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NASA NTRS2001

Asymptotic Solutions for Optical Properties of Large Particles with Strong Absorption

The transverse wave condition is not applicable to the refracted electromagnetic wave within the context of geometrical optics when absorption is involved. Either the transverse magnetic (TM) or the transverse electric (TE) wave condition can be assumed for the wave to locally satisfy the electromagnetic boundary condition in a ray-tracing calculation. The assumed wave mode affects both the reflection and the refraction coefficients. As a result, nonunique solutions for these coefficients are inevitable. In this study the appropriate solutions for the Fresnel reflection-refraction coefficients are identified in light-scattering calculations based on the ray-tracing technique. In particular, a 3x2 refraction or transmission matrix is derived to account for the inhomogeneity of the refracted wave in an absorbing medium. An asymptotic solution that completely includes the effect of medium absorption on Fresnel coefficients is obtained for the scattering properties of a general polyhedral particle. Numerical results are presented for hexagonal plates and columns with both preferred and random orientations.

Yang, Ping↗

NASA NTRS2000

Solution of Third Computational Workshop Internal Propagation Problems using Low Order Schemes

The problems solved are propagation of sound waves through a transonic nozzle and shock-sound interaction. The first problem is solved using a MacCormack scheme. The second problem is solved by perturbation of a conservative Euler equation solution to the steady state. The problems are solved on evenly spaced grids. While solutions were found, the methods selected and not using stretched grids lead to solutions which do not compare well with those found using more accurate schemes. However, the perturbation of the mean flow scheme used to solve the second problem shows promise.

Miles, Jeffrey Hilton↗

NASA NTRS1997

Comparison of Chain Conformation of Poly(vinyl alcohol) in Solutions and Melts from Quantum Chemistry Based Molecular Dynamics Simulations

Confirmations of 2,4-dihydroxypentane (DHP), a model molecule for poly(vinyl alcohol), have been studied by quantum chemistry (QC) calculations and molecular dynamics (MD) simulations. QC calculations at the 6-311G MP2 level show the meso tt conformer to be lowest in energy followed by the racemic tg, due to intramolecular hydrogen bond between the hydroxy groups. The Dreiding force field has been modified to reproduce the QC conformer energies for DHP. MD simulations using this force field have been carried out for DHP molecules in the gas phase, melt, and CHCl3 and water solutions. Extensive intramolecular hydrogen bonding is observed for the gas phase and CHCl3 solution, but not for the melt or aqueous solution, Such a condensed phase effect due to intermolecular interactions results in a drastic change in chain conformations, in agreement with experiments.

Jaffe, Richard↗

NASA NTRS2002

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

Atluri, Satya N.↗

NASA NTRS2003

An Exact Dual Adjoint Solution Method for Turbulent Flows on Unstructured Grids

An algorithm for solving the discrete adjoint system based on an unstructured-grid discretization of the Navier-Stokes equations is presented. The method is constructed such that an adjoint solution exactly dual to a direct differentiation approach is recovered at each time step, yielding a convergence rate which is asymptotically equivalent to that of the primal system. The new approach is implemented within a three-dimensional unstructured-grid framework and results are presented for inviscid, laminar, and turbulent flows. Improvements to the baseline solution algorithm, such as line-implicit relaxation and a tight coupling of the turbulence model, are also presented. By storing nearest-neighbor terms in the residual computation, the dual scheme is computationally efficient, while requiring twice the memory of the flow solution. The scheme is expected to have a broad impact on computational problems related to design optimization as well as error estimation and grid adaptation efforts.

Nielsen, Eric J.↗

NASA NTRS2003

Spurious States-Free Solution of the k dot p Hamiltonian for Heterostructures

A method for eliminating spurious solution in the k dot p Hamiltonian has been proposed. Introduction of additional off-diagonal alpha k(exp 2) term converts spurious solution with large real wave vector to evanescent solution with large imaginary wave vector. This modification keeps the same effective masses at Gamma point and introduces negligible deviation from original nonparabolicity. A set of unphysical fast oscillation eigenfunctions in confined states of heterostructures are removed.

