While these samples are representative of the content of Science.gov,

they are not comprehensive nor are they the most current set.

We encourage you to perform a real-time search of Science.gov

to obtain the most current and comprehensive results.

Last update: November 12, 2013.

1

Fractal dimension and classification of music

The fractal aspect of different kinds of music was analyzed in keeping with the time domain. The fractal dimension of a great number of different musics (180 scores) is calculated by the Variation method. By using an analysis of variance, it is shown that fractal dimension helps discriminate different categories of music. Then, we used an original statistical technique based

M. Bigerelle; A. Iost

2000-01-01

2

At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D-italic = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D-italic = 1 to the cantorus is governed by an exponent ..nu.. = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent.

Li, W.; Bak, P.

1986-08-11

3

Video fire detection based on three-state Markov modal and fractal dimension calculation

NASA Astrophysics Data System (ADS)

Fire detection based on video surveillance is a very effective method for large area outdoor fire prevention, but the unpredictable place and time makes automatic fire detection a difficult problem. This paper adopts a loose color selection and frame differential to narrow down possible fire regions, where every pixel's temporal color variations are analyzed by 3-state Markov modals. One of the Markov modal is used for brightness variation examination and the other one is used for fire color likeness that is measured by color difference. In order to eliminate false detections, the fractal dimension calculation and texture match are performed. Experimental results prove the proposed method is feasible and suitable for outdoor or indoor fire detection in surveillance videos.

Lei, Bo; Zhang, Zhijie; Wang, Chensheng

2012-11-01

4

A note on fractal dimensions of biomedical waveforms.

In this paper, we study performance of Katz method of computing fractal dimension of waveforms, and its estimation accuracy is compared with Higuchi's method. The study is performed on four synthetic parametric fractal waveforms for which true fractal dimensions can be calculated, and real sleep electroencephalogram. The dependence of Katz's fractal dimension on amplitude, frequency and sampling frequency of waveforms is noted. Even though the Higuchi's method has given more accurate estimation of fractal dimensions, the study suggests that the results of Katz's based fractal dimension analysis of biomedical waveforms have to be carefully interpreted. PMID:19716555

Raghavendra, B S; Narayana Dutt, D

2009-11-01

5

Exterior dimension of fat fractals

NASA Technical Reports Server (NTRS)

Geometric scaling properties of fat fractal sets (fractals with finite volume) are discussed and characterized via the introduction of a new dimension-like quantity which is called the exterior dimension. In addition, it is shown that the exterior dimension is related to the 'uncertainty exponent' previously used in studies of fractal basin boundaries, and it is shown how this connection can be exploited to determine the exterior dimension. Three illustrative applications are described, two in nonlinear dynamics and one dealing with blood flow in the body. Possible relevance to porous materials and ballistic driven aggregation is also noted.

Grebogi, C.; Mcdonald, S. W.; Ott, E.; Yorke, J. A.

1985-01-01

6

Texture Segmentation Using Fractal Dimension

This paper deals with the problem of recognizing and segmenting textures in images. For this purpose the authors employ a technique based on the fractal dimension (FD) and the multi-fractal concept. Six FD features are based on the original image, the above average\\/high gray level image, the below average\\/low gray level image, the horizontally smoothed image, the vertically smoothed image,

B. B. Chaudhuri; Nirupam Sarkar

1995-01-01

7

Fractal Dimension in Epileptic EEG Signal Analysis

NASA Astrophysics Data System (ADS)

Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include greater speed and the criterion to choose the maximum and minimum values for time intervals. Comparisons with the other waveform fractal dimension algorithms are also demonstrated. In order to discriminate the Healthy and the Epileptic EEGs, an improved method of Multifractal Measure such as Generalized Fractal Dimensions (GFD) is also proposed. Finally we conclude that there are significant differences between the Healthy and Epileptic Signals in the designed method than the GFD through graphical and statistical tools. The improved multifractal measure is very efficient technique to analyze the EEG Signals and to compute the state of illness of the Epileptic patients.

Uthayakumar, R.

8

A comparison of waveform fractal dimension algorithms

The fractal dimension of a waveform represents a powerful tool for transient detection. In particular, in analysis of electroencephalograms and electrocardiograms, this feature has been used to identify and distinguish specific states of physiologic function. A variety of algorithms are available for the computation of fractal dimension. In this study, the most common methods of estimating the fractal dimension of

Rosana Esteller; George Vachtsevanos; Javier Echauz; Brian Litt

2001-01-01

9

Fractal Dimension Analysis of Putative Martian Coastlines

NASA Astrophysics Data System (ADS)

Prior research is equivocal on the existence and location of Martian coastlines. This study proposes a novel method of analyzing putative coastlines; fractal dimensions provide a quantitative measurement of the complexity and nature of a fractal. Geological evidence points to a coastline at the elevation of -3790 meters, called the Deuteronilus contact. It is hypothesized that the fractal dimensions of this putative Martian coastline will be comparable to those of Earth shorelines. A topographic map with a contour line at -3790 meters was obtained from the U. S. Geological Survey, reflecting the most recent Mars Orbiter Laser Altimeter data. The map was cropped into sixty and twenty degree segments, and the putative coastline was isolated from extraneous features. A program which used the box-counting method calculated the fractal dimensions of the putative shorelines. The 22 results were tabulated and compared to 17 fractal dimensions of Earth shorelines, collected from published articles. Ranges were 1.07 to 1.66 for Earth and 1.141 to 1.436 for Mars. The mean was 1.28 for the Mars data and 1.22 for the Earth data, a slight difference that asteroid craters could account for. An unpaired t-test could not prove that the two data sets were significantly different. Although the past existence of a coastline at the Deuteronilus contact cannot be definitively proven without on site investigations, the hypothesis that the fractal dimensions of the putative Martian coastline would be comparable to those of Earth's was accepted, thereby substantiating the claims for the existence of a large northern ocean.

Gianelli, G. A.

2005-08-01

10

Spatial Fractal Dimension Ds and Its Application in Earthquake Prediction.

National Technical Information Service (NTIS)

Using the correlation function approach to calculate the spatial fractal dimension of D(sub s), this paper studies the variation features of the pre-strong earthquake spatial fractal dimension D(sub s) associated with M > or = 6 events occurring in Yunnan...

J. Cai J. Tang Z. Xu

1993-01-01

11

Use of Fractal Dimension for Texture Classification.

National Technical Information Service (NTIS)

This paper addresses the idea of using fractal dimension as a measure of image texture. The computation of the fractal dimension of a grey-scale image and also of the 'fractal signature' of the image is presented. Two methods of scanning the image for the...

K. E. Dixon

1989-01-01

12

Image Segmentation via Fractal Dimension.

National Technical Information Service (NTIS)

The purpose of this study was to investigate the suitability of algorithms derived from the study of fractal geometry to the specific problem of image segmentation. The use of two widely used methods and an original hybrid technique for calculating fracta...

A. L. Jones

1987-01-01

13

A Fractal Dimension Survey of Active Region Complexity

NASA Technical Reports Server (NTRS)

A new approach to quantifying the magnetic complexity of active regions using a fractal dimension measure is presented. This fully-automated approach uses full disc MDI magnetograms of active regions from a large data set (2742 days of the SoHO mission; 9342 active regions) to compare the calculated fractal dimension to both Mount Wilson classification and flare rate. The main Mount Wilson classes exhibit no distinct fractal dimension distribution, suggesting a self-similar nature of all active regions. Solar flare productivity exhibits an increase in both the frequency and GOES X-ray magnitude of flares from regions with higher fractal dimensions. Specifically a lower threshold fractal dimension of 1.2 and 1.25 exists as a necessary, but not sufficient, requirement for an active region to produce M- and X-class flares respectively .

McAteer, R. T. James; Gallagher, Peter; Ireland, Jack

2005-01-01

14

NASA Astrophysics Data System (ADS)

In this paper, by discussing the basic hypotheses about the continuous orbit and discrete orbit in two research directions of the background medium theory for celestial body motion, the concrete equation forms and their summary of the theoretic frame of celestial body motion are introduced. Future more, by discussing the general form of Binet's equation of celestial body motion orbit and it's solution of the advance of the perihelion of planets, the relations and differences between the continuous orbit theory and Newton's gravitation theory and Einstein's general relativity are given. And by discussing the fractional-dimension expanded equation for the celestial body motion orbits, the concrete equations and the prophesy data of discrete orbit or stable orbits of celestial bodies which included the planets in the Solar system, satellites in the Uranian system, satellites in the Earth system and satellites obtaining the Moon obtaining from discrete orbit theory are given too. Especially, as the preliminary exploration and inference to the gravitation curve of celestial bodies in broadly range, the concept for the ideal black hole with trend to infinite in mass density difficult to be formed by gravitation only is explored. By discussing the position hypothesis of fractional-dimension derivative about general function and the formula form the hypothesis of fractional-dimension derivative about power function, the concrete equation formulas of fractional-dimension derivative, differential and integral are described distinctly further, and the difference between the fractional-dimension derivative and the fractional-order derivative are given too. Subsequently, the concrete forms of measure calculation equations of self-similar fractal obtaining by based on the definition of form in fractional-dimension calculus about general fractal measure are discussed again, and the differences with Hausdorff measure method or the covering method at present are given. By applying the measure calculation equations, the me asure of self-similar fractals which include middle-third Cantor set, Koch curve, Sierpinski gasket and orthogonal cross star are calculated and analyzed.

Yan, Kun

2007-04-01

15

Temporal Fractal Dimension of the Ontogenic Growth

NASA Astrophysics Data System (ADS)

The West-Brown-Enquist curve describing ontogenic growth is mapped on the power law fractal function with the time-dependent scaling factor and exponent representing the temporal fractal dimension. The model has been applied to obtain the fractal characteristics of growth of 13 species and 13 tumours. The results obtained reveal that the maximum value of the fractal dimension for the system considered increases with the limiting number of the cells and is attained at 50% of cells doublings both in the case of species and tumours.

Molski, Marcin

16

On the fractal dimension of stream networks

NASA Astrophysics Data System (ADS)

The geometric pattern of the stream network of a drainage basin can be viewed as a "fractal" with a fractional dimension (Mandelbrot, 1982). For an ordered drainage system, the authors first proposed to derive the fractal dimension from Horton's laws of stream number and stream lengths (La Barbera and Rosso, 1987). This results in a simple function of bifurcation and stream length ratios of the drainage system, the analytical derivation of which is presented. Accordingly, the fractal dimension could generally vary from 1 to 2, the latter value descending from the modal values of Horton's order ratios for topological randomness. However, the analysis of a large sample of field data shows the typical fractal dimension of river networks to lie between 1.5 and 2, with an average of 1.6÷1.7. Fractality can be used to investigate the scaling properties of the attributes and parameters describing drainage basin form and process.

La Barbera, Paolo; Rosso, Renzo

1989-04-01

17

Application of Fractal Dimension on Palsar Data

NASA Astrophysics Data System (ADS)

Study of land cover is the primal task of remote sensing where microwave imaging plays an important role. As an alternate of optical imaging, microwave, in particular, Synthetic Aperture Radar (SAR) imaging is very popular. With the advancement of technology, multi-polarized images are now available, e.g., ALOS-PALSAR (Phased Array type L-band SAR), which are beneficial because each of the polarization channel shows different sensitivity to various land features. Further, using the textural features, various land classes can be classified on the basis of the textural measures. One of the textural measure is fractal dimension. It is noteworthy that fractal dimension is a measure of roughness and thus various land classes can be distinguished on the basis of their roughness. The value of fractal dimension for the surfaces lies between 2.0 and 3.0 where 2.0 represents a smooth surface while 3.0 represents drastically rough surface. The study area covers subset images lying between 2956'53"N, 7750'32"E and 2950'40"N, 7757'19"E. The PALSAR images of the year 2007 and 2009 are considered for the study. In present paper a fractal based classification of PALSAR images has been performed for identification of Water, Urban and Agricultural Area. Since fractals represent the image texture, hence the present study attempts to find the fractal properties of land covers to distinguish them from one another. For the purpose a context has been defined on the basis of a moving window, which is used to estimate the local fractal dimension and then moved over the whole image. The size of the window is an important issue for estimation of textural measures which is considered to be 55 in present study. This procedure, in response, produces a textural map called fractal map. The fractal map is constituted with the help of local fractal dimension values and can be used for contextual classification. In order to study the fractal properties of PALSAR images, the three polarization images viz. HH (Horizontal-Horizontal Polarization), VV (Vertical-Vertical Polarization) and HV (Horizontal-Vertical Polarization) are considered individually. First of all each polarized image is classified in an unsupervised way and various clusters, i.e., four clusters are identified with the help of reference data as Water, Urban and Agricultural Area. For each cluster, the fractal dimension is obtained from the fractal map. Based on the study the ranges of fractal dimension for three classes are Water: 2.0-2.17, Agricultural Area: 2.24-2.72, Urban Area: 2.63-2.92 for HH polarized image; Water: 2.0-2.21, Agricultural Area: 2.20-2.64, Urban; 2.58-2.94 for VV polarized image and Water: 2.0-2.14, Agricultural Area: 2.18-2.58, Urban: 2.46-2.94 for HV polarized image. Since the class Others represents a mixture of various classes, an explicit range of D for this class can not be determined. A closer look at the ranges of fractal dimension indicates that there is an overlapping of the values for different classes, despite of which the classes can be distinguished. Also, the class Water having low value of fractal dimension can be treated as smooth and Urban Area having higher values of fractal dimension can be considered rough in structure while the class Agricultural Area shows an intermediate roughness.

Singh, Dharmendra; Pant, Triloki

18

Trabecular Bone Mechanical Properties and Fractal Dimension

NASA Technical Reports Server (NTRS)

Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremity and spinal column. These models will permit analysis and evaluation specific to each individual and thereby provide more efficient and effective exercise protocols. Inflight countermeasures and post-flight rehabilitation can then be customized and targeted on a case-by-case basis. Recent Summer Faculty Fellowship participants have focused upon finite element mesh generation, muscle force estimation, and fractal calculations of trabecular bone microstructure. Methods have been developed for generating the three-dimensional geometry of the femur from serial section magnetic resonance images (MRI). The use of MRI as an imaging modality avoids excessive exposure to radiation associated with X-ray based methods. These images can also detect trabecular bone microstructure and architecture. The goal of the current research is to determine the degree to which the fractal dimension of trabecular architecture can be used to predict the mechanical properties of trabecular bone tissue. The elastic modulus and the ultimate strength (or strain) can then be estimated from non-invasive, non-radiating imaging and incorporated into the finite element models to more accurately represent the bone tissue of each individual of interest. Trabecular bone specimens from the proximal tibia are being studied in this first phase of the work. Detailed protocols and procedures have been developed for carrying test specimens through all of the steps of a multi-faceted test program. The test program begins with MRI and X-ray imaging of the whole bones before excising a smaller workpiece from the proximal tibia region. High resolution MRI scans are then made and the piece further cut into slabs (roughly 1 cm thick). The slabs are X-rayed again and also scanned using dual-energy X-ray absorptiometry (DEXA). Cube specimens are then cut from the slabs and tested mechanically in compression. Correlations between mechanical properties and fractal dimension will then be examined to assess and quantify the predictive capability of the fractal calculations.

Hogan, Harry A.

1996-01-01

19

Fractal dimensions and geometries of caves

Lengths of all caves in a region have been observed previously to be distributed hyperbolically, like self-similar geomorphic phenomena identified by Mandelbrot as exhibiting fractal geometry. Proper cave lengths exhibit a fractal dimension of about 1.4. These concepts are extended to other self-similar geometric properties of caves with the following consequences.Lengths of a cave is defined as the sum of

Rane L. Curl

1986-01-01

20

Fractal Dimension in Eeg Signals during Muscle Fatigue

NASA Astrophysics Data System (ADS)

Fractal dimension (FD) has been successfully used to characterize signals in the format of time series. In this study, we calculated FD of EEG signals recorded during human muscle fatigue as a measure of changes in the EEG signal complexity along fatigue. Subjects performed 200 intermittent handgrip contractions at 100contraction level. Each contraction lasted 2 s, followed by a 5-s rest. EEG data were recorded from the scalp along with handgrip force and muscle EMG signals. The FD computation was based on measurements of the length (Lk) of the signal at 6 different temporal resolutions (k = 1, 2, ¡, 6). FD was determined from the relationship between Lk and k using the least square fit. The results showed that: (1) EEG fractal dimension associated with the motor performance was significantly higher than that during the rest period; (2) changes in the fractal dimension along the process of fatigue showed a significant correlation with the decline in force and EMG signals.

Huang, Haibin; Yao, Bin; Yue, Guang; Brown, Robert; Jing, Liu

2003-10-01

21

ERIC Educational Resources Information Center

Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

Esbenshade, Donald H., Jr.

1991-01-01

22

Fast algorithm for computing the fractal dimension of binary images

NASA Astrophysics Data System (ADS)

Methods for determining fractal dimensions of image objects have gained increasing importance in recent developments of image processing. Mainly for the classification of shape and textures of natural objects the fractal dimension has proven its usefulness.

Creutzburg, Reiner

1999-03-01

23

Fractal dimension of alumina aggregates grown in two dimensions

NASA Technical Reports Server (NTRS)

The concepts of fractal geometry are applied to the analysis of 0.4-micron alumina constrained to agglomerate in two dimensions. Particles were trapped at the bottom surface of a drop of a dilute suspension, and the agglomeration process was directly observed, using an inverted optical microscope. Photographs were digitized and analyzed, using three distinct approaches. The results indicate that the agglomerates are fractal, having a dimension of approximately 1.5, which agrees well with the predictions of the diffusion-limited cluster-cluster aggregation model.

Larosa, Judith L.; Cawley, James D.

1992-01-01

24

Estimation of fractal dimensions from transect data

Fractals are a useful tool for analyzing the topology of objects such as coral reefs, forest canopies, and landscapes. Transects are often studied in these contexts, and fractal dimensions computed from them. An open question is how representative a single transect is. Transects may also be used to estimate the dimensionality of a surface. Again the question of representativeness of the transect arises. These two issues are related. This note qualifies the conditions under which transect data may be considered to be representative or may be extrapolated, based on both theoretical and empirical results.

Loehle, C. [Argonne National Lab., IL (United States)

1994-04-01

25

Multi-resolution estimation of fractal dimension from noisy images

NASA Astrophysics Data System (ADS)

A well-suited approach to calculate the fractal dimension of digital images stems from the power spectrum of a fractional Brownian motion: the ratio between powers at different scales is related to the persistence parameter H and, thus, to the fractal dimension D equals 3 - H. The signal- dependent nature of the speckle noise, however, prevents a correct estimation of fractal dimension from synthetic aperture radar (SAR) images. Here, we propose an assess a novel method to obtain D based on the multi-scale decomposition provided by the normalized Laplacian pyramid (LP), which is a bandpass representation obtained by dividing the layers of a LP by its expanded base band and is designed to force the noise to become signal independent. Extensive experiments on synthetic fractal textures, both noise free and noisy, corroborate the underlying assumptions and show the performances, in terms of both accuracy and confidence of estimation, of pyramid methods compared with the well-established method based on the wavelet transform. Preliminary results on true SAR images from ERS-1 look promising as well.

Aiazzi, Bruno; Alparone, Luciano; Baronti, Stefano; Garzelli, Andrea

2001-01-01

26

Fractal dimension analyses of lava surfaces and flow boundaries

NASA Technical Reports Server (NTRS)

An improved method of estimating fractal surface dimensions has been developed. The accuracy of this method is illustrated using artificially generated fractal surfaces. A slightly different from usual concept of linear dimension is developed, allowing a direct link between that and the corresponding surface dimension estimate. These methods are applied to a series of images of lava flows, representing a variety of physical and chemical conditions. These include lavas from California, Idaho, and Hawaii, as well as some extraterrestrial flows. The fractal surface dimension estimations are presented, as well as the fractal line dimensions where appropriate.

Cleghorn, Timothy F.

1993-01-01

27

An efficient fractal dimension based clustering algorithm

NASA Astrophysics Data System (ADS)

Clustering plays an important role in data mining. It helps to reveal intrinsic structure in data sets with little or no prior knowledge. The approaches of clustering have received great attention in recent years. However many published algorithms fail to do well in determining the number of cluster, finding arbitrary shapes of clusters or identifying the presence of noise. In this paper we present an efficient clustering algorithm which employs the theory of grid, density and fractal that can partition points in the same cluster with minimum change of fractal dimension meanwhile maximizing the self-similarity in the clusters. We show via experiments that FDC can quickly deal with multidimensional large data sets, identify the number of clusters, be capable of recognizing clusters of arbitrary shape and furthermore explore some qualitative information from data sets.

Xiong, Xiao; Zhang, Jie; Shi, Qingwei

2007-09-01

28

Examination of the Fractal Dimension of Fatty Acid Aggregates

NASA Astrophysics Data System (ADS)

This study explore the relationship between the length of the carbon chain on various ?-alkanoic acids and the fractal dimension of the resulting aggregates they form. Fractal dimension was chosen as a quantified measure of roughness of an aggregate formed when a solution of acid in chloroform is evaporated from a water surface. Measurements of 11 fatty acids were made at room temperature and yielded fractal dimensions between 1.0 and 1.4. Fractal dimension was found to vary with carbon number. In addition, the statistical distribution of fractal dimension for each acid was recorded. The dependence of fractal dimension upon carbon number follows a trend similar to that seen in bulk-melting point versus carbon number. This research was supported by NSF grant DMR-9619406.

Kuck, Andrew J.; Hayward, Michele C.; Andrews, Anna P.

1998-03-01

29

Local Earth's gravity field in view of fractal dimension

NASA Astrophysics Data System (ADS)

The poster presents the relative roughness of chosen characteristics of the Earth's gravity field in several small regions in area of Slovakia (e.g. free-air anomaly, Bouguer anomaly, gravity disturbance...) using the values of fractal dimension. In this approach, a three dimensional box counting method and the Hurst analysis method are applied to estimate the values of fractal dimensions. Then the computed fractal dimension values are used to compare all 3D models of all chosen characteristics.

Mészárosová, Katarína; Minarechová, Zuzana; Janák, Juraj

2013-04-01

30

FRACTAL DIMENSION RESULTS FOR CONTINUOUS TIME RANDOM WALKS

Continuous time random walks impose random waiting times between particle jumps. This paper computes the fractal dimensions of their process limits, which represent particle traces in anomalous diffusion.

Meerschaert, Mark M.; Nane, Erkan; Xiao, Yimin

2013-01-01

31

Fractal dimension in nonhyperbolic chaotic scattering

NASA Technical Reports Server (NTRS)

In chaotic scattering there is a Cantor set of input-variable values of zero Lebesgue measure (i.e., zero total length) on which the scattering function is singular. For cases where the dynamics leading to chaotic scattering is nonhyperbolic (e.g., there are Kolmogorov-Arnol'd-Moser tori), the nature of this singular set is fundamentally different from that in the hyperbolic case. In particular, for the nonhyperbolic case, although the singular set has zero total length, strong evidence is presented to show that its fractal dimension is 1.

Lau, Yun-Tung; Finn, John M.; Ott, Edward

1991-01-01

32

Fractal dimension based corneal fungal infection diagnosis

NASA Astrophysics Data System (ADS)

We present a fractal measure based pattern classification algorithm for automatic feature extraction and identification of fungus associated with an infection of the cornea of the eye. A white-light confocal microscope image of suspected fungus exhibited locally linear and branching structures. The pixel intensity variation across the width of a fungal element was gaussian. Linear features were extracted using a set of 2D directional matched gaussian-filters. Portions of fungus profiles that were not in the same focal plane appeared relatively blurred. We use gaussian filters of standard deviation slightly larger than the width of a fungus to reduce discontinuities. Cell nuclei of cornea and nerves also exhibited locally linear structure. Cell nuclei were excluded by their relatively shorter lengths. Nerves in the cornea exhibited less branching compared with the fungus. Fractal dimensions of the locally linear features were computed using a box-counting method. A set of corneal images with fungal infection was used to generate class-conditional fractal measure distributions of fungus and nerves. The a priori class-conditional densities were built using an adaptive-mixtures method to reflect the true nature of the feature distributions and improve the classification accuracy. A maximum-likelihood classifier was used to classify the linear features extracted from test corneal images as 'normal' or 'with fungal infiltrates', using the a priori fractal measure distributions. We demonstrate the algorithm on the corneal images with culture-positive fungal infiltrates. The algorithm is fully automatic and will help diagnose fungal keratitis by generating a diagnostic mask of locations of the fungal infiltrates.

Balasubramanian, Madhusudhanan; Perkins, A. Louise; Beuerman, Roger W.; Iyengar, S. Sitharama

2006-09-01

33

Time evolution of the fractal dimension of a mixing front

We present a description of an experimental study of an array of turbulent plumes (from one to nine plumes), investigating the time evolution of the fractal dimension of the plumes and also the spatial evolution of the fractal dimension from one plume to other. We also investigate the effects of bouyancy (different Atwood numbers), the number of plumes and the

P. Lopez Gonzalez-Nieto; J. Grau

2009-01-01

34

Aggregation of liposomes in presence of La3+ : A study of the fractal dimension

A study of the fractal dimension of the aggregation of three different types of large unilamellar vesicles, formed by egg yolk phosphatidylcholine (EYPC), dimyristoyl-phosphocholine (DMPC), and dipalmitoyl-phosphocholine (DPPC), in the presence of La3+ , is presented. Aggregate liposome fractal dimensions were calculated by two methods, aggregation kinetics, using the approaches diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA) and

Juan Sabín; Gerardo Prieto; Juan M. Ruso; Paula Messina; Félix Sarmiento

2007-01-01

35

NASA Astrophysics Data System (ADS)

New field of application of fractal dimensions is proposed. A technique, based on the calculation of fractal dimension, was used for express-diagnostics and identification of bacteria of the vaccine strain Yersinia pestis EV line NIIEG. Purpose of this study was the experimental investigation of properties of speckle patterns, formed under laser illumination of a single colony of the strain that was grown on different agars.

Ulyanov, Alexander S.; Lyapina, Anna M.; Ulianova, Onega V.; Feodorova, Valentina A.

2010-10-01

36

Evaluation of Fractal Dimension of Injected Sand

The aim of this study is to show how fractal analysis can be effectively used to characterize the texture of porous solids. The materials under study were series of injected Loire Sand. Data from MIP tests were analyzed using fractal models. The employed methods were those proposed by Neimark, Friesen and Mikula. These approaches are able to supply a fractal

A. Aït; N. Saiyouri; Y. Hicher

37

Stochastic flows in integral and fractal dimensions and morphogenesis

The effect of dimensionality and spatial extent on the dynamics of an irreversible reaction confined to a finite system was studied by a Monte Carlo simulation. Stochastic flows on surfaces of integral and fractal dimensions and the consequences of reducing the dimensionality of the reaction space are described. As regards the timing and efficiency of chemical reactions in small systems, our simulations show that placing the reactive site at a central location may be favored at an early stage of growth but, as the system evolves in size, a location on the boundary becomes favored. The possible relevance of these calculations to the problem of morphogenesis is brought out.

Hatlee, M.D.; Kozak, J.J.

1981-02-01

38

Shower fractal dimension analysis in a highly-granular calorimeter

NASA Astrophysics Data System (ADS)

We report on an investigation of the self-similar structure of particle showers recorded at a highly-granular calorimeter. On both simulated and experimental data, a strong correlation between the number of hits and the spatial scale of the readout channels is observed, from which we define the shower fractal dimension. The measured fractal dimension turns out to be strongly dependent on particle type, which enables new approaches for particle identification. A logarithmic dependence of the particle energy on the fractal dimension is also observed.

Ruan, Manqi

2014-03-01

39

Spectral Asymmetry and Higuchi's Fractal Dimension Measures of Depression Electroencephalogram

This study was aimed to compare two electroencephalogram (EEG) analysis methods, spectral asymmetry index (SASI) and Higuchi's fractal dimension (HFD), for detection of depression. Linear SASI method is based on evaluation of the balance of powers in two EEG frequency bands in one channel selected higher and lower than the alpha band spectrum maximum. Nonlinear HFD method calculates fractal dimension directly in the time domain. The resting EEG signals of 17 depressive patients and 17 control subjects were used as a database for calculations. SASI values were positive for depressive and negative for control group (P < 0.05). SASI provided the true detection rate of 88% in the depressive and 82% in the control group. The calculated HFD values detected a small (3%) increase with depression (P < 0.05). HFD provided the true detection rate of 94% in the depressive group and 76% in the control group. The rate of correct indication in the both groups was 85% using SASI or HFD. Statistically significant variations were not revealed between hemispheres (P > 0.05). The results indicated that the linear EEG analysis method SASI and the nonlinear HFD method both demonstrated a good sensitivity for detection of characteristic features of depression in a single-channel EEG.

Bachmann, Maie; Lass, Jaanus; Suhhova, Anna; Hinrikus, Hiie

2013-01-01

40

Fractal dimension computation with the Parzon window and its application in target detection

NASA Astrophysics Data System (ADS)

The automatic target detection under natural backgrounds is an important topic in the field of automatic target recognition. Fractal dimension is generally related to the roughness of the surface. The fractal dimension of the man-made object is usually lower than the background"s because mostly it is smoother than natural background. This feature can be used to detect the target automatically. In the computing of the fractal dimension, the irregular values often appear at the boundary of the different textures in the image. This phenomenon can be called 'edge effect'. It may result in the difficulty in the followed image processing such as thresholding and cluster segmentation. The main reason of the edge effect is the same contribution of the every pixel in the neighborhood of the pixel where the fractal dimension being calculated. In this paper, in order to weaken the 'edge effect' in the fractal dimension computation, a 2-D Parzon window is designed. The accuracy of fractal dimension calculated after multiplied by the Parzon window is discussed, and a new algorithm is proposed to apply in the automatic target detection. The proposed automatic target detection algorithm is adopted in the experiments in images under complex land or sea backgrounds. The correctly detection rate is above 95%. The robust of this algorithm is represented in the cases of the variety of the light, rotation, size changing and occlusion of the target.

Wang, Lidi; Shi, Zelin; Huang, Shabai

2005-07-01

41

Time evolution of the fractal dimension of a mixing front

NASA Astrophysics Data System (ADS)

We present a description of an experimental study of an array of turbulent plumes (from one to nine plumes), investigating the time evolution of the fractal dimension of the plumes and also the spatial evolution of the fractal dimension from one plume to other. We also investigate the effects of bouyancy (different Atwood numbers), the number of plumes and the height of the bouyancy source on the fractal dimension. The plumes are formed by injecting a dense fluid from a small source (from one to nine orifices) into a stationary body of lighter brime (saline solution) contained in a tank. The source fluid was dyed with fluorescein and we use the LIF technique. The plumes were fully turbulent and we have both momentum and bouyancy regimes. The fractal dimensions of contours of concentration were measured. The fractal analysis of the turbulent convective plumes was performed with the box counting algorithm for different intensities of evolving plume images using the special software Ima_Calc. Fractal dimensions between 1.3 and 1.35 are obtained from box counting methods for free convection and neutral boundary layers. Other results have been published which use the box counting method to analyze images of jet sections -produced from LIF techniques. The regions where most of the mixing takes place are also compared with Reactive flow experiments using phenolphthalein and acid-base interfaces performed by Redondo(1994) IMA 43. Eds M. Farge, JC Hunt and C. Vassilicos.

Lopez Gonzalez-Nieto, P.; Grau, J.

2009-04-01

42

Fractal dimensions of rampart impact craters on Mars

NASA Technical Reports Server (NTRS)

Ejecta blanket morphologies of Martian rampart craters may yield important clues to the atmospheric densities during impact, and the nature of target materials (e.g., hard rock, fine-grained sediments, presence of volatiles). In general, the morphologies of such craters suggest emplacement by a fluidized, ground hugging flow instead of ballistic emplacement by dry ejecta. We have quantitatively characterized the shape of the margins of the ejecta blankets of 15 rampart craters using fractal geometry. Our preliminary results suggest that the craters are fractals and are self-similar over scales of approximately 0.1 km to 30 km. Fractal dimensions (a measure of the extent to which a line fills a plane) range from 1.06 to 1.31. No correlations of fractal dimension with target type, elevation, or crater size were observed, though the data base is small. The range in fractal dimension and lack of correlation may be due to a complex interplay of target properties (grain size, volatile content), atmospheric pressure, and crater size. The mere fact that the ejecta margins are fractals, however, indicates that viscosity and yield strength of the ejecta were at least as low as those of basalts, because silicic lava flows are not generally fractals.

