Two counterexamples to Aizerman's conjecture.
Oscillation formation by violation of sufficient conditions of asymptotic stability in linear system
STABILITY TEST↗
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On asymptotic analysis of gaseous squeeze-film bearings.
HF gaseous squeeze film bearing asymptotically analyzed by considering internal and edge regions separately
GASEOUS DIFFUSION↗
Degeneration of the solutions of certain well- posed systems of partial differential equations depending on a small parameter.
Degeneration of solutions of well-posed systems of first order partial differential equations when particular parameter approaches zero
BOUNDARY VALUE↗
On the asymptotic kinetic equation for inhomogeneous plasmas.
Asymptotic kinetic equation for inhomogeneous plasma compared to results for initial value problem and Bogoliubov method
ASYMPTOTIC FUNCTION↗
An asymptotic solution of conical shells of constant thickness.
Constant thickness elastic conical shells subject to lateral loads, deriving asymptotic solution
ELASTIC SHELL↗
Cosmic-ray variations and the interplanetary sector structures.
Fifteen passages of interplanetary sector structures that occurred between December 1967 and June 1968 are examined. A spherical harmonic analysis of cosmic ray intensity is performed to obtain cosmic ray intensity variations as a function of asymptotic latitude, longitude, and universal time. A clear north-south asymmetry of cosmic ray intensity, which depends on the sign of the interplanetary sector magnetic fields, is revealed.
Yoshida, S.↗
Some recent developments in predicting unsteady loadings caused by control surface motions
Solution instabilities are identified within the procedures used to predict unsteady loadings due to motions of swept hingeline control surfaces. A preferred solution process that demonstrates the need of calculating smooth residual downwash distributions is described. Numerical results displaying erratic solution behavior when use is made of various forms of pressure expressions currently employed in control surface analyses are presented. A new expression of the asymptotic pressure function is derived, which exactly satisfies the change in boundary conditions around the boundary of the control surface. Results of applying the new pressure function are presented and indicate that stable converged solutions may be achieved for predicting the unsteady loadings caused by motions of swept hingeline control surfaces.
Rowe, W. S.↗
The Investigation of Optimal Discrete Approximations for Real Time Flight Simulations
The results are presented of an investigation of discrete approximations for real time flight simulation. Major topics discussed include: (1) consideration of the particular problem of approximation of continuous autopilots by digital autopilots; (2) use of Bode plots and synthesis of transfer functions by asymptotic fits in a warped frequency domain; (3) an investigation of the various substitution formulas, including the effects of nonlinearities; (4) use of pade approximation to the solution of the matrix exponential arising from the discrete state equations; and (5) an analytical integration of the state equation using interpolated input.
Parrish, E. A.↗
Analysis of the physical atomic forces between noble gas atoms, alkali ions and halogen ions
The physical forces between atoms and molecules are important in a number of processes of practical importance, including line broadening in radiative processes, gas and crystal properties, adhesion, and thin films. The components of the physical forces between noble gas atoms, alkali ions, and halogen ions are analyzed and a data base for the dispersion forces is developed from the literature based on evaluations with the harmonic oscillator dispersion model for higher order coefficients. The Zener model of the repulsive core is used in the context of the recent asymptotic wave functions of Handler and Smith; and an effective ionization potential within the Handler and Smith wave functions is defined to analyze the two body potential data of Waldman and Gordon, the alkali-halide molecular data, and the noble gas crystal and salt crystal data. A satisfactory global fit to this molecular and crystal data is then reproduced by the model to within several percent. Surface potentials are evaluated for noble gas atoms on noble gas and salt crystal surfaces with surface tension neglected. Within this context, the noble gas surface potentials on noble gas and salt crystals are considered to be accurate to within several percent.
Wilson, J. W.↗
Development of confidence limits by pivotal functions for estimating software reliability
The utility of pivotal functions is established for assessing software reliability. Based on the Moranda geometric de-eutrophication model of reliability growth, confidence limits for attained reliability and prediction limits for the time to the next failure are derived using a pivotal function approach. Asymptotic approximations to the confidence and prediction limits are considered and are shown to be inadequate in cases where only a few bugs are found in the software. Departures from the assumed exponentially distributed interfailure times in the model are also investigated. The effect of these departures is discussed relative to restricting the use of the Moranda model.
Dotson, Kelly J.↗
A Kinematically Consistent Two-Point Correlation Function
A simple kinematically consistent expression for the longitudinal two-point correlation function related to both the integral length scale and the Taylor microscale is obtained. On the inner scale, in a region of width inversely proportional to the turbulent Reynolds number, the function has the appropriate curvature at the origin. The expression for two-point correlation is related to the nonlinear cascade rate, or dissipation epsilon, a quantity that is carried as part of a typical single-point turbulence closure simulation. Constructing an expression for the two-point correlation whose curvature at the origin is the Taylor microscale incorporates one of the fundamental quantities characterizing turbulence, epsilon, into a model for the two-point correlation function. The integral of the function also gives, as is required, an outer integral length scale of the turbulence independent of viscosity. The proposed expression is obtained by kinematic arguments; the intention is to produce a practically applicable expression in terms of simple elementary functions that allow an analytical evaluation, by asymptotic methods, of diverse functionals relevant to single-point turbulence closures. Using the expression devised an example of the asymptotic method by which functionals of the two-point correlation can be evaluated is given.
