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Results for “stochastic geometry”

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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Probabilistic methods for robot motion determination

The outline of a research effort in probabilistic approaches to robot motion determination is presented. A heuristic path planner that has met with considerable success in the JPL telerobot testbed is presented together with an interpretation of its performance. The relevance of techniques from stochastic geometry and stochastic diffusion is addressed, as is the possibility of using sensor data directly in the motion determination process.

Balaram, J.↗
DOE OSTI2022

Uncoordinated Spectrum Sharing in Millimeter Wave Networks Using Carrier Sensing

Here, we propose using Carrier Sensing (CS) for distributed interference management in millimeter-wave (mmWave) cellular networks where spectrum is shared by multiple operators that do not coordinate among themselves. In addition, even the base station sites can be shared by the operators. We describe important challenges in using traditional CS in this setting and propose enhanced CS protocols to address these challenges. Using stochastic geometry, we develop a general framework for downlink coverage probability analysis of our shared mmWave network in the presence of CS and derive the downlink coverage probability expressions for several CS protocols. Our work is the first to investigate and analyze (using stochastic geometry) CS for mmWave networks with spectrum and BS sites shared among non-coordinating operators. We evaluate the downlink coverage probability of our shared mmWave network using simulations as well as numerical examples based on our analysis. Our evaluations show that our proposed approach leads to an improvement in coverage probability, compared to the coverage probability with no CS, for higher values of signal-to-interference and noise ratio (SINR). Interestingly, our evaluations also reveal that for lower values of SINR, not using any CS is the best strategy in terms of the downlink coverage probability.

42 ENGINEERING↗
NASA NTRS1997

Radio Occultation Investigation of the Rings of Saturn and Uranus

The proposed work addresses two main objectives: (1) to pursue the development of the random diffraction screen model for analytical/computational characterization of the extinction and near-forward scattering by ring models that include particle crowding, uniform clustering, and clustering along preferred orientations (anisotropy). The characterization is crucial for proper interpretation of past (Voyager) and future (Cassini) ring, occultation observations in terms of physical ring properties, and is needed to address outstanding puzzles in the interpretation of the Voyager radio occultation data sets; (2) to continue the development of spectral analysis techniques to identify and characterize the power scattered by all features of Saturn's rings that can be resolved in the Voyager radio occultation observations, and to use the results to constrain the maximum particle size and its abundance. Characterization of the variability of surface mass density among the main ring, features and within individual features is important for constraining the ring mass and is relevant to investigations of ring dynamics and origin. We completed the developed of the stochastic geometry (random screen) model for the interaction of electromagnetic waves with of planetary ring models; used the model to relate the oblique optical depth and the angular spectrum of the near forward scattered signal to statistical averages of the stochastic geometry of the randomly blocked area. WE developed analytical results based on the assumption of Poisson statistics for particle positions, and investigated the dependence of the oblique optical depth and angular spectrum on the fractional area blocked, vertical ring profile, and incidence angle when the volume fraction is small. Demonstrated agreement with the classical radiative transfer predictions for oblique incidence. Also developed simulation procedures to generate statistical realizations of random screens corresponding to uniformly packed ring models, and used the results to characterize dependence of the extinction and near-forward scattering on ring thickness, packing fraction, and the ring opening angle.

Marouf, Essam A.↗
NASA NTRS1982

Fokker-Planck response of stochastic satellites

The present investigation is concerned with the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The study of pointing accuracies requires a knowledge of the rates of error growth over and above any criteria for the asymptotic stability of the satellites. For this reason the investigation is oriented toward the determination of the statistical properties of the responses of the satellites. The geometries of the satellites are considered stochastic so as to have a phenomenological model of the motions of the flexible structural elements of the satellites. A widely used method of solving stochastic equations is the Fokker-Planck approach where the equations are assumed to define a Markoff process and the transition probability densities of the responses are computed directly as a function of time. The Fokker-Planck formulation is used to analyze the response vector of a rigid satellite.

