SEARCH · Search NASA

Results for “Mathematical 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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 613 records · Page 34

All sources NASA NTRS DOE OSTI

NASA NTRSDate not supplied

Dude Where's My Stars: A Novel Topologically Justified Approach to Star Tracking

In this paper, we consider two novel approaches to celestial navigation for spacecraft. Determining attitude without any prior knowledge using star tracking is known to be a difficult task, particularly given the computational complexity and the many potential sources of misinformation. We consider localization by optimizing matching parameters without explicit star identification in a computationally tractable manner. This is achieved using the mathematical tools of topological data analysis (TDA) and cellular sheaves to study the geometry and distribution of cataloged stars. A framework is gained that enhances the statistical approach to noise handling and false star detection, and heterogeneous sensor fusion. Finally, we discuss confidence bounds and minimum information requirements for successful operation.

Sheaf theory↗

DOE OSTI2024

MFANS 2024 - Dimensional Analysis Made Easy

There is a significant impact of dimensional errors in systems. Dimensional analysis is difficult due to the large size of systems. SA4U and Scalpel are practical programs which can have an impact beyond traditional software as they are able to perform precise dimensional analysis and repair C++ source code.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS2007

Nonstandard Analysis and Shock Wave Jump Conditions in a One-Dimensional Compressible Gas

Nonstandard analysis is a relatively new area of mathematics in which infinitesimal numbers can be defined and manipulated rigorously like real numbers. This report presents a fairly comprehensive tutorial on nonstandard analysis for physicists and engineers with many examples applicable to generalized functions. To demonstrate the power of the subject, the problem of shock wave jump conditions is studied for a one-dimensional compressible gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. To use conservations laws, smooth pre-distributions of the Dirac delta measure are applied whose supports are contained within the shock thickness. Furthermore, smooth pre-distributions of the Heaviside function are applied which vary from zero to one across the shock wave. It is shown that if the equations of motion are expressed in nonconservative form then the relationships between the jump functions for the flow parameters may be found unambiguously. The analysis yields the classical Rankine-Hugoniot jump conditions for an inviscid shock wave. Moreover, non-monotonic entropy jump conditions are obtained for both inviscid and viscous flows. The report shows that products of generalized functions may be defined consistently using nonstandard analysis; however, physically meaningful products of generalized functions must be determined from the physics of the problem and not the mathematical form of the governing equations.

Baty, Roy S.↗

NASA NTRS1993

Multiscale Morphological Filtering for Analysis of Noisy and Complex Images

Images acquired with passive sensing techniques suffer from illumination variations and poor local contrasts that create major difficulties in interpretation and identification tasks. On the other hand, images acquired with active sensing techniques based on monochromatic illumination are degraded with speckle noise. Mathematical morphology offers elegant techniques to handle a wide range of image degradation problems. Unlike linear filters, morphological filters do not blur the edges and hence maintain higher image resolution. Their rich mathematical framework facilitates the design and analysis of these filters as well as their hardware implementation. Morphological filters are easier to implement and are more cost effective and efficient than several conventional linear filters. Morphological filters to remove speckle noise while maintaining high resolution and preserving thin image regions that are particularly vulnerable to speckle noise were developed and applied to SAR imagery. These filters used combination of linear (one-dimensional) structuring elements in different (typically four) orientations. Although this approach preserves more details than the simple morphological filters using two-dimensional structuring elements, the limited orientations of one-dimensional elements approximate the fine details of the region boundaries. A more robust filter designed recently overcomes the limitation of the fixed orientations. This filter uses a combination of concave and convex structuring elements. Morphological operators are also useful in extracting features from visible and infrared imagery. A multiresolution image pyramid obtained with successive filtering and a subsampling process aids in the removal of the illumination variations and enhances local contrasts. A morphology-based interpolation scheme was also introduced to reduce intensity discontinuities created in any morphological filtering task. The generality of morphological filtering techniques in extracting information from a wide variety of images obtained with active and passive sensing techniques is discussed. Such techniques are particularly useful in obtaining more information from fusion of complex images by different sensors such as SAR, visible, and infrared.

