Linear random operator equations in mathematical physics. II
Stochastic, random and ordinary Green function relations for two point correlation functions in mathematical physics
Adomian, G.↗
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Mathematical models of human operators in simple two-axis manual control systems.
Mathematical model of human compensatory tracking behavior
COMPENSATORY TRACKING↗
Mathematical techniques for estimating operational readiness of complex systems
Development of methods for predicting operational readiness of complex systems based on probability theory is discussed. Operational readiness of systems is defined and mathematical relationships involved in determining readiness are presented. Example of reliability engineering and quality control is included.
Jacquier, I. D.↗
Nonlinear and Digital Man-machine Control Systems Modeling
An adaptive modeling technique is examined by which controllers can be synthesized to provide corrective dynamics to a human operator's mathematical model in closed loop control systems. The technique utilizes a class of Liapunov functions formulated for this purpose, Liapunov's stability criterion and a model-reference system configuration. The Liapunov function is formulated to posses variable characteristics to take into consideration the identification dynamics. The time derivative of the Liapunov function generate the identification and control laws for the mathematical model system. These laws permit the realization of a controller which updates the human operator's mathematical model parameters so that model and human operator produce the same response when subjected to the same stimulus. A very useful feature is the development of a digital computer program which is easily implemented and modified concurrent with experimentation. The program permits the modeling process to interact with the experimentation process in a mutually beneficial way.
Mekel, R.↗
Design of inducers for two-phase operation
A mathematical model and a digital computer program were developed for the design and evaluation of inducers for pumping two-phase oxygen. The mathematical model indicated that any design would have to be run at relatively low speeds to pump two-phase oxygen and that the J-2S oxygen inducer was close to optimum and should perform the task. A J-2S pump was built up and tested in two-phase oxygen at speeds indicated by the mathematical model. The pump was able to handle two-phase oxygen over a wide range of inducer incidence angles and up to a vapor content of 37 percent by volume with very little loss in head. The pump was still able to produce some head at vapor fractions approaching 60 percent.
King, J. A.↗
IMAGES: A digital computer program for interactive modal analysis and gain estimation for eigensystem synthesis
An interactive digital computer program for modal analysis and gain estimation for eigensystem synthesis was written. Both mathematical and operation considerations are described; however, the mathematical presentation is limited to those concepts essential to the operational capability of the program. The program is capable of both modal and spectral synthesis of multi-input control systems. It is user friendly, has scratchpad capability and dynamic memory, and can be used to design either state or output feedback systems.
Jones, R. L.↗
Mathematical models of human operators in simple two-axis manual control systems.
Continuous parameter optimization techniques applied to synthesis of model of human operators in simple two-axis manual control system
MATHEMATICAL MODEL↗
Synthesis and identification of mathematical models for the discrete control behavior of human operators
Synthesis and identification of mathematical models which characterize discrete control behavior of human operators
OPERATOR↗
Research on battery-operated electric road vehicles
Mathematical analysis of battery-operated electric vehicles is presented. Attention is focused on assessing the influence of the battery on the mechanical and dynamical characteristics of dc electric motors with series and parallel excitation, as well as on evaluating the influence of the excitation mode and speed control system on the performance of the battery. The superiority of series excitation over parallel excitation with respect to vehicle performance is demonstrated. It is also shown that pulsed control of the electric motor, as compared to potentiometric control, provides a more effective use of the battery and decreases the cost of recharging.
Varpetian, V. S.↗
Cyber Physical Security (CPS) Extension to Air Traffic Management (ATM) Testbed
The Air Traffic Management (ATM) Testbed is being developed at NASA to enable benefit, impact, safety and cost assessments for accelerating the deployment of Concept and Technologies (C&T) in the National Airspace System (NAS). Today, C&T introduction into the NAS takes decades. The primary reason for this is an inability to assess the operational impact of the interaction between the proposed C&T and operationally deployed systems (Realistic Technologies) in terms of NAS-wide safety, traffic flow efficiency, roles and workload of controllers and traffic managers, and impact on airline fleet operations. Transition of C&T to operations requires mathematical modeling and simulation, Human-in-the-Loop (HITL) testing and shadow-mode evaluation driven by operational data. Whereas interaction with the operational system during testing and stages of deployment is not permissible due to safety concerns, it is certainly possible to create a simulation environment that closely mimics the NAS using the same operational systems/hardware for enabling such assessments. This presentation focuses on a proposed Cyber Physical Security extension to the ATM Testbed for creating a modeling and simulation architecture to study how well the Air Traffic Management system will perform and analyze effectiveness of mitigating security measures against particular cyber-attack scenarios.
Datta, Koushik↗
Graph Theory Roots of Spatial Operators for Kinematics and Dynamics
Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.
Jain, Abhinandan↗
A life cycle cost economics model for projects with uniformly varying operating costs
A mathematical model is developed for calculating the life cycle costs for a project where the operating costs increase or decrease in a linear manner with time. The life cycle cost is shown to be a function of the investment costs, initial operating costs, operating cost gradient, project life time, interest rate for capital and salvage value. The results show that the life cycle cost for a project can be grossly underestimated (or overestimated) if the operating costs increase (or decrease) uniformly over time rather than being constant as is often assumed in project economic evaluations. The following range of variables is examined: (1) project life from 2 to 30 years; (2) interest rate from 0 to 15 percent per year; and (3) operating cost gradient from 5 to 90 percent of the initial operating costs. A numerical example plus tables and graphs is given to help calculate project life cycle costs over a wide range of variables.
