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Results for “generalized functions”

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At least 1,315 records · Page 73
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Protective coatings with nanoscale multilayer architecture: current state and main trends

Binary systems (layers) and multicomponent layers with bilayer thicknesses varying from microns to a few nanometers are considered. A strong dependence of the microstructure formation on the deposition conditions (the magnitude of the bias potential, the flow of inert and reactive gases, the ion beam power (current density) supplied to the target) is found. General regularities in the change in the functional properties and structural state of the coatings are formulated. The conditions for the formation of a columnar structure and growth texture are noted; various mechanisms and their interpretation are proposed. Finally, the relationship among the size of nanograins, diffusion at the interphase boundary, and effects determining the physico-mechanical, tribological characteristics, as well as resistance to corrosion and oxidation, is shown.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Analytical Approximations for Beamstrahlung at Very High Energy Electron-Positron Colliders

Among the many effects that occur in beam-beam electron-positron collisions at TeV energies, emission of hard synchrotron radiation, or beamstrahlung, has special importance. Beamstrahlung determines the energy spectrum of the most energetic electrons, positrons, and photons and supplies the initial condition for the calculation of all other QED processes. In this paper, we show that the description of beamstrahlung simplifies in the limit of large quantum parameter $Υ$, which is realized in 10 TeV collider designs. The beamstrahlung spectra for electrons and photons are given in terms of universal functions. We supply approximations to these functions that will be useful for more general studies of the beam-beam interaction at very high energies.

Accelerator Physics (physics.acc-ph)↗
NASA NTRS1963

A Hypergeometric Mean Value

Generalization of hypergeometric mean value from hypergeometric function without loss of homogeneity - derivation and properties of hypergeometric mean value

HYPERGEOMETRIC FUNCTION↗
NASA NTRS1966

Generalized Sternheimer potential.

Generalization of Sternheimer potential to include wave functions involving spin in nonfactorable way, exhibiting approximate Hamiltonian

QUANTUM THEORY↗
NASA NTRS1972

Stability and CMG wobble damping of flexible, spinning space stations.

Consideration of the uncontrolled vehicle stability and control moment gyro (CMG) wobble damping of two typical modular-spinning-space-station configurations. General stability trends are established as a function of structural parameters. Results of investigations using a unique CMG wobble damping concept are presented, and requirements are formulated. Modifications to the basic control law required as a result of structural flexibility are described. The majority of the analyses were performed with the aid of a digital simulation of the flexible body dynamics. The description of the vehicles, the flexible body simulation, and the CMG wobble damping concept are presented. Previously established theory is supported insofar as the stabilization and control problems associated with a minimum inertia type spinning spacecraft are shown to be significantly greater than those of a maximum inertia vehicle. For example, the maximum inertia configuration investigated is stable for all structural flexibility conditions studied, while the stability of the minimum inertia configuration is dependent upon the distribution of energy dissipating material throughout the structure.

Berman, H.↗
NASA NTRS1972

Electron precipitation pattern and substorm morphology

Patterns of the precipitation of low energy electrons observed by polar satellites were examined as functions of substorm phase. Precipitation boundaries are generally identifiable at the low latitude edge of polar cusp electron precipitation and at the poleward edge of precipitation in the premidnight sector. Both of these boundaries move equatorward when the interplanetary magnetic field turns southward.

Hoffman, R. A.↗
NASA NTRS1973

Proton-radiation damage in Gunn oscillators

The irradiation effects of 22 MeV protons on the electrical characteristics of GaAs continuous-wave Gunn oscillators was studied. The radio frequency power output was reduced by 3 decibels at proton fluences in the neighborhood of 1.5 x 10 to the 12th power protons/sq cm. Conductance measurements indicate that the carrier removal rate at high electric fields remained roughly 40 percent less than at low fields. Diode efficiencies of two device groups were found to be monotonically descreasing functions of fluence. Frequency modulation noise was generally unaffected by radiation, but the magnitude of the noise in the noise power spectrum increased significantly. These effects are partially accounted for, in a qualitative fashion, by a model of electron traps having field-dependent net-carrier capture rates and various response times.

Johnson, J. W.↗
NASA NTRS1974

A computer graphics display and data compression technique

The computer program discussed is intended for the graphical presentation of a general dependent variable X that is a function of two independent variables, U and V. The required input to the program is the variation of the dependent variable with one of the independent variables for various fixed values of the other. The computer program is named CRP, and the output is provided by the SD 4060 plotter. Program CRP is an extremely flexible program that offers the user a wide variety of options. The dependent variable may be presented in either a linear or a logarithmic manner. Automatic centering of the plot is provided in the ordinate direction, and the abscissa is scaled automatically for a logarithmic plot. A description of the carpet plot technique is given along with the coordinates system used in the program. Various aspects of the program logic are discussed and detailed documentation of the data card format is presented.