Huang, T. C.↗
NASA NTRS1984

Analog simulation of stochastic satellite response

A numerical study was performed on the effects of stochastic geometry and random environmental torques on the pointing accuracy of spinning and three-axis stabilized satellites. The Euler equations for the motions of satellites yielded the stochastic principal moments and a Fokker-Planck analog simulation was employed to model the response vector of a rigid satellite. White noise inputs were obtained from a random number generator. Attention was given to both fast and slow spin satellites. Responses grew with time in all cases. The growth was initially exponential and eventually reached stable values. In comparison with other theoretical techniques, the Fokker-Planck model detailed the most responses and showed that spin-stabilization is preferable for satellites with low inertial noise levels.

Huang, T. C.↗
DOE OSTI2025

Emulation of radiation transport in 3D stochastic media using 1D planar Monte Carlo stochastic media radiation transport algorithms

A subset of stochastic media radiation transport problems involves those in which radiation is incident on a thin slab of stochastic material. Particle tracking in 3D for such problems is expensive, and 1D planar models lack accuracy because they only allow the material to change in one dimension. Therefore, we propose dimensional emulation, which through a slight modification allows existing 1D planar geometry stochastic media radiation transport models to reproduce results from the equivalent 3D models by allowing the material to change in all three dimensions, reproducing the fidelity of the 3D model for the low computational cost of the 1D planar model. In this work, we apply dimensional emulation to three Monte Carlo stochastic media radiation transport models: Chord Length Sampling (CLS), the Local Realization Preserving method (LRP), and a variant of Conditional Point Sampling (CoPS). For a common Markovian benchmark set, the 3D emulation variants of these algorithms are numerically verified to reproduce the results of the 3D variants within statistics while running 1.3 to 2 times faster in the implementation within Sandia National Laboratories open-source research code PlaybookMC. The 3D emulation variants are also shown to yield a 72%–92% reduction in error for the thin slab problems in comparison to the 1D benchmark. As a result, the 3D emulation variant of CLS and CoPS-1 are shown to reproduce 3D CLS results that were used to approximate results for a 3D spherical inclusion geometry benchmark set.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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↗
NASA NTRS1987

Reconnection-driven oscillations in dwarf nova disks

A class of oscillations observed during eruption of dwarf novae has been interpreted as oscillations of the accretion disks in these systems.These oscillations are quasi-periodic with coherence times typically between three and 15 cycles. It is shown that magnetic field reconnection at high magnetic Reynolds number can drive disk oscillations. The expected stochastic geometry of disk magnetic fields could naturally produce the observed phase incoherency.

Tajima, T.↗
NASA NTRS2017

Planetary Crater Detection and Registration Using Marked Point Processes, Graph Cut Algorithms, and Wavelet Transforms

This paper addresses the problem of semi-automatic image registration on planetary images. A joint feature-based and area-based approach is proposed. Firstly, the most relevant craters are extracted from the two images to register, and then, registration is performed in two steps. The first step matches the craters extracted from the images based on a generalized Hausdorff distance. In the second step, the mutual information between the two images is maximized to achieve high registration accuracy. Craters are detected by a stochastic-geometry approach based on a marked point process model and of a multiple-birth-and-cut energy minimization algorithm. The experimental validation is carried out with 13 images for the crater extraction stage, and with 20 semi-synthetic pairs of images with ground truth and several images extracted from actual multi-temporal lunar scenes for the registration phase.

