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NASA NTRS1995

Non-WKB Alfven waves in the solar wind: Propagation and reflection of pulses

The non-WKB propagation of Alfven waves has been studied either for harmonic waves, or in terms of the evolution of power spectra. Here we present analytical and numerical solutions for the propagation of pulses, the goal being to understand how waves reflect in a smoothly varying medium. We here limit our discussion to a radial magnetic field. If we launch an outward-propagating delta function, it leaves behind an inward-propagaing signal which is roughly a square wave whose amplitude is proportional to the area under the initial pulse. The inward-propagating signal also reflects, producing an outward propagating pulse which is roughly triangular in shape and which grows with time. These signals also oscillate if v is less than v(A), but they grow if v is greater than v(A). The result reported by us earlier, that the 'ingoing Elsasser variable' can have outgoing phase, is now understood to be a consequence of interference. The inward-propagating signal depends to lowest order on the integral of the outgoing waves which have preceded it. Thus the ingoing signal can be expected to develop as a random walk. This will affect the radial evolution of cross-helicity in the solar wind.

Hollweg, J. V.↗
NASA NTRS1995

On the upstream boundary of electron foreshocks in the solar wind

The upstream boundary of electron foreshocks is defined as the path of the fastest electrons reflected by collisionless shocks and moving along the magnetic field in the solar wind. Considerable levels of magnetic fluctuations are found in these regions of the solar wind, and their effect is to create both a broadening and a fine structure of the electron foreshock boundary. The magnetic structure is studied by means of a 3-D numerical simulation of a turbulent magnetic field. Enhanced, anomalous diffusion is found, (Delta x(exp 2)) varies as s(sup alpha), where alpha is greater than 1 for typical values of the parameters (here, Delta x(exp 2) is the mean square width of the tangent magnetic surface and s is the field line length). This corresponds to a Levy flight regime for the magnetic field line random walk, and allows very efficient electron propagation perpendicular to the magnetic field. Implications on the observations of planetary foreshocks and of the termination shock foreshock are considered.

Zimbardo, G.↗
NASA NTRS1996

Variance Analysis of Unevenly Spaced Time Series Data

We have investigated the effect of uneven data spacing on the computation of delta (sub chi)(gamma). Evenly spaced simulated data sets were generated for noise processes ranging from white phase modulation (PM) to random walk frequency modulation (FM). Delta(sub chi)(gamma) was then calculated for each noise type. Data were subsequently removed from each simulated data set using typical two-way satellite time and frequency transfer (TWSTFT) data patterns to create two unevenly spaced sets with average intervals of 2.8 and 3.6 days. Delta(sub chi)(gamma) was then calculated for each sparse data set using two different approaches. First the missing data points were replaced by linear interpolation and delta (sub chi)(gamma) calculated from this now full data set. The second approach ignored the fact that the data were unevenly spaced and calculated delta(sub chi)(gamma) as if the data were equally spaced with average spacing of 2.8 or 3.6 days. Both approaches have advantages and disadvantages, and techniques are presented for correcting errors caused by uneven data spacing in typical TWSTFT data sets.

Hackman, Christine↗
NASA NTRS1999

Approximation for Horizontal Photon Transport in Cloud Remote Sensing Problems

The effect of horizontal photon transport within real-world clouds can be of consequence to remote sensing problems based on plane-parallel cloud models. An analytic approximation for the root-mean-square horizontal displacement of reflected and transmitted photons relative to the incident cloud-top location is derived from random walk theory. The resulting formula is a function of the average number of photon scatterings, and particle asymmetry parameter and single scattering albedo. In turn, the average number of scatterings can be determined from efficient adding/doubling radiative transfer procedures. The approximation is applied to liquid water clouds for typical remote sensing solar spectral bands, involving both conservative and non-conservative scattering. Results compare well with Monte Carlo calculations. Though the emphasis is on horizontal photon transport in terrestrial clouds, the derived approximation is applicable to any multiple scattering plane-parallel radiative transfer problem. The complete horizontal transport probability distribution can be described with an analytic distribution specified by the root-mean-square and average displacement values. However, it is shown empirically that the average displacement can be reasonably inferred from the root-mean-square value. An estimate for the horizontal transport distribution can then be made from the root-mean-square photon displacement alone.

