Magnetic field variations in interplanetary space
Magnetic field variations and structures in interplanetary space relationship to sun, discussing photospheric field lines random walk transport
Wilcox, J. M.↗
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Method for analyses of cyclic physiological data that are nonstationary in time.
The proposed method of studying biologic rhythms permits the biologist to view physiological data dynamically without assuming that the data are stationary in time. Vector representation of data points is employed, and the summation of the vectors (train of vectors) produces a summation dial that is able to detect dynamic changes in the time of the peak as well as random walks (arrhythmia).
Winget, C. M.↗
Composition and physics of the lunar atmosphere.
The existence in the lunar atmosphere of helium, neon, argon, and possibly molecular hydrogen has been confirmed by the Apollo 17 mass spectrometer. The observed helium concentrations and distribution agree closely with model predictions for a non-condensable gas based on a solar wind source, thermal escape and a Monte Carlo random walk calculated longitudinal distribution. Heavier gases are lost by photoionization and subsequent sweeping away by the solar wind electric field. The observed nighttime neon concentration of 80,000 molecules per cu cm is consistent with expected amounts. Argon, however, is adsorbed on the lunar surface late at night when the surface temperature is lowest. It shows the expected predawn enhancement exhibited by condensable gases released into the atmosphere at the sunrise terminator. Hydrogen appears to exist in the molecular rather than atomic state. Its observed concentration is less than a factor of 3 higher than that predicted by a model similar to that used for helium.
Hoffman, J. H.↗
Magnetic fields and the distribution of cosmic rays in the Galaxy
If a galactic origin for the bulk of cosmic-ray particles is assumed, it is the magnetic field which regulates the propagation and escape of the particles from the Galaxy. Questions of the anisotropy of the cosmic-ray flux are considered together with magnetic-field models which can confine the particles and produce low anisotropies. In one standard approach it is postulated that the particles random walk through the presumably irregular magnetic field. In view of the difficulties associated with a diffusion hypothesis other confinement mechanisms have been proposed.
Jokipii, J. R.↗
Fokker-Planck equations for charged-particle transport with a discussion of some higher-order effects
A derivation of the Fokker-Planck equation, based on the central limit theorem, is presented which clearly illustrates the conditions for its validity. It is reiterated that previous use of the Fokker-Planck equation in cosmic-ray transport is correct. Higher-order effects associated with magnetic mirroring and field line random walk at low energies are discussed heuristically.
Jokipii, J. R.↗
The abundances of nuclei in the cosmic radiation
The relative abundances are treated as a consequence of processes in cosmic ray transport occurring during passage of the radiation through interstellar material at high velocity. Some of the subjects mentioned are nuclear fragmentation and the production of secondary nuclei, nuclear reactions, energy loss and nuclear decay, ionization, the range-energy relation and propagation variables, capture and loss of electrons, the propagation of nuclei, the transport equation, equilibrium solutions, energy-dependent path length distribution, exponential path length distributions, discrete spectra, sources, supernovae, and the origin of the abundances. The connection between the space-time features of the sources, the material traversed, and the effects of magnetic fields is established by describing the particle-field interaction as a diffusive or random-walk process.
Reames, D. V.↗
Thermodynamic properties of small aggregates of rare-gas atoms
The present work reports on the equilibrium thermodynamic properties of small clusters of xenon, krypton, and argon atoms, determined from a biased random-walk Monte Carlo procedure. Cluster sizes ranged from 3 to 13 atoms. Each cluster was found to have an abrupt liquid-gas phase transition at a temperature much less than for the bulk material. An abrupt solid-liquid transition is observed for thirteen- and eleven-particle clusters. For cluster sizes smaller than 11, a gradual transition from solid to liquid occurred over a fairly broad range of temperatures. Distribution of number of bond lengths as a function of bond length was calculated for several systems at various temperatures. The effects of box boundary conditions are discussed. Results show the importance of a correct description of boundary conditions. A surprising result is the slow rate at which system properties approach bulk behavior as cluster size is increased.
