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NASA NTRS1994

Understanding the Biosphere From Space: Strategies to Exploit Remote Sensing Data

The quantitative interpretation of satellite observations requires the use of mathematical tools to extract the desired information on terrestrial environments from the radiation data collected in space. A whole range of approaches can be pursued, from the development of models capable of explaining the nature of the physical signal being measured and of characterizing the state of the system under observation, to the empirical correlations between the variables of interest and the space measurements. The premises and implications of these approaches are outlined, paying special attention to the mathematical and numerical requirements. The role and specific applications of empirical bidirectional reflectance models is also discussed, even though these models do not contribute to the understanding of the theory of radiation transfer or to the assessment of the variables of interest. The advantages and drawbacks of these various approaches and the research priorities for the next few years are discussed in the context of the planned availability of new sensors.

Michel M Verstraete↗

NASA NTRS1999

Integrated Aeroservoelastic Optimization: Status and Direction

The interactions of lightweight flexible airframe structures, steady and unsteady aerodynamics, and wide-bandwidth active controls on modern airplanes lead to considerable multidisciplinary design challenges. More than 25 years of mathematical and numerical methods' development, numerous basic research studies, simulations and wind-tunnel tests of simple models, wind-tunnel tests of complex models of real airplanes, as well as flight tests of actively controlled airplanes, have all contributed to the accumulation of a substantial body of knowledge in the area of aeroservoelasticity. A number of analysis codes, with the capabilities to model real airplane systems under the assumptions of linearity, have been developed. Many tests have been conducted, and results were correlated with analytical predictions. A selective sample of references covering aeroservoelastic testing programs from the 1960s to the early 1980s, as well as more recent wind-tunnel test programs of real or realistic configurations, are included in the References section of this paper. An examination of references 20-29 will reveal that in the course of development (or later modification), of almost every modern airplane with a high authority active control system, there arose a need to face aeroservoelastic problems and aeroservoelastic design challenges.

Livne, Eli↗

NASA NTRS2000

Progress in The Semantic Analysis of Scientific Code

This paper concerns a procedure that analyzes aspects of the meaning or semantics of scientific and engineering code. This procedure involves taking a user's existing code, adding semantic declarations for some primitive variables, and parsing this annotated code using multiple, independent expert parsers. These semantic parsers encode domain knowledge and recognize formulae in different disciplines including physics, numerical methods, mathematics, and geometry. The parsers will automatically recognize and document some static, semantic concepts and help locate some program semantic errors. These techniques may apply to a wider range of scientific codes. If so, the techniques could reduce the time, risk, and effort required to develop and modify scientific codes.

Stewart, Mark↗

NASA NTRS2000

An Experiment in Scientific Program Understanding

This paper concerns a procedure that analyzes aspects of the meaning or semantics of scientific and engineering code. This procedure involves taking a user's existing code, adding semantic declarations for some primitive variables, and parsing this annotated code using multiple, independent expert parsers. These semantic parsers encode domain knowledge and recognize formulae in different disciplines including physics, numerical methods, mathematics, and geometry. The parsers will automatically recognize and document some static, semantic concepts and help locate some program semantic errors. Results are shown for three intensively studied codes and seven blind test cases; all test cases are state of the art scientific codes. These techniques may apply to a wider range of scientific codes. If so, the techniques could reduce the time, risk, and effort required to develop and modify scientific codes.

Stewart, Mark E. M.↗

NASA NTRS2003

Positron Physics

I will give a review of the history of low-energy positron physics, experimental and theoretical, concentrating on the type of work pioneered by John Humberston and the positronics group at University College. This subject became a legitimate subfield of atomic physics under the enthusiastic direction of the late Sir Harrie Massey, and it attracted a diverse following throughout the world. At first purely theoretical, the subject has now expanded to include high brightness beams of low-energy positrons, positronium beams, and, lately, experiments involving anti-hydrogen atoms. The theory requires a certain type of persistence in its practitioners, as well as an eagerness to try new mathematical and numerical techniques. I will conclude with a short summary of some of the most interesting recent advances.

Drachman, Richard J.↗

NASA NTRS2010

Dynamic Analysis of Sounding Rocket Pneumatic System Revision

The recent fusion of decades of advancements in mathematical models, numerical algorithms and curve fitting techniques marked the beginning of a new era in the science of simulation. It is becoming indispensable to the study of rockets and aerospace analysis. In pneumatic system, which is the main focus of this paper, particular emphasis will be placed on the efforts of compressible flow in Attitude Control System of sounding rocket.

