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Results for “Fractal modelling”

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 NTRS2001

Do Fractal Models of Clouds Produces the Right 3D Radiative Effects?

Stochastic fractal models of clouds are often used to study 3D radiative effects and their influence on the remote sensing of cloud properties. Since it is important that the cloud models produce a correct radiative response, some researchers require the model parameters to match observed cloud properties such as scale-independent optical thickness variability. Unfortunately, matching these properties does not necessarily imply that the cloud models will cause the right 3D radiative effects. First, the matched properties alone only influence the 3D effects but do not completely determine them. Second, in many cases the retrieved cloud properties have been already biased by 3D radiative effects, and so the models may not match the true real clouds. Finally, the matched cloud properties cannot be considered independent from the scales at which they have been retrieved. This paper proposes an approach that helps ensure that fractal cloud models are realistic and produce the right 3D effects. The technique compares the results of radiative transfer simulations for the model clouds to new direct observations of 3D radiative effects in satellite images.

Varnai, Tamas↗
NASA NTRS1997

Analysis of Texture Using the Fractal Model

Properties such as the fractal dimension (FD) can be used for feature extraction and classification of regions within an image. The FD measures the degree of roughness of a surface, so this number is used to characterize a particular region, in order to differentiate it from another. There are two basic approaches discussed in the literature to measure FD: the blanket method, and the box counting method. Both attempt to measure FD by estimating the change in surface area with respect to the change in resolution. We tested both methods but box counting resulted computationally faster and gave better results. Differential Box Counting (DBC) was used to segment a collage containing three textures. The FD is independent of directionality and brightness so five features were used derived from the original image to account for directionality and gray level biases. FD can not be measured on a point, so we use a window that slides across the image giving values of FD to the pixel on the center of the window. Windowing blurs the boundaries of adjacent classes, so an edge-preserving, feature-smoothing algorithm is used to improve classification within segments and to make the boundaries sharper. Segmentation using DBC was 90.8910 accurate.

Navas, William↗
NASA NTRS2011

A Fractal Model for the Capacitance of Lunar Dust and Lunar Dust Aggregates

Lunar dust grains and dust aggregates exhibit clumping, with an uneven mass distribution, as well as features that span many spatial scales. It has been observed that these aggregates display an almost fractal repetition of geometry with scale. Furthermore, lunar dust grains typically have sharp protrusions and jagged features that result from the lack of aeolian weathering (as opposed to space weathering) on the Moon. A perfectly spherical geometry, frequently used as a model for lunar dust grains, has none of these characteristics (although a sphere may be a reasonable proxy for the very smallest grains and some glasses). We present a fractal model for a lunar dust grain or aggregate of grains that reproduces (1) the irregular clumpy nature of lunar dust, (2) the presence of sharp points, and (3) dust features that span multiple scale lengths. We calculate the capacitance of the fractal lunar dust analytically assuming fixed dust mass (i.e. volume) for an arbitrary number of fractal levels and compare the capacitance to that of a non-fractal object with the same volume, surface area, and characteristic width. The fractal capacitance is larger than that of the equivalent non-fractal object suggesting that for a given potential, electrostatic forces on lunar dust grains and aggregates are greater than one might infer from assuming dust grains are sphericaL Consequently, electrostatic transport of lunar dust grains, for example lofting, appears more plausible than might be inferred by calculations based on less realistic assumptions about dust shape and associated capacitance.

Collier, Michael R.↗
NASA NTRS1986

A fractal model of a cometary nucleus formed by random accretion

Numerical simulations of the structure of aggregates of grains in the solar system show they are fractals with low density and irregular shapes. Comet nuclei forming from a mixture of ice and dust grains are likely to have nonuniform composition as well as structure. Such a nucleus appears to account for observed characteristic of comets. The structure has significant implications for the evolution of cometary nuclei.