Remer, D. S.↗
Theory Of A Pyrotechnically Driven Device
Report presents relations that predict behavior of pyrolytically operated device. Mathematical analysis motivated by need to evaluate performances of squib-driven release nuts. Analysis takes into account most significant of complicated interrelated processes involved in operation of pyrotechnically driven devices and aids in their design and evaluation of test data.
Richter, Robert↗
A theoretical model of phase changes of a klystron due to variation of operating parameters
A mathematical model for phase changes of the VA-876 CW klystron amplifier output is presented and variations of several operating parameters are considered. The theoretical approach to the problem is based upon a gridded gap modeling with inclusion of a second order correction term so that actual gap geometry is reflected in the formulation. Physical measurements are contrasted to theoretical calculations.
Kupiszewski, A.↗
Radiometry Measurements of Mars at 1064 nm Using the Mars Orbiter Laser Altimeter
Measurements by the Mars Orbiter Laser Altimeter (MOLA) on board the Mars Global Surveyor (MGS) may be used to provides a radiometric measurement of Mars in addition to the topographic measurement. We will describe the principle of operation, a mathematical model, and the receiver calibration in this presentation. MOLA was designed primarily to measure Mars topography, surface roughness end the bidirectional reflectance to the laser beam. To achieve the highest sensitivity the receiver detection threshold is dynamically adjusted to be as low as possible while keeping a predetermined false alarm rate. The average false alarm rate 29 monitored in real time on board MOLA via a noise counter, whose output is fed to the threshold control loop. The false alarm rate at a given threshold is a function of the detector output noise which is the sum of the photo detector, shot noise due to the background light seen by the detector and the dark noise. A mathematical model has been developed that can be used to numerically solve for the optical background power given the MOLA threshold setting and the average noise count. The radiance of Mars can then be determined by dividing the optical power by the solid angle subtended by the MOLA receiver, the receiver optical band-width, end the Mars surface area within the receiver field of view. The phase angle which is the sun-Mars-MOLA angle is available from the MGS database. MOLA also measures simultaneously the bidirectional reflectance of Mars vie its 106-lum loser beam at nadir with nearly zero phase angle. The optical bandwidth of the MOLA receiver is 2um full width at half maximum (FWHM) and centered at 106-lum. The receiver field of view is 0.95mrad FWHM. The nominated spacecraft altitude is 100km and the ground track speed is about 3km/s. Under normal operation, the noise counter are read and the threshold levels are updated at 1Hz. The receiver sensitivity is limited by the detector dark noise to about 0.1nW, which corresponds to less than 2% the maximum radiance during daytime from the brightest area on Mars. The results from the mathematical model agree well with the prelaunch measurements at several calibrated optical power levels. The radiance of sunlit Mars estimated with this technique correlates well with the measurement from the MGS. Thermal Emission Spectrometer (TES) and the Hubble Space Telescope at similar wavelength.
Sun, Xiao-Li↗
Baseline mathematics and geodetics for tracking operations
Various geodetic and mapping algorithms are analyzed as they apply to radar tracking systems and tested in extended BASIC computer language for real time computer applications. Closed-form approaches to the solution of converting Earth centered coordinates to latitude, longitude, and altitude are compared with classical approximations. A simplified approach to atmospheric refractivity called gradient refraction is compared with conventional ray tracing processes. An extremely detailed set of documentation which provides the theory, derivations, and application of algorithms used in the programs is included. Validation methods are also presented for testing the accuracy of the algorithms.
James, R.↗
Physical and mathematical modelling of ladle metallurgy operations
Experimental measurements are reported, on the velocity fields and turbulence parameters on a water model of an argon stirred ladle. These velocity measurements are complemented by direct heat transfer measurements, obtained by studying the rate at which ice rods immersed into the system melt, at various locations. The theoretical work undertaken involved the use of the turbulence Navier-Stokes equations in conjunction with the kappa-epsilon model to predict the local velocity fields and the maps of the turbulence parameters. Theoretical predictions were in reasonably good agreement with the experimentally measured velocity fields; the agreement between the predicted and the measured turbulence parameters was less perfect, but still satisfactory. The implications of these findings to the modelling of ladle metallurgical operations are discussed.
El-Kaddah, N.↗
Optimization methods and silicon solar cell numerical models
The goal of this project is the development of an optimization algorithm for use with a solar cell model. It is possible to simultaneously vary design variables such as impurity concentrations, front junction depth, back junctions depth, and cell thickness to maximize the predicted cell efficiency. An optimization algorithm has been developed and interfaced with the Solar Cell Analysis Program in 1 Dimension (SCAPID). SCAPID uses finite difference methods to solve the differential equations which, along with several relations from the physics of semiconductors, describe mathematically the operation of a solar cell. A major obstacle is that the numerical methods used in SCAPID require a significant amount of computer time, and during an optimization the model is called iteratively until the design variables converge to the value associated with the maximum efficiency. This problem has been alleviated by designing an optimization code specifically for use with numerically intensive simulations, to reduce the number of times the efficiency has to be calculated to achieve convergence to the optimal solution. Adapting SCAPID so that it could be called iteratively by the optimization code provided another means of reducing the cpu time required to complete an optimization. Instead of calculating the entire I-V curve, as is usually done in SCAPID, only the efficiency is calculated (maximum power voltage and current) and the solution from previous calculations is used to initiate the next solution.
Girardini, K.↗