Similarity analysis of partial differential equations Final report
Explore the source record for details and available documents.
Abbott, D. E.↗
SEARCH · Engineering Papers
Results for “differential analysis”
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.
Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.
Development of Methods of Characterizing Coal in Its Plastic State
Coal in its plastic state (typically 400-460 C) was examined by the isothermal Gieseler plastometry of seven selected coals of widely varying plastic properties. Kinetic models were proposed for the isothermal plastometric curves. Plastic behavior was compared with a variety of laboratory analyses and characterizations of these coals, including classical coal analysis; mineral analysis; microstructural analysis (extractable fractions, surface area measurement, and petrographic analysis); and thermal analysis (thermogravimetric analysis, thermomechanical analysis, and differential scanning calorimetry). The phenomenon of a sharp, large, poorly reproducible exotherm in the differential scanning calorimetric analysis of coking coals was examined. Several coal extrudates show mineral distribution, organic maceral composition and overall calorific value to be little affected by 800 F extrusion. Volatile matter and plastic properties are moderately reduced, and the network structure (as gauged by extractables) appears to be slightly degraded in the extrusion process.
Lloyd, W. G.↗
Morphometric analysis of epidermal differentiation in primary roots of Zea mays
Epidermal differentiation in primary roots of Zea mays was divided into six cell types based on cellular shape and cytoplasmic appearance. These six cell types are: 1) apical protoderm, located at the tip of the root pole and characterized by periclinally flattened cells; 2) cuboidal protoderm, located approximately 230 microns from the root pole and characterized by cuboidal cells; 3) tabular epidermis, located approximately 450 microns from the root pole and characterized by anticlinally flattened cells; 4) cuboidal epidermis, located approximately 900 microns from the root pole and characterized by cuboidal cells having numerous small vacuoles; 5) vacuolate cuboidal epidermis, located approximately 1,500 microns from the root pole and characterized by cuboidal cells containing several large vacuoles; and 6) columnar epidermis, located approximately 2,200 microns from the root pole (i.e., at the beginning of the zone of elongation) and characterized by elongated cells. We also used stereology to quantify the cellular changes associated with epidermal differentiation. The quiescent center and the apical protoderm have significantly different ultrastructures. The relative volume of dictyosomes increases dramatically during the early stages of epidermal differentiation. This increase correlates inversely with the amount of coverage provided by the root cap and mucilage.
NASA Discipline Plant Biology↗
Estimation of Sorption Behavior of Europium to Calcium Silicate Hydrate by Thermal Analysis - 20172
High-level radioactive waste generated from reprocessing processes will be disposed in a geological disposal that is deep underground. Calcium silicate hydrate is formed as a secondary mineral in the repository via the reaction of calcium ions leaching from the cement and the silicic acid dissolved from the host rocks. In this study, the sorption behavior of europium, which is also known as a chemical analog of americium, on calcium silicate hydrate was examined. The solid phase was analyzed via thermogravimetry- differential thermal analysis, differential scanning calorimetry, Raman spectroscopy, fluorescence spectroscopy, and fluorescence lifetime analysis. To understand the behavior of calcium silicate hydrate under conditions saturated with groundwater, the study samples were analyzed using the above methods, except for deferential scanning calorimetry, without a drying process. The results of the differential scanning calorimetry analyses showed that the temperatures for the endothermic peaks of calcium silicate hydrate for the lower Ca/Si ratios were larger than those for the higher Ca/Si ratios for coexistent conditions of europium ions. Hence, the relationships of the temperatures of the endothermic peaks and the Ca/Si ratios were reversed by the addition of europium ions. These study results suggest that calcium silicate hydrate can immobilize europium ions, thus preventing the production of colloidal forms. (authors)
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Automatic differentiation for design sensitivity analysis of structural systems using multiple processors
An automatic differentiation tool (ADIFOR) is incorporated into a finite element based structural analysis program for shape and non-shape design sensitivity analysis of structural systems. The entire analysis and sensitivity procedures are parallelized and vectorized for high performance computation. Small scale examples to verify the accuracy of the proposed program and a medium scale example to demonstrate the parallel vector performance on multiple CRAY C90 processors are included.
Nguyen, Duc T.↗
Internal energy of reaction products by velocity analysis. III.
