Fundamental inequalities for discrete and dis- continuous functional equations
Inequalities for theory of finite difference equations and more general discontinuous functional equations
FINITE DIFFERENCE METHOD↗
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Results for “generalized functions”
Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.
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General Forms of Wave Functions for Dipositronium, Ps2
The consequences of particle interchange symmetry for the structure of wave functions of the states of dipositronium was recently discussed by the author [I]. In the present work, the methodology is simply explained, and the wave functions are explicitly given.
Schrader, D.M.↗
ANL/RBC: A computer code for the analysis of Rankine bottoming cycles, including system cost evaluation and off-design performance
This report describes, and is a User's Manual for, a computer code (ANL/RBC) which calculates cycle performance for Rankine bottoming cycles extracting heat from a specified source gas stream. The code calculates cycle power and efficiency and the sizes for the heat exchangers, using tabular input of the properties of the cycle working fluid. An option is provided to calculate the costs of system components from user defined input cost functions. These cost functions may be defined in equation form or by numerical tabular data. A variety of functional forms have been included for these functions and they may be combined to create very general cost functions. An optional calculation mode can be used to determine the off-design performance of a system when operated away from the design-point, using the heat exchanger areas calculated for the design-point.
Mclennan, G. A.↗
Genetic algorithm based fuzzy control of spacecraft autonomous rendezvous
The U.S. Bureau of Mines is currently investigating ways to combine the control capabilities of fuzzy logic with the learning capabilities of genetic algorithms. Fuzzy logic allows for the uncertainty inherent in most control problems to be incorporated into conventional expert systems. Although fuzzy logic based expert systems have been used successfully for controlling a number of physical systems, the selection of acceptable fuzzy membership functions has generally been a subjective decision. High performance fuzzy membership functions for a fuzzy logic controller that manipulates a mathematical model simulating the autonomous rendezvous of spacecraft are learned using a genetic algorithm, a search technique based on the mechanics of natural genetics. The membership functions learned by the genetic algorithm provide for a more efficient fuzzy logic controller than membership functions selected by the authors for the rendezvous problem. Thus, genetic algorithms are potentially an effective and structured approach for learning fuzzy membership functions.
Karr, C. L.↗
Direct Linearization and Adjoint Approaches to Evaluation of Atmospheric Weighting Functions and Surface Partial Derivatives: General Principles, Synergy and Areas of Application
This slide presentation reviews the observable radiances as functions of atmospheric parameters and of surface parameters; the mathematics of atmospheric weighting functions (WFs) and surface partial derivatives (PDs) are presented; and the equation of the forward radiative transfer (RT) problem is presented. For non-scattering atmospheres this can be done analytically, and all WFs and PDs can be computed analytically using the direct linearization approach. For scattering atmospheres, in general case, the solution of the forward RT problem can be obtained only numerically, but we need only two numerical solutions: one of the forward RT problem and one of the adjoint RT problem to compute all WFs and PDs we can think of. In this presentation we discuss applications of both the linearization and adjoint approaches
remote sensing↗
Shear buckling of specially orthotropic plates with centrally located cutouts
The shear loading of a composite rectangular plate with a centrally located circular cutout was analyzed in order to predict the buckling load of the plate. The first step in this analysis is to calculare the in-plane stress distribution of the plate prior to buckling. This problem can be solved using finite element methods, but a quicker and more cost efficient method is desired. The method chosen to determine the pre-buckling stresses is that of boundary collocation using complex variables. The real valued force functions are written in terms of two complex valued functions, each of which is a function of a different complex variable. The solution of the generalized biharmonic function is a superposition of functions of these two complex variables. For this analysis, the force functions are represented with a Laurent series. The constants in these series are found using boundary collocation. Two force equations for complex variables are satisfied over the plate boundaries to obtain these constants. The stresses in the plate are then known for any particular locations on the plate given the applied shear on the edges of the plate.
Klang, Eric C.↗
Wigner expansions for partition functions of nonrelativistic and relativistic oscillator systems
The equilibrium quantum statistics of various anharmonic oscillator systems including relativistic systems is considered within the Wigner phase space formalism. For this purpose the Wigner series expansion for the partition function is generalized to include relativistic corrections. The new series for partition functions and all thermodynamic potentials yield quantum corrections in terms of powers of h(sup 2) and relativistic corrections given by Kelvin functions (modified Hankel functions) K(sub nu)(mc(sup 2)/kT). As applications, the symmetric Toda oscillator, isotonic and singular anharmonic oscillators, and hindered rotators, i.e. oscillators with cosine potential, are addressed.
