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Results for “Analytic derivatives”

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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At least 307 records · Page 17
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NASA NTRS1982

Cosmic-ray acceleration by stellar winds. II - The spectrum of accelerated particles

Consideration is given to the spectrum of particles accelerated at a stellar wind terminal shock and, at the same time, modulated by convection and diffusion in the stellar wind and decelerated by adiabatic expansion of the unshocked wind. It is noted that a proper study of this problem combines the whole of the cosmic-ray modulation problem with first-order Fermi acceleration at the shock due to repeated diffusive scattering across the shock. The modulation aspect of the model described here is much simpler than modern models of modulation alone; this makes it possible to derive illustrative analytical expressions for the accelerated spectra. Particular cases of monoenergetic and truncated power laws are computed. Energy losses and convective modulation compete with acceleration at the shock so effectively in this model that enhancement of the background cosmic-ray flux by a factor of more than 2 is extremely unlikely.

Forman, M. A.↗
NASA NTRS1982

Correlation and assessment of structural airplane crash data with flight parameters at impact

Crash deceleration pulse data from a crash dynamics program on general aviation airplanes and from transport crash data were analyzed. Structural airplane crash data and flight parameters at impact were correlated. Uncoupled equations for the normal and longitudinal floor impulses in the cabin area of the airplane were derived, and analytical expressions for structural crushing during impact and horizontal slide out were also determined. Agreement was found between experimental and analytical data for general aviation and transport airplanes over a relatively wide range of impact parameter. Two possible applications of the impulse data are presented: a postcrash evaluation of crash test parameters and an assumed crash scenario.

Carden, H. D.↗
NASA NTRS1983

Space Shuttle propulsion parameter estimation using optimal estimation techniques

This fourth monthly progress report again contains corrections and additions to the previously submitted reports. The additions include a simplified SRB model that is directly incorporated into the estimation algorithm and provides the required partial derivatives. The resulting partial derivatives are analytical rather than numerical as would be the case using the SOBER routines. The filter and smoother routine developments have continued. These routines are being checked out.

Source record↗
NASA NTRS1984

On the Kelvin-Helmholtz instabilities of supersonic shear layers

Analytical consideration is given to a Kelvin-Helmholtz instability in a finite width supersonic shear layer with linear and sinusoidal velocity profiles in the transition region. An analogy is explored between the pressure perturbation and the bound and scattering wave states of the one-dimensional Schroedinger equation. A numerical model is obtained for generating contour maps of the real and imaginary parts of the perturbation frequency in the (A,B)-plane. A comparison is made between the numerical results and analytical expressions derived for very small Mach numbers. Two unstable regimes are characterized in the (A,B)-plane. The method is concluded useful for both laboratory and astrophysics problems.

Choudhury, S. R.↗
NASA NTRS1985

Relativistic electron in curved magnetic fields

Making use of the perturbation method based on the nonlinear differential equation theory, the author investigates the classical motion of a relativistic electron in a class of curved magnetic fields which may be written as B=B(O,B sub phi, O) in cylindrical coordinates (R. phi, Z). Under general astrophysical conditions the author derives the analytical expressions of the motion orbit, pitch angle, etc., of the electron in their dependence upon parameters characterizing the magnetic field and electron. The effects of non-zero curvature of magnetic field lines on the motion of electrons and applicabilities of these results to astrophysics are also discussed.

An, S.↗
NASA NTRS1985

Diffusion-convection function of cosmic rays

The fundamental properties and some numerical results of the solution of the diffusion equation of an impulsive cosmic-ray point source in an uniform, unbounded and spherically symmetrical moving medium is presented. The diffusion-convection(D-C) function is an elementary composite function of the solution of the D-C equation for the particles injected impulsively from a diffusive point source into the medium. It is the analytic solution derived by the dimensional method for the propagation equation of solar cosmic rays in the heliosphere, i.e. the interplanetary space. Because of the introduction of convection effect of solar wind, a nonhomogeneous term appears in the propagation equation, it is difficult to express its solution in terms of the ordinary special functions. The research made so far has led to a solution containing only the first order approximation of the convection effect.

