Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematica”

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.

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

43 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

Simple Analytic Expressions for the Magnetic Field of a Circular Current Loop

Analytic expressions for the magnetic induction (magnetic flux density, B) of a simple planar circular current loop have been published in Cartesian and cylindrical coordinates [1,2], and are also known implicitly in spherical coordinates [3]. In this paper, we present explicit analytic expressions for B and its spatial derivatives in Cartesian, cylindrical, and spherical coordinates for a filamentary current loop. These results were obtained with extensive use of Mathematica "TM" and are exact throughout all space outside of the conductor. The field expressions reduce to the well-known limiting cases and satisfy V · B = 0 and V x B = 0 outside the conductor. These results are general and applicable to any model using filamentary circular current loops. Solenoids of arbitrary size may be easily modeled by approximating the total magnetic induction as the sum of those for the individual loops. The inclusion of the spatial derivatives expands their utility to magnetohydrodynamics where the derivatives are required. The equations can be coded into any high-level programming language. It is necessary to numerically evaluate complete elliptic integrals of the first and second kind, but this capability is now available with most programming packages.

Simpson, James C.↗
NASA NTRS2013

Assessing the Temperature Dependence of Narrow-Band Raman Water Vapor Lidar Measurements: A Practical Approach

Narrow-band detection of the Raman water vapor spectrum using the lidar technique introduces a concern over the temperature dependence of the Raman spectrum. Various groups have addressed this issue either by trying to minimize the temperature dependence to the point where it can be ignored or by correcting for whatever degree of temperature dependence exists. The traditional technique for performing either of these entails accurately measuring both the laser output wavelength and the water vapor spectral passband with combined uncertainty of approximately 0.01 nm. However, uncertainty in interference filter center wavelengths and laser output wavelengths can be this large or larger. These combined uncertainties translate into uncertainties in the magnitude of the temperature dependence of the Raman lidar water vapor measurement of 3% or more. We present here an alternate approach for accurately determining the temperature dependence of the Raman lidar water vapor measurement. This alternate approach entails acquiring sequential atmospheric profiles using the lidar while scanning the channel passband across portions of the Raman water vapor Q-branch. This scanning is accomplished either by tilt-tuning an interference filter or by scanning the output of a spectrometer. Through this process a peak in the transmitted intensity can be discerned in a manner that defines the spectral location of the channel passband with respect to the laser output wavelength to much higher accuracy than that achieved with standard laboratory techniques. Given the peak of the water vapor signal intensity curve, determined using the techniques described here, and an approximate knowledge of atmospheric temperature, the temperature dependence of a given Raman lidar profile can be determined with accuracy of 0.5% or better. A Mathematica notebook that demonstrates the calculations used here is available from the lead author.

Raman lidar↗
NASA NTRS2012

Software Analysis of New Space Gravity Data for Geophysics and Climate Research

Both the Gravity Recovery and Climate Experiment (GRACE) and Gravity field and steady-state Ocean Circulation Explorer (GOCE) satellites are returning rich data for the study of the solid earth, the oceans, and the climate. Current software analysis tools do not provide researchers with the ease and flexibility required to make full use of this data. We evaluate the capabilities and shortcomings of existing software tools including Mathematica, the GOCE User Toolbox, the ICGEM's (International Center for Global Earth Models) web server, and Tesseroids. Using existing tools as necessary, we design and implement software with the capability to produce gridded data and publication quality renderings from raw gravity data. The straight forward software interface marks an improvement over previously existing tools and makes new space gravity data more useful to researchers. Using the software we calculate Bouguer anomalies of the gravity tensor's vertical component in the Gulf of Mexico, Antarctica, and the 2010 Maule earthquake region. These maps identify promising areas of future research.