Plantnick, Steven↗
NASA NTRS2000

Inertial Effects in Suspension Dynamics

The present work analyses the dynamics of a suspension of heavy particles in shear flow. The magnitude of the particle inertia is given by the Stokes number St = m(gamma/6(pi)a, which is the ratio of the viscous relaxation time of a particle tau(sub p) = m=6pi(eta)a to the flow time gamma(sup -1). Here, m is the mass of the particle, a is its size, eta is the viscosity of the suspending fluid and gamma is the shear rate. The ratio of the Stokes number to the Reynolds number, Re = (rho)f(gamma)a(exp 2)/eta, is the density ratio rho(sub p)/rho(sub f). Of interest is to understand the separate roles of particle (St) and fluid (Re) inertia in the dynamics of suspensions. In this study we focus on heavy particles, rho(sub p)/rho(sub f) much greater than 1, for which the Stokes number is finite, but the Reynolds number is sufficiently small for inertial forces in the fluid to be neglected; thus, the fluid motion is governed by the Stokes equations. On the other hand, the probability density governing the statistics of the suspended particles satisfies a Fokker-Planck equation that accounts for both configuration and momentum coordinates, the latter being essential for finite St. The solution of the Fokker-Planck equation is obtained to O(St) via a Chapman-Enskog type-procedure, and the conditional velocity distribution so obtained is used to derive a configuration-space Smoluchowski equation with inertial corrections. The inertial effects are responsible for asymmetry in the relative trajectories of two spheres in shear flow, in contrast to the well known symmetric structure in the absence of inertia. Finite St open trajectories in the plane of shear suffer a downward lateral displacement resulting from the inability of a particle of finite mass to follow the curvature of the zero-Stokes-number pathlines. In addition to the induced asymmetry, the O(St) inertial perturbation dramatically alters the nature of the near-field trajectories. The stable closed orbits (for St = 0) in the plane of shear now spiral in, approaching particle-particle contact in the limit. All trajectories starting from an initial offset of O(St(sup 1/2) or less (which remain open for St = 0) also spiral in. The asymmetry of the trajectories leads to a non-Newtonian rheology and diffusive behavior. The latter because a given particle (moving along a finite St open trajectory) suffers a net displacement in the transverse direction after a single interaction. A sequence of such uncorrelated displacements leads to the particle executing a random walk. The inertial diffusivity tensor is anisotropic on account of differing strengths of interaction in the gradient and vorticity directions. Since the entire region (constituting an in finite area) of closed orbits in the plane of shear spirals onto contact for #finite St, the latter represents a singular surface for the pair-distribution function. The exact form of the pair-distribution function at contact is still, however, indeterminate in the absence of non-hydrodynamic effects. It should also be noted that finite St non-rectilinear flows do not support a spatially uniform number density owing to the cross-streamline inertial migration of particles.

J. F. Brady↗
NASA NTRS2001

Analysis of GPS Data Collected on the Greenland Ice Sheet

For several years, GPS observations have been made year round at the Swiss Camp, Greenland. The GPS data are recorded for 12 hours every 10-15 days; data are stored in memory and downloaded during the annual field season. Traditional GPS analysis techniques, where the receiver is assumed not to move within a 24 hour period, is not appropriate at the Swiss Camp, where horizontal velocities are on the order of 30 cm/day. Comparison of analysis strategies for these GPS data indicate that a random walk parameterization, with a constraint of 1-2 x 10(exp -7) km/sqrt(sec) minimizes noise due to satellite outages without corrupting the estimated ice velocity. Low elevation angle observations should be included in the analysis in order to increase the number of satellites viewed at each data epoch. Carrier phase ambiguity resolution is important for improving the accuracy of receiver coordinates.

