Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “random walk”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS1995

A digital boxcar integrator for IMS spectra

When trying to detect or quantify a signal at or near the limit of detectability, it is invariably embeded in the noise. This statement is true for nearly all detectors of any physical phenomena and the limit of detectability, hopefully, occurs at very low signal-to-noise levels. This is particularly true of IMS (Ion Mobility Spectrometers) spectra due to the low vapor pressure of several chemical compounds of great interest and the small currents associated with the ionic detection process. Gated Integrators and Boxcar Integrators or Averagers are designed to recover fast, repetitive analog signals. In a typical application, a time 'Gate' or 'Window' is generated, characterized by a set delay from a trigger or gate pulse and a certain width. A Gated Integrator amplifies and integrates the signal that is present during the time the gate is open, ignoring noise and interference that may be present at other times. Boxcar Integration refers to the practice of averaging the output of the Gated Integrator over many sweeps of the detector. Since any signal present during the gate will add linearly, while noise will add in a 'random walk' fashion as the square root of the number of sweeps, averaging N sweeps will improve the 'Signal-to-Noise Ratio' by a factor of the square root of N.

Cohen, Martin J.↗
NASA NTRS1994

Charged-particle motion in multidimensional magnetic-field turbulence

We present a new analysis of the fundamental physics of charged-particle motion in a turbulent magnetic field using a numerical simulation. The magnetic field fluctuations are taken to be static and to have a power spectrum which is Kolmogorov. The charged particles are treated as test particles. It is shown that when the field turbulence is independent of one coordinate (i.e., k lies in a plane), the motion of these particles across the magnetic field is essentially zero, as required by theory. Consequently, the only motion across the average magnetic field direction that is allowed is that due to field-line random walk. On the other hand, when a fully three-dimensional realization of the turbulence is considered, the particles readily cross the field. Transport coefficients both along and across the ambient magnetic field are computed. This scheme provides a direct computation of the Fokker-Planck coefficients based on the motions of individual particles, and allows for comparison with analytic theory.

Giacalone, J.↗
NASA NTRS1993

A diffusion-limited aggregation model for the evolution of drainage networks

We propose a modified diffusion-limited aggregation (DLA) model for the evolution of fluvial drainage networks. Random walkers are introduced randomly on a grid, and each two-dimensional random walk proceeds until the walker finds a drainage network on which to accrete. This model for headward growth of drainage networks generates drainage patterns remarkably similar to actual drainages. The model also predicts statistical features which agree with actual networks, including the frequency-order (bifurcation) ratio (R(sub b) = 3.98) and the stream length-order (R(sub r) = 2.09). Using the definition of network fractal dimension D = log R(sub b)/log R(sub r), we find that our DLA model gives D = 1.87, near the observed range of D approximately equal to 1.80 - 1.85.

Masek, Jeffrey G.↗
NASA NTRS1994

The short-term prediction of universal time and length of day using atmospheric angular momentum

The ability to predict short-term variations in the Earth's rotation has gained importance in recent years owing to more precise spacecraft tracking requirements. Universal time (UT1), that component of the Earth's orientation corresponding to the rotation angle, can be measured by number of high-precision space geodetic techniques. A Kalman filter developed at the Jet Propulsion Laboratory (JPL) optimally combines these different data sets and generates a smoothed times series and a set of predictions for UT1, as well as for additional Earth orientation components. These UT1 predictions utilize an empirically derived random walk stochastic model for the length of the day (LOD) and require frequent and up-to-date measurements of either UT1 or LOD to keep errors from quickly accumulating. Recent studies have shown that LOD variations are correlated with changes in the Earth's axial atmospheric angular momentum (AAM) over timescales of several years down to as little as 8 days. AAM estimates and forecasts out to 10 days are routinely available from meteorological analysis centers; these data can supplement geodetic measurements to improve the short-term prediction of LOD and have therefore been incorporated as independent data types in the JPL Kalman filter. We find that AAM and, to a lesser extent, AAM forecast data are extremely helpful in generating accurate near-real-time estimates of UT1 and LOD and in improving short-term predictions of these quantities out to about 10 days.