Zhang, G.↗
NASA NTRS1985

Design of stiffened composite panels with a fracture constraint

An automated procedure for designing minimum-weight composite panels subject to a local damage constraint under tensile loading was developed. A finite element program based on linear elastic fracture mechanics for calculating stress intensity factors (SIF) was incorporated in the design cycle. Panel fracture toughness was obtained by using a strain based criterion. A general purpose mathematical optimization algorithm was used for the weight minimization. Analytical sensitivity derivatives of the SIF employing the adjoint variable technique was used to enhance the computational efficiency of the procedure. Design results for both unstiffened and stiffened plates are presented.

Gurdal, Z.↗
NASA NTRS1986

Theoretical research program to study chemical reactions in AOTV bow shock tubes

Progress in the development of computational methods for the characterization of chemical reactions in aerobraking orbit transfer vehicle (AOTV) propulsive flows is reported. Two main areas of code development were undertaken: (1) the implementation of CASSCF (complete active space self-consistent field) and SCF (self-consistent field) analytical first derivatives on the CRAY X-MP; and (2) the installation of the complete set of electronic structure codes on the CRAY 2. In the area of application calculations the main effort was devoted to performing full configuration-interaction calculations and using these results to benchmark other methods. Preprints describing some of the systems studied are included.

Taylor, P.↗
NASA NTRS1986

Methods for computing comet core temperatures

The temperature profile within the comet nucleus provides the key to an understanding of the history of the volatiles within a comet. Certain difficulties arise in connection with current cometary temperature models. It is shown that the constraint of zero net heat flow can be used to derive general analytical expressions which will allow for the determination of comet core temperature for a spherically symmetric comet, taking into account information about the surface temperature and the thermal conductivity. The obtained results are compared with the expression for comet core temperatures considered by Klinger (1981). Attention is given to analytical results, an example case, and numerical models. The formalization developed makes it possible to determine the core temperature on the basis of the numerical models of the surface temperature.

Mckay, C. P.↗
NASA NTRS1987

Design sensitivity analysis of nonlinear structural response

A unified theory is described of design sensitivity analysis of linear and nonlinear structures for shape, nonshape and material selection problems. The concepts of reference volume and adjoint structure are used to develop the unified viewpoint. A general formula for design sensitivity analysis is derived. Simple analytical linear and nonlinear examples are used to interpret various terms of the formula and demonstrate its use.

Cardoso, J. B.↗
NASA NTRS1986

The global evolution of the primordial solar nebula

Complete radial, time-dependent calculations of the structure and evolution of the primordial solar nebula during the viscous diffusion stage are presented. The viscous stress is derived from analytic one-zone models of the vertical nebular structure based on detailed grain opacities. Comparisons with full numerical integrations indicate that the effective viscous alpha parameter is about 0.01. The evolution time of a minimum mass nebula is one-million yr or less. The flow pattern of fluid elements in the disk is examined and the implications the results have on the theory of the formation of the solar system are discussed.

Ruden, S. P.↗
NASA NTRS1986

A simulation study of the critical ionization velocity process

The critical ionization velocity process is studied by first investigating a coupled system of equations describing the production of several ion species and electrons by impact ionization, their collisions with neutrals, and the heating of electrons. Analytic relations derived from this were tested with the help of a particle simulation, including collisional processes between neutrals and plasma particles. It was found that resistive heating of electrons plays an important role when the density of the neutrals is high, and that electron heating due to lower hybrid waves is significant when the neutral density is low. In both cases, the control of the plasma production rate by the ratio of the beam velocity to the critical velocity was verified.