Ching, Delwyn; Taylor, G. Jeffrey; Mouginis-Mark, Peter; Bruno, Barbara C.

1993-01-01

43

Describing soil surface microrelief by crossover length and fractal dimension

NASA Astrophysics Data System (ADS)

Accurate description of soil surface topography is essential because different tillage tools produce different soil surface roughness conditions, which in turn affects many processes across the soil surface boundary. Advantages of fractal analysis in soil microrelief assessment have been recognised but the use of fractal indices in practice remains challenging. There is also little information on how soil surface roughness decays under natural rainfall conditions. The objectives of this work were to investigate the decay of initial surface roughness induced by natural rainfall under different soil tillage systems and to compare the performances of a classical statistical index and fractal microrelief indices. Field experiments were performed on an Oxisol at Campinas, São Paulo State (Brazil). Six tillage treatments, namely, disc harrow, disc plow, chisel plow, disc harrow + disc level, disc plow + disc level and chisel plow + disc level were tested. Measurements were made four times, firstly just after tillage and subsequently with increasing amounts of natural rainfall. Duplicated measurements were taken per treatment and date, yielding a total of 48 experimental surfaces. The sampling scheme was a square grid with 25×25 mm point spacing and the plot size was 1350×1350 mm, so that each data set consisted of 3025 individual elevation points. Statistical and fractal indices were calculated both for oriented and random roughness conditions, i.e. after height reading have been corrected for slope and for slope and tillage tool marks. The main drawback of the standard statistical index random roughness, RR, lies in its no spatial nature. The fractal approach requires two indices, fractal dimension, D, which describes how roughness changes with scale, and crossover length, l, specifying the variance of surface microrelief at a reference scale. Fractal parameters D and l, were estimated by two independent self-affine models, semivariogram (SMV) and local root mean square (RMS). Both algorithms, SMV and RMS, gave equivalent results for D and l indices, irrespective of trend removal procedure, even if some bias was present which is in accordance with previous work. Treatments with two tillage operations had the greatest D values, irrespective of evolution stage under rainfall and trend removal procedure. Primary tillage had the greatest initial values of RR and l. Differences in D values between treatments with primary tillage and those with two successive tillage operations were significant for oriented but not for random conditions. The statistical index RR and the fractal indices l and D decreased with increasing cumulative rainfall following different patterns. The l and D decay from initial value was very sharp after the first 24.4 mm cumulative rainfall. For five out of six tillage treatments a significant relationship between D and l was found for the random microrelief conditions allowing a covariance analysis. It was concluded that using RR or l together with D best allow joint description of vertical and horizontal soil roughness variations.

Vidal Vázquez, E.; Miranda, J. G. V.; Paz González, A.

2007-05-01

44

SAR image analysis of the sea surface by local fractal dimension estimation

NASA Astrophysics Data System (ADS)

A wavelet-based approach to local fractal dimension estimation of SAR images of the sea surface is presented. Fractal analysis is considered as a tool for image texture characterization which can play a fundamental role to automatically detect oil slicks, and possibly distinguish them from natural surface films. A fractional Brownian motion (fBm) model is assumed for the clean sea surface. FBm processes have been proved to be suitable to describe signals backscattered by many natural surfaces, particularly by the sea surface within a certain range of scales. By using the properties of the average power spectra of fBm's, it is possible to estimated the fractal dimension, as demonstrated on synthetic fBm realizations. In this paper, a redundant wavelet representation is applied for estimating the local fractal dimension of the sea surface. By using this technique, which allows to operate at the original image resolution, all discontinuities of the fractal sea surface can be detected and accurately localized. Experimental results on true SAR images show that without considering the backscatter coefficient for calculating the fractal dimension, but only textural features, it is possible to detect oil slicks and man-made objects on the sea surface.

Garzelli, Andrea

2003-03-01

45

NASA Astrophysics Data System (ADS)

Based on the fractal theory, proceeding from the observed data of the random content of underground water, the fractal dimension of the sequence of sudden changes of the radon content of 27 wells (springs) in North China before and after the Tangshan earthquake has been calculated using a month-by-month sliding method. The variation of fractal dimensions anomalies before and after the main shock in time and space was studied. The following phenomena were discovered: The fractal dimension of the radon content changed distinctly before the earthquake; the stations where the fractal dimension anomalies of the radon content appeared are within 300 km from the epicenter; the increase and decrease areas of the fractal dimensions of the radon content appeared clearly; just before the earthquake, the increase area filled the whole of North China except the epicentral area, where the fractal dimensions are decreasing.

Yang, Chang-Chun; Chen, Dang-Min; Wang, Xiu-Lian; Zhang, Zhi-Xia

1995-02-01

46

Exploring relationships between fractal dimension and trabecular bone characteristics

NASA Astrophysics Data System (ADS)

Bone microarchitecture is the predictor of bone quality or bone disease. It can only be measured on a bone biopsy, which is invasive and not available for all clinical situations. Texture analysis on radiographs is a common way to investigate bone microarchitecture. But relationships between three-dimension histomorphometric parameters and two-dimension texture parameters are not always well known, with poor results. The aim of this paper is twofold : to study one classical parameter namely the fractal dimension which is easily computed on the 2D binary texture and to explore its relationships with the microarchitecture. We performed several experiments in order to check from ground truth the different possible values and their possible explanations. The results show great variations of the fractal dimension according to the size of the window and its location. These variations can be explained both by a misuse of the algorithm and by the number of trabecular and their characteristics inside the window where the fractal dimension is computed. This study also shows a specific interest to work with dual fractal dimension of the bone-spongious tissues.

Guédon, Jeanpierre; Autrusseau, Florent; Amouriq, Yves; Bléry, Pauline; Bouler, Jean-Michel; Weiss, Pierre; Barbarin, Francois-Xavier; Dallet, Thomas; Dallerit, Valentin

2012-02-01

47

Fractal dimensions of small (15-200 ?m) particles in Eastern Pacific coastal waters

NASA Astrophysics Data System (ADS)

Particles 3-300 ?m (average length) in seawater include single cells, non-viable particles of identifiable origin (such as fecal pellets), aggregated particles formed from water column debris, and aggregated mixtures of all of these materials. While macroscopic marine snow-sized aggregates (>0.5 mm in average length) have been shown to be fractal, relatively less is known about the average characteristics of smaller particles. We calculated the fractal dimensions of microscopic particles 15-200 ?m in length through simultaneous measurements of particle size distributions as a function of solid equivalent diameter (from solid volumes measured using a Coulter Counter) and average length (from image analysis of acridine-orange stained filtered particles). Particle size distributions were measured at two eastern Pacific coastal areas, one in Monterey Bay, CA, and the other in East Sound, WA. Average fractal dimensions of particles indicated that D was highest in East Sound ( D=2.59±0.17) during a phytoplankton bloom that did not appear to be aggregating, and lowest at one site in Monterey Bay ( D=1.77±0.34), where old diatom flocs and marine snow-size aggregates were observed. There was no direct relationship between D and total particle concentration, chlorophyll a, or transparent exopolymer particles (TEP) concentration, although the highest concentration of TEP was found at the site with the lowest fractal dimension. Particles with low fractal dimensions are produced through coagulation. Our subjective assessment of the importance of aggregate formation at these sites, based on diving and microscopic observations, indicated that aggregates were more abundant at sites where particles had lower fractal dimensions. Thus, we attribute the low fractal dimensions of these small particles to be the result of their formation through coagulation processes.

Li, Xiaoyan; Passow, Uta; Logan, Bruce E.

48

Planetary boundary layer detection with fractal dimension of three-wavelength lidar signals

NASA Astrophysics Data System (ADS)

Lidar backscatter signal resulting from laser light scattering from the aerosol and molecular in the atmosphere contains various information about the geometrical and physical properties of aerosol and molecular. The lidar backscatter signal can provide information about the planetary boundary layer (PBL) stratification by using aerosol as a tracer for convective and mixing processes. A PBL height and structure detecting technique based on the fractal dimension of three-wavelength backscatter signals is advanced. In this PBL height detecting technique, the three-wavelength backscatter signals are obtained by the Hampton University (HU, 37.02° N, 76.33° W) lidar. The fractal dimension was calculated using the three-wavelength lidar signals. The PBL heights obtained from fractal dimension of threewavelength lidar signals is compared with PBL heights obtained from the potential temperature profiles which are provided by NASA Langely Research Center (10 miles from HU). And results of the two methods agree well. Moreover, fractal dimension method can reduce the influence of the geometrical form factor on the PBL detecting to expand the detecting range of PBL and remove the effect of plume. Also, the fractal dimension method can show the PBL dynamics and the PBL evolution clearly.

Lei, Liqiao; McCormick, M. Patrick; Su, Jia

2013-05-01

49

NASA Astrophysics Data System (ADS)

The aim of this study is to develop a computer program (FRACEK) for fractal dimensions of amorphous areas, and to apply this program on various mass movements. FRACEK has been developed using Java technology with an object-oriented approach. The input of FRACEK is a set of 2-dimensional images including the amorphous areas of which fractal values are to be computed. FRACEK is a user-friendly program that can be used to calculate fractal dimensions easily and can be used in various earth science applications. In this study, published maps were utilized when applying FRACEK to various mass movements. A total of 116 mass movement data were employed. In addition to the fractal dimensions ( D), the width ( W) to length ( L) ratio of each mass movement was calculated. The relationship between the W/ L ratio and the D was investigated. Relatively high correlations were found between the D and the W/ L ratio. The results of this study indicate that it is possible to make a differentiation among the mass movements using the fractal dimension. However, further research is required for evaluation all types of mass movements.

Sezer, Ebru

2010-03-01

50

Ginzburg-Landau theory of superconductivity at fractal dimensions

NASA Astrophysics Data System (ADS)

The post-Gaussian effective potential in D=2+2? dimensions is evaluated for the Ginzburg-Landau theory of superconductivity. Two- and three-loop integrals for the post-Gaussian correction terms in D=2+2? dimensions are calculated and ? expansions for these integrals are constructed. In D=2+2? fractal dimensions the Ginzburg-Landau parameter turned out to be sensitive to ? and the contribution of the post-Gaussian term is larger than that for D=3 . Adjusting ? to the recent experimental data on ?(T) for the high- Tc cuprate superconductor Tl2Ca2Ba2Cu3O10 , we found that ?=0.21 is the best choice for this material. The result clearly shows that, in order to understand high- Tc superconductivity, it is necessary to include the fluctuation contribution as well as the contribution from the dimensionality of the sample. The method gives a theoretical tool to estimate the effective dimensionality of samples.

Kim, Chul Koo; Rakhimov, Abdulla; Yee, Jae Hyung

2005-01-01

51

Matrix crack detection in spatially random composite structures using fractal dimension

NASA Astrophysics Data System (ADS)

Fractal dimension based damage detection method is studied for a composite structure with random material properties. A composite plate with localized matrix crack is considered. Matrix cracks are often seen as the initial damage mechanism in composites. Fractal dimension based method is applied to the static deformation curve of the structure to detect localized damage. Static deflection of a cantilevered composite plate under uniform loading is calculated using the finite element method. Composite material shows spatially varying random material properties because of complex manufacturing processes. Spatial variation of material property is represented as a two dimensional homogeneous Gaussian random field. Karhunen-Loeve (KL) expansion is used to generate a random field. The robustness of fractal dimension based damage detection methods is studied considering the composite plate with spatial variation in material properties.

Umesh, K.; Ganguli, Ranjan

2014-03-01

52

Fractal dimension algorithms and their application to time series associated with natural phenomena

NASA Astrophysics Data System (ADS)

Chaotic invariants like the fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of systems, because it contains information about their geometrical structure at multiple scales. In this work, three algorithms are applied to non-linear time series: spectral analysis, rescaled range analysis and Higuchi's algorithm. The analyzed time series are associated with natural phenomena. The disturbance storm time (Dst) is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a self-similar behavior, which depends on the time scale of measurements. It is also observed that fractal dimensions, D, calculated with Higuchi's method may not be constant over-all time scales. This work shows that during 2001, D reaches its lowest values in March and November. The possibility that D recovers a change pattern arising from self-organized critical phenomena is also discussed.

Cervantes-De la Torre, F.; González-Trejo, J. I.; Real-Ramírez, C. A.; Hoyos-Reyes, L. F.

2013-12-01

53

Daily variation of the fractal dimension of the velocity components in the turbulent surface layer

NASA Astrophysics Data System (ADS)

The turbulence is a dominant property within the Planetary Boundary Layer (PBL). It is the main characteristic of the mixing in the lower atmosphere since the atmospheric turbulent fluxes are more efficient than the molecular diffusion. Turbulence can be observed in time series of meteorological variables (wind velocity for example). The sampling rate of observation in that time series has to be high in order to detect the turbulent regime. The analysis of these series presents a self-similarity structure, so the wind velocity can be considered as a fractal magnitude. This work shows a study of the fractal dimension of the wind perturbation series u'and w'components of the wind speed. Fractal dimension of velocity components can be related to others turbulent characteristics of the fluxes close to the ground. Fluctuation of longitudinal and, specially, vertical components depend on stability and, therefore, on the solar cycle. In consequence, the behaviour of fractal dimension should be in agreement with that cycle also. These series have been obtained once it has carried out the necessary transformation to get the mean wind series in short intervals, namely 5 minutes, to ensure the consistent properties of turbulence. The original records available were taken every thirty minutes by sonic anemometers (20 Hz sampling rate) during a week of a field campaign. The data analysed was recorded in the experimental campaign SABLES-98 at the Research Centre for the Lower Atmosphere (CIBA), located in Valladolid province (Spain). It has been calculated the fractal dimension (Komolgorov capacity or box- counting dimension) of the time series of fluctuations of the velocity component along of the mean wind direction and the vertical component (u' = u-U, w' = w -W), both in the physical spaces (velocity-time). It has been studied the time evolution of the fractal dimension during several days and at three levels above the ground (5.8 m, 13.5 m, 32 m). The fractal dimension of theu' and w' components of wind velocity series have been studied, as well as the influence of different turbulent parameters depending on daily cycle: turbulent kinetic energy, friction velocity, difference of temperature between the extreme of the layer studied close of the surface (?T50-0.22m),etc. It has been observed that there is a possible correlation between the fractal dimension and some of these turbulent parameters. Finally, it has been analysed the variation of the fractal dimension versus stability obtained from the Richardson number along of the day.

Tijera, M.; Maqueda, G.; Yagüe, C.; Cano, J. L.

2012-04-01

54

Estimating the fractal dimension and the predictability of the atmosphere

The fractal dimension, Lyapunov-exponent spectrum, Kolmogorov entropy, and predictability are analyzed for chaotic attractors in the atmosphere by analyzing the time series of daily surface temperature and pressure over several regions of the US and the North Atlantic Ocean with different climatic signal-to-noise ratios. Though the total number of data points is larger than those used in previous studies, it is still too small to obtain a reliable estimate of the Grassberger-Procaccia correlation dimension because of the limitations discussed by Ruelle. It can be shown that this dimension is greater than 8. It is pointed out that most, if not all, of the previous estimates of low fractal dimensions in the atmosphere are spurious. These results lead the authors to claim that there probably exist no low-dimensional strange attractors in the atmosphere. Because the fractal dimension has not yet been saturated, the Kolmogorov entropy and the error-doubling time obtained by the method of Grassberger and Procaccia are sensitive to the selection of the time delay and are thus unreliable. Geographic variability of the fractal dimension is suggested, but further verification is needed. A practical and more reliable method for estimating the Kolmogorov entropy and error-doubling time involves the computation of the Lyapunov-exponent spectrum using the algorithm of Zeng et al. Using this method, it is found that the error-doubling time is about 2-3 days in Fort Collins, Colorado, about 4-5 days in Los Angeles, California, and about 5-8 days in the North Atlantic Ocean. The difference between these estimates of error-doubling time and estimates based on general circulation models (GCMs) is discussed. It is also mentioned that the computation of the Lyapunov exponents is slightly sensitive to the selection of the time delay, possibly because the fractal dimension is very high in the atmosphere. 48 refs., 10 figs., 3 tabs.

Zeng, X.; Pielke, R.A.; Eykholt, R. (Colorado State Univ., Fort Collins, CO (United States))

1992-04-15

55

Agreement between two methods of computing the fractal dimensions of complex figures.

Agreement between two methods of computing the fractal dimensions of complex figures was examined. 16 complex figures were scanned and the fractal dimensions were computed under two conditions. There was no significant difference between the two methods. PMID:7675564

House, G; Zelhart, P F

1995-04-01

56

Aggregate fractal dimensions and thermal conduction in nanofluids

NASA Astrophysics Data System (ADS)

The mechanism producing enhanced thermal conductivities of nanofluids has been the subject of much debate. The formation of aggregates allowing for percolation paths within the fluid has shown the most promise. This work studies the aggregate formation of a nanofluid and compares the results to earlier thermal conductivity measurements and Monte Carlo simulation results. Static light scattering is employed to measure the fractal dimension of aggregates formed in the nanofluid over time at various temperatures and concentrations. As expected, aggregates form more quickly at higher concentrations and temperatures, which explains the increased enhancement with temperature reported by other research groups. The permanent aggregates in the nanofluid are found to have a fractal dimension of 2.4 and the aggregate formations that grow over time are found to have a fractal dimension of 1.8, which is consistent with diffusion limited aggregation. Predictions indicate that as aggregates grow the viscosity increases at a faster rate than thermal conductivity making the highly aggregated nanofluids unfavorable, especially at the low fractal dimension of 1.8.

Gharagozloo, Patricia E.; Goodson, Kenneth E.

2010-10-01

57

Fractal dimension analysis for crack identification in beam structures

A new technique for crack identification in beam structures based on fractal dimension analysis is presented. The fundamental vibration mode of a cracked cantilever beam is analysed and both the location and size of the crack are estimated. The location of the crack is determined by the sudden changes in the spatial variation of the analysed response, while the size

L. J. Hadjileontiadis; E. Douka; A. Trochidis

2005-01-01

58

Estimation of Fractal Dimension in Differential Diagnosis of Pigmented Skin Lesions

NASA Astrophysics Data System (ADS)

Medical differential diagnosis is a method of identifying the presence of a particular entity (disease) within a set of multiple possible alternatives. The significant problem in dermatology and pathology is the differential diagnosis of malignant melanoma and other pigmented skin lesions, especially of dysplastic nevi. Malignant melanoma is the most malignant skin neoplasma, with increasing incidence in various parts of the world. It is hoped that the methods of quantitative pathology, i.e. morphometry, can help objectification of the diagnostic process, since early discovery of melanoma results in 10-year survival rate of 90%. The aim of the study was to use fractal dimension calculated from the perimeter-area relation of the cell nuclei as a tool for the differential diagnosis of pigmented skin lesions. We analyzed hemalaun-eosin stained pathohistological slides of pigmented skin lesions: intradermal naevi (n = 45), dysplastic naevi (n = 47), and malignant melanoma (n = 50). It was found that fractal dimension of malignant melanoma cell nuclei differs significantly from the intradermal and dysplastic naevi (p ? 0. 001, Steel-Dwass Multiple Comparison Test). Additionaly, ROC analysis confirmed the value of fractal dimension based evaluation. It is suggested that the estimation of fractal dimension from the perimeter-area relation of the cell nuclei may be a potentially useful morphometric parameter in the medical differential diagnosis of pigmented skin lesions.

Aralica, Gorana; Miloševi?, Danko; Konjevoda, Paško; Seiwerth, Sven; Štambuk, Nikola

59

Fractal dimension estimations of drainage network in the Carpathian Pannonian system

NASA Astrophysics Data System (ADS)

The development of drainage network in the intra-Carpathian realm is influenced by a complex Quaternary tectonic evolution manifested with differential vertical motions. The present-day configuration of the left-hand side tributary system of the Tisza river was studied by means of fractal analysis. Fractal dimensions describing the complexity of the network were obtained by different methods. These include the early estimations based on stream ordering hierarchy and the application of the box-counting and sandbox algorithms representing fixed-size algorithms considered as efficient tools in fractal set analysis. Besides calculations made for the entire drainage system, the region was subdivided into three distinct areas characterised by different Quaternary uplift history. These are the Apuseni Mts., the Transylvanian basin and a part of the Eastern Carpathians, investigated separately. The concept of multifractality was also taken into consideration and dimensions of both higher and lower orders were determined along with the corresponding singularity spectra. Non-space-filling and multifractal behaviour of the network structure was validated. However, small but tendentious variations of the support dimensions ( D0) were observed in the three sub-regions. The Transylvanian basin is characterised by the lowest estimated dimensions, while higher values represent the Apuseni Mts., and the western slopes of the Eastern Carpathians. In addition, fractal dimension values showed consistency within each sub-region. Correlation of these measures with average uplift rates was performed. As a major outcome, differential uplift, affecting the morphology of catchments, appears to influence the obtained fractal dimensions, whereas surface lithology conceivably plays only a secondary role.

Dombrádi, Endre; Timár, Gábor; Bada, Gábor; Cloetingh, Sierd; Horváth, Frank

2007-07-01

60

Classification of surface EMG signal with fractal dimension

Surface EMG (electromyography) signal is a complex nonlinear signal with low signal to noise ratio (SNR). This paper is aimed\\u000a at identifying different patterns of surface EMG signals according to fractal dimension. Two patterns of surface EMG signals\\u000a are respectively acquired from the right forearm flexor of 30 healthy volunteers during right forearm supination (FS) or forearm\\u000a pronation (FP). After

Hu Xiao; Wang Zhi-zhong; Ren Xiao-mei

2005-01-01

61

Marfan Syndrome Exon CpG Percentage and Fractal Dimension

The CpG di-nucleotide percentage and exon fractal dimension fluctuation were investigated with respect to the recently identified Marfan syndrome exons in the FBN1 gene. The CpG di-nucleotide percentage was found to rank high in exon 1 (9%), exon 44 (6.5%), exon 24 (5.3%) and exon 27 (4.8%). The most significant Marfan exon group was reported to be exon 24- 32.

Todd Holden; G. Tremberger; E. Cheung; R. Subramaniam; R. Sullivan; P. Schneider; A. Flamholz; D. Lieberman; T. Cheung

2008-01-01

62

Fractal dimensions of flocs between clay particles and HAB organisms

NASA Astrophysics Data System (ADS)

The impact of harmful algal blooms (HABs) on public health and related economics have been increasing in many coastal regions of the world. Sedimentation of algal cells through flocculation with clay particles is a promising strategy for controlling HABs. Previous studies found that removal efficiency (RE) was influenced by many factors, including clay type and concentration, algal growth stage, and physiological aspects of HAB cells. To estimate the effect of morphological characteristics of the aggregates on HAB cell removal, fractal dimensions were measured and the RE of three species of HAB organism, Heterosigma akashiwo, Alexandrium tamarense, and Skeletonema costatum, by original clay and modified clay, was determined. For all HAB species, the modified clay had a higher RE than original clay. For the original clay, the two-dimensional fractal dimension ( D 2) was 1.92 and three-dimensional fractal dimension ( D 3) 2.81, while for the modified clay, D 2 was 1.84 and D 3 was 2.50. The addition of polyaluminum chloride (PACl) lead to a decrease of the repulsive barrier between clay particles, and resulted in lower D 2 and D 3. Due to the decrease of D 3, and the increase of the effective sticking coefficient, the flocculation rate between modified clay particles and HAB organisms increased, and thus resulted in a high RE. The fractal dimensions of flocs differed in HAB species with different cell morphologies. For example, Alexandrium tamarense cells are ellipsoidal, and the D 3 and D 2 of flocs were the highest, while for Skeletonema costatum, which has filamentous cells, the D 3 and D 2 of flocs were the lowest.

Wang, Hongliang; Yu, Zhiming; Cao, Xihua; Song, Xiuxian

2011-05-01

63

Infrared image quality assessment based on fractal dimension method

NASA Astrophysics Data System (ADS)

The operation and observation experience of users is affected by the quality of infrared images which are collected by infrared imager. And image quality is a significant indicator for the performance of image processing algorithm and the optimization of system parameters as well. An image quality reduced reference assessment model is put forward to evaluate the degree of infrared image quality reduction. The detail characteristic of infrared image texture is extracted by the fractal dimension analysis method proposed in this paper as the representation of image quality. The method computes the fractal dimension of every pixel one by one with a multi-scale window over the entire image to get the information of corresponding image block. A quality information image is mapped from the fractal dimension of all pixels to describe the infrared image quality. The parameters of the quality information image combined with the peak SNR of original infrared image are adopted as the metric of infrared image quality. The method can be embedded into image processing system to optimize image processing algorithms and parameters settings, and provide reference for fault diagnosis.

Zhang, Zhijie; Zhang, Jufeng; Yue, Song; Wang, Chensheng

2012-12-01

64

Fractal dimension analysis of malignant and benign endobronchial ultrasound nodes

Background Endobronchial ultrasonography (EBUS) has been applied as a routine procedure for the diagnostic of hiliar and mediastinal nodes. The authors assessed the relationship between the echographic appearance of mediastinal nodes, based on endobronchial ultrasound images, and the likelihood of malignancy. Methods The images of twelve malignant and eleven benign nodes were evaluated. A previous processing method was applied to improve the quality of the images and to enhance the details. Texture and morphology parameters analyzed were: the image texture of the echographies and a fractal dimension that expressed the relationship between area and perimeter of the structures that appear in the image, and characterizes the convoluted inner structure of the hiliar and mediastinal nodes. Results Processed images showed that relationship between log perimeter and log area of hilar nodes was lineal (i.e. perimeter vs. area follow a power law). Fractal dimension was lower in the malignant nodes compared with non-malignant nodes (1.47(0.09), 1.53(0.10) mean(SD), Mann–Whitney U test p?Fractal dimension of ultrasonographic images of mediastinal nodes obtained through endobronchial ultrasound differ in malignant nodes from non-malignant. This parameter could differentiate malignat and non-malignat mediastinic and hiliar nodes.

2014-01-01

65

The exact mathematical relationship between FFT spectrum and fractal dimension (FD) of an experimentally recorded signal is not known. In this work, we tried to calculate signal FD directly from its Fourier amplitudes. First, dependence of Higuchi's FD of mathematical sinusoids on their individual frequencies was modeled with a two-parameter exponential function. Next, FD of a finite sum of sinusoids was found to be a weighted average of their FDs, weighting factors being their Fourier amplitudes raised to a fractal degree. Exponent dependence on frequency was modeled with exponential, power and logarithmic functions. A set of 280 EEG signals and Weierstrass functions were analyzed. Cross-validation was done within EEG signals and between them and Weierstrass functions. Exponential dependence of fractal exponents on frequency was found to be the most accurate. In this work, signal FD was for the first time expressed as a fractal weighted average of FD values of its Fourier components, also allowing researchers to perform direct estimation of signal fractal dimension from its FFT spectrum. PMID:22588703

Kalauzi, Aleksandar; Boji?, Tijana; Vuckovic, Aleksandra

2012-07-01

66

Multiresolution estimation of fractal dimension from images affected by signal-dependent noise

NASA Astrophysics Data System (ADS)

A well-suited approach to calculate the fractal dimension of digital images stems from the power spectrum of a fractional Brownian motion: the ratio between powers at different scales is related to the persistence parameter H and, thus, to the fractal dimension D equals 3 - H. The signal- dependent nature of the speckle noise, however, prevents from a correct estimation of fractal dimension from Synthetic Aperture Radar (SAR) images. Here, we propose and assess a novel method to obtain D based on the multiscale decomposition provided by the normalized Laplacian pyramid, which is a bandpass representation obtained by dividing the layers of an LP by its expanded baseband and is designed to force the noise to become signal-independent. Extensive experiments on synthetic fractal textures, both noise-free and noisy, corroborate the underlying assumptions and show the performances, in terms of both accuracy and confidence of estimation, of pyramid methods compared with the well- established method based on the wavelet transform. Preliminary results on true SAR images from ERS-1 look promising as well.

Aiazzi, Bruno; Alparone, Luciano; Baronti, Stefano; Garzelli, Andrea

1999-10-01

67

Mapping soil fractal dimension in agricultural fields with GPR

NASA Astrophysics Data System (ADS)

We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM) accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H, the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging) in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean HR/S=0.15), significantly different to Andosol under conventional tillage (HR/S=0.47).

Oleschko, K.; Korvin, G.; Muñoz, A.; Velazquez, J.; Miranda, M. E.; Carreon, D.; Flores, L.; Martínez, M.; Velásquez-Valle, M.; Brambila, F.; Parrot, J.-F.; Ronquillo, G.

2008-09-01

68

NASA Astrophysics Data System (ADS)

The wind velocity series of the atmospheric turbulent flow in the planetary boundary layer (PBL), in spite of being highly erratic, present a self-similarity structure (Frisch, 1995; Peitgen et., 2004; Falkovich et., 2006). So, the wind velocity can be seen as a fractal magnitude. We calculate the fractal dimension (Komolgorov capacity or box-counting dimension) of the wind perturbation series (u' = u- ) in the physical spaces (namely velocity-time). It has been studied the time evolution of the fractal dimension along different days and at three levels above the ground (5.8 m, 13.5 m, 32 m). The data analysed was recorded in the experimental campaign SABLES-98 (Cuxart et al., 2000) at the Research Centre for the Lower Atmosphere (CIBA) located in Valladolid (Spain). In this work the u, v and w components of wind velocity series have been measured by sonic anemometers (20 Hz sampling rate). The fractal dimension versus the integral length scales of the mean wind series have been studied, as well as the influence of different turbulent parameters. A method for estimating these integral scales is developed using the normalized autocorrelation function and a Gaussian fit. Finally, it will be analysed the variation of the fractal dimension versus stability parameters (as Richardson number) in order to explain some of the dominant features which are likely immersed in the fractal nature of these turbulent flows. References - Cuxart J, Yagüe C, Morales G, Terradellas E, Orbe J, Calvo J, Fernández A, Soler MR, Infante C, Buenestado P, Espinalt A, Joergensen HE, Rees JM, Vilá J, Redondo JM, Cantalapiedra IR and Conangla L (2000) Stable atmospheric boundary-layer experiment in Spain (SABLES98): a report. Boundary- Layer Meteorol 96:337-370 - Falkovich G and Kattepalli R. Sreenivasan (2006) Lessons from Hidrodynamic Turbulence. Physics Today 59: 43-49 - Frisch U (1995) Turbulence the legacy of A.N. Kolmogorov Cambridge University Press 269pp - Peitgen H, Jürgens H and Saupe D (2004) Chaos and Fractals Springer-Verlag 971pp

Tijera, Manuel; Maqueda, Gregorio; Cano, José L.; López, Pilar; Yagüe, Carlos

2010-05-01

69

Speech Emotion Recognition Based on Parametric Filter and Fractal Dimension

NASA Astrophysics Data System (ADS)

In this paper, we propose a new method that employs two novel features, correlation density (Cd) and fractal dimension (Fd), to recognize emotional states contained in speech. The former feature obtained by a list of parametric filters reflects the broad frequency components and the fine structure of lower frequency components, contributed by unvoiced phones and voiced phones, respectively; the latter feature indicates the non-linearity and self-similarity of a speech signal. Comparative experiments based on Hidden Markov Model and K Nearest Neighbor methods are carried out. The results show that Cd and Fd are much more closely related with emotional expression than the features commonly used.

Mao, Xia; Chen, Lijiang

70

Retinal vascular fractal dimension is associated with cognitive dysfunction.

