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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 217 records · Page 12

Determining the Accuracy of Aerodynamic Model Parameters Estimated from Flight Test Data

An important part of building mathematical models based on measured data is calculating the accuracy associated with statistical estimates of the model parameters. Indeed, without some idea of this accuracy, the parameter estimates themselves have limited value. In this work, an expression for computing quantitatively correct parameter accuracy measures for maximum likelihood parameter estimates with colored residuals is developed and validated. This result is important because experience in analyzing flight test data reveals that the output residuals from maximum likelihood estimation are almost always colored. The calculations involved can be appended to conventional maximum likelihood estimation algorithms. Monte Carlo simulation runs were used to show that parameter accuracy measures from the new technique accurately reflect the quality of the parameter estimates from maximum likelihood estimation without the need for correction factors or frequency domain analysis of the output residuals. The technique was applied to flight test data from repeated maneuvers flown on the F-18 High Alpha Research Vehicle (HARV). As in the simulated cases, parameter accuracy measures from the new technique were in agreement with the scatter in the parameter estimates from repeated maneuvers, while conventional parameter accuracy measures were optimistic.

Morelli, Eugene A.↗

Measurement of shear-wave velocity by ultrasound critical-angle reflectometry (UCR)

There exists a growing body of research that relates the measurement of pressure-wave velocity in bone to different physiological conditions and treatment modalities. The shear-wave velocity has been less studied, although it is necessary for a more complete understanding of the mechanical properties of bone. Ultrasound critical-angle reflectometry (UCR) is a noninvasive and nondestructive technique previously used to measure pressure-wave velocities both in vitro and in vivo. This note describes its application to the measurement of shear-wave velocity in bone, whether directly accessible or covered by soft tissue.

NASA Discipline Cardiopulmonary↗

Parallelization of a Six Degree of Freedom Entry Vehicle Trajectory Simulation Using OpenMP and OpenACC

The art and science of writing parallelized software, using methods such as Open Multi-Processing (OpenMP) and Open Accelerators (OpenACC), is dominated by computer scientists. Engineers and non-computer scientists looking to apply these techniques to their project applications face a steep learning curve, especially when looking to adapt their original single threaded software to run multi-threaded on graphics processing units (GPUs). There are significant changes in mindset that must occur; such as how to manage memory, the organization of instructions, and the use of if statements (also known as branching). The purpose of this work is twofold: 1) to demonstrate the applicability of parallelized coding methodologies, OpenMP and OpenACC, to tasks outside of the typical large scale matrix mathematics; and 2) to discuss, from an engineer’s perspective, the lessons learned from parallelizing software using these computer science techniques. This work applies OpenMP, on both multi-core central processing units (CPUs) and Intel® Xeon Phi™ 7210, and OpenACC on GPUs. These parallelization techniques are used to tackle the simulation of thousands of entry vehicle trajectories through the integration of six degree of freedom (DoF) equations of motion (EoM). The forces and moments acting on the entry vehicle, and used by the EoM, are estimated using multiple models of varying levels of complexity. Several benchmark comparisons are made on the execution of six DoF trajectory simulation: single thread Intel® Xeon® E5-2670 CPU, multi-thread CPU using OpenMP, multi-thread Xeon Phi™ 7210 using OpenMP, and multi-thread NVIDIA® Tesla® K40 GPU using OpenACC. These benchmarks are run on the Pleiades Supercomputer Cluster at the National Aeronautics and Space Administration (NASA) Ames Research Center (ARC), and a Xeon Phi™ 7210 node at NASA Langley Research Center (LaRC).