Machida, S.↗
NASA NTRS1987

The structure of the time-dependent interstellar shocks and grain destruction in the interstellar medium

A new theoretical analysis of the structure of interstellar shocks and the grain dynamics of these shocks is presented. The basic hydrodynamic equations for J-shocks in interstellar gas are given in which shock-driving pressure is allowed to be weakly time-dependent and the grains are treated as a separate two-dimensional fluid. Specific equations for the grain dynamics in the cooling postshock gas are derived. An analytic theory for the propagation of a shock driven into an interstellar cloud by the blast wave of a supernova remnant which sweeps over the cloud is developed. An improved calculation of the grain charge in postshock gas is described, giving a simple analytic approximation for the results. The consequences of including these processes in the numerical code of Seab and Shull (1983) are addressed, including the effect of realistic magnetic fields in low-density gas.

Mckee, Christopher F.↗
NASA NTRS1986

Dynamic modelling and estimation of the error due to asynchronism in a redundant asynchronous multiprocessor system

The use of Redundant Asynchronous Multiprocessor System to achieve ultrareliable Fault Tolerant Control Systems shows great promise. The development has been hampered by the inability to determine whether differences in the outputs of redundant CPU's are due to failures or to accrued error built up by slight differences in CPU clock intervals. This study derives an analytical dynamic model of the difference between redundant CPU's due to differences in their clock intervals and uses this model with on-line parameter identification to idenitify the differences in the clock intervals. The ability of this methodology to accurately track errors due to asynchronisity generate an error signal with the effect of asynchronisity removed and this signal may be used to detect and isolate actual system failures.

Huynh, Loc C.↗
NASA NTRS1987

Prediction of tip vortex self-induced motion parameters in terms of rotor blade loading

The self-induced motion of curved vortex filaments at the tip of a helicopter rotor blade is investigated analytically. The derivation of a method for inviscid roll-up (IRU) is presented in detail, with attention to the cutoff-distance reformulation of the problem, a control-volume analysis of the self-induction properties of the vortex core, the adaptation of the roll-up method of Betz (1932) to IRU in three dimensions, the treatment of linear and elliptic loading, vortices with turbulent central cores, and the effect of cutoff distance on helicopter free-wake computations. Numerical results showing the significant effect of core properties on the geometry of a rotor wake in hover are presented in graphs and briefly characterized.

Bliss, Donald B.↗
NASA NTRS1988

Criteria for the limit cycle mechanism

The limit cycle accretion disk mechanism originally proposed to account for periodic eruptions seen in dwarf novae (interacting binaries with orbital periods of a few hours) has been shown to have a wide potential for application. General criteria for the presence of the limit cycle in disks with either dominant self-gravity or central object gravity, and with flux transport either by radiation or convection are discussed. The analytic criteria derived agree qualitatively with numerical studies.

Cannizzo, J. K.↗
NASA NTRS1988

Two lines of sight with exceedingly anomalous ultraviolet interstellar extinction

Low-resolution IUE data toward HD 62542 reveal an extinction curve with an extremely broad and weak UV extinction bump and the highest FUV extinction yet observed in the Milky Way. Parameters describing the central position and FWHM for weak bumps observed toward HD 62542 and HD 29647 are derived using analytical fitting techniques. In both cases, the bump central positions are shifted shortward of 2175 A with an initial wavelength of 2110 A for HD 62542 and an initial wavelength of 2128 A for HD 29647. The bump FWHM is found to be 1.29/micron and 1.62/micron for HD 62542 and HD 29647, respectively.

Cardelli, Jason A.↗
NASA NTRS1988

Weak solutions of the three-dimensional vorticity equation with vortex singularities

The extension of the concept of vortex singularities, developed by Saffman and Meiron (1986) for the case of two-dimensional point vortices in an incompressible vortical flow, to the three-dimensional case of vortex sticks (vortons) is investigated analytically. The derivation of the governing equations is explained, and it is demonstrated that the formulation obtained conserves total vorticity and is a weak solution of the vorticity equation, making it an appropriate means for representing three-dimensional vortical flows with limited numbers of vortex singularities.

Winckelmans, G.↗