Image Processing; Pattern Recognition↗
DOE OSTI2025

Numerical simulation of asteroid geometry variance on airburst threat

For an atmospheric airburst the primary source of concern when assessing uncertainty is the size and velocity. Determining these properties provides the basis for threat assessment, as the total energy of the asteroid may then be estimated, and the threat investigated thoroughly. Even with clarity as to how much energy an asteroid may deposit, a great deal of uncertainty still exists for the actual energy deposition process. One such source of uncertainty is the geometry of the incoming asteroid. The geometry of an asteroid will alter the stress distribution during entry, which adds uncertainty to when fracture will occur. Here, in this study, we use Smoothed Particle Hydrodynamics to model the atmospheric airburst of Tunguska-scale asteroids with varying geometric profiles, including a sphere, ellipsoid, binary and superellipsoid. Each asteroid is modeled as a homogenous structure with strength. We assess uncertainty through a series of planar 2D simulation cases for each geometry, comparing the source of stochasticity across geometries. A single 3D airburst simulation for each geometry is also analyzed. Additionally, the 3D cases are compared to the highly uncertain Tunguska event, predicting variance in burst height across geometries, but all bounded by theoretical burst heights proposed for Tunguska.

Airburst↗
DOE OSTI2022

Tunable Geometries in Sparse Clifford Circuits

We investigate the emergence of different effective geometries in stochastic Clifford circuits with sparse coupling. By changing the probability distribution for choosing two-site gates as a function of distance, we generate sparse interactions that either decay or grow with distance as a function of a single tunable parameter. Tuning this parameter reveals three distinct regimes of geometry for the spreading of correlations and growth of entanglement in the system. We observe linear geometry for short-range interactions, treelike geometry on a sparse coupling graph for long-range interactions, and an intermediate fast scrambling regime at the crossover point between the linear and treelike geometries. This transition in geometry is revealed in calculations of the subsystem entanglement entropy and tripartite mutual information. We also study emergent lightcones that govern these effective geometries by teleporting a single qubit of information from an input qubit to an output qubit. These tools help to analyze distinct geometries arising in dynamics and correlation spreading in quantum many-body systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Kinetics of particles with short-range interactions

Self-assembly is one of the grand challenges of the 21st century – as the devices and materials we would like to build become too complex or small-scale for top-down manufacturing to be efficient, it is increasingly important to find ways to create these through bottom-up, dynamical approaches. Many particles used in self-assembly have very short-ranged attractive interactions, making simulations expensive or impossible. This proposal develops a set of conceptual and computational tools to study the dynamics of self-assembly for particles with short-ranged interactions, harnessing ideas in differential and computational geometry, and stochastic analysis, to accelerate simulations.

74 ATOMIC AND MOLECULAR PHYSICS↗
NASA NTRS1993

The isolation limits of stochastic vibration

The vibration isolation problem is formulated as a 1D kinematic problem. The geometry of the stochastic wall trajectories arising from the stroke constraint is defined in terms of their significant extrema. An optimal control solution for the minimum acceleration return path determines a lower bound on platform mean square acceleration. This bound is expressed in terms of the probability density function on the significant maxima and the conditional fourth moment of the first passage time inverse. The first of these is found analytically while the second is found using a Monte Carlo simulation. The rms acceleration lower bound as a function of available space is then determined through numerical quadrature.

Knopse, C. R.↗
DOE OSTI2020

Microstructure reconstruction of battery polymer separators by fusing 2D and 3D image data for transport property analysis

A new approach to generate high-fidelity 3D microstructure reconstructions by leveraging resolution and sample volume characteristics from 2D and 3D microscopy methods is presented here. This approach is employed to model the microstructure of a highly orthotropic polypropylene separator used in lithium-ion batteries, which have challenging multi-scale features of fibrils (<100 nm) and lamellae (>100 nm) to resolve in 3D. Phase contrast nano X-ray computed tomographic data are used to reconstruct the lamellae phase, while 2D scanning electron microscopy data are used to characterize sub-100 nm microstructure features such as the thin fibrils that are beyond the effective resolution of X-ray computed tomography. Fibril geometries are reconstructed stochastically based on the 2D higher resolution data, and integrated with the lamellae geometries in 3D space. Transport property analyses are performed to investigate the bias of microstructure models without considering the fibrils. A sensitivity study is also conducted to facilitate understanding of the relationship between microstructure characteristics and transport properties.