Fractal analysis is a method used to quantify the geometric branching complexity and density of retinal vessels. This study examined the relationship of retinal vascular fractal dimension and other retinal vascular parameters with cognitive dysfunction in an older Asian population. Subjects aged 60 years and older from the Singapore Malay Eye Study were selected for analysis. Retinal vascular fractal dimension (Df) and other quantitative retinal vascular parameters (branching angle, tortuosity, and caliber) were measured based on a standardized grading protocol from photographs of the retinal fundus using a computer-assisted program. Qualitative retinal signs were also assessed from photographs. Cognitive dysfunction was defined as a locally validated Abbreviated Mental Test (AMT) score ?6/10 in participants with 0-6 years of formal education and an AMT score ?8/10 in those with more than 6 years of formal education. Cognitive dysfunction was identified in 262 of the 1202 participants (21.8%). Decreased retinal vascular Df was significantly associated with lower AMT score (P = .019). In multivariate logistic regression analysis, participants with lower retinal vascular Df values were more likely to have cognitive dysfunction (odds ratio, 1.71; 95% confidence interval, 1.03-2.82, comparing the lowest and highest Df quintiles). In subgroup analysis stratified for cardiovascular risk factors, this association was present in participants with hypertension and current smokers. Other retinal vascular signs were not associated with cognitive dysfunction. Decreased retinal vascular Df is associated with cognitive dysfunction in older persons. Rarefaction of the retinal vasculature may reflect similar changes in the cerebral microvasculature that may contribute to cognitive deterioration. PMID:23099042

Cheung, Carol Yim-lui; Ong, ShinYeu; Ikram, M Kamran; Ong, Yi Ting; Chen, Christopher P; Venketasubramanian, N; Wong, Tien Yin

2014-01-01

71

Texture segmentation of non-cooperative spacecrafts images based on wavelet and fractal dimension

NASA Astrophysics Data System (ADS)

With the increase of on-orbit manipulations and space conflictions, missions such as tracking and capturing the target spacecrafts are aroused. Unlike cooperative spacecrafts, fixing beacons or any other marks on the targets is impossible. Due to the unknown shape and geometry features of non-cooperative spacecraft, in order to localize the target and obtain the latitude, we need to segment the target image and recognize the target from the background. The data and errors during the following procedures such as feature extraction and matching can also be reduced. Multi-resolution analysis of wavelet theory reflects human beings' recognition towards images from low resolution to high resolution. In addition, spacecraft is the only man-made object in the image compared to the natural background and the differences will be certainly observed between the fractal dimensions of target and background. Combined wavelet transform and fractal dimension, in this paper, we proposed a new segmentation algorithm for the images which contains complicated background such as the universe and planet surfaces. At first, Daubechies wavelet basis is applied to decompose the image in both x axis and y axis, thus obtain four sub-images. Then, calculate the fractal dimensions in four sub-images using different methods; after analyzed the results of fractal dimensions in sub-images, we choose Differential Box Counting in low resolution image as the principle to segment the texture which has the greatest divergences between different sub-images. This paper also presents the results of experiments by using the algorithm above. It is demonstrated that an accurate texture segmentation result can be obtained using the proposed technique.

Wu, Kanzhi; Yue, Xiaokui

2011-06-01

72

Fractal Dimension as a Quantitative Measure of Complexity in Plant Development

The shapes of 51 fronds from three species of brown algae (Fucus vesiculosus, Fucus serratus and Ascophyllum nodosum) were evaluated by computing the fractal dimensions (D) of their outlines. There was no difference in fractal dimension among mature fronds of the three species, and D was highly correlated with both developmental stage and structural complexity. With increasing age the plants

John D. Corbit; David J. Garbary

1995-01-01

73

Classification of surface EMG signals with fractal dimension based on wavelet packet transform

Surface EMG signal is a complex nonlinear signal and has low signal-to-noise ratio (SNR). The purpose of this paper is to identify different patterns of surface EMG signals according to fractal dimension, so that an appropriate fractal dimension is found to control forearm prosthesis. After raw surface EMG signal is decomposed into several subspaces with wavelet packet transform (WPT) to

Xiao Hu; Zhizhong Wang; Xiaomei Ren

2005-01-01

74

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

NASA Technical Reports Server (NTRS)

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.

Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.

2001-01-01

75

An efficient differential box-counting approach to compute fractal dimension of image

Fractal dimension is an interesting feature proposed to characterize roughness and self-similarity in a picture. This feature has been used in texture segmentation and classification, shape analysis and other problems. An efficient differential box-counting approach to estimate fractal dimension is proposed in this note. By comparison with four other methods, it has been shown that the authors, method is both

N. Sarkar; B. B. Chaudhuri

1994-01-01

76

Sudden increase of the fractal dimension in a hydrodynamic system

NASA Astrophysics Data System (ADS)

Experimental evidence is presented to support the extension of modeling of weak turbulence by strange attractors in a low-dimensional phase space to spiraling Taylor vortex flows. Mercury was driven between concentric steady cylinders by electromagnetic forces. A steady state of 12 spiraling vortices appeared and featured two pseudo-periodic oscillations. Chaos appeared above a threshold value of the radial current, causing aperiodicity in both angular and axial directions. Two-dimensional Poincare sections for the system in three-dimensional phase space for a given plane reveal that the strange attractors move to a higher dimensional (fractal) phase space when an attractor is destroyed by upping the radial current. A lower bound can be determined for the dimensions of the new attractors. The presence of dimensional jumps in the chaotic attractor indicate that the generation of turbulence by an increased Re should be treated as a discontinuous process.

Tabeling, P.

1985-05-01

77

Optimal surface fractal dimension for heat and fluid flow in microchannels

NASA Astrophysics Data System (ADS)

The fractal Weierstrass-Mandelbrot function was introduced to characterize the multiscale self-affine rough surface of microchannels. Based on this fractal characterization, the role of the rough surface structure on the thermal and hydrodynamic properties in microchannels was evaluated using a computational fluid dynamic simulation. Once identified, these were used to determine the optimal surface dimension for heat and fluid flow. It was found that, no matter what the Reynolds number and roughness height are, the flow heat transfer performance is being optimized with increasing fractal dimension of the surface until to the dimension value of three (infinitely crumpled).

Chen, Yongping; Zhang, Chengbin; Shi, Mingheng; Peterson, George P.

2010-08-01

78

Pulmonary hypertension (PH) can result in vascular pruning and increased tortuosity of the blood vessels. In this study we examined whether automatic extraction of lung vessels from contrast-enhanced thoracic computed tomography (CT) scans and calculation of tortuosity as well as 3D fractal dimension of the segmented lung vessels results in measures associated with PH. In this pilot study, 24 patients (18 with and 6 without PH) were examined with thorax CT following their diagnostic or follow-up right-sided heart catheterisation (RHC). Images of the whole thorax were acquired with a 128-slice dual-energy CT scanner. After lung identification, a vessel enhancement filter was used to estimate the lung vessel centerlines. From these, the vascular trees were generated. For each vessel segment the tortuosity was calculated using distance metric. Fractal dimension was computed using 3D box counting. Hemodynamic data from RHC was used for correlation analysis. Distance metric, the readout of vessel tortuosity, correlated with mean pulmonary arterial pressure (Spearman correlation coefficient: ??=?0.60) and other relevant parameters, like pulmonary vascular resistance (??=?0.59), arterio-venous difference in oxygen (??=?0.54), arterial (??=??0.54) and venous oxygen saturation (??=??0.68). Moreover, distance metric increased with increase of WHO functional class. In contrast, 3D fractal dimension was only significantly correlated with arterial oxygen saturation (??=?0.47). Automatic detection of the lung vascular tree can provide clinically relevant measures of blood vessel morphology. Non-invasive quantification of pulmonary vessel tortuosity may provide a tool to evaluate the severity of pulmonary hypertension. Trial Registration ClinicalTrials.gov NCT01607489

Urschler, Martin; Kullnig, Peter; Stollberger, Rudolf; Kovacs, Gabor; Olschewski, Andrea; Olschewski, Horst; Balint, Zoltan

2014-01-01

79

NASA Astrophysics Data System (ADS)

This study investigates the surface fractal dimensions (SFDs) of pore structure of cement pastes and mortars with/without ground granulated blast-furnace slag (GGBS) incorporated into binder. The samples were subject to water curing and sealed curing. The fractal dimensions of samples are determined by Zhang's model (Ind Eng Chem Res, 34 (1995):1383-1386) on the basis of mercury intrusion porosimetry (MIP) data. The results confirm the scale-dependent property of fractal dimension of pore structures and the micro-fractal, transition and macro-fractal regions are identified for all samples. The upper pore size range for micro-fractal regions is around 30 nm, the transition regions cover 0.5-2 magnitude orders of pore size and macro fractal regions cover 1.5-3 magnitude orders. Both curing conditions and GGBS in binder have impact on the fractal properties of pore structure, and samples incorporating GGBS have substantially larger values for micro-fractal regions.

Zeng, Qiang; Luo, Mingyong; Pang, Xiaoyun; Li, Le; Li, Kefei

2013-10-01

80

Correlations and characterization of porous solids by fractal dimension and porosity

NASA Astrophysics Data System (ADS)

The fractal dimensions of zeolite A, zeolite X, Dowex MSC-1, Mordenite, zeolite Y, ZSM-5 and MSC-5A carbon sieve have been obtained by physical adsorption of different-sized adsorbates. The porosity of the solids is obtained from literature. Two simple equations with two integral variables can be employed to characterize a porous solid with finite fractal dimension and porosity. These two equations also illustrate the correlation between fractal dimension and porosity of the porous solid and are also helpful to construct the fractal structure of the porous solids. Two integral variables are the number of divisions (cuts) in each dimension, and the number of the d-dimensional objects ( d can be 1, 2 or 3) that must be taken for iteration. Seven examples of porous solids are employed to characterize and illustrate the applicability of the two equations.

Huang, S. J.; Yu, Y. C.; Lee, T. Y.; Lu, T. S.

1999-12-01

81

NASA Astrophysics Data System (ADS)

Optical coherence tomography (OCT) images of left-descending coronary tissues harvested from three porcine specimens were acquired with a home-build swept-source OCT setup. Despite the fact that OCT is capable of acquiring high resolution circumferential images of vessels, many distinct histological features of a vessel have comparable optical properties leading to poor contrast in OCT images. Two classification methods were tested in this report for the purpose of enhancing contrast between soft-tissue components of porcine coronary vessels. One method involved analyzing the attenuation of the OCT signal as a function of light penetration into the tissue. We demonstrated that by analyzing the signal attenuation in this manner we were able to differentiate two media sub-layers with different orientations of the smooth muscle cells. The other classification method used in our study was fractal analysis. Fractal analysis was implemented in a box-counting (fractal dimension) image-processing code and was used as a tool to differentiate and quantify variations in tissue texture at various locations in the OCT images. The calculated average fractal dimensions had different values in distinct regions of interest (ROI) within the imaged coronary samples. When compared to the results obtained by using the attenuation of the OCT signal, the method of fractal analysis demonstrated better classification potential for distinguishing amongst the tissue ROI.

Flueraru, C.; Popescu, D. P.; Mao, Y.; Chang, S.; Sowa, M. G.

2010-04-01

82

Optical coherence tomography (OCT) images of left-descending coronary tissues harvested from three porcine specimens were acquired with a home-build swept-source OCT setup. Despite the fact that OCT is capable of acquiring high resolution circumferential images of vessels, many distinct histological features of a vessel have comparable optical properties leading to poor contrast in OCT images. Two classification methods were tested in this report for the purpose of enhancing contrast between soft-tissue components of porcine coronary vessels. One method involved analyzing the attenuation of the OCT signal as a function of light penetration into the tissue. We demonstrated that by analyzing the signal attenuation in this manner we were able to differentiate two media sub-layers with different orientations of the smooth muscle cells. The other classification method used in our study was fractal analysis. Fractal analysis was implemented in a box-counting (fractal dimension) image-processing code and was used as a tool to differentiate and quantify variations in tissue texture at various locations in the OCT images. The calculated average fractal dimensions had different values in distinct regions of interest (ROI) within the imaged coronary samples. When compared to the results obtained by using the attenuation of the OCT signal, the method of fractal analysis demonstrated better classification potential for distinguishing amongst the tissue ROI. PMID:20360632

Flueraru, C; Popescu, D P; Mao, Y; Chang, S; Sowa, M G

2010-04-21

83

It is demonstrated that fluorescence resonance energy transfer may be used to determine the fractal dimension of aggregates of membrane-bound proteins. Theoretical and experimental results are presented for two different experimental designs: energy transfer between proteins and energy transfer from lipids to proteins. For energy transfer between proteins the lattice spacing must be known independently for a fractal dimension to be uniquely determined, and this represents a disadvantage to this experimental design. Results are presented for the calcium ATPase and a fractal dimension of 1.9 is estimated for ATPase aggregates by assuming a lattice spacing of 50 A. Energy transfer from lipids to protein provides a means of estimating the length of the "coast-line" of the aggregate. In this case the fractal dimension is uniquely determined from a log-log plot. An analysis of data for bacteriohodopsin reconstituted in phospholipid vesicles gives a fractal dimension of 1.6. The structural basis of the value for the fractal dimension is discussed for these two systems. These techniques provide a means of assessing the nature of protein-protein interactions in membranous systems.

Dewey, T G; Datta, M M

1989-01-01

84

A surface fractal dimension research of soil-pore interface based on image analysis

NASA Astrophysics Data System (ADS)

The inner spatial formation and structure of soils has been the basic and important subject of investigation. With the development of digital image technology, it's easier to obtain images of soil-pore at the extent between micron and millimeter. In this study, we acquire soil-pore binary image by application of Fast Fourier Transform (FFT) and filter technique, combined with actual soil porosity. The soil-pore fractal dimension depicts the irregular and rugged boundaries between soil pores and particles. The fractal dimension research of soil-pore interface indicates the obvious correlativity existed between fractal properties and soil texture, though pore-size distribution pattern significantly alters soil properties.

Zhu, Lei; Li, Yawen; Zhou, Qing

2010-08-01

85

Processing of gray scale images in order to determine the corresponding fractal dimension is very important due to widespread use of imaging technologies and application of fractal analysis in many areas of science, technology, and medicine. To this end, many methods for estimation of fractal dimension from gray scale images have been developed and routinely used. Unfortunately different methods (dimension estimators) often yield significantly different results in a manner that makes interpretation difficult. Here, we report results of comparative assessment of performance of several most frequently used algorithms/methods for estimation of fractal dimension. To that purpose, we have used scanning electron microscope images of aluminum oxide surfaces with different fractal dimensions. The performance of algorithms/methods was evaluated using the statistical Z-score approach. The differences between performances of six various methods are discussed and further compared with results obtained by electrochemical impedance spectroscopy on the same samples. The analysis of results shows that the performance of investigated algorithms varies considerably and that systematically erroneous fractal dimensions could be estimated using certain methods. The differential cube counting, triangulation, and box counting algorithms showed satisfactory performance in the whole investigated range of fractal dimensions. Difference statistic is proved to be less reliable generating 4% of unsatisfactory results. The performances of the Power spectrum, Partitioning and EIS were unsatisfactory in 29%, 38%, and 75% of estimations, respectively. The results of this study should be useful and provide guidelines to researchers using/attempting fractal analysis of images obtained by scanning microscopy or atomic force microscopy. SCANNING 9999:XX-XX, 2013. © 2013 Wiley Periodicals, Inc. PMID:23483485

Risovi?, Dubravko; Pavlovi?, Zivko

2013-03-01

86

Fractal dimensions of silica gels generated using reactive molecular dynamics simulations

We have used molecular dynamics simulations based on a three-body potential with charge transfer to generate nanoporous silica aerogels. Care was taken to reproduce the sol-gel condensation reaction that forms the gel backbone as realistically as possible and to thereby produce credible gel structures. The self-similarity of aerogel structures was investigated by evaluating their fractal dimension from geometric correlations. For comparison, we have also generated porous silica glasses by rupturing dense silica and computed their fractal dimension. The fractal dimension of the porous silica structures was found to be process dependent. Finally, we have determined that the effect of supercritical drying on the fractal nature of condensed silica gels is not appreciable.

Bhattacharya, Sudin; Kieffer, John [Department of Mechanical Engineering, University of Michigan, Ann Arbor, Michigan 48109-2158 (United States); Department of Materials Science and Engineering, University of Michigan, Ann Arbor, Michigan 48109-2136 (United States)

2005-03-01

87

Fractal Dimension Characterization of in-vivo Laser Doppler Flowmetry signals

NASA Astrophysics Data System (ADS)

Laser Doppler Blood Flow meter uses tissue backscattered light to non-invasively assess the blood flow rate. qualitatively. As there is large spatial variability and the temporal heterogeneity in tissue microvasculature, the measured blood flow rate is expressed in relative units. A non-linear approach in order to understand the dynamics of the microcirculation led to the fractal characterization of the blood flow signals. The study presented in the paper aims to analyze the fractal behavior of Laser Doppler Flow (LDF) signals and to quantitatively estimate the fractal dimension of waveforms using Box-Counting method. The measured Fractal dimension is an estimate of temporal variability of tissue perfusion. The rate at which fractal dimension varies as a function of location between individuals, exhibits a weak correlation with time. Further studies with a larger number of subjects are necessary to test the generality of the findings and if changes in dimension are reproducible in given individuals. In conclusion, the fractal dimension determined by Box-counting method may be useful for characterizing LDF time series signals. Future experiments evaluating whether the technique can be used to quantify microvascular dysfunction, as commonly occurring in conditions such as Diabetes, Raynaud's phenomenon, Erythromelalgia and Achenbach syndrome needs to be evaluated.

Srinivasan, Gayathri; Sujatha, N.

88

Lattice Dynamics of the Binary Aperiodic Chains of Atoms I:. Fractal Dimension of Phonon Spectra

NASA Astrophysics Data System (ADS)

The microscopic harmonic model of lattice dynamics of the binary chains of atoms is formulated and studied numerically. The dependence of spring constants of the nearest-neighbor (NN) interactions on the average distance between atoms are taken into account. The covering fractal dimensions Df{( c ; )} of the Cantor-set-like phonon spec-tra (PS) of generalized Fibonacci and non-Fibonaccian aperiodic chains containing of 16384?N?33461 atoms are determined numerically. The dependence of Df{( c ; )} on the strength Q of NN interactions and on R=mH/mL, where mH and mL denotes the mass of heavy and light atoms, respectively, are calculated for a wide range of Q and R. In particular we found: (1) The fractal dimension Df{( c ; )} of the PS for the so-called goldenmean, silver-mean, bronze-mean, dodecagonal and Severin chain shows a local maximum at increasing magnitude of Q and R>1 (2) At sufficiently large Q we observe power-like diminishing of Df{( c ; )} , i.e. Df{( c ; )} ( {R > 1, Q} ; ) = a ?ot Q? , where ?=-0.14±0.02 and ?=-0.10±0.02 for the above specified chains and so-called octagonal, copper-mean, nickel-mean, Thue-Morse, Rudin-Shapiro chain, respectively.

Salejda, W?odzimierz

89

The b-value and fractal dimension of local seismicity around Koyna Dam (India)

NASA Astrophysics Data System (ADS)

Earthquakes began to occur in Koyna region (India) soon after the filling of Koyna Dam in 1962. In the present study, three datasets 1964-1993, 1993-1995, and 1996-1997 are analyzed to study the b-value and fractal dimension. The b-value is calculated using the Gutenberg-Richter relationship and fractal dimension D corr. using correlation integral method. The estimated b-value and D corr. of this region before 1993 are found to be in good agreement with previously reported studies. In the subsequent years after 1995, the b-value shows an increase. The estimated b-values of this region are found within the limits of global average. Also, the pattern of spatial clustering of earthquakes show increase in clustering and migration along the three zones called North-East Zone, South-East Zone (SEZ), and Warna Seismic Zone. The earthquake events having depth ?5 km are largely confined to SEZ. After 1993, the D corr. shows decrease, implying that earthquake activity gets clustered. This seismic clustering could be helpful for earthquake forecasting.

Kumar, Arjun; Rai, S. S.; Joshi, Anand; Mittal, Himanshu; Sachdeva, Rajiv; Kumar, Rohtash; Ghangas, Vandana

2013-11-01

90

Fractal dimension analysis of weight-bearing bones of rats during skeletal unloading

NASA Technical Reports Server (NTRS)

Fractal analysis was used to quantify changes in trabecular bone induced through the use of a rat tail-suspension model to simulate microgravity-induced osteopenia. Fractal dimensions were estimated from digitized radiographs obtained from tail-suspended and ambulatory rats. Fifty 4-month-old male Sprague-Dawley rats were divided into groups of 24 ambulatory (control) and 26 suspended (test) animals. Rats of both groups were killed after periods of 1, 4, and 8 weeks. Femurs and tibiae were removed and radiographed with standard intraoral films and digitized using a flatbed scanner. Square regions of interest were cropped at proximal, middle, and distal areas of each bone. Fractal dimensions were estimated from slopes of regression lines fitted to circularly averaged plots of log power vs. log spatial frequency. The results showed that the computed fractal dimensions were significantly greater for images of trabecular bones from tail-suspended groups than for ambulatory groups (p < 0.01) at 1 week. Periods between 1 and 4 weeks likewise yielded significantly different estimates (p < 0.05), consistent with an increase in bone loss. In the tibiae, the proximal regions of the suspended group produced significantly greater fractal dimensions than other regions (p < 0.05), which suggests they were more susceptible to unloading. The data are consistent with other studies demonstrating osteopenia in microgravity environments and the regional response to skeletal unloading. Thus, fractal analysis could be a useful technique to evaluate the structural changes of bone.

Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Sanhueza, A. I.; Yamauchi, M.

2001-01-01

91

NASA Astrophysics Data System (ADS)

The optical coefficients (?s, ?a, ?'s and g)of human cancerous and normal prostate tissues were investigated and compared in the spectral range of 750nm - 860 nm. The fractal dimensional parameters including fractal dimension (Df), cutoff diameter (dmax) and the most efficient diameter (dm) between the cancerous and normal prostate tissues were determined based on the extinction and diffusion reflection intensity measurements and the determination of?s, ?a, ?'s and g. The results are in good agreement with prostate cancer evolution defined by Gleason Grades. The difference of fractal dimensional parameters and optic

Pu, Yang; Wang, Wubao; Alrubaiee, M.; Gayen, S. K.; Xu, Min

2012-02-01

92

Crack detection in beams in noisy conditions using scale fractal dimension analysis of mode shapes

NASA Astrophysics Data System (ADS)

Fractal dimension analysis of mode shapes has been actively studied in the area of structural damage detection. The most prominent features of fractal dimension analysis are high sensitivity to damage and instant determination of damage location. However, an intrinsic deficiency is its susceptibility to measurement noise, likely obscuring the features of damage. To address this deficiency, this study develops a novel damage detection method, scale fractal dimension (SFD) analysis of mode shapes, based on combining the complementary merits of a stationary wavelet transform (SWT) and Katz’s fractal dimension in damage characterization. With this method, the SWT is used to decompose a mode shape into a set of scale mode shapes at scale levels, with damage information and noise separated into distinct scale mode shapes because of their dissimilar scale characteristics; the Katz’s fractal dimension individually runs on every scale mode shape in the noise-adaptive condition provided by the SWT to canvass damage. Proof of concept for the SFD analysis is performed on cracked beams simulated by the spectral finite element method; the reliability of the method is assessed using Monte Carlo simulation to mimic the operational variability in realistic damage diagnosis. The proposed method is further experimentally validated on a cracked aluminum beam with mode shapes acquired by a scanning laser vibrometer. The results show that the SFD analysis of mode shapes provides a new strategy for damage identification in noisy conditions.

Bai, R. B.; Ostachowicz, W.; Cao, M. S.; Su, Z.

2014-06-01

93

Use of the fractal dimension for the analysis of electroencephalographic time series

. ?Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their\\u000a fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by\\u000a means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals\\u000a are needed and consequently only long-term events can be analysed;

A. Accardo; M. Affinito; M. Carrozzi; F. Bouquet

1997-01-01

94

NASA Technical Reports Server (NTRS)

The accuracy of traditional multispectral maximum-likelihood image classification is limited by the skewed statistical distributions of reflectances from the complex heterogenous mixture of land cover types in urban areas. This work examines the utility of local variance, fractal dimension and Moran's I index of spatial autocorrelation in segmenting multispectral satellite imagery. Tools available in the Image Characterization and Modeling System (ICAMS) were used to analyze Landsat 7 imagery of Atlanta, Georgia. Although segmentation of panchromatic images is possible using indicators of spatial complexity, different land covers often yield similar values of these indices. Better results are obtained when a surface of local fractal dimension or spatial autocorrelation is combined as an additional layer in a supervised maximum-likelihood multispectral classification. The addition of fractal dimension measures is particularly effective at resolving land cover classes within urbanized areas, as compared to per-pixel spectral classification techniques.

Emerson, Charles W.; Sig-NganLam, Nina; Quattrochi, Dale A.

2004-01-01

95

Fractal dimension in butterflies' wings: a novel approach to understanding wing patterns?

The geometrical complexity in the wings of several, taxonomically different butterflies, is analyzed in terms of their fractal dimension. Preliminary results provide some evidence on important questions about the (dis)similarity of the wing patterns in terms of their fractal dimension. The analysis is restricted to two groups which are widely used in the literature as typical examples of mimicry, and a small number of unrelated species, thus implying the consideration of only a fraction of the wing pattern diversity. The members of the first mimicry ring, composed by the species Danaus plexippus (better known as the monarch butterfly), and the two subspecies Basilarchia archippus obsoleta (or northern viceroy) and Basilarchia archippus hoffmanni (or tropical viceroy), are found to have a very similar value for the fractal dimension of their wing patterns, even though they do not look very similar at first sight. It is also found that the female of another species (Neophasia terlootii), which looks similar to the members of the previous group, does not share the same feature, while the Lycorea ilione albescens does share it. For the members of the second group of mimicry related butterflies, the Greta nero nero and the Hypoleria cassotis, it is shown that they also have very close values for the fractal dimension of their wing patterns. Finally, it is shown that other species, which apparently have very similar wing patterns, do not have the same fractal dimension. A possible, not completely tested hypothesis is then conjectured: the formation of groups by individuals whose wing patterns have an almost equal fractal dimension may be due to the fact that they do share the same developmental raw material, and that this common feature is posteriorly modified by natural selection, possibly through predation. PMID:15614549

Castrejón-Pita, A A; Sarmiento-Galán, A; Castrejón-Pita, J R; Castrejón-García, R

2005-05-01

96

Diagnosis System Based on Wavelet Transform, Fractal Dimension and Neural Network

NASA Astrophysics Data System (ADS)

In this study we introduce a diagnosis system based on wavelet and fractal dimension for diagnose the Heart Mitral Valve Diseases. This study deals with the feature extraction from the Doppler signal waveform at heart mitral valve using ultrasound. Wavelet packet transforms, Fourier transform and Fractal Dimension methods are used for feature extraction from the DHS signals. The back-propagation neural network is used to classify the extracted features. The system has been evaluated in 162 samples that contain 89 normal and 73 abnormal. The results showed that the classification was about 91% for normal and abnormal cases.

El-Ramsisi, Abdallah M.; Khalil, Hassan A.

97

Fractal analysis has been used as a method to study fracture surfaces of brittle materials. However, it has not been determined if the fractal characteristics of brittle materials is consistent throughout the fracture surface. Therefore, the fractal dimensional increment of the mirror, mist, and hackle regions of the fracture surface of silica glass was determined using atomic force microscopy. The fractal dimensional increment of the mirror region (0.17-0.26) was determined to be statistically greater than that for the mist (0.08-0.12) and hackle (0.08-0.13) regions. It is thought that the increase in the fractal dimensional increment is caused by a greater tortuosity in the mirror region due to, most likely, the slower crack velocity of the propagating crack in that region and that there is a point between the mirror and mist region at which the fractal dimension decreases and becomes constant. - Research Highlights: {yields} The fracture surface of silica glass does not have a constant fractal dimension. {yields} Mirror region has greater fractal dimension than mist or hackle region. {yields} Fractal dimension decreases between mirror and mist region. {yields} Greater fractal dimension could be due to slower crack velocity in mirror region.

Smith, R.L., E-mail: firefan@ufl.edu; Mecholsky, J.J., E-mail: jmech@ufl.edu

2011-05-15

98

In order to study the changes of visual attention against the stimuli based on the fractal dimensions of the stimulus, this research focuses on the difference of the searching reaction time resulted from the manipulation of the fractal dimensions of the stimulus in visual search assignments. In this study we have carried out two experiments. Experiment 1 was conducted with

Yasuo Itoh; Mayumi Oyama-Higa; Tuan D. Pham

2009-01-01

99

Using fractal dimensions of stained flow patterns in a clay soil to predict bypass flow

NASA Astrophysics Data System (ADS)

Methylene blue staining patterns of five undisturbed unsaturated soil cores, 200 mm long and 200 mm in diameter, taken from a well-structured clay soil classified as a Hydric Fluvaquent, were characterized by using the fractal dimension of structure to predict measured bypass flow. Cumulative outflow curves in all cores were well described by a spherical model. Outflow in each core started after a significant time lag from the start ofirrigation. Outflow rates during irrigation in all cores were almost equal to irrigation rates; nearly all the water applied, after outflow had started, contributed to bypass flow. Total outflow ( Om, mm) was regressed on the time lag ( T1, min) as: Om = -0.181 T1 + 9.85. This time lag was caused by the effect of internal catchment of discontinuous macropores and surface storage. The three-dimensional fractal dimension of structure ( Ds3) was calculated for the upper and lower halves of the core, by using values of Ds2 and stained area in cross-sections. A statistically significant empirical equation, relating the total amount of outflow ( Om) to both upper and lower values of Ds3 and to the volume fraction of stained parts ( Vs) is: Om = -230.6( VsDs3-1 ) upper + 232.4( VsDs3-1 ) lower + 12.6 Thus, a greater Ds3 value in the upper half of the core and a lower Ds3 value in the lower half of the core induce larger amounts of outflow: hence vertically continuous macropores, such as fragments of cracks or tubes, play a significant role in the process of bypass flow.

Hatano, R.; Booltink, H. W. G.

1992-07-01

100

Evaluation of fractal dimension for mixing and combustion by the schlieren method

The evaluation of fractal dimension values from schlieren flow images has been investigated. It was found for passive mixing heated jet flows that a value of 2.31, close to that obtained by tomographic imaging, was obtained. For turbulent diffusion flames a value of 2.40 was obtained, and this increased slightly with axial movement and with acoustic excitation of the flame.

M. R. Davis; H. L. Li

1996-01-01

101

NASA Astrophysics Data System (ADS)

There has been considerable debate on the relative dependence of broadband ultrasound attenuation (nBUA, ) upon the density and structure of cancellous bone. A nonlinear relationship between nBUA and porosity has recently been demonstrated using stereolithography models, indicating a high structural dependence for nBUA. We report here on the measurement of trabecular perimeter and fractal dimension on the two-dimensional images used to create the stereolithography models. Adjusted coefficients of determination with nBUA were 94.4% and 98.4% for trabecular perimeter and fractal dimension respectively. The feature of fractal dimension representing both the porosity and connectivity of a given structure is most exciting. Further work is required to determine the relationship between broadband ultrasound attenuation and fractal dimension in complex three-dimensional cancellous bone structures.

Langton, C. M.; Whitehead, M. A.; Haire, T. J.; Hodgskinson, R.

1998-02-01

102

The structure of many natural objects exhibits a self-similar or self-affine scaling behavior. Examples range from porous media to mountain ranges, river networks, clouds in the atmosphere or the mass distribution in the universe. The fractal dimension of those objects can be measured by image analyzing techniques. Concerning the structure of porous media, there are different features which may show

A. Dathe; P. Baveye

2003-01-01

103

The fractal dimension of pore distribution patterns in variously-compacted soil

Pore-size distribution pattern significantly alters many soil properties affecting water movement and root growth. The distribution is largely influenced by soil compaction but information on how to describe this effect is very limited. In this study we used the fractal dimension to characterize pore distribution patterns in variously-compacted soil. The soil used was an Orthic Luvisol (Lublin Region, Poland). The

J Lipiec; R Hatano; A S?owi?ska-Jurkiewicz

1998-01-01

104

It is well known that angiogenesis is a complex process that accompanies neoplastic growth, but pituitary tumours are less vascularized than normal pituitary glands. Several analytical methods aimed at quantifying the vascular system in two-dimensional histological sections have been proposed, with very discordant results. In this study we investigated the non-Euclidean geometrical complexity of the two-dimensional microvasculature of normal pituitary glands and pituitary adenomas by quantifying the surface fractal dimension that measures its space-filling property. We found a statistical significant difference between the mean vascular surface fractal dimension estimated in normal versus adenomatous tissues (P = 0.01), normal versus secreting adenomatous tissues (P = 0.0003), and normal versus non-secreting adenomatous tissues (P = 0.047), whereas the difference between the secreting and non-secreting adenomatous tissues was not statistically significant. This study provides the first demonstration that fractal dimension is an objective and valid quantitator of the two-dimensional geometrical complexity of the pituitary gland microvascular network in physiological and pathological states. Further studies are needed to compare the vascular surface fractal dimension estimates in different subtypes of pituitary tumours and correlate them with clinical parameters in order to evaluate whether the distribution pattern of vascular growth is related to a particular state of the pituitary gland.

