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All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

An analytical evaluation of mascon effects in a semi-analytic theory

A semianalytic method to predict the orbit of a spacecraft orbiting a planet and perturbed by oblateness and a gravity anomaly (mascon) is presented. The Hamiltonian is first expressed in closed form in terms of the nonsingular canonical set of Poincare elements where the mascon is represented by a point-mass. The planet global potential is limited to the second and third harmonics. The mascon potential in harmonics is limited to second degree and first order. The original Lie-Hori method is then applied to transform the canonical equations of motion from the osculating element space to the mean element space. Numerical integration of the new equations is used.

Salama, Ahmed H.↗
NASA NTRS2016

Earth Science Data Analytics: Preparing for Extracting Knowledge from Information

Data analytics is the process of examining large amounts of data of a variety of types to uncover hidden patterns, unknown correlations and other useful information. Data analytics is a broad term that includes data analysis, as well as an understanding of the cognitive processes an analyst uses to understand problems and explore data in meaningful ways. Analytics also include data extraction, transformation, and reduction, utilizing specific tools, techniques, and methods. Turning to data science, definitions of data science sound very similar to those of data analytics (which leads to a lot of the confusion between the two). But the skills needed for both, co-analyzing large amounts of heterogeneous data, understanding and utilizing relevant tools and techniques, and subject matter expertise, although similar, serve different purposes. Data Analytics takes on a practitioners approach to applying expertise and skills to solve issues and gain subject knowledge. Data Science, is more theoretical (research in itself) in nature, providing strategic actionable insights and new innovative methodologies. Earth Science Data Analytics (ESDA) is the process of examining, preparing, reducing, and analyzing large amounts of spatial (multi-dimensional), temporal, or spectral data using a variety of data types to uncover patterns, correlations and other information, to better understand our Earth. The large variety of datasets (temporal spatial differences, data types, formats, etc.) invite the need for data analytics skills that understand the science domain, and data preparation, reduction, and analysis techniques, from a practitioners point of view. The application of these skills to ESDA is the focus of this presentation. The Earth Science Information Partners (ESIP) Federation Earth Science Data Analytics (ESDA) Cluster was created in recognition of the practical need to facilitate the co-analysis of large amounts of data and information for Earth science. Thus, from a to advance science point of view: On the continuum of ever evolving data management systems, we need to understand and develop ways that allow for the variety of data relationships to be examined, and information to be manipulated, such that knowledge can be enhanced, to facilitate science. Recognizing the importance and potential impacts of the unlimited ways to co-analyze heterogeneous datasets, now and especially in the future, one of the objectives of the ESDA cluster is to facilitate the preparation of individuals to understand and apply needed skills to Earth science data analytics. Pinpointing and communicating the needed skills and expertise is new, and not easy. Information technology is just beginning to provide the tools for advancing the analysis of heterogeneous datasets in a big way, thus, providing opportunity to discover unobvious scientific relationships, previously invisible to the science eye. And it is not easy It takes individuals, or teams of individuals, with just the right combination of skills to understand the data and develop the methods to glean knowledge out of data and information. In addition, whereas definitions of data science and big data are (more or less) available (summarized in Reference 5), Earth science data analytics is virtually ignored in the literature, (barring a few excellent sources).

data analytics↗
NASA NTRS2015

Deriving Earth Science Data Analytics Requirements

Data Analytics applications have made successful strides in the business world where co-analyzing extremely large sets of independent variables have proven profitable. Today, most data analytics tools and techniques, sometimes applicable to Earth science, have targeted the business industry. In fact, the literature is nearly absent of discussion about Earth science data analytics. Earth science data analytics (ESDA) is the process of examining large amounts of data from a variety of sources to uncover hidden patterns, unknown correlations, and other useful information. ESDA is most often applied to data preparation, data reduction, and data analysis. Co-analysis of increasing number and volume of Earth science data has become more prevalent ushered by the plethora of Earth science data sources generated by US programs, international programs, field experiments, ground stations, and citizen scientists.Through work associated with the Earth Science Information Partners (ESIP) Federation, ESDA types have been defined in terms of data analytics end goals. Goals of which are very different than those in business, requiring different tools and techniques. A sampling of use cases have been collected and analyzed in terms of data analytics end goal types, volume, specialized processing, and other attributes. The goal of collecting these use cases is to be able to better understand and specify requirements for data analytics tools and techniques yet to be implemented. This presentation will describe the attributes and preliminary findings of ESDA use cases, as well as provide early analysis of data analytics toolstechniques requirements that would support specific ESDA type goals. Representative existing data analytics toolstechniques relevant to ESDA will also be addressed.

data analytics↗
NASA NTRS1980

The Finite Analytic Method for steady and unsteady heat transfer problems

A new numerical method called the Finite Analytical Method for solving partial differential equations is introduced. The basic idea of the finite analytic method is the incorporation of the local analytic solution in obtaining the numerical solution of the problem. The finite analytical method first divides the total region of the problem into small subregions in which local analytic solutions are obtained. Then an algebraic equation is derived from the local analytic solution for each subregion relating an interior nodal value at a point P in the subregion to its neighboring nodal values. The assembly of all the local analytic solutions thus provides the finite-analytic numerical solution of the problem. In this paper the finite analytic method is illustrated in solving steady and unsteady heat transfer problems.