25 ENERGY STORAGE↗
DOE OSTI2022

Particle transport in Markov stochastic mixtures with spatial gradients

Markov geometries are a prototype class of stochastic media that are widely used to model complex disordered systems. In a series of recent works, we have shown that spatially homogeneous (but possibly non-isotropic) Poisson tessellations can be conveniently used in order to generate three-dimensional realizations of Markov media and thus characterize the features of particle transport e.g. in fragmented fuel elements following severe nuclear accidents or Rayleigh-Taylor turbulent mixing for inertial confinement fusion. In this paper we show that Poisson tessellations can be extended to take into account the presence of spatial gradients, which commonly occur in real-world applications due to material stratification. For this purpose, we will provide an explicit construction of spatially-non-homogeneous Poisson tessellations, fully characterize their statistical properties, and finally illustrate the behaviour of particle transport in such random media. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
NASA NTRS1985

Probabilistic Finite Element Development

The probabilistic finite element computer program known as Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) is being developed for the analysis of critical structural components for reusable space propulsion systems. First year efforts involve the formulation of the probabilistic analysis strategy and the development of a probabilistic linear analysis code. The ultimate goal of the 3-year program is the development of a finite element code capable of performing nonlinear dynamic analysis of structures having stochastic material properties, geometry, and boundary conditions and subjected to random loading. Three levels of sophistication are envisioned for the stochastic description of the structural problem, namely: (1) homogeneous random variable for stiffness, mass, damping, and external loading; (2) stochastic characterization of variables at the element level, with specified interelement correlations; and (3) stochastic interpolation of variables within a finite element. Two alternative probabilistic analysis methods will be developed, allowing for all three levels of modeling sophistication.

Nagtegaal, J.↗
DOE OSTI2022

A hierarchical stochastic modeling approach for representing point bar geometries and petrophysical property variations

The flow of fluids in point bars is affected by the existence of heterogeneities like shale drapes that are found on the surfaces of inclined heterolithic stratifications. In fact, these shale drapes can act as fluid flow baffles; therefore, developing a framework for modeling point bars and their associated heterogeneities is vital. In this study, a stochastic process-based modeling approach is presented for capturing the main point bar heterogeneities: accretion surfaces (i.e., the aerial heterogeneity) and inclined heterolithic stratifications (i.e., the vertical heterogeneity). The former was modeled using a sine-generation function and the latter, with a sigmoidal function after which they were combined into a 3D point bar model. To ensure proper modeling of petrophysical properties, we developed a more representative gridding scheme which generates curvilinear grids representative of the point bar geometry. This grid was then transformed into a rectilinear grid to allow for geostatistical simulation after which all petrophysical properties were mapped back into the original curvilinear grid. An essential element of this modeling approach is the stochastic representation of shale drapes at the interface between successive accretion surfaces. The workflow was tested using a real field dataset for the Cranfield field, Mississippi. The constructed model was then subjected to a flow simulation study mimicking a CO 2 storage scenario. Various sensitivities were simulated to evaluate the effect of heterogeneities on CO 2 flow within the point-bar. Results demonstrate the importance of representing point-bar related heterogeneity and the spatial distribution of shale drapes on CO 2 plume migration and storage.

58 GEOSCIENCES↗
NASA NTRS1994

The kinetic response of a stochastic plasma to low frequency perturbations

Following suggestion that substorm breakup might be caused by an interchange or ballooning instability, several magnetohydrodynamic (MHD) and gyro-kinetic stability analysis have been performed for plasma sheet magnetic field geometries. However, the stochastic ion dynamics in the highly stressed, thin high-beta near earth plasma sheet violate the locality requirements of MHD and the invarience of the magnetic moment, mu, required by gyro-kinetic theories. In this paper we develop a new linear Vlasov kinetic theory (for low frequency modes omega less than omega(sub b), omega(sub b) being the bounce frequency) which includes the dynamics of stochastic ions.

Hurricane, Omar A.↗