Di Ieva, Antonio; Grizzi, Fabio; Ceva-Grimaldi, Giorgia; Russo, Carlo; Gaetani, Paolo; Aimar, Enrico; Levi, Daniel; Pisano, Patrizia; Tancioni, Flavio; Nicola, Giancarlo; Tschabitscher, Manfred; Dioguardi, Nicola; Baena, Riccardo Rodriguez y

2007-01-01

105

Comparison of fractal dimension estimation algorithms for epileptic seizure onset detection

The fractal dimension (FD) is a natural measure of the irregularity of a curve. In this study the performances of two FD-based methodologies are compared in terms of their ability to detect the onset of epileptic seizures in scalp EEG. The FD algorithms used is Katzpsilas, which has been broadly utilized in the EEG analysis literature, and the k-nearest neighbor

Georgia E. Polychronaki; Periklis Y. Ktonas; Stylianos Gatzonis; Pantelis A. Asvestas; Eirini Spanou; Anna Siatouni; Hara Tsekou; Damianos Sakas; Konstantina S. Nikita

2008-01-01

106

A review of methods used to determine the fractal dimension of linear features

An in-depth review of the more commonly applied methods used in the determination of the fractal dimension of one-dimensional curves is presented. Many often conflicting opinions about the different methods have been collected and are contrasted with each other. In addition, several little known but potentially useful techniques are also reviewed. General recommendations which should be considered whenever applying any

Brian Klinkenberg

1994-01-01

107

NASA Astrophysics Data System (ADS)

The islets of Langerhans, responsible for controlling blood glucose levels, are dispersed within the pancreas. A universal power law governing the fractal spatial distribution of islets in two-dimensional pancreatic sections has been reported. However, the fractal geometry in the actual three-dimensional pancreas volume, and the developmental process that gives rise to such a self-similar structure, has not been investigated. Here, we examined the three-dimensional spatial distribution of islets in intact mouse pancreata using optical projection tomography and found a power law with a fractal dimension of 2.1. Furthermore, based on two-dimensional pancreatic sections of human autopsies, we found that the distribution of human islets also follows a universal power law with a fractal dimension of 1.5 in adult pancreata, which agrees with the value previously reported in smaller mammalian pancreas sections. Finally, we developed a self-avoiding growth model for the development of the islet distribution and found that the fractal nature of the spatial islet distribution may be associated with the self-avoidance in the branching process of vascularization in the pancreas.

Jo, Junghyo; Hörnblad, Andreas; Kilimnik, German; Hara, Manami; Ahlgren, Ulf; Periwal, Vipul

2013-06-01

108

NASA Astrophysics Data System (ADS)

ABSTRACT: Chaotic invariants like fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of fractals that contains information about their geometrical structure at multiple scales. In this work four fractal dimension estimation algorithms are applied to non-linear time series. The algorithms employed are the Higuchi's algorithm, the Petrosian's algorithm, the Katz's Algorithm and the Box counting method. The analyzed time series are associated with natural phenomena, the Dst a geomagnetic index which monitors the world wide magnetic storm; the Dst index is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a behavior self-similar, which depend on the time scale of measurements. It is also observed that fractal dimensions may not be constant over all time scales.

Cervantes, F.; Gonzalez, J.; Real, C.; Hoyos, L.

2012-12-01

109

[Influencing factors of floc size distribution and fractal dimension of activated sludge].

Floc size distribution (FSD) and fractal dimension are the important parameters for activated sludge. FSD of aerobic activated sludge during flocculation process was measured by a laser particle size analyzer, and the influence of velocity gradient, VSS/ SS, EPS content and Zeta potential on FSD was investigated. The results showed that the floc volume-average size was negatively correlated to velocity gradient (R > 0. 80) , and the order-of-magnitude of the floc volume-average size was equivalent to that of Kolmogorov scale (their differences were dependent on sludge VSS/SS, floc strength and etc). At a fixing velocity gradient, the floc volume-average size was positively correlated to VSS/SS or EPS (R2 >0. 85) , whereas negatively correlated to Zeta potential. Organic matter and EPS played important roles on the flocculation of activated sludge by enhancing the floc strength and improving the flocculation effect. Compared with polysaccharides, proteins in EPS seemed to be more beneficial for the flocculation of activated sludge. Based on microscopy and image analysis, the 2D and 3D fractal dimension of aerobic activated sludge floc was determined to be 1.28-1.72 and 1.70-2.69, respectively. It was found that fractal dimension (2D and 3D)was decreased with increasing VSS/SS (or EPS content). For the same activated sludge, the 3D fractal dimension was decreased with increasing floc size, and the relationship between 3D fractal dimension and floc size could be approximately described by a power function. PMID:24364319

Li, Zhen-Liang; Zhang, Dai-Jun; Lu, Pei-Li; Zeng, Shan-Wen; Yang, Yong-Hao

2013-10-01

110

Introduction Most animal studies of VF waveform characteristics involve healthy animals with VF initiated by electric shock. However, clinical VF is usually the result of ischemia. The waveform characteristics in these two types of VF may differ. The angular velocity (AV), frequency ratio (FR) and median frequency (MF) are three frequency based measures of VF. The scaling exponent (ScE), the logarithm of the absolute correlations (LAC) and the Hurst exponent (HE) are three measures of the fractal dimension of VF. Hypothesis We hypothesized that these quantitative measures would differ between ischemic and electrically initiated VF. Methods VF was induced in 14 swine by electric shock and in 12 swine by ischemia. For ischemia induced VF animals, an angioplasty catheter was positioned in the mid-LAD and the balloon inflated. A mean of 891 +/- 608 (SD) seconds later, VF occurred. For electrically induced animals, an AC current was passed through a catheter in the RV. Following initiation by either method, VF was recorded for 7 minutes. Sequential 5 second epochs were analyzed for AV, FR, MF and fractal dimension measures. Results Ischemic VF demonstrated a significantly higher fractal dimension as estimated by the ScE for the first 0 to 90 seconds (p = 0.021) and for 90 to 180 seconds (p = 0.016). The Hurst exponent was significantly higher for ischemic VF for both 0 to 90 seconds (p<0.0001) and 90 to 180 seconds (p<0.0001). The fractal dimension as estimated by the LAC method was not significantly different for 0-90 seconds (p = 0.056) but was highly significant for 90-180 seconds (p = 0.001). During the initial 90 seconds the groups did differ in all measures of frequency as follows: AV (p<0.001), FR (p<0.001), MF (p<0.001). These differences did not persist beyond 90 seconds except for a mild elevation of the FR after 270 seconds (p<0.02). Conclusion Fractal based measures indicate an increase in the fractal dimension of ischemia induced VF for the first 180 seconds when compared to electrically induced VF. Frequency based measures uniformly demonstrate a pattern of higher frequencies for electrically induced VF for the first 90 seconds. The increased fractal dimension and decreased frequencies associated with ischemia induced VF may reflect changes in the underlying myocardial physiology that can be used to guide therapies.

Sherman, Lawrence D.; Niemann, James T.; Rosborough, John P.; Menegazzi, James J.

2008-01-01

111

Are fractal dimensions of the spatial distribution of mineral deposits meaningful?

It has been proposed that the spatial distribution of mineral deposits is bifractal. An implication of this property is that the number of deposits in a permissive area is a function of the shape of the area. This is because the fractal density functions of deposits are dependent on the distance from known deposits. A long thin permissive area with most of the deposits in one end, such as the Alaskan porphyry permissive area, has a major portion of the area far from known deposits and consequently a low density of deposits associated with most of the permissive area. On the other hand, a more equi-dimensioned permissive area, such as the Arizona porphyry permissive area, has a more uniform density of deposits. Another implication of the fractal distribution is that the Poisson assumption typically used for estimating deposit numbers is invalid. Based on datasets of mineral deposits classified by type as inputs, the distributions of many different deposit types are found to have characteristically two fractal dimensions over separate non-overlapping spatial scales in the range of 5-1000 km. In particular, one typically observes a local dimension at spatial scales less than 30-60 km, and a regional dimension at larger spatial scales. The deposit type, geologic setting, and sample size influence the fractal dimensions. The consequence of the geologic setting can be diminished by using deposits classified by type. The crossover point between the two fractal domains is proportional to the median size of the deposit type. A plot of the crossover points for porphyry copper deposits from different geologic domains against median deposit sizes defines linear relationships and identifies regions that are significantly underexplored. Plots of the fractal dimension can also be used to define density functions from which the number of undiscovered deposits can be estimated. This density function is only dependent on the distribution of deposits and is independent of the definition of the permissive area. Density functions for porphyry copper deposits appear to be significantly different for regions in the Andes, Mexico, United States, and western Canada. Consequently, depending on which regional density function is used, quite different estimates of numbers of undiscovered deposits can be obtained. These fractal properties suggest that geologic studies based on mapping at scales of 1:24,000 to 1:100,000 may not recognize processes that are important in the formation of mineral deposits at scales larger than the crossover points at 30-60 km. ?? 2008 International Association for Mathematical Geology.

Raines, G. L.

2008-01-01

112

Fractal Dimension of EEG Activity Senses Neuronal Impairment in Acute Stroke

The brain is a self-organizing system which displays self-similarities at different spatial and temporal scales. Thus, the complexity of its dynamics, associated to efficient processing and functional advantages, is expected to be captured by a measure of its scale-free (fractal) properties. Under the hypothesis that the fractal dimension (FD) of the electroencephalographic signal (EEG) is optimally sensitive to the neuronal dysfunction secondary to a brain lesion, we tested the FD’s ability in assessing two key processes in acute stroke: the clinical impairment and the recovery prognosis. Resting EEG was collected in 36 patients 4–10 days after a unilateral ischemic stroke in the middle cerebral artery territory and 19 healthy controls. National Health Institute Stroke Scale (NIHss) was collected at T0 and 6 months later. Highuchi FD, its inter-hemispheric asymmetry (FDasy) and spectral band powers were calculated for EEG signals. FD was smaller in patients than in controls (1.447±0.092 vs 1.525±0.105) and its reduction was paired to a worse acute clinical status. FD decrease was associated to alpha increase and beta decrease of oscillatory activity power. Larger FDasy in acute phase was paired to a worse clinical recovery at six months. FD in our patients captured the loss of complexity reflecting the global system dysfunction resulting from the structural damage. This decrease seems to reveal the intimate nature of structure-function unity, where the regional neural multi-scale self-similar activity is impaired by the anatomical lesion. This picture is coherent with neuronal activity complexity decrease paired to a reduced repertoire of functional abilities. FDasy result highlights the functional relevance of the balance between homologous brain structures’ activities in stroke recovery.

Zappasodi, Filippo; Olejarczyk, Elzbieta; Marzetti, Laura; Assenza, Giovanni; Pizzella, Vittorio; Tecchio, Franca

2014-01-01

113

NASA Technical Reports Server (NTRS)

The use of renormalization group techniques on fragmentation problems is examined. The equations which represent fractals and the size-frequency distributions of fragments are presented. Method for calculating the size distributions of asteriods and meteorites are described; the frequency-mass distribution for these interplanetary objects are due to fragmentation. The application of two renormalization group models to fragmentation is analyzed. It is observed that the models yield a fractal behavior for fragmentation; however, different values for the fractal dimension are produced . It is concluded that fragmentation is a scale invariant process and that the fractal dimension is a measure of the fragility of the fragmented material.

Turcotte, D. L.

1986-01-01

114

NASA Astrophysics Data System (ADS)

A set of Maple routines is presented, fully compatible with the new releases of Maple (14 and higher). The package deals with the numerical evolution of dynamical systems and provide flexible plotting of the results. The package also brings an initial conditions generator, a numerical solver manager, and a focusing set of routines that allow for better analysis of the graphical display of the results. The novelty that the package presents an optional C interface is maintained. This allows for fast numerical integration, even for the totally inexperienced Maple user, without any C expertise being required. Finally, the package provides the routines to calculate the fractal dimension of boundaries (via box counting). New version program summary Program Title: Ndynamics Catalogue identifier: %Leave blank, supplied by Elsevier. Licensing provisions: no. Programming language: Maple, C. Computer: Intel(R) Core(TM) i3 CPU M330 @ 2.13 GHz. Operating system: Windows 7. RAM: 3.0 GB Keywords: Dynamical systems, Box counting, Fractal dimension, Symbolic computation, Differential equations, Maple. Classification: 4.3. Catalogue identifier of previous version: ADKH_v1_0. Journal reference of previous version: Comput. Phys. Commun. 119 (1999) 256. Does the new version supersede the previous version?: Yes. Nature of problem Computation and plotting of numerical solutions of dynamical systems and the determination of the fractal dimension of the boundaries. Solution method The default method of integration is a fifth-order Runge-Kutta scheme, but any method of integration present on the Maple system is available via an argument when calling the routine. A box counting [1] method is used to calculate the fractal dimension [2] of the boundaries. Reasons for the new version The Ndynamics package met a demand of our research community for a flexible and friendly environment for analyzing dynamical systems. All the user has to do is create his/her own Maple session, with the system to be studied, and use the commands on the package to (for instance) calculate the fractal dimension of a certain boundary, without knowing or worrying about a single line of C programming. So the package combines the flexibility and friendly aspect of Maple with the fast and robust numerical integration of the compiled (for example C) basin. The package is old, but the problems it was designed to dealt with are still there. Since Maple evolved, the package stopped working, and we felt compelled to produce this version, fully compatible with the latest version of Maple, to make it again available to the Maple user. Summary of revisions Deprecated Maple Packages and Commands: Paraphrasing the Maple in-built help files, "Some Maple commands and packages are deprecated. A command (or package) is deprecated when its functionality has been replaced by an improved implementation. The newer command is said to supersede the older one, and use of the newer command is strongly recommended". So, we have examined our code to see if some of these occurrences could be dangerous for it. For example, the "readlib" command is unnecessary, and we have removed its occurrences from our code. We have checked and changed all the necessary commands in order for us to be safe in respect to danger from this source. Another change we had to make was related to the tools we have implemented in order to use the interface for performing the numerical integration in C, externally, via the use of the Maple command "ssystem". In the past, we had used, for the external C integration, the DJGPP system. But now we present the package with (free) Borland distribution. The compilation and compiling commands are now slightly changed. For example, to compile only, we had used "gcc-c"; now, we use "bcc32-c", etc. All this installation (Borland) is explained on a "README" file we are submitting here to help the potential user. Restrictions Besides the inherent restrictions of numerical integration methods, this version of the package only deals w

Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.; de Melo, N.; Skea, J. E. F.

2012-09-01

115

Low fractal dimension of clusters with repulsive interactions in colloidal aggregation

NASA Astrophysics Data System (ADS)

Monte Carlo simulations of colloidal aggregation were performed showing that, by increasing the range or the height of a repulsive barrier of non-negligible width between the particles, the fractal dimension of the formed clusters decreases, at least for not very large clusters. This result offers an explanation of old experimental findings of 2D aggregates, with a low fractal dimensionality, made of silica colloids confined on the air–water interface, as well as of very recent experimental results of low fractal dimensionality of clusters of diverse colloids in 3D, when the size of the primary particles is increased. This second case was studied through an analysis of the Derjaguin–Landau–Verwey–Overbeek (DLVO) potential between the particles.

González, Agustín E.

2014-03-01

116

Transition of fractal dimension in a latticed dynamical system

We study a recursion relation that manifests two distinct routes to turbulence, both of which reproduce commonly observed phenomena: the Feigenbaum route, with period-doubling frequencies; and a much more general route with noncommensurate frequencies and frequency entrainment, and locking. Intermittency and large-scale aperiodic spatial patterns are reproduced in this new route. In the oscillatory instability regime the fracal dimension saturates at D/sub F/ approx. = 2.6 with imbedding dimensions while in the turbulent regime D/sub F/ saturates at 6.0. 19 refs., 3 figs.

Duong-van, M.

1986-03-01

117

Fractional Brownian surfaces have been widely discussed as an appropriate model for the statistical behavior of topographic surfaces. The fractals model proposes that topographic surfaces are statistically self-similar, and that a single parameter, the fractal dimension, applies at all scales. This paper presents the results of empirical examinations of 17 topographic samples. Only one of these samples shows the statistical

David M. Mark; Peter B. Aronson

1984-01-01

118

Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations.

The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs. PMID:22815946

Reishofer, Gernot; Koschutnig, Karl; Enzinger, Christian; Ebner, Franz; Ahammer, Helmut

2012-01-01

119

Fractal Dimension and Vessel Complexity in Patients with Cerebral Arteriovenous Malformations

The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.

Reishofer, Gernot; Koschutnig, Karl; Enzinger, Christian; Ebner, Franz; Ahammer, Helmut

2012-01-01

120

Overlapping-box-covering method for the fractal dimension of complex networks

NASA Astrophysics Data System (ADS)

The fractality and self-similarity of complex networks have been widely investigated by evaluating the fractal dimension, the crux of which is how to locate the optimal solution or how to tile the network with the fewest boxes. The results yielded by the box-covering method with separated boxes possess great randomness or large errors. In this paper, we adopt the overlapping box to tile the entire network, called the overlapping-box-covering method. In such a case, for verifying its validity, we propose an overlapping-box-covering algorithm; we first apply it to three deterministic networks, then to four real-world fractal networks. It produces optimums or more accurate fractal dimension for the former; the quantities of boxes finally obtained for the latter are fewer and more deterministic, with the redundant box reaching up to 33.3%. The experimental results show that the overlapping-box-covering method is available and that the overlapping box outperforms the previous case, rendering the errors smaller. Moreover, we conclude that the overlapping box is an important determinant to acquire the fewest boxes for complex networks.

Sun, Yuanyuan; Zhao, Yujie

2014-04-01

121

Overlapping-box-covering method for the fractal dimension of complex networks.

The fractality and self-similarity of complex networks have been widely investigated by evaluating the fractal dimension, the crux of which is how to locate the optimal solution or how to tile the network with the fewest boxes. The results yielded by the box-covering method with separated boxes possess great randomness or large errors. In this paper, we adopt the overlapping box to tile the entire network, called the overlapping-box-covering method. In such a case, for verifying its validity, we propose an overlapping-box-covering algorithm; we first apply it to three deterministic networks, then to four real-world fractal networks. It produces optimums or more accurate fractal dimension for the former; the quantities of boxes finally obtained for the latter are fewer and more deterministic, with the redundant box reaching up to 33.3%. The experimental results show that the overlapping-box-covering method is available and that the overlapping box outperforms the previous case, rendering the errors smaller. Moreover, we conclude that the overlapping box is an important determinant to acquire the fewest boxes for complex networks. PMID:24827295

Sun, Yuanyuan; Zhao, Yujie

2014-04-01

122

A fractal model is established for simulating the space-filling process of cement hydrates in cement paste. Based on this model, it is predicted that the fractal dimension D of the pore structure of hardened cement paste (hcp) is between 0 and 3, and that the water-to-cement ratio, degree of hydration of cement, and the addition of pozzolanic materials will affect

X. Ji; S. Y. N. Chan; N. Feng

1997-01-01

123

Fractal dimension of intersection sets in the dielectric breakdown model

NASA Astrophysics Data System (ADS)

Clusters grown with the dielectric breakdown model (DBM) in the cylinder geometry show two growth phases: a scaling regime for cluster heights smaller than the cylinder circumference and a subsequent steady state, which is translational invariant in the main growth direction. The box-counting dimension of one-dimensional intersection sets of the clusters is studied for six different values of the growth parameter eta and four cylinder circumferences. The author finds that in the scaling regime this dimension depends on the height at which the intersection is made and the clusters are thus inhomogeneous. The results also show that clusters in the steady state are translational invariants in the main growth direction and self-similar in the direction perpendicular to it. A comparison between his findings and the theoretical results obtained from the fixed scale transformation approach by Pietronero et al. (1988), shows good agreement.

Evertsz, C.

1989-11-01

124

On generating conductivity fields with known fractal dimension and nonstationary increments

NASA Astrophysics Data System (ADS)

Fractional Brownian motion (fBm) is a stochastic process that has stationary increments with long-range correlations and known fractal dimension. We study a multiple-dimensional extension of fBm with nonstationary increments that allows for trends in the statistical structure while maintaining the Gaussian nature and fractal dimension of fBm. Two methods for simulating this extension are employed and described in detail. One approach combines Cholesky decomposition with a generalization of random midpoint displacement. The other makes repeated use of the Cholesky decomposition. The resulting fields can be employed in various geophysical settings, e.g., as log conductivity fields in hydrology and topographic elevation in geomorphology.

O'Malley, Daniel; Cushman, John H.; O'Rear, Patrick

2012-03-01

125

Advances in the implementation of the box-counting method of fractal dimension estimation

The box-counting analysis is an appropriate method of fractal dimension estimation for images with or without self-similarity. However, this technique, including processing of the image and definition of the range of box sizes, requires a proper implementation to be effective in practice. The objectives of this study were thus (1) to determine how to prepare an image for box-counting analysis;

K. Foroutan-pour; P. Dutilleul; D. L. Smith

1999-01-01

126

NASA Astrophysics Data System (ADS)

For the system with colored multiplicative noise the nonlinearity of the synergetic potential like ?^{2+m} model in Langevin equation was shown to be capable of providing the expanse of the stochastic system phase space. The concrete system of the population dynamics with the noise correlation time ?_cto? is examined. The fractal dimension of that kind of a system is defined as D=m, in contrast to the system with a white noise were D=0.

Kharchenko, D. O.

127

Fractal dimension of U373 astrocytoma cells in DMEM or RPMI cultures

In order to characterize a possible difference in the organization of U373 astrocytoma cells under different culture medium (DMEM or RPMI), we have obtained the fractal dimension (FD) of cell cultures using HarFA image analysis in the whole range of thresholding conditions (http:\\/\\/www.fch.vutbr.cz\\/lectures\\/imagesci\\/). The obtained results showed a significant increase in the astrocytoma FD depending on the time culture but

J. Cobo-Molinos; M. Garrido-García; J. Navas; P. Rueda; C. Torres; A. Caruz; F. J. Esteban

128

Fractal Dimension for Detection of ERD\\/ERS Patterns in Asynchronous Brain Computer Interface

Detection of motor-related events is the key issue in asynchronous brain-computer interface design. In this study we exploited for the first time Katz's fractal dimension for detection of motor related changes characterized by ERD\\/ERS patterns in electroencephalogram signal. Our observation was that the activation\\/deactivation of brain's cortical neural systems, during occurrence of motor activity, changes the complexity or randomness of

Elnaz Banan Sadeghian; Mohammad Hassan Moradi

2008-01-01

129

Comparison of fractal dimension estimation algorithms for epileptic seizure onset detection

Fractal dimension (FD) is a natural measure of the irregularity of a curve. In this study the performances of three waveform FD estimation algorithms (i.e. Katz's, Higuchi's and the k-nearest neighbour (k-NN) algorithm) were compared in terms of their ability to detect the onset of epileptic seizures in scalp electroencephalogram (EEG). The selection of parameters involved in FD estimation, evaluation

G. E. Polychronaki; P. Y. Ktonas; S. Gatzonis; A. Siatouni; P. A. Asvestas; H. Tsekou; D. Sakas; K. S. Nikita

2010-01-01

130

Background and Aims. Hepatocellular carcinoma (HCC) remains a leading cause of death by cancer worldwide. Computerized diagnosis systems relying on novel imaging markers gained significant importance in recent years. Our aim was to integrate a novel morphometric measurement—the fractal dimension (FD)—into an artificial neural network (ANN) designed to diagnose HCC. Material and Methods. The study included 21 HCC and 28 liver metastases (LM) patients scheduled for surgery. We performed hematoxylin staining for cell nuclei and CD31/34 immunostaining for vascular elements. We captured digital images and used an in-house application to segment elements of interest; FDs were calculated and fed to an ANN which classified them as malignant or benign, further identifying HCC and LM cases. Results. User intervention corrected segmentation errors and fractal dimensions were calculated. ANNs correctly classified 947/1050 HCC images (90.2%), 1021/1050 normal tissue images (97.23%), 1215/1400 LM (86.78%), and 1372/1400 normal tissues (98%). We obtained excellent interobserver agreement between human operators and the system. Conclusion. We successfully implemented FD as a morphometric marker in a decision system, an ensemble of ANNs designed to differentiate histological images of normal parenchyma from malignancy and classify HCCs and LMs.

Gheonea, Dan Ionut; Streba, Costin Teodor; Vere, Cristin Constantin; Serbanescu, Mircea; Pirici, Daniel; Comanescu, Maria; Streba, Letitia Adela Maria; Ciurea, Marius Eugen; Mogoanta, Stelian; Rogoveanu, Ion

2014-01-01

131

Surface fractal dimensions and textural properties of mesoporous alkaline-earth hydroxyapatites

NASA Astrophysics Data System (ADS)

This work examines the surface fractal dimensions (Df) and textural properties of three different alkaline-earth hydroxyapatites. Calcium, strontium and barium hydroxyapatite compounds were successfully synthesized via chemical precipitation method and characterized using X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectrometry, Fourier transform infrared spectroscopy, and N2-physisorption measurements. Surface fractal dimensions were determined using single N2-adsorption/desorption isotherms method to quantify the irregular surface of as-prepared compounds. The obtained materials were also characterized through their surface hydroxyl group content, determined by the mass titration method. It was found that the Df values for the three materials covered the range of 0.77 ± 0.04-2.33 ± 0.11; these results indicated that the materials tend to have smooth surfaces, except the irregular surface of barium hydroxyapatite. Moreover, regarding the synthesized calcium hydroxyapatite exhibited better textural properties compared with the synthesized strontium and barium hydroxyapatites for adsorbent purposes. However, barium hydroxyapatite shows irregular surface, indicating a high population of active sites across the surface, in comparison with the others studied hydroxyapatites. Finally, the results showed a linear correlation between the surface hydroxyl group content at the external surface of materials and their surface fractal dimensions.

Vilchis-Granados, J.; Granados-Correa, F.; Barrera-Díaz, C. E.

2013-08-01

132

Estimation of fractal dimension of colloidal gels in the presence of multiple scattering

NASA Astrophysics Data System (ADS)

Colloidal dispersions of fluorinated polymer particles with a refractive index very close to that of water, have been used to investigate the effect of multiple scattering on the estimated fractal dimension of colloidal gels, at high-particle volume fractions. The extent of multiple scattering was varied by using cuvettes of different internal diameters, from 3 to 18 mm. Three gelation systems with different sizes and volume fractions of primary particles have been characterized by static light scattering SLS. The obtained results indicate that multiple scattering affects only the magnitude of the scattered radiation, but not the estimated fractal dimension of the gels. This result confirms the conclusion of the theoretical study reported by Chen et al. [Phys. Rev. B 37, 5232 (1988)]. As a further confirmation, the same gels have been formed in a specially designed cell, with only 0.1 mm thickness (where multiple scattering is negligible) and characterized using small-angle neutron scattering (SANS). It is found that the fractal dimension estimated from SANS measurements, without multiple scattering, is the same as that estimated from SLS measurements, in the presence of substantial multiple scattering.

Lattuada, Marco; Wu, Hua; Morbidelli, Massimo

2001-12-01

133

Surface Deformation Analysis by Means of Fractal Dimension and Lacunarity Approaches

NASA Astrophysics Data System (ADS)

Fractals and scaling laws such as river networks and runoff series are abundant in nature, and geometry of river networks and basins is a superb example of this. The unrelenting competition between tectonics, surface uplift and erosional processes on the earth has resulted in a variety of drainage patterns by linearizing the normal flow patterns of river networks. These patterns are fractals and their variable spatial distribution can be used to examine the vulnerability of surface deformation. At first we extract the drainage network from Shuttle Radar Topographic Mission's digital elevation data (SRTM-90m) using D8 algorithm. We convert the drainage network into a binary image where the area of interests (AOIs) i.e. drainage are represented with pixels value of 1. The fractal dimension (D) analysis using Box Counting method is used to identify the anomalous drainage patterns of vulnerable sites. We prepare a D distribution map using a moving window of 1 arc sec. by 1 arc sec. on the binary image of river network. The space occupied by AOIs reveals variable distribution of D and lower values suggest that the drainage pattern has become linearized due to the influence of tectonics and surface processes. We use lacunarity analysis using Gliding Box method to see the relative vulnerability as two AOIs can have similar D values. The AOIs with a high lacunarity of drainage pattern are more vulnerable than AOIs with lower lacunarity values. Three AOIs i.e. Vanch and Yazgulem Basin (VYB) in northwestern Pamir, Tirch Mir Fault Zone (TMFZ) in Hindukush region, and Central Badakhshan (CB) with high vulnerability and three sites i.e. Central Pamir, Shiveh Lake Region in Afghanistan and Darvaz Fault Zone with medium vulnerability were identified using fractal dimension. The lacunarity analysis was used to diferentiate between the relative vulnerability of these AOIs. Results from Pyanj river network and adjacent areas show that VYB, TMFZ, and CB have relatively high vulnerability to surface deformation. The fractal dimensions derived from two different drainage patterns may be not sufficient for distinguishing them genetically. For this reason, lacunarity analysis is applied as a useful tool for the distinction between different textural patterns with similar fractal dimension.

Mahmood, S.; Shahzad, F.; Glaouguen, R.

2009-05-01

134

NASA Astrophysics Data System (ADS)

Image processing analysis is used to check the ability of the fractal dimension for quantitatively describing the shape of volcanic ash particles. Digitized scanning electron microscopy images of fine pyroclasts from the eruptions of Monte Pilato-Rocche Rosse (Lipari, Italy) are investigated to test the efficiency of the fractal dimension to discriminate between particles of different eruptive processes. Multivariate analysis of multiple fractal components allows distinction between magmatic particles and phreatomagmatic particles, which however is less significant than the discrimination obtained in previous studies by the use of simple 'adimensional' shape parameters. Approximation of the actual particle boundary and the not rotation invariant nature of the fractal data frequently result in a significant scatter of data points in the Mandelbrot-Richardson plot. Such behavior obscures in some cases the actual information of particle shape and renders the discriminating power of fractal analysis less effective than classical shape descriptors. Data less affected by scatter reveal that phreatomagmatic particles of the Monte Pilato-Rocche Rosse eruptions are true (mono) fractals, whereas magmatic particles are multifractals. The textural (small-scale) fractal of magmatic particles is similar to the fractal dimension value of phreatomagmatic particles, and is attributed to the rheological behavior of melt upon brittle fragmentation. The structural (large-scale) fractal of magmatic particles refers to the walls of ruptured vesicles that lay on the particle outline. The high difference between the values of the textural and structural fractals of magmatic particles of the Monte Pilato-Rocche Rosse eruptions suggests two distinct and independent processes in the formation of such pyroclasts. At the scales corresponding to the textural fractal, the fragmentation process is independent of vesicles. Magmatic fragmentation is not simply related to growth, expansion, interference and explosion of vesicles but to a brittle cracking of the highly viscous melt, likely related to rapid decompression.

Dellino, P.; Liotino, G.

2002-03-01

135

NASA Astrophysics Data System (ADS)

Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated.

Ul'yanov, A. S.; Lyapina, A. M.; Ulianova, O. V.; Fedorova, V. A.; Uianov, S. S.

