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At least 163 records · Page 9

Scattering Properties of Heterogeneous Mineral Particles with Absorbing Inclusions

We analyze the results of numerically exact computer modeling of scattering and absorption properties of randomly oriented poly-disperse heterogeneous particles obtained by placing microscopic absorbing grains randomly on the surfaces of much larger spherical mineral hosts or by imbedding them randomly inside the hosts. These computations are paralleled by those for heterogeneous particles obtained by fully encapsulating fractal-like absorbing clusters in the mineral hosts. All computations are performed using the superposition T-matrix method. In the case of randomly distributed inclusions, the results are compared with the outcome of Lorenz-Mie computations for an external mixture of the mineral hosts and absorbing grains. We conclude that internal aggregation can affect strongly both the integral radiometric and differential scattering characteristics of the heterogeneous particle mixtures.

minerals↗

Grain Properties of Comet C/1995 O1 (Hale-Bopp) Deduced Through Computational Techniques

We present the computational analysis of the 7.6 - 13.2 micrometer infrared (IR) spectrophotometry (R approximately equal to 120) of comet C/1995 O1 (Hale-Bopp) in conjunction with concurrent observations which extend the spectral energy distribution from the near-infrared to far-infrared wavelengths. The observations include temporal epochs pre-perihelion, (1996 October UT and 1997 February UT), near perihelion (1997 April UT), and postperihelion (1997 June UT). Through the computational modeling of small amorphous carbon, and crystalline and amorphous silicate grains in Hale-Bopp's coma, we find that as the comet approached perihelion, the grain size distribution (the Hanner modified power law) steepened (N = 3.4 pre-perihelion, to N = 3.7 near and post-perihelion) along with an increase in the fractal porosity of larger (greater than 1 micrometer) grains. The peak of the grain size distribution remained constant (ap = 0.2 micrometer) at each epoch. We attribute the emergence of the 9.3 micrometer peak near perihelion to crystalline orthopyroxeno grains released from inside the nucleus. Crystalline silicates (olivine and orthopyroxene) make up about 30% (by mass) of the submicron sized (less than 1 micrometer) dust grains in Hale-Bopp's coma during each epoch.

Harker, David E.↗

Loss of 'complexity' and aging. Potential applications of fractals and chaos theory to senescence

The concept of "complexity," derived from the field of nonlinear dynamics, can be adapted to measure the output of physiologic processes that generate highly variable fluctuations resembling "chaos." We review data suggesting that physiologic aging is associated with a generalized loss of such complexity in the dynamics of healthy organ system function and hypothesize that such loss of complexity leads to an impaired ability to adapt to physiologic stress. This hypothesis is supported by observations showing an age-related loss of complex variability in multiple physiologic processes including cardiovascular control, pulsatile hormone release, and electroencephalographic potentials. If further research supports this hypothesis, measures of complexity based on chaos theory and the related geometric concept of fractals may provide new ways to monitor senescence and test the efficacy of specific interventions to modify the age-related decline in adaptive capacity.

Non-NASA Center↗

Statistical and linguistic features of DNA sequences

We present evidence supporting the idea that the DNA sequence in genes containing noncoding regions is correlated, and that the correlation is remarkably long range--indeed, base pairs thousands of base pairs distant are correlated. We do not find such a long-range correlation in the coding regions of the gene. We resolve the problem of the "non-stationary" feature of the sequence of base pairs by applying a new algorithm called Detrended Fluctuation Analysis (DFA). We address the claim of Voss that there is no difference in the statistical properties of coding and noncoding regions of DNA by systematically applying the DFA algorithm, as well as standard FFT analysis, to all eukaryotic DNA sequences (33 301 coding and 29 453 noncoding) in the entire GenBank database. We describe a simple model to account for the presence of long-range power-law correlations which is based upon a generalization of the classic Levy walk. Finally, we describe briefly some recent work showing that the noncoding sequences have certain statistical features in common with natural languages. Specifically, we adapt to DNA the Zipf approach to analyzing linguistic texts, and the Shannon approach to quantifying the "redundancy" of a linguistic text in terms of a measurable entropy function. We suggest that noncoding regions in plants and invertebrates may display a smaller entropy and larger redundancy than coding regions, further supporting the possibility that noncoding regions of DNA may carry biological information.

