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Fokker-Planck equation used to describe process of electron loss from Van Allen zones due to pitch angle scattering by electromagnetic disturbances
Van Allen belt radiation on Tiros/TOS/ITOS spacecrafts - graphs
Nonadiabatic effects in van der Waal line broadening, taking into account mixing between degenerate magnetic sublevels in atomic collisions
Estimates were made of the number of trapped protons and electrons encountered by vehicles on low-thrust trajectories through the Van Allen belts. The estimates serve as a first step in assessing whether these radiations present a problem to on-board sensitive components and payload. The integrated proton spectra and electron spectra are presented for the case of a trajectory described by a vehicle with a constant-thrust acceleration A sub c equal to 0.001 meter/sq sec. This value of acceleration corresponds to a trip time of about 54 days from low earth orbit to synchronous orbit. It is shown that the time spent in the belts and hence the radiation encountered vary nearly inversely with the value of thrust acceleration. Thus, the integrated spectral values presented for the case of A sub c = 0.001 meter/sq sec can be generalized for any other value of thrust acceleration by multiplying them by the factor 0.001/A sub c.
Variational functionals of Braunn and Rebane (1972) for the imagery-frequency polarizability (IFP) have been generalized by the method of Gramian inequalities to give rigorous upper and lower bounds, valid even when the true (but unknown) unperturbed wavefunction must be represented by a variational approximation. Using these formulas in conjunction with flexible variational trial functions, tight error bounds are computed for the IFP and the associated two- and three-body van der Waals interaction constants of the ground 1(1S) and metastable 2(1,3S) states of He and Li(+). These bounds generally establish the ground-state properties to within a fraction of a per cent and metastable properties to within a few per cent, permitting a comparative assessment of competing theoretical methods at this level of accuracy. Unlike previous 'error bounds' for these properties, the present results have a completely a priori theoretical character, with no empirical input data.
Vehicle maximum speed, range at constant speed, range over stop-and-go driving schedules, maximum acceleration, gradeability, gradeability limit, road energy consumption, road power, indicated energy consumption, braking capability, battery charger efficiency, and battery characteristics were determined for a modified utility van powered by sixteen 6-volt batteries connected in series. A chopper controller actuated by a foot accelerator pedal changes the voltage applied to the 22-kilowatt (30-hp) series-wound drive motor. In addition to the conventional hydraulic braking system, the vehicle has hydraulic regenerative braking. Cycle tests and acceleration tests were conducted with and without hydraulic regeneration.
A theoretical procedure to determine the heat transfer characteristics of the interline region (junction of liquid-solid-vapor) from the macroscopic optical and thermophysical properties of the system is outlined. The analysis is based on the premise that the interline transport processes are controlled by the London-van der Waals dispersion force between condensed phases (solid and liquid). Numerical values of the dispersion constant are presented. The procedure is used to compare the relative size of the interline heat sink of various systems using a constant heat flux mode. This solution demonstrates the importance of the interline heat flow number, which is evaluated for various systems.
Inert-gas measurements were conducted with three soil samples collected from a trench of about 17 cm depth which had been dug at Station 9, approximately 60-m southeast of the rim of Van Serg Crater on the moon. The particular trench is interesting because it is located in the continuous ejecta blanket of a relatively young crater. The results of the inert-gas measurements are presented in a table. They confirm an earlier conclusion reported by Heymann et al. (1974) that fines from Station 9 are among the most gas rich in the whole landing site. The three fines are agglutinate rich and most of the trapped gas is contained in the constructional particles. Agglutinate contents of fines tend to decrease rapidly for particles greater than about 250 micrometers.
The paper presents measurements of cosmic-ray produced (Cl-36) in Antarctic meteorites and ice using a Van de Graaff accelerator as an ultrasensitive mass spectrometer. Results from this ion counting technique are used to support a two-stage irradiation model for the Yamato-7301 and Allan Hills-76008 meteorites and to show a long terrestrial age for Allan Hills-77002. Yamato-7304 has a terrestrial age of less than 0.1 m.y., and the (Cl-36) content of the Antarctic ice sample from the Yamato mountain is consistent with levels expected in currently depositing snow implying that the age of the ice cap at this site is less than on (Cl-36) half-life.
