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NASA NTRS1995

Spatial Factors in the Integration of Speed Information

We reported that, for a 21FC task with multiple Gabor patches in each interval, thresholds for speed discrimination decreased with the number of patches, while simply increasing the area of a single patch produced no such effect. This result could be explained by multiple patches reducing spatial uncertainty. However, the fact that thresholds decrease with number even when the patches are in fixed positions argues against this explanation. We therefore performed additional experiments to explore the lack of an area effect. Three observers did a 21FC speed discrimination task with 6 Gabor patches in each interval, and were asked to pick the interval in which the gratings moved faster. The 50% contrast patches were placed on a circle at 4 deg. eccentricity, either equally spaced and maximally separated (hexagonal array), or closely-spaced, in consecutive positions (string of pearls). For the string-of-pearls condition, the grating phases were either random, or consistent with a full-field grating viewed through multiple Gaussian windows. When grating phases were random, the thresholds for the hexagonal and string-of-pearls layouts were indistinguishable. For the string-of-pearls layout, thresholds in the consistent-phase condition were higher by 15 +/- 6% than in the random-phase condition. (Thresholds increased by 57 +/- 7% in going from 6 patches to a single patch of equivalent area.). For random-phase patches, the lower thresholds for 6 patches does not depend on a specific spacing or spatial layout. Multiple, closely-spaced, consistent-phase patches that can be interpreted as a single grating, result in thresholds closer to that produced by a single patch. Together, our results suggest that object segmentation may play a role in the integration of speed information.

Verghese, P.↗

NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. II: The Coherent Field

The computation of the coherent field in the case of a plane electromagnetic wave obliquely incident on a discrete random layer with non-scattering boundaries is addressed. For dense media, the analysis is based on a special-form solution for the conditional configuration-averaged exciting field coefficients, and is restricted to the computation of the so-called zeroth-order fields without a special treatment of the boundary regions. In this setting, we calculate the coherent fields reflected and transmitted by the layer, and the coherent field inside the layer. We found that these fields are analytically equivalent to plane electromagnetic waves, and investigated the fulfillment of the boundary conditions for the electric fields at the layer interfaces. The results are then particularized to the cases of normal incidence and a semi-infinite discrete random medium. For sparsely distributed particles, we present a self-consistent derivation of the coherent field and discuss the Twersky and Foldy approximations.

Adrian Doicu↗

DOE OSTI2021

Evaluation of residual gas fraction estimation methods for cycle-to-cycle combustion variability analysis and modeling

Cycle-to-cycle combustion variability in spark-ignition engines during normal operation is mainly caused by random perturbations of the in-cylinder conditions such as the flow velocity field, homogeneity of the air-fuel distribution, spark energy discharge, and turbulence intensity of the flame front. Such perturbations translate into the variability of the energy released observed at the end of the combustion process. During normal operating conditions, the cycle-to-cycle variability (CCV) of the energy release behaves as random uncorrelated noise. However, during diluted combustion, in either the form of exhaust gas recirculation (EGR) or excess air (lean operation), the CCV tends to increase as dilution increases. Moreover, when the ignition limit is reached at high dilution levels, the combustion CCV is exacerbated by sporadic occurrences of incomplete combustion events, and the uncorrelation assumption no longer holds. The low or null energy released by partial burns and misfires has an impact on the following combustion event due to the residual gas that carries burned and unburned gases, which contributes to the deterministic coupling between engine cycles. Many residual gas fraction estimation methods, however, only address the nominal case where complete combustion occurs and combustion events are uncorrelated. Here we evaluate the efficacy of such methods on capturing the effects of partial burns and misfires on the residual gas estimate for high-EGR operation. The advantages and disadvantages of each method are discussed based on their ability to generate cycle-to-cycle estimates. Finally, a comparison between the different estimation techniques is presented based on their usefulness for control-oriented modeling.

