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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1971

Two examples in the time optimal control theory of distributed parameter systems.

The behavior of hyperbolic and parabolic partial differential equations is contrasted by studying the point-to-point time-optimal control problem for the equation of heat conduction and the equation of motion of a vibrating string. A maximal principle is obtained for the time-optimal control of the one-dimensional heat equation, and it is proven that time optimal controls are weakly bang-bang. The bang-bang principle is proven to be invalid for hyperbolic equations because of the finite speed of wave propagation. In the case of boundary value control of the vibrating spring, the latter is demonstrated by deriving an explicit formula for the time optimal control.

Quinn, J. P.↗
NASA NTRS1973

Sufficient Statistics: an Example

The feature selection problem is considered resulting from the transformation x = Bz where B is a k by n matrix of rank k and k is or = to n. Such a transformation can be considered to reduce the dimension of each observation vector z, and in general, such a transformation results in a loss of information. In terms of the divergence, this information loss is expressed by the fact that the average divergence D sub B computed using variable x is less than or equal to the average divergence D computed using variable z. If D sub B = D, then B is said to be a sufficient statistic for the average divergence D. If B is a sufficient statistic for the average divergence, then it can be shown that the probability of misclassification computed using variable x (of dimension k is or = to n) is equal to the probability of misclassification computed using variable z. Also included is what is believed to be a new proof of the well known fact that D is or = to D sub B. Using the techniques necessary to prove the above fact, it is shown that the Brattacharyya distance as measured by variable x is less than or equal to the Brattacharyya distance as measured by variable z.

Quirein, J.↗
NASA NTRS1973

Avalanche mode of motion - Implications from lunar examples.

A large avalanche (21 square kilometers) at the Apollo 17 landing site moved out several kilometers over flat ground beyond its source slope. If not triggered by impacts, then it was as 'efficient' as terrestrial avalanches attributed to air-cushion sliding. Evidently lunar avalanches are able to flow despite the lack of lubricating or cushioning fluid.

Howard, K. A.↗
NASA NTRS1973

19-20 May 1969, an example of type III emission during the impulsive phase of flares.

Examination of two multiple impulsive events in May 1969, and comparison of their impulsive Ha, hard X-ray, and microwave components with the observed type III emission. No good correlation was observed between meter intensity and the degree of simultaneous Ha outflow, although almost every type III burst had some associated Ha activity. Correspondingly, an inverse relationship existed between X-ray and type III emission - i.e., a strong meter burst accompanied weak X-radiation. This, along with the fact that sufficient energetic electrons were normally present to produce the X rays, implies that the trajectory, rather than electron spectrum or supply, determines whether type III noise is observed during an impulsive event.

Vorpahl, J.↗
NASA NTRS1973

An example of anticorrelation of auroral particles and electric fields.

The question of whether correlation or anticorrelation should occur is complex and depends on many factors, e.g., the internal impedance of the source; the Pedersen conductivity, which in turn is dependent on the incident energy of the precipitated particles; whether space charge can build up; and the magnitude of the incoming flux. Data are presented from a case in which an anticorrelation between auroral particles and electric fields is especially striking. The data were obtained from a Nike Tomahawk launched from the Norwegian rocket range at Andoya. The experiments carried are described briefly. The data support the anticorrelation model as one mechanism that can affect the electric field strength in auroral regions.

Maynard, N. C.↗
NASA NTRS1974

A discussion of interplanetary post-shock flows with two examples

Plasma and magnetometer observations are described for two flare-associated shock flows and the comparison of them with models. One represents a class of flows where the shock is followed by a stream and separated from it by a region in which density temperature and speed decrease monotonically. The other is characterized by a complex region between the shock and the following stream, which has many discontinuities and fluctuations, but in which there is no increase in helium concentration. These two types of flow can be distinguished using ground magnetograms, since the former shows no sudden impulses following the shock, whereas the latter shows many.

Ogilvie, K. W.↗
NASA NTRS1974

Examples of oil cavitation erosion in positive displacement pumps

The effects of cavitation flow on piston type, positive displacement, hydraulic pumps are discussed. The operating principles of the pump and the components which are most subject to erosion effects are described. The mechanisms of cavitation phenomena are identified from photographic records. Curves are developed to show the solubility of air in water, oil-water emulsion, and industrial hydraulic oil.

Halat, J. A.↗
NASA NTRS1974

Finite elasto-plastic deformation. I - Theory and numerical examples

It is demonstrated that the problem of elasto-plastic finite deformation is governed by a quasi-linear model irrespective of deformation magnitude. This feature follows from the adoption of a rate viewpoint toward finite deformation analysis in an Eulerian reference frame. Objectivity of the formulation is preserved by introduction of a frame-invariant stress rate. Equations for piece-wise linear incremental finite element analysis are developed by application of the Galerkin method to the instantaneously linear governing differential equations of the quasi-linear model. Numerical solution capability has been established for problems of plane strain and plane stress. The accuracy of the numerical analysis is demonstrated by consideration of a number of problems of homogeneous finite deformation admitting comparative analytic solution. It is shown that accurate, objective numerical solutions can be obtained for problems involving dimensional changes of an order of magnitude and rotations of a full radian.

Osias, J. R.↗
NASA NTRS1974

Some examples of exact and approximate solutions in small particle scattering - A progress report

The formulation of basic equations from which the scattering of radiation by a localized variation in a medium is discussed. These equations are developed in both the differential and the integral form. Primary interest is in the scattering of electromagnetic waves for which the solution of the vector wave equation with appropriate boundary conditions must be considered. Scalar scattering by an infinite homogeneous isotropic circular cylinder, and scattering of electromagnetic waves by infinite circular cylinders are treated, and the case of the finite circular cylinder is considered. A procedure is given for obtaining angular scattering distributions from spheroids.

Greenberg, J. M.↗
NASA NTRS1975

An example of the use of laboratory results in the optics of the sea

A relation between the average cosine in underwater conditions and the coefficient of diffuse reflection is used to determine the optical characteristics of the sea. The cosine is considered equal to the ratio of the radiation flux through a horizontal cross section to the flux irradiating a spherical surface surrounding the observation point.

Timofeyeva, V. A.↗
NASA NTRS1975

A counter example in linear feature selection theory

The linear feature selection problem in multi-class pattern recognition is described as that of linearly transforming statistical information from n-dimensional (real Euclidean) space into k-dimensional space, while requiring that average interclass divergence in the transformed space decrease as little as possible. Divergence is the expected interclass divergence derived from Hajek two-class divergence; it is known that there always exists a k x n matrix B such that the transformation determined by B maximizes the divergence in k-dimensional space. It is known that, if Q is any k x k invertible matrix, and B is as defined above, then QB again maximizes the divergence in k-space. It is shown that the converse of this result is false: two matrices exist, B sub 1 and B sub 2, each of which maximizes transformed divergence, which are not related in the fashion B sub 2 = QB sub 1 for any k x k matrix Q.

Brown, D. R.↗
NASA NTRS1974

Discretized partial differential equations - Examples of control systems defined on modules

The purpose of this paper is to show how the important problems of linear system theory can be solved concisely for a particular class of linear systems, namely block circulant systems, by exploiting the algebraic structure. This type of system arises in lumped approximations to linear partial differential equations. The computation of the transition matrix, the variation of constants formula, observability, controllability, pole allocation, realization theory, stability and quadratic optimal control are discussed. In principle, all questions which are solved here could also be solved by standard methods; the present paper clearly exposes the structure of the solution, and thus permits various savings in computational effort.

Brockett, R. W.↗