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Results for “Analytical mathematics”

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 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

A mathematical model for spatial orientation from pictorial perspective displays

A previously formulated mathematical model, describing how observers reconstruct three-dimensional spatial layouts from perspective projections, has been extended to more complex situations. The model assumes that the observer has a priori knowledge of certain characteristics of the viewed objects, like size, shape, or parallelism or perpendicularity of lines or planes. These assumptions are used in a three-dimensional process to reconstruct a spatial layout that `best matches' the perceived lines of sight to the object coordinates. Sources of errors and biases in this process are specified and their effects on model outputs are discussed. An experiment, in which eight subjects judged the relative direction of one object with respect to another, has been conducted to validate the model. The model has been found to generally reproduce the systematic trends of the experimental results and also has provided an analytical explanation for them. The mathematical model is expected to be a useful tool in analyzing and developing pictorial perspective flight displays.

Grunwald, Arthur J.↗
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 OSTI2021

(U) A Theoretical Study of Asay Foil Trajectories (V.02)

We consider the trajectory of a generic Asay foil ejecta momentum diagnostic sensor, for scenarios where ejecta are produced at a planar surface and fly ballistically through a perfect vacuum to the sensor. To do so, we build upon a previously established mathematical formalism derived for the analytic study of stationary sensors (i.e., piezopins). First, we derive the momentum conservation equation for the problem, in a form amenable to accelerating sensors, in terms of a generic ejecta source areal mass function (“source model”). This defines an integro-differential equation (IDE) for the foil trajectory. When ejecta production is instantaneous - as is generally assumed in momentum diagnostic data analyses - the IDE leads to an implicit and easily calculable closed-form solution for the foil trajectory in a perfect system, as long as the ejecta particle velocity distribution is twice-integrable. General properties of the instant-production trajectory solution indicate the existence of a boundary condition the particle velocity distribution must satisfy in order for the analytically predicted foil trajectories to be compatible with certain features commonly observed in foil data. This boundary condition is identical to one derived previously from a consideration of piezopin data. Armed with the analytic solution for instant production, we also consider various techniques used to extract time-dependent cumulative ejecta masses from foil trajectories, and derive an expression for the error imposed by using an approximated equation of motion. This analytic trajectory solution furthermore makes it possible to examine the common practice of presenting inferred cumulative ejecta masses as a function of a normalized implied velocity; we derive conditions under which this methodology is and is not meaningful. We also propose a strategy for extending the instant-production trajectory solution to time-dependent source functions.

42 ENGINEERING↗
NASA NTRS1967

Analytical drafting curves provide exact equations for plotted data

Analytical drafting curves provide explicit mathematical expressions for any numerical data that appears in the form of graphical plots. The curves each have a reference coordinate axis system indicated on the curve as well as the mathematical equation from which the curve was generated.

Stewart, R. B.↗
NASA NTRS1969

Investigation of the development of cracks in solder joints

Study consisted of an analytical approach, in which a mathematical model of existing printed circuit board component mounting techniques was analyzed, and an empirical investigation was performed to determine the extent of damage caused by temperature cycling of the printed circuit boards.

Moore, R. L.↗
NASA NTRS1974

A representation of Jacchia's thermospheric models in spherical harmonic functions

The Jacchia models are represented in terms of spherical harmonic functions. This representation has the advantage of ease of comparison with other global theoretical and empirical models that use this mathematical form. Furthermore, it is analytic, continuous, and has continuous derivatives all over the globe. The representation of the exospheric temperatures shows clearly the amplitudes of the various periodic terms and uses relatively few constants. An example of a similar representation for the total mass density at a particular height and level of solar activity is given as well.