Ristorcelli, J. R.↗
Determination of the scaled optical thickness of clouds from reflected solar radiation measurements
A method for determination of scaled optical thickness from reflected solar radiation measurements is described in which measurements of the reflected function are compared with asymptotic expressions for the reflection function of optically thick layers. Analytic formulas are derived which show the dependence of the reflection and transmission functions of nonabsorbing atmospheres on cloud optical thickness, ground albedo, and the asymmetry factor. An expression is derived which shows that the ground albedo produces a constant bias in the derived optical thickness, regardless of the value of the measured reflection function. Results from an analysis of high-resolution images, obtained in Oklahoma, of the reflection function of clouds shows the impact of details of the single scattering phase function on the derived optical thickness.
King, Michael D.↗
On the Applicability of High-frequency Approximations to Lilley's Equation
Three forms of the high-frequency asymptotic Green's function for Lilley's equation are reviewed and compared to the exact solution over wide range of Strouhal numbers. The asymmetric approximation, which applies to sources away form the jet axis, and the quasi-symmetric approximation, which is arrived at by making a near-axis source assumption, are both obtained for parallel round jets from a formal Fourier-transform solution. The ray-theory solution, which is the only high-frequency approximation that can be applied to more general mean flows, follows from a WKB ansatz and is shown to be closely related to the asymmetric approximation. The comparisons show that the best overall prediction of the exact Green's function is given by the asymmetric approximation which remains accurate down to a Strouhal number of 1/2. The close relationship between the asymmetric and ray-theory approximations suggests that the high-frequency asymptotic Green's function for more general mean flows would be similarly successful.
Wundrow, David W.↗
Asymptotic fixed points theorems and periodic systems of functional-differential equations correlation function calculation of higher order corrections to the lattice thermal conductivity
Asymptotic fixed point theorems and periodic systems of functional-differential equations
DIFFERENTIAL EQUATION↗
Computer program for Bessel and Hankel functions
A set of FORTRAN subroutines for calculating Bessel and Hankel functions is presented. The routines calculate Bessel and Hankel functions of the first and second kinds, as well as their derivatives, for wide ranges of integer order and real or complex argument in single or double precision. Depending on the order and argument, one of three evaluation methods is used: the power series definition, an Airy function expansion, or an asymptotic expansion. Routines to calculate Airy functions and their derivatives are also included.
Kreider, Kevin L.↗
Numerical evaluation of the incomplete airy functions and their application to high frequency scattering and diffraction
The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals of such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. Here, a convergent series solution form for the incomplete Airy functions is derived. Asymptotic expansions involving several terms were also developed and serve as large argument approximations. The combination of the series solution form with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.
Constantinides, E. D.↗
Efficient and accurate computation of the incomplete Airy functions
The incomplete Airy integrals serve as canonical functions for the uniform ray optical solutions to several high-frequency scattering and diffraction problems that involve a class of integrals characterized by two stationary points that are arbitrarily close to one another or to an integration endpoint. Integrals with such analytical properties describe transition region phenomena associated with composite shadow boundaries. An efficient and accurate method for computing the incomplete Airy functions would make the solutions to such problems useful for engineering purposes. In this paper a convergent series solution for the incomplete Airy functions is derived. Asymptotic expansions involving several terms are also developed and serve as large argument approximations. The combination of the series solution with the asymptotic formulae provides for an efficient and accurate computation of the incomplete Airy functions. Validation of accuracy is accomplished using direct numerical integration data.
Constantinides, E. D.↗
A critical evaluation of two-equation models for near wall turbulence
A variety of two-equation turbulence models,including several versions of the K-epsilon model as well as the K-omega model, are analyzed critically for near wall turbulent flows from a theoretical and computational standpoint. It is shown that the K-epsilon model has two major problems associated with it: the lack of natural boundary conditions for the dissipation rate and the appearance of higher-order correlations in the balance of terms for the dissipation rate at the wall. In so far as the former problem is concerned, either physically inconsistent boundary conditions have been used or the boundary conditions for the dissipation rate have been tied to higher-order derivatives of the turbulent kinetic energy which leads to numerical stiffness. The K-omega model can alleviate these problems since the asymptotic behavior of omega is known in more detail and since its near wall balance involves only exact viscous terms. However, the modeled form of the omega equation that is used in the literature is incomplete-an exact viscous term is missing which causes the model to behave in an asymptotically inconsistent manner. By including this viscous term and by introducing new wall damping functions with improved asymptotic behavior, a new K-tau model (where tau is identical with 1/omega is turbulent time scale) is developed. It is demonstrated that this new model is computationally robust and yields improved predictions for turbulent boundary layers.
Speziale, Charles G.↗