Comment on 'Optimal control via mathematical programming'
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Wood, L. J.↗
SEARCH · Engineering Papers
Results for “Mathematics”
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A mathematical model of turbulence in flows with uniform stationary velocity gradients
Certain cases of turbulence as a postinstability state of a fluid in motion modeled by the introduction of multivalued velocity fields are examined. The turbulence is regarded as occurring in the form of random pulsations which grow until the external energy input in the average flow is balanced by the dissipated energy of pulsations by means of turbulent friction. Closed form analytic solutions are shown to be possible when the considered velocity fields, the pulsation velocity and the fluid velocity, are decoupled.
Zak, M. A.↗
CARE 3 phase 2 report - mathematical description
CARE III (Computer-Aided Reliability Estimation, version three) a computer program designed to help estimate the reliability of complex, redundant systems is described. Although the program can model a wide variety of redundant structures, it was developed specifically for fault tolerant avionics systems. CARE III generalizes the class of system structures that can be modeled and greatly expands the coverage model to take into account such effects as intermittent and transient faults, latent faults, and error propagation.
Stiffler, J. J.↗
Description of a mathematical model and computer simulation of separation of the nose cap from the solid rocket booster
A system of equations which models the motion of the Solid Rocket Booster Nose Cap upon separation is described. The computer program which utilizes these equations to generate nose cap trajectories is described in detail. Application of the program to simulate a rocket sled test of the nose cap separation is discussed and the results of the applications are presented. With the information given a user should be able to exercise the computer program with a minimum of effort.
Schwaniger, A. J., Jr.↗
Mathematical models of physiological systems
Calcium/musculoskeletal, cardiovascular, erythropoieses, and fluid and electrolyte/renal regulation are discussed. Modeling and software development are also discussed.
White, R. J.↗
Establishment of a center of excellence for applied mathematical and statistical research
The state of the art was assessed with regards to efforts in support of the crop production estimation problem and alternative generic proportion estimation techniques were investigated. Topics covered include modeling the greeness profile (Badhwarmos model), parameter estimation using mixture models such as CLASSY, and minimum distance estimation as an alternative to maximum likelihood estimation. Approaches to the problem of obtaining proportion estimates when the underlying distributions are asymmetric are examined including the properties of Weibull distribution.
Woodward, W. A.↗
Mathematical developments regarding the general theory of the Earth magnetism
A literature survey on the Earth's magnetic field, citing the works of Gauss, Erman-Petersen, Quintus Icilius and Neumayer is presented. The general formulas for the representation of the potential and components of the Earth's magnetic force are presented. An analytical representation of magnetic condition of the Earth based on observations is also made.
Schmidt, A.↗
A mathematical characterization of vegetation effect on microwave remote sensing from the Earth
In passive microwave remote sensing of the earth, a theoretical model that utilizes the radiative transfer equations was developed to account for the volume scattering effects of the vegetation canopy. Vegetation canopies such as alfalfa, sorghum, and corn are simulated by a layer of ellipsoidal scatterers and cylindrical structures. The ellipsoidal scatterers represent the leaves of vegetation and are randomly positioned and oriented. The orientation of ellipsoids is characterized by a probability density function of Eulerian angles of rotation. The cylindrical structures represent the stalks of vegetation and their radii are assumed to be much smaller than their lengths. The underlying soil is represented by a half-space medium with a homogeneous permittivity and uniform temperature profile. The radiative transfer quations are solved by a numerical method using a Gaussian quadrature formula to compute both the vertical and horizontal polarized brightness temperature as a function of observation angle. The theory was applied to the interpretation of experimental data obtained from sorghum covered fields near College Station, Texas.
Choe, Y.↗
Development of a distributed-parameter mathematical model for simulation of cryogenic wind tunnels
A one-dimensional distributed-parameter dynamic model of a cryogenic wind tunnel was developed which accounts for internal and external heat transfer, viscous momentum losses, and slotted-test-section dynamics. Boundary conditions imposed by liquid-nitrogen injection, gas venting, and the tunnel fan were included. A time-dependent numerical solution to the resultant set of partial differential equations was obtained on a CDC CYBER 203 vector-processing digital computer at a usable computational rate. Preliminary computational studies were performed by using parameters of the Langley 0.3-Meter Transonic Cryogenic Tunnel. Studies were performed by using parameters from the National Transonic Facility (NTF). The NTF wind-tunnel model was used in the design of control loops for Mach number, total temperature, and total pressure and for determining interactions between the control loops. It was employed in the application of optimal linear-regulator theory and eigenvalue-placement techniques to develop Mach number control laws.