Larson, K.↗
NASA NTRS2001

The Steady Spin-down Rate of 4U 1907+09

Using X-ray data from the Rossi X-ray Timing Explorer, we report the pulse timing results of the accretion-powered, high-mass X-ray binary pulsar 4UU 1907+09, covering a time-span of almost two years. We measured three new pulse periods in addition to the previously measured four pulse periods. We are able to connect pulse arrival times in phase for more than a year. The source has been spinning down almost at a constant rate, with a spin-down rate of v = (- 3.54 +/- 0.02) x 10(exp -14) Hz s(exp -1) for more than 15 yr. Residuals of pulse arrival times yield a very low level of random-walk noise, with a strength of approximately 2 x 10(exp -20) rad(exp 2) s(exp -3) on a time-scale of 383 d, which is 40 times lower than that of the high-mass X-ray binary pulsar Vela X-1. The noise strength is only a factor of five greater than that of the low-mass X-ray binary pulsar 4U 1626-67. The low level of the timing noise and the very stable spin-down rate of 4U 1907+09 make this source unique among the high-mass X-ray binary pulsars, providing another example, in addition to 4U 1626-67, of long-term quiet spin down from an accruing source. These examples show that the extended quiet spin-down episodes observed in the anomalous X-ray pulsars 1RXS J170849.0-400910 and 1E 2259+586 do not necessarily imply that these sources are not accreting pulsars.

Baykal, Altan↗
NASA NTRS1996

Age-related alterations in the fractal scaling of cardiac interbeat interval dynamics

We postulated that aging is associated with disruption in the fractallike long-range correlations that characterize healthy sinus rhythm cardiac interval dynamics. Ten young (21-34 yr) and 10 elderly (68-81 yr) rigorously screened healthy subjects underwent 120 min of continuous supine resting electrocardiographic recording. We analyzed the interbeat interval time series using standard time and frequency domain statistics and using a fractal measure, detrended fluctuation analysis, to quantify long-range correlation properties. In healthy young subjects, interbeat intervals demonstrated fractal scaling, with scaling exponents (alpha) from the fluctuation analysis close to a value of 1.0. In the group of healthy elderly subjects, the interbeat interval time series had two scaling regions. Over the short range, interbeat interval fluctuations resembled a random walk process (Brownian noise, alpha = 1.5), whereas over the longer range they resembled white noise (alpha = 0.5). Short (alpha s)- and long-range (alpha 1) scaling exponents were significantly different in the elderly subjects compared with young (alpha s = 1.12 +/- 0.19 vs. 0.90 +/- 0.14, respectively, P = 0.009; alpha 1 = 0.75 +/- 0.17 vs. 0.99 +/- 0.10, respectively, P = 0.002). The crossover behavior from one scaling region to another could be modeled as a first-order autoregressive process, which closely fit the data from four elderly subjects. This implies that a single characteristic time scale may be dominating heartbeat control in these subjects. The age-related loss of fractal organization in heartbeat dynamics may reflect the degradation of integrated physiological regulatory systems and may impair an individual's ability to adapt to stress.

NASA Discipline Cardiopulmonary↗
NASA NTRS1996

A test of the deadline model for speed-accuracy tradeoffs

Two experiments were conducted to evaluate the deadline model for speed-accuracy tradeoffs. According to the deadline model, participants in speeded-response tasks terminate stimulus discrimination as soon as it has run to completion or as soon as a predetermined time deadline has arrived, whichever comes first. Speed is traded for accuracy by varying the time deadlines; short deadlines yield fast but sometimes inaccurate responses, whereas long deadlines allow for slow, accurate responses. A new prediction of this model, based on a comparison of reaction time distributions, was derived and tested in experiments involving the joint manipulation of speed stress and stimulus discriminability. Clear violations of this prediction were observed when participants made relative brightness judgments (Experiment 1) and when they made lexical decisions (Experiment 2), rejecting both the deadline model and the fast-guess model. Several alternative models for speed-accuracy tradeoffs, including random-walk and accumulator models, are compatible with the results.