Green, Justin S.↗

Techniques for designing rotorcraft control systems

This report summarizes the work that was done on the project from 1 Apr. 1992 to 31 Mar. 1993. The main goal of this research is to develop a practical tool for rotorcraft control system design based on interactive optimization tools (CONSOL-OPTCAD) and classical rotorcraft design considerations (ADOCS). This approach enables the designer to combine engineering intuition and experience with parametric optimization. The combination should make it possible to produce a better design faster than would be possible using either pure optimization or pure intuition and experience. We emphasize that the goal of this project is not to develop an algorithm. It is to develop a tool. We want to keep the human designer in the design process to take advantage of his or her experience and creativity. The role of the computer is to perform the calculation necessary to improve and to display the performance of the nominal design. Briefly, during the first year we have connected CONSOL-OPTCAD, an existing software package for optimizing parameters with respect to multiple performance criteria, to a simplified nonlinear simulation of the UH-60 rotorcraft. We have also created mathematical approximations to the Mil-specs for rotorcraft handling qualities and input them into CONSOL-OPTCAD. Finally, we have developed the additional software necessary to use CONSOL-OPTCAD for the design of rotorcraft controllers.

Levine, William S.↗

Mathematical description of complex chemical kinetics and application to CFD modeling codes

A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.

Bittker, D. A.↗

Mathematical Description of Complex Chemical Kinetics and Application to CFD Modeling Codes

A major effort in combustion research at the present time is devoted to the theoretical modeling of practical combustion systems. These include turbojet and ramjet air-breathing engines as well as ground-based gas-turbine power generating systems. The ability to use computational modeling extensively in designing these products not only saves time and money, but also helps designers meet the quite rigorous environmental standards that have been imposed on all combustion devices. The goal is to combine the very complex solution of the Navier-Stokes flow equations with realistic turbulence and heat-release models into a single computer code. Such a computational fluid-dynamic (CFD) code simulates the coupling of fluid mechanics with the chemistry of combustion to describe the practical devices. This paper will focus on the task of developing a simplified chemical model which can predict realistic heat-release rates as well as species composition profiles, and is also computationally rapid. We first discuss the mathematical techniques used to describe a complex, multistep fuel oxidation chemical reaction and develop a detailed mechanism for the process. We then show how this mechanism may be reduced and simplified to give an approximate model which adequately predicts heat release rates and a limited number of species composition profiles, but is computationally much faster than the original one. Only such a model can be incorporated into a CFD code without adding significantly to long computation times. Finally, we present some of the recent advances in the development of these simplified chemical mechanisms.

Bittker, D. A.↗

A More Accurate and Efficient Technique Developed for Using Computational Methods to Obtain Helical Traveling-Wave Tube Interaction Impedance

The phenomenal growth of commercial communications has created a great demand for traveling-wave tube (TWT) amplifiers. Although the helix slow-wave circuit remains the mainstay of the TWT industry because of its exceptionally wide bandwidth, until recently it has been impossible to accurately analyze a helical TWT using its exact dimensions because of the complexity of its geometrical structure. For the first time, an accurate three-dimensional helical model was developed that allows accurate prediction of TWT cold-test characteristics including operating frequency, interaction impedance, and attenuation. This computational model, which was developed at the NASA Lewis Research Center, allows TWT designers to obtain a more accurate value of interaction impedance than is possible using experimental methods. Obtaining helical slow-wave circuit interaction impedance is an important part of the design process for a TWT because it is related to the gain and efficiency of the tube. This impedance cannot be measured directly; thus, conventional methods involve perturbing a helical circuit with a cylindrical dielectric rod placed on the central axis of the circuit and obtaining the difference in resonant frequency between the perturbed and unperturbed circuits. A mathematical relationship has been derived between this frequency difference and the interaction impedance (ref. 1). However, because of the complex configuration of the helical circuit, deriving this relationship involves several approximations. In addition, this experimental procedure is time-consuming and expensive, but until recently it was widely accepted as the most accurate means of determining interaction impedance. The advent of an accurate three-dimensional helical circuit model (ref. 2) made it possible for Lewis researchers to fully investigate standard approximations made in deriving the relationship between measured perturbation data and interaction impedance. The most prominent approximations made in the analysis were addressed and fully investigated for their accuracy by using the three-dimensional electromagnetic simulation code MAFIA (Solution of Maxwell's Equations by the Finite Integration Algorithm) (refs. 3 and 4). We found that several approximations introduced significant error (ref. 5).