42 ENGINEERING↗

NASA NTRS1995

Test particle study of minor ions in solar wind turbulence

We perform a parameter study of the temporal evolution of a test particle distribution function in MHD turbulence. The turbulent fields are calculated using a pseudo-spectral method and periodic boundary conditions on a regular grid of 180(exp 3) points, appropriate for incompressible, homogeneous and isotropic turbulence. Initially, the kinetic and the magnetic energy are equal on the average. Both, deterministic and random initial conditions are used, in the former case with zeros of the magnetic field located at grid points, in the latter case located by interpolation between grid points. The evolution of the minor ion distribution function is studied in detail as these turbulent fields evolve, developing strong current and vorticity sheets. Using the full collisionless equation of motion for the test particles, the efficiency of nonlinear interactions can be studied. The results are compared to theoretical predictions and are then discussed in connection with the observations of the dynamical properties of solar wind minor ions derived from in situ observations.

Zurbuchen, Th.↗

DOE OSTI2019

Acceleration of charged particles to extremely large energies by a sub-Dreicer electric field

Acceleration of a fraction of initially low-energy electrons in a cold, collisional plasma to energies orders of magnitude larger than thermal is shown to be possible with a sub-Dreicer electric field. Because such an electric field does not satisfy the runaway condition, any acceleration will be statistical. Random scattering collisions are probabilistic such that there is 63% chance that a particle collides after traveling one mean free path and a 37% chance of not colliding. If one considers only the electrons that do not collide on traversing a mean free path and also considers that the collisional mean free path scales quadratically with particle kinetic energy, one realizes that there will be a small fraction of electrons that never collide and are accelerated to increasingly high energy. Because the mean free path scales quadratically with kinetic energy, after each successfully traveled mean free path, continued acceleration becomes more likely. This model is applied to an MHD-driven plasma jet experiment at Caltech and it is shown that electrons are accelerated by an electric field associated with a fast magnetic reconnection event occurring as the jet breaks apart. This statistical acceleration model indicates that a fraction ~1.3 × 10 -7 of electrons with initial energy distributed according to a Maxwellian with T = 2 eV will be accelerated to 6 keV in the Caltech experiment and then collide to produce the observed X-ray signal. It is demonstrated that the statistical acceleration model provides a credible explanation for the production of solar energetic electrons.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2019

Electromagnetic Scattering by Discrete Random Media. I: The Dispersion Equation and the Configuration-Averaged Exciting Field

We consider the scattering of a plane electromagnetic wave obliquely incident on a plane-parallel layer of discrete random medium with non-scattering boundaries. We solve the Lax integral equation for the conditional configuration-averaged exciting field coefficients by assuming a special-form solution, that is, by representing the conditional configuration-averaged exciting field coefficients as a linear combination of the coefficients corresponding to an up-going and a down-going wave. This solution representation is supposed to be valid within the whole domain occupied by the particles, even in the close proximity of the boundaries. By balancing the waves with different propagation directions and wavenumbers we derive two homogeneous systems of equations corresponding to the generalized Lorenz–Lorentz law and two inhomogeneous systems of equations corresponding to the generalized Ewald–Oseen extinction theorem. It is shown that (i) the two homogeneous systems of equations of the generalized Lorenz–Lorentz law reduce to a single homogeneous system of equations corresponding to a semi-infinite discrete random medium at normal incidence; (ii) the dispersion equation is direction and polarization independent; and (iii) the two inhomogeneous systems of equations of the generalized Ewald–Oseen extinction theorem can be reduced to two scalar equations by means of the addition theorem for vector spherical harmonics. It is also shown that the same dispersion equation can be obtained without assuming a special-form solution representation in the proximity of the boundaries.