2011-04-01

136

Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated. (optical technologies in biophysics and medicine)

Ul'yanov, A S; Lyapina, A M; Ulianova, O V; Fedorova, V A; Uianov, S S

2011-04-30

137

NASA Astrophysics Data System (ADS)

Satellite image data have become an important source of information for monitoring vegetation and mapping land cover at several scales. Beside this, the distribution and phenology of vegetation is largely associated with climate, terrain characteristics and human activity. Various vegetation indices have been developed for qualitative and quantitative assessment of vegetation using remote spectral measurements. In particular, sensors with spectral bands in the red (RED) and near-infrared (NIR) lend themselves well to vegetation monitoring and based on them [(NIR - RED) / (NIR + RED)] Normalized Difference Vegetation Index (NDVI) has been widespread used. Given that the characteristics of spectral bands in RED and NIR vary distinctly from sensor to sensor, NDVI values based on data from different instruments will not be directly comparable. The spatial resolution also varies significantly between sensors, as well as within a given scene in the case of wide-angle and oblique sensors. As a result, NDVI values will vary according to combinations of the heterogeneity and scale of terrestrial surfaces and pixel footprint sizes. Therefore, the question arises as to the impact of differences in spectral and spatial resolutions on vegetation indices like the NDVI. The aim of this study is to establish a comparison between two different sensors in their NDVI values at different spatial resolutions. Scaling analysis and modeling techniques are increasingly understood to be the result of nonlinear dynamic mechanisms repeating scale after scale from large to small scales leading to non-classical resolution dependencies. In the remote sensing framework the main characteristic of sensors images is the high local variability in their values. This variability is a consequence of the increase in spatial and radiometric resolution that implies an increase in complexity that it is necessary to characterize. Fractal and multifractal techniques has been proven to be useful to extract such complexities from remote sensing images and will applied in this study to see the scaling behavior for each sensor in generalized fractal dimensions. The studied area is located in the provinces of Caceres and Salamanca (east of Iberia Peninsula) with an extension of 32 x 32 km2. The altitude in the area varies from 1,560 to 320 m, comprising natural vegetation in the mountain area (forest and bushes) and agricultural crops in the valleys. Scaling analysis were applied to Landsat-5 and MODIS TERRA to the normalized derived vegetation index (NDVI) on the same region with one day of difference, 13 and 12 of July 2003 respectively. From these images the area of interest was selected obtaining 1024 x 1024 pixels for Landsat image and 128 x 128 pixels for MODIS image. This implies that the resolution for MODIS is 250x250 m. and for Landsat is 30x30 m. From the reflectance data obtained from NIR and RED bands, NDVI was calculated for each image focusing this study on 0.2 to 0.5 ranges of values. Once that both NDVI fields were obtained several fractal dimensions were estimated in each one segmenting the values in 0.20-0.25, 0.25-0.30 and so on to rich 0.45-0.50. In all the scaling analysis the scale size length was expressed in meters, and not in pixels, to make the comparison between both sensors possible. Results are discussed. Acknowledgements This work has been supported by the Spanish MEC under Projects No. AGL2010-21501/AGR, MTM2009-14621 and i-MATH No. CSD2006-00032

Alonso, C.; Benito, R. M.; Tarquis, A. M.

2012-04-01

138

Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis.

Fractal characteristics of chromatin, revealed by light or electron microscopy, have been reported during the last 20 years. Fractal features can easily be estimated in digitalized microscopic images and are helpful for diagnosis and prognosis of neoplasias. During carcinogenesis and tumor progression, an increase of the fractal dimension (FD) of stained nuclei has been shown in intraepithelial lesions of the uterine cervix and the anus, oral squamous cell carcinomas or adenocarcinomas of the pancreas. Furthermore, an increased FD of chromatin is an unfavorable prognostic factor in squamous cell carcinomas of the oral cavity and the larynx, melanomas and multiple myelomas. High goodness-of-fit of the regression line of the FD is a favorable prognostic factor in acute leukemias and multiple myelomas. The nucleus has fractal and power-law organization in several different levels, which might in part be interrelated. Some possible relations between modifications of the chromatin organization during carcinogenesis and tumor progression and an increase of the FD of stained chromatin are suggested. Furthermore, increased complexity of the chromatin structure, loss of heterochromatin and a less-perfect self-organization of the nucleus in aggressive neoplasias are discussed. PMID:24063399

Metze, Konradin

2013-09-01

139

Fractal dust grains of different shapes are observed in a radially confined magnetized radio frequency plasma. The fractal dimensions of the dust structures in two-dimensional (2D) horizontal dust layers are calculated, and their evolution in the dust growth process is investigated. It is found that as the dust grains grow the fractal dimension of the dust structure decreases. In addition, the fractal dimension of the center region is larger than that of the entire region in the 2D dust layer. In the initial growth stage, the small dust particulates at a high number density in a 2D layer tend to fill space as a normal surface with fractal dimension D = 2. The mechanism of the formation of fractal dust grains is discussed.

Huang, F. [College of Science, China Agricultural University, Beijing 100083 (China); Peng, R. D. [State Key Laboratory of Coal Resources and Safe Mining, China University of Mining and Technology, Beijing 100083 (China); Liu, Y. H. [Institute of Complexity Science, Qingdao University, Qingdao 266071 (China); Chen, Z. Y. [Department of Physics, Beijing University of Chemical Technology, Beijing 100029 (China); Ye, M. F.; Wang, L. [Institute of Physics, Chinese Academy of Science, Beijing 100190 (China)

2012-09-15

140

This paper presents a novel and non-destructive approach to the appearance characterization and classification of commercial pork, turkey and chicken ham slices. Ham slice images were modelled using directional fractal (DF(0°;45°;90°;135°)) dimensions and a minimum distance classifier was adopted to perform the classification task. Also, the role of different colour spaces and the resolution level of the images on DF analysis were investigated. This approach was applied to 480 wafer thin ham slices from four types of hams (120 slices per type): i.e., pork (cooked and smoked), turkey (smoked) and chicken (roasted). DF features were extracted from digitalized intensity images in greyscale, and R, G, B, L(?), a(?), b(?), H, S, and V colour components for three image resolution levels (100%, 50%, and 25%). Simulation results show that in spite of the complexity and high variability in colour and texture appearance, the modelling of ham slice images with DF dimensions allows the capture of differentiating textural features between the four commercial ham types. Independent DF features entail better discrimination than that using the average of four directions. However, DF dimensions reveal a high sensitivity to colour channel, orientation and image resolution for the fractal analysis. The classification accuracy using six DF dimension features (a(90°)(?),a(135°)(?),H(0°),H(45°),S(0°),H(90°)) was 93.9% for training data and 82.2% for testing data. PMID:22064169

Mendoza, Fernando; Valous, Nektarios A; Allen, Paul; Kenny, Tony A; Ward, Paddy; Sun, Da-Wen

2009-02-01

141

Fractal dimension and energetic heterogeneity of gold-modified Al-Fe-Ce pilc’s

NASA Astrophysics Data System (ADS)

This paper studies the energetic and topographical changes that occur on the surface of a series of clays pillared with the mixed Al-Fe-Ce system and on the surface of solids synthesized by the deposition of gold nanoparticles over these pillared clays. The energetic heterogeneity of the solids was analyzed by means of the distribution of the adsorption potential, while the variations in the fractal dimension were determined from the nitrogen adsorption isotherms at 77 K, using the equation proposed by Avnir-Jaroniec. Results show the generation of microporous structures with important topographical modifications indicating an increase in the roughness (fractal geometry) of the surface of the solids as a consequence of the pillaring, revealing a positive effect of cerium addition in the synthesis process and the possible formation of nanoparticles of iron species and gold on the surface of pillared clays. The solids were also analyzed by transmission electron microscopy (TEM), confirming the formation of nanoparticles on the surface.

Carriazo, J. G.; Molina, R.; Moreno, S.

2008-12-01

142

ERIC Educational Resources Information Center

The divider dimensions of a range of maps of Ireland dating from 1567 to 1893 are evaluated, and it is shown that for maps produced before 1650 the fractal dimension of the map can be correlated to its date of publication. Various classroom uses and extensions are discussed. (Contains 2 figures.)

McCartney, M.; Myers, D.; Sun, Y.

2008-01-01

143

THE FRACTAL DIMENSION OF STAR-FORMING REGIONS AT DIFFERENT SPATIAL SCALES IN M33

We study the distribution of stars, H II regions, molecular gas, and individual giant molecular clouds in M33 over a wide range of spatial scales. The clustering strength of these components is systematically estimated through the fractal dimension. We find scale-free behavior at small spatial scales and a transition to a larger correlation dimension (consistent with a nearly uniform distribution) at larger scales. The transition region lies in the range {approx}500-1000 pc. This transition defines a characteristic size that separates the regime of small-scale turbulent motion from that of large-scale galactic dynamics. At small spatial scales, bright young stars and molecular gas are distributed with nearly the same three-dimensional fractal dimension (D {sub f,3D} {approx}< 1.9), whereas fainter stars and H II regions exhibit higher values, D {sub f,3D} {approx_equal} 2.2-2.5. Our results indicate that the interstellar medium in M33 is on average more fragmented and irregular than in the Milky Way.

Sanchez, Nestor; Alfaro, Emilio J. [Instituto de Astrofisica de AndalucIa, CSIC, Apdo. 3004, E-18080, Granada (Spain); Anez, Neyda [Departamento de Fisica, Facultad Experimental de Ciencias, Universidad del Zulia, Maracaibo (Venezuela, Bolivarian Republic of); Odekon, Mary Crone, E-mail: nestor@iaa.e [Department of Physics, Skidmore College, Saratoga Springs, NY 12866 (United States)

2010-09-01

144

The Fractal Dimensions of The Soil-pore Interface and The Pore Size Distribution

NASA Astrophysics Data System (ADS)

Soil structure can be regarded as self-similar, though it should be noted that for natural structures the similarity occurs only over a few orders of magnitude. Nevertheless, the measurement of fractal dimensions yields a powerful tool for characterizing any struc- ture in a quantitative sense. For the work presented, thin sections from the Bt-horizon of a Luvisol were prepared. Digital images for different magnifications and resolu- tions, respectively, were taken with a FE-REM. For image analysis, the system KS400 (ZeissVision) was used. It allows the application of user-defined macros. The fractal dimension (Ds) of the pore-solid interface was measured with the box counting and the dilation procedure. As the fractal dimension of a line was measured within a plain, 1

Dathe, Annette

145

Calculation of a static potential created by plane fractal cluster

NASA Astrophysics Data System (ADS)

In this paper we demonstrate new approach that can help in calculation of electrostatic potential of a fractal (self-similar) cluster that is created by a system of charged particles. For this purpose we used the simplified model of a plane dendrite cluster [1] that is generated by a system of the concentric charged rings located in some horizontal plane (see Fig. 2). The radiuses and charges of the system of concentric rings satisfy correspondingly to relationships: rn = r0?n and en = e0bn, where n determines the number of a current ring. The self-similar structure of the system considered allows to reduce the problem to consideration of the functional equation that similar to the conventional scaling equation. Its solution represents itself the sum of power-low terms of integer order and non-integer power-law term multiplied to a log-periodic function [5,6]. The appearance of this term was confirmed numerically for internal region of the self-similar cluster ( r0 ? r ? rN-1 ), where r0, rN-1 determine the smallest and the largest radiuses of the limiting rings correspondingly. The results were obtained for homogeneously ( b > 0) and heterogeneously ( b < 0) charged rings. We expect that this approach allows to consider more complex self-similar structures with different geometries of charge distributions.

Nigmatullin, Raoul R.; Alekhin, Alexander P.

2011-12-01

146

Fractal structure of interstellar cirrus

NASA Technical Reports Server (NTRS)

The paper investigates the fractal structure of some of the infrared cirrus discovered by IRAS. The clouds studied are characterized by a perimeter with fractal dimension 1.26 + or - 0.04 using the method of Lovejoy. This dimension was found to be essentially constant from region to region. Methods of calculating this dimension are compared and the relation of this quantity to some other observable cloud properties is discussed.

Bazell, D.; Desert, F. X.

1988-01-01

147

Mathis and Whiffen (1989) have recently suggested that interstellar dust particles are fluffy aggregates of submicron-size particles composed of various astronomical minerals. These dust particles should exhibit optical properties that are quite different from standard dust, characterized by spherical particles of various homogeneous mineral composition. In this paper, the discrete dipole approximation (DDA) method is used to examine the effects of chemical inhomogeneities and spatial structure on the optical properties of interstellar Mathis-Whiffen-type dust particles. The spatial structure of the dust is represented by its fractal dimension, and the chemical inhomogeneities are simulated by randomly assigning the composition of the occupied sites in the structure to be either carbon or silicate. It is found that compositional inhomogeneities are the dominant parameter affecting the shape of the 9.7 and 18 micron silicate bands. Some bands-shape variations can be attributed to the fractal dimension of the dust. The results derived here can be used to explain or constrain variations in these parameters among various astronomical objects. 23 refs.

Bazell, D.; Dwek, E (Applied Research Corp., Landover, MD (USA) NASA, Goddard Space Flight Center, Greenbelt, MD (USA))

1990-09-01

148

Objective Auscultation of TCM Based on Wavelet Packet Fractal Dimension and Support Vector Machine.

This study was conducted to illustrate that auscultation features based on the fractal dimension combined with wavelet packet transform (WPT) were conducive to the identification the pattern of syndromes of Traditional Chinese Medicine (TCM). The WPT and the fractal dimension were employed to extract features of auscultation signals of 137 patients with lung Qi-deficient pattern, 49 patients with lung Yin-deficient pattern, and 43 healthy subjects. With these features, the classification model was constructed based on multiclass support vector machine (SVM). When all auscultation signals were trained by SVM to decide the patterns of TCM syndromes, the overall recognition rate of model was 79.49%; when male and female auscultation signals were trained, respectively, to decide the patterns, the overall recognition rate of model reached 86.05%. The results showed that the methods proposed in this paper were effective to analyze auscultation signals, and the performance of model can be greatly improved when the distinction of gender was considered. PMID:24883068

Yan, Jian-Jun; Guo, Rui; Wang, Yi-Qin; Liu, Guo-Ping; Yan, Hai-Xia; Xia, Chun-Ming; Shen, Xiaojing

2014-01-01

149

NASA Technical Reports Server (NTRS)

Mathis and Whiffen (1989) have recently suggested that interstellar dust particles are fluffy aggregates of submicron-size particles composed of various astronomical minerals. These dust particles should exhibit optical properties that are quite different from standard dust, characterized by spherical particles of various homogeneous mineral composition. In this paper, the discrete dipole approximation (DDA) method is used to examine the effects of chemical inhomogeneities and spatial structure on the optical properties of interstellar Mathis-Whiffen-type dust particles. The spatial structure of the dust is represented by its fractal dimension, and the chemical inhomogeneities are simulated by randomly assigning the composition of the occupied sites in the structure to be either carbon or silicate. It is found that compositional inhomogeneities are the dominant parameter affecting the shape of the 9.7 and 18 micron silicate bands. Some bands-shape variations can be attributed to the fractal dimension of the dust. The results derived here can be used to explain or constrain variations in these parameters among various astronomical objects.

Bazell, David; Dwek, Eli

1990-01-01

150

Objective Auscultation of TCM Based on Wavelet Packet Fractal Dimension and Support Vector Machine

This study was conducted to illustrate that auscultation features based on the fractal dimension combined with wavelet packet transform (WPT) were conducive to the identification the pattern of syndromes of Traditional Chinese Medicine (TCM). The WPT and the fractal dimension were employed to extract features of auscultation signals of 137 patients with lung Qi-deficient pattern, 49 patients with lung Yin-deficient pattern, and 43 healthy subjects. With these features, the classification model was constructed based on multiclass support vector machine (SVM). When all auscultation signals were trained by SVM to decide the patterns of TCM syndromes, the overall recognition rate of model was 79.49%; when male and female auscultation signals were trained, respectively, to decide the patterns, the overall recognition rate of model reached 86.05%. The results showed that the methods proposed in this paper were effective to analyze auscultation signals, and the performance of model can be greatly improved when the distinction of gender was considered.

Yan, Jian-Jun; Wang, Yi-Qin; Liu, Guo-Ping; Yan, Hai-Xia; Xia, Chun-Ming; Shen, Xiaojing

2014-01-01

151

A new version of Visual tool for estimating the fractal dimension of images

NASA Astrophysics Data System (ADS)

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images (Grossu et al., 2009 [1]). The earlier version was limited to bi-dimensional sets of points, stored in bitmap files. The application was extended for working also with comma separated values files and three-dimensional images. New version program summaryProgram title: Fractal Analysis v02 Catalogue identifier: AEEG_v2_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v2_0.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 9999 No. of bytes in distributed program, including test data, etc.: 4 366 783 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 30 M Classification: 14 Catalogue identifier of previous version: AEEG_v1_0 Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 1999 Does the new version supersede the previous version?: Yes Nature of problem: Estimating the fractal dimension of 2D and 3D images. Solution method: Optimized implementation of the box-counting algorithm. Reasons for new version:The previous version was limited to bitmap image files. The new application was extended in order to work with objects stored in comma separated values (csv) files. The main advantages are: Easier integration with other applications (csv is a widely used, simple text file format); Less resources consumed and improved performance (only the information of interest, the "black points", are stored); Higher resolution (the points coordinates are loaded into Visual Basic double variables [2]); Possibility of storing three-dimensional objects (e.g. the 3D Sierpinski gasket). In this version the optimized box-counting algorithm [1] was extended to the three-dimensional case. Summary of revisions:The application interface was changed from SDI (single document interface) to MDI (multi-document interface). One form was added in order to provide a graphical user interface for the new functionalities (fractal analysis of 2D and 3D images stored in csv files). Additional comments: User friendly graphical interface; Easy deployment mechanism. Running time: In the first approximation, the algorithm is linear. References:[1] I.V. Grossu, C. Besliu, M.V. Rusu, Al. Jipa, C.C. Bordeianu, D. Felea, Comput. Phys. Comm. 180 (2009) 1999-2001.[2] F. Balena, Programming Microsoft Visual Basic 6.0, Microsoft Press, US, 1999.

Grossu, I. V.; Felea, D.; Besliu, C.; Jipa, Al.; Bordeianu, C. C.; Stan, E.; Esanu, T.

2010-04-01

152

We used Translational Asymmetry (TA) of the annual stem, branch growth pattern and fractal dimension to quantify stress during development of argan (Argania spinosa (L.) Skeels) throughout its range in Morocco. Under communal grazing conditions known as “mouchâa” (Grazing Management), the branch fractal dimension was reduced and the TA of plants increased, reflecting the stressful conditions in which the argan

C. L. Alados; A. El Aich

2008-01-01

153

Fractal Structure in Human Cerebellum Measured by MRI

NASA Astrophysics Data System (ADS)

Fractal dimension has been used to quantify the structures of a wide range of objects in biology and medicine. We measured fractal dimension of human cerebellum (CB) in magnetic resonance images of 24 healthy young subjects (12 men, 12 women). CB images were resampled to a series of image sets with different three-dimensional resolutions. At each resolution, the skeleton of the CB white matter was obtained and the number of pixels belonging to the skeleton was determined. Fractal dimension of the CB skeleton was calculated using the box-counting method. The results indicated that the CB skeleton is a highly fractal structure, with a fractal dimension of 2.57+/-0.01. No significant difference in the CB fractal dimension was observed between men and women. Fractal dimension may serve as a quantitative index for structural complexity of the CB at its developmental, degenerative, or evolutionary stages.

Zhang, Luduan; Yue, Guang; Brown, Robert; Liu, Jingzhi

2003-10-01

154

We tested the hypotheses (1) that the fractal dimension, D, of hypo- centers are different in a locked and a creeping segment of the San Andreas fault and (2) that the relationship D 2b holds approximately, where b is the slope of the frequency-magnitude relationship. The test area was the 30- to 50-km fault seg- ment north of Parkfield for

Max Wyss; Charles G. Sammis; Robert M. Nadeau; Stefan Wiemer

2004-01-01

155

Fractal dimension has emerged as a clinically useful tool in the diagnosis and management of breast cancer. The aim of the present study was to determine if fractal dimension can be applied for the analysis of a pre-clinical breast cancer mouse model, MMTV-cNeu. Using fractal dimension in conjunction with conventional morphometric measurements, the ductal epithelial networks of pubertal-stage MMTV-cNeu mice were quantitatively compared with those of wild-type mice. Significant alterations in ductal epithelial network growth and organization were detected during early neoplasia in MMTV-cNeu mice. Moreover, the left-side networks were significantly more affected relative to their wild-type counterparts than were the right-side networks, a finding that is consistent with elevated left-side tumor incidence reported for breast cancer patients. Taken together these results demonstrate that combined fractal dimension and morphometric analysis is an objective and sensitive approach to quantitatively identify ductal epithelial aberrancies that precede overt mammary carcinoma formation. PMID:24596356

Fuseler, John W; Robichaux, Jacqulyne P; Atiyah, Huda I; Ramsdell, Ann F

2014-03-01

156

A new approach in the BCI research based on fractal dimension as feature and Adaboost as classifier

High rate classification of imagery tasks is still one of the hot topics among the brain computer interface (BCI) groups. In order to improve this rate, a new approach based on fractal dimension as feature and Adaboost as classifier is presented for five subjects in this paper. To have a comparison, features such as band power, Hjorth parameters along with

Reza Boostani; Mohammad Hassan Moradi

2004-01-01

157

Study of the pore size distribution and fractal dimension of HNO 3-treated activated carbons

NASA Astrophysics Data System (ADS)

In the present work, the effect of the oxidizing treatment with nitric acid on three activated carbon samples has been studied. The influence of the acid treatment on the surface groups of the different samples has been investigated by means of FT-IR spectroscopy. The pore size distributions of the different samples were determined by means of the HK and DFT methods. The HK method points out a moderate increment of the microporosity due to the action of the nitric acid, whereas the DFT method shows an increase in the microporosity range above 17 Å. Finally, the values of the fractal dimension reveal that the treatment of the samples with nitric acid leads to chemical reactions of a limited extent.

Macías-García, A.; Díaz-Díez, M. A.; Cuerda-Correa, E. M.; Olivares-Marín, M.; Gañan-Gómez, J.

2006-06-01

158

The aim of this study was to explore new techniques in analysing postural control using nonlinear time-series analysis and to relate these results with the clinical knowledge on the postural system in Down syndrome (DS) subjects. In order to achieve the goal, we analysed the time domain and the frequency domain behaviour, the fractal dimension and the entropy of the centre of pressure signal in both directions during quiet standing in 35 participants with DS, comparing the results with a control population. DS patients evidenced a lack in postural control in anterior-posterior direction due to the impairment both in the high organisation and synergies and in the impairments due to ligament laxity and hypotonia. Maintaining posture is a task achieved by the integration of visual, vestibular and somatosensory receptors and the dynamical nature of this signal gives fundamental data about the lack of postural control in specific pathological condition. PMID:22657255

Rigoldi, C; Galli, M; Mainardi, L; Albertini, G

2014-04-01

159

Imaging of the parafoveal capillary network and its integrity analysis using fractal dimension

Using a spectral domain OCT system, equipped with a broadband Ti:sapphire laser, we imaged the human retina with 5 µm x 1.3 µm transverse and axial resolution at acquisition rate of 100 kHz. Such imaging speed significantly reduces motion artifacts. Combined with the ultra-high resolution, this allows observing microscopic retinal details with high axial definition without the help of adaptive optics. In this work we apply our system to image the parafoveal capillary network. We demonstrate how already on the intensity level the parafoveal capillaries can be segmented by a simple structural high pass filtering algorithm. This data is then used to quantitatively characterize the capillary network of healthy and diseased eyes. We propose to use the fractal dimension as index for capillary integrity of pathologic disorders.

Schmoll, Tilman; Singh, Amardeep S. G.; Blatter, Cedric; Schriefl, Sabine; Ahlers, Christian; Schmidt-Erfurth, Ursula; Leitgeb, Rainer A.

2011-01-01

160

Background Prostate cancer is a serious public health problem that affects quality of life and has a significant mortality rate. The aim of the present study was to quantify the fractal dimension and Shannon’s entropy in the histological diagnosis of prostate cancer. Methods Thirty-four patients with prostate cancer aged 50 to 75 years having been submitted to radical prostatectomy participated in the study. Histological slides of normal (N), hyperplastic (H) and tumor (T) areas of the prostate were digitally photographed with three different magnifications (40x, 100x and 400x) and analyzed. The fractal dimension (FD), Shannon’s entropy (SE) and number of cell nuclei (NCN) in these areas were compared. Results FD analysis demonstrated the following significant differences between groups: T vs. N and H vs. N groups (p?

2013-01-01

161

NASA Technical Reports Server (NTRS)

The surface roughness of the Vastitas Borealis Formation on Mars was analyzed with fractal statistics. Root mean square slopes and fractal dimensions were calculated for 74 topographic profiles. Results have implications for radar scattering models.

Garneau, S.; Plaut, J. J.

2000-01-01

162

Theory of Laplacian Fractals: Diffusion Limited Aggregation and Dielectric Breakdown Model.

National Technical Information Service (NTIS)

A theoretical approach that clarifies the origin of fractal structures in irreversible growth models based on the Laplace equation and a stochastic field is described. This theory provides a systematic method for the calculation of the fractal dimension D...

L. Pietronero A. Erzan C. Evertsz

1988-01-01

163

Determination of the fractal dimension for the epitaxial n-GaAs surface in the local limit

Atomic-force microscopy studies of epitaxial n-GaAs surfaces prepared to deposit barrier contacts showed that major relief for such surfaces is characterized by a roughness within 3-15 nm, although 'surges' up to 30-70 nm are observed. Using three independent methods for determining the spatial dimension of the surface, based on the fractal analysis for the surface (triangulation method), its section contours in the horizontal plane, and the vertical section (surface profile), it was shown that the active surface for epitaxial n-GaAs obeys all main features of behavior for fractal Brownian surfaces and, in the local approximation, can be characterized by the fractal dimension D{sub f} slightly differing for various measuring scales. The most accurate triangulation method showed that the fractal dimensions for the studied surface of epitaxial n-GaAs for measurement scales from 0.692 to 0.0186 {mu}m are in the range D{sub f} = 2.490-2.664. The real surface area S{sub real} for n-GaAs epitaxial layers was estimated using a graphical method in the approximation {delta} {sup {yields}} 0 {delta} is the measurement scale parameter). It was shown that the real surface area for epitaxial n-GaAs can significantly (ten times and more) exceed the area of the visible contact window.

Torkhov, N. A., E-mail: trkf@mail.ru; Bozhkova, V. G. [Scientific-Research Institute of Semiconductor Devices (Russian Federation); Ivonin, I. V.; Novikov, V. A. [Tomsk State University (Russian Federation)

2009-01-15

164

NASA Astrophysics Data System (ADS)

Structural texture measures are used to address the aspect of breast cancer risk assessment in screening mammograms. The current study investigates whether texture properties characterized by local Fractal Dimension (FD) and Lacunarity contribute to asses breast cancer risk. FD represents the complexity while the Lacunarity characterize the gappiness of a fractal. Our cross-sectional case-control study includes mammograms of 50 patients diagnosed with breast cancer in the subsequent 2-4 years and 50 matched controls. The longitudinal double blind placebo controlled HRT study includes 39 placebo and 36 HRT treated volunteers for two years. ROIs with same dimension (250*150 pixels) were created behind the nipple region on these radiographs. Box counting method was used to calculate the fractal dimension (FD) and the Lacunarity. Paired t-test and Pearson correlation coefficient were calculated. It was found that there were no differences between cancer and control group for FD (P=0.8) and Lacunarity (P=0.8) in crosssectional study whereas earlier published heterogeneity examination of radiographs (BC-HER) breast cancer risk score separated groups (p=0.002). In the longitudinal study, FD decreased significantly (P<0.05) in the HRT treated population while Lacunarity remained insignificant (P=0.2). FD is negatively correlated to Lacunarity (-0.74, P<0.001), BIRADS (-0.34, P<0.001) and Percentage Density (-0.41, P<0.001). FD is invariant to the mammographic texture change from control to cancer population but marginally varying in HRT treated population. This study yields no evidence that lacunarity or FD are suitable surrogate markers of mammographic heterogeneity as they neither pick up breast cancer risk, nor show good sensitivity to HRT.

Karemore, Gopal; Nielsen, Mads

2009-02-01

165

Small-angle scattering from fat fractals

NASA Astrophysics Data System (ADS)

A number of experimental small-angle scattering (SAS) data are characterized by a succession of power-law decays with arbitrarily decreasing values of scattering exponents. To describe such data, here we develop a new theoretical model based on 3D fat fractals (sets with fractal structure, but nonzero volume) and show how one can extract structural information about the underlying fractal structure. We calculate analytically the monodisperse and polydisperse SAS intensity (fractal form factor and structure factor) of a newly introduced model of fat fractals and study its properties in momentum space. The system is a 3D deterministic mass fractal built on an extension of the well-known Cantor fractal. The model allows us to explain a succession of power-law decays and respectively, of generalized power-law decays (GPLD; superposition of maxima and minima on a power-law decay) with arbitrarily decreasing scattering exponents in the range from zero to three. We show that within the model, the present analysis allows us to obtain the edges of all the fractal regions in the momentum space, the number of fractal iteration and the fractal dimensions and scaling factors at each structural level in the fractal. We applied our model to calculate an analytical expression for the radius of gyration of the fractal. The obtained quantities characterizing the fat fractal are correlated to variation of scaling factor with the iteration number.

Anitas, Eugen M.

2014-06-01

166

NASA Astrophysics Data System (ADS)

The volcanic unit of Montaña Reventada is an example of magma mixing in Tenerife (Canary Islands, Spain). The eruptive process has been detonated by a basanite intruding into a phonolite magma chamber. This eruption started with a basanite followed by a phonolite. Montaña Reventada phonolite is characterized by the presence of mafic enclaves. These enclaves represent about the 2% of the outcrop and have been classified like basanites, phono-tephrite and tephri-phonolite. The enclaves have different morphologies, from rounded to complex fingers-like structures, and usually exhibit cuspate terminations. This study aims to provide a new perspective on the 1100 AD Montaña Reventada eruption quantifying the textural heterogeneities related to the enclaves generated by the mixing process. The textural study was carried out using a fractal geometry approach, and its results were used to calculate some parameters related to magma chamber dynamics. Photographs of 67 samples were taken normal to the surface of the enclaves with the aim of delineating the contact between the enclaves and the host rocks. The resulted pictures were processed with the NIH (National Institutes of Health) image analysis software to generate binary images in which enclaves and host rock were replaced by black and white pixels, respectively. The fractal dimension (Dbox) has been computed by using the box-counting method in order to quantify the complexity of the enclaves morphology. Viscosity ratio (?R) between the phonolite and the enclaves has been calculated as follows: log(?R) = 0.013e3.34Dbox PIC The viscosity of the enclaves has been calculated according to the ?Rvalue with the higher frequency and to the calculated viscosity of the phonolite between 900° and 1200° . We hypothesized that this value corresponds to the amount of mafic magma present in the system, while the other values represent different degrees of mingling and chemical diffusion. Viscosity of the basanite can be computed like: ?enclave = (%phonolite *?phonolite)+ (%basanite *?basanite) PIC ?enclaves--(%phonolite *?phonolite) ?basanite = %basanite PIC The minimum percentages which satisfy the relation are 69.5% of basanite and 30.5% of phonolite. Although the amount of mafic magma reaches the 69.5%, the presence of enclaves in the phonolite is just the ?1% and the amount of basanite erupted before could correspond to the 15% of the phonolite (estimated from stratigraphic sections). Probably a magma body of basanite was still stored in the magma chamber. The volume of basanite still stored during this time may have evolved to a more explosive magma and hence increases the volcanic risk in the area.

Albert, Helena; Perugini, Diego; Martí, Joan

2014-05-01

167

ERIC Educational Resources Information Center

The complexity (fractal dimension value) of responses to the Rey-Osterrieth Complex Figure Test (ROCFT) between 10 undergraduate students with learning disabilities and a comparison group of 10 students without learning disabilities were compared. The fractal value of responses was assessed under three conditions (copy, immediate, and delay) by…

House, Garvey; Zelhart, Paul F.

168

NASA Astrophysics Data System (ADS)

Quantitative analyses of soil texture with the help of the fractal dimensions of soil particle sizes show that fractal dimensions exhibit a significant linear negative correlation with the sand content (>0.1 mm) and a significant power-law positive correlation with the content of clay and silt (<0.05 mm) ( P < 0.0001). However, results revealed that the range of spatial heterogeneity was not restricted to the range of the shrub canopies of the dominant Ammopiptanthus mongolicus communities in the desert region. These results did not support the theory of the “fertile island effect” arising from the interception of fine-grained materials including dust by the shrubs in a desert ecosystem. We hypothesize that the high spatial heterogeneity existing beyond the scope of the shrub canopies and the lack of proper soil substrate conditions required for the invasion of other species, lead to the steady dominance of A. mongolicus communities in these arid desert regions.

