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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.

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At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Stochastic level-set method for shape optimisation

We present a new method for stochastic shape optimisation of engineering structures. The method generalises an existing deterministic scheme, in which the structure is represented and evolved by a level-set method coupled with mathematical programming. The stochastic element of the algorithm is built on the methods of statistical mechanics and is designed so that the system explores a Boltzmann–Gibbs distribution of structures. In non-convex optimisation problems, the deterministic algorithm can get trapped in local optima: the stochastic generalisation enables sampling of multiple local optima, which aids the search for the globally-optimal structure. The method is demonstrated for several simple geometrical problems, and a proof-of-principle calculation is shown for a simple engineering structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1973

Active cavity radiometer.

The active cavity radiometer (ACR) is a pyrheliometer that accurately defines the absolute radiation scale. The physics of the pyrheliometric method and the ACR approach to this method are presented in detail. A mathematical abstraction of the method is generated through a quasi-equilibrium analysis of the power balance of the ACR's cavity detector. An error analysis is carried out on the quasi-equilibrium equation to determine the uncertainties of ACR measurements relative to the absolute radiation scale. The uncertainty of ACR measurements as a function of irradiance level is presented in graphical form.

Willson, R. C.↗
NASA NTRS1980

An improved panel method for the solution of three-dimensional leading-edge vortex flows. Volume 1: Theory document

An improved panel method for the solution of three dimensional flow and wing and wing-body combinations with leading edge vortex separation is presented. The method employs a three dimensional inviscid flow model in which the configuration, the rolled-up vortex sheets, and the wake are represented by quadratic doublet distributions. The strength of the singularity distribution as well as shape and position of the vortex spirals are computed in an iterative fashion starting with an assumed initial sheet geometry. The method calculates forces and moments as well as detail surface pressure distributions. Improvements include the implementation of improved panel numerics for the purpose of elimination the highly nonlinear effects of ring vortices around double panel edges, and the development of a least squares procedure for damping vortex sheet geometry update instabilities. A complete description of the method is included. A variety of cases generated by the computer program implementing the method are presented which verify the mathematical assumptions of the method and which compare computed results with experimental data to verify the underlying physical assumptions made by the method.

Johnson, F. T.↗
NASA NTRS1980

Evolution of solar magnetic fields - A new approach to MHD initial-boundary value problems by the method of nearcharacteristics

A method of analysis for the MHD initial-boundary problem is presented in which the model's formulation is based on the method of nearcharacteristics developed by Werner (1968) and modified by Shin and Kot (1978). With this method, the physical causality relationship can be traced from the perturbation to the response as in the method of characteristics, while achieving the advantage of a considerable reduction in mathematical procedures. The method offers the advantage of examining not only the evolution of nonforce free fields, but also the changes of physical conditions in the atmosphere accompanying the evolution of magnetic fields. The physical validity of the method is demonstrated with examples, and their significance in interpreting observations is discussed.

Nakagawa, Y.↗
NASA NTRS2009

Compatibility of Segments of Thermoelectric Generators

A method of calculating (usually for the purpose of maximizing) the power-conversion efficiency of a segmented thermoelectric generator is based on equations derived from the fundamental equations of thermoelectricity. Because it is directly traceable to first principles, the method provides physical explanations in addition to predictions of phenomena involved in segmentation. In comparison with the finite-element method used heretofore to predict (without being able to explain) the behavior of a segmented thermoelectric generator, this method is much simpler to implement in practice: in particular, the efficiency of a segmented thermoelectric generator can be estimated by evaluating equations using only hand-held calculator with this method. In addition, the method provides for determination of cascading ratios. The concept of cascading is illustrated in the figure and the definition of the cascading ratio is defined in the figure caption. An important aspect of the method is its approach to the issue of compatibility among segments, in combination with introduction of the concept of compatibility within a segment. Prior approaches involved the use of only averaged material properties. Two materials in direct contact could be examined for compatibility with each other, but there was no general framework for analysis of compatibility. The present method establishes such a framework. The mathematical derivation of the method begins with the definition of reduced efficiency of a thermoelectric generator as the ratio between (1) its thermal-to-electric power-conversion efficiency and (2) its Carnot efficiency (the maximum efficiency theoretically attainable, given its hot- and cold-side temperatures). The derivation involves calculation of the reduced efficiency of a model thermoelectric generator for which the hot-side temperature is only infinitesimally greater than the cold-side temperature. The derivation includes consideration of the ratio (u) between the electric current and heat-conduction power and leads to the concept of compatibility factor (s) for a given thermoelectric material, defined as the value of u that maximizes the reduced efficiency of the aforementioned model thermoelectric generator.