Gravity Recovery and Climate Experiment (GRACE)↗
NASA NTRS2012

Model Based Systems Engineering on the Europa Mission Concept Study

At the start of 2011, the proposed Jupiter Europa Orbiter (JEO) mission was staffing up in expectation of becoming an official project later in the year for a launch in 2020. A unique aspect of the pre-project work was a strong emphasis and investment on the foundations of Model-Based Systems Engineering (MBSE). As so often happens in this business, plans changed: NASA's budget and science priorities were released and together fundamentally changed the course of JEO. As a result, it returned to being a study task whose objective is to propose more affordable ways to accomplish the science. As part of this transition, the question arose as to whether it could continue to afford the investment in MBSE. In short, the MBSE infusion has survived and is providing clear value to the study effort. By leveraging the existing infrastructure and a modest additional investment, striking advances in the capture and analysis of designs using MBSE were achieved. In the process, the need to remain relevant in the new environment has brought about a wave of innovation and progress. The effort has reaffirmed the importance of architecting. It has successfully harnessed the synergistic relationship of architecting to system modeling. We have found that MBSE can provide greater agility than traditional methods. We have also found that a diverse 'ecosystem' of modeling tools and languages (SysML, Mathematica, even Excel) is not only viable, but an important enabler of agility and adaptability. This paper will describe the successful application of MBSE in the dynamic environment of early mission formulation, the significant results produced and lessons learned in the process.

Bayer, Todd J.↗
NASA NTRS2012

Getting a Cohesive Answer from a Common Start: Scalable Multidisciplinary Analysis through Transformation of a System Model

One of the challenges of systems engineering is in working multidisciplinary problems in a cohesive manner. When planning analysis of these problems, system engineers must tradeoff time and cost for analysis quality and quantity. The quality is associated with the fidelity of the multidisciplinary models and the quantity is associated with the design space that can be analyzed. The tradeoff is due to the resource intensive process of creating a cohesive multidisciplinary system model and analysis. Furthermore, reuse or extension of the models used in one stage of a product life cycle for another is a major challenge. Recent developments have enabled a much less resource-intensive and more rigorous approach than handwritten translation scripts or codes of multidisciplinary models and their analyses. The key is to work from a core system model defined in a MOF-based language such as SysML and in leveraging the emerging tool ecosystem, such as Query-View- Transform (QVT), from the OMG community. SysML was designed to model multidisciplinary systems and analyses. The QVT standard was designed to transform SysML models. The Europa Hability Mission (EHM) team has begun to exploit these capabilities. In one case, a Matlab/Simulink model is generated on the fly from a system description for power analysis written in SysML. In a more general case, a symbolic mathematical framework (supported by Wolfram Mathematica) is coordinated by data objects transformed from the system model, enabling extremely flexible and powerful tradespace exploration and analytical investigations of expected system performance.

Cole, Bjorn↗
NASA NTRS2022

Solar Temperature Variations Computed from SORCE SIM Irradiances Observed During 2003-2020

NASA’s Solar Radiation and Climate Experiment (SORCE) Spectral Irradiance Monitor (SIM) instrument produced about 17 years of daily average Spectral Solar Irradiance ( SSI ) data for wavelengths 240 nm – 2416 nm. We choose a day of minimal solar activity, 2008-08-24, during the 2008 − 2009 minimum between cycles 23 and 24, and compute the brightness temperature (𝑇 o ) from that day’s solar spectral irradiance (𝑆𝑆𝐼 o ). We consider small variations of T and SSI about these reference values, and derive linear and quadratic analytic approximations by Taylor expansion about the reference day values. To determine approximation accuracy, we compare to exact brightness temperatures T computed from the Planck spectrum, by solving analytically for T , or equivalent root-finding in Wolfram Mathematica. We find that the linear analytic approximation overestimates, while the quadratic underestimates the exact result. This motivates search for statistical “fit” models “in between” the two analytic models, with minimum root-mean-square-error RMSE. We make this search using open-source statistical R software, determine coefficients for linear and quadratic fit models, and compare statistical with analytic RMSE’s. When only linear analytic and fit models are compared, the fit model is superior at ultraviolet, visible, and near infrared wavelengths. This again holds true when comparing only quadratic models. Quadratic is superior to linear for both analytic and statistical models, and statistical fits give smallest RMSE’s. Lastly, we use linear analytic and fit models to find an interpolating function in wavelength, useful in case the SIM results need adjustment to another choices of wavelengths, to compare or extend to any other instrument.

SORCE↗
NASA NTRS2016

Fast Simulation of the NICER Instrument

The NICER mission uses a complicated physical system to collect information from objects that are, by x-ray timing science standards, rather faint. To get the most out of the data we will need a rigorous understanding of all instrumental effects. We are in the process of constructing a very fast, high fidelity simulator that will help us to assess instrument performance, support simulation-based data reduction, and improve our estimates of measurement error. We will combine and extend existing optics, detector, and electronics simulations. We will employ the Compute Unied Device Architecture (CUDA2) to parallelize these calculations. The price of suitable CUDA-compatible multi-gigaflop cores is about $0.20/core, so this approach will be very cost-effective.

gEDA↗