Tripp, J. S.↗
Mathematical modeling of damage in unidirectional composites
Extending the work of Goree and Gross (1979), solutions are given for a two-dimensional region of unidirectional fibers embedded in an elastic matrix whose initial flaw may take the form of a transverse notch, a rectangular cutout, or a circular hole. Subsequent flaw-induced damage is generated by remote stresses acting parallel to the fibers. For the case of such ductile matrix composites as boron/aluminum, present results indicate that both longitudinal matrix yielding and transverse notch extension must be included in order for the model to agree with experimental results. Little difference is found for the three types of initial damage considered. In all cases, the presence of additional damage changes the nature of stress distribution through the unbroken fibers.
Goree, J. G.↗
Mathematical analysis for radiometric calorimetry of a radiating sphere
Equations are derived from which the temperature dependence of both the specific heat and the thermal diffusivity of a spherical sample of material can be calculated from observations of the time dependence of the surface temperature and the time-rate of energy loss from the sample as it cools. The derivation takes into account the nonuniformity of the interior temperature field of the sample, and the resulting equations can be applied not only to radiative cooling, but also to any other cooling mechanism that does not violate the assumed spherical symmetry. The analysis excludes change of phase, but it does take thermal expansion into account. To permit the making of estimates necessary for the design of radiative cooling experiments, a universal temperature-time cooling curve is derived for the post-transient cooling regime of a radiating sphere of any size with arbitrary, but constant, thermal parameters.
Schmid, L. A.↗
Mathematical Storage-Battery Models
Empirical formula represents performance of electrical storage batteries. Formula covers many battery types and includes numerous coefficients adjusted to fit peculiarities of each type. Battery and load parameters taken into account include power density in battery, discharge time, and electrolyte temperature. Applications include electric-vehicle "fuel" gages and powerline load leveling.
Chapman, C. P.↗
Center of Excellence for Applied Mathematical and Statistical Research in support of development of multicrop production monitoring capability
Efforts in support of the development of multicrop production monitoring capability are reported. In particular, segment level proportion estimation techniques based upon a mixture model were investigated. Efforts have dealt primarily with evaluation of current techniques and development of alternative ones. A comparison of techniques is provided on both simulated and LANDSAT data along with an analysis of the quality of profile variables obtained from LANDSAT data.
Woodward, W. A.↗
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.↗
Finite-difference fluid dynamics computer mathematical models for the design and interpretation of experiments for space flight
Numerical methods are used to design a spherical baroclinic flow model experiment of the large scale atmosphere flow for Spacelab. The dielectric simulation of radial gravity is only dominant in a low gravity environment. Computer codes are developed to study the processes at work in crystal growing systems which are also candidates for space flight. Crystalline materials rarely achieve their potential properties because of imperfections and component concentration variations. Thermosolutal convection in the liquid melt can be the cause of these imperfections. Such convection is suppressed in a low gravity environment. Two and three dimensional finite difference codes are being used for this work. Nonuniform meshes and implicit iterative methods are used. The iterative method for steady solutions is based on time stepping but has the options of different time steps for velocity and temperature and of a time step varying smoothly with position according to specified powers of the mesh spacings. This allows for more rapid convergence. The code being developed for the crystal growth studies allows for growth of the crystal as the solid-liquid interface. The moving interface is followed using finite differences; shape variations are permitted. For convenience in applying finite differences in the solid and liquid, a time dependent coordinate transformation is used to make this interface a coordinate surface.
Roberts, G. O.↗
Mathematical analysis
Simple continuum models used in the design, analysis, and control of large space structures are examined. Particular emphasis is placed on boundary value problems associated with the Load Correction Method and control problems involving partial differential equations for the large space structure models. Partial differential equations will be used to model a large space structure, base the design of an optimal controller on this model, approximate the resulting optimal control model, and compare the results with data from other methods.
Donaldson, J. A.↗
Mathematical Modelling of High-speed Ribbbon Systems: a Case Study of Edge-defined Film-fed Growth
Finite element numerical analysis was used to solve the coupled problem of heat transfer and capillarity to describe low and high speed silicon sheet growth in meniscus defined systems. Heat transfer models which neglect the details of convective heat flow in the melt are used to establish operating limits for an EFG system in terms of the growth rate, die temperature and the static head acting on the meniscus. It is shown that convective heat transfer in the melt becomes important only at high growth rates or for materials with low thermal conductivities.
Ettouney, H. M.↗
OMV: A simplified mathematical model of the orbital maneuvering vehicle
A model of the orbital maneuvering vehicle (OMV) is presented which contains several simplications. A set of hand controller signals may be used to control the motion of the OMV. Model verification is carried out using a sequence of tests. The dynamic variables generated by the model are compared, whenever possible, with the corresponding analytical variables. The results of the tests show conclusively that the present model is behaving correctly. Further, this model interfaces properly with the state vector transformation module (SVX) developed previously. Correct command sentence sequences are generated by the OMV and and SVX system, and these command sequences can be used to drive the flat floor simulation system at MSFC.
Teoh, W.↗