Teague, M. J.↗
NASA NTRS1973

Aircraft symmetric flight optimization

Review of the development of gradient techniques and their application to aircraft optimal performance computations in the vertical plane of flight. Results obtained using the method of gradients are presented for attitude- and throttle-control programs which extremize the fuel, range, and time performance indices subject to various trajectory and control constraints, including boundedness of engine throttle control. A penalty function treatment of state inequality constraints which generally appear in aircraft performance problems is outlined. Numerical results for maximum-range, minimum-fuel, and minimum-time climb paths for a hypothetical supersonic turbojet interceptor are presented and discussed. In addition, minimum-fuel climb paths subject to various levels of ground overpressure intensity constraint are indicated for a representative supersonic transport. A variant of the Gel'fand-Tsetlin 'method of ravines' is reviewed, and two possibilities for further development of continuous gradient processes are cited - namely, a projection version of conjugate gradients and a curvilinear search.

Falco, M.↗
NASA NTRS1974

Multiconfiguration self-consistent-field calculation of the dipole moment function of CO/X 1 sigma +/

Using the optimized valence configurations (OVC) multiconfiguration self-consistent-field (MCSCF) method, the dipole moment function for the ground state of CO in the vicinity of the equilibrium internuclear distance has been calculated. The OVC MCSCF calculation results are compared with existing Hartree-Fock and configuration interaction treatments of this molecule at single points and also the dipole moment function deduced from experimental infrared intensities. A general prescription for constructing OVC wavefunctions for diatomic molecules is also presented.

Billingsley, F. P., II↗
NASA NTRS1977

Dilation of force-free magnetic flux tubes

A general study is presented of the mapping functions which relate the magnetic-field profiles across a force-free rope in segments subjected to various external pressures. The results reveal that if the external pressure falls below a certain critical level (dependent on the flux-current relation which defines the tube), the magnetic profile consists of an invariant core sheathed in a layer permeated by an azimuthal magnetic field.

Frankenthal, S.↗
NASA NTRS1978

New formulation of de Sitter's theory of motion for Jupiter I-IV. I - Equations of motion and the disturbing function

Elliptic orbits are substituted for circular orbits in the first approximation, in an analysis of the common retrograde motion of Jupiter's satellites. A modification of the de Sitter theory, made possible by extended observations of the satellites, is presented with attention to that aspect of the theory which eliminates small divisors at all stages of the solution. The convergence problem is circumvented by use of Poincare's canonical relative coordinates. In addition, modified Delaunay variables and their associated Poincare variables are applied to the disturbing function, which is expanded by means of generalized Newcomb operators.

Aksnes, K.↗
NASA NTRS1980

Iterative solutions for one-dimensional diffusion with time varying surface composition and composition-dependent diffusion coefficient

Solutions are given for one-dimensional diffusion problems with a time varying surface composition and also a composition dependent diffusion coefficient. The most general solution does not require special mathematical functions to fit the variation in surface composition or D(C). In another solution, a series expansion may be used to fit the time dependent surface concentration. These solutions make use of iterative calculations that converge rapidly and are highly stable. Computer times are much shorter than that required for finite difference calculations and can efficiently make use of interactive graphics terminals. Existing gas carburization data were used to provide an illustration of an iterative approach with a time varying carbon composition at the free surface.

Chow, M.↗
NASA NTRS1982

Closed-form solutions of performability

It is noted that if computing system performance is degradable then system evaluation must deal simultaneously with aspects of both performance and reliability. One approach is the evaluation of a system's performability which, relative to a specified performance variable Y, generally requires solution of the probability distribution function of Y. The feasibility of closed-form solutions of performability when Y is continuous are examined. In particular, the modeling of a degradable buffer/multiprocessor system is considered whose performance Y is the (normalized) average throughput rate realized during a bounded interval of time. Employing an approximate decomposition of the model, it is shown that a closed-form solution can indeed be obtained.

Meyer, J. F.↗
NASA NTRS1981

Two-dimensional turbulence models

Two-dimensional turbulence models are compared with experimental measurements made using an array of instrumented towers. The spatial correlation coefficient, the two-point spectrum or cross spectrum, and the coherence function are discussed. The prediction techniques in general agree reasonably well with the experimental results. Measurements of the integral length scale however, do not correlate well with the prediction model.

Frost, W.↗
NASA NTRS1982

Threshold law for electron-atom impact ionization

A derivation of the explicit form of the threshold law for electron impact ionization of atoms is presented, based on the Coulomb-dipole theory. The important generalization is made of using a dipole function whose moment is the dipole moment formed by an inner electron and the nucleus. The result is a modulated quasi-linear law for the yield of positive ions which applies to positron-atom impact ionization.

Temkin, A.↗