Blum, P.↗
NASA NTRS1989

Manipulators with flexible links: A simple model and experiments

A simple dynamic model proposed for flexible links is briefly reviewed and experimental control results are presented for different flexible systems. A simple dynamic model is useful for rapid prototyping of manipulators and their control systems, for possible application to manipulator design decisions, and for real time computation as might be applied in model based or feedforward control. Such a model is proposed, with the further advantage that clear physical arguments and explanations can be associated with its simplifying features and with its resulting analytical properties. The model is mathematically equivalent to Rayleigh's method. Taking the example of planar bending, the approach originates in its choice of two amplitude variables, typically chosen as the link end rotations referenced to the chord (or the tangent) motion of the link. This particular choice is key in establishing the advantageous features of the model, and it was used to support the series of experiments reported.

Shimoyama, Isao↗
NASA NTRS1990

Postbuckling analysis of shear deformable composite flat panels taking into account geometrical imperfections

The effects of initial geometrical imperfections on the postbuckling response of flat laminated composite panels to uniaxial and biaxial compressive loading are investigated analytically. The derivation of the mathematical model on the basis of first-order transverse shear deformation theory is outlined, and numerical results for perfect and imperfect, single-layer and three-layer square plates with free-free, clamped-clamped, or free-clamped edges are presented in graphs and briefly characterized. The present approach is shown to be more accurate than analyses based on the classical Kirchhoff plate model.

Librescu, L.↗
NASA NTRS1990

Magnetic cleanliness verification approach on tethered satellite

Magnetic cleanliness testing was performed on the Tethered Satellite as the last step of an articulated verification campaign aimed at demonstrating the capability of the satellite to support its TEMAG (TEthered MAgnetometer) experiment. Tests at unit level and analytical predictions/correlations using a dedicated mathematical model (GANEW program) are also part of the verification activities. Details of the tests are presented, and the results of the verification are described together with recommendations for later programs.

Messidoro, Piero↗
NASA NTRS2006

Recent trends in digital human modeling and the concurrent issues that face human modeling approach

Tremendous strides have been made in the recent years to digitally represent human beings in computer simulation models ranging from assembly plant maintenance operations to occupants getting in and out of vehicles to action movie scenarios. While some of these tools are being actively pursued by the engineering communities, there is still a lot of work that remains to be done for the newly planned planetary exploration missions. For example, certain unique and several common challenges are seen in developing computer generated suited human models for designing the next generation space vehicle. The purpose of this presentation is to discuss NASA s potential needs for better human models and to show also many of the inherent yet not too obvious pitfalls that still are left unresolved in this new arena of digital human modeling. As part of NASA s Habitability and Human Factors Branch, the Anthropometry and Biomechanics Facility has been engaged in studying the various facets of computer generated human physical performance models; for instance, it has been engaged in utilizing three-dimensional laser scan data along with three dimensional video based motion and reach data to gather suited anthropometric and shape and size information that are not available yet in the form of computer mannequins. Our goal is to bring in new approaches to deal with heavily clothed humans (such as, suited astronauts) and to overcome the current limitations of wrongly identifying humans (either real or virtual) as univariate percentiles. We are looking at whole-body posture based anthropometric models as a means to identify humans of significantly different shapes and sizes to arrive at mathematically sound computer models for analytical purposes.

Rajulu, Sudhakar↗
DOE OSTI2020

Analytic Insights into the Neutronic Characteristics of Neutron Moderators from MCNP Calculations

In the course of re-processing the ENDF/B VIII.0 thermal scattering law data, formulas and data checking insights were developed from MCNP calculations into the neutronic characteristics of moderators. Infinite medium test calculations were carried out in MCNP as part of the verification effort for the ACE formatted thermal scattering files. Edit results from MCNP were combined with derived results to formulate several equations which give analytic insights into the neutronic behavior of moderators.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS1977

Application of perturbation methods to improve analytical model correlation with test data

A linear perturbation method developed by White (1972) to improve the correlation between analytical models and experimental data is applied to modeling of the Viking Propulsion Subsystem (VPS), flown successfully as part of the Viking Spacecraft launch of 1975. Analytical models and modal test data developed for the VPS are employed in the application; a set of mathematically generated data and a corresponding perturbed analytical model, representative of actual flight hardware, are also subjected to the White method. It is found that the linear perturbation method does not yield a single unique improved model.