Adrian Doicu↗

DOE OSTI2014

Quantum transport equation for systems with rough surfaces and its application to ultracold neutrons in a quantizing gravity field

We discuss transport of particles along random rough surfaces in quantum size effect conditions. As an intriguing application, we analyze gravitationally quantized ultracold neutrons in rough waveguides in conjunction with GRANIT experiments (ILL, Grenoble). We present a theoretical description of these experiments in the biased diffusion approximation for neutron mirrors with both one- and two-dimensional (1D and 2D) roughness. All system parameters collapse into a single constant which determines the depletion times for the gravitational quantum states and the exit neutron count. This constant is determined by a complicated integral of the correlation function (CF) of surface roughness. The reliable identification of this CF is always hindered by the presence of long fluctuation-driven correlation tails in finite-size samples. We report numerical experiments relevant for the identification of roughness of a new GRANIT waveguide and make predictions for ongoing experiments. We also propose a radically new design for the rough waveguide.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Closures and Simulation for Thermal Radiation Transport in Stochastic Media with Nonlinear Temperature Dependence

Because of the practical challenge of rendering very complex realistic spatial structures for numerical work, it is common practice to resort to characterizing such media as stochastic mixtures of materials, ideally parametrized with low order statistics such as the mean, variance, and correlation functions of the now random material properties. This enables realizations of the medium to be repeatedly generated and radiation transport computations to, in principle, be performed for a large ensemble of these realizations to obtain a statistically well-characterized radiation field. Statistical post-processing yields desired quantities such as conditional and unconditional mean radiation flux and probability distributions of transmitted radiation. However, such computations prove expensive for all but the simplest stochastic geometries and are most suited for benchmarking approximate models. The most common approximations lead to homogenized media so that transport computations are required only on a single medium realization but by construct provide only limited statistical information on the radiation field. Almost all approximate approaches to this problem attempt to develop equations for low order moments of the radiation intensity (mean, second moment, correlation function) but inevitably encounter a closure problem: the equation for any statistical moment will contain terms depending on unknown higher-order moments. Thus, the challenge shifts to one of developing closure relations that relate the unknown moments to the lower order moments. Under very special conditions, an exact closure can be derived but in general closures are heuristically stated constitutive relations. Also, closure approaches depend on whether the mixing statistics are spatially and/or temporally continuous as in fluctuating turbulent fields, or discontinuous as in randomly mixed solid chunks of material. Thus, unconditional averaging is generally applied in the former case but conditional averaging is more appropriate when the mixing is discontinuous. In this work, the emphasis is on binary statistical mixtures of immiscible fluids as as such the quantities of interest are averages (flux, temperature) conditioned on the material type.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2015

Algorithms for propagating uncertainty across heterogeneous domains

We address an important research area in stochastic multi-scale modeling, namely the propagation of uncertainty across heterogeneous domains characterized by partially correlated processes with vastly different correlation lengths. This class of problems arise very often when computing stochastic PDEs and particle models with stochastic/stochastic domain interaction but also with stochastic/deterministic coupling. The domains may be fully embedded, adjacent or partially overlapping. The fundamental open question we address is the construction of proper transmission boundary conditions that preserve global statistical properties of the solution across different subdomains. Often, the codes that model different parts of the domains are black-box and hence a domain decomposition technique is required. No rigorous theory or even effective empirical algorithms have yet been developed for this purpose, although interfaces defined in terms of functionals of random fields (e.g., multi-point cumulants) can overcome the computationally prohibitive problem of preserving sample-path continuity across domains. The key idea of the different methods we propose relies on combining local reduced-order representations of random fields with multi-level domain decomposition. Specifically, we propose two new algorithms: The first one enforces the continuity of the conditional mean and variance of the solution across adjacent subdomains by using Schwarz iterations. The second algorithm is based on PDE-constrained multi-objective optimization, and it allows us to set more general interface conditions. The effectiveness of these new algorithms is demonstrated in numerical examples involving elliptic problems with random diffusion coefficients, stochastically advected scalar fields, and nonlinear advection-reaction problems with random reaction rates.