Differential reaction cross section and internal excitation function from K and Br molecule crossed beam velocity analysis
EXCITED STATE↗
In situ identification of the Martian surface material and its interaction with the Martian atmosphere using DTA/GC
Little is known about the mineralogy of the martian surface material. Several techniques have been suggested as candidates for the in situ identification of the martian surface material. The most promising of these techniques include differential thermal analysis (DTA) coupled with gas chromatography (GC) and differential scanning calorimetry (DSC) coupled with either mass spectrometry (MS) or GC. Our studies showed that differential thermal analysis coupled with gas chromatography (DTA/GC) is a more appropriate analytical technique than DSC/MS or DSC/GC to identify the mineralogy of the martian surface material in situ. DTA/GC can be regarded as an advancement from pyrolytic GC analyses that were successfully flown on previous missions, but have supplied only limited mineralogical information.
Mancinelli, R. L.↗
Air-to-air combat analysis - Review of differential-gaming approaches
The problem of evaluating the combat performance of fighter/attack aircraft is discussed, and the mathematical nature of the problem is examined. The following approaches to air combat analysis are reviewed: (1) differential-turning differential game and (2) coplanar differential game. Selected numerical examples of these approaches are presented. The relative advantages and disadvantages of each are analyzed, and it is concluded that air combat analysis is an extremely difficult mathematical problem and that no one method of approach is best for all purposes. The paper concludes with a discussion of how the two approaches might be used in a complementary manner.
Ardema, M. D.↗
Mass analysis addition to the Differential Ion Flux Probe (DIFP) study
The objective of this study is to develop a technique to measure the characteristics of space plasmas under highly disturbed conditions; e.g., non-Maxwellian plasmas with strong drifting populations and plasmas contaminated by spacecraft outgassing. The approach, conducted in conjunction with current MSFC activities, is to extend the capabilities of the Differential Ion Flux Probe (DIFP) to include a high throughput mass measurement that does not require either high voltage or contamination sensitive devices such as channeltron electron multipliers or microchannel plates. This will significantly reduce the complexity and expense of instrument fabrication, testing, and integration of flight hardware compared to classical mass analyzers. The feasibility of the enhanced DIFP has been verified by using breadboard test models in a controlled plasma environment. The ability to manipulate particles through the instrument regardless of incident angle, energy, or ionic component has been amply demonstrated. The energy analysis mode is differential and leads directly to a time-of-flight mass measurement. With the new design, the DIFP will separate multiple ion streams and analyze each stream independently for ion flux intensity, velocity (including direction of motion), mass, and temperature (or energy distribution). In particular, such an instrument will be invaluable on follow-on electrodynamic TSS missions and, possibly, for environmental monitoring on the space station.
Wright, K. H., Jr.↗
Differential methods for assessing sensitivity in biological models
Differential sensitivity analysis is indispensable in fitting parameters, understanding uncertainty, and forecasting the results of both thought and lab experiments. Although there are many methods currently available for performing differential sensitivity analysis of biological models, it can be difficult to determine which method is best suited for a particular model. In this paper, we explain a variety of differential sensitivity methods and assess their value in some typical biological models. First, we explain the mathematical basis for three numerical methods: adjoint sensitivity analysis, complex perturbation sensitivity analysis, and forward mode sensitivity analysis. We then carry out four instructive case studies. (a) The CARRGO model for tumor-immune interaction highlights the additional information that differential sensitivity analysis provides beyond traditional naive sensitivity methods, (b) the deterministic SIR model demonstrates the value of using second-order sensitivity in refining model predictions, (c) the stochastic SIR model shows how differential sensitivity can be attacked in stochastic modeling, and (d) a discrete birth-death-migration model illustrates how the complex perturbation method of differential sensitivity can be generalized to a broader range of biological models. Finally, we compare the speed, accuracy, and ease of use of these methods. We find that forward mode automatic differentiation has the quickest computational time, while the complex perturbation method is the simplest to implement and the most generalizable.
59 BASIC BIOLOGICAL SCIENCES↗
Numerical integration of asymptotic solutions of ordinary differential equations
Classical asymptotic analysis of ordinary differential equations derives approximate solutions that are numerically stable. However, the analysis also leads to tedious expansions in powers of the relevant parameter for a particular problem. The expansions are replaced with integrals that can be evaluated by numerical integration. The resulting numerical solutions retain the linear independence that is the main advantage of asymptotic solutions. Examples, including the Falkner-Skan equation from laminar boundary layer theory, illustrate the method of asymptotic analysis with numerical integration.