Kory, Carol L.↗

"Novel Techniques in Non-Stationary Analysis of Rotorcraft Vibration Signitures"

This research effort produced new methods to analyze the performance of linear predictors that track non-stationary processes. Specifically, prediction methods have been applied to the vibration pattern of rotorcraft drivetrains. This analysis is part or a larger rotorcraft Health and Usage Monitoring System (HUMS) that can diagnose immediate failures of the subsystems, as indicated by abrupt change in the vibration signature, and prognosticate future health, by examining the vibration patterns against long-term trends. This problem is described by a earlier joint paper co-authored by members of the funding agency and the recipient institutions prior to this grant effort. Specific accomplishments under this grant include the following: (1) Definition of a framework for analysis of non-stationary time-series estimation using the coefficients of an adaptive filter. (2) Description of a novel method of combining short-term predictor error and long-term regression error to analyze the performance of a non-stationary predictor. (3) Formulation of a multi-variate probability density function that quantifies the performance of a adaptive predictor by using the short- and long-term error variables in a Gamma function distribution. and (4) Validation of the mathematical formulations with empirical data from NASA flight tests and simulated data to illustrate the utility beyond the domain of vibrating machinery.

Meng, Teresa↗

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.↗

Using the Abitibi Greenstone Belt to Understand Martian Hydrothermal Systems and the Potential for Biosignature Preservation in High Temperature Aqueous Environments

Metabolic bone diseases like osteoporosis result from the disruption of normal bone mineral balance (BMB) resulting in bone loss. During spaceflight astronauts lose substantial bone. Bed rest provides an analog to simulate some of the effects of spaceflight; including bone and calcium loss and provides the opportunity to evaluate new methods to monitor BMB in healthy individuals undergoing environmentally induced-bone loss. Previous research showed that natural variations in the Ca isotope ratio occur because bone formation depletes soft tissue of light Ca isotopes while bone resorption releases that isotopically light Ca back into soft tissue (Skulan et al, 2007). Using a bed rest model, we demonstrate that the Ca isotope ratio of urine shifts in a direction consistent with bone loss after just 7 days of bed rest, long before detectable changes in bone mineral density (BMD) occur. The Ca isotope variations tracks changes observed in urinary N-teleopeptide, a bone resorption biomarker. Bone specific alkaline phosphatase, a bone formation biomarker, is unchanged. The established relationship between Ca isotopes and BMB can be used to quantitatively translate the changes in the Ca isotope ratio to changes in BMD using a simple mathematical model. This model predicts that subjects lost 0.25 +/- 0.07% (+/- SD) of their bone mass from day 7 to day 30 of bed rest. Given the rapid signal observed using Ca isotope measurements and the potential to quantitatively assess bone loss; this technique is well suited to study the short-term dynamics of bone metabolism.

Hurowitz, J.↗

Using Natural Stable Calcium Isotopes to Rapidly Assess Changes in Bone Mineral Balance Using a Bed Rest Model to Induce Bone Loss

Metabolic bone diseases like osteoporosis result from the disruption of normal bone mineral balance (BMB) resulting in bone loss. During spaceflight astronauts lose substantial bone. Bed rest provides an analog to simulate some of the effects of spaceflight; including bone and calcium loss and provides the opportunity to evaluate new methods to monitor BMB in healthy individuals undergoing environmentally induced-bone loss. Previous research showed that natural variations in the Ca isotope ratio occur because bone formation depletes soft tissue of light Ca isotopes while bone resorption releases that isotopically light Ca back into soft tissue (Skulan et al, 2007). Using a bed rest model, we demonstrate that the Ca isotope ratio of urine shifts in a direction consistent with bone loss after just 7 days of bed rest, long before detectable changes in bone mineral density (BMD) occur. The Ca isotope variations tracks changes observed in urinary N-teleopeptide, a bone resorption biomarker. Bone specific alkaline phosphatase, a bone formation biomarker, is unchanged. The established relationship between Ca isotopes and BMB can be used to quantitatively translate the changes in the Ca isotope ratio to changes in BMD using a simple mathematical model. This model predicts that subjects lost 0.25 0.07% ( SD) of their bone mass from day 7 to day 30 of bed rest. Given the rapid signal observed using Ca isotope measurements and the potential to quantitatively assess bone loss; this technique is well suited to study the short-term dynamics of bone metabolism.