Donn, Bertram↗
NASA NTRS1986

A fractal model for crustal deformation

It is hypothesized that crustal deformation occurs on a scale-invariant matrix of faults. For simplicity, a two-dimensional pattern of hexagons on which strike-slip faulting occurs is considered. The behavior of the system is controlled by a single parameter, the fractal dimension. Deformation occurs on all scales of faults. The fractal dimension determines the fraction of the total displacement that occurs on the first-order or primary faults. The value of the fractal dimension can be obtained from the frequency-magnitude relation for earthquakes. The results are applied to the San Andreas fault system in central California. Earthquake studies give D = 1.90. The main strand of the San Andreas fault is associated with the primary faults of the fractal system. It is predicted that the relative velocity across the main strand is 2.93 cm/yr. The remainder of the relative velocity of 5.5 cm/yr between the Pacific and North American plates occurs on higher-order faults. The predicted value is in reasonably good agreement with the value 3.39 + or - 0.29 cm/yr obtained from geological studies.

Turcotte, D. L.↗
NASA NTRS1987

Improvements in the perturbation simulations of the global reference atmospheric model

The Global Reference Atmospheric Model (GRAM) program includes the capability for simulating pseudo-random perturbations in density, temperature, pressure, or wind components along a simulated reentry trajectory or other path through the atmosphere. Some concerns were expressed by GRAM users, however, that the mean-square perturbation gradients may be too large for small values of the vertical separation Delta z. The present GRAM perturbation simulations, based on a one-step autoregressive model, yield a power spectrum versus wavenumber k which is proportional to k sup -2 at high wavenumbers. This feature also produces mean-square perturbation differences which are directly proportional to Delta z, and mean-square perturbation gradients which are inversely proportional to Delta z. Thus, root-mean-square gradients, (Delta f/Delta z) sub rms, increase with decreasing Delta a as Delta z sup -1/2. A simple modification to GRAM is suggested which overcomes this problem, i.e., which produce root-mean-square gradient that remain bound as Delta z approaches zero. Possible applications of more sophisticated simulation approaches, e.g., second order autoregressive models, or fractal model techniques, were also explored briefly but found to yield improvements which appear too small to justify their considerable added complexity for use in the GRAM programs.

Justus, C. G.↗
DOE OSTI2021

Predicting Fluid Flow Regime, Permeability, and Diffusivity in Mudrocks from Multiscale Pore Characterisation

In geoenergy applications, mudrocks prevent fluids to leak from temporary (H 2 , CH 4 ) or permanent (CO 2 , radioactive waste) storage/disposal sites and serve as a source and reservoir for unconventional oil and gas. Understanding transport properties integrated with dominant fluid flow mechanisms in mudrocks is essential to better predict the performance of mudrocks within these applications. In this study, small-angle neutron scattering (SANS) experiments were conducted on 71 samples from 13 different sets of mudrocks across the globe to capture the pore structure of nearly the full pore size spectrum (2 nm–5 μm). We develop fractal models to predict transport properties (permeability and diffusivity) based on the SANS-derived pore size distributions. The results indicate that transport phenomena in mudrocks are intrinsically pore size-dependent. Depending on hydrostatic pore pressures, transition flow develops in micropores, slip flow in meso- and macropores, and continuum flow in larger macropores. Fluid flow regimes progress towards larger pore sizes during reservoir depletion or smaller pore sizes during fluid storage, so when pressure is decreased or increased, respectively. Capturing the heterogeneity of mudrocks by considering fractal dimension and tortuosity fractal dimension for defined pore size ranges, fractal models integrate apparent permeability with slip flow, Darcy permeability with continuum flow, and gas diffusivity with diffusion flow in the matrix. This new model of pore size-dependent transport and integrated transport properties using fractal models yields a systematic approach that can also inform multiscale multi-physics models to better understand fluid flow and transport phenomena in mudrocks on the reservoir and basin scale.

36 MATERIALS SCIENCE↗
NASA NTRS1993

Generalized Levy-walk model for DNA nucleotide sequences

We propose a generalized Levy walk to model fractal landscapes observed in noncoding DNA sequences. We find that this model provides a very close approximation to the empirical data and explains a number of statistical properties of genomic DNA sequences such as the distribution of strand-biased regions (those with an excess of one type of nucleotide) as well as local changes in the slope of the correlation exponent alpha. The generalized Levy-walk model simultaneously accounts for the long-range correlations in noncoding DNA sequences and for the apparently paradoxical finding of long subregions of biased random walks (length lj) within these correlated sequences. In the generalized Levy-walk model, the lj are chosen from a power-law distribution P(lj) varies as lj(-mu). The correlation exponent alpha is related to mu through alpha = 2-mu/2 if 2 < mu < 3. The model is consistent with the finding of "repetitive elements" of variable length interspersed within noncoding DNA.