Discrimination (Psychology)↗
NASA NTRS2005

Adaptive Metropolis Sampling with Product Distributions

The Metropolis-Hastings (MH) algorithm is a way to sample a provided target distribution pi(z). It works by repeatedly sampling a separate proposal distribution T(x,x') to generate a random walk {x(t)}. We consider a modification of the MH algorithm in which T is dynamically updated during the walk. The update at time t uses the {x(t' less than t)} to estimate the product distribution that has the least Kullback-Leibler distance to pi. That estimate is the information-theoretically optimal mean-field approximation to pi. We demonstrate through computer experiments that our algorithm produces samples that are superior to those of the conventional MH algorithm.

Wolpert, David H.↗
NASA NTRS2003

Vortex Loops at the Superfluid Lambda Transition: An Exact Theory?

A vortex-loop theory of the superfluid lambda transition has been developed over the last decade, with many results in agreement with experiments. It is a very simple theory, consisting of just three basic equations. When it was first proposed the main uncertainty in the theory was the use Flory scaling to find the fractal dimension of the random-walking vortex loops. Recent developments in high-resolution Monte Carlo simulations have now made it possible to verify the accuracy of this Flory-scaling assumption. Although the loop theory is not yet rigorously proven to be exact, the Monte Carlo results show at the least that it is an extremely good approximation. Recent loop calculations of the critical Casimir effect in helium films in the superfluid phase T < Tc will be compared with similar perturbative RG calculations in the normal phase T > Tc; the two calculations are found to match very nicely right at Tc.

Williams, Gary A.↗
NASA NTRS1996

A Derivation of the Long-Term Degradation of a Pulsed Atomic Frequency Standard from a Control-Loop Model

The phase of a frequency standard that uses periodic interrogation and control of a local oscillator (LO) is degraded by a long-term random-walk component induced by downconversion of LO noise into the loop passband. The Dick formula for the noise level of this degradation is derived from an explicit solution of an LO control-loop model.

Dick formula local oscillator frequency phase freq↗
NASA NTRS1996

A Derivation of the Dick Effect from Control-Loop Models for Periodically Interrogated Passive Frequency Standards

The phase of a frequency standard that uses periodic interrogation and control of a local oscillator (LO) is degraded by a long-term random-walk component induced by downconversion of LO noise into the loop passband. The Dick formula for the noise level of this degradation can be derived from explicit solotions of two LO control-loop models. A summary of the derivations is given here.

Dick Effect Dick Formula local oscillator noise fr↗
NASA NTRS2006

Exploring the Connection Between Sampling Problems in Bayesian Inference and Statistical Mechanics

The Bayesian and statistical mechanical communities often share the same objective in their work - estimating and integrating probability distribution functions (pdfs) describing stochastic systems, models or processes. Frequently, these pdfs are complex functions of random variables exhibiting multiple, well separated local minima. Conventional strategies for sampling such pdfs are inefficient, sometimes leading to an apparent non-ergodic behavior. Several recently developed techniques for handling this problem have been successfully applied in statistical mechanics. In the multicanonical and Wang-Landau Monte Carlo (MC) methods, the correct pdfs are recovered from uniform sampling of the parameter space by iteratively establishing proper weighting factors connecting these distributions. Trivial generalizations allow for sampling from any chosen pdf. The closely related transition matrix method relies on estimating transition probabilities between different states. All these methods proved to generate estimates of pdfs with high statistical accuracy. In another MC technique, parallel tempering, several random walks, each corresponding to a different value of a parameter (e.g. "temperature"), are generated and occasionally exchanged using the Metropolis criterion. This method can be considered as a statistically correct version of simulated annealing. An alternative approach is to represent the set of independent variables as a Hamiltonian system. Considerab!e progress has been made in understanding how to ensure that the system obeys the equipartition theorem or, equivalently, that coupling between the variables is correctly described. Then a host of techniques developed for dynamical systems can be used. Among them, probably the most powerful is the Adaptive Biasing Force method, in which thermodynamic integration and biased sampling are combined to yield very efficient estimates of pdfs. The third class of methods deals with transitions between states described by rate constants. These problems are isomorphic with chemical kinetics problems. Recently, several efficient techniques for this purpose have been developed based on the approach originally proposed by Gillespie. Although the utility of the techniques mentioned above for Bayesian problems has not been determined, further research along these lines is warranted