Kher, A.↗

NASA NTRS1996

The problem of assuring performance robustness of biological life support systems

A perspective of the process of obtaining performance robustness of space exploration life support systems is presented. Some useful definitions are made, some relevant issues are addressed, and a procedure for establishing performance robustness, so far as it now known, is explained. An example is given to illustrate the procedure.

NASA Center ARC↗

DOE OSTI2026

buhito

buhito is a Python library for graph analysis and machine learning. Graphs can represent networks with objects as nodes and their relationships as edges. buhito focuses on graphlet methods that study graphs through enumerating their component subgraphs to enable interpretable and fast models of complex systems. The package provides tools for different algorithmic designs for computing, analyzing, and applying graphlets to research problems such as machine learning, data compression, and anomaly detection in graph-structured data. A central feature is performing decomposition data analysis on graphs for machine learning models. Implemented in Python and built upon open-source scientific libraries such as NetworkX, NumPy, and SciPy, buhito provides high-performance methods for researchers exploring the mathematical and computational foundations of graphlet analysis applicable to systems of different sizes.

Pimonova, Yulia↗

NASA NTRS1976

Equivalence of equations describing trace element distribution during equilibrium partial melting

It is shown that four equations used for calculating the evolution of trace-element abundances during equilibrium partial melting are mathematically equivalent. The equations include those of Hertogen and Gijbels (1976), Shaw (1970), Schilling (1971), and O'Nions and Clarke (1972). The general form to which all these equations reduce is presented, and an analysis is performed to demonstrate their mathematical equivalence. It is noted that the utility of the general equation flows from the nature of equilibrium (i.e., the final state is independent of the path by which that state is attained).

Consolmagno, G. J.↗

NASA NTRS2001

Spatial/Spectral Identification of Endmembers from AVIRIS Data using Mathematical Morphology

During the last several years, a number of airborne and satellite hyperspectral sensors have been developed or improved for remote sensing applications. Imaging spectrometry allows the detection of materials, objects and regions in a particular scene with a high degree of accuracy. Hyperspectral data typically consist of hundreds of thousands of spectra, so the analysis of this information is a key issue. Mathematical morphology theory is a widely used nonlinear technique for image analysis and pattern recognition. Although it is especially well suited to segment binary or grayscale images with irregular and complex shapes, its application in the classification/segmentation of multispectral or hyperspectral images has been quite rare. In this paper, we discuss a new completely automated methodology to find endmembers in the hyperspectral data cube using mathematical morphology. The extension of classic morphology to the hyperspectral domain allows us to integrate spectral and spatial information in the analysis process. In Section 3, some basic concepts about mathematical morphology and the technical details of our algorithm are provided. In Section 4, the accuracy of the proposed method is tested by its application to real hyperspectral data obtained from the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) imaging spectrometer. Some details about these data and reference results, obtained by well-known endmember extraction techniques, are provided in Section 2. Finally, in Section 5 we expose the main conclusions at which we have arrived.

Plaza, Antonio↗

NASA NTRS2016

Design and Analysis of an X-Ray Mirror Assembly Using the Meta-Shell Approach

Lightweight and high resolution optics are needed for future space-based x-ray telescopes to achieve advances in high-energy astrophysics. Past missions such as Chandra and XMM-Newton have achieved excellent angular resolution using a full shell mirror approach. Other missions such as Suzaku and NuSTAR have achieved lightweight mirrors using a segmented approach. This paper describes a new approach, called meta-shells, which combines the fabrication advantages of segmented optics with the alignment advantages of full shell optics. Meta-shells are built by layering overlapping mirror segments onto a central structural shell. The resulting optic has the stiffness and rotational symmetry of a full shell, but with an order of magnitude greater collecting area. Several meta-shells so constructed can be integrated into a large x-ray mirror assembly by proven methods used for Chandra and XMM-Newton. The mirror segments are mounted to the meta-shell using a novel four point semi-kinematic mount. The four point mount deterministically locates the segment in its most performance sensitive degrees of freedom. Extensive analysis has been performed to demonstrate the feasibility of the four point mount and meta-shell approach. A mathematical model of a meta-shell constructed with mirror segments bonded at four points and subject to launch loads has been developed to determine the optimal design parameters, namely bond size, mirror segment span, and number of layers per meta-shell. The parameters of an example 1.3 m diameter mirror assembly are given including the predicted effective area. To verify the mathematical model and support opto-mechanical analysis, a detailed finite element model of a meta-shell was created. Finite element analysis predicts low gravity distortion and low sensitivity to thermal gradients.