Cho, Heyrim↗

NASA NTRS1993

The effect of tidal fields on the shapes and kinematics of dark halos

We have carried out a series of N-body simulations to investigate the effect of tidal shear on the structure and kinematics of dark halos. We simulate the collapse of density perturbations using a tree code as described in Dubinski & Carlberg (1991). Density peaks are selected from a random realization of a CDM density field and used as the initial conditions for N-body simulations. We use an experimental approach to examine the effects of tidal shear on collapse. The cosmological tidal field is treated as an external time dependent potential whose strength and orientation can be varied freely. We examine the effects of the tidal field with two experiments. In the first experiment, we simulate a sample of 14 dark halos from the collapse of density peaks in the presence of a 1(sigma) tidal field. In the second experiment, we use the same initial conditions though the tidal field is turned off allowing an experimental control for comparison to highlight the influence of tidal shear on the development of the structure and kinematics of the dark halos.

Dubinski, John↗

DOE OSTI2015

NONLINEAR EFFECTS IN PARTICLE TRANSPORT IN STOCHASTIC MAGNETIC FIELDS

Collisional particle transport in stochastic magnetic fields is studied using a semi-analytical method. The aim is to determine the influence of the nonlinear effects that occur in the magnetic field line random walk on particle transport. We show that particle transport coefficients can be strongly influenced by the magnetic line trapping. The conditions that correspond to these nonlinear regimes are determined. We also analyze the effects produced by the space variation of the large-scale magnetic field. We show that an average drift is generated by the gradient of the magnetic field, which strongly increases and reverses its orientation in the nonlinear regime.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS2020

Designing an Optimal Ensemble Strategy for GMAO S2S Forecast System

GMAO Sub/Seasonal prediction system (S2S) is being readied for a major upgrade to GEOS-S2S Version 3. An important factor in successful extended range forecast is the definition of an ensemble For initialization of the ensemble we propose a combination of lagged and burst initial conditions. We plan to run a relatively large ensemble of 40 members for sub-seasonal forecast (up to 3 months), at which point we sub-sample the ensemble, and continue the forecast with 10 members (up to 12 months). Here we present the results of the extensive testing of various ways to generate the perturbations to the initial conditions and the validation of the stratified sampling strategy we chose.To generate perturbations for the burst ensemble members we used scaled differences of pairs of analysis states separated by 1-10 days, randomly chosen from a corresponding season. We considered perturbing separately only the atmospheric fields or only the ocean or both of the forecast initial conditions. Considering varying separation times between the analysis states, we were able to produce perturbations sampling various modes of variability. Focusing on the ENSO SST indices, we found that all types of perturbations are important for the ensemble spread.Our ensemble size for sub-seasonal forecasts was determined as to maximize the skill of predicting some of the leading modes of boreal winter atmospheric modes, NAO, PNA and AO. It is not feasible to run equally large ensemble for seasonal forecasts. Using a stratified sampling procedure we can identify the emerging directions of error growth. By comparing the stratified ensemble with randomly sampled ensemble of the same size, we were able to show that the former better estimates the mean of the original large ensemble.

Borovikov, Anna↗

NASA NTRS1998

Estimation of 3-D Cloud Effects on TOMS Satellite Retrieval of Surface UV Irradiance