NASA Discipline Number 14-10↗
NASA NTRS1994

Independent pixel and Monte Carlo estimates of stratocumulus albedo

Monte Carlo radiative transfer methods are employed here to estimate the plane-parallel albedo bias for marine stratocumulus clouds. This is the bias in estimates of the mesoscale-average albedo, which arises from the assumption that cloud liquid water is uniformly distributed. The authors compare such estimates with those based on a more realistic distribution generated from a fractal model of marine stratocumulus clouds belonging to the class of 'bounded cascade' models. In this model the cloud top and base are fixed, so that all variations in cloud shape are ignored. The model generates random variations in liquid water along a single horizontal direction, forming fractal cloud streets while conserving the total liquid water in the cloud field. The model reproduces the mean, variance, and skewness of the vertically integrated cloud liquid water, as well as its observed wavenumber spectrum, which is approximately a power law. The Monte Carlo method keeps track of the three-dimensional paths solar photons take through the cloud field, using a vectorized implementation of a direct technique. The simplifications in the cloud field studied here allow the computations to be accelerated. The Monte Carlo results are compared to those of the independent pixel approximation, which neglects net horizontal photon transport. Differences between the Monte Carlo and independent pixel estimates of the mesoscale-average albedo are on the order of 1% for conservative scattering, while the plane-parallel bias itself is an order of magnitude larger. As cloud absorption increases, the independent pixel approximation agrees even more closely with the Monte Carlo estimates. This result holds for a wide range of sun angles and aspect ratios. Thus, horizontal photon transport can be safely neglected in estimates of the area-average flux for such cloud models. This result relies on the rapid falloff of the wavenumber spectrum of stratocumulus, which ensures that the smaller-scale variability, where the radiative transfer is more three-dimensional, contributes less to the plane-parallel albedo bias than the larger scales, which are more variable. The lack of significant three-dimensional effects also relies on the assumption of a relatively simple geometry. Even with these assumptions, the independent pixel approximation is accurate only for fluxes averaged over large horizontal areas, many photon mean free paths in diameter, and not for local radiance values, which depend strongly on the interaction between neighboring cloud elements.

Cahalan, Robert F.↗
DOE OSTI2023

Skyrmion‐Excited Spin‐Wave Fractal Networks

Magnetic skyrmions exhibit unique, technologically relevant pseudo-particle behaviors which arise from their topological protection, including well-defined, 3D dynamic modes that occur at microwave frequencies. During dynamic excitation, spin waves are ejected into the interstitial regions between skyrmions, creating the magnetic equivalent of a turbulent sea. However, since the spin waves in these systems have a well-defined length scale, and the skyrmions are on an ordered lattice, ordered structures from spin-wave interference can precipitate from the chaos. This work uses small-angle neutron scattering (SANS) to capture the dynamics in hybrid skyrmions and investigate the spin-wave structure. Performing simultaneous ferromagnetic resonance and SANS, the diffraction pattern shows a large increase in low-angle scattering intensity, which is present only in the resonance condition. This scattering pattern is best fit using a mass fractal model, which suggests the spin waves form a long-range fractal network. The fractal structure is constructed of fundamental units with a size that encodes the spin-wave emissions and are constrained by the skyrmion lattice. Furthermore, these results offer critical insights into the nanoscale dynamics of skyrmions, identify a new dynamic spin-wave fractal structure, and demonstrate SANS as a unique tool to probe high-speed dynamics.

