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NASA NTRS2004

The Goddard Profiling Algorithm (GPROF): Description and Current Applications

Atmospheric scientists use different methods for interpreting satellite data. In the early days of satellite meteorology, the analysis of cloud pictures from satellites was primarily subjective. As computer technology improved, satellite pictures could be processed digitally, and mathematical algorithms were developed and applied to the digital images in different wavelength bands to extract information about the atmosphere in an objective way. The kind of mathematical algorithm one applies to satellite data may depend on the complexity of the physical processes that lead to the observed image, and how much information is contained in the satellite images both spatially and at different wavelengths. Imagery from satellite-borne passive microwave radiometers has limited horizontal resolution, and the observed microwave radiances are the result of complex physical processes that are not easily modeled. For this reason, a type of algorithm called a Bayesian estimation method is utilized to interpret passive microwave imagery in an objective, yet computationally efficient manner.

Olson, William S.↗

NASA NTRS1995

Shear-induced opening of the coronal magnetic field

This work describes the evolution of a model solar corona in response to motions of the footpoints of its magnetic field. The mathematics involved is semianalytic, with the only numerical solution being that of an ordinary differential equation. This approach, while lacking the flexibility and physical details of full MHD simulations, allows for very rapid computation along with complete and rigorous exploration of the model's implications. We find that the model coronal field bulges upward, at first slowly and then more dramatically, in response to footpoint displacements. The energy in the field rises monotonically from that of the initial potential state, and the field configuration and energy appraoch asymptotically that of a fully open field. Concurrently, electric currents develop and concentrate into a current sheet as the limiting case of the open field is approached. Examination of the equations shows rigorously that in the asymptotic limit of the fully open field, the current layer becomes a true ideal MHD singularity.

Wolfson, Richard↗

NASA NTRS1972

Generalized simulation technique for turbojet engine system analysis

A nonlinear analog simulation of a turbojet engine was developed. The purpose of the study was to establish simulation techniques applicable to propulsion system dynamics and controls research. A schematic model was derived from a physical description of a J85-13 turbojet engine. Basic conservation equations were applied to each component along with their individual performance characteristics to derive a mathematical representation. The simulation was mechanized on an analog computer. The simulation was verified in both steady-state and dynamic modes by comparing analytical results with experimental data obtained from tests performed at the Lewis Research Center with a J85-13 engine. In addition, comparison was also made with performance data obtained from the engine manufacturer. The comparisons established the validity of the simulation technique.

Seldner, K.↗

NASA NTRS2001

Stochastic Modeling and Generation of Partially Polarized or Partially Coherent Electromagnetic Waves

Many new Earth remote-sensing instruments are embracing both the advantages and added complexity that result from interferometric or fully polarimetric operation. To increase instrument understanding and functionality a model of the signals these instruments measure is presented. A stochastic model is used as it recognizes the non-deterministic nature of any real-world measurements while also providing a tractable mathematical framework. A stationary, Gaussian-distributed model structure is proposed. Temporal and spectral correlation measures provide a statistical description of the physical properties of coherence and polarization-state. From this relationship the model is mathematically defined. The model is shown to be unique for any set of physical parameters. A method of realizing the model (necessary for applications such as synthetic calibration-signal generation) is given and computer simulation results are presented. The signals are constructed using the output of a multi-input multi-output linear filter system, driven with white noise.

Davis, Brynmor↗

NASA NTRS2009

Evolutionary Computing Methods for Spectral Retrieval

A methodology for processing spectral images to retrieve information on underlying physical, chemical, and/or biological phenomena is based on evolutionary and related computational methods implemented in software. In a typical case, the solution (the information that one seeks to retrieve) consists of parameters of a mathematical model that represents one or more of the phenomena of interest. The methodology was developed for the initial purpose of retrieving the desired information from spectral image data acquired by remote-sensing instruments aimed at planets (including the Earth). Examples of information desired in such applications include trace gas concentrations, temperature profiles, surface types, day/night fractions, cloud/aerosol fractions, seasons, and viewing angles. The methodology is also potentially useful for retrieving information on chemical and/or biological hazards in terrestrial settings. In this methodology, one utilizes an iterative process that minimizes a fitness function indicative of the degree of dissimilarity between observed and synthetic spectral and angular data. The evolutionary computing methods that lie at the heart of this process yield a population of solutions (sets of the desired parameters) within an accuracy represented by a fitness-function value specified by the user. The evolutionary computing methods (ECM) used in this methodology are Genetic Algorithms and Simulated Annealing, both of which are well-established optimization techniques and have also been described in previous NASA Tech Briefs articles. These are embedded in a conceptual framework, represented in the architecture of the implementing software, that enables automatic retrieval of spectral and angular data and analysis of the retrieved solutions for uniqueness.