Snyder, G. Jeffrey↗
NASA NTRS1990

Computerized tomographic imaging for space plasma physics

The measurement of plasma electron velocity distribution functions as a problem in imaging and image reconstruction is considered. A model instrument that measures the integral of the distribution function along lines in velocity space is presented. This allows the use of the powerful mathematical and numerical methods that have recently been so successful in other areas of imaging. It is found that this approach leads to classes of instruments that are qualitatively different from contemporary designs. An investigation of different methods of reconstruction of the distribution function from integral measurements reveals that the mathematical tools appropriate to one particular imaging problem may be very different from those required to deal with another.

Zhang, Yuhong↗
DOE OSTI2017

Preserving Simplecticity in the Numerical Integration of Linear Beam Optics

Presented are mathematical tools and methods for the development of numerical integration techniques that preserve the symplectic condition inherent to mechanics. The intended audience is for beam physicists with backgrounds in numerical modeling and simulation with particular attention to beam optics applications. The paper focuses on Lie methods that are inherently symplectic regardless of the integration accuracy order. Section 2 provides the mathematically tools used in the sequel and necessary for the reader to extend the covered techniques. Section 3 places those tools in the context of charged-particle beam optics; in particular linear beam optics is presented in terms of a Lie algebraic matrix representation. Section 4 presents numerical stepping techniques with particular emphasis on a third-order leapfrog method. Section 5 discusses the modeling of field imperfections with particular attention to the fringe fields of quadrupole focusing magnets. The direct computation of a third order transfer matrix for a fringe field is shown.

43 PARTICLE ACCELERATORS↗
NASA NTRS1990

Implementation of efficient sensitivity analysis for optimization of large structures

The paper presents the theoretical bases and implementation techniques of sensitivity analyses for efficient structural optimization of large structures, based on finite element static and dynamic analysis methods. The sensitivity analyses have been implemented in conjunction with two methods for optimization, namely, the Mathematical Programming and Optimality Criteria methods. The paper discusses the implementation of the sensitivity analysis method into our in-house software package, AutoDesign.

Umaretiya, J. R.↗
DOE OSTI2023

Decomposition of multi-particle azimuthal correlations in Q-cumulant analysis*

Abstract The method of Q -cumulants is a powerful tool for studying the fine details of azimuthal anisotropies in high energy nuclear collisions. This paper presents a new method, based on mathematical induction, to evaluate the analytical form of high-order Q -cumulants. The capability of this method is demonstrated via a toy model that uses the elliptic power distribution to simulate the anisotropic emission of particles, quantified in terms of Fourier flow harmonics . The method can help in studying the large amount of event statistics that can be collected in the future and allow measurements of the very high central moments of the distribution. This can, in turn, facilitate progress in understanding the initial geometry, the input to the hydrodynamic calculations of medium expansion in high energy nuclear collisions, and the constraints on it.

Physics↗
DOE OSTI2019

Combining simulations and data with deep learning and uncertainty quantification for advanced energy modeling

A novel and modern framework for energy modeling is developed in this paper with a focus on nuclear energy modeling and simulation. The framework combines multiphysics simulations and real data, with validation by uncertainty quantification tasks and facilitation by machine and deep learning methods. The hybrid framework is built on the basis of a wide range of physical models, real data, mathematical and statistical methods, and artificial intelligence techniques. The framework is demonstrated in different applications, including quantifying uncertainties in computer simulations, multiphysics coupling, analysis of variance using machine learning surrogate models, deep learning of time series phenomena, and propagating parametric uncertainties of nuclear data. The applications demonstrated are oriented to nuclear engineering simulations, even though majority of the methods are applicable to other energy sources (eg, renewable). Efficient utilization of this framework is expected to yield a much better understanding of the physical phenomena analyzed as well as an improvement in the performance of the energy design/model under construction.

42 ENGINEERING↗
DOE OSTI2018

Finite-Difference Methods for Fractional Differential Equations of Order 1/2

In this work, we study approximations of solutions of fractional differential equations of order 1/2. We present a new method of approximation and obtain the order of convergence. The presentation is given within the abstract framework of a semidiscrete approximation scheme, which includes finite-element methods, finite-difference schemes, and projection methods.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1986

Computational Simplification of Robot-Arm Dynamics

Report presents two general methods for reducing mathematical complexities of state equations of robot-arm dynamics. Robot arms contain both rotary and linear joints. Both methods start with homogenous coordinates and Lagrangian formulation of mechanics briefly summarized in report. First method uses matrix-analysis techniques; second, vector-analysis techniques. Vector-analysis method includes new differential-vector representation of centripetal and Coriolis forces.