Zylka, Christian↗
Generalized Barker sequences.
Transformations with correlation function unaltered, changing generalized Barker sequences
CORRELATION FUNCTION↗
Unsteady aerodynamic modeling and active aeroelastic control
Unsteady aerodynamic modeling techniques are developed and applied to the study of active control of elastic vehicles. The problem of active control of a supercritical flutter mode poses a definite design goal stability, and is treated in detail. The transfer functions relating the arbitrary airfoil motions to the airloads are derived from the Laplace transforms of the linearized airload expressions for incompressible two dimensional flow. The transfer function relating the motions to the circulatory part of these loads is recognized as the Theodorsen function extended to complex values of reduced frequency, and is termed the generalized Theodorsen function. Inversion of the Laplace transforms yields exact transient airloads and airfoil motions. Exact root loci of aeroelastic modes are calculated, providing quantitative information regarding subcritical and supercritical flutter conditions.
Edwards, J. W.↗
Approximate formulation of redistribution in the Ly-alpha, Ly-beta, H-alpha system
Simple approximate formulas are given for the coupled redistribution of Ly-alpha, Ly-beta, and H-alpha, by using well-defined approximations to an essentially exact formulation. These formulas incorporate all the essential physics including Raman scattering, lower state radiative decay, and correlated terms representing emission during a collision which must be retained in order that the emission coefficients are properly behaved in the line wings. Approximate expressions for the appropriate line broadening parameters are collected. Finally, practical expressions for the source functions are given. These are formulated through newly introduced nonimpact redistribution functions, which are shown to be reasonably approximated by existing (ordinary and generalized) redistribution functions.
Cooper, J.↗
Spin bipolaron in the framework of emery model for high-T(sub c) copper oxide superconductors
The high-T(sub c) oxide compounds discovered recently exhibit a number of interesting physical properties. Two-dimensional antiferromagnetic spin order has been observed in these materials at the oxygen deficiency. This fact can be explained by strong correlation of the spins, situated on Cu sites in the conducting planes of the oxide superconductors. The doping or the oxygen deficiency lead to the occurrence of holes, occupying the oxygen p-orbitals according to the Emery model. At the small hole concentration they can move along the antiferromagnetic lattice of spins, localized on Cu sites. Researchers consider the two holes situation and describe in what way their behavior depends on the antiferromagnetic exchange interation J. It is known that in the framework of Hubbard model with strong on-site Coulomb repulsion, a single hole can form a spin polaron of the large radius. It is reasonable to admit that two holes with parallel spins (triplet) form the spin bipolaron complex owing to the hole excitations' capability to polarize Cu spin surroundings. Such an excitation was considered in the phenomenological way. Here the problem is discussed on the basis of the microscopic approach in the framework of the variational principle. A special kind of wave function is used for such a purpose. The wave function is constructed by generalizing the trial functions proposed in over two holes excitation situation (triplet) and then the region of spin bipolaron existance in the framework of Emery model is studied. In this model the Hamiltonian can be easily rewritten by forming the oxygen states transforming as the irreducible representations of the group D(sub 4).
Golub, A. A.↗
Stability regions of large-scale systems.
Using an aggregated comparison system, methods are developed for estimating regions of asymptotic stability for large-scale systems composed of interconnected, exponentially stable subsystems; in general some of these subsystems are not globally stable. Three different forms of Liapunov functions are shown to be suitable for describing the stability behavior of the aggregated system, but one form in particular (heretofore not used in this context) is found to be the most natural. Using this function, some general results are obtained.
Weissenberger, S.↗
Stability regions of large-scale systems
Using an aggregated comparison system, methods are developed for estimating regions of asymptotic stability for large-scale systems composed of interconnected, exponentially stable subsystems; in general, some of these subsystems are not globally stable. Three different forms of Liapunov functions are shown to be suitable for describing the stability behavior of the aggregated system, but one form in particular, heretofore not used in this context, is found to be the most natural. Using this function, some general results are obtained.
Weissenberger, S.↗
Structural Properties and Estimation of Delay Systems
Two areas in the theory of delay systems were studied: structural properties and their applications to feedback control, and optimal linear and nonlinear estimation. The concepts of controllability, stabilizability, observability, and detectability were investigated. The property of pointwise degeneracy of linear time-invariant delay systems is considered. Necessary and sufficient conditions for three dimensional linear systems to be made pointwise degenerate by delay feedback were obtained, while sufficient conditions for this to be possible are given for higher dimensional linear systems. These results were applied to obtain solvability conditions for the minimum time output zeroing control problem by delay feedback. A representation theorem is given for conditional moment functionals of general nonlinear stochastic delay systems, and stochastic differential equations are derived for conditional moment functionals satisfying certain smoothness properties.