Freedman, A. P.↗
NASA NTRS1995

A count probability cookbok: Spurious effects and the scaling model

We study the errors brought by finite volume effects and dilution effects on the practical determination of the count probability distribution function P(sub N)(n,l), which is the probability of having N objects in a cell of volume l cubed for a set of average number density n. Dilution effects are particularly revelant to the so-called sparse sampling strategy. This work is mainly done in the framework of the Bailan & Schaeffer scaling model, which assumes that the Q-body correlation functions obey the scaling relation Xi(sub Q)(lambda r(sub l),....lambda r(sub Q) = lambda(exp -(Q-1)gamma) Xi(sub Q)(r(sub 1),....r(sub Q)). We use three synthetic samples as references to perform our analysis: a fractal generated by a Rayleigh-Levy random walk with approximately 3 x 10(exp 4) objects, a sample dominated by a spherical power-law cluster with approximately 3 x 10(exp 4) objects and a cold dark matter (CDM) universe involving approximately 3 x 10(exp 5) matter particles.

Colombi, S.↗
NASA NTRS1994

On the effects of a weak magnetic field on turbulent transport

We discuss the effects of a weak large-scale magnetic field on turbulent transport. We show by means of a series of two-dimensional numerical experiments that turbulent diffusion can be effectively suppressed by a (large scale) magnetic field whose energy is small compared to equipartition. The suppression mechanism is associated with a subtle modification of the Lagrangian energy spectrum, and it does not require any substantial reduction of the turbulent amplitude. We exploit the relation between diffusion and random walking to emphasize that the effect of a large-scale magnetic field is to induce a long-term memory in the field of turbulence. The implications of the general case of three-dimensional transport are briefly discussed.

Cattaneo, F.↗
NASA NTRS1995

Solar wind eddies and the heliospheric current sheet

Ulysses has collected data between 1 and 5 AU during, and just following solar maximum, when the heliospheric current sheet (HCS) can be thought of as reaching its maximum tilt and being subject to the maximum amount of turbulence in the solar wind. The Ulysses solar wind plasma instrument measures the vector velocity and can be used to estimate the flow speed and direction in turbulent 'eddies' in the solar wind that are a fraction of an astronomical unit in size and last (have either a turnover or dynamical interaction time of) several hours to more than a day. Here, in a simple exercise, these solar wind eddies at the HCS are characterized using Ulysses data. This character is then used to define a model flow field with eddies that is imposed on an ideal HCS to estimate how the HCS will be deformed by the flow. This model inherently results in the complexity of the HCS increasing with heliocentric distance, but the result is a measure of the degree to which the observed change in complexity is a measure of the importance of solar wind flows in deforming the HCS. By comparison with randomly selected intervals not located on the HCS, it appears that eddies on the HCS are similar to those elsewhere at this time during the solar cycle, as is the resultant deformation of the interplanetary magnetic field (IMF). The IMF deformation is analogous to what is often termed the 'random walk' of interplanetary magnetic field lines.

Suess, S. T.↗
NASA NTRS1995

Large-scale magnetic variances near the South Solar Pole

We summarize recent Ulysses observations of the variances over large temporal scales in the interplanetary magnetic field components and their increase as Ulysses approached the South Solar Pole. A model of these fluctuations is shown to provide a very good fit to the observed amplitude and temporal variation of the fluctuations. In addition, the model predicts that the transport of cosmic rays in the heliosphere will be significantly altered by this level of fluctuations. In addition to altering the inward diffusion and drift access of cosmic rays over the solar poles, we find that the magnetic fluctuations also imply a large latitudinal diffusion, caused primarily by the associated field-line random walk.

Jokipii, J. R.↗
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.↗