Non-NASA Center↗

Soot and Radiation Measurements in Microgravity Jet Diffusion Flames

The subject of soot formation and radiation heat transfer in microgravity jet diffusion flames is important not only for the understanding of fundamental transport processes involved but also for providing findings relevant to spacecraft fire safety and soot emissions and radiant heat loads of combustors used in air-breathing propulsion systems. Our objectives are to measure and model soot volume fraction, temperature, and radiative heat fluxes in microgravity jet diffusion flames. For this four-year project, we have successfully completed three tasks, which have resulted in new research methodologies and original results. First is the implementation of a thermophoretic soot sampling technique for measuring particle size and aggregate morphology in drop-tower and other reduced gravity experiments. In those laminar flames studied, we found that microgravity soot aggregates typically consist of more primary particles and primary particles are larger in size than those under normal gravity. Comparisons based on data obtained from limited samples show that the soot aggregate's fractal dimension varies within +/- 20% of its typical value of 1.75, with no clear trends between normal and reduced gravity conditions. Second is the development and implementation of a new imaging absorption technique. By properly expanding and spatially-filtering the laser beam to image the flame absorption on a CCD camera and applying numerical smoothing procedures, this technique is capable of measuring instantaneous full-field soot volume fractions. Results from this technique have shown the significant differences in local soot volume fraction, smoking point, and flame shape between normal and reduced gravity flames. We observed that some laminar flames become open-tipped and smoking under microgravity. The third task we completed is the development of a computer program which integrates and couples flame structure, soot formation, and flame radiation analyses together. We found good agreements between model predictions and experimental data for laminar and turbulent flames under both normal and reduced gravity. We have also tested in the laboratory the techniques of rapid-insertion fine-wire thermocouples and emission pyrometry for temperature measurements. These techniques as well as laser Doppler velocimetry and spectral radiative intensity measurement have been proposed to provide valuable data and improve the modeling analyses.

Ku, Jerry C.↗

Multifractality in human heartbeat dynamics

There is evidence that physiological signals under healthy conditions may have a fractal temporal structure. Here we investigate the possibility that time series generated by certain physiological control systems may be members of a special class of complex processes, termed multifractal, which require a large number of exponents to characterize their scaling properties. We report on evidence for multifractality in a biological dynamical system, the healthy human heartbeat, and show that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure.

Non-NASA Center↗

Fractal statistics of cloud fields

Landsat Multispectral Scanner (MSS) and Thematic Mapper (TM) data, with 80 and 30 m spatial resolution, respectively, have been employed to study the spatial structure of boundary-layer and intertropical convergence zone (ITCZ) clouds. The probability distributions of cloud areas and cloud perimeters are found to approximately follow a power-law, with a different power (i.e., fractal dimension) for each cloud type. They are better approximated by a double power-law behavior, indicating a change in the fractal dimension at a characteristic size which depends upon cloud type. The fractal dimension also changes with threshold. The more intense cloud areas are found to have a higher perimeter fractal dimension, perhaps indicative of the increased turbulence at cloud top. A detailed picture of the inhomogeneous spatial structure of various cloud types will contribute to a better understanding of basic cloud processes, and also has implications for the remote sensing of clouds, for their effects on remote sensing of other parameters, and for the parameterization of clouds in general circulation models, all of which rely upon plane-parallel radiative transfer algorithms.