Kwong, R. H. S.↗
Loop transfer recovery for general nonminimum phase discrete time systems. II - Design
The authors consider the design of controllers for the recovery of target loop transfer function or sensitivity and complementary sensitivity functions for general nonminimum phase discrete time systems. The necessary design constraints and the available design freedom are reviewed. In view of the available freedom, possible specifications on the eigenstructure of the observer dynamic matrix are formulated. Three different types of controllers which are respectively based on prediction, current, and reduced-order estimators are considered. For each one of those controllers, three different design techniques are developed. The first one is an eigenstructure assignment scheme, while the other two are optimization-based designs. The eigenstructure assignment method yields a controller design which achieves any chosen recovery error matrix among a set of admissible recovery error matrices. On the other hand, one of the optimization-based design methods leads to a controller that achieves a recovery error matrix having the infimum H-infinity norm, while the other does the same except it achieves a recovery error matrix having the infimum H2 norm.
Chen, Ben M.↗
A generalization of Petterssen's frontogenesis function and its relation to the forcing of vertical motion
The classic Peterssen frontogenesis function, defined as the Lagrangian rate of change of the magnitude of the potential temperature gradient, is generalized to apply to the vector potential temperature gradient. The derivation of vector frontogenesis in natural coordinates is shown, and analytical examples of frontal evolution in nondivergent horizontal velocity fields are given which suggest that both the frontogenetic and rotational components of the vector frontogenesis function F may be comparable in developing frontal zones observed in nature. The relative importance of the magnitude and direction contributions to F is quantitatively investigated, and it is found that the Lagrangian rates of change of the magnitude and direction of the potential temperature gradient are comparable. The frontal circulation is found to be related to the magnitude component of the Q vector, whereas the background circulation is related to the direction component.
Keyser, Daniel↗
The quantum dynamics of electronically nonadiabatic chemical reactions
Considerable progress was achieved on the quantum mechanical treatment of electronically nonadiabatic collisions involving energy transfer and chemical reaction in the collision of an electronically excited atom with a molecule. In the first step, a new diabatic representation for the coupled potential energy surfaces was created. A two-state diabatic representation was developed which was designed to realistically reproduce the two lowest adiabatic states of the valence bond model and also to have the following three desirable features: (1) it is more economical to evaluate; (2) it is more portable; and (3) all spline fits are replaced by analytic functions. The new representation consists of a set of two coupled diabatic potential energy surfaces plus a coupling surface. It is suitable for dynamics calculations on both the electronic quenching and reaction processes in collisions of Na(3p2p) with H2. The new two-state representation was obtained by a three-step process from a modified eight-state diatomics-in-molecules (DIM) representation of Blais. The second step required the development of new dynamical methods. A formalism was developed for treating reactions with very general basis functions including electronically excited states. Our formalism is based on the generalized Newton, scattered wave, and outgoing wave variational principles that were used previously for reactive collisions on a single potential energy surface, and it incorporates three new features: (1) the basis functions include electronic degrees of freedom, as required to treat reactions involving electronic excitation and two or more coupled potential energy surfaces; (2) the primitive electronic basis is assumed to be diabatic, and it is not assumed that it diagonalizes the electronic Hamiltonian even asymptotically; and (3) contracted basis functions for vibrational-rotational-orbital degrees of freedom are included in a very general way, similar to previous prescriptions for locally adiabatic functions in various quantum scattering algorithms.
Truhlar, Donald G.↗
A theoretical study of plasmaspheric hiss generation
An investigation of the generation of plasmaspheric hiss by the whistler mode instability has been carried out. Using combined ray-tracing and growth rate calculations, the path-integrated growth rates of a large number of waves have been calculated using a distribution function. In general, the waves damp out before being magnetospherically reflected, or soon after. This is true of all the waves traced, independent of the distribution functions used for the energetic (resonant) electrons. Thus the growth rates are generally low, since the waves undergo few equatorial transits. A comparison of these results with observed spectra indicates that while some spectral characteristics are in qualitative agreement, there is a major discrepancy in the intensity levels.
Huang, C. Y.↗