Morgan, J. L. L.↗

1985 International Geoscience and Remote Sensing Symposium (IGARSS '85), University of Massachusetts, Amherst, October 7-9, 1985, Digest. Volumes 1 & 2

The present conference on remote sensing instrumentation considers topics in water resources research, planetary remote sensing and mathematical geophysics, sea ice behavior in view of the Cold Regions Research and Engineering Laboratories pond measurements, Shuttle Imaging Radar-B (SIR-B) system performance and calibration results, geological applications of remote sensing, and microwave scattering from vegetation. Further attention is given to atmospheric probing with lasers, image processing for remote sensing, forest inventory and condition assessment, atmospheric remote sensing, SIR-B geological results, the reflectance, emission, and scattering characteristics of vegetation, sea ice sensing, multipolarization SAR results, the theoretical modeling of surfaces and volumes, crop condition assessment and productivity estimates, and SIR-B results for vegetation cover. Also considered are the microwave remote sensing of soil moisture, advanced sensors, advanced information extraction, wind and wave remote observations, results from the ESA Remote Sensing satellite, large area crop and land cover statistics, SIR-B results for directional ocean wave spectra, seasonal snow cover, ice sheets, and lake ice, fundamental research in terrain remote sensing, image classification methods, vegetation stress detection, remote sensing of coastal processes, SAR systems and calibration, electromagnetic geophysical methods and signal processing, image processing techniques, and SAR internal wave measurements.

Carver, K. R.↗

Single-Vector Calibration of Wind-Tunnel Force Balances

An improved method of calibrating a wind-tunnel force balance involves the use of a unique load application system integrated with formal experimental design methodology. The Single-Vector Force Balance Calibration System (SVS) overcomes the productivity and accuracy limitations of prior calibration methods. A force balance is a complex structural spring element instrumented with strain gauges for measuring three orthogonal components of aerodynamic force (normal, axial, and side force) and three orthogonal components of aerodynamic torque (rolling, pitching, and yawing moments). Force balances remain as the state-of-the-art instrument that provide these measurements on a scale model of an aircraft during wind tunnel testing. Ideally, each electrical channel of the balance would respond only to its respective component of load, and it would have no response to other components of load. This is not entirely possible even though balance designs are optimized to minimize these undesirable interaction effects. Ultimately, a calibration experiment is performed to obtain the necessary data to generate a mathematical model and determine the force measurement accuracy. In order to set the independent variables of applied load for the calibration 24 NASA Tech Briefs, October 2003 experiment, a high-precision mechanical system is required. Manual deadweight systems have been in use at Langley Research Center (LaRC) since the 1940s. These simple methodologies produce high confidence results, but the process is mechanically complex and labor-intensive, requiring three to four weeks to complete. Over the past decade, automated balance calibration systems have been developed. In general, these systems were designed to automate the tedious manual calibration process resulting in an even more complex system which deteriorates load application quality. The current calibration approach relies on a one-factor-at-a-time (OFAT) methodology, where each independent variable is incremented individually throughout its full-scale range, while all other variables are held at a constant magnitude. This OFAT approach has been widely accepted because of its inherent simplicity and intuitive appeal to the balance engineer. LaRC has been conducting research in a "modern design of experiments" (MDOE) approach to force balance calibration. Formal experimental design techniques provide an integrated view to the entire calibration process covering all three major aspects of an experiment; the design of the experiment, the execution of the experiment, and the statistical analyses of the data. In order to overcome the weaknesses in the available mechanical systems and to apply formal experimental techniques, a new mechanical system was required. The SVS enables the complete calibration of a six-component force balance with a series of single force vectors.