An equation reported by van der Pol (1926) in connection with relaxation-oscillations studies is considered. The equation contains the factor epsilon which can assume values in the range from zero to infinity. The period T(epsilon), or equivalently the frequency nu(epsilon) of the limit cycle has been studied. However, to date there has been little success in discovering the analytical structure of T(epsilon) as a function of epsilon. The present investigation has the objectives to present the Taylor series expansion of nu(epsilon), to locate the singularities which determine the radius of convergence of that expansion, to introduce a new damping variable in terms of which the expansion converges for all epsilon, to form a new expansion for the period T(epsilon) which improves the rate of convergence of the series, to attempt to 'complete' the series, and to compare the obtained results with the numerically determined values of T(epsilon) and with the asymptotic approximation valid for large epsilon.
A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Pade approximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.
A power series expansion in the damping parameter, epsilon, of the limit cycle of the free van der Pol equation is constructed and analyzed. Coefficients in the expansion are computed in exact rational arithmetic using the symbolic manipulation system MACSYMA and using a FORTRAN program. The series is analyzed using Padeapproximants. The convergence of the series for the maximum amplitude of the limit cycle is limited by two pair of complex conjugate singularities in the complex epsilon-plane. A new expansion parameter is introduced which maps these singularities to infinity and leads to a new expansion for the amplitude which converges for all real values of epsilon. Amplitudes computed from this transformed series agree very well with reported numerical and asymptotic results. For the limit cycle itself, convergence of the series expansion is limited by three pair of complex conjugate branch point singularities. Two pair remain fixed throughout the cycle, and correspond to the singularities found in the maximum amplitude series, while the third pair moves in the epsilon-plane as a function of t from one of the fixed pairs to the other. The limit cycle series is transformed using a new expansion parameter, which leads to a new series that converges for larger values of epsilon.
Results of the first numerical evolutionary calculations for very low-mass stars with ages up to the age of the Galaxy are presented. The calculations shed new light on the nature of the recently discovered object VB 8B, the companion to Van Biesbroeck's star no. 8, and support the identification of this object as a low-mass star in which hydrogen burning was never able to establish thermal equilibrium. For plausible ages of this binary stellar system, the mass of VB 8B is estimated to be in the range 0.04-0.08 solar mass. The object is supported primarily by degenerate electron pressure; its present values of central density and temperature are found to be 500-2000 g/cu cm and 1.0-1.5 million K. An orbital period of more than about 40 yr is predicted for the binary system. The presented evolutionary tracks are also applicable to the interpretation of observations of other very low-luminosity dwarfs.
The Feshbach projection-operator formalism is used to derive the asymptotic effective interaction potential between two atoms. Beyond the usual van der Waals potential, falling like x exp -6, three x exp -8 terms are also obtained: an attractive dipole-quadrupole term (absent in the positronium-positronium case because of symmetry), a repulsive energy-dependent term, and a repulsive mass-dependent but energy-independent one. This last term was not obtained by Manson and Ritchie (1985) using an independent method.
Closed-form expressions are derived for the finite-mass nonadiabatic corrections to the van der Waals potential in the electric-dipole approximations in terms of London-analog two-center atomic spectral sums. The nonadiabatic corrections to all orders at threshold energy and also those with first-order energy dependence are given.
The lifetimes of high-energy (greater than 55 MeV) protons in the Van Allen radiation belt are calculated, assuming that in time the protons will collide with and be absorbed by particulate orbiting material. The calculations are based on the NASA/DoD Civil Needs Database for orbital debris (Gaines, 1966) and moderate assumptions of future space traffic. It is found that the lifetimes of high-energy protons below 1500 km will decrease, leading to a noticeable redution in their fluxes.
The soil maturity and the concentration of Fe metal and 18 major and trace elements were determined along the length of the 79001/2 double drive tube collected near the Van Serg crater at the Apollo 17 station 9. Samples from the top 8.5 cm of the core are found to be very mature and to be enriched in Fe metal and siderophile elements compared to soil lower in the core. It is suggested that this enrichment may have resulted from a significant exposure at some time in the past. A soil component of metallic Fe may be related to micrometeorite impact.
A theory describing plasma double layers in terms of multiple roots of the charge density expression is presented. The theory presented uses the fact that equilibrium plasmas shield small potential perturbations linearly; for high potentials, the shielding decreases. The approach is analogous to Van der Waals' theory of simple fluids in which inclusion of approximate expressions for both excluded volume and long range attractive forces sufficiently describes the first-order liquid-gas phase transition.