Communication theory applied to antenna systems
Communication theory applied to antenna systems - Fourier analysis, linear circuit theory, and aperture theory
ANTENNA↗
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The Theories of Turbulence
The theory of turbulence reached its full growth at the end of the 19th century as a result of the work by Boussinesq and Reynolds. It then underwent a long period of stagnation which ended under the impulse given to it by the development of wind tunnels caused by the needs of aviation. Numerous researchers, attempted to put Reynolds' elementary statistical theory into a more precise form. During the war, some isolated scientists - von Weizsacker and Heisenberg in Germany, Kolmogoroff in Russia, Onsager in the U.S.A. - started a program of research. By a system of assumptions which make it possible to approach the structure of turbulence in well-defined limiting conditions quantitatively, they obtained a certain number of laws on the correlations and the spectrum. Since the late reports have improved the mathematical language of turbulence, it was deemed advisable to start with a detailed account of the mathematical methods applicable to turbulence, inspired at first by the work of the French school, above all for the basic principles, then the work of the foreigners, above all for the theory of the spectrum.
MECHANICS, STATISTICAL↗
Some problems on the theory of creep
The term creep of metals is applied to the phenomenon in which, at temperatures beyond a certain limit, the metal subjected to a load slowly undergoes deformation with time. For the case of steel, the creep phenomenon must be taken into account at temperatures above 400 degrees C. Very slow deformations for a prolonged period are cumulative and lead either to inadmissible changes in the dimensions of a structural part or to its failure. The theory of creep constitutes part of the mechanics of dense media and the mechanical formulation of the problem may be given as the following: a body is subjected to the action of a given system of forces, or initial displacements are prescribed on its surface. It is required to find the stress distribution in the body and the changes or its deformations with time. For the solution of the problem of creep as thus formulated, a mechanical theory of creep is required. Such theory must necessarily bear an external, overall character based, not on the investigation of microprocesses, but on the results of mechanical tests.
METALS - CREEP↗
Applications of Ergodic Theory to Coverage Analysis
The study of differential equations, or dynamical systems in general, has two fundamentally different approaches. We are most familiar with the construction of solutions to differential equations. Another approach is to study the statistical behavior of the solutions. Ergodic Theory is one of the most developed methods to study the statistical behavior of the solutions of differential equations. In the theory of satellite orbits, the statistical behavior of the orbits is used to produce 'Coverage Analysis' or how often a spacecraft is in view of a site on the ground. In this paper, we consider the use of Ergodic Theory for Coverage Analysis. This allows us to greatly simplify the computation of quantities such as the total time for which a ground station can see a satellite without ever integrating the trajectory, see Lo 1,2. More over, for any quantity which is an integrable function of the ground track, its average may be computed similarly without the integration of the trajectory. For example, the data rate for a simple telecom system is a function of the distance between the satellite and the ground station. We show that such a function may be averaged using the Ergodic Theorem.
Ergodic Theory↗
The Orbital Motion of the Martian Satellites: An Application of Artificial Satellite Theory
Since the Martian satellites Phobos and Deimos were discovered in 1877, several theories have been developed to represent their orbital motions. In 1972, Sinclair created a dynamical theory, which Morley made more accurate in 1990. The author uses the Sinclair-Morley theory to develop Martian satellite ephemerides for JPL s Mars Exploration Program.
ephemerides↗
Scattering theories and radar return
Scattering theories and radar return - theory of bistatic radar return from statistically rough surface and literature survey on scattering theories
SURFACE ROUGHNESS↗
On the thermodynamics and approximation theory of viscoelastic materials.
Thermodynamics and approximation theory of viscoelastic materials, developing Coleman-Noll theory, thermodynamic theory for fluids, etc
MATERIALS SCIENCE↗
Lifting-surface theory for calculating the loading induced on a wing by a flap
A method is described for using lifting-surface theory to obtain the pressure distribution on a wing with a trailing-edge flap or control surface. The loading has a logarithmic singularity at the flap edges, which may be determined directly by the method of matched asymptotic expansions. Expressions are given for the singular flap loading for various flap hinge line and side edge geometries, both for steady and unsteady flap deflection. The regular part of the flap loading must be obtained by inverting the lifting-surface-theory integral equation relating the pressure and the downwash on the wing: procedures are described to accomplish this for a general wing and flap geometry. The method is applied to several example wings, and the results are compared with experimental data. Theory and test correlate well.
Johnson, W. A.↗
A note on 'The main problem of satellite theory for small eccentricities, by A. Deprit and A. Rom, 1970.'
Criticism of Deprit and Rom's (1970) extension of Brouwer's (1959) first-order satellite theory to the third order in J sub 2. It is noted that Deprit and Rom's theory suffers from the drawback that the perturbations of all orders are expressed as infinite power series in the eccentricity e. It is demonstrated that Deprit and Rom's reported failure to extend Brouwer's theory to the second order in a closed form by means of Lie transforms is due to an oversight and is not caused by difficulties inherent in the problem or in the particular perturbation method used.
Aksnes, K.↗
A generalized theory on the noise generation from supersonic shear layers.
A generalization is presented of Phillips' (1960) theory of noise generation by supersonic turbulent shear layers. Both Mach wave radiation and non-Mach wave noise radiation mechanisms are considered. The range of validity of Phillips' theory has been expanded to include the low supersonic and transonic ranges. These generalizations are important not only for their analytical rigor, but also for their prospective applications to practical problems in jet noise prediction and control. The noise generation mechanisms in a supersonic jet are found to differ from those in a subsonic jet. The theory is considered to offer some prospects of answering important questions in supersonic jet noise, such as noise source distribution, mean flow refraction effects, directivity, spectrum, and efficiency of noise radiation.