Bejczy, A. K.↗
NASA NTRS2004

A Simplified Mesh Deformation Method Using Commercial Structural Analysis Software

Mesh deformation in response to redefined or moving aerodynamic surface geometries is a frequently encountered task in many applications. Most existing methods are either mathematically too complex or computationally too expensive for usage in practical design and optimization. We propose a simplified mesh deformation method based on linear elastic finite element analyses that can be easily implemented by using commercially available structural analysis software. Using a prescribed displacement at the mesh boundaries, a simple structural analysis is constructed based on a spatially varying Young s modulus to move the entire mesh in accordance with the surface geometry redefinitions. A variety of surface movements, such as translation, rotation, or incremental surface reshaping that often takes place in an optimization procedure, may be handled by the present method. We describe the numerical formulation and implementation using the NASTRAN software in this paper. The use of commercial software bypasses tedious reimplementation and takes advantage of the computational efficiency offered by the vendor. A two-dimensional airfoil mesh and a three-dimensional aircraft mesh were used as test cases to demonstrate the effectiveness of the proposed method. Euler and Navier-Stokes calculations were performed for the deformed two-dimensional meshes.

Hsu, Su-Yuen↗
NASA NTRS1994

An investigation of the use of temporal decomposition in space mission scheduling

This research involves an examination of techniques for solving scheduling problems in long-duration space missions. The mission timeline is broken up into several time segments, which are then scheduled incrementally. Three methods are presented for identifying the activities that are to be attempted within these segments. The first method is a mathematical model, which is presented primarily to illustrate the structure of the temporal decomposition problem. Since the mathematical model is bound to be computationally prohibitive for realistic problems, two heuristic assignment procedures are also presented. The first heuristic method is based on dispatching rules for activity selection, and the second heuristic assigns performances of a model evenly over timeline segments. These heuristics are tested using a sample Space Station mission and a Spacelab mission. The results are compared with those obtained by scheduling the missions without any problem decomposition. The applicability of this approach to large-scale mission scheduling problems is also discussed.

Bullington, Stanley E.↗
NASA NTRS2018

Remote Sensing, Uncertainty Quantification, and a Theory of Data Systems; Workshop Report

The purpose of the workshop was to invite statisticians, applied mathematicians, computer scientists, data system architects, experts in remote sensing technology, and Climate and Earth System scientists to review, discuss, and plan research on issues related to large-scale, efficient analysis of distributed data using spatial statistical methods. Our motivation in organizing this event was to catalyze interchange among experts on the fast-emerging problem of analysis of distributed data. As part of SAMSI's 2017-2018 Program on Mathematical and Statistical Methods for Climate and the Earth System, a Working Group on Remote Sensing was established to address statistical and mathematical research problems in the analysis of remote sensing data. The Working Group has five subgroups: 1) Spatial Retrieval Methodology (the so-called \Spatial-X" subgroup); 2) Spatial Analysis for Hyperspectral Data (the so-called \Spatial-Y" subgroup); 3) Emulators for Complex Forward Models; 4) Optimization for Remote Sensing Retrievals; and 5) Theory of Data Systems (ToDS). The ToDS subgroup spent the first half of this academic year formulating a framework in which to consider the joint problem of a) optimizing statistical methods for environments where data are distributed and too large to move to a central location, and b) the design of data system infrastructures within which to implement those statistical methods. To x ideas, the Workshop focused on spatial statistical methods. To date there are many new spatial statistical methods designed with massive data sets in mind, in the literature. However, very few have been implemented for remote sensing data, and none have been implemented in operational settings like those used by NASA and NOAA. A major impediment to their use in these cases is that the data are not only massive, but are stored in different physical locations. These data must be brought together in some way in order to estimate spatial covariance functions, but moving data to a central location for analysis is tedious at best and impossible at worst. Some remote data reduction is almost certainly necessary, but how much? What are the consequences for inference? The fundamental issue underlying these questions is how to navigate the trade-space between costs and uncertainty in the estimates or inferences that are ultimately produced.

Braverman, Amy↗
DOE OSTI2017

(U) Introduction to Monte Carlo Methods

Monte Carlo methods are very valuable for representing solutions to particle transport problems. Here we describe a “cook book” approach to handling the terms in a transport equation using Monte Carlo methods. Focus is on the mechanics of a numerical Monte Carlo code, rather than the mathematical foundations of the method.

97 MATHEMATICS AND COMPUTING↗