Terrile, Richard↗

NASA NTRS1970

Simplified computation of compressible fluid flow parameters

Mathematical techniques analyze fluid flow through circular duct, enlarged or constricted circular duct, and across an orifice or nozzle. Using subsonic Mach number as basic flow parameter, a series of working graphs displays the variation of various physical parameters in each of the flow conditions.

Beimgraben, H. W.↗

NASA NTRS1992

Mathematical model of the Space Shuttle Main Engine gaseous oxygen control valve

A computer program for modeling transient flow behavior of the GOX control valve (GCV) has been developed which makes it possible to model a variety of operating conditions and changes of physical hardware. The SSME GCV controls the flow of GOX that pressurizes the Pogo accumulator. The model simulates the transient flow behavior of the original, tight stacked, and redesigned valve configurations during start and shutdown. The model reads a user-prepared input file that defines the valve configurations and thus provides maximum flexibility.

Langer, Susan L.↗

NASA NTRS1982

Modelling the core magnetic field of the earth

It is suggested that radial off-center dipoles located within the core of the earth be used instead of spherical harmonics of the magnetic potential in modeling the core magnetic field. The off-center dipoles, in addition to more realistically modeling the physical current systems within the core, are if located deep within the core more effective at removing long wavelength signals of either potential or field. Their disadvantage is that their positions and strengths are more difficult to compute, and such effects as upward and downward continuation are more difficult to manipulate. It is nevertheless agreed with Cox (1975) and Alldredge and Hurwitz (1964) that physical realism in models is more important than mathematical convenience. A radial dipole model is presented which agrees with observations of secular variation and excursions.

Harrison, C. G. A.↗

NASA NTRS1987

An algorithm for a semiempirical nuclear fragmentation model

In the present paper, an algorithm for HZE (High Charge and Energy) fragmentation based upon a combination of a two step abrasion/ablation model and electromagnetic dissociation is presented. Development of the model and detailed comparison with available experimental data are given elsewhere. The abrasion process accounts for the removal of nuclear matter in the overlap region of the colliding ions. An average transmission factor is used for the projectile and target nuclei at a given impact parameter to account for the finite mean free path in nuclear matter. The ions are treated otherwise on a geometric basis assuming uniform spheres. The ablation process is treated as a single nucleon-evaporation for every 10 MeV of excitation energy as used by Bowman in the original form of the model. The charge distribution of final fragments are calculated according to the Rudstam formula, except for some correction in mass 5, 8 and 9 fragments which show strong structure effects and correspondingly significant deviation from Rudstam's values. The nuclear electromagnetic dissociation is based on the Weizsacker-Williams (WW) method of virtual quanta where due to its simplicity, the virtual photon spectrum for individual multipoles, and finite extent of the charge distribution are not included. Comparisons of the model are made with the available experimental data here and more extensively elsewhere.

NASA Program Space Medicine↗

NASA NTRS1999

A Textbook for a First Course in Computational Fluid Dynamics

This paper describes and discusses the textbook, Fundamentals of Computational Fluid Dynamics by Lomax, Pulliam, and Zingg, which is intended for a graduate level first course in computational fluid dynamics. This textbook emphasizes fundamental concepts in developing, analyzing, and understanding numerical methods for the partial differential equations governing the physics of fluid flow. Its underlying philosophy is that the theory of linear algebra and the attendant eigenanalysis of linear systems provides a mathematical framework to describe and unify most numerical methods in common use in the field of fluid dynamics. Two linear model equations, the linear convection and diffusion equations, are used to illustrate concepts throughout. Emphasis is on the semi-discrete approach, in which the governing partial differential equations (PDE's) are reduced to systems of ordinary differential equations (ODE's) through a discretization of the spatial derivatives. The ordinary differential equations are then reduced to ordinary difference equations (O(Delta)E's) using a time-marching method. This methodology, using the progression from PDE through ODE's to O(Delta)E's, together with the use of the eigensystems of tridiagonal matrices and the theory of O(Delta)E's, gives the book its distinctiveness and provides a sound basis for a deep understanding of fundamental concepts in computational fluid dynamics.