Kolokolov, Konstantin I.↗

NASA NTRS2003

Step Bunching and Solution Flow

Imagine a sequence of equidistant steps parallel to one another on a crystal face growing from solution. Steps may be one or part of a lattice spacing high. With such ideal morphology, the most perfect material is expected to be produced. Sometimes this happens. Much more often, however, steps form bunches, acquire wavy shapes and interlace. With time, these spontaneous perturbations may be increased in amplitude, i.e. the stepped surface becomes morphologically unstable. Interferometric studies of Y.G. Kuznetsov, L.N. Rashkovich, P.G. Vekilov and N.A. Booth and the author demonstrated that the step bunching depends at least on direction and rate of solution flow over the interface, supersaturation and presence of impurities. In particular, if solution and step flow are parallel to one another, the steps convene into bunches. If these flows are antiparallel, the bunches disappear. As the step train propagates, the overall bunch height often increases infinitely. However, we have found recently that if the flow rate is large enough, (approximately 1 meter per second), the bunch height may be limited. All these phenomena come from interaction between steps. The interaction mechanisms are still not fully understood. I plan to overview major approaches to the still unresolved problem on how these dissipative structures on growing crystal face appear and evolve.

Chernov, A. A.↗

NASA NTRS2003

Constraint Maintenance with Preferences and Underlying Flexible Solution

This paper describes an aspect of the constraint reasoning mechanism. that is part of a ground planning system slated to be used for the Mars Exploration Rovers mission, where two rovers are scheduled to land on Mars in January of 2003. The planning system combines manual planning software from JPL with an automatic planning/scheduling system from NASA Ames Research Center, and is designed to be used in a mixed-initiative mode. Among other things, this means that after a plan has been produced, the human operator can perform extensive modifications under the supervision of the automated. system. For each modification to an activity, the automated system must adjust other activities as needed to ensure that constraints continue to be satisfied. Thus, the system must accommodate change in an interactive setting. Performance is of critical importance for interactive use. This is achieved by maintaining an underlying flexible solution to the temporal constraints, while the system presents a fixed schedule to the user. Adjustments are then a matter of constraint propagation rather than completely re-solving the problem. However, this begs the important question of which fixed schedule (among the ones sanctioned by the underlying flexible solution) should be presented to the user.Our approach uses least-change and other preferences as a prism through which the user views the flexible solution.

Bresina, John↗

NASA NTRS1994

Nucleation of Crystals From Solution in Microgravity (USML-1 Glovebox (GBX) Investigation)

A new method for initiating nucleation from solutions in microgravity which avoids nucleation on container walls and other surfaces is described. This method consists of injecting a small quantity of highly concentrated, heated solution into the interior of a lightly supersaturated, cooler host gowth solution. It was tested successfully on USML-I, producing a large number of LAP crystals whose longest dimension averaged 1 mm.

Kroes, Roger L.↗

NASA NTRS1961

The General Equations of Equilibrium of Rotationally Symmetric Membranes and some Static Solutions for Uniform Centrifugal Loading

The general equations of equilibrium of a rotationally symmetrical body undergoing large arbitrary deflections but small strains are derived by means of the principle of virtual work. All deflections are referred to a reference surface which, in general, may be taken to coincide with any intermediate state of the membrane. Static solutions of the general equations for steadily rotating membranes are considered for the cases in which the final or the initial configuration of the membrane is specified. For problems in which the final configuration is specified, conditions are given under which such a configuration is obtainable from a stress-free initial state. Such conditions being satisfied, it is shown that the stresses and radial displacements are determinate while axial displacements may be obtained by quadrature. For problems in which the initial configuration is given, the determination of the stresses and deflections is reduced to the solution of a second-order nonlinear differential equation for a stress function. An approximate method of solution based on boundary-layer considerations is presented for the case of a spinning sphere of constant thickness. Specific examples are given for both classes of problems.

Simmonds, James G.↗

NASA NTRS1961

An Explicit Linear Filtering Solution for the Optimization of Guidance Systems with Statistical Inputs

The determination of optimum filtering characteristics for guidance system design is generally a tedious process which cannot usually be carried out in general terms. In this report a simple explicit solution is given which is applicable to many different types of problems. It is shown to be applicable to problems which involve optimization of constant-coefficient guidance systems and time-varying homing type systems for several stationary and nonstationary inputs. The solution is also applicable to off-design performance, that is, the evaluation of system performance for inputs for which the system was not specifically optimized. The solution is given in generalized form in terms of the minimum theoretical error, the optimum transfer functions, and the optimum transient response. The effects of input signal, contaminating noise, and limitations on the response are included. From the results given, it is possible in an interception problem, for example, to rapidly assess the effects on minimum theoretical error of such factors as target noise and missile acceleration. It is also possible to answer important questions regarding the effect of type of target maneuver on optimum performance.