Pao, S. P.↗
Theory of discrete wave packets in the solar wind.
Discrete wave packets were observed by Ogo 5 and earlier satellites. These waves were believed to be in the whistler mode. Since their group velocities were found to be smaller than the solar-wind speed, these waves could not have been generated in the bow shock and could not have propagated upstream later. The present theory discusses a mechanism similar to that of the echo phenomenon in plasma physics discovered in recent years. The present theory enables us to explain (a) why the wave packets were associated with the bow shock, (b) why the wave packets were characterized by coherent oscillations, and (c) why the wave packets had group velocities smaller than the solar wind and yet could still occur in the solar wind. In short, our theory is able to interpret all the essential features deduced from the observational data.
Wu, C. S.↗
The Martian bow wave - Theory and observation.
Refinement of the relationship between the trajectory of Mariner 4 in its fly-by of Mars and the calculated location of a proposed Martian bow arising from interaction of the solar wind and the ionosphere by inclusion of aberration effects of the planet's motion about the sun. The modified theory indicates that the bow wave was crossed twice during a three-hour interval following the time of closest approach of Mariner 4 to Mars, instead of being missed slightly by the spacecraft as indicated in a previous paper in which the theory of this interaction was presented, and the solar wind was considered, for simplicity, to flow along the sun-Mars line. It is shown that the observed magnetic field changed abruptly at virtually the precise times of the shock crossings indicated by the theory. Although malfunction of the plasma probe prevents observational confirmation of these as shock crossings, this coincidence supports the recent suggestion of the magnetometer experimenters that a bow wave may have been traversed. It also supports the interpretation that the bow wave results from interaction of the solar wind with the ionosphere, and not with a weak planetary magnetic field.
Spreiter, J. R.↗
Formation of spectral lines in planetary atmospheres. I - Theory for cloudy atmospheres: Application to Venus.
The theory of the formation of spectral lines in a cloudy planetary atmosphere is studied in detail. It is shown that models based upon homogeneous, isotropically scattering atmospheres cannot be used to reproduce observed spectroscopic features of phase effect and the shape of spectral lines for weak and strong bands. The theory must, therefore, be developed using an inhomogeneous (gravitational) model of a planetary atmosphere, accurately incorporating all the physical processes of radiative transfer. Such a model of the lower Venus atmosphere, consistent with our present knowledge, is constructed. The results discussed in this article demonstrate the effects of the parameters that describe the atmospheric model on the spectroscopic features of spectral line profile and phase effect, at visible and near infrared wavelengths. This information enables us to develop a comprehensive theory of line formation in a Venus atmosphere.
Hunt, G. E.↗
Theory of a general class of dissipative processes.
Development of a theory of periodic processes that is of sufficient generality for being applied to systems defined by partial differential equations (distributed parameter systems) and functional differential equations of the retarded and neutral type (hereditary systems), as well as to systems arising in the theory of elasticity. In particular, the attempt is made to develop a meaningful general theory of dissipative periodic systems with a wide range of applications.
Hale, J. K.↗
Assessment of a transitional boundary layer theory at low hypersonic Mach numbers
An investigation was carried out to assess the accuracy of a transitional boundary layer theory in the low hypersonic Mach number regime. The theory is based upon the simultaneous numerical solution of the boundary layer partial differential equations for the mean motion and an integral form of the turbulence kinetic energy equation which controls the magnitude and development of the Reynolds stress. Comparisions with experimental data show the theory is capable of accurately predicting heat transfer and velocity profiles through the transitional regime and correctly predicts the effects of Mach number and wall cooling on transition Reynolds number. The procedure shows promise of predicting the initiation of transition for given free stream disturbance levels. The effects on transition predictions of the pressure dilitation term and of direct absorption of acoustic energy by the boundary layer were evaluated.
Shamroth, S. J.↗
Hydrostatic figure of the earth: Theory and results
The complete development of the mathematical theory of hydrostatic equilibrium for the earth is recounted. Modifications of the first order theory are given along with the subsequent extension to the second order. In addition, the equations are presented which resulted from a revision of the second order theory to suit the new applications and data types of the post-artificial earth satellite era.
Khan, M. A.↗
The BMW analytic aerodynamic drag method for the Vinti satellite theory
In order to retain separability in the Vinti theory of earth satellite motion when a non conservative force such as air drag is considered, a set of variational equations for the orbital elements are introduced, and expressed as functions of the transverse, radial, and normal components of the nonconservative forces acting on the system. In particular, the atmospheric density profile is written as a fitted exponential function of the eccentric anomaly, which reproduces tabular values of static model atmospheric densities at all altitudes to within ninety-eight percent and simultaneously reduces the variational equations to indefinite integrals with closed form evaluations, whose limits are in terms of the eccentric anomaly. The values of the limits for any arbitrary time interval are obtained from the Vinti program. Results of the BMW (Bonavito, Mistretta, Watson) theory for the case of the intense air drag satellites San Marco-2 and Air Force Cannonball are given. These results indicate that the satellite ephemerides produced by the BMW theory in conjunction with the Vinti program are of very high accuracy. In addition, since the program is entirely analytic, several months of ephemerides can be obtained within a few seconds of computer time.
Watson, J. S.↗
Numerical analysis of stiffened shells of revolution. Volume 1: Theory manual for STARS-2S, 2B, 2V digital computer programs
The theoretical analysis background for the STARS-2 (shell theory automated for rotational structures) program is presented. The theory involved in the axisymmetric nonlinear and unsymmetric linear static analyses, and the stability and vibrations (including critical rotation speed) analyses involving axisymmetric prestress are discussed. The theory for nonlinear static, stability, and vibrations analyses, involving shells with unsymmetric loadings are included.
Svalbonas, V.↗