To improve surface UV irradiance retrieval from the Total Ozone Mapping Spectrometer (TOMS) we simulate errors of the TOMS cloud correction algorithm for summertime broken cloud conditions. Cloud scenes (50 km by 50 km) are modeled by a normal random (Gaussian) field with a fixed lower boundary and conservative scattering. The model relates stochastic field characteristics with the cloud amount, mean cloud diameter and aspect ratio. Clouds are embedded into Rayleigh atmosphere with standard ozone profile. Radiative transfer calculations of the radiance at the top of the atmosphere and irradiance at the surface were performed using 3-D Monte Carlo (MC) code. The results are averaged over the satellite field of view on the surface (50 km by 50 km) and compared with TOMS predicted surface irradiance for the same scene reflectance. The TOMS algorithm assumes horizontally homogeneous Cl-type cloud between 3 km and 5.5 km. The effective optical depth is determined by fitting observed (MC) radiance at 380 nm. Having the same radiance at the satellite the homogeneous and broken cloud models predict different average irradiances at the surface. This is due to the differences in Bidirectional Reflection Distribution Function (BRDF) for homogeneous and broken cloud scenes with the same hemispherical albedo. For typical TOMS observational geometry at mid-latitudes the simulated single pixels errors may be as large as +/- 20%. Qualitatively these errors are due to the dominance of the non-horizontal cloud surfaces, which are not accounted for in the homogeneous cloud model. However, due to high variability of the real cloud shapes and types it is unclear how these single pixel errors would affect TOMS time-integrated UV exposure over extended periods (weeks to months) for different regions.

Krotkov, Nickolay A.↗

DOE OSTI2025

Turbulent-like flows in quasi two-dimensional dense suspensions of motile colloids

Dense bacterial suspensions exhibit turbulent-like flows at low Reynolds numbers, driven by the activity of the microswimmers. In this study, we develop a model system to examine these dynamics using motile colloids that mimic bacterial locomotion. The colloids are powered by the Quincke instability, which causes them to spontaneously roll in a random-walk pattern when exposed to a square-wave electric field. We experimentally investigate the flow dynamics in dense suspensions of these Quincke random walkers under quasi two-dimensional conditions, where the particle size is comparable to the gap between the electrodes. The results suggest a scaling regime in the energy spectrum ∼k −4 at high wavenumbers, observed consistently across activity levels and particle concentrations. We observe that velocity time correlations decay within a single period of the square-wave field, yet an anti-correlation appears between successive field applications, indicative of a dynamic structural memory of the ensemble.

Luo, Rui [Northwestern Univ., Evanston, IL (United↗

DOE OSTI2016

SU-G-IeP4-03: Cone Beam X-Ray Luminescence Computed Tomography Based On Generalized Gaussian Markov Random Field

Purpose: Cone beam X-ray luminescence computed tomography (CB-XLCT), which aims to achieve molecular and functional imaging by X-rays, has recently been proposed as a new imaging modality. However, the inverse problem of CB-XLCT is seriously ill-conditioned, hindering us to achieve good image quality. In this work, a novel reconstruction method based on Bayesian theory is proposed to tackle this problem Methods: Bayesian theory provides a natural framework for utilizing various kinds of available prior information to improve the reconstruction image quality. A generalized Gaussian Markov random field (GGMRF) model is proposed here to construct the prior model of the Bayesian theory. The most important feature of GGMRF model is the adjustable shape parameter p, which can be continuously adjusted from 1 to 2. The reconstruction image tends to have more edge-preserving property when p is slide to 1, while having more noise tolerance property when p is slide to 2, just like the behavior of L1 and L2 regularization methods, respectively. The proposed method provides a flexible regularization framework to adapt to a wide range of applications. Results: Numerical simulations were implemented to test the performance of the proposed method. The Digimouse atlas were employed to construct a three-dimensional mouse model, and two small cylinders were placed inside to serve as the targets. Reconstruction results show that the proposed method tends to obtain better spatial resolution with a smaller shape parameter, while better signal-to-noise image with a larger shape parameter. Quantitative indexes, contrast-to-noise ratio (CNR) and full-width at half-maximum (FWHM), were used to assess the performance of the proposed method, and confirmed its effectiveness in CB-XLCT reconstruction. Conclusion: A novel reconstruction method for CB-XLCT is proposed based on GGMRF model, which enables an adjustable performance tradeoff between L1 and L2 regularization methods. Numerical simulations were conducted to demonstrate its performance.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2014