Jia, X. H.; Li, X. R.; Zhang, J. G.; Zhang, Z. S.

2009-09-01

169

Fractal Dimension and Size Scaling of Domains in Thin Films of Multiferroic BiFeO3

NASA Astrophysics Data System (ADS)

Domains in ferroelectric films are usually smooth, stripelike, very thin compared with magnetic ones, and satisfy the Landau-Lifshitz-Kittel scaling law (width proportional to square root of film thickness). However, the ferroelectric domains in very thin films of multiferroic BiFeO3 have irregular domain walls characterized by a roughness exponent 0.5 0.6 and in-plane fractal Hausdorff dimension H||=1.4±0.1, and the domain size scales with an exponent 0.59±0.08 rather than (1)/(2). The domains are significantly larger than those of other ferroelectrics of the same thickness, and closer in size to those of magnetic materials, which is consistent with a strong magnetoelectric coupling at the walls. A general model is proposed for ferroelectrics, ferroelastics or ferromagnetic domains which relates the fractal dimension of the walls to domain size scaling.

Catalan, G.; Béa, H.; Fusil, S.; Bibes, M.; Paruch, P.; Barthélémy, A.; Scott, J. F.

2008-01-01

170

The regeneration of compact bone involves the deposition of a poorly organized connective tissue template that remodels into compact lamellar bone. An objective description of this process is difficult because classical histomorphometry is unable to correctly characterize qualitative changes in tissue complexity. In this study, we demonstrated the use of two distinct methods of image texture analysis, the Shannon's entropy [standard error (SE)], and the fractal dimension (FD) to characterize the formation and remodeling of newly formed compact bone within two different polyanionic collagen-elastin matrices. The matrices were implanted in defects created into parietal bones of rats. The SE and FD were calculated for histological images of the experimental groups collected 3, 7, 15, 30, 60, and 365 days postsurgery and for the original bone only at day 365. Results showed that the SE and the FD initially increased and then diminished for all groups from day 3 to day 365 approaching the values of the original bone. These results are consistent with poor tissue organization during early osteogenesis that remodels into an organized lamellar structure, showing that these methods can be valuable tools to describe bone tissue remodeling during the regeneration process of compact bones. PMID:18512741

Rocha, Lenaldo B; Adam, Randall L; Leite, Neucimar J; Metze, Konradin; Rossi, Marcos A

2008-08-01

171

[Ma &etal;, Nat. Mater. 8, 30 (2009)] have uncovered the fractal dimension Df=2.31 associated with the medium-range order in a variety of bulk metallic glasses, reflected in the first sharp diffraction peak q1 determined from neutron and x-ray measurements. Here, based on the proposal in this journal of [Yang &etal;, Appl. Phys. Lett. 88, 221911 (2006)], which related the strength

D. J. Klein; N. H. March; J. A. Alonso

2009-01-01

172

Application of Fractal Dimension to Optimum Deposition of NiCrAlY Coating by D-Gun Spray

NiCrAlY coatings were fabricated by detonation gun (D-gun) spray under several process conditions to examine process optimization. The spray processes were adjusted by altering the composition of the mixed C2H2\\/O2 fuel gas, and a higher fuel temperature was obtained by increasing the ratio of C2H2 to O2 To preduce complexity for process optimization, an attempt to apply fractal dimension (FD)

X. Q. Ma; Y. M. Rhyim; H. W. Jin; C. G. Park; M. C. Kim

1999-01-01

173

Fractal Dimension and Size Scaling of Domains in Thin Films of Multiferroic BiFeO3

Domains in ferroelectric films are usually smooth, stripelike, very thin compared with magnetic ones, and satisfy the Landau-Lifshitz-Kittel scaling law (width proportional to square root of film thickness). However, the ferroelectric domains in very thin films of multiferroic BiFeO3 have irregular domain walls characterized by a roughness exponent 0.5 0.6 and in-plane fractal Hausdorff dimension H||=1.4±0.1, and the domain size

G. Catalan; H. Béa; S. Fusil; M. Bibes; P. Paruch; A. Barthélémy; J. F. Scott

2008-01-01

174

Alzheimer's disease (AD) is an irreversible brain disorder of unknown aetiology that gradually destroys brain cells and represents the most prevalent form of dementia in western countries. The main aim of this study was to analyse the magnetoencephalogram (MEG) background activity from 20 AD patients and 21 elderly control subjects using Higuchi's fractal dimension (HFD). This non-linear measure can be used to estimate the dimensional complexity of biomedical time series. Before the analysis with HFD, the stationarity and the non-linear structure of the signals were proved. Our results showed that MEG signals from AD patients had lower HFD values than control subjects' recordings. We found significant differences between both groups at 71 of the 148 MEG channels (p<0.01; Student's t-test with Bonferroni's correction). Additionally, five brain regions (anterior, central, left lateral, posterior and right lateral) were analysed by means of receiver operating characteristic curves, using a leave-one-out cross-validation procedure. The highest accuracy (87.8%) was achieved when the mean HFD over all channels was analysed. To sum up, our results suggest that spontaneous MEG rhythms are less complex in AD patients than in healthy control subjects, hence indicating an abnormal type of dynamics in AD. PMID:18676171

Gómez, Carlos; Mediavilla, Angela; Hornero, Roberto; Abásolo, Daniel; Fernández, Alberto

2009-04-01

175

The average roughness and fractal dimension of articular cartilage during drying.

Cartilage is a unique material in part because of it biphasic properties. The structure of cartilage is a porous matrix of collagen fibers, permeated with synovial fluid which creates a gliding and near frictionless motion in articulating joints. However, during in vitro testing or surgery, there exists potential for cartilage to dehydrate, or dry out. The effects of this drying can influence experimental results. It is likely that drying also changes joint performance in vivo. In in vitro testing of equine cartilage explants exposed to open air, the average roughness of cartilage changes from 1.85?±?0.78 to 3.66?±?1.41?µm SD in a 5-h period. Significant changes in roughness in individual samples are seen within 10?min of exposure to open air. However, the multi-scale nature of cartilage, characterized by the fractal dimension, does not significantly change during the same period. The current study attempts to quantify the magnitude of error that is introduced when cartilage is removed from its native environment. SCANNING 36:368-375, 2014. © 2013 Wiley Periodicals, Inc. PMID:24173958

Smyth, P A; Rifkin, R; Jackson, R L; Hanson, R R

2014-05-01

176

Gene Entropy-Fractal Dimension Informatics with Application to Mouse-Human Translational Medicine

DNA informatics represented by Shannon entropy and fractal dimension have been used to form 2D maps of related genes in various mammals. The distance between points on these maps for corresponding mRNA sequences in different species is used to study evolution. By quantifying the similarity of genes between species, this distance might be indicated when studies on one species (mouse) would tend to be valid in the other (human). The hypothesis that a small distance from mouse to human could facilitate mouse to human translational medicine success is supported by the studied ESR-1, LMNA, Myc, and RNF4 sequences. ID1 and PLCZ1 have larger separation. The collinearity of displacement vectors is further analyzed with a regression model, and the ID1 result suggests a mouse-chimp-human translational medicine approach. Further inference was found in the tumor suppression gene, p53, with a new hypothesis of including the bovine PKM2 pathways for targeting the glycolysis preference in many types of cancerous cells, consistent with quantum metabolism models. The distance between mRNA and protein coding CDS is proposed as a measure of the pressure associated with noncoding processes. The Y-chromosome DYS14 in fetal micro chimerism that could offer protection from Alzheimer's disease is given as an example.

Holden, T.; Cheung, E.; Dehipawala, S.; Ye, J.; Tremberger, G.; Lieberman, D.; Cheung, T.

2013-01-01

177

The suitability of new dynamic system analysis was investigated to compare postural control in Prader-Willi syndrome (PWS) and Down syndrome (DS) patients. Time-domain, frequency-domain parameters and fractal dimension (FD) of centre of pressure (CoP) were computed in maintaining normal standing on a force platform in 20 DS and 13 PWS patients, compared to 26 obese (obese control group, OCG) and 20 healthy individuals (healthy control group, HCG). DS and PWS showed greater displacements along both directions and longer sway path (SP) parameter than HCG and OCG, with statistical differences between PWS and DS for anteroposterior displacement and SP. DS used higher frequency strategy when compared to PWS, OCG and HCG. Both DS and PWS were characterised by greater values of FD than OCG and HCG, with higher values in DS. The analyses in frequency domain and of the dynamic nature of CoP suggest that DS patients are characterised by a more complex and irregular signal than PWS patients. PMID:23360287

Cimolin, Veronica; Galli, Manuela; Rigoldi, Chiara; Grugni, Graziano; Vismara, Luca; de Souza, Shirley Aparecida Fabris; Mainardi, Luca; Albertini, Giorgio; Capodaglio, Paolo

2014-11-01

178

Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals. PMID:24151522

Fuss, Franz Konstantin

2013-01-01

179

The time-evolutions of nanoparticle hydrodynamic radius and aggregate fractal dimension during the aggregation of fullerene (C(60)) nanoparticles (FNPs) were measured via simultaneous multiangle static and dynamic light scattering. The FNP aggregation behavior was determined as a function of monovalent (NaCl) and divalent (CaCl(2)) electrolyte concentration, and the impact of addition of dissolved natural organic matter (humic acid) to the solution was also investigated. In the absence of humic acid, the fractal dimension decreased over time with monovalent and divalent salts, suggesting that aggregates become slightly more open and less compact as they grow. Although the aggregates become slightly more open, the magnitude of the fractal dimension suggests intermediate aggregation between the diffusion- and reaction-limited regimes. We observed different aggregation behavior with monovalent and divalent salts upon the addition of humic acid to the solution. For NaCl-induced aggregation, the introduction of humic acid significantly suppressed the aggregation rate of FNPs at NaCl concentrations lower than 150mM. In this case, the aggregation was intermediate or reaction-limited even at NaCl concentrations as high as 500mM, giving rise to aggregates with a fractal dimension of 2.0. For CaCl(2)-induced aggregation, the introduction of humic acid enhanced the aggregation of FNPs at CaCl(2) concentrations greater than about 5mM due to calcium complexation and bridging effects. Humic acid also had an impact on the FNP aggregate structure in the presence of CaCl(2), resulting in a fractal dimension of 1.6 for the diffusion-limited aggregation regime. Our results with CaCl(2) indicate that in the presence of humic acid, FNP aggregates have a more open and loose structure than in the absence of humic acid. The aggregation results presented in this paper have important implications for the transport, chemical reactivity, and toxicity of engineered nanoparticles in aquatic environments. PMID:23211871

Meng, Zhiyong; Hashmi, Sara M; Elimelech, Menachem

2013-02-15

180

Generalized Fibonacci Description of Fractal aggregates

NASA Astrophysics Data System (ADS)

We present a theory for calculating the fractal dimension of Diffusion Limited Cluster Aggregates (DLCA) based on cluster shape preservation. The shape is described by a d-dimensional Golden Mean, which is the ratio of consecutive d-dimensional Fibonacci numbers. For d =2 the canonical Fibonacci series is found with the Golden Mean value known since antiquity, phi = 1.618 to yield a fractal dimension of 1.44, in agreement with simulations and experiment. Generalizations to other dimensions are equally successful. Recent computer simulations also yield accurate values for the fractal aggregate prefactor, thus completing the theory.

Sorensen, Chris; Heinson, William; Chakrabarti, Amit

2009-10-01

181

Fractal analysis of engineering ceramics ground surface

NASA Astrophysics Data System (ADS)

Traditional methods of roughness characterization cannot properly reflect the differences between metal and engineering ceramics surfaces. Therefore, fractal method is introduced to characterize the engineering ceramics ground surface in this paper. This article compares various methods to calculate profile dimension. By comparison, the variation method is suitable for extracting fractal dimension of engineering ceramics ground surface. The precision of variation method is further improved by modifying the error. In view of engineering ceramics ground surface, we have analyzed the relationship between fractal dimension and traditional roughness parameters, surface texture, surface function and material property using modified variation method.

Liang, Xiaohu; Lin, Bin; Han, Xuesong; Chen, Shangong

2012-06-01

182

Brain White Matter Shape Changes in Amyotrophic Lateral Sclerosis (ALS): A Fractal Dimension Study

Amyotrophic lateral sclerosis (ALS) is a fatal progressive neurodegenerative disorder. Current diagnosis time is about 12-months due to lack of objective methods. Previous brain white matter voxel based morphometry (VBM) studies in ALS reported inconsistent results. Fractal dimension (FD) has successfully been used to quantify brain WM shape complexity in various neurological disorders and aging, but not yet studied in ALS. Therefore, we investigated WM morphometric changes using FD analyses in ALS patients with different clinical phenotypes. We hypothesized that FD would better capture clinical features of the WM morphometry in different ALS phenotypes than VBM analysis. High resolution MRI T1-weighted images were acquired in controls (n?=?11), and ALS patients (n?=?89). ALS patients were assigned into four subgroups based on their clinical phenotypes.VBM analysis was carried out using SPM8. FD values were estimated for brain WM skeleton, surface and general structure in both controls and ALS patients using our previously published algorithm. No significant VBM WM changes were observed between controls and ALS patients and among the ALS subgroups. In contrast, significant (p<0.05) FD reductions in skeleton and general structure were observed between ALS with dementia and other ALS subgroups. No significant differences in any of the FD measures were observed between control and ALS patients. FD correlated significantly with revised ALS functional rating scale (ALSFRS-R) score a clinical measure of function. Results suggest that brain WM shape complexity is more sensitive to ALS disease process when compared to volumetric VBM analysis and FD changes are dependent on the ALS phenotype. Correlation between FD and clinical measures suggests that FD could potentially serve as a biomarker of ALS pathophysiology, especially after confirmation by longitudinal studies.

Allexandre, Didier; Zhang, Luduan; Wang, Xiao-Feng; Pioro, Erik P.; Yue, Guang H.

2013-01-01

183

Objectives The aim of this study was to (1) evaluate the fractal dimension (FD) in regions of the mandible on cone beam CT (CBCT) images of patients with bisphosphonate-associated osteonecrosis of the jaws (BP-ONJ) and (2) to select the most suitable region of interest (ROI) for further study on detection of bone alterations associated with bisphosphonates. Methods CBCT images of patients with BP-ONJ were included with matched controls. Values of FD were compared between groups. Selected ROIs were: ROI-1 — below the mandibular foramen; ROI-2 — above the mandibular foramen; ROI-3 — anterior to the mental foramen; ROI-4 — above the mandibular canal. The area of bone exposure was included as ROI-5. The results were analysed using generalized estimating equations and conditional logistic regression. Results There were 36 patients (67% female) with a mean age of 60.7 years. The mean FDs were: ROI-1 — 1.678 for controls and 1.673 for patients (P = 0.81); ROI-2 — 1.657 for controls and 1.653 for patients (P = 0.78); ROI-3 — 1.661 for controls and 1.684 for patients (P = 0.17); and ROI-4 — 1.670 for controls and 1.698 for patients (P = 0.03). The value of the FD in the area of exposed bone was the highest (1.729). The odds of being a BP-ONJ patient vs being a control was six times as high for individuals with a higher FD score at ROI-4, although the confidence interval was quite wide owing to the small sample size. Conclusion In this preliminary study, BP-ONJ patients had higher FD values than controls at regions close to the alveolar process. The results suggest that FD is a promising tool for detection of bone alterations associated with BP-ONJ.

Torres, SR; Chen, CSK; Leroux, BG; Lee, PP; Hollender, LG; Schubert, MM

2011-01-01

184

Comparison of different fractal dimension measuring algorithms for RE-TM M-O films

NASA Technical Reports Server (NTRS)

Noise in magneto-optical recording devices is discussed. In general, it appears that either the divider technique or amplitude spectrum technique may be used interchangeably to measure the fractal dimension (D) in the domain wall structure of ideal images. However, some caveats must be observed for best results. The divider technique is attractive for its simplicity and relatively modest computation requirements. However, it is sensitive to noise, in that noise pixels that touch the domain boundary are interpreted as being part of the boundary, skewing the measurement. Also, it is not useful in measuring nucleation-dominated films or domains that have significant amounts of structure within the interior of the domain wall. The amplitude spectrum method is more complex, and less intuitive than the divider method, and somewhat more expensive to implement computationally. However, since the camera noise tends to be white, the noise can be avoided in the measurement of D by avoiding that portion of the curve that is flat (due to the white noise) when the least squares line is fit to the plot. Also, many image processing software packages include a Fast Fourier Transformation (FFT) facility, while the user will most likely have to write his own edge extraction routine for the divider method. The amplitude spectrum method is a true two dimensional technique that probes the interior of the domain wall, and in fact, can measure arbitrary clusters of domains. It can also be used to measure grey-level images, further reducing processing steps needed to threshold the image.

Bernacki, Bruce E.; Mansuripur, M.

1991-01-01

185

The cognitive regulation of emotions is important for human adaptation. Self-focused emotion regulation (ER) strategies have been linked to the development and persistence of anxiety and depression. A vast array of research has provided valuable knowledge about the neural correlates of the use of specific self-focused ER strategies; however, the resting neural correlates of cognitive ER styles, which reflect an individual's disposition to engage in different forms of ER in order to manage distress, are largely unknown. In this study, associations between theoretically negative ER style (self-focused or not) and the complexity (fractal dimension, FD) of the resting EEG at frontal, central, parietal, and occipital regions were investigated in 58 healthy volunteers. The Cognitive Emotion Regulation Questionnaire was used as the self-report measure of ER style. Results showed that a diminished FD over the scalp significantly correlated with self-focused ER style scores, even after controlling for negative affect, which has been also considered to influence the use of ER strategies. The lower the EEG FD, the higher were the self-focused ER style scores. Correlational analyses of specific self-focused ER strategies showed that self-blaming and rumination were negatively associated with diminished FD of the EEG, but catastrophizing and blaming others were not. No significant correlations were found for ER strategies more focused on situation or others. Results are discussed within the self-organized criticality theory of brain dynamics: The diminished FD of the EEG may reflect a disposition to engage in self-focused ER strategies as people prone to ruminate and self-blame show a less complex resting EEG activity, which may make it more difficult for them to exit their negative emotional state. PMID:22519470

Bornas, Xavier; Tortella-Feliu, Miquel; Balle, Maria; Llabrés, Jordi

2013-01-01

186

National Technical Information Service (NTIS)

This paper addresses the question of finding a suitable analogue of Weyl's asymptotic formula for the eigenvalue distribution of Laplacians on (certain classes of self-similar) fractals. We propose, in particular, an analogue of the notion of 'Riemannian ...

M. L. Lapidus

1995-01-01

187

NASA Astrophysics Data System (ADS)

In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe in Japan, Merapi in Indonesia. Preliminary results reveal that the fractal dimension of natural areas, being related only to the roughness of the observed surface, is very stable as the radar illumination geometry, the resolution and the wavelength change, thus holding a very unique property in SAR data inversion. Such a behavior is not verified in case of non-natural objects. As a matter of fact, when the fractal estimation is performed in the presence of either man-made objects or SAR image features depending on geometrical distortions due to the SAR system acquisition (i.e. layover, shadowing), fractal dimension (D) values outside the range of fractality of natural surfaces (2 < D < 3) are retrieved. These non-fractal characteristics show to be heavily dependent on sensor acquisition parameters (e.g. view angle, resolution). In this work, the behaviour of the maps generated starting from the C- and X- band SAR data, relevant to all the considered volcanoes, is analyzed: the distribution of the obtained fractal dimension values is investigated on different zones of the maps. In particular, it is verified that the fore-slope and back-slope areas of the image share a very similar fractal dimension distribution that is placed around the mean value of D=2.3. We conclude that, in this context, the fractal dimension could be considered as a signature of the identification of the volcano growth as a natural process. The COSMO-SkyMed data used in this study have been processed at IREA-CNR within the SAR4Volcanoes project under Italian Space Agency agreement n. I/034/11/0.

Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.

2012-04-01

188

Building Fractal Models with Manipulatives.

ERIC Educational Resources Information Center

Uses manipulative materials to build and examine geometric models that simulate the self-similarity properties of fractals. Examples are discussed in two dimensions, three dimensions, and the fractal dimension. Discusses how models can be misleading. (Contains 10 references.) (MDH)

Coes, Loring

1993-01-01

189

NASA Astrophysics Data System (ADS)

Clogging is an important limitation to essentially any technology or environmental process involving flow in porous media. Examples include (1) groundwater remediation, (2) managed or natural aquifer recharge, (3) hydrocarbon reservoir damage, (4) head loss in water treatment filters, (5) fouling in porous media reactors, and (6) nutrient flow for plants or bacteria. Clogging, that is, a detrimental reduction in permeability, is a common theme in each of these examples. Clogging results from a number of mechanisms, including deposition of colloidal particles (such as clay minerals), which is the focus of this research. Colloid deposits reduce porosity, which is recognized to play an important role in clogging, as expressed in the Kozeny-Carman equation. However, recent research has demonstrated that colloid deposit morphology is also a crucial variable in the clogging process. Accordingly, this presentation reports an ongoing series of laboratory experiments whose goal is to quantify deposit morphology as a fractal dimension, using an innovative technique based on static light scattering (SLS) in refractive index matched (RIM) porous media. For experiments conducted at constant flow, with constant influent suspension concentration, and initially clean porous media, results indicate that clogging is associated with colloid deposits having smaller fractal dimensions, that is, more dendritic and space-filling deposits. This result is consistent with previous research that quantified colloid deposit morphology using an empirical parameter. Clogging by colloid deposits also provides insight into the more complex clogging mechanisms of bioclogging, mineralization, and biomineralization. Although this line of work was originally motivated by problems of clogging in groundwater remediation, the methods used and the insight gained by correlating clogging with fractal dimension are expected to have relevance to other areas where flow in porous media overlaps with colloid science: Hydrogeology, petrology, water treatment, and chemical engineering.

Roth, E. J.; Mays, D. C.

2013-12-01

190

The use of fractal for prediction of burning rate of composite solid propellants

By using the fractal geometry it is possible to calculate the actual AP (Ammonium Perchlorate) surface area and oxidizer-binder\\u000a interface fractal dimension in the prediction of burning rate of composite solid propellants. In this investigation, the fractal\\u000a dimension was determined by a procedure known as the “Box Counting Method”. Using this dimension, surface area relations were\\u000a developed for the rough

Manouchehr Nikazar; Mohammad B. Bagherpour; Bahram Dabir

2000-01-01

191

Fractal-based image processing for mine detection

NASA Astrophysics Data System (ADS)

A fractal-based analysis algorithm has been developed to perform the task of automated recognition of minelike targets in side scan sonar images. Because naturally occurring surfaces, such as the sea bottom, are characterized by irregular textures they are well suited to modeling as fractal surfaces. Manmade structures, including mines, are composed of Euclidean shapes, which makes fractal-based analysis highly appropriate for discrimination of mines from a natural background. To that end, a set of fractal features, including fractal dimension, was developed to classify image areas as minelike targets, nonmine areas, or clutter. Four different methods of fractal dimension calculation were compared and the Weierstrass function was used to study the effect of various signal processing procedures on the fractal qualities of an image. The difference in fractal dimension between different images depends not only on the physical features extant in the images but in the underlying statistical characteristics of the processing procedures applied to the images and the underlying mathematical assumptions of the fractal dimension calculation methods. For the image set studied, fractal-based analysis achieved a classification rate similar to human operators, and was very successful in identifying areas of clutter. The analysis technique presented here is applicable to any type of signal that may be configured as an image, making this technique suitable for multisensor systems.

Nelson, Susan R.; Tuovila, Susan M.

1995-06-01

192

Fractal dimension of chromatin is an independent prognostic factor for survival in melanoma

BACKGROUND: Prognostic factors in malignant melanoma are currently based on clinical data and morphologic examination. Other prognostic features, however, which are not yet used in daily practice, might add important information and thus improve prognosis, treatment, and survival. Therefore a search for new markers is desirable. Previous studies have demonstrated that fractal characteristics of nuclear chromatin are of prognostic importance

Valcinir Bedin; Randall L Adam; Bianca CS de Sá; Gilles Landman; Konradin Metze

2010-01-01

193

On techniques for the measurement of the mass fractal dimension of aggregates

A review is presented of a number of techniques available for the characterisation of the structure of aggregates formed from suspensions of sub-micron particles. Amongst the experimental techniques that have been commonly used are scattering (light, X-ray or neutron), settling and imaging and these are the focus of this work. The theoretical basis for the application of fractal geometry to

G. C. Bushell; Y. D. Yan; D. Woodfield; J. Raper; R. Amal

2002-01-01

194

Shape Analysis of Breast Masses in Mammograms via the Fractal Dimension

Masses due to benign breast diseases and tumors due to breast cancer present significantly different shapes on mammograms. In general, malignant tumors appear with rough and complex boundaries or contours, whereas benign masses present smooth, round, or oval contours. Fractal analysis may be used to derive shape features to perform pattern classification of breast masses and tumors. Several procedures have

Thanh M. Nguyen; Rangaraj M. Rangayyan

2005-01-01

195

Effect of fractal dimension on drug permeation through porous ethylcellulose films

Fractal geometry was applied to quantify the complexity of an internal structure of a porous film prepared with ethylcellulose (EC) and diethylphthalate (DEP) as a plasticizer. EC was dissolved together with DEP in a water–ethanol mixture solution, and then evaporated on Teflon petri dishes in order to make porous EC films. Boundary lines of the porous structures in the EC

Shogo Yamane; Kozo Takayama; Tsuneji Nagai

1998-01-01

196

Chromatin is a major nuclear component, and it is an active matter of debate to understand its different levels of spatial organization, as well as its implication in gene regulation. Measurements of nuclear chromatin compaction were recently used to understand how DNA is folded inside the nucleus and to detect cellular dysfunctions such as cancer. Super-resolution imaging opens new possibilities to measure chromatin organization in situ. Here, we performed a direct measure of chromatin compaction at the single cell level. We used histone H2B, one of the 4 core histone proteins forming the nucleosome, as a chromatin density marker. Using photoactivation localization microscopy (PALM) and adaptive optics, we measured the three-dimensional distribution of H2B with nanometric resolution. We computed the distribution of distances between every two points of the chromatin structure, namely the Ripley K(r) distribution. We found that the K(r) distribution of H2B followed a power law, leading to a precise measurement of the correlation fractal dimension of chromatin of 2.7. Moreover, using photoactivable GFP fused to H2B, we observed dynamic evolution of chromatin sub-regions compaction. As a result, the correlation fractal dimension of chromatin reported here can be interpreted as a dynamically maintained non-equilibrium state. PMID:24637833

Récamier, Vincent; Izeddin, Ignacio; Bosanac, Lana; Dahan, Maxime; Proux, Florence; Darzacq, Xavier

2014-01-01

197

Comprehensive Fractal Description of Porosity of Coal of Different Ranks

We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to 10?nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to 100?nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between 2.03?nm and 361.14?nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of 10?nm and 100?nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure.

Ren, Jiangang; Zhang, Guocheng; Song, Zhimin; Liu, Gaofeng; Li, Bing

2014-01-01

198

Diffraction by fractally serrated apertures

NASA Technical Reports Server (NTRS)

An investigation of light diffracted by irregularly serrated apertures yields a closed-form analytical solution that confirms experimental recording of the diffracted patterns. These serrated apertures are modeled by a fractal function. Examples are given for both sinusoidal and fractal aperture perimeters with varying fractal dimension. Relations between the far-zone diffracted fields and the fractal dimension are examined.

Kim, Y.; Grebel, H.; Jaggard, D. L.

1991-01-01

199

NASA Astrophysics Data System (ADS)

The advent of vascular diseases, such as hypertension and atherosclerosis, is associated to significant alterations in the physical properties of arterial vessels. Evaluation of arterial biomechanical behaviour is related to the assessment of three representative indices: arterial compliance, arterial distensibility and arterial stiffness index. Elasticity is the most important mechanical property of the arterial wall, whose natures is strictly non-linear. Intervention of elastin and collagen fibres, passive constituent elements of the arterial wall, is related to the applied wall stress level. Concerning this, appropriate tools are required to analyse the temporal dynamics of the signals involved, in order to characterize the whole phenomenon. Fractal geometry can be mentioned as one of those techniques. The aim of this study consisted on arterial pressure and diameter signals processing, by means of nonlinear techniques based on fractal geometry. Time series morphology was related to different arterial stiffness states, generated by means of blood flow variations, during experiences performed in vitro.

Cymberknop, L.; Legnani, W.; Pessana, F.; Bia, D.; Zócalo, Y.; Armentano, R. L.

2011-12-01

200

The Fractal Dimension as a Measure of the Quality of Habitats

Habitat fragmentation produces isolated patches characterized by increased edge effects from an originally continuous habitat.\\u000a The shapes of these patches often show a high degree of irregularity: their shapes deviate significantly from regular geometrical\\u000a shapes such as rectangular and elliptical ones. In fractal theory, the geometry of patches created by a common landscape transformation\\u000a process should be statistically similar, i.e.

A. R. Imre; J. Bogaert

2004-01-01

201

There are persistent difficulties in monitoring nonpoint source pollution and in the related field of hydrology. The problems stem from variations in spatial distribution which are poorly understood and difficult to model with established methods. Two recent developments may offer a solution, if they are combined with care. The first development is the increasing capability of computer mapping, called geographic information systems (GIS). These systems can store, retrieve, and manipulate data with an explicit spatial structure. The second development is the field of fractal mathematics. Fractal mathematics includes geometric sets which have simple descriptions, despite complex appearances. One family of such fractal sets are the Brownian surfaces, which capture many of the qualities of natural land surfaces in a simple statistical model. Up until now, the Brownian models have been constrained by the assumption that the same statistical relationship holds over the entire surface. This is called the constraint of stationarity. The need to study how the landscape differs by location leads to relaxing the constraint of stationarity. This, in turn, causes some profound changes in the model. A special computer program applies the new model to a set of three-dimensional digital maps of natural terrain (DEMs). The model performs well, and highlights differences in landforms. This suggests several new approaches to spatial variation.

Wagenseil, R.

1991-01-01

202

Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions

A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/r{sup D}propor tor{sup -D} where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A 'box-counting' procedure could also be applied giving the 'capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term 'fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis.The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are: - Simple way to quantify scale-invariant distributions of complex objects or phenomena by a small number of parameters. - It is becoming evident that the applicability of fractal distributions to geological problems could have a more fundamental basis. Chaotic behaviour could underlay the geotectonic processes and the applicable statistics could often be fractal.The application of fractal distribution analysis has, however, some specific aspects. It is usually difficult to present an adequate interpretation of the obtained values of fractal coefficients for earthquake epicenter or hypocenter distributions. That is why in this paper we aimed at other goals - to verify how a fractal coefficient depends on different spatial distributions. We simulated earthquake spatial data by generating randomly points first in a 3D space - cube, then in a parallelepiped, diminishing one of its sides. We then continued this procedure in 2D and 1D space. For each simulated data set we calculated the points' fractal coefficient (correlation fractal dimension of epicentres) and then checked for correlation between the coefficients values and the type of spatial distribution.In that way one can obtain a set of standard fractal coefficients' values for varying spatial distributions. These then can be used when real earthquake data is analyzed by comparing the real data coefficients values to the standard fractal coefficients. Such an approach can help in interpreting the fractal analysis results through different types of spatial distributions.