Thurston, Gaylen A.↗
Stability analysis of a reinforced carbon carbon shell
This paper presents the development of a stability analysis for the nose cap of the NASA Space Shuttle Orbiter. Stability is evaluated by the differential stiffness analysis of the NASTRAN finite-element computer code, addressing those nonstandard characteristics in the nose cap such as nonuniform curvature, asymmetrical and nonuniform loads, support fixity, and various combinations of membrane and bending stresses. A full-sized nose cap, thinner than production, was statically tested and stability analyzed. The failing load level correlated to within 30%. The region and mode of buckling that occurred during test was accurately predicted by analysis. The criterion for predicting instability is based on the behavior of the nonlinear deflections. The deflections are nonlinear elastic in that the stresses are well within the elastic range of the material, but the geometry-load relationship produces nonlinear deflections. The load-deflection relationship is well defined by differential stiffness analysis up to the zero-slope portion of the curve, the point of neutral stability or where the shell 'snaps through' just prior to general instability.
Agan, W. E.↗
Evaluation of methods for rapid determination of freezing point of aviation fuels
Methods for identification of the more promising concepts for the development of a portable instrument to rapidly determine the freezing point of aviation fuels are described. The evaluation process consisted of: (1) collection of information on techniques previously used for the determination of the freezing point, (2) screening and selection of these techniques for further evaluation of their suitability in a portable unit for rapid measurement, and (3) an extensive experimental evaluation of the selected techniques and a final selection of the most promising technique. Test apparatuses employing differential thermal analysis and the change in optical transparency during phase change were evaluated and tested. A technique similar to differential thermal analysis using no reference fuel was investigated. In this method, the freezing point was obtained by digitizing the data and locating the point of inflection. Results obtained using this technique compare well with those obtained elsewhere using different techniques. A conceptual design of a portable instrument incorporating this technique is presented.
Mathiprakasam, B.↗
Demonstration of Automatically-Generated Adjoint Code for Use in Aerodynamic Shape Optimization
Gradient-based optimization requires accurate derivatives of the objective function and constraints. These gradients may have previously been obtained by manual differentiation of analysis codes, symbolic manipulators, finite-difference approximations, or existing automatic differentiation (AD) tools such as ADIFOR (Automatic Differentiation in FORTRAN). Each of these methods has certain deficiencies, particularly when applied to complex, coupled analyses with many design variables. Recently, a new AD tool called ADJIFOR (Automatic Adjoint Generation in FORTRAN), based upon ADIFOR, was developed and demonstrated. Whereas ADIFOR implements forward-mode (direct) differentiation throughout an analysis program to obtain exact derivatives via the chain rule of calculus, ADJIFOR implements the reverse-mode counterpart of the chain rule to obtain exact adjoint form derivatives from FORTRAN code. Automatically-generated adjoint versions of the widely-used CFL3D computational fluid dynamics (CFD) code and an algebraic wing grid generation code were obtained with just a few hours processing time using the ADJIFOR tool. The codes were verified for accuracy and were shown to compute the exact gradient of the wing lift-to-drag ratio, with respect to any number of shape parameters, in about the time required for 7 to 20 function evaluations. The codes have now been executed on various computers with typical memory and disk space for problems with up to 129 x 65 x 33 grid points, and for hundreds to thousands of independent variables. These adjoint codes are now used in a gradient-based aerodynamic shape optimization problem for a swept, tapered wing. For each design iteration, the optimization package constructs an approximate, linear optimization problem, based upon the current objective function, constraints, and gradient values. The optimizer subroutines are called within a design loop employing the approximate linear problem until an optimum shape is found, the design loop limit is reached, or no further design improvement is possible due to active design variable bounds and/or constraints. The resulting shape parameters are then used by the grid generation code to define a new wing surface and computational grid. The lift-to-drag ratio and its gradient are computed for the new design by the automatically-generated adjoint codes. Several optimization iterations may be required to find an optimum wing shape. Results from two sample cases will be discussed. The reader should note that this work primarily represents a demonstration of use of automatically- generated adjoint code within an aerodynamic shape optimization. As such, little significance is placed upon the actual optimization results, relative to the method for obtaining the results.