Armen, Jerald↗

NASA NTRS2013

Modeling Non-homologous End Joining

Non-homologous end joining (NHEJ) is the dominant DNA double strand break (DSB) repair pathway and involves several NHEJ proteins such as Ku, DNA-PKcs, XRCC4, Ligase IV and so on. Once DSBs are generated, Ku is first recruited to the DNA end, followed by other NHEJ proteins for DNA end processing and ligation. Because of the direct ligation of break ends without the need for a homologous template, NHEJ turns out to be an error-prone but efficient repair pathway. Some mechanisms have been proposed of how the efficiency of NHEJ repair is affected. The type of DNA damage is an important factor of NHEJ repair. For instance, the length of DNA fragment may determine the recruitment efficiency of NHEJ protein such as Ku [1], or the complexity of the DNA breaks [2] is accounted for the choice of NHEJ proteins and subpathway of NHEJ repair. On the other hand, the chromatin structure also plays a role of the accessibility of NHEJ protein to the DNA damage site. In this talk, some mathematical models of NHEJ, that consist of series of biochemical reactions complying with the laws of chemical reaction (e.g. mass action, etc.), will be introduced. By mathematical and numerical analysis and parameter estimation, the models are able to capture the qualitative biological features and show good agreement with experimental data. As conclusions, from the viewpoint of modeling, how the NHEJ proteins are recruited will be first discussed for connection between the classical sequential model [4] and recently proposed two-phase model [5]. Then how the NHEJ repair pathway is affected, by the length of DNA fragment [6], the complexity of DNA damage [7] and the chromatin structure [8], will be addressed

Li, Yongfeng↗

NASA NTRS2014

Using the NASA GRC Sectored-One-Dimensional Combustor Simulation

The document is a user manual for the NASA GRC Sectored-One-Dimensional (S-1-D) Combustor Simulation. It consists of three sections. The first is a very brief outline of the mathematical and numerical background of the code along with a description of the non-dimensional variables on which it operates. The second section describes how to run the code and includes an explanation of the input file. The input file contains the parameters necessary to establish an operating point as well as the associated boundary conditions (i.e. how it is fed and terminated) of a geometrically configured combustor. It also describes the code output. The third section describes the configuration process and utilizes a specific example combustor to do so. Configuration consists of geometrically describing the combustor (section lengths, axial locations, and cross sectional areas) and locating the fuel injection point and flame region. Configuration requires modifying the source code and recompiling. As such, an executable utility is included with the code which will guide the requisite modifications and insure that they are done correctly.

Combustion Stability↗

NASA NTRS1991

Three-Dimensional Analysis and Modeling of a Wankel Engine

A new computer code, AGNI-3D, has been developed for the modeling of combustion, spray, and flow properties in a stratified-charge rotary engine (SCRE). The mathematical and numerical details of the new code are described by the first author in a separate NASA publication. The solution procedure is based on an Eulerian-Lagrangian approach where the unsteady, three-dimensional Navier-Stokes equations for a perfect gas-mixture with variable properties are solved in generalized, Eulerian coordinates on a moving grid by making use of an implicit finite-volume, Steger-Warming flux vector splitting scheme. The liquid-phase equations are solved in Lagrangian coordinates. The engine configuration studied was similar to existing rotary engine flow-visualization and hot-firing test rigs. The results of limited test cases indicate a good degree of qualitative agreement between the predicted and measured pressures. It is conjectured that the impulsive nature of the torque generated by the observed pressure nonuniformity may be one of the mechanisms responsible for the excessive wear of the timing gears observed during the early stages of the rotary combustion engine (RCE) development. It was identified that the turbulence intensities near top-dead-center were dominated by the compression process and only slightly influenced by the intake and exhaust processes. Slow mixing resulting from small turbulence intensities within the rotor pocket and also from a lack of formation of any significant recirculation regions within the rotor pocket were identified as the major factors leading to incomplete combustion. Detailed flowfield results during exhaust and intake, fuel injection, fuel vaporization, combustion, mixing and expansion processes are also presented. The numerical procedure is very efficient as it takes 7 to 10 CPU hours on a CRAY Y-MP for one entire engine cycle when the computations are performed over a 31 x16 x 20 grid.