Chen, C.-J.↗
NASA NTRS2015

ESIP Earth Sciences Data Analytics (ESDA) Cluster - Work in Progress

The purpose of this poster is to promote a common understanding of the usefulness of, and activities that pertain to, Data Analytics and more broadly, the Data Scientist; Facilitate collaborations to better understand the cross usage of heterogeneous datasets and to provide accommodating data analytics expertise, now and as the needs evolve into the future; Identify gaps that, once filled, will further collaborative activities. Objectives Provide a forum for Academic discussions that provides ESIP members a better understanding of the various aspects of Earth Science Data Analytics Bring in guest speakers to describe external efforts, and further teach us about the broader use of Data Analytics. Perform activities that:- Compile use cases generated from specific community needs to cross analyze heterogeneous data- Compile sources of analytics tools, in particular, to satisfy the needs of the above data users- Examine gaps between needs and sources- Examine gaps between needs and community expertise- Document specific data analytics expertise needed to perform Earth science data analytics Seek graduate data analytics Data Science student internship opportunities.

science data analysis↗
DOE OSTI2022

Standard Analytical Methods for Pyrolysis Bio-Oils

There has been significant recent interest in the production of renewable fuels and chemicals from biomass and waste feedstocks. Pyrolysis pathways produce a liquid bio-oil product, which must be processed further, or upgraded, to yield fuel or chemical products. Bio-oils are very complex and often unstable samples, and research and development on upgrading processes needs reliable analytical information. In particular, chemical characterization techniques are needed to quantify both functional groups and individual compounds present in bio-oils. Reliable analytics are also needed to enable the bioenergy industry, as industrial facilities often have different analytical needs and capabilities than research facilities. In this presentation, we will discuss the development of a suite of standard analytical methods for pyrolysis bio-oils. Analytical methods to be discussed include: Determination of Carbon, Hydrogen, Nitrogen, and Oxygen in bio-oils; Accelerated Aging of Fast Pyrolysis Bio-oil using Carbonyl Titration; Determination of Water Content in Bio-oils by Volumetric Karl Fischer Titration; Determination of Carbon Functional Groups; Elemental Analysis of Bio-oils by Inductively Coupled Plasma Optical Emission Spectroscopy (ICP-OES) - Na, K, Mg, Ca, S, P, and Fe; Determination of Phenolic Groups in Bio-oils using Revised Folin-Ciocalteu Methods: Single Cuvette and Plate Reader; Corrosivity of Bio-oils: Screening Test using Metal Leaching; Determination of Biogenic Content by 14C Measurement using Liquid Scintillation Counter. These new analytical methods are publicly available as Laboratory Analytical Procedures (https://www.nrel.gov/bioenergy/bio-oil-analysis.html), along with previously developed standard methods: GC-MS, Acid Titration, Carbonyl Titration, and 31P NMR. Additionally, the development of diffusion ordered NMR for characterization of bio-oil molecular weight will be discussed. Collectively, this suite of analytical methods represents the most comprehensive set of standard methods available for pyrolysis bio-oils. These standard methods are commonly used by the bioenergy community, and provide reliable information that enables research, scaleup, and industrial processing of biomass to produce renewable fuels and chemicals.

analytical↗
DOE OSTI2021

BETO 2021 Peer Review - Analytical Development & Support WBS 2.5.1.101

The objective of the Analytical Development and Support (ADS) Project is to produce and maintain the critical analytical methods and tools that enable evaluation of emerging biofuels R&D at NREL and in the broader biofuels research community. Our project is divided into two tasks: one task to develop novel analytical techniques and improve existing methods and one task to maintain existing analytical capabilities at NREL and provide outreach to the wider community. The ADS Project is world-recognized for our Laboratory Analytical Procedures (LAPS) which provide detailed procedures for compositional analysis of biomass and have been adopted as the de facto standards within the biofuels community largely due to the transparency of the methods and the high reputation of NREL's research. Our dialog with stakeholders allows us to provide robust, precise, accurate, and publicly available analytical procedures for better valuation of scientific tools such as our recent accomplishment in developing a cellulose assay to support the EPA and industry in calculation of converted cellulose during starch ethanol production. We continue to develop analytical capabilities to support BETO's directives to research cost advantaged fuels such as animal wastes and novel bioproducts like 2,3-Butane-diol.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
NASA NTRS2006