Progress of a Cross-Correlation Based Optical Strain Measurement Technique for Detecting Radial Growth on a Rotating Disk

The Aeronautical Sciences Project under NASA's Fundamental Aeronautics Program is interested in the development of novel measurement technologies, such as optical surface measurements for the in situ health monitoring of critical constituents of the internal flow path. In situ health monitoring has the potential to detect flaws, i.e. cracks in key components, such as engine turbine disks, before the flaws lead to catastrophic failure. The present study, aims to further validate and develop an optical strain measurement technique to measure the radial growth and strain field of an already cracked disk, mimicking the geometry of a sub-scale turbine engine disk, under loaded conditions in the NASA Glenn Research Center's High Precision Rotordynamics Laboratory. The technique offers potential fault detection by imaging an applied high-contrast random speckle pattern under unloaded and loaded conditions with a CCD camera. Spinning the cracked disk at high speeds (loaded conditions) induces an external load, resulting in a radial growth of the disk of approximately 50.0-μm in the flawed region and hence, a localized strain field. When imaging the cracked disk under static conditions, the disk will be undistorted; however, during rotation the cracked region will grow radially, thus causing the applied particle pattern to be 'shifted'. The resulting particle displacements between the two images is measured using the two-dimensional cross-correlation algorithms implemented in standard Particle Image Velocimetry (PIV) software to track the disk growth, which facilitates calculation of the localized strain field. A random particle distribution is adhered onto the surface of the cracked disk and two bench top experiments are carried out to evaluate the technique's ability to measure the induced particle displacements. The disk is shifted manually using a translation stage equipped with a fine micrometer and a hotplate is used to induce thermal growth of the disk, causing the particles to become shifted. For both experiments, reference and test images are acquired before and after the induced shifts, respectively, and then processed using PIV software. The controlled manual translation of the disk resulted in detection of the particle displacements accurate to ~1.75% of full scale and the thermal expansion experiment resulted in successful detection of the disk's thermal growth as compared to the calculated thermal expansion results. After validation of the technique through the induced shift experiments, the technique is implemented in the Rotordynamics Lab for preliminary assessment in a simulated engine environment. The discussion of the findings and plans for future work to improve upon the results are addressed in the paper.

rotordynamics↗

NASA NTRS1990

Stabilization functions of unforced cumulus clouds - Their nature and components

The nature and the spatial distribution of cumuli within an unforced cumulus cloud field are investigated. The thermodynamic effects of convection are quantified as functions of changes of convective available potential energy (CAPE) induced by the convective overturning, and the time rate of change of CAPE is parameterized in terms of a kernel of influence or stabilization function. A three-dimensional cloud model is used to infer and quantify stabilization functions by performing single-cloud experiments. On the basis of the results obtained, a new hypothesis with respect to the spatial distribution of cumuli is postulated, which states that, under completely homogeneous external conditions and assuming a spatially random distribution of cloud-triggering mechanisms, the spatial distribution of cumuli in the resulting cloud field must be regular, as opposed to either random or clustered, because cumulus clouds tend to reduce the available energy for convection, thereby inhibiting further convection nearby.

Ramirez, Jorge A.↗

NASA NTRS1982

Comparison of hot wire/laser velocimeter turbulence intensity measurements

The question of whether a random measure of particle velocities yields a good statistical estimate of the stationary condition of the turbulence flow field was investigated by comparing hot-wire and laser velocimeter turbulence intensity measurements. Great care was taken to insure that the instrument precision of both the laser velocimeter and hot wire was maximized. In this attempt to reduce the measurement uncertainties in the hot wire, direct digitization of the analog output signal was performed with point-by-point conversion to velocity through a spline fit calibration curve and the turbulence intensity function was calculated statistically. Frequent calibrations of the hot wire were performed using the laser velocimeter as the velocity standard to account for the presence of the small seed particles in the air flow and signal drift in the hot wire.

Meyers, J. F.↗