Zingg, D. W.↗

NASA NTRS1991

A system approach to aircraft optimization

Mutual couplings among the mathematical models of physical phenomena and parts of a system such as an aircraft complicate the design process because each contemplated design change may have a far reaching consequence throughout the system. Techniques are outlined for computing these influences as system design derivatives useful for both judgemental and formal optimization purposes. The techniques facilitate decomposition of the design process into smaller, more manageable tasks and they form a methodology that can easily fit into existing engineering organizations and incorporate their design tools.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS1992

A system approach to aircraft optimization

Mutual couplings among the mathematical models of physical phenomenon and parts of a system such as an aircraft complicate the design process because each contemplated design change may have far reaching consequences throughout the system. This paper outlines techniques for computing these influences as system design derivatives useful in both judgmental and formal optimization purposes. The techniques facilitate decomposition of the design process into smaller, more manageable tasks and they form a methodology that can easily fit into existing engineering optimizations and incorporate their design tools.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS2007

NASA Langley's Approach to the Sandia's Structural Dynamics Challenge Problem

The objective of this challenge is to develop a data-based probabilistic model of uncertainty to predict the behavior of subsystems (payloads) by themselves and while coupled to a primary (target) system. Although this type of analysis is routinely performed and representative of issues faced in real-world system design and integration, there are still several key technical challenges that must be addressed when analyzing uncertain interconnected systems. For example, one key technical challenge is related to the fact that there is limited data on target configurations. Moreover, it is typical to have multiple data sets from experiments conducted at the subsystem level, but often samples sizes are not sufficient to compute high confidence statistics. In this challenge problem additional constraints are placed as ground rules for the participants. One such rule is that mathematical models of the subsystem are limited to linear approximations of the nonlinear physics of the problem at hand. Also, participants are constrained to use these models and the multiple data sets to make predictions about the target system response under completely different input conditions. Our approach involved initially the screening of several different methods. Three of the ones considered are presented herein. The first one is based on the transformation of the modal data to an orthogonal space where the mean and covariance of the data are matched by the model. The other two approaches worked solutions in physical space where the uncertain parameter set is made of masses, stiffnesses and damping coefficients; one matches confidence intervals of low order moments of the statistics via optimization while the second one uses a Kernel density estimation approach. The paper will touch on all the approaches, lessons learned, validation 1 metrics and their comparison, data quantity restriction, and assumptions/limitations of each approach. Keywords: Probabilistic modeling, model validation, uncertainty quantification, kernel density

Horta, Lucas G.↗

NASA NTRS1992

Multidisciplinary design and optimization

Mutual couplings among the mathematical models of physical phenomena and parts of a system such as an aircraft complicate the design process because each contemplated design change may have a far reaching consequence throughout the system. This paper outlines techniques for computing these influences as system design derivatives useful to both judgmental and formal optimization purposes. The techniques facilitate decomposition of the design process into smaller, more manageable tasks and they form a methodology that can easily fit into existing engineering optimizations and incorporate their design tools.