Gospodinov, Dragomir [Plovdiv University 'Paisii Hilendarski', 24, Tsar Asen Str., Plovdiv (Bulgaria); Geophysical Institute of Bulgarian Academy of Sciences, Akad. G. Bonchev Str., bl.3, Sofia (Bulgaria); Marekova, Elisaveta; Marinov, Alexander [Plovdiv University 'Paisii Hilendarski', 24, Tsar Asen Str., Plovdiv (Bulgaria)

2010-01-21

203

The neovascularisation formation and regression process of the peripheral retina in diabetic retinopathy was studied by means of fractal analysis. The fractal dimension of the local retinal vessel pattern was calculated to be significantly lower before formation of relevant neovascularisations than 2.5 years later, after formation of strong preretinal neovascularisations. Another year later the new vessels had regressed partially and the fractal dimension was again significantly reduced. This behaviour is almost independent of the representation of the vessel thickness during calculation. Since the retinal vasculature is a fractal, the fractal dimension appears as the "natural" measure of proliferative retinal vessel changes. It is demonstrated that the fractal dimension can be applied to characterise proliferative diabetic retinopathy. These features offer the possibility for computer-driven ("automated") quantitative characterisation of the treatment effect in proliferative diabetic retinopathy and possibly automated detection of proliferative diabetic retinopathy in the future. The limitations of the method are discussed. PMID:8299974

Daxer, A

1993-12-01

204

The degree of irregularity in oceanic coastlines and in vertical sections of the Earth, the distribution of the numbers of islands according to area, and the commonality of global shape between continents and islands, all suggest that the Earth's surface is statistically self-similar. The preferred parameter, one which increases with the degree of irregularity, is the fractal dimension, D, of

Benoit B. Mandelbrot

1975-01-01

205

A fractal analysis of quaternary, Cenozoic-Mesozoic, and Late Pennsylvanian sea level changes

NASA Technical Reports Server (NTRS)

Sea level changes are related to both climatic variations and tectonic movements. The fractal dimensions of several sea level curves were compared to a modern climatic fractal dimension of 1.26 established for annual precipitation records. A similar fractal dimension (1.22) based on delta(O-18/O-16) in deep-sea sediments has been suggested to characterize climatic change during the past 2 m.y. Our analysis indicates that sea level changes over the past 150,000 to 250,000 years also exhibit comparable fractal dimensions. Sea level changes for periods longer than about 30 m.y. are found to produce fractal dimensions closer to unity and Missourian (Late Pennsylvanian) sea level changes yield a fractal dimension of 1.41. The fact that these sea level curves all possess fractal dimensions less than 1.5 indicates that sea level changes exhibit nonperiodic, long-run persistence. The different fractal dimensions calculated for the various time periods could be the result of a characteristic overprinting of the sediment recored by prevailing processes during deposition. For example, during the Quaternary, glacio-eustatic sea level changes correlate well with the present climatic signature. During the Missourian, however, mechanisms such as plate reorganization may have dominated, resulting in a significantly different fractal dimension.

Hsui, Albert T.; Rust, Kelly A.; Klein, George D.

1993-01-01

206

Fresnel diffraction of fractal grating and self-imaging effect.

Based on the self-similarity property of fractal, two types of fractal gratings are produced according to the production and addition operations of multiple periodic gratings. Fresnel diffractions of fractal grating are analyzed theoretically, and the general mathematic expressions of the diffraction intensity distributions of fractal grating are deduced. The gray-scale patterns of the 2D diffraction distributions of fractal grating are provided through numerical calculations. The diffraction patterns take on the periodicity along the longitude and transverse directions. The 1D diffraction distribution at some certain distances shows the same structure as the fractal grating. This indicates that the self-image of fractal grating is really formed in the Fresnel diffraction region. The experimental measurement of the diffraction intensity distribution of fractal grating with different fractal dimensions and different fractal levels is performed, and the self-images of fractal grating are obtained successfully in experiments. The conclusions of this paper are helpful for the development of the application of fractal grating. PMID:24787168

Wang, Junhong; Zhang, Wei; Cui, Yuwei; Teng, Shuyun

2014-04-01

207

Fault diagnosis of diesel engine based on adaptive wavelet packets and EEMD-fractal dimension

NASA Astrophysics Data System (ADS)

In this paper a novel method for de-noising nonstationary vibration signal and diagnosing diesel engine faults is presented. The method is based on the adaptive wavelet threshold (AWT) de-noising, ensemble empirical mode decomposition (EEMD) and correlation dimension (CD). A new adaptive wavelet packet (WP) thresholding function for vibration signal de-noising is used in this paper. To alleviate the mode mixing problem occurring in EMD, ensemble empirical mode decomposition (EEMD) is presented. With EEMD, the components with truly physical meaning can be extracted from the signal. Utilizing the advantage of EEMD, this paper proposes a new AWT-EEMD-based method for fault diagnosis of diesel engine. A study of correlation dimension in engine condition monitoring is reported also. Some important influencing factors relating directly to the computational precision of correlation dimension are discussed. Industrial engine normal and fault vibration signals measured from different operating conditions are analyzed using the above method.

Wang, Xia; Liu, Changwen; Bi, Fengrong; Bi, Xiaoyang; Shao, Kang

2013-12-01

208

Fractal analysis of high-resolution CT images as a tool for quantification of lung diseases

NASA Astrophysics Data System (ADS)

Fractal geometry is increasingly being used to model complex naturally occurring phenomena. There are two types of fractals in nature-geometric fractals and stochastic fractals. The pulmonary branching structure is a geometric fractal and the intensity of its grey scale image is a stochastic fractal. In this paper, we attempt to quantify the texture of CT lung images using properties of both types of fractals. A simple algorithm for detection of abnormality in human lungs, based on 2D and 3D fractal dimensions, is presented. This method involves calculating the local fractal dimensions, based on intensities, in the 2D slice to aid enhancement. Following this, grey level thresholding is performed and a global fractal dimension, based on structure, for the entire data is estimated in 2D and 3D. High resolution CT images of normal and abnormal lungs were analyzed. Preliminary results showed that classification of normal and abnormal images could be obtained based on the differences between their global fractal dimensions.

Uppaluri, Renuka; Mitsa, Theophano; Galvin, Jeffrey R.

1995-05-01

209

Fractal Spectrum Technique for Quantitative Analysis of Volcanic Particle Shapes

NASA Astrophysics Data System (ADS)

The shapes of volcanic particles reflect numerous eruptive parameters (e.g. magma viscosity, volatile content, degree of interaction with water) and are useful for understanding fragmentation and transport processes associated with volcanic eruptions. However, quantitative analysis of volcanic particle shapes has proven difficult due to their morphological complexity and variability. Shape analysis based on fractal geometry has been successfully applied to a wide variety of particles and appears to be well suited for describing complex features. The technique developed and applied to volcanic particles in this study uses fractal data produced by dilation of the 2-D particle boundary to produce a full spectrum of fractal dimensions over a range of scales for each particle. Multiple fractal dimensions, which can be described as a fractal spectrum curve, are calculated by taking the first derivative of data points on a standard Richardson plot. Quantitative comparisons are carried out using multivariate statistical techniques such as cluster and principal components analysis. Compared with previous fractal methods that express shape in terms of only one or two fractal dimensions, use of multiple fractal dimensions results in more effective discrimination between samples. In addition, the technique eliminates the subjectivity associated with selecting linear segments on Richardson plots for fractal dimension calculation, and allows direct comparison of particles as long as instantaneous dimensions used as input to multivariate analyses are selected at the same scales for each particle. Applications to samples from well documented eruptions (e.g. Mt. St. Helens, Tambora, Surtsey) indicate that the fractal spectrum technique provides a useful means of characterizing volcanic particles and can be helpful for identifying the products of specific fragmentation processes (volatile exsolution, phreatomagmatic, quench granulation) and modes of volcanic deposition (tephra fall, pyroclastic flow, blast/surge).

Maria, A. H.; Carey, S. N.

2001-12-01

210

NASA Astrophysics Data System (ADS)

The Basin and Range fault blocks, which were formed by an extensional event around 17 Ma, have continuously been deforming by younger, diachronous system of cross normal faults in southwest Montana and southeastern Idaho since 16.6 Ma. Reactivation of these two mid-Tertiary-Quaternary systems of normal faults, and two older, approximately N-S and E-W sets of regional normal faults, has evolved into a seismically active block faulted terrain. For both fault systems, high fractal dimensions occur in areas characterized by a large number of fault traces, high fault trace linear density, and maximum fault trace azimuthal variation. The major axis of the anisotropy ellipse of the fractal dimensions for each set of the two normal fault systems is sub-perpendicular to the linear directional mean of the faults, and gives an estimate for the direction of extension.

Davarpanah, Armita; Babaie, Hassan A.

2013-11-01

211

FRACTAL DIMENSION ANALYSIS OF KINETIC FEATURE MAPS IN BREAST DYNAMIC CONTRAST-ENHANCED MRI

Information and correlation dimension methods were retrospectively applied to the task of binary lesion classification on a database of 181 breast lesions visible in breast dynamic contrast-enhanced magnetic resonance imaging (DCE-MRI). Prior to this study, all 181 lesions were biopsied and classified as benign or malignant at histological examina- tion. Initially, the DCE-MRI data were used to obtain a kinetic

JEREMY BANCROFT BROWN

212

In this paper, Ni-Co compositional coatings were electrodeposited by brush-plating and the surface topography images were obtained with the help of scanning electron microscope. The surface topography of Ni-Co coating and the Co element in Ni-Co alloy coating were changed by changing the proportion of Co in plating solution. The fractal dimensions of the surface topography of Ni-Co coating with

Yucai Dong; Tianyuan Jiang; Ling Zhang; Lianghai Yi; Min Lin; Hongtao Shi

2011-01-01

213

Background The evaluation of intestinal trophism, mainly the mucosal layer, is an important issue in various conditions associated with injury, atrophy, recovery, and healing of the gut. The aim of the present study was to evaluate the kinetics of the proliferation and apoptosis of enterocytes by immunohistochemistry and to assess the complexity of intestinal mucosa by fractal dimension (FD) analysis in Solea solea fed different experimental diets. Results Histomorphological evaluation of all intestinal segments did not show signs of degeneration or inflammation. Cell proliferation index and FD were significantly reduced with a diet high in mussel meal (MM; p?=?0.0034 and p?=?0.01063, respectively), while apoptotic index did not show any significant difference for the same comparison (p?=?0.3859). Linear regression analysis between apoptotic index (independent variable) and FD (dependent variable) showed a statistically significant inverse relationship (p?=?0.002528). Linear regression analysis between cell proliferation index (independent variable) and FD (dependent variable) did not show any significant correlation (p?=?0.131582). Conclusions The results demonstrated that diets containing increasing levels of mussel meal in substitution of fishmeal did not incite a hyperplastic response of the intestinal mucosa. The mussel meal, which is derived from molluscs, could mimic the characteristics of the sole’s natural prey, being readily digestible, even without increasing the absorptive surface of intestinal mucosa. Interestingly, from this study emerged that FD could be used as a numeric indicator complementary to in situ quantification methods to measure intestinal trophism, in conjunction with functional parameters.

2014-01-01

214

NASA Astrophysics Data System (ADS)

Lipase B from Candida Antarctica (also known as Candida antarctica lipase B or CALB) was immobilized onto titanium dioxide (TiO 2) in a buffer-free, bidistilled aqueous medium. The adsorption isotherm was determined by UV-vis analysis of supernatant solution at 280 nm, revealing that in 7 h 98% of the theoretical lipase monolayer on the TiO 2 (with 45.7 m 2/g BET area) was achieved. Samples withdrawn from the supernatant immobilization medium were analyzed by Fourier-transform infrared spectroscopy in the 1700-1600 cm -1 range (where the Amide I Proteins band appears) in order to obtain quantitative information on the evolution of the secondary-structure elements of the protein. The analysis performed revealed that lipase conformation suffers only minor changes during its adsorption onto TiO 2. However, water associated to the lipase may interact of several ways with the surface of the hydrated oxide. Characterization of the immobilized biocatalyst (CALB/TiO 2) implied SEM, fractal dimension analysis and FTIR techniques. A proposal of lipase-hydrated oxide interaction is presented.

Foresti, M. L.; Valle, G.; Bonetto, R.; Ferreira, M. L.; Briand, L. E.

2010-01-01

215

Fractal dimension analysis (FDA) is modern mathematical method widely used to describing of complex and chaotic shapes when classic methods fail. The main aim of this study was evaluating the influence of photodynamic therapy (PDT) with cystein proteases inhibitors (CPI) on the number and morphology of blood vessels inside tumor and on increase of effectiveness of combined therapy in contrast to PDT and CPI used separately. Animals were divided into four groups: control, treated using only PDT, treated using only CPI and treated using combined therapy, PDT and CPI. Results showed that time of animal survival and depth of necrosis inside tumor were significantly higher in CPI+PDT group in contrast to other groups. The higher value of fractal dimension (FD) was observed in control group, while the lowest value was found in the group which was treated by cystein protease inhibitors. The differences between FD were observed in CPI group and PDT+CPI group in comparison to control group. Our results revealed that fractal dimension analysis is a very useful tool in estimating differences between irregular shapes like blood vessels in PDT treated tumors. Thus, the implementation of FDA algorithms could be useful method in evaluating the efficacy of PDT.

Jurczyszyn, Kamil; Osiecka, Beata J.; Ziolkowski, Piotr

2012-01-01

216

Context: Several studies have investigated the fractal and multifractal nature of magnetic features in the solar photosphere and its variation with the solar magnetic activity cycle. Aims: Here we extend those studies by examining the fractal geometry of bright magnetic features at higher atmospheric levels, specifically in the solar chromosphere. We analyze structures identified in CaIIK images obtained with the

S. Criscuoli; M. P. Rast; I. Ermolli; M. Centrone

2007-01-01

217

NASA Astrophysics Data System (ADS)

We have studied using the KLUN sample of 5171 spiral galaxies having Tully-Fisher distance moduli, the average radial space distribution of galaxies out to a distance of about 200 Mpc (for H_0=50 km s(-1) Mpc(-1) ). One motivation came from the debate on the fractal dimension mathcal {D} and maximum fractality scale lambda_max of the large-scale galaxy distribution (Davis 1997, Guzzo 1997, Pietronero et al. 1997). A specific recent study is the 3-dimensional correlation analysis of the all-sky LEDA data base by Di Nella et al. (1996) who concluded that the galaxy distribution is fractal up to scales of at least 300 Mpc, with fractal dimension ~ 2.2. One would expect to see a signal of this result in the radial space distribution of the all-sky KLUN sample. We have studied this question with a new method based on photometric TF distances, independent of redshift, to construct the number density distribution. Our main results are: While scattered below about 20 Mpc, at larger distances the radial distribution starts to follow, in terms of distance modulus mu_TF , the law log {N} = (0.46 +/- 0.01) mu + const., using diameter TF relation, and log {N} = (0.40 +/- 0.01) mu + const. for magnitudes. These are the predictions based on fractal dimensions 2.3 and 2.0, respectively. These radial density gradients are valid up to the limits of KLUN, or about 200 Mpc. We have tried to understand the derived radial density behaviour as a result of some bias in KLUN or our analysis, however, without success. Numerical simulations have shown that the method itself works, though it somewhat underestimates the radial distribution exponent. If the density law is caused by incompleteness in the diameter limited KLUN sample, then the incompleteness should start at widely different angular diameters d25 for different values of rotation parameter log {V_M, which would be quite unexpected. On the other hand, if the derived distribution is correct, the completeness is good down to d25 = 1'.6, as originally intended and previously concluded. If correlation studies favoring long scale fractality (200 Mpc or more) and mathcal {D} ~ 2 are correct, the position of our Galaxy would be close to average in the Universe, with the galaxy density decreasing around us according to the expected law (Mandelbrot 1982).

Teerikorpi, P.; Hanski, M.; Theureau, G.; Baryshev, Yu.; Paturel, G.; Bottinelli, L.; Gouguenheim, L.

1998-06-01

218

Recent advances in dynamic elastography and biorheology have revealed that the complex shear modulus, G*, of various biological soft tissues obeys a frequency-dependent powerlaw. This viscoelastic powerlaw behavior implies that mechanical properties are communicated in tissue across the continuum of scales from microscopic to macroscopic. For deriving constitutive constants from the dispersion of G* in a biological tissue, a hierarchical fractal model is introduced that accounts for multiscale networks. Effective-media powerlaw constants are derived by a constitutive law based on cross-linked viscoelastic clusters embedded in a rigid environment. The spatial variation of G* is considered at each level of hierarchy by an iterative coarse-graining procedure. The establishment of cross-links in this model network is associated with an increasing fractal dimension and an increasing viscoelastic powerlaw exponent. This fundamental relationship between shear modulus dynamics and fractal dimension of the mechanical network in tissue is experimentally reproduced in phantoms by applying shear oscillatory rheometry to layers of tangled paper strips embedded in agarose gel. Both model and experiments demonstrate the sensitivity of G* to the density of the mechanical network in tissue, corroborating disease-related alterations of the viscoelastic powerlaw exponent in human parenchyma demonstrated by in vivo elastography. PMID:22674184

Posnansky, Oleg; Guo, Jing; Hirsch, Sebastian; Papazoglou, Sebastian; Braun, Jürgen; Sack, Ingolf

2012-06-21

219

Obtaining soluble proteins in sufficient concentrations is a major obstacle in various experimental studies. How to predict the propensity of targets in large-scale proteomics projects to be soluble is a significant but not fairly resolved scientific problem. Chaos game representation (CGR) can investigate the patterns hiding in protein sequences, and can visually reveal previously unknown structure. Fractal dimensions are good tools to measure sizes of complex, highly irregular geometric objects. In this paper, we convert each protein sequence into a high-dimensional vector by CGR algorithm and fractal dimension, and then predict protein solubility by these fractal features together with Chou's pseudo amino acid composition features and support vector machine (SVM). We extract and study six groups of features computed directly from the primary sequence, and each group is evaluated by the 10-fold cross-validation test. As the results of comparisons, the group of 445-dimensional vector gets the best results, the average accuracy is 0.8741 and average MCC is 0.7358. The resulting predictor is also compared with existing methods and shows significant improvement. PMID:22486614

Niu, Xiao-Hui; Hu, Xue-Hai; Shi, Feng; Xia, Jing-Bo

2012-09-01

220

NASA Astrophysics Data System (ADS)

The interface between air and a rectangular block of sulphur hexafluoride (SF6), impulsively accelerated by the passage of a planar shock wave, undergoes Richtmyer-Meshkov instability and the flow becomes turbulent. The evolution of the interface was previously simulated using a multi-component model based on a thermodynamically consistent and fully conservative formulation and results were validated against available experimental data (Bates et al. Richtmyer-Meshkov instability induced by the interaction of a shock wave with a rectangular block of SF6, Phys Fluids, 2007; 19:036101). In this study, the CFD results are analyzed using the fractal theory approach and the evolution of fractal dimension of the interface during the transition of the flow into fully developed turbulence is measured using the standard box-counting method. It is shown that as the Richtmyer-Meshkov instability on the interface develops and the flow becomes turbulent, the fractal dimension of the interface increases asymptotically toward a value close to 1.39, which agrees well to those measured for classical shear and fully developed turbulences.

Ng, Hoi Dick; Abderrahmane, Hamid Ait; Bates, Kevin R.; Nikiforakis, Nikos

2011-11-01

221

Application of fractal analysis to mammography

We report on a morphological study of 192 breast masses as seen in mammograms, with the aim of discrimination between benign masses and malignant tumors. From the contour of each mass, we computed the fractal dimension (FD) and a few shape factors, including compactness, fractional concavity, and spiculation index. We calculated FD using four different methods: the ruler and box-counting

Grazia Raguso; Antonietta Ancona; Loredana Chieppa; Samuela L'Abbate; Maria Luisa Pepe; Fabio Mangieri; Miriam De Palo; Rangaraj M. Rangayyan

2010-01-01

222

Several studies have investigated the fractal and multifractal nature of\\u000amagnetic features in the solar photosphere and its variation with the solar\\u000amagnetic activity cycle. Here we extend those studies by examining the fractal\\u000ageometry of bright magnetic features at higher atmospheric levels, specifically\\u000ain the solar chromosphere. We analyze structures identified in CaIIK images\\u000aobtained with the Precision Solar

Serena Criscuoli; Mark Rast; Ilaria Ermolli; Mauro Centrone

2006-01-01

223

Small-angle X-ray scattering (SAXS) was used to characterize the bacteriophage ? N protein, a 107 residue intrinsically disordered protein (IDP) that functions as a transcriptional antitermination factor. The SAXS data were used to estimate both the average radius of gyration and the fractal dimension, a measure of the protein's internal scaling properties, under a variety of solution conditions. In the absence of denaturants, the radius of gyration was 38 ± 3.5 Å and the fractal dimension was 1.76 ± 0.05, slightly larger than the value predicted for a well-solvated polymer with excluded volume (1.7). Neither the radius of gyration nor the fractal dimension changed significantly on the addition of urea, further indicating that the protein is extensively unfolded and well solvated in the absence of denaturant. The addition of NaCl or D2O was found to promote aggregation, but did not appear to affect the properties of the monomeric form. The experimental SAXS profiles were also compared with those predicted by a computational model for a random-coil polypeptide, with an adjustable solvation energy term. The experimental data were well fit to the model with the solvation energy close to zero. These results indicate that the ? N protein is among the more expanded members of the broad class of IDPs, most likely because of its high content of charged residues and a large net charge (+15 at neutral pH). The expanded nature of the conformational ensemble may play a role in facilitating the interactions of the protein with other components of the dynamic transcriptional complex.

Johansen, Daniel; Trewhella, Jill; Goldenberg, David P

2011-01-01

224

Eternal fractal in the universe

Models of eternal inflation predict a stochastic self-similar geometry of the universe at very large scales and allow the existence of points that never thermalize. I explore the fractal geometry of the resulting spacetime, using coordinate-independent quantities. The formalism of stochastic inflation can be used to obtain the fractal dimension of the set of eternally inflating points (the ``eternal fractal'').

Serge Winitzki

2002-01-01

225

NASA Astrophysics Data System (ADS)

The interaction of the thermally induced stress field of the Yellowstone hotspot (YHS) with existing Basin and Range (BR) fault blocks, over the past 17 m.y., has produced a new, spatially and temporally variable system of normal faults around the Snake River Plain (SRP) in Idaho and Wyoming-Montana area. Data about the trace of these new cross faults (CF) and older BR normal faults were acquired from a combination of satellite imageries, DEM, and USGS geological maps and databases at scales of 1:24,000, 1:100,000, 1:250,000, 1:1000, 000, and 1:2,500, 000, and classified based on their azimuth in ArcGIS 10. The box-counting fractal dimension (Db) of the BR fault traces, determined applying the Benoit software, and the anisotropy intensity (ellipticity) of the fractal dimensions, measured with the modified Cantor dust method applying the AMOCADO software, were measured in two large spatial domains (I and II). The Db and anisotropy of the cross faults were studied in five temporal domains (T1-T5) classified based on the geologic age of successive eruptive centers (12 Ma to recent) of the YHS along the eastern SRP. The fractal anisotropy of the CF system in each temporal domain was also spatially determined in the southern part (domain S1), central part (domain S2), and northern part (domain S3) of the SRP. Line (fault trace) density maps for the BR and CF polylines reveal a higher linear density (trace length per unit area) for the BR traces in the spatial domain I, and a higher linear density of the CF traces around the present Yellowstone National Park (S1T5) where most of the seismically active faults are located. Our spatio-temporal analysis reveals that the fractal dimension of the BR system in domain I (Db=1.423) is greater than that in domain II (Db=1.307). It also shows that the anisotropy of the fractal dimension in domain I is less eccentric (axial ratio: 1.242) than that in domain II (1.355), probably reflecting the greater variation in the trend of the BR system in domain I. The CF system in the S1T5 domain has the highest fractal dimension (Db=1.37) and the lowest anisotropy eccentricity (1.23) among the five temporal domains. These values positively correlate with the observed maxima on the fault trace density maps. The major axis of the anisotropy ellipses is consistently perpendicular to the average trend of the normal fault system in each domain, and therefore approximates the orientation of extension for normal faulting in each domain. This fact gives a NE-SW and NW-SE extension direction for the BR system in domains I and II, respectively. The observed NE-SW orientation of the major axes of the anisotropy ellipses in the youngest T4 and T5 temporal domains, oriented perpendicular to the mean trend of the normal faults in the these domains, suggests extension along the NE-SW direction for cross faulting in these areas. The spatial trajectories (form lines) of the minor axes of the anisotropy ellipses, and the mean trend of fault traces in the T4 and T5 temporal domains, define a large parabolic pattern about the axis of the eastern SRP, with its apex at the Yellowstone plateau.

Davarpanah, A.; Babaie, H. A.

2012-12-01

226

Fractal theory based Non-linear analysis of sEMG

This research examines the use of fractal theory to study the properties of surface electromyogram (sEMG). The paper reports identifying a new fractal feature, maximum fractal length (MFL) that, along with fractal dimensions, has been found to be useful in modelling the muscle activity. Exper- imental results demonstrate that the combination of fractal dimension and maximum fractal length of sEMG

Sridhar P Arjunan; Dinesh K Kumar

2010-01-01

227

Fractal characteristics of ozonometric network

NASA Technical Reports Server (NTRS)

The fractal (correlation) dimensions are calculated which characterize the distribution of stations in the ground-based total ozone measuring network and the distribution of nodes in a latitude-longitude grid. The dimension of the ground-based ozonometric network equals 1.67 +/- 0.1 with an appropriate scaling in the 60 to 400 km range. For the latitude-longitude grid two scaling regimes are revealed. One regime, with the dimension somewhat greater than one, is peculiar to smaller scales and limited from a larger scale by the latitudinal resolution of the grid. Another scaling regime, with the dimension equal 1.84, ranges up to 15,000 km scale. The fact that the dimension of a measuring network is less than two possesses problems in observing sparse phenomena. This has to have important consequences for ozone statistics.

Gruzdev, Alexander N.

1994-01-01

228

Retarded hydrodynamic properties of fractal clusters.

Fractal clusters are commonly encountered when working with the stability and the aggregation of colloidal suspensions. In spite of the number of studies that have focused on their stationary hydrodynamic properties, no information is currently known on their retarded hydrodynamic properties. The objective of this work is to close this gap. Clusters with a broad range of fractal dimension values, generated via Monte-Carlo simulations have been analyzed. A rigorous model based on multipole expansion of time-dependent Stokes equations has been developed, and then the full cluster resistance matrix as a function of the frequency has been computed. An attempt has been made to extend Basset, Boussinesque and Oseen equations to fractal clusters, but it was found that the corresponding hydrodynamic radius needs to be a function of frequency. In the case of translational motion, the cluster hydrodynamic radius loses any structural information at high frequencies, becoming independent of the fractal dimension, but depending only on its mass. A simplified model, based on an extension of Kirkwood-Rieseman approach has also been developed. This allows one to perform calculations for clusters with arbitrary masses and fractal dimensions, with good accuracy and very low computational time. It is the first time that the frequency dependence of hydrodynamic properties of complex non-spherical objects has been investigated. PMID:24935184

Lattuada, Marco

2014-09-01

229

Persistence intervals of fractals

NASA Astrophysics Data System (ADS)

Objects and structures presenting fractal like behavior are abundant in the world surrounding us. Fractal theory provides a great deal of tools for the analysis of the scaling properties of these objects. We would like to contribute to the field by analyzing and applying a particular case of the theory behind the P.H. dimension, a concept introduced by MacPherson and Schweinhart, to seek an intuitive explanation for the relation of this dimension and the fractality of certain objects. The approach is based on recently elaborated computational topology methods and it proves to be very useful for investigating scaling hidden in dimensions lower than the “native” dimension in which the investigated object is embedded. We demonstrate the applicability of the method with two examples: the Sierpinski gasket-a traditional fractal-and a two dimensional object composed of short segments arranged according to a circular structure.

Máté, Gabriell; Heermann, Dieter W.

2014-07-01

230

Calculation of fractal dimension of magnetic footprint in double-null divertor tokamaks

The simplest symplectic map that represents the magnetic topology of double-null divertor tokamaks is the double-null map, given by the map equations: x1=x0-ky0(1-y0^2 ), y1=y0+kx1. k is the map parameter. The map parameter k represents the generic topological effects of toroidal asymmetries. The O-point is at (0,0). The X-points are at (0,±1). We set k=0.51763, and Np=12. Np is the

Willie Crank; Alkesh Punjabi; Halima Ali

2010-01-01

231

Using fractal analysis to quantitatively characterize the shapes of volcanic particles

NASA Astrophysics Data System (ADS)

The shapes of volcanic particles reflect numerous eruptive parameters (e.g., magma viscosity, volatile content, and degree of interaction with water) and are useful for understanding fragmentation and transport processes associated with volcanic eruptions. However, quantitative analysis of volcanic particle shapes has proven difficult because of their morphological complexity and variability. Here a newly developed procedure for shape analysis based on fractal geometry is described and tested. Although volcanic particle shapes are not truly fractal, their complexity can be effectively characterized in terms of fractal values (pseudofractal dimensions) reflecting morphological invariance over discrete ranges of scale. Using fractal data produced by dilation of a particle's two-dimensional boundary, a spectrum of fractal dimensions is calculated for each particle by taking the first derivative of the dilation data. Compared with fractal methods that express shape in terms of only one or two fractal dimensions, typically derived from the slope of data on a Richardson plot, this technique results in better discrimination between samples. In addition, use of multiple fractal values allows incorporation of multivariate statistical analysis, further strengthening the differentiating power of the technique. This fractal spectrum technique yields promising results for samples of sideromelane shards from Iceland and is likely to be effective at characterizing other kinds of volcanic particle shapes.

Maria, Anton; Carey, Steven

2002-11-01

232

Map of fluid flow in fractal porous medium into fractal continuum flow

NASA Astrophysics Data System (ADS)

This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow ds is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.

Balankin, Alexander S.; Elizarraraz, Benjamin Espinoza

2012-05-01

233

Fractal characterization of fracture surfaces in concrete

Fractal geometry is used to characterize the roughness of cracked concrete surfaces through a specially built profilometer, and the fractal dimension is subsequently correlated to the fracture toughness and direction of crack propagation. Preliminary results indicate that the fracture surface is indeed fractal over two orders of magnitudes with a dimension of approximately 1.20. ?? 1990.

Saouma, V. E.; Barton, C. C.; Gamaleldin, N. A.

1990-01-01

234

Fractal analysis: A new remote sensing tool for lava flows

NASA Technical Reports Server (NTRS)

Many important quantitative parameters have been developed that relate to the rheology and eruption and emplacement mechanics of lavas. This research centers on developing additional, unique parameters, namely the fractal properties of lava flows, to add to this matrix of properties. There are several methods of calculating the fractal dimension of a lava flow margin. We use the 'structured walk' or 'divider' method. In this method, we measure the length of a given lava flow margin by walking rods of different lengths along the margin. Since smaller rod lengths transverse more smaller-scaled features in the flow margin, the apparent length of the flow outline will increase as the length of the measuring rod decreases. By plotting the apparent length of the flow outline as a function of the length of the measuring rod on a log-log plot, fractal behavior can be determined. A linear trend on a log-log plot indicates that the data are fractal. The fractal dimension can then be calculated from the slope of the linear least squares fit line to the data. We use this 'structured walk' method to calculate the fractal dimension of many lava flows using a wide range of rod lengths, from 1/8 to 16 meters, in field studies of the Hawaiian islands. We also use this method to calculate fractal dimensions from aerial photographs of lava flows, using lengths ranging from 20 meters to over 2 kilometers. Finally, we applied this method to orbital images of extraterrestrial lava flows on Venus, Mars, and the Moon, using rod lengths up to 60 kilometers.

Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.

1992-01-01

235

Cluster-Cluster Aggregation Calculations of Fractal Haze Particles: Titan and the Early Earth

NASA Astrophysics Data System (ADS)

The atmosphere of the Archean Earth (3.8 to 2.5 billion years ago) is thought to have been dominated by a thick hydrocarbon haze similar to that of Titan's current atmosphere. To understand radiative transport in the atmospheres of the early Earth and of Titan, it is necessary to compute light scattering in UV, visible, and IR wavelength ranges for realistic fractal aggregate hydrocarbon aerosol particles. We report preliminary work on MATLAB, True BASIC, and Fortran programs to simulate the growth of fractal aggregate aerosols through diffusion limited aggregation (DLA) and cluster-cluster aggregation (CCA) physical processes. The results of these computations are being used with a T-Matrix light scattering program to test recently published, widely-reported conclusions about the early Earth and the faint young Sun paradox [E. T. Wolf and O. B. Toon, Science 328, 1266 (2010)]. This modeling is also relevant to understanding atmospheric carbonaceous soot aerosol anthropogenic and natural effects on climate change of Earth today.

Terrell-Martinez, Bernice; Boness, David

2010-10-01

236

Fractal Characterization of Metallic Fracture Surfaces.

National Technical Information Service (NTIS)

Mandelbrot, Passoja, and Paullay defined the slit island method (SIM), established the fractal nature of fracture surfaces, and reported the negative correlation of fractal dimension D with fracture toughness in a selection of steel alloys in 1984. They a...