36 MATERIALS SCIENCE↗
NASA NTRS1986

Dark matter and cosmological nucleosynthesis

Existing dark matter problems, i.e., dynamics, galaxy formation and inflation, are considered, along with a model which proposes dark baryons as the bulk of missing matter in a fractal universe. It is shown that no combination of dark, nonbaryonic matter can either provide a cosmological density parameter value near unity or, as in the case of high energy neutrinos, allow formation of condensed matter at epochs when quasars already existed. The possibility that correlations among galactic clusters are scale-free is discussed. Such a distribution of matter would yield a fractal of 1.2, close to a one-dimensional universe. Biasing, cosmic superstrings, and percolated explosions and hot dark matter are theoretical approaches that would satisfy the D = 1.2 fractal model of the large-scale structure of the universe and which would also allow sufficient dark matter in halos to close the universe.

Schramm, D. N.↗
NASA NTRS2001

Fractal Risk Assessment of ISS Propulsion Module in Meteoroid and Orbital Debris Environments

A unique and innovative risk assessment of the International Space Station (ISS) Propulsion Module is conducted using fractal modeling of the Module's response to the meteoroid and orbital debris environments. Both the environment models and structural failure modes due to the resultant hypervelocity impact phenomenology, as well as Module geometry, are investigated for fractal applicability. The fractal risk assessment methodology could produce a greatly simplified alternative to current methodologies, such as BUMPER analyses, while maintaining or increasing the number of complex scenarios that can be assessed. As a minimum, this innovative fractal approach will provide an independent assessment of existing methodologies in a unique way.

Mog, Robert A.↗
DOE OSTI2022

Sea Ice Rheology Experiment (SIREx): 1. Scaling and Statistical Properties of Sea-Ice Deformation Fields

As the sea-ice modeling community is shifting to advanced numerical frameworks, developing new sea-ice rheologies, and increasing model spatial resolution, ubiquitous deformation features in the Arctic sea ice are now being resolved by sea-ice models. Initiated at the Forum for Arctic Modeling and Observational Synthesis, the Sea Ice Rheology Experiment (SIREx) aims at evaluating state-of-the-art sea-ice models using existing and new metrics to understand how the simulated deformation fields are affected by different representations of sea-ice physics (rheology) and by model configuration. Part 1 of the SIREx analysis is concerned with evaluation of the statistical distribution and scaling properties of sea-ice deformation fields from 35 different simulations against those from the RADARSAT Geophysical Processor System (RGPS). For the first time, the viscous-plastic (and the elastic-viscous-plastic variant), elastic-anisotropic-plastic, and Maxwell-elasto-brittle rheologies are compared in a single study. We find that both plastic and brittle sea-ice rheologies have the potential to reproduce the observed RGPS deformation statistics, including multi-fractality. Model configuration (e.g., numerical convergence, atmospheric representation, spatial resolution) and physical parameterizations (e.g., ice strength parameters and ice thickness distribution) both have effects as important as the choice of sea-ice rheology on the deformation statistics. It is therefore not straightforward to attribute model performance to a specific rheological framework using current deformation metrics. In light of these results, we further evaluate the statistical properties of simulated Linear Kinematic Features in a SIREx Part 2 companion paper.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1990

Inhomogeneities of stratocumulus liquid water

There is a growing body of observational evidence on inhomogeneous cloud structure, most recently from the extensive measurements of the FIRE field program. Knowledge of cloud structure is important because it strongly influences the cloud radiative properties, one of the major factors in determining the global energy balance. Current atmospheric circulation models use plane-parallel radiation, so that the liquid water in each gridbox is assumed to be uniform, which gives an unrealistically large albedo. In reality cloud liquid water occupies only a subset of each gridbox, greatly reducing the mean albedo. If future climate models are to treat the hydrological cycle in a manner consistent with energy balance, a better treatment of cloud liquid is needed. FIRE concentrated upon two cloud types of special interest: cirrus and marine stratocumulus. Cirrus tend to be high and optically thin, thus reducing the effective radiative temperature without increasing the albedo significantly, leading to an enhanced greenhouse heating. In contrast, marine stratocumulus are low and optically thick, thus producing a large increase in reflected radiation with a small change in emitted radiation, giving a net cooling which could potentially mitigate the expected greenhouse warming. The FIRE measurements in California stratocumulus during June and July of 1987 show variations in cloud liquid water on all scales. Such variations are associated with inhomogeneous entrainment, in which entrained dry air, rather than mixing uniformly with cloudy air, remains intact in blobs of all sizes, which decay only slowly by invasion of cloudy air. Two important stratocumulus observations are described, followed by a simple fractal model which reproduces these properties, and finally, the model radiative properties are discussed.