Pohorille, Andrew↗
NASA NTRS2008

A Stable Clock Error Model Using Coupled First and Second Order Gauss-Markov Processes

Long data outages may occur in applications of global navigation satellite system technology to orbit determination for missions that spend significant fractions of their orbits above the navigation satellite constellation(s). Current clock error models based on the random walk idealization may not be suitable in these circumstances, since the covariance of the clock errors may become large enough to overflow flight computer arithmetic. A model that is stable, but which approximates the existing models over short time horizons is desirable. A coupled first- and second-order Gauss-Markov process is such a model.

Carpenter, Russell↗
NASA NTRS2008

Using LDPC Code Constraints to Aid Recovery of Symbol Timing

A method of utilizing information available in the constraints imposed by a low-density parity-check (LDPC) code has been proposed as a means of aiding the recovery of symbol timing in the reception of a binary-phase-shift-keying (BPSK) signal representing such a code in the presence of noise, timing error, and/or Doppler shift between the transmitter and the receiver. This method and the receiver architecture in which it would be implemented belong to a class of timing-recovery methods and corresponding receiver architectures characterized as pilotless in that they do not require transmission and reception of pilot signals. Acquisition and tracking of a signal of the type described above have traditionally been performed upstream of, and independently of, decoding and have typically involved utilization of a phase-locked loop (PLL). However, the LDPC decoding process, which is iterative, provides information that can be fed back to the timing-recovery receiver circuits to improve performance significantly over that attainable in the absence of such feedback. Prior methods of coupling LDPC decoding with timing recovery had focused on the use of output code words produced as the iterations progress. In contrast, in the present method, one exploits the information available from the metrics computed for the constraint nodes of an LDPC code during the decoding process. In addition, the method involves the use of a waveform model that captures, better than do the waveform models of the prior methods, distortions introduced by receiver timing errors and transmitter/ receiver motions. An LDPC code is commonly represented by use of a bipartite graph containing two sets of nodes. In the graph corresponding to an (n,k) code, the n variable nodes correspond to the code word symbols and the n-k constraint nodes represent the constraints that the code places on the variable nodes in order for them to form a valid code word. The decoding procedure involves iterative computation of values associated with these nodes. A constraint node represents a parity-check equation using a set of variable nodes as inputs. A valid decoded code word is obtained if all parity-check equations are satisfied. After each iteration, the metrics associated with each constraint node can be evaluated to determine the status of the associated parity check. Heretofore, normally, these metrics would be utilized only within the LDPC decoding process to assess whether or not variable nodes had converged to a codeword. In the present method, it is recognized that these metrics can be used to determine accuracy of the timing estimates used in acquiring the sampled data that constitute the input to the LDPC decoder. In fact, the number of constraints that are satisfied exhibits a peak near the optimal timing estimate. Coarse timing estimation (or first-stage estimation as described below) is found via a parametric search for this peak. The present method calls for a two-stage receiver architecture illustrated in the figure. The first stage would correct large time delays and frequency offsets; the second stage would track random walks and correct residual time and frequency offsets. In the first stage, constraint-node feedback from the LDPC decoder would be employed in a search algorithm in which the searches would be performed in successively narrower windows to find the correct time delay and/or frequency offset. The second stage would include a conventional first-order PLL with a decision-aided timing-error detector that would utilize, as its decision aid, decoded symbols from the LDPC decoder. The method has been tested by means of computational simulations in cases involving various timing and frequency errors. The results of the simulations ined in the ideal case of perfect timing in the receiver.