module↗

NASA NTRS2016

Meta-shell Approach for Constructing Lightweight and High Resolution X-Ray Optics

Lightweight and high resolution optics↗

NASA NTRS2008

Risk Analysis for Resource Planning Optimization

This paper describes a systems engineering approach to resource planning by integrating mathematical modeling and constrained optimization, empirical simulation, and theoretical analysis techniques to generate an optimal task plan in the presence of uncertainties.

optimization↗

NASA NTRS1981

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.↗

NASA NTRS1984

Analysis of head-down tilt as an analog of weightlessness using a methematical simulation model

Antiorthostasis or head down tilt of a moderate degree was used as a ground based analog of weightless space flight to study headward fluid shifts, decreased plasma volume, orthostatic intolerance and muscular skeletal degradation. A mathematical model was used to help interpret these observations. The model proved most valuable for these studies was originally developed as a description of the major circulatory, fluid and electrolyte control systems. Two different experimental studies are employed to validate the model. The first is a 24 hour head down tilt study and the second is a 7 day head down bed rest study. The major issues addressed include the reduction in plasma volume, the dynamic changes of venous pressure and cardiac output, the extent of central hypervolemia during long term zero g exposure, the existence of an early diuresis, the mechanisms which alter the renal regulating hormones during the short term and long term periods, the significance of potassium loss on other zero g responses, and the role of transcapillary filtration in adjusting fluid shifts. The use of mathematical models as an interpretive and analysis technique for experimental research for space life science is illustrated.

Leonard, J. I.↗

NASA NTRS1967

Functions of relaxed controls

Mathematical control theory problems involving solutions of certain partial differential equations, nonadditive set functions, or other functionals - approximation and existence theorems

FUNCTIONAL ANALYSIS↗

NASA NTRS1983

Analysis of Wind Gust Data

Wind gust data were analyzed by statistical and mathematical procedures, developed for the bivariate gamma distribution. The results of the analysis are summarized.

Tubbs, J. D.↗

NASA NTRS1965

Analysis of the F-corona according to the Mie theory. Part I - Mathematical formulation and uniqueness of the derived theoretical models

Mathematical model for removing integrals over scattering angle and particle size in analyzing observations of zodiacal light

INTERPLANETARY DUST↗

NASA NTRS2005

Foundations of Tensor Analysis for Students of Physics and Engineering With an Introduction to the Theory of Relativity

Tensor analysis is one of the more abstruse, even if one of the more useful, higher math subjects enjoined by students of physics and engineering. It is abstruse because of the intellectual gap that exists between where most physics and engineering mathematics leave off and where tensor analysis traditionally begins. It is useful because of its great generality, computational power, and compact, easy to use, notation. This paper bridges the intellectual gap. It is divided into three parts: algebra, calculus, and relativity. Algebra: In tensor analysis, coordinate independent quantities are sought for applications in physics and engineering. Coordinate independence means that the quantities have such coordinate transformations as to leave them invariant relative to a particular observer s coordinate system. Calculus: Non-zero base vector derivatives contribute terms to dynamical equations that correspond to pseudoaccelerations in accelerated coordinate systems and to curvature or gravity in relativity. These derivatives have a specific general form in tensor analysis. Relativity: Spacetime has an intrinsic geometry. Light is the tool for investigating that geometry. Since the observed geometry of spacetime cannot be made to match the classical geometry of Euclid, Einstein applied another more general geometry differential geometry. The merger of differential geometry and cosmology was accomplished in the theory of relativity. In relativity, gravity is equivalent to curvature.

Kolecki, Joseph C.↗

NASA NTRS1987

Computer-aided-engineering system for modeling and analysis of ECLSS integration testing

The accurate modeling and analysis of two-phase fluid networks found in environmental control and life support systems is presently undertaken by computer-aided engineering (CAE) techniques whose generalized fluid dynamics package can solve arbitrary flow networks. The CAE system for integrated test bed modeling and analysis will also furnish interfaces and subsystem/test-article mathematical models. Three-dimensional diagrams of the test bed are generated by the system after performing the requisite simulation and analysis.

Sepahban, Sonbol↗