Parker, P. A.↗

Vibration-Induced Droplet Atomization

Thermal management is critical to a number of technologies used in a microgravity environment and in Earth-based systems. Examples include electronic cooling, power generation systems, metal forming and extrusion, and HVAC (heating, venting, and air conditioning) systems. One technique that can deliver the large heat fluxes required for many of these technologies is two-phase heat transfer. This type of heat transfer is seen in the boiling or evaporation of a liquid and in the condensation of a vapor. Such processes provide very large heat fluxes with small temperature differences. Our research program is directed toward the development of a new, two-phase heat transfer cell for use in a microgravity environment. In this paper, we consider the main technology used in this cell, a novel technique for the atomization of a liquid called vibration-induced droplet atomization. In this process, a small liquid droplet is placed on a thin metal diaphragm that is made to vibrate by an attached piezoelectric transducer. The vibration induces capillary waves on the free surface of the droplet that grow in amplitude and then begin to eject small secondary droplets from the wave crests. In some situations, this ejection process develops so rapidly that the entire droplet seems to burst into a small cloud of atomized droplets that move away from the diaphragm at speeds of up to 50 cm/s. By incorporating this process into a heat transfer cell, the active atomization and transport of the small liquid droplets could provide a large heat flux capability for the device. Experimental results are presented that document the behavior of the diaphragm and the droplet during the course of a typical bursting event. In addition, a simple mathematical model is presented that qualitatively reproduces all of the essential features we have seen in a burst event. From these two investigations, we have shown that delayed droplet bursting results when the system passes through a resonance condition. This occurs when the initial acceleration of the diaphragm is higher than the critical acceleration and the driving frequency is larger than the initial resonance frequency of the diaphragm-droplet system. We have incorporated this droplet atomization device into a design for a new heat transfer cell for use in a microgravity environment. The cell is essentially a cylindrical container with a hot surface on one end and a cold surface on the other. The vibrating diaphragm is mounted in the center of the cold surface. Heat transfer occurs through droplet evaporation and condensation on the hot and cold ends of the cell. A prototype of this heat transfer cell has been built and tested. It can operate continuously and provides a modest level of heat transfer, about 20 W/sq cm. Our work during the next few years will be to optimize the design of this cell to see if we can produce a device that has significantly better performance than conventional heat exchangers and heat pipes.

Smith, M. K.↗

The Integrated Medical Model: Statistical Forecasting of Risks to Crew Health and Mission Success

The Integrated Medical Model (IMM) helps capture and use organizational knowledge across the space medicine, training, operations, engineering, and research domains. The IMM uses this domain knowledge in the context of a mission and crew profile to forecast crew health and mission success risks. The IMM is most helpful in comparing the risk of two or more mission profiles, not as a tool for predicting absolute risk. The process of building the IMM adheres to Probability Risk Assessment (PRA) techniques described in NASA Procedural Requirement (NPR) 8705.5, and uses current evidence-based information to establish a defensible position for making decisions that help ensure crew health and mission success. The IMM quantitatively describes the following input parameters: 1) medical conditions and likelihood, 2) mission duration, 3) vehicle environment, 4) crew attributes (e.g. age, sex), 5) crew activities (e.g. EVA's, Lunar excursions), 6) diagnosis and treatment protocols (e.g. medical equipment, consumables pharmaceuticals), and 7) Crew Medical Officer (CMO) training effectiveness. It is worth reiterating that the IMM uses the data sets above as inputs. Many other risk management efforts stop at determining only likelihood. The IMM is unique in that it models not only likelihood, but risk mitigations, as well as subsequent clinical outcomes based on those mitigations. Once the mathematical relationships among the above parameters are established, the IMM uses a Monte Carlo simulation technique (a random sampling of the inputs as described by their statistical distribution) to determine the probable outcomes. Because the IMM is a stochastic model (i.e. the input parameters are represented by various statistical distributions depending on the data type), when the mission is simulated 10-50,000 times with a given set of medical capabilities (risk mitigations), a prediction of the most probable outcomes can be generated. For each mission, the IMM tracks which conditions occurred and decrements the pharmaceuticals and supplies required to diagnose and treat these medical conditions. If supplies are depleted, then the medical condition goes untreated, and crew and mission risk increase. The IMM currently models approximately 30 medical conditions. By the end of FY2008, the IMM will be modeling over 100 medical conditions, approximately 60 of which have been recorded to have occurred during short and long space missions.