Jones, Christopher↗
NASA NTRS2009

A Monte-Carlo Model for the Formation of Radiation-induced Chromosomal Aberrations

Purpose: To simulate radiation-induced chromosome aberrations in mammalian cells (e.g., rings, translocations, and dicentrics) and to calculate their frequency distributions following exposure to DNA double strand breaks (DSBs) produced by high-LET ions. Methods: The interphase genome was assumed to be comprised of a collection of 2 kbp rigid-block monomers following the random-walk geometry. Additional details for the modeling of chromosomal structure, such as chromosomal domains and chromosomal loops, were included. A radial energy profile for heavy ion tracks was used to simulate the high-LET pattern of induced DSBs. The induced DSB pattern depended on the ion charge and kinetic energy, but always corresponded to the DSB yield of 25 DSBs/cell/Gy. The sum of all energy contributions from Poisson-distributed particle tracks was taken to account for all possible one-track and multi-track effects. The relevant output of the model was DNA fragments produced by DSBs. The DSBs, or breakpoints, were defined by (x, y, z, l) positions, where x, y, z were the Euclidian coordinates of a DSB, and where l was the relative position along the genome. Results: The code was used to carry out Monte Carlo simulations for DSB rejoinings at low doses. The resulting fragments were analyzed to estimate the frequencies of specific types of chromosomal aberrations. Histograms for relative frequencies of chromosomal aberrations and P.D.F.s (probability density functions) of a given aberration type were produced. The relative frequency of dicentrics to rings was compared to empirical data to calibrate rejoining probabilities. Of particular interest was the predicted distribution of ring sizes, irrespective of their frequencies relative to other aberrations. Simulated ring sizes were . 4 kbp, which are far too small to be observed experimentally (i.e., by microscopy) but which, nevertheless, are conjectured to exist. Other aberrations, for example, inversions, translocations, as well as multi-centrics were also recorded. Conclusion: High-LET DNA damage affects the frequencies of chromosomal aberrations. The ratio of rings to dicentrics is correct for the genomic size cut-offs corresponding to available experimental data. The present work predicts a relative abundance of small rings following irradiation by heavy ions.

Ponomarev, Artem L.↗
NASA NTRS2008

Modeling of the Ablation of Fibrous Materials in the Knudsen Regime

During atmospheric entry of planetary probes, the thermal protection system (TPS) of the probe is exposed to high temperatures under low pressures. In these conditions, carbonous TPS materials undergo gasification in the Knudsen regime leading to mass loss and wall recession called ablation. This work aims to improve the understanding of materiaVenvironment interactions through a study of the coupling between carbon dioxide transport in the Knudsen regime, heterogeneous oxidation of carbon, and sutface recession. A 3D Monte-Carlo simulation tool is used for this study. The fibrous architecture of the materiils, consisting of high porosity random array of carbon fibers, is numerically reproduced on a 3D Cartesian grid. Mass transport in the Knudsen regime from the boundary layer to the surface, and inside this porous material is simulated by random walk. A reaction probability is used to simulate the heterogeneous oxidation reaction. The surface recession is followed by front tracking using a simplified marching cube approach. The output data of the simulations are ablation velocity and dynamic evolution of the material porosity. A parametric study is carried out to analyze the material behavior as a function of Knudsen number for the porous media (length of the mean free path compared to the mean pore diameter) and the intrinsic reactivity of the carbon fibers. The results enable extrapolation of laboratory experimental data to actual entry conditions.

Lachaud, J.↗