Cahalan, Robert F.↗
NASA NTRS1985

Pattern formation by particles settling in viscous flows

Results are reported of several simulations of the motions of small objects in two-dimensional cellular flows performed to study the evolution of the distributions of particle flows over time in processes such as sedimentation. Stream functions are defined in the form of a Hamiltonian system for the particle motions, with inertial and particle acceleration being neglected. Conditions are found for which the particles will become trapped in an oscillatory motion or the particle orbits attain an oscillary motion. Various simulation images are provided to illustrate the usefulness of the technique for modeling fractal swarms.

Smith, L. A.↗
NASA NTRS1999

Cloud Power Spectra-Dependence on Solar Zenith Angle and Wavelength, Implications for Cloud Optical Property Retrievals

Scale breaks (spatial scales at which power-law exponent changes occur) observed in Landsat radiances have proven to be useful indicators of radiative interactions, and have aided the development of improved techniques in the remote sensing of clouds. This work extends previous theoretical studies to absorbing wavelengths by using both Landsat Thematic Mapper (TM) observations and Monte Carlo (MC) simulations to infer the systematic dependencies of power spectral shape on cloud characteristics, illumination conditions, and wavelength. We show that MC simulations operating on a simple fractal model of horizontally inhomogeneous clouds produce power spectra that qualitatively resemble observed spectra. We also show that the decrease in the spectra power-law exponent seen at intermediate scales (referred to as "roughening") as the Sun becomes more oblique is more pronounced at absorbing wavelengths. An automated procedure designed to detect the small scale break location is unable to find systematic differences between TM Band 4 and Band 7, despite the fact that MC simulations point to systematic differences in horizontal fluxes. The effect of these qualitative characteristics of the spatial spectra on the retrieval of cloud optical properties is examined by comparing power spectra of nadir radiances with power spectra of optical properties retrieved using either traditional Independent Pixel Approximation approaches or modifications based on normalized radiance indices and the inverse Non-local Independent Pixel Approximation. Assuming that the actual cloud properties follow perfect scaling behavior at all scales, we show the improvement of the proposed retrieval modifications.

Oreopoulos, Lazaros↗
NASA NTRS2002

A Stochastic Approach For Extending The Dimensionality Of Observed Datasets

This paper addresses the problem that in many cases, observations cannot provide complete fields of the measured quantities, because they yield data only along a single cross-section through the examined fields. The paper describes a new Fourier-adjustment technique that allows existing fractal models to build realistic surroundings to the measured cross-sections. This new approach allows more representative calculations of cloud radiative processes and may be used in other areas as well.

Varnai, Tamas↗
NASA NTRS2003

The "RED Versa NIR" Plane to Retrieve Broken-Cloud Optical Depth from Ground-Based Measurements"

A new method for retrieving cloud optical depth from ground-based measurements of zenith radiance in the RED and near infrared (MR) spectral regions is introduced. Because zenith radiance does not have a one-to-one relationship with optical depth, it is absolutely impossible to use a monochromatic retrieval. On the other side, algebraic combinations of spectral radiances such as NDCI while largely removing nouniquiness and the radiative effects of cloud inhomogeneity, can result in poor retrievals due to its insensitivity to cloud fraction. Instead, both RED and NIR radiances as points on the 'RED vs. NIR' plane are proposed to be used for retrieval. The proposed retrieval method is applied to Cimel measurements at the Atmospheric Radiation Measurements (ARM) site in Oklahoma. Cimel, a multi-channel sunphotometer, is a part of AERONET - a ground-based network for monitoring aerosol optical properties. The results of retrieval are compared with the ones from Microwave Radiometer (MWR) and Multi-Filter Rotating Shadowband Radiometers (MFRSR) located next to Cimel at the ARM site. In addition, the performance of the retrieval method is assessed using a fractal model of cloud inhomogeneity and broken cloudiness. The preliminary results look very promising both theoretically and from measurements.

Marshak, A.↗