Raju, M. S.↗

NASA NTRS2017

Development of an Unstructured, Three-Dimensional Material Response Design Tool

A preliminary verification and validation of a new material response model is presented. This model, Icarus, is intended to serve as a design tool for the thermal protection systems of re-entry vehicles. Currently, the capability of the model is limited to simulating the pyrolysis of a material as a result of the radiative and convective surface heating imposed on the material from the surrounding high enthalpy gas. Since the major focus behind the development of Icarus has been model extensibility, the hope is that additional physics can be quickly added. The extensibility is critical since thermal protection systems are becoming increasing complex, e.g. woven carbon polymers. Additionally, as a three-dimensional, unstructured, finite-volume model, Icarus is capable of modeling complex geometries as well as multi-dimensional physics, which have been shown to be important in some scenarios and are not captured by one-dimensional models. In this paper, the mathematical and numerical formulation is presented followed by a discussion of the software architecture and some preliminary verification and validation studies.

Material Response Model↗

NASA NTRS2017

Development of a Three-Dimensional, Unstructured Material Response Design Tool

A preliminary verification and validation of a new material response model is presented. This model, Icarus, is intended to serve as a design tool for the thermal protection systems of re-entry vehicles. Currently, the capability of the model is limited to simulating the pyrolysis of a material as a result of the radiative and convective surface heating imposed on the material from the surrounding high enthalpy gas. Since the major focus behind the development of Icarus has been model extensibility, the hope is that additional physics can be quickly added. This extensibility is critical since thermal protection systems are becoming increasing complex, e.g. woven carbon polymers. Additionally, as a three-dimensional, unstructured, finite-volume model, Icarus is capable of modeling complex geometries. In this paper, the mathematical and numerical formulation is presented followed by a discussion of the software architecture and some preliminary verification and validation studies.

Thermal Protection System↗

NASA NTRS2017

Numerical Modeling of Saturated Boiling in a Heated Tube

This paper describes a mathematical formulation and numerical solution of boiling in a heated tube. The mathematical formulation involves a discretization of the tube into a flow network consisting of fluid nodes and branches and a thermal network consisting of solid nodes and conductors. In the fluid network, the mass, momentum and energy conservation equations are solved and in the thermal network, the energy conservation equation of solids is solved. A pressure-based, finite-volume formulation has been used to solve the equations in the fluid network. The system of equations is solved by a hybrid numerical scheme which solves the mass and momentum conservation equations by a simultaneous Newton-Raphson method and the energy conservation equation by a successive substitution method. The fluid network and thermal network are coupled through heat transfer between the solid and fluid nodes which is computed by Chen's correlation of saturated boiling heat transfer. The computer model is developed using the Generalized Fluid System Simulation Program and the numerical predictions are compared with test data.

Majumdar, Alok↗

NASA NTRS1995

Scientific Visualization and Computational Science: Natural Partners

Scientific visualization is developing rapidly, stimulated by computational science, which is gaining acceptance as a third alternative to theory and experiment. Computational science is based on numerical simulations of mathematical models derived from theory. But each individual simulation is like a hypothetical experiment; initial conditions are specified, and the result is a record of the observed conditions. Experiments can be simulated for situations that can not really be created or controlled. Results impossible to measure can be computed.. Even for observable values, computed samples are typically much denser. Numerical simulations also extend scientific exploration where the mathematics is analytically intractable. Numerical simulations are used to study phenomena from subatomic to intergalactic scales and from abstract mathematical structures to pragmatic engineering of everyday objects. But computational science methods would be almost useless without visualization. The obvious reason is that the huge amounts of data produced require the high bandwidth of the human visual system, and interactivity adds to the power. Visualization systems also provide a single context for all the activities involved from debugging the simulations, to exploring the data, to communicating the results. Most of the presentations today have their roots in image processing, where the fundamental task is: Given an image, extract information about the scene. Visualization has developed from computer graphics, and the inverse task: Given a scene description, make an image. Visualization extends the graphics paradigm by expanding the possible input. The goal is still to produce images; the difficulty is that the input is not a scene description displayable by standard graphics methods. Visualization techniques must either transform the data into a scene description or extend graphics techniques to display this odd input. Computational science is a fertile field for visualization research because the results vary so widely and include things that have no known appearance. The amount of data creates additional challenges for both hardware and software systems. Evaluations of visualization should ultimately reflect the insight gained into the scientific phenomena. So making good visualizations requires consideration of characteristics of the user and the purpose of the visualization. Knowledge about human perception and graphic design is also relevant. It is this breadth of knowledge that stimulates proposals for multidisciplinary visualization teams and intelligent visualization assistant software. Visualization is an immature field, but computational science is stimulating research on a broad front.