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Gnoffo, Peter A.↗
NASA NTRS2017

Simple Analytical Expressions for Electron Pitch Angle Diffusion Coefficients

In the present paper, we have calculated electron pitch angle diffusion coefficients due to resonant interactions with whistler mode lower band chorus (LBC), upper band chorus (UBC), and electrostatic electron cyclotron harmonic (ECH) waves. Calculations have been performed at two values of the ratio of electron plasma frequency to gyro-frequency and thirteen representative values of electron energies for the plasma sheet electrons. The numerical data of diffusion coefficients have been fitted to simple analytical expressions for each wave mode. These analytical expressions allow for simple evaluation of pitch angle diffusion coefficients for the arbitrary pitch angle, energy, the ambient magnetic field, the wave amplitude, and the ratio of plasma frequency to gyro-frequency. In the case of LBC waves, the analytical coefficients are generally within a factor of two to the numerical coefficients, except at higher pitch angles where the numerical coefficients drop to show negligible values. Likewise, also for UBC waves, the analytical coefficients are generally within a factor of two to the numerical coefficients. The analytical coefficients for ECH waves are generally in agreement with numerical coefficients. However, the analytical expressions developed for ECH waves do not reproduce sharp fluctuations, dips, and gaps, the so-called banded structure observed in the data of numerical coefficients. The effect of the shape variation on the profile of the wave spectral intensity and the effect of cold temperature on the numerical coefficients are also investigated. Applications of the analytical expressions of diffusion coefficients are discussed.

coefficients↗
DOE OSTI2023

ExactPack: A python library of exact analytic solutions

Verification of multi-physics simulation software against problems with known analytic or semi-analytic solutions is an important aspect of research into a wide variety of fields involving the motion of fluids, shock physics and other dynamic material properties. Previous work comparing simulation results against analytic solutions has been ad-hoc, with developers frequently writing their own analytic solvers. This has resulted in a large amount of duplicated effort. The python library ExactPack has been developed as a collection of analytic and semi-analytic solvers to a variety of multi-physics problems, providing a consistent API to a set of well-tested solver implementations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A note on the analytic structure of celestial amplitudes

Celestial amplitudes, obtained by applying Mellin transform and analytic continuation on “ordinary” amplitudes, have interesting properties which may provide useful insights on the underlying theory. Their analytic structures are thus of great interest and need to be better understood. In this paper, we critically examine the analytic structure of celestial amplitudes in a massless low-energy effective field theory. We find that, fixed-order loop contributions, which generate multipoles on the negative β-plane, in general do not provide an accurate description of the analytic structure of celestial amplitudes. By resumming over the leading logarithmic contributions using renormalization group equations (RGEs), we observe much richer analytic structures, which generally contain branch cuts. It is also possible to generate multipoles or shifted single poles if the RGEs satisfy certain relations. Including sub-leading logarithmic contributions is expected to introduce additional corrections to the picture. However, without a new approach, it is difficult to make a general statement since the analytic form of the Mellin transform is challenging to obtain.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

An Analytical Solution for the Initiation and Early Progression of Fretting Wear in Spherical Contacts

Abstract This article derives analytical solutions to calculate the wear volume at the initiation of fretting motion and its early progression over the first few oscillation cycles. The Archard-based model considers a deformable hemisphere that is contact with a deformable flat block. The material pairs investigated are special alloys, the Inconel 617/Incoloy 800H, and Inconel 617/Inconel 617. The analytical study begins with a unidirectional frictional sliding contact, where the local interfacial sliding distance and the nominal sliding distance at the initiation of gross slip are derived. The obtained analytical expressions for unidirectional sliding are then used to derive the corresponding wear volume for the initiation and early progression of gross slip and the wear volume for a general fretting cycle under elastic conditions. These analytical derivations are all verified by the finite element analysis (FEA). The FEA method and the analytical solutions render virtually identical results for both similar and dissimilar material pairs. The effects of plasticity on the wear volume under elastic–plastic conditions are also investigated. It is found that the fretting wear volumes obtained from the FEA simulations, which include plasticity, are close to those obtained from the analytical expressions for purely elastic regimes. All the results are presented in normalized forms, which can be easily generalized and applied to three-dimensional fretting wear of other material pairs.

