Results for “Mathematical Computing” — Page 38

NASA NTRS1997

Determination of Coronal Magnetic Fields from Vector Magnetograms

During the course of the present contract we developed an 'evolutionary technique' for the determination of force-free coronal magnetic fields from vector magnetograph observations. The method can successfully generate nonlinear force- free fields (with non-constant-a) that match vector magnetograms. We demonstrated that it is possible to determine coronal magnetic fields from photospheric measurements, and we applied it to vector magnetograms of active regions. We have also studied theoretical models of coronal fields that lead to disruptions. Specifically, we have demonstrated that the determination of force-free fields from exact boundary data is a well-posed mathematical problem, by verifying that the computed coronal field agrees with an analytic force-free field when boundary data for the analytic field are used; demonstrated that it is possible to determine active-region coronal magnetic fields from photospheric measurements, by computing the coronal field above active region 5747 on 20 October 1989, AR6919 on 15 November 1991, and AR7260 on 18 August 1992, from data taken with the Stokes Polarimeter at Mees Solar Observatory, University of Hawaii; started to analyze active region 7201 on 19 June 1992 using measurements made with the Advanced Stokes Polarimeter at NSO/Sac Peak; investigated the effects of imperfections in the photospheric data on the computed coronal magnetic field; documented the coronal field structure of AR5747 and compared it to the morphology of footpoint emission in a flare, showing that the 'high- pressure' H-alpha footpoints are connected by coronal field lines; shown that the variation of magnetic field strength along current-carrying field lines is significantly different from the variation in a potential field, and that the resulting near-constant area of elementary flux tubes is consistent with observations; begun to develop realistic models of coronal fields which can be used to study flare trigger mechanisms; demonstrated that magnetic nonequilibrium can disrupt sheared coronal arcades, and that helmet streamers can disrupt, leading to coronal mass ejections. Our model has significantly extended the realism with which the coronal magnetic field can be inferred from actual observations. In a subsequent contract awarded by NASA, we have continued to apply and improve the evolutionary technique, to study the physical properties of active regions, and to develop theoretical models of magnetic fields.

Mikic, Zoran↗

NASA NTRS1998

Making the Learning of Mathematics More Meaningful

In the early 1980's, the National Commission on Excellence in Education responded to the call for reform in the teaching and learning of mathematics. In particular, the Commission developed a document addressing the consensus that all students need to learn more, and often different, mathematics and that instruction in mathematics must be significantly revised. In a response to these calls for mathematics education reform, the National Council of Teachers of Mathematics (NCTM) developed its Curriculum and Evaluation Standards (1989) with a two-fold purpose: 1) to create a coherent vision of what it means to be mathematically literate in a world that relies on calculators and computers, and 2) to create a set of standards to guide the revisions of school mathematics curriculum.

Ward, Robin A.↗

NASA NTRS2000

Information Power Grid: Distributed High-Performance Computing and Large-Scale Data Management for Science and Engineering

The term "Grid" refers to distributed, high performance computing and data handling infrastructure that incorporates geographically and organizationally dispersed, heterogeneous resources that are persistent and supported. The vision for NASN's Information Power Grid - a computing and data Grid - is that it will provide significant new capabilities to scientists and engineers by facilitating routine construction of information based problem solving environments / frameworks that will knit together widely distributed computing, data, instrument, and human resources into just-in-time systems that can address complex and large-scale computing and data analysis problems. IPG development and deployment is addressing requirements obtained by analyzing a number of different application areas, in particular from the NASA Aero-Space Technology Enterprise. This analysis has focussed primarily on two types of users: The scientist / design engineer whose primary interest is problem solving (e.g., determining wing aerodynamic characteristics in many different operating environments), and whose primary interface to IPG will be through various sorts of problem solving frameworks. The second type of user if the tool designer: The computational scientists who convert physics and mathematics into code that can simulate the physical world. These are the two primary users of IPG, and they have rather different requirements. This paper describes the current state of IPG (the operational testbed), the set of capabilities being put into place for the operational prototype IPG, as well as some of the longer term R&D tasks.

Johnston, William E.↗

NASA NTRS2003

Experimental Study of Supercooled Large Droplet Impingement Effects

Typically, ice accretion results from small supercooled droplets (droplets cooled below freezing), usually 5 to 50 microns in diameter, which can freeze upon impact with an aircraft surface. Recently, ice accretions resulting from supercooled large droplet (SLD) conditions have become a safety concern. Current ice accretion codes have been extensively tested for Title 14 Code of Federal Regulations Part 25, Appendix C icing conditions but have not been validated for SLD icing conditions. This report presents experimental methods for investigating large droplet impingement dynamics and for obtaining small and large water droplet impingement data.

ICE ACCRETION CODE↗

NASA NTRS2003

Software for Simulating Remote Sensing Systems

The Application Research Toolbox (ART) is a collection of computer programs that implement algorithms and mathematical models for simulating remote sensing systems. The ART is intended to be especially useful for performing design-tradeoff studies and statistical analyses to support the rational development of design requirements for multispectral imaging systems. Among other things, the ART affords a capability to synthesize coarser-spatial-resolution image-data sets from finer-spatial-resolution data sets and multispectral-image-data products from hyperspectral-image-data products. The ART also provides for synthesis of image-degradation effects, including point-spread functions, misregistration of spectral images, and noise. The ART can utilize real or synthetic data sets, along with sensor specifications, to create simulated data sets. In one example of a typical application, simulated data pertaining to an existing multispectral sensor system are used to verify the data collected by the system in operation. In the case of a proposed sensor system, the simulated data can be used to conduct trade studies and statistical analyses to ensure that the sensor system will satisfy the requirements of potential scientific, academic, and commercial user communities.

Zanoni, Vicki↗

NASA NTRS2003

Software for Simulating Remote Sensing Systems

The Application Research Toolbox (ART) is a collection of computer programs that implement algorithms and mathematical models for simulating remote sensing systems. The ART is intended to be especially useful for performing design-tradeoff studies and statistical analyses to support the rational development of design requirements for multispectral imaging systems. Among other things, the ART affords a capability to synthesize coarser-spatial-resolution image-data sets from finer-spatial-resolution data sets and multispectral-image-data products from hyperspectral-image-data products. The ART also provides for synthesis of image-degradation effects, including point-spread functions, misregistration of spectral images, and noise. The ART can utilize real or synthetic data sets, along with sensor specifications, to create simulated data sets. In one example of a typical application, simulated data pertaining to an existing multispectral sensor system are used to verify the data collected by the system in operation. In the case of a proposed sensor system, the simulated data can be used to conduct trade studies and statistical analyses to ensure that the sensor system will satisfy the requirements of potential scientific, academic, and commercial user communities.

Vicki Zanoni↗

NASA NTRS1986

NASA Tech Briefs, March/April 1986

Topics covered include: NASA TU Services; New Product Ideas; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences.

Source record↗

NASA NTRS1986