Garba, J. A.↗
NASA NTRS1970

Empirical analytic transformations between geographic and corrected geomagnetic coordinates

Based upon a mathematical model of contours of constant corrected geomagnetic latitude in a polar projection of geographic coordinates, analytic equations are developed for converting geographic coordinates to corrected geomagnetic coordinates and vice versa. The equations were programmed for use on a small computer. This treatment is restricted to the Northern Hemisphere.

Comfort, R. H.↗
DOE OSTI2021

Scattering matrix pole expansions for complex wave numbers in R -matrix theory

In this followup article to Ducru et al., we establish new results on scattering matrix pole expansions for complex wave numbers in R-matrix theory. In the past, two branches of theoretical formalisms emerged to describe the scattering matrix in nuclear physics: R-matrix theory and pole expansions. The two have been quite isolated from one another. Recently, our study of Brune's alternative parametrization of R-matrix theory has shown the need to extend the scattering matrix (and the underlying R-matrix operators) to complex wave numbers. Two competing ways of doing so have emerged from a historical ambiguity in the definitions of the shift S and penetration P functions: the legacy Lane and Thomas's “force closure” approach versus analytic continuation (which is the standard in mathematical physics). The R-matrix community has not yet come to a consensus as to which to adopt for evaluations in standard nuclear data libraries, such as ENDF. Here, in this article, we argue in favor of analytic continuation of R-matrix operators. We bridge R-matrix theory with the Humblet-Rosenfeld pole expansions, and discover new properties of the Siegert-Humblet radioactive poles and widths, including their invariance properties to changes in channel radii a c . We then show that analytic continuation of R-matrix operators preserves important physical and mathematical properties of the scattering matrix—canceling spurious poles and guaranteeing generalized unitarity—while still being able to close channels below thresholds.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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↗
NASA NTRS1975

The accuracy of far-field noise obtained by the mathematical extrapolation of near-field noise data

Results are described of an analytical study of the accuracy and limitations of a technique that permits the mathematical extrapolation of near-field noise data to far-field conditions. The effects of the following variables on predictive accuracy of the far-field pressure were examined: (1) number of near-field microphones; (2) length of source distribution; (3) complexity of near-field and far-field distributions; (4) source-to-microphone distance; and (5) uncertainties in microphone data and imprecision in the location of the near-field microphones. It is shown that the most important parameters describing predictive accuracy are the number of microphones, the ratio of source length to acoustic wavelength, (L/wavelength), and the error in location of near-field microphones. If microphone measurement and location errors are not included, then far-field pressures can be accurately predicted up to L/wavelength values of 15 using approximately 50 microphones. For maximum microphone location errors of + or - 1 cm, only an accuracy of + or - 2-1/2 db can be attained with approximately 40 microphones for the highest L/wavelength of 10.

Ahtye, W. F.↗
NASA NTRS1975

The accuracy of far-field noise obtained by the mathematical extrapolation of near-field noise data

Results are presented for an analytical study of the accuracy and limitations of a technique that permits the mathematical extrapolation of near-field noise data to far-field conditions. The effects of the following variables on predictive accuracy of the far-field pressure were examined: (1) number of near-field microphones; (2) length of source distribution; (3) complexity of near-field and far-field distributions; (4) source-to-microphone distance; and (5) uncertainties in microphone data and imprecision in the location of the near-field microphones. It is shown that the most important parameters describing predictive accuracy are the number of microphones, the ratio of source length to acoustic wavelength (L/lambda), and the error in location of near-field microphones. For maximum microphone location errors of plus or minus 1 cm, only an accuracy of plus or minus 2.5 dB can be attained with approximately 40 microphones for the highest L/lambda of 10.

Ahtye, W. F.↗