Engineering↗
NASA NTRS1976

Analysis of structural dynamic data from Skylab. Volume 2: Skylab analytical and test modal data

A compendium is presented of orbital configuration test modal data, analytical test modal data, analytical test correlation modal data and analytical flight configuration 1.2 modal data. Section A presents tables showing the generalized mass contributions for each of the thirty test modes. Section B presents the two dimensional mode shape plots for the thirty test modes. Tables of GMC's for the test correlated analytical modes are presented in Section C. These analytical modes were generated from a model that was adjusted to match test results by use of the methodology discussed in Sections 2.3 and 5.4 of Volume I of this report. Section D presents the two dimensional mode shape plots for the analytical modes. Sections E and F contain the uncoupled and coupled modes of the orbital flight configuration 1.2 at three development phases of the model.

Demchak, L.↗
NASA NTRS1981

Finite-analytic numerical solution of heat transfer in two-dimensional cavity flow

Heat transfer in cavity flow is numerically analyzed by a new numerical method called the finite-analytic method. The basic idea of the finite-analytic method is the incorporation of local analytic solutions in the numerical solutions of linear or nonlinear partial differential equations. In the present investigation, the local analytic solutions for temperature, stream function, and vorticity distributions are derived. When the local analytic solution is evaluated at a given nodal point, it gives an algebraic relationship between a nodal value in a subregion and its neighboring nodal points. A system of algebraic equations is solved to provide the numerical solution of the problem. The finite-analytic method is used to solve heat transfer in the cavity flow at high Reynolds number (1000) for Prandtl numbers of 0.1, 1, and 10.

Chen, C.-J.↗
NASA NTRS1982

Finite analytic numerical solution of axisymmetric Navier-Stokes and energy equations

Convective heat transfer for steady state laminar flow in axisymmetric coordinates is considered. Numerical solutions for flow pattern and temperature distribution are obtained by the finite analytic numerical method applied to the Navier-Stokes equations expressed in terms of vorticity and stream function, and the energy equation. The finite analytic numerical method differs from other numerical methods in that it utilizes a local analytic solution in an element of the problem to construct the total numerical solution. Finite analytic solutions of vorticity, stream function, temperature and heat transfer coefficients for flow with Reynolds number of 5.0, 100.0, 1000.0, and 2000.0, and Prandtl number of 0.1, 1.0, and 10.0 with uniform grid sizes are reported for axisymmetric pipe with sudden expansion and contraction. The wall temperature is considered to be isothermal and differs from the inlet temperature. It is shown that the finite analytic solution is stable, converges rapidly, and simulates the convection of fluid flow accurately since the local analytic solution is capable of simulating automatically the influence of skewed convection through the element boundary on the interior nodal values thereby minimizing the false numerical diffusion.

Chen, C.-J.↗
NASA NTRS1990

Analytical aerodynamic model of a high alpha research vehicle wind-tunnel model

A 6 DOF analytical aerodynamic model of a high alpha research vehicle is derived. The derivation is based on wind-tunnel model data valid in the altitude-Mach flight envelope centered at 15,000 ft altitude and 0.6 Mach number with Mach range between 0.3 and 0.9. The analytical models of the aerodynamics coefficients are nonlinear functions of alpha with all control variable and other states fixed. Interpolation is required between the parameterized nonlinear functions. The lift and pitching moment coefficients have unsteady flow parts due to the time range of change of angle-of-attack (alpha dot). The analytical models are plotted and compared with their corresponding wind-tunnel data. Piloted simulated maneuvers of the wind-tunnel model are used to evaluate the analytical model. The maneuvers considered are pitch-ups, 360 degree loaded and unloaded rolls, turn reversals, split S's, and level turns. The evaluation finds that (1) the analytical model is a good representation at Mach 0.6, (2) the longitudinal part is good for the Mach range 0.3 to 0.9, and (3) the lateral part is good for Mach numbers between 0.6 and 0.9. The computer simulations show that the storage requirement of the analytical model is about one tenth that of the wind-tunnel model and it runs twice as fast.

Cao, Jichang↗
NASA NTRS1991

An analytic performance model of disk arrays and its application

As disk arrays become widely used, tools for understanding and analyzing their performance become increasingly important. In particular, performance models can be invaluable in both configuring and designing disk arrays. Accurate analytic performance models are desirable over other types of models because they can be quickly evaluated, are applicable under a wide range of system and workload parameters, and can be manipulated by a range of mathematical techniques. Unfortunately, analytical performance models of disk arrays are difficult to formulate due to the presence of queuing and fork-join synchronization; a disk array request is broken up into independent disk requests which must all complete to satisfy the original request. We develop, validate, and apply an analytic performance model for disk arrays. We derive simple equations for approximating their utilization, response time, and throughput. We then validate the analytic model via simulation and investigate the accuracy of each approximation used in deriving the analytical model. Finally, we apply the analytical model to derive an equation for the optimal unit of data striping in disk arrays.

Lee, Edward K.↗