Cahalan, Robert F.↗

Dimensional analysis of acoustically propagated signals

Traditionally, long term measurements of atmospherically propagated sound signals have consisted of time series of multiminute averages. Only recently have continuous measurements with temporal resolution corresponding to turbulent time scales been available. With modern digital data acquisition systems we now have the capability to simultaneously record both acoustical and meteorological parameters with sufficient temporal resolution to allow us to examine in detail relationships between fluctuating sound and the meteorological variables, particularly wind and temperature, which locally determine the acoustic refractive index. The atmospheric acoustic propagation medium can be treated as a nonlinear dynamical system, a kind of signal processor whose innards depend on thermodynamic and turbulent processes in the atmosphere. The atmosphere is an inherently nonlinear dynamical system. In fact one simple model of atmospheric convection, the Lorenz system, may well be the most widely studied of all dynamical systems. In this paper we report some results of our having applied methods used to characterize nonlinear dynamical systems to study the characteristics of acoustical signals propagated through the atmosphere. For example, we investigate whether or not it is possible to parameterize signal fluctuations in terms of fractal dimensions. For time series one such parameter is the limit capacity dimension. Nicolis and Nicolis were among the first to use the kind of methods we have to study the properties of low dimension global attractors.

Hansen, Scott D.↗

Fuzzy set methods for object recognition in space applications

Progress on the following tasks is reported: (1) fuzzy set-based decision making methodologies; (2) feature calculation; (3) clustering for curve and surface fitting; and (4) acquisition of images. The general structure for networks based on fuzzy set connectives which are being used for information fusion and decision making in space applications is described. The structure and training techniques for such networks consisting of generalized means and gamma-operators are described. The use of other hybrid operators in multicriteria decision making is currently being examined. Numerous classical features on image regions such as gray level statistics, edge and curve primitives, texture measures from cooccurrance matrix, and size and shape parameters were implemented. Several fractal geometric features which may have a considerable impact on characterizing cluttered background, such as clouds, dense star patterns, or some planetary surfaces, were used. A new approach to a fuzzy C-shell algorithm is addressed. NASA personnel are in the process of acquiring suitable simulation data and hopefully videotaped actual shuttle imagery. Photographs have been digitized to use in the algorithms. Also, a model of the shuttle was assembled and a mechanism to orient this model in 3-D to digitize for experiments on pose estimation is being constructed.

Keller, James M.↗

Fractal mechanisms in the electrophysiology of the heart

The mathematical concept of fractals provides insights into complex anatomic branching structures that lack a characteristic (single) length scale, and certain complex physiologic processes, such as heart rate regulation, that lack a single time scale. Heart rate control is perturbed by alterations in neuro-autonomic function in a number of important clinical syndromes, including sudden cardiac death, congestive failure, cocaine intoxication, fetal distress, space sickness and physiologic aging. These conditions are associated with a loss of the normal fractal complexity of interbeat interval dynamics. Such changes, which may not be detectable using conventional statistics, can be quantified using new methods derived from "chaos theory.".

NASA Discipline Cardiopulmonary↗

An optical systems analysis approach to image resampling

All types of image registration require some type of resampling, either during the registration or as a final step in the registration process. Thus the image(s) must be regridded into a spatially uniform, or angularly uniform, coordinate system with some pre-defined resolution. Frequently the ending resolution is not the resolution at which the data was observed with. The registration algorithm designer and end product user are presented with a multitude of possible resampling methods each of which modify the spatial frequency content of the data in some way. The purpose of this paper is threefold: (1) to show how an imaging system modifies the scene from an end to end optical systems analysis approach, (2) to develop a generalized resampling model, and (3) empirically apply the model to simulated radiometric scene data and tabulate the results. A Hanning windowed sinc interpolator method will be developed based upon the optical characterization of the system. It will be discussed in terms of the effects and limitations of sampling, aliasing, spectral leakage, and computational complexity. Simulated radiometric scene data will be used to demonstrate each of the algorithms. A high resolution scene will be "grown" using a fractal growth algorithm based on mid-point recursion techniques. The result scene data will be convolved with a point spread function representing the optical response. The resultant scene will be convolved with the detection systems response and subsampled to the desired resolution. The resultant data product will be subsequently resampled to the correct grid using the Hanning windowed sinc interpolator and the results and errors tabulated and discussed.