Fitts, M. A.↗

Development of a Multivariable Parametric Cost Analysis for Space-Based Telescopes

Over the past 400 years, the telescope has proven to be a valuable tool in helping humankind understand the Universe around us. The images and data produced by telescopes have revolutionized planetary, solar, stellar, and galactic astronomy and have inspired a wide range of people, from the child who dreams about the images seen on NASA websites to the most highly trained scientist. Like all scientific endeavors, astronomical research must operate within the constraints imposed by budget limitations. Hence the importance of understanding cost: to find the balance between the dreams of scientists and the restrictions of the available budget. By logically analyzing the data we have collected for over thirty different telescopes from more than 200 different sources, statistical methods, such as plotting regressions and residuals, can be used to determine what drives the cost of telescopes to build and use a cost model for space-based telescopes. Previous cost models have focused their attention on ground-based telescopes due to limited data for space telescopes and the larger number and longer history of ground-based astronomy. Due to the increased availability of cost data from recent space-telescope construction, we have been able to produce and begin testing a comprehensive cost model for space telescopes, with guidance from the cost models for ground-based telescopes. By separating the variables that effect cost such as diameter, mass, wavelength, density, data rate, and number of instruments, we advance the goal to better understand the cost drivers of space telescopes.. The use of sophisticated mathematical techniques to improve the accuracy of cost models has the potential to help society make informed decisions about proposed scientific projects. An improved knowledge of cost will allow scientists to get the maximum value returned for the money given and create a harmony between the visions of scientists and the reality of a budget.

Dollinger, Courtnay↗

[Development of New Mathematical Methodology in Air Traffic Control for the Analysis of Hybrid Systems]

The aim of this research is to develop new mathematical methodology for the analysis of hybrid systems of the type involved in Air Traffic Control (ATC) problems. Two directions of investigation were initiated. The first used the methodology of nonlinear generalized functions, whose mathematical foundations were initiated by Colombeau and developed further by Oberguggenberger; it has been extended to apply to ordinary differential. Systems of the type encountered in control in joint work with the PI and M. Oberguggenberger. This involved a 'mixture' of 'continuous' and 'discrete' methodology. ATC clearly involves mixtures of two sorts of mathematical problems: (1) The 'continuous' dynamics of a standard control type described by ordinary differential equations (ODE) of the form: {dx/dt = f(x, u)} and (2) the discrete lattice dynamics involved of cellular automata. Most of the CA literature involves a discretization of a partial differential equation system of the type encountered in physics problems (e.g. fluid and gas problems). Both of these directions requires much thinking and new development of mathematical fundamentals before they may be utilized in the ATC work. Rather than consider CA as 'discretization' of PDE systems, I believe that the ATC applications will require a completely different and new mathematical methodology, a sort of discrete analogue of jet bundles and/or the sheaf-theoretic techniques to topologists. Here too, I have begun work on virtually 'virgin' mathematical ground (at least from an 'applied' point of view) which will require considerable preliminary work.

Hermann, Robert↗

Fragmentation cross sections of 28Si at 14.5 GeV/nucleon

We used CR39 plastic nuclear track detectors (C12H18O7) in combination with automatic track measurement techniques to determine total charge changing and partial cross sections for the production of fragments of charge ZF = 6 to ZF = 13 in collisions of 28Si beam nuclei at 14.5 GeV/nucleon in targets H, C, CR39, (C18H38O), Al, Cu, Ag, and Pb. By application of factorization rules, measured partial cross sections are separated into pure nuclear and electromagnetic components. The cross sections for electromagnetic dissociation agree with theoretical models. The results are consistent with a Z2 dependence of virtual photon spectra.

NASA Discipline Number 04-10↗