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All sourcesNASA NTRSDOE OSTI
NASA NTRS2000

Possible Statistics of Two Coupled Random Fields: Application to Passive Scalar

We use the relativity postulate of scale invariance to derive the similarity transformations between two coupled scale-invariant random elds at different scales. We nd the equations leading to the scaling exponents. This formulation is applied to the case of passive scalars advected i) by a random Gaussian velocity field; and ii) by a turbulent velocity field. In the Gaussian case, we show that the passive scalar increments follow a log-Levy distribution generalizing Kraichnan's solution and, in an appropriate limit, a log-normal distribution. In the turbulent case, we show that when the velocity increments follow a log-Poisson statistics, the passive scalar increments follow a statistics close to log-Poisson. This result explains the experimental observations of Ruiz et al. about the temperature increments.

Dubrulle, B.↗
NASA NTRS1973

Synthetic aperture radar system design for random field classification

An optimum design study is carried out for synthetic aperture radar systems intended for classifying randomly reflecting areas (such as agricultural fields) characterized by a reflectivity density spectral density. The problem solution is obtained, neglecting interfield interference and assuming areas of known configuration and location, as well as a certain Gaussian signal field property. The optimum processor is nonlinear, but includes conventional matched filter processing. A set of summary design curves is plotted, and is applied to the design of a satellite synthetic aperture radar system.

Harger, R. O.↗
NASA NTRS1972

Fokker-Planck equations for charged-particle transport in random fields.

The Fokker-Planck equations for charged-particle dynamics are rederived, extending somewhat the elegant discussion of Hasselmann and Wibberenz. It is shown that the usual results are obtae and the conclusions in many cases are correct over a very broad range in energy. In particular, the rate for pitch-angle scattering may be accurately given down to energies much lower than previously thought. Recent claims that these Fokker-Planck equations are in general incorrect are thus shown to be in error.

Jokipii, J. R.↗
NASA NTRS1988

Subpixel translation-registration of random fields

The author examines both theoretically and through a simulation study the feasibility of identifying the location within a large reference gray-level array of a smaller sensed array to an accuracy finer than one pixel. It is assumed that the sensed image before discretization into pixels consists of a translated, but not rotated, section of the reference image with some superposed noise. The theoretical and empirical results show that when the noise has standard deviation no larger than that of a realistic reference field, the upper quartile of the registration error is on the order of 0.25-0.5 pixels.

Slud, Eric V.↗
NASA NTRS1992

Effect of magnetic helicity upon rectilinear propagation of charged particles in random magnetic fields

When charged particles spiral along a large constant magnetic field, their trajectories are scattered by any random field components that are superposed on the guiding field. If the random field configuration embodies helicity, the scattering is asymmetrical with respect to a plane perpendicular to the guiding field, for particles moving into the forward hemisphere are scattered at different rates from those moving into the backward hemisphere. This asymmetry gives rise to new terms in the transport equations that describe propagation of charged particles. Helicity has virtually no impact on qualitative features of the diffusive mode of propagation. However, characteristic velocities of the coherent modes that appear after a highly anisotropic injection exhibit an asymmetry related to helicity. Explicit formulas, which embody the effects of helicity, are given for the anisotropies, the coefficient diffusion, and the coherent velocities. Predictions derived from these expressions are in good agreement with Monte Carlo simulations of particle transport, but the simulations reveal certain phenomena whose explanation calls for further analytical work.

Earl, James A.↗
NASA NTRS1972

Random walk study of electron motion in helium in crossed electromagnetic fields

Random walk theory, previously adapted to electron motion in the presence of an electric field, is extended to include a transverse magnetic field. In principle, the random walk approach avoids mathematical complexity and concomitant simplifying assumptions and permits determination of energy distributions and transport coefficients within the accuracy of available collisional cross section data. Application is made to a weakly ionized helium gas. Time of relaxation of electron energy distribution, determined by the random walk, is described by simple expressions based on energy exchange between the electron and an effective electric field. The restrictive effect of the magnetic field on electron motion, which increases the required number of collisions per walk to reach a terminal steady state condition, as well as the effect of the magnetic field on electron transport coefficients and mean energy can be quite adequately described by expressions involving only the Hall parameter.

Englert, G. W.↗
NASA NTRS1976

The effect of adiabatic focusing upon charged-particle propagation in random magnetic fields

The charged particles considered are scattered by random fields while they propagate along the diverging lines of force of a spatially inhomogeneous guiding field. Their longitudinal transport is described in terms of the eigenfunctions of a Sturm-Liouville operator which incorporates the effect of adiabatic focusing along with that of scattering. The relaxation times and characteristic velocities which appear in this matrix formulation of the transport problem are graphed and tabulated. Explicit formulas which describe the particle-density profile that results from a localized impulsive injection are derived for two different regimes. In the first regime, where focusing is relatively weak, a diffusive mode of propagation is dominant, but coherent modes are also present, and they become prominent as the intensity of focusing increases. In the second regime, where focusing is strong and where diffusion does not occur, the propagation is purely coherent. The existence of this supercoherent mode of particle transport opens up many possibilities for the interpretation of astrophysical phenomena.

Earl, J. A.↗
NASA NTRS1992

Effective diffusion equation in a random velocity field

The effects are studied of assumed random velocity fields on diffusion in a binary fluid. Random velocity fields can result, for example, from the high-frequency components of residual accelerations onboard spacecraft (often called g-jitter). An effective diffusion equation is derived for an average concentration which includes spatial and temporal correlations induced by the fluctuating velocity fields assumed to be Gaussianly distributed. The resulting equation becomes nonlocal, and if correlations between different components of the velocity field exist, it is also anisotropic. The simple limiting case of short correlation times is discussed and an effective diffusivity is obtained which reflects the enhanced mixing caused by the velocity fields. The results obtained in the limit of short correlation times are valid even if the probability distribution of the velocity field is not Gaussian.

Vinals, Jorge↗
NASA NTRS1973

The parallel diffusion of cosmic rays in a random magnetic field.

Within the quasi-linear approximation, the existence of the parallel diffusion coefficient for cosmic rays in a random magnetic field (homogeneous, isotropic), despite the slow decay of the interaction between particles and random field, is demonstrated. As an example, the results of a numerical calculation of the parallel diffusion coefficient for a Gaussian random-field correlation function are presented. The numerical results are corroborated by asymptotic analysis and are compared to those of other theories.

Klimas, A.↗
NASA NTRS1985

The dispersive evolution of charged-particle bunches in random magnetic fields

Shortly after a strongly anisotropic beam of charged particles is injected along a guiding magnetic field on which is superimposed a small random conponent, the particle density can be represented by a Gaussian profile whose center moves with the coherent velocity and whose width increases with time at a rate controlled by the coefficient of dispersion. Both parameters depend upon the mean free path, which characterizes scattering by the random fields, and the focusing length, which characterizes spatial variations of the guiding field. These dependencies are known explicitly for the coherent velocity. Formulae for coefficient of dispersion are available only in the limits of very weak and very strong focusing. A new expression for coefficient of dispersion, which spans this gap, is presented.

Earl, J. A.↗