Etters, R. D.↗
Information about accretion flows from X-ray timing of pulsating sources
The response was studied of a rotating neutron star to fluctuating torques and it was found that the observed variations in the pulsation periods of the compact X-ray sources Cen X-3 and Her X-1 could be caused by short time scale fluctuations in the accretion torques acting on the neutron stars. The sizes and rates of the required fluctuations are consistent with current accretion models. Such fluctuations can cause period variations either (a) directly, by causing a random walk of the star's angular velocity or (b) indirectly, by exciting a long-period mode of the neutron star, such as the Tkachenko mode of the rotating neutron superfluid. Phenomena in compact X-ray sources and cataclysmic variables which may be caused by fluctuating mass flow rates are also discussed.
Lamb, F. K.↗
On the character of the melting transition in small atomic aggregates
A biased random walk, Monte Carlo procedure is used to study the melting transition in small clusters of N atoms. Results show an abrupt change in physical properties near melting, but there is no evidence that the transition is either first or second order; rather the transition is more gradual.
Etters, R. D.↗
Energy distributions and radiation transport in uranium plasmas
An approximate analytic model, based on continuous electron slowing, has been used for survey calculations. Where more accuracy is required, a Monte Carlo technique is used which combines an analytic representation of Coulombic collisions with a random walk treatment of inelastic collisions. The calculated electron distributions have been incorporated into another code that evaluates both the excited atomic state densities within the plasma and the radiative flux emitted from the plasma.
Miley, G. H.↗
Fiber optic rotation sensor /FORS/ signal detection and processing
The recent development of low-loss single-mode optical fiber waveguides for light has made possible a new class of inertial reference devices built on the principle of a closed loop interferometer. Light circulating through the loop in both directions experiences a relative phase delay proportional to rotation rate about the loop axis. This paper derives the phase delay and discusses signal detection, signal processing techniques and error sources. It is concluded that synchronous modulation and demodulation and an active gain control at the signal calculation level are required to eliminate drift errors. Potential performance is extraordinarily good; rotation rate sensitivity of a few milli-arc seconds per second and angular position random walk errors of an arc second per square root hour appear feasible.
Goss, W. C.↗
Permanent magnetic trapping
It is shown that the global nature of trapped particle motion in phase space makes it entirely plausible that particles with pitch angles near 90 deg are trapped for extremely long times, probably indefinitely. The long observed lifetimes of trapped particles can immediately be accounted for by this former population. For particles with low pitch angles an 'overstability' develops which serves to produce rapid variations in pitch angle and, presumably, random walk into the loss cone.
Michel, F. C.↗
Use of generalized population ratios to obtain Fe XV line intensities and linewidths at high electron densities
A generalized method for obtaining individual level population ratios is used to obtain relative intensities of extreme ultraviolet Fe XV emission lines in the range 284-500 A, which are density dependent for electron densities in the tokamak regime or higher. Four lines in particular are found to attain quite high intensities in the high-density limit. The same calculation provides inelastic contributions to linewidths. The method connects level populations and level widths through total probabilities t(ij), related to 'taboo' probabilities of Markov chain theory. The t(ij) are here evaluated for a real atomic system, being therefore of potential interest to random-walk theorists who have been limited to idealized systems characterized by simplified transition schemes.
Kastner, S. O.↗
The stochastic evolution of asteroidal regoliths and the origin of brecciated and gas-rich meteorites
A model is constructed which views regolith evolution on asteroids as a stochastic process. Average values are shown to be poor descriptors of regolith depth. The utility of the average depth is not significantly increased by avoiding large craters or thick ejecta deposits, a procedure adopted in previous regolith studies. The statistical uncertainty associated with regolith depth severely limits the power of regolith models in predicting parent-body size for brecciated meteorites. A Monte Carlo algorithm was used to simulate the random walks and corresponding charged-particle irradiation histories of grains in regoliths. On rocky asteroids, only about 20 percent of the grains was exposed to solar cosmic ray ions. Results based on present-day conditions in the asteroid belt agree well with irradiation features observed in gas-rich meteorites. An origin during epochs of early solar system evolution is not required.