Green, Lawrence↗
Effects of orbital exposure on Halar during the LDEF mission
Thermomechanical Analysis (TMA), Differential Scanning Calorimetry (DSC), and Thermogravimetric Analysis (TGA) were performed on samples of Halar exposed on the LDEF Mission for 6 years in orbit and unexposed Halar control samples. Sections 10-100 microns thick were removed from the exposed surface down to a depth of 1,000 microns through the 3 mm thick samples. The TMA and DSC results, which arise from the entire slice and not just its surface, showed no differences between the LDEF and the control samples. TMA scans were run from ambient to 300 C; results were compared by a tabulation of the glass transition temperatures. DSC scans were run from ambient to 700 C; the enthalpy of melting was compared for the samples as a function of section depth with the sample. The TGA results, which arise from the surface of the sample initially, showed a sharp increase in the topmost 50 micron section (the exposed, discolored side) in the weight loss of 170 C in oxygen. This weight loss dropped to bulk values in the range of depth of 50-200 microns. The control sample showed only a slight increase in weight loss as the top surface was approached. The LDEF Halar sample appears to be mechanically undamaged, with a surface layer which oxidizes faster as a result of orbital exposure.
Brower, William E., Jr.↗
Effects of orbital exposure on RTV during the LDEF mission
Thermomechanical analysis (TMA), differential scanning calorimetry (DSC), and thermogravimetric analysis (TGA) were performed on samples of RTV 511 exposed on the Long Duration Exposure Facility (LDEF) mission for 6 years in orbit and unexposed RTV 511 control samples. Slices 20- to 400-microns thick were removed from the exposed surface down to a depth of 1,500 microns through the 3-mm thick samples. The TMA and DSC results, which arise from the entire slice and not just its surface, showed no significant differences between the LDEF exposed and the control samples. TMA scans were run from ambient to 500 C; results were compared by a tabulation of the onset temperatures for flow. DSC scans were run from ambient to 600 C; no endotherms or exotherms occurred over the range observed. What appear to be glass transition temperatures were compared for the samples as a function of section depth within the sample and between the exposed and control samples. The TGA scans from 25 to 900 C, which arise from the surface of the sample initially, showed a slight increase in the top most 105-micron slice (the exposed, discolored side) in the weight loss at 600 C in oxygen. This weight loss dropped to bulk values at the next slice below the top section, a mean depth of 258 microns. The control sample also showed an increase in weight loss as the top surface was approached, but the 600 C weight losses were very inconsistent. The LDEF RTV sample appears to be mechanically undamaged, with a surface layer which oxidizes slightly faster as a result of orbital exposure.
Brower, William E., Jr.↗
Analysis of Electricity Price Differentials for the Utah Office of Energy Development
Operation Gigawatt is a vision for Utah to meet its growing energy needs with a focus on doubling energy generation. One of the greatest challenges to meet this goal will be the transmission and distribution system. Utah seeks analysis to inform discussions on new generation, the likely network congestion based on new power flows, and modeling of the state's energy infrastructure. To support this need, LBNL developed a baseline understanding of recent historical congestion in the existing transmission system based on electricity market prices. The resulting products visualize and provide metrics on congestion within Utah and between Utah and its neighbors during 2015-2023.
24 POWER TRANSMISSION AND DISTRIBUTION↗
Phase diagram and electrical behavior of silicon-rich iridium silicide compounds
The iridium-silicon phase diagram on the silicon-rich side was investigated by means of X-ray powder diffraction, density, differential thermal analysis, metalography, microprobe analysis, and electrical resistivity. Attempts were made to prepare eight previously reported silicon-rich iridium silicide compounds by arc melting and Bridgman-like growth. However, microprobe analysis identified only four distinct compositions: IrSi, Ir3Si4, Ir3Si5 and IrSi sub about 3. The existence of Ir4Si5 could not be confirmed in this study, even though the crystal structure has been previously reported. Differential thermal analysis (DTA) in conjunction with X-ray powder diffraction confirm polymorphism in IrSi sub about 3, determined to have orthorhombic and monoclinic unit cells in the high and low temperature forms. A eutectic composition alloy of 83 +/- 1 atomic percent silicon was observed between IrSi sub about 3 and silicon. Ir3Si4 exhibits distinct metallic behavior while Ir3Si5 is semiconducting. Both and IrSi and IrSi sub about 3 exhibit nearly temperature independent electrical resistivities on the order of 5-10 x 10 exp -6 ohms-m.
Allevato, C. E.↗