Sobieszczanski-Sobieski, Jaroslaw↗

NASA NTRS2016

Developing the Next Generation of Science Data System Engineers

At Goddard, engineers and scientists with a range of experience in science data systems are needed to employ new technologies and develop advances in capabilities for supporting new Earth and Space science research. Engineers with extensive experience in science data, software engineering and computer-information architectures are needed to lead and perform these activities. The increasing types and complexity of instrument data and emerging computer technologies coupled with the current shortage of computer engineers with backgrounds in science has led the need to develop a career path for science data systems engineers and architects.The current career path, in which undergraduate students studying various disciplines such as Computer Engineering or Physical Scientist, generally begins with serving on a development team in any of the disciplines where they can work in depth on existing Goddard data systems or serve with a specific NASA science team. There they begin to understand the data, infuse technologies, and begin to know the architectures of science data systems. From here the typical career involves peermentoring, on-the-job training or graduate level studies in analytics, computational science and applied science and mathematics. At the most senior level, engineers become subject matter experts and system architect experts, leading discipline-specific data centers and large software development projects. They are recognized as a subject matter expert in a science domain, they have project management expertise, lead standards efforts and lead international projects. A long career development remains necessary not only because of the breadth of knowledge required across physical sciences and engineering disciplines, but also because of the diversity of instrument data being developed today both by NASA and international partner agencies and because multidiscipline science and practitioner communities expect to have access to all types of observational data.This paper describes an approach to defining career-path guidance for college-bound high school and undergraduate engineering students, junior and senior engineers from various disciplines.

Next Generation of Science↗

NASA NTRS1991

Software For Design Of Life-Support Systems

Design Assistant Workstation (DAWN) computer program is prototype of expert software system for analysis and design of regenerative, physical/chemical life-support systems that revitalize air, reclaim water, produce food, and treat waste. Incorporates both conventional software for quantitative mathematical modeling of physical, chemical, and biological processes and expert system offering user stored knowledge about materials and processes. Constructs task tree as it leads user through simulated process, offers alternatives, and indicates where alternative not feasible. Also enables user to jump from one design level to another.

Rudokas, Mary R.↗

NASA NTRS1946

On laminar and turbulent friction

Report deals, first with the theory of the laminar friction flow, where the basic concepts of Prandtl's boundary layer theory are represented from mathematical and physical points of view, and a method is indicated by means of which even more complicated cases can be treated with simple mathematical means, at least approximately. An attempt is also made to secure a basis for the computation of the turbulent friction by means of formulas through which the empirical laws of the turbulent pipe resistance can be applied to other problems on friction drag. (author)

Von Karman, TH↗

NASA NTRS1998

MAPS of Cancer

Our goal was to produce an interactive visualization from a mathematical model that successfully predicts metastases from head and neck cancer. We met this goal early in the project. The visualization is available for the public to view. Our work appears to fill a need for more information about this deadly disease. The idea of this project was to make an easily interpretable visualization based on what we call "functional maps" of disease. A functional map is a graphic summary of medical data, where distances between parts of the body are determined by the probability of disease, not by anatomical distances. Functional maps often beat little resemblance to anatomical maps, but they can be used to predict the spread of disease. The idea of modeling the spread of disease in an abstract multidimensional space is difficult for many people. Our goal was to make the important predictions easy to see. NASA must face this problem frequently: how to help laypersons and professionals see important trends in abstract, complex data. We took advantage of concepts perfected in NASA's graphics libraries. As an analogy, consider a functional map of early America. Suppose we choose travel times, rather than miles, as our measures of inter-city distances. For Abraham Lincoln, travel times would have been the more meaningful measure of separation between cities. In such a map New Orleans would be close to Memphis because of the Mississippi River. St. Louis would be close to Portland because of the Oregon Trail. Oklahoma City would be far from Little Rock because of the Cheyenne. Such a map would look puzzling to those of us who have always seen physical maps, but the functional map would be more useful in predicting the probabilities of inter-site transit. Continuing the analogy, we could predict the spread of social diseases such as gambling along the rivers and cattle rustling along the trails. We could simply print the functional map of America, but it would be more interesting to show meaningful patterns of dispersal. We had previously published the functional map of the head and neck, but it was difficult to explain to either patients or surgeons because that view of our body did not resemble anatomy. This discrepancy between functional and physical maps is just a mathematical restatement of the well-known fact that some diseases, such as head and neck cancer, spread in complex patterns, not always to the next nearest site. We had discovered that a computer could re-arrange anatomy so that this particular disease spreads to the next nearest site. The functional map explains over 95% of the metastases in 1400 patients. In a sense, we had graphed what our body "looks like" to a tumor. The tumor readily travels between adjacent areas in the functional map. The functional map is a succinct visual display of trends that are not easily appreciated in tables of probabilities.

Gray, Lincoln↗