional servo control, and static/dynamic Coulomb friction. The frequency loop (speed control) servo of the VO75 tape recorder is used to illustrate the analytical tools and methodology of system redundancy elimination and high order transfer function verification. The paper compares time-domain performance parameters derived from a series of nonlinear time responses with the available experimental data in order to select the best possible analytical transfer function representation of the tape transport (mechanical segment of the tape recorder) from several possible candidates. The study also shows how an analytical time-response simulation taking into account most system nonlinearities can pinpoint system redundancy and overdesign stemming from a strictly empirical design approach. System order reduction is achieved through truncation of individual transfer functions and elimination of redundant blocks.

Mukhopadhyay, A. K.↗

Structural optimization by methods of feasible directions.

A general design algorithm based on methods of feasible directions is presented. Zoutendijk's method of feasible directions is first presented as applied to structural design. This method is modified to improve numerical stability of the design process and is then further modified to deal efficiently with infeasible designs. The algorithm requires the analytic gradient of the objective function and the constraint functions which are active at a given stage in the design process. Gradient information is not required for nonactive constraints. Complex constraint functions may be ignored in the initial design stages because violation of these constraints is efficiently overcome later in the design process. The algorithm is demonstrated with elastic design of redundant trusses.

Vanderplaats, G. N.↗

High-Fidelity Micromechanics Model Developed for the Response of Multiphase Materials

A new high-fidelity micromechanics model has been developed under funding from the NASA Glenn Research Center for predicting the response of multiphase materials with arbitrary periodic microstructures. The model's analytical framework is based on the homogenization technique, but the method of solution for the local displacement and stress fields borrows concepts previously employed in constructing the higher order theory for functionally graded materials. The resulting closed-form macroscopic and microscopic constitutive equations, valid for both uniaxial and multiaxial loading of periodic materials with elastic and inelastic constitutive phases, can be incorporated into a structural analysis computer code. Consequently, this model now provides an alternative, accurate method.

Aboudi, Jacob↗

Introduction to the Contributions of A. Temkin and R. J. Drachman to Atomic Physics

Their work, as is the work of most atomic theorists, is concerned with solving the Schroedinger equation accurately for wave function in cases where there is no exact analytical solution. In particular, Temkin is associated with electron scattering from atoms and ions. When he started there already were a number of methods to study the scattering of electrons from atoms.

Bhatia, A.K.↗

Practical Methodology for the Inclusion of Nonlinear Slosh Damping in the Stability Analysis of Liquid-Propelled Space Vehicles

A method is presented that allows for the prediction of the magnitude of limit cycles due to adverse control-slosh interaction in liquid propelled space vehicles using non-linear slosh damping. Such a method is an alternative to the industry practice of assuming linear damping and relying on: mechanical slosh baffles to achieve desired stability margins; accepting minimal slosh stability margins; or time domain non-linear analysis to accept time periods of poor stability. Sinusoidal input describing functional analysis is used to develop a relationship between the non-linear slosh damping and an equivalent linear damping at a given slosh amplitude. In addition, a more accurate analytical prediction of the danger zone for slosh mass locations in a vehicle under proportional and derivative attitude control is presented. This method is used in the control-slosh stability analysis of the NASA Space Launch System.

Ottander, John A.↗

Numerical solution of the vertical structure equation in the normal mode method

In the present model of multilayered stability stratification, aimed at obtaining the analytic eigensolutions of the vertical structure equation, each layer is characterized by its own static stability value. By requiring continuity of pressure and vertical velocity across each interface level, and by imposing suitable upper and lower boundary conditions, matching eigensolutions are obtained in terms of the Bessel functions. Attention is given to an explicit example of a double-layered stratified atmosphere which demonstrates the mathematical manipulations involved; the resultant vertical structure functions are used to check the accuracy of the numerical solutions by the finite difference and finite element methods.

Sasaki, Y. K.↗