Stewart, Elwood C.↗

NASA NTRS2004

Approximate Solution for Choked Flow in Gas Seal Pads

Previous analyses of high pressure seals have considered adiabatic flow with friction but neglected effects of seal rotation. Most of this work analyzed a one-dimensional flow field. This works well to calculate stiffness and leakage of full circular seals, either face seals or annular ring seals. However, it cannot provide accurate results for a rectangular seal pad with its strongly two-dimensional flow field and its reliance on hydrodynamic forces to maintain a full fluid film. On the other hand, solutions of Reynolds lubrication equation have been obtained for the two-dimensional flow in a seal pad. But these solutions do not account for choking which occurs at high seal pressure ratios, nor do they consider the pressure loss that occurs in the entrance region of the flow field. The aim of the present work is to build on the Reynolds equation solution by use of an approximate choked flow analysis. This will account for the pressure losses in the flow entrance region, ensure that fluid velocities remain subsonic, and enable fluid inertial effects within the pad film to be accounted for. Results show that, in general, fluid inertia acts to decrease pad film load capacity and leakage, and increase film stiffness.

Fleming, David P.↗

NASA NTRS2004

Integrated Force Method Solution to Indeterminate Structural Mechanics Problems

Strength of materials problems have been classified into determinate and indeterminate problems. Determinate analysis primarily based on the equilibrium concept is well understood. Solutions of indeterminate problems required additional compatibility conditions, and its comprehension was not exclusive. A solution to indeterminate problem is generated by manipulating the equilibrium concept, either by rewriting in the displacement variables or through the cutting and closing gap technique of the redundant force method. Compatibility improvisation has made analysis cumbersome. The authors have researched and understood the compatibility theory. Solutions can be generated with equal emphasis on the equilibrium and compatibility concepts. This technique is called the Integrated Force Method (IFM). Forces are the primary unknowns of IFM. Displacements are back-calculated from forces. IFM equations are manipulated to obtain the Dual Integrated Force Method (IFMD). Displacement is the primary variable of IFMD and force is back-calculated. The subject is introduced through response variables: force, deformation, displacement; and underlying concepts: equilibrium equation, force deformation relation, deformation displacement relation, and compatibility condition. Mechanical load, temperature variation, and support settling are equally emphasized. The basic theory is discussed. A set of examples illustrate the new concepts. IFM and IFMD based finite element methods are introduced for simple problems.

Patnaik, Surya N.↗

NASA NTRS2004

Particles Growing in Solutions: Depletion Forces and Instability of Homogeneous Particle Distribution

Crystallites, droplets and amorphous precipitates growing from supersaturated solution are surrounded by zones, which are depleted with respect to the molecules they are built of. If two such particles of colloidal size are separated by a distance comparable to their diameters, then the depletion within the gap between particles is deeper than that at the outer portion of the particles. This will cause depletion attraction between the particles should appear. It may cause particle coagulation and decay of the originally homogeneous particle distribution into a system of clouds within which the particle number density is higher, separated by the region of the lower number density. Stability criterion, Q = 4 pi R(exp 3)c/3 >> 1, was analytically found along with typical particle density distribution wavevector q = (Q/I)(exp 1/2)(a/R)(exp 1/4). Here, R and a are the particle and molecular radii, respectively, c is the average molecular number density in solution and I is the squared diffusion length covered by a molecule during a typical time characterizing decay of molecular concentration in solution due to consumption of the molecules by the growing particles.

Chernov, A. A.↗

NASA NTRS2003

Biogeochemistry of fluoride in a plant-solution system

Fluoride (F-) pollutants can harm plants and the animals feeding on them. However, it is largely unknown how complexing and chelating agents affect F bioavailability. Two studies were conducted that measured F- bioavailability and uptake by rice (Oryza sativa L.). In the first study, rice was grown in solution culture (pH 5.0) with 0, 2, or 4 mM F- as KF to compare the interaction of F- with humic acid (HA) and with a conventional chelating agent, N-hydroxyethylenthylenediaminetriacetic acid (HEDTA). In the second study, F was supplied at 0, 0.5, 1.0, and 2.0 mM KF with an additional 2 mM F- treatment containing solution Ca at 2x (2 mM Ca) the level used in the first study, to test the effect added Ca had on F- availability and uptake. Total biomass was greatest with HEDTA and F- < 1 mM. Leaf and stem F concentrations increased exponentially as solution F- increased linearly, with nearly no F partitioning into the seed. Results suggest that F was taken up as HF0 while F- uptake was likely restricted. Additionally, F- competed with HA for Ca, thus preventing the formation of Ca-HA flocculents. The addition of soluble Ca resulted in the precipitation of CaF2 solids on the root surface, as determined by tissue analysis and energy dispersive X-ray spectroscopy.