Lyon, Richard G.↗

Dynamic Light Scattering From Colloidal Gels

We present a brief, preliminary account of the interpretation of dynamic light scattering from fractal colloidal gels. For small scattering angles, and for high initial colloid particle volume fractions, the correlation functions exhibit arrested decay, reflecting the non-ergodic nature of these systems and allowing us to directly determine the elastic modulus of the gels. For smaller initial volume fractions, the correlation functions decay completely. In all cases, the initial decay is not exponential, but is instead described by a stretched exponential. We summarize the principles of a model that accounts for these data and discuss the scaling behavior of the measured parameters.

Krall, A. H.↗

Measurement Via Optical Near-Nulling and Subaperture Stitching

A subaperture stitching interferometer system provides near-nulling of a subaperture wavefront reflected from an object of interest over a portion of a surface of the object. A variable optical element located in the radiation path adjustably provides near-nulling to facilitate stitching of subaperture interferograms, creating an interferogram representative of the entire surface of interest. This enables testing of aspheric surfaces without null optics customized for each surface prescription. The surface shapes of objects such as lenses and other precision components are often measured with interferometry. However, interferometers have a limited capture range, and thus the test wavefront cannot be too different from the reference or the interference cannot be analyzed. Furthermore, the performance of the interferometer is usually best when the test and reference wavefronts are nearly identical (referred to as a null condition). Thus, it is necessary when performing such measurements to correct for known variations in shape to ensure that unintended variations are within the capture range of the interferometer and accurately measured. This invention is a system for nearnulling within a subaperture stitching interferometer, although in principle, the concept can be employed by wavefront measuring gauges other than interferometers. The system employs a light source for providing coherent radiation of a subaperture extent. An object of interest is placed to modify the radiation (e.g., to reflect or pass the radiation), and a variable optical element is located to interact with, and nearly null, the affected radiation. A detector or imaging device is situated to obtain interference patterns in the modified radiation. Multiple subaperture interferograms are taken and are stitched, or joined, to provide an interferogram representative of the entire surface of the object of interest. The primary aspect of the invention is the use of adjustable corrective optics in the context of subaperture stitching near-nulling interferometry, wherein a complex surface is analyzed via multiple, separate, overlapping interferograms. For complex surfaces, the problem of managing the identification and placement of corrective optics becomes even more pronounced, to the extent that in most cases the null corrector optics are specific to the particular asphere prescription and no others (i.e. another asphere requires completely different null correction optics). In principle, the near-nulling technique does not require subaperture stitching at all. Building a near-null system that is practically useful relies on two key features: simplicity and universality. If the system is too complex, it will be difficult to calibrate and model its manufacturing errors, rendering it useless as a precision metrology tool and/or prohibitively expensive. If the system is not applicable to a wide range of test parts, then it does not provide significant value over conventional null-correction technology. Subaperture stitching enables simpler and more universal near-null systems to be effective, because a fraction of a surface is necessarily less complex than the whole surface (excepting the extreme case of a fractal surface description). The technique of near-nulling can significantly enhance aspheric subaperture stitching capability by allowing the interferometer to capture a wider range of aspheres. More over, subaperture stitching is essential to a truly effective near-nulling system, since looking at a fraction of the surface keeps the wavefront complexity within the capability of a relatively simple nearnull apparatus. Furthermore, by reducing the subaperture size, the complexity of the measured wavefront can be reduced until it is within the capability of the near-null design.