Uselton, Samuel P.↗

NASA NTRS1984

Mathematical algorithms to maximize performance in numerical weather prediction

Numerical weather prediction models, which involve the solution of non-linear partial differential equations at points on an extensive three dimensional grid, are ideally suited for processing on vector machines. It was logical therefore that the new global forecast model to be implemented at the Meteorological Office should be written in vector code for the CYBER 205. In order to achieve full efficiency and to reduce storage requirements the model used 32-bit arithmetic which was found to provide high enough precision. Unfortunately, however, the trigonometrical and logarithmic functions provided by CDC could only handle 64-bit vectors and, although written in efficient scalar code, did not take advantage of the special facilities of a vector processor. It was therefore necessary to rewrite the functions in vector code to handle both 32 and 64-bit vectors. There was also no half-precision compiler available for the Cyber 205 at that time and so the functions, like the model, had to make extensive use of the special call syntax. This made the code more difficult to write but it allowed much greater flexibility in that it became possible to access the exponent of a floating-point number independently of its coefficient. A description is given of the technique and the results which were achieved are summarized.

Foreman, A.↗

NASA NTRS1987

A global time-dependent model of thunderstorm electricity. I - Mathematical properties of the physical and numerical models

A time-dependent model is introduced that can be used to simulate the interaction of a thunderstorm with its global electrical environment. The model solves the continuity equation of the Maxwell current, which is assumed to be composed of the conduction, displacement, and source currents. Boundary conditions which can be used in conjunction with the continuity equation to form a well-posed initial-boundary value problem are determined. Properties of various components of solutions of the initial-boundary value problem are analytically determined. The results indicate that the problem has two time scales, one determined by the background electrical conductivity and the other by the time variation of the source function. A numerical method for obtaining quantitative results is introduced, and its properties are studied. Some simulation results on the evolution of the displacement and conduction currents during the electrification of a storm are presented.

Browning, G. L.↗

NASA NTRS1980

Comments on numerical solution of boundary value problems of the Laplace equation and calculation of eigenvalues by the grid method

The mathematics involved in numerically solving for the plane boundary value of the Laplace equation by the grid method is developed. The approximate solution of a boundary value problem for the domain of the Laplace equation by the grid method consists of finding u at the grid corner which satisfies the equation at the internal corners (u=Du) and certain boundary value conditions at the boundary corners.

Lyusternik, L. A.↗

NASA NTRS1994

Direct numerical simulations of on-demand vortex generators: Mathematical formulation

The objective of the present research is the development and application of efficient adaptive numerical algorithms for the study, via direct numerical simulations, of active vortex generators. We are using innovative computational schemes to investigate flows past complex configurations undergoing arbitrary motions. Some of the questions we try to answer are: Can and how may we control the dynamics of the wake? What is the importance of body shape and motion in the active control of the flow? What is the effect of three-dimensionality in laboratory experiments? We are interested not only in coupling our results to ongoing, related experimental work, but furthermore to develop an extensive database relating the above mechanisms to the vortical wake structures with the long-range objective of developing feedback control mechanisms. This technology is very important to aircraft, ship, automotive, and other industries that require predictive capability for fluid mechanical problems. The results would have an impact in high angle of attack aerodynamics and help design ways to improve the efficiency of ships and submarines (maneuverability, vortex induced vibration, and noise).

Koumoutsakos, Petros↗

NASA NTRS1971

An on-line system for hand-printed input

The capability of graphic input/output systems is described. Topics considered are a character recognizer and dictionary building program, an initial flow chart element input program, and a system entitled The Assistant Mathematician, which uses ordinary mathematics to specify numeric computation. All three parts are necessary to allow a user to carry on a mathematical dialogue with the computer in the language and notation of his discipline or problem domain.

Williams, T. G.↗