NASA Discipline Life Support Systems↗

NASA NTRS1984

Tomato growth as affected by root-zone temperature and the addition of gibberellic acid and kinetin to nutrient solutions

The effect of root-zone temperature on young tomato plants (Lycopersicon esculentum Mill. cv. Heinz 1350) was evaluated in controlled environments using a recirculating solution culture system. Growth rates were measured at root-zone temperatures of 15 degrees, 20 degrees, 25 degrees, and 30 degrees C in a near optimum foliar environment. Optimum growth occurred at 25 degrees to 30 degrees during the first 4 weeks of growth and 20 degrees to 25 degrees during the 5th and 6th weeks. Growth was severely restricted at 15 degrees. Four concentrations of gibberellic acid (GA3) and kinetin were added to the nutrient solution in a separate trial; root-zone temperature was maintained at 15 degrees and 25 degrees. Addition of 15 micromoles GA3 to solutions increased specific leaf area, total leaf area, and dry weight production of plants in both temperature treatments. GA3-induced growth stimulation was greater at 15 degrees than at 25 degrees. GA3 may promote growth by increasing leaf area, enhancing photosynthesis per unit leaf area, or both. Kinetic was not useful in promoting growth at either temperature.

NASA Program CELSS↗

NASA NTRS1996

Excess chemical potential of small solutes across water--membrane and water--hexane interfaces

The excess chemical potentials of five small, structurally related solutes, CH4, CH3F, CH2F2, CHF3, and CF4, across the water-glycerol 1-monooleate bilayer and water-hexane interfaces were calculated at 300, 310, and 340 K using the particle insertion method. The excess chemical potentials of nonpolar molecules (CH4 and CF4) decrease monotonically or nearly monotonically from water to a nonpolar phase. In contrast, for molecules that possess permanent dipole moments (CH3F, CH2F, and CHF3), the excess chemical potentials exhibit an interfacial minimum that arises from superposition of two monotonically and oppositely changing contributions: electrostatic and nonelectrostatic. The nonelectrostatic term, dominated by the reversible work of creating a cavity that accommodates the solute, decreases, whereas the electrostatic term increases across the interface from water to the membrane interior. In water, the dependence of this term on the dipole moment is accurately described by second order perturbation theory. To achieve the same accuracy at the interface, third order terms must also be included. In the interfacial region, the molecular structure of the solvent influences both the excess chemical potential and solute orientations. The excess chemical potential across the interface increases with temperature, but this effect is rather small. Our analysis indicates that a broad range of small, moderately polar molecules should be surface active at the water-membrane and water-oil interfaces. The biological and medical significance of this result, especially in relation to the mechanism of anesthetic action, is discussed.

NASA Center ARC↗

NASA NTRS2004

An Operator Method for Field Moments from the Extended Parabolic Wave Equation and Analytical Solutions of the First and Second Moments for Atmospheric Electromagnetic Wave Propagation

The extended wide-angle parabolic wave equation applied to electromagnetic wave propagation in random media is considered. A general operator equation is derived which gives the statistical moments of an electric field of a propagating wave. This expression is used to obtain the first and second order moments of the wave field and solutions are found that transcend those which incorporate the full paraxial approximation at the outset. Although these equations can be applied to any propagation scenario that satisfies the conditions of application of the extended parabolic wave equation, the example of propagation through atmospheric turbulence is used. It is shown that in the case of atmospheric wave propagation and under the Markov approximation (i.e., the delta-correlation of the fluctuations in the direction of propagation), the usual parabolic equation in the paraxial approximation is accurate even at millimeter wavelengths. The comprehensive operator solution also allows one to obtain expressions for the longitudinal (generalized) second order moment. This is also considered and the solution for the atmospheric case is obtained and discussed. The methodology developed here can be applied to any qualifying situation involving random propagation through turbid or plasma environments that can be represented by a spectral density of permittivity fluctuations.

Manning, Robert M.↗