Forbes, Greg↗

Moments of catchment storm area

The portion of a catchment covered by a stationary rainstorm is modeled by the common area of two overlapping circles. Given that rain occurs within the catchment and conditioned by fixed storm and catchment sizes, the first two moments of the distribution of the common area are derived from purely geometrical considerations. The variance of the wetted fraction is shown to peak when the catchment size is equal to the size of the predominant storm. The conditioning on storm size is removed by assuming a probability distribution based upon the observed fractal behavior of cloud and rainstorm areas.

Eagleson, P. S.↗

Computer Simulation of Fracture in Aerogels

Aerogels are of interest to the aerospace community primarily for their thermal properties, notably their low thermal conductivities. While the gels are typically fragile, recent advances in the application of conformal polymer layers to these gels has made them potentially useful as lightweight structural materials as well. In this work, we investigate the strength and fracture behavior of silica aerogels using a molecular statics-based computer simulation technique. The gels' structure is simulated via a Diffusion Limited Cluster Aggregation (DLCA) algorithm, which produces fractal structures representing experimentally observed aggregates of so-called secondary particles, themselves composed of amorphous silica primary particles an order of magnitude smaller. We have performed multi-length-scale simulations of fracture in silica aerogels, in which the interaction b e e n two secondary particles is assumed to be described by a Morse pair potential parameterized such that the potential range is much smaller than the secondary particle size. These Morse parameters are obtained by atomistic simulation of models of the experimentally-observed amorphous silica "bridges," with the fracture behavior of these bridges modeled via molecular statics using a Morse/Coulomb potential for silica. We consider the energetics of the fracture, and compare qualitative features of low-and high-density gel fracture.

Good, Brian S.↗

NASA Tech Briefs, July 2005

Thin-Film Resistance Heat-Flux Sensors Circuit Indicates that Voice-Recording Disks are Nearly Full Optical Sensing of Combustion Instabilities in Gas Turbines Topics include: Crane-Load Contact Sensor; Hexagonal and Pentagonal Fractal Multiband Antennas; Multifunctional Logic Gate Controlled by Temperature; Multifunctional Logic Gate Controlled by Supply Voltage; Power Divider for Waveforms Rich in Harmonics; SCB Quantum Computers Using iSWAP and 1-Qubit Rotations; CSAM Metrology Software Tool; Update on Rover Sequencing and Visualization Program; Selecting Data from a Star Catalog; Rotating Desk for Collaboration by Two Computer Programmers; Variable-Pressure Washer; Magnetically Attached Multifunction Maintenance Rover; Improvements in Fabrication of Sand/Binder Cores for Casting; Solid Freeform Fabrication of Composite-Material Objects; Efficient Computational Model of Hysteresis; Gauges for Highly Precise Metrology of a Compound Mirror; Improved Electrolytic Hydrogen Peroxide Generator; High-Power Fiber Lasers Using Photonic Band Gap Materials; Ontology-Driven Information Integration; Quantifying Traversability of Terrain for a Mobile Robot; More About Arc-Welding Process for Making Carbon Nanotubes; Controlling Laser Spot Size in Outer Space; or Software-Reconfigurable Processors for Spacecraft.

Source record↗

Observations, theoretical ideas and modeling of turbulent flows: Past, present and future

Turbulence was analyzed in a historical context featuring the interactions between observations, theoretical ideas, and modeling within three successive movements. These are identified as predominantly statistical, structural and deterministic. The statistical movement is criticized for its failure to deal with the structural elements observed in turbulent flows. The structural movement is criticized for its failure to embody observed structural elements within a formal theory. The deterministic movement is described as having the potential of overcoming these deficiencies by allowing structural elements to exhibit chaotic behavior that is nevertheless embodied within a theory. Four major ideas of this movement are described: bifurcation theory, strange attractors, fractals, and the renormalization group. A framework for the future study of turbulent flows is proposed, based on the premises of the deterministic movement.

Chapman, G. T.↗

Analysis of fractal dimensions of rat bones from film and digital images

OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.

NASA Discipline Musculoskeletal↗