Housen, K. R.↗
The structure of particle-laden jets and nonevaporating sprays
Mean and fluctuating gas velocities, liquid mass fluxes and drop sizes were in nonevaporating sprays. These results, as well as existing measurements in solid particle-laden jets, were used to evaluate models of these processes. The following models were considered: (1) a locally homogeneous flow (LHF) model, where slip between the phases was neglected; (2) a deterministic separated flow (DSF) model, where slip was considered but effects of particle dispersion by turbulence were ignored; and (3) a stochastic separated flow (SSF) model, where effects of interphase slip and turbulent dispersion were considered using random-walk computations for particle motion. The LHF and DSF models did not provide very satisfactory predictions over the present data base. In contrast, the SSF model performed reasonably well - including conditions in nonevaporating sprays where enhanced dispersion of particles by turbulence caused the spray to spread more rapidly than single-phase jets for comparable conditions. While these results are encouraging, uncertainties in initial conditions limit the reliability of the evaluation. Current work is seeking to eliminate this deficiency.
Shuen, J. S.↗
The structure of evaporating and combusting sprays: Measurements and predictions
The structure of particle-laden jets and nonevaporating and evaporating sprays was measured in order to evaluate models of these processes. Three models are being evaluated: (1) a locally homogeneous flow model, where slip between the phases is neglected and the flow is assumed to be in local thermodynamic equilibrium; (2) a deterministic separated flow model, where slip and finite interphase transport rates are considered but effects of particle/drop dispersion by turbulence and effects of turbulence on interphase transport rates are ignored; and (3) a stochastic separated flow model, where effects of interphase slip, turbulent dispersion and turbulent fluctuations are considered using random sampling for turbulence properties in conjunction with random-walk computations for particle motion. All three models use a k-e-g turbulence model. All testing and data reduction are completed for the particle laden jets. Mean and fluctuating velocities of the continuous phase and mean mixture fraction were measured in the evaporating sprays.
Shuen, J. S.↗
The fundamental structure function of oscillator noise models
Continuous-time models of oscillator phase noise x(t) usually have stationary nth differences, for some n. The covariance structure of such a model can be characterized in the time domain by the structure function: D sub n (t;gamma sub 1, gamma sub 2) = E delta (n) sub gamma sub 1 x(s+t) delta(n) sub gamma sub 2 x (s). Although formulas for the special case D sub 2 (0;gamma,gamma) (the Allan variance times 2 gamma(2)) exist for power-law spectral models, certain estimation problems require a more complete knowledge of (0). Exhibited is a much simpler function of one time variable, D(t), from which (0) can easily be obtained from the spectral density by uncomplicated integrations. Believing that D(t) is the simplest function of time that holds the same information as (0), D(t) is called the fundamental structure function. D(t) is computed for several power-law spectral models. Two examples are D(t) = K/t/(3) for random walk FM, D(t) = Kt(2) 1n/t/ for flicker FM. Then, to demonstrate its use, a BASIC program is given that computes means and variances of two Allan variance estimators, one of which incorporates a method of frequency drift estimation and removal.
Greenhall, C. A.↗
A second-order effect of stratospheric vertical motions
A byproduct of stratospheric motion distinct from the normal downgradient transport represented by vertical eddy diffusion is studied. It is suggested that an air parcel executes a random walk over a range that could be several kilometers, and similar amplitudes could be present in wavelike oscillations. The photochemical loss rate should therefore be averaged over this range, which give an effect that is proportional to the curvature of the profile of loss rate, and is particularly large for fluorocarbon-11, CFCl3. Test computations are presented which indicate that the known discrepancy between observations and predictions for this compound can be at least partly reconciled for plausible values of the amplitude.
Hunten, D. M.↗