L. V. Meisel

1991-01-01

237

The nature of fractals and the use of fractals instead of classical scaling concepts to describe the irregular surfaces, structures, and processes exhibited by physiological systems are described. The mathematical development of fractals is reviewed, and examples of natural fractals are cited. Relationships among power laws, noise, and fractal time signals are examined

William Deering; Bruce J. West

1992-01-01

238

Dynamic Internal Electromagnetic Pulse Calculations in Three Spatial Dimensions

When a photon pulse impinges on a cavity, it causes electrons to be emitted from the cavity walls, thereby producing electromagnetic fields in the cavity. This constitutes what is known as Internal Electromagnetic Pulse (IEMP). The produced fields for a given incident photon pulse and spectrum (in the case where transient space charge effects are important) is calculated by means

O. Lopez; W. F. Rich

1973-01-01

239

An Approximate Method for Calculating Scattering and Absorption of Light by Fractal Aggregates

NASA Astrophysics Data System (ADS)

A simplified version of the coupled dipole method (CDM) is proposed which allows one to reduce the initial system of 3 N×3 N equations to a simpler system of N× N equations. The method neglects depolarization effects in the interaction of dipoles but, unlike the mean field approximation, it takes into account local fluctuations of the scalar amplitudes of the excited dipole moments. Simple analytic solutions are obtained for integrated cross sections averaged over aggregate orientations. It is shown by the example of ballistic fractal aggregates that this method provides the accuracy close to that of a standard CDM, being substantially less time-consuming. In the case of biospheres, the approximate method is compared with the exact results of the multipole expansion.

Khlebtsov, N. G.

2000-04-01

240

NSDL National Science Digital Library

The "Mountains of Fractals" article in the Math DL develops algorithms to produce coastlines and mountains in two dimensions by adapting mathematical ideas related to the construction of such fractals as Koch's curve. EJS is used to create a hands-on activity that allows a reader to create a coastline with a rubberband, six-sided die, and thumb tacks. Java applications allow for exploration of these algorithms and the influence of their associated parameters. After discussing 2D fractal mountains, this article extends the 2D algorithm to produce 3D mountains. Finally, mathematical issues in random number generation are discussed. More specifically, linear congruential generators are considered and shown to be suitable as a random number generator for the 3D fractal landscape algorithm. The use of fractal landscapes in movies is also discussed.

Chartier, Tim

2009-09-11

241

Routes to fractality and entropy in Liesegang systems

NASA Astrophysics Data System (ADS)

Liesegang bands are formed when solutions of co-precipitate ions interdiffuse in a 1D gel matrix. In a recent study [R. F. Sultan, Acta. Mech. Sin. 27, 119 (2011)], Liesegang patterns have been characterized as fractal structures. In addition to experimentally obtained patterns, geometric Liesegang patterns were constructed in conformity with the well-known empirical laws. Both mathematical fractal dimensions and box count dimensions for images of PbF2 and PbI2 Liesegang patterns have been calculated. Liesegang patterns can also be described by the entropy state function, and categorized as more or less ordered structures. We revisit the relation between entropy and fractal dimension, and apply it to simulated geometrical Liesegang patterns. We have resort to three different routes for the estimation of the entropy of a Liesegang pattern. The HarFA software enabled the calculation of the Hausdorff dimension and the topological entropy, then the information dimension and the Shannon entropy. In a third pathway, analytical calculations were carried out by estimating the probability of occurrence of a fractal element or coverage. The product of Shannon entropy and Boltzmann constant yields the thermodynamic entropy. The values for PbF2 and PbI2 Liesegang patterns attained the order of magnitude of the reported Third Law entropies, but yet remained lower, in conformity with the more ordered Liesegang structures.

Kalash, Leen; Sultan, Rabih

2014-06-01

242

Anomalous thermal conduction in one dimension: a quantum calculation.

In this paper, we study the thermal conductivity of an anharmonically coupled chain of atoms. Numerical studies using classical dynamics have shown that the conductivity of a chain with nearest neighbor couplings diverges with chain length L as L(alpha); earlier studies found alpha approximately = 0.4 under a range of conditions, but a recent study on longer chains claims alpha = 1/3. Analytically, this problem has been studied by calculating the relaxation rate gamma(q) of the normal modes of vibration as a function of its wave vector q. Two theoretical studies of classical chains, one using the mode-coupling formulation and the other the Boltzmann equation method, led to gamma(q) proportional to q(5/3), which is consistent with alpha = 0.4. Here we study the problem for a quantum anharmonic chain with quartic anisotropy. We develop a low-temperature expansion for gamma(q) and find that, in the regime Dirac's constant omega(q) < k(B)T, gamma(q) is proportional to q(5/3)T2, where omega(q) is the frequency of the mode. In our analysis, the relaxation arises due to umklapp scattering processes. We further evaluate the thermal conductivity of the chain using the Kubo formula, which enables us to take into account the transport relaxation time through vertex corrections for the current-current correlator. This calculation also yields alpha = 0.4. PMID:17930004

Santhosh, G; Kumar, Deepak

2007-08-01

243

Roughness Perception of Haptically Displayed Fractal Surfaces

NASA Technical Reports Server (NTRS)

Surface profiles were generated by a fractal algorithm and haptically rendered on a force feedback joystick, Subjects were asked to use the joystick to explore pairs of surfaces and report to the experimenter which of the surfaces they felt was rougher. Surfaces were characterized by their root mean square (RMS) amplitude and their fractal dimension. The most important factor affecting the perceived roughness of the fractal surfaces was the RMS amplitude of the surface. When comparing surfaces of fractal dimension 1.2-1.35 it was found that the fractal dimension was negatively correlated with perceived roughness.

Costa, Michael A.; Cutkosky, Mark R.; Lau, Sonie (Technical Monitor)

2000-01-01

244

The analysis of small- and ultra-small-angle neutron scattering data for sedimentary rocks shows that the pore-rock fabric interface is a surface fractal (D{sub s}=2.82) over 3 orders of magnitude of the length scale and 10 orders of magnitude in intensity. The fractal dimension and scatterer size obtained from scanning electron microscopy image processing are consistent with neutron scattering data. {copyright} {ital 1999} {ital The American Physical Society}

Radlinski, A.P. [Australian Geological Survey Organization, GPO Box 378, Canberra, Australian Capital Territory 2601 (Australia)] [Australian Geological Survey Organization, GPO Box 378, Canberra, Australian Capital Territory 2601 (Australia); Radlinska, E.Z. [Department of Applied Mathematics, The Australian National University, GPO Box 4, Canberra, Australian Capital Territory 0200 (Australia)] [Department of Applied Mathematics, The Australian National University, GPO Box 4, Canberra, Australian Capital Territory 0200 (Australia); Agamalian, M.; Wignall, G.D. [Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393 (United States)] [Solid State Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6393 (United States); Lindner, P.; Randl, O.G. [Institut Max von Laue--Paul Langevin, 38042 Grenoble Cedex (France)] [Institut Max von Laue--Paul Langevin, 38042 Grenoble Cedex (France)

1999-04-01

245

The analysis of small- and ultra-small-angle neutron scattering data for sedimentary rocks shows that the pore-rock fabric interface is a surface fractal (D{sub s}=2.82) over 3 orders of magnitude of the length scale and 10 orders of magnitude in intensity. The fractal dimension and scatterer size obtained from scanning electron microscopy image processing are consistent with neutron scattering data. {copyright}

A. P. Radlinski; E. Z. Radlinska; M. Agamalian; G. D. Wignall; P. Lindner; O. G. Randl

1999-01-01

246

NASA Astrophysics Data System (ADS)

We initially prepared films of poly(vinylidene fluoride-co-hexafluoropropylene)/poly(ethyl methacrylate)-ammonium trifluorome-thanesulfonate dispersed with various wt.% of chromium oxide to study their properties and potential application in electrochemical devices. However, a few months later the nanocomposite polymer electrolyte membranes were found to become a sort of medium for fractal growth. This discovery led to a simulation of the fractals observed in these polymer electrolyte films using a diffusion-limited aggregation model that is based on Brownian motion theory (random walk). The fractal dimensions, D, of the fractal patterns obtained from experimental and simulation work were calculated using the box-counting method. The fractal patterns and dimensions of the simulated fractal patterns were comparable with those obtained from the original fractals observed in the polymer electrolyte films.

Amir, S.; Hashim Ali, S. A.; Mohamed, N. S.

2011-10-01

247

Fractal branching pattern in the pial vasculature in the cat.

Arborization pattern was studied in pial vascular networks by treating them as fractals. Rather than applying elaborate taxonomy assembled from measures from individual vessel segments and bifurcations arranged in their branching order, the authors' approach captured the structural details at once in high-resolution digital images processed for the skeleton of the networks. The pial networks appear random and at the same time having structural elements similar to each other when viewed at different scales--a property known as self-similarity revealed by the geometry of fractals. Fractal (capacity) dimension, Dcap, was calculated to evaluate the network's spatial complexity by the box counting method (BCM) and its variant, the extended counting method (XCM). Box counting method and XCM were subject to numerical testing on ideal fractals of known D. The authors found that precision of these fractal methods depends on the fractal character (branching, nonbranching) of the structure they evaluate. Dcaps (group mean +/- SD) for the arterial and venous pial networks in the cat (n = 6) are 1.37 +/- 0.04, 1.37 +/- 0.02 by XCM, and 1.30 +/- 0.04, 1.31 +/- 0.03 by BCM, respectively. The arterial and venous systems thus appear to be developed according to the same fractal generation rule in the cat. PMID:11488543

Hermán, P; Kocsis, L; Eke, A

2001-06-01

248

NASA Astrophysics Data System (ADS)

We study the betweenness centrality of fractal and nonfractal scale-free network models as well as real networks. We show that the correlation between degree and betweenness centrality C of nodes is much weaker in fractal network models compared to nonfractal models. We also show that nodes of both fractal and nonfractal scale-free networks have power-law betweenness centrality distribution P(C)˜C-? . We find that for nonfractal scale-free networks ?=2 , and for fractal scale-free networks ?=2-1/dB , where dB is the dimension of the fractal network. We support these results by explicit calculations on four real networks: pharmaceutical firms (N=6776) , yeast (N=1458) , WWW (N=2526) , and a sample of Internet network at the autonomous system level (N=20566) , where N is the number of nodes in the largest connected component of a network. We also study the crossover phenomenon from fractal to nonfractal networks upon adding random edges to a fractal network. We show that the crossover length ?* , separating fractal and nonfractal regimes, scales with dimension dB of the network as p-1/dB , where p is the density of random edges added to the network. We find that the correlation between degree and betweenness centrality increases with p .

Kitsak, Maksim; Havlin, Shlomo; Paul, Gerald; Riccaboni, Massimo; Pammolli, Fabio; Stanley, H. Eugene

2007-05-01

249

Continuum diffusion on networks: Trees with hyperbranched trunks and fractal branches

NASA Astrophysics Data System (ADS)

The probability that a random walker returns to its origin for large times scales as t- dmacr /2 , where dmacr is the spectral dimension. We calculate dmacr for a class of tree structures using a renormalization technique on an infinite continued fraction. We consider a wide range of homogeneous networks based on replacing the branches of a self-similar tree with arbitrary fractals and composite fractals. We also consider a new class of inhomogeneous hyperbranched trees.

Haynes, C. P.; Roberts, A. P.

2009-03-01

250

Target detection using fractal geometry

NASA Technical Reports Server (NTRS)

The concepts and theory of fractal geometry were applied to the problem of segmenting a 256 x 256 pixel image so that manmade objects could be extracted from natural backgrounds. The two most important measurements necessary to extract these manmade objects were fractal dimension and lacunarity. Provision was made to pass the manmade portion to a lookup table for subsequent identification. A computer program was written to construct cloud backgrounds of fractal dimensions which were allowed to vary between 2.2 and 2.8. Images of three model space targets were combined with these backgrounds to provide a data set for testing the validity of the approach. Once the data set was constructed, computer programs were written to extract estimates of the fractal dimension and lacunarity on 4 x 4 pixel subsets of the image. It was shown that for clouds of fractal dimension 2.7 or less, appropriate thresholding on fractal dimension and lacunarity yielded a 64 x 64 edge-detected image with all or most of the cloud background removed. These images were enhanced by an erosion and dilation to provide the final image passed to the lookup table. While the ultimate goal was to pass the final image to a neural network for identification, this work shows the applicability of fractal geometry to the problems of image segmentation, edge detection and separating a target of interest from a natural background.

Fuller, J. Joseph

1991-01-01

251

Fourier Fractal Descriptors for Colored Texture Analysis

\\u000a This work proposes the use of a texture descriptor based on the Fourier fractal dimension applied to the analysis of colored\\u000a textures. The technique consists in the transform of the color space of the texture through a colorimetry approach followed\\u000a by the extraction of fractal descriptors from each transformed color channell. The fractal descriptors are obtained from the\\u000a Fourier fractal

Joao B. Florindo; Odemir M. Bruno

252

Diffusion on regular random fractals

NASA Astrophysics Data System (ADS)

We study random walks on structures intermediate to statistical and deterministic fractals called regular random fractals, constructed introducing randomness in the distribution of lacunas of Sierpinski carpets. Random walks are simulated on finite stages of these fractals and the scaling properties of the mean square displacement 0305-4470/29/24/007/img1 of N-step walks are analysed. The anomalous diffusion exponents 0305-4470/29/24/007/img2 obtained are very near the estimates for the carpets with the same dimension. This result motivates a discussion on the influence of some types of lattice irregularity (random structure, dead ends, lacunas) on 0305-4470/29/24/007/img2, based on results on several fractals. We also propose to use these and other regular random fractals as models for real self-similar structures and to generalize results for statistical systems on fractals.

Aarão Reis, Fábio D. A.

1996-12-01

253

“Explosive energy” during volcanic eruptions from fractal analysis of pyroclasts

NASA Astrophysics Data System (ADS)

Despite recent advances by means of experiments and high-resolution surveys and the growing understanding of the physical processes before and during volcanic eruptions, duration and type of eruptive activity still remain highly unpredictable. This uncertainty hinders appropriate hazard and associated risk assessment tremendously. In an effort to counter this problem, experimentally generated pyroclasts have been studied by fractal statistics with the aim of evaluating possible relationships between eruption energy and fragmentation efficiency. Rapid decompression experiments have been performed on three differently porous sample sets of the 1990-1995 eruption of Unzen volcano (Japan) at 850 °C and at initial pressure values above the respective fragmentation threshold [U. Kueppers, B. Scheu, O. Spieler, D.B. Dingwell, Fragmentation efficiency of explosive volcanic eruptions: a study of experimentally generated pyroclasts. J. Volcanol. Geotherm. Res. 153 (2006) 125-135.,O. Spieler, B. Kennedy, U. Kueppers, D.B. Dingwell, B. Scheu, J. Taddeucci, The fragmentation threshold of pyroclastic rocks. EPSL 226 (2004) 139-148.]. The size distribution of generated pyroclasts has been studied by fractal fragmentation theory and the fractal dimension of fragmentation ( Df), a value quantifying the intensity of fragmentation, has been measured for each sample. Results show that size distribution of pyroclastic fragments follows a fractal law (i.e. power-law) in the investigated range of fragment sizes, indicating that fragmentation of experimental samples reflects a scale-invariant mechanism. In addition, Df is correlated positively with the potential energy for fragmentation (PEF) while showing a strong influence of the open porosity of the samples. Results obtained in this work indicate that fractal fragmentation theory may allow for quantifying fragmentation processes during explosive volcanic eruptions by calculating the fractal dimension of the size distribution of pyroclasts. It emerges from this study that fractal dimension may be utilised as a proxy for estimating the explosivity of volcanic eruptions by analysing their natural pyroclastic deposits.

Kueppers, Ulrich; Perugini, Diego; Dingwell, Donald B.

2006-08-01

254

Fractal applications to complex crustal problems

NASA Technical Reports Server (NTRS)

Complex scale-invariant problems obey fractal statistics. The basic definition of a fractal distribution is that the number of objects with a characteristic linear dimension greater than r satisfies the relation N = about r exp -D where D is the fractal dimension. Fragmentation often satisfies this relation. The distribution of earthquakes satisfies this relation. The classic relationship between the length of a rocky coast line and the step length can be derived from this relation. Power law relations for spectra can also be related to fractal dimensions. Topography and gravity are examples. Spectral techniques can be used to obtain maps of fractal dimension and roughness amplitude. These provide a quantitative measure of texture analysis. It is argued that the distribution of stress and strength in a complex crustal region, such as the Alps, is fractal. Based on this assumption, the observed frequency-magnitude relation for the seismicity in the region can be derived.

Turcotte, Donald L.

1989-01-01

255

NSDL National Science Digital Library

The Center for Cultural Design presents this site on African Fractals. Fractals are both visually interesting and mathematically relevant patterns that repeat themselves at different scales. The site includes an interactive applet that helps students understand fractals as applied to geometric concepts. Examples from African culture are included, which makes the site an interesting interdisciplinary learning tool. Be sure to watch Ron Eglash's presentation on African fractals, which is linked to on the front page of the website.

2011-01-03

256

Fractality in the neuron axonal topography of the human brain based on 3-D diffusion MRI

NASA Astrophysics Data System (ADS)

In this work the fractal architecture of the neuron axonal topography of the human brain is evaluated, as derived from 3-D diffusion MRI (dMRI) acquisitions. This is a 3D extension of work performed previously in 2D regions of interest (ROIs), where the fractal dimension of the neuron axonal topography was computed from dMRI data. A group study with 18 subjects is here conducted and the fractal dimensions D f of the entire 3-D volume of the brains is estimated via the box counting, the correlation dimension and the fractal mass dimension methods. The neuron axon data is obtained using tractography algorithms on diffusion tensor imaging of the brain. We find that all three calculations of D f give consistent results across subjects, namely, they demonstrate fractal characteristics in the short and medium length scales: different fractal exponents prevail at different length scales, an indication of multifractality. We surmise that this complexity stems as a collective property emerging when many local brain units, performing different functional tasks and having different local topologies, are recorded together.

Katsaloulis, P.; Ghosh, A.; Philippe, A. C.; Provata, A.; Deriche, R.

2012-05-01

257

NASA Astrophysics Data System (ADS)

Traditional biological and chemical methods for pathogen identification require complicated sample preparation for reliable results. The process of identification of malignant and non-malignant growths is not easier. Two new techniques of analysis of speckle-patterns, formed by histological sections with malignant and non-malignant growths illuminated by laser light, were proposed in this article. One of these techniques is based on calculation of invariant Zernike moments of speckle-field intensity spatial distribution. The second technique is based on calculation of fractal dimension of intensity spatial distribution in speckle structure. It was shown that both of these methods give the same results, which drastically depends on tissues features. Possibility of using Zernike moments and fractal dimensions, formed by laser light dispersed on histological sections, in express-diagnostics of tissues with pathological changes carrying out in vitro was investigated. Dependence of fractal dimension n conditions of irradiation of object with laser light discussed.

Ulyanov, Alexander S.; Zotov, Alexander V.

2010-10-01

258

Fractal scattering of microwaves from soils.

Using a combination of laboratory experiments and computer simulation we show that microwaves reflected from and transmitted through soil have a fractal dimension correlated to that of the soil's hierarchic permittivity network. The mathematical model relating the ground-penetrating radar record to the mass fractal dimension of soil structure is also developed. The fractal signature of the scattered microwaves correlates well with some physical and mechanical properties of soils. PMID:12398644

Oleschko, K; Korvin, G; Balankin, A S; Khachaturov, R V; Flores, L; Figueroa, B; Urrutia, J; Brambila, F

2002-10-28

259

Fractal analysis in studies of mycelium in soil

Like many naturally irregular structures mycelia are approximately fractal; thus fractal dimension can be used to quantify the extent to which mycelia permeate space in relation to the extent of the system. Since it is important to be able to quantify both space filling at mycelial margins, i.e., `search fronts', and within systems, both surface\\/border and mass fractal dimensions are

Lynne Boddy; John M. Wells; Claire Culshaw; Damian P. Donnelly

1999-01-01

260

Fractal and Multiresolution Techniques for the Understanding of Geo-Information

The techniques based on fractals show promising results in the field of image understanding and visualization of high complexity data. In the aim to give an introduction to the theory of fractals the following topics will be summarised in this paper: the definition and analysis of fractals based on self-similarity and self-affinity behaviours, definitions for fractal dimension, fractal synthesis, multiresolution

Mihai Datcu; Klaus Seidel

261

Quantitative Characterization Of Basaltic Tephra Using The Fractal Spectrum Technique

NASA Astrophysics Data System (ADS)

Geologists have studied volcanic eruptions on Hawaii more closely than anywhere else. Even so, processes of magma fragmentation during Hawaiian style eruptions (e.g. lava fountaining) are not well understood. Furthermore, the products of these eruptions have not been fully characterized. Analysis of tephra shape is particularly useful for understanding the nature of eruptions, as particle morphology reflects numerous volcanic parameters (e.g. magma viscosity, volatile content, interaction with water, transport processes). The technique applied in this study, based on fractal geometry, uses data produced by dilation of the 2-D particle boundary to produce a full spectrum of fractal dimensions over a range of scales for each particle. Multiple fractal dimensions, which can be described as a fractal spectrum curve, are calculated by taking the first derivative of data points on a standard Richardson plot. Previous applications of this technique have proven helpful for characterizing basaltic to rhyolitic products of specific fragmentation processes, and modes of volcanic transport/deposition. In this study, all the samples are basaltic, eliminating the variable of composition, and include material from two Hawaiian lava-fountaining events (Mauna Ulu, 1969; Kilauea Iki, 1959), as well as material from Masaya, Nicaragua (San Judas Formation) that is thought to have been unusually explosive, for comparison. One of our goals is to identify characteristic particle shapes formed during the lava-fountain events. Use of multiple fractal dimensions results in more effective discrimination than expressions of shape based on one or two fractal dimensions, and also allows use of multivariate statistical techniques. Cluster analysis provides a visual display of the similarities of particles in a sample, and facilitates identification of the types of shapes that are most characteristic of a given deposit. Use of principal components analysis to summarize the data as accurately as possible using a few components, facilitates comparison between samples.

Maria, A.

2006-12-01

262

NASA Astrophysics Data System (ADS)

Soil CO2 emission (FCO2) is influenced by chemical, physical and biological factors that affect the production of CO2 in the soil and its transport to the atmosphere, varying in time and space depending on environmental conditions, including the management of agricultural area. The aim of this study was to investigate the structure of spatial variability of FCO2 and soil properties by using fractal dimension (DF), derived from isotropic variograms at different scales, and construction of fractograms. The experimental area consisted of a regular grid of 60 × 60 m on sugarcane area under green management, containing 141 points spaced at minimum distances ranging from 0.5 to 10 m. Soil CO2 emission, soil temperature and soil moisture were evaluated over a period of 7 days, and soil chemical and physical properties were determined by sampling at a depth of 0.0 to 0.1 m. FCO2 showed an overall average of 1.51 µmol m-2 s-1, correlated significantly (p < 0.05) with soil physical factors such as soil bulk density, air-filled pore space, macroporosity and microporosity. Significant DF values were obtained in the characterization of FCO2 in medium and large scales (from 20 m). Variations in DF with the scale, which is the fractogram, indicate that the structure of FCO2 variability is similar to that observed for the soil temperature and total pore volume, and reverse for the other soil properties, except for macroporosity, sand content, soil organic matter, carbon stock, C/N ratio and CEC, which fractograms were not significantly correlated to the FCO2 fractogram. Thus, the structure of spatial variability for most soil properties, characterized by fractogram, presents a significant relationship with the structure of spatial variability of FCO2, generally with similar or dissimilar behavior, indicating the possibility of using the fractogram as tool to better observe the behavior of the spatial dependence of the variables along the scale.

Bicalho, E. S.; Teixeira, D. B.; Panosso, A. R.; Perillo, L. I.; Iamaguti, J. L.; Pereira, G. T.; La Scala, N., Jr.

2012-04-01

263

Instrumented postural control analysis plays an important role in evaluating the effects of injury on dynamic stability during balance tasks, and is often conveyed with measures based on the displacement of the center-of-pressure (COP) assessed with a force platform. However, the desired outcome of the task is frequently characterized by a loss of dynamic stability, secondary to injury. Typically, these failed trials are discarded during research investigations, with the potential loss of informative data pertaining to task success. The novelty of the present study is that COP characteristics of failed trials in injured participants are compared to successful trial data in another injured group, and a control group of participants, using the fractal dimension (FD) method. Three groups of participants attempted a task of eyes closed single limb stance (SLS): twenty-nine participants with acute ankle sprain successfully completed the task on their non-injured limb (successful injury group); twenty eight participants with acute ankle sprain failed their attempt on their injured limb (failed injury group); sixteen participants with no current injury successfully completed the task on their non-dominant limb (successful non-injured group). Between trial analyses of these groups revealed significant differences in COP trajectory FD (successful injury group: 1.58±0.06; failed injury group: 1.54±0.07; successful non-injured group: 1.64±0.06) with a large effect size (0.27). These findings demonstrate that successful eyes-closed SLS is characterized by a larger FD of the COP path when compared to failed trials, and that injury causes a decrease in COP path FD. PMID:24746034

Doherty, Cailbhe; Bleakley, Chris; Hertel, Jay; Caulfield, Brian; Ryan, John; Delahunt, Eamonn

2014-05-01

264

The concept of fractal mapping is introduced and applied to digitized topography of Arizona. It is shown that the fractal statistics satisfy the topography of the state to a good approximation. The fractal dimensions and roughness amplitudes from subregions are used to construct maps of these quantities. It is found that the fractal dimension of actual two-dimensional topography is not

J. Huang; D. L. Turcotte

1989-01-01

265

Heat transfer and fluid flow during manual metal arc welding of low alloy steels were investigated by solving the equations of conservation of mass, momentum, and energy in three dimensions. Cooling rates were calculated at various locations in the weldment. Calculated cooling rates were coupled with an existing phase transformation model to predict percentages of acicular, allotriomorphic, and Widmanstaetten ferrites in various low alloy steel welds containing different concentration of V and Mn. Computed microstructures were in good agreement with experiment, indicating promise for predicting weld metal microstructure from the fundamentals of transport phenomena.

Mundra, K.; DebRoy, T.; Babu, S.S. [Pennsylvania State Univ., University Park, PA (United States). Dept. of Materials Science and Engineering; David, S.A. [Oak Ridge National Lab., TN (United States)

1995-12-31

266

Phases and fractal structures of three-dimensional simplicial gravity

NASA Astrophysics Data System (ADS)

We study phases and fractal structures of three-dimensional simplicial quantum gravity by a Monte Carlo calculation with a lattice size V=104. After measuring the surface area distribution (SAD) which is the three-dimensional analog of the loop length distribution (LLD) in two-dimensional quantum gravity, we classify the fractal structures into three types: (i) In the strong coupling (hot) phase, strong gravity makes the space-time one crumpled mother universe with many fluctuating baby universes of small size around it. This is a crumpled phase with a large Hausdorff dimension dH=4.98+/-0.05. The topologies of the sections are extremely complicated. (ii) At the critical point, we observe that the space-time is a pseudo-fractal manifold which has one mother universe with many baby universes of small and middle size around it. The Hausdorff dimension dH is 3.93+/-0.05. We observe some scaling behaviors for the sections of the manifold. This manifold resembles the fractal surface observed in two-dimensional quantum gravity. (iii) In the weak coupling (cold) phase, the mother universe disappears completely and the space-time seems to be a branched-polymer with a small Hausdorff dimension dH=1.948+/-0.003. almost all of the sections have the spherical topology S2 in the weak coupling phase.

Hagura, Hiroyuki; Tsuda, Noritsugu; Yukawa, Tetsuyuki

1998-02-01

267

Study of the fractal correlation method in displacement measurement

NASA Astrophysics Data System (ADS)

The classical digital speckle pattern, or digital image, correlation method of deformation measurement is based on gray level correlation between unformed and deformed digital images. Since the pattern of artificial random speckles and the natural texture have fractal characteristics, and their fractal dimensions represent both gray and morph information, a fractal correlation method of displacement measurement is developed in this paper. The in-plane displacement field of a body can be acquired. In order to verify the validity of the new method, an experiment has been designed and the results have been compared with those tested by gray correlation method. The calculation speed is over 20 times fast than the digital image correlation method. The results how that its precision is less than 0.05 pixels.

Hou, Zhende; Qin, Yuwen

2001-06-01

268

Generalized dimensions applied to speaker identification

NASA Astrophysics Data System (ADS)

This paper describes an application of fractal dimensions to speech processing and speaker identification. There are several dimensions that can be used to characterize speech signals such as box dimension, correlation dimension, etc. We are mainly concerned with the generalized dimensions of speech signals as they provide more information than individual dimensions. Generalized dimensions of arbitrary orders are used in speaker identification in this work. Based on the experimental data, the artificial phase space is generated and smooth behavior of correlation integral is obtained in a straightforward and accurate analysis. Using the dimension D(2) derived from the correlation integral, the generalized dimension D(q) of an arbitrary order q is calculated. Moreover, experiments applying the generalized dimension in speaker identification have been carried out. A speaker recognition dedicated Chinese language speech corpus with PKU-SRSC, recorded by Peking University, was used in the experiments. The results are compared to a baseline speaker identification that uses MFCC features. Experimental results have indicated the usefulness of fractal dimensions in characterizing speaker's identity.

Hou, Limin; Wang, Shuozhong

2004-08-01

269

Fractal dynamics of earthquakes

Many objects in nature, from mountain landscapes to electrical breakdown and turbulence, have a self-similar fractal spatial structure. It seems obvious that to understand the origin of self-similar structures, one must understand the nature of the dynamical processes that created them: temporal and spatial properties must necessarily be completely interwoven. This is particularly true for earthquakes, which have a variety of fractal aspects. The distribution of energy released during earthquakes is given by the Gutenberg-Richter power law. The distribution of epicenters appears to be fractal with dimension D {approx} 1--1.3. The number of after shocks decay as a function of time according to the Omori power law. There have been several attempts to explain the Gutenberg-Richter law by starting from a fractal distribution of faults or stresses. But this is a hen-and-egg approach: to explain the Gutenberg-Richter law, one assumes the existence of another power-law--the fractal distribution. The authors present results of a simple stick slip model of earthquakes, which evolves to a self-organized critical state. Emphasis is on demonstrating that empirical power laws for earthquakes indicate that the Earth`s crust is at the critical state, with no typical time, space, or energy scale. Of course the model is tremendously oversimplified; however in analogy with equilibrium phenomena they do not expect criticality to depend on details of the model (universality).

Bak, P.; Chen, K. [Brookhaven National Lab., Upton, NY (United States). Dept. of Physics

1995-05-01

270

Calculations were performed with the CTH and HULL finite difference wavecodes to evaluate computational capabilities for predicting depth and diameter of target cavities produced in high velocity penetration events. The calculations simulated selected tests in a set of armor penetration experiments conducted by the US Army Ballistic Research Laboratory and reported earlier in the literature. The tests and simulations involved penetration of semi-infinite targets by long rod projectiles over a range of impact velocities from 1.3 to 4.5 km/sec. Comparisons are made between the calculated and measured dimensions of the target cavities, and the sensitivity of the predicted results to target property variations is investigated. 9 refs., 18 figs., 3 tabs.

Kmetyk, L.N.; Yarrington, P.

1989-05-01

271

Large-dimension configuration-interaction calculations of positron binding to the group-II atoms

The configuration-interaction (CI) method is applied to the calculation of the structures of a number of positron binding systems, including e{sup +}Be, e{sup +}Mg, e{sup +}Ca, and e{sup +}Sr. These calculations were carried out in orbital spaces containing about 200 electron and 200 positron orbitals up to l=12. Despite the very large dimensions, the binding energy and annihilation rate converge slowly with l, and the final values do contain an appreciable correction obtained by extrapolating the calculation to the l{yields}{infinity} limit. The binding energies were 0.00317 hartree for e{sup +}Be, 0.0170 hartree for e{sup +}Mg, 0.0189 hartree for e{sup +}Ca, and 0.0131 hartree for e{sup +}Sr.

Bromley, M. W. J.; Mitroy, J. [Department of Physics, San Diego State University, San Diego, California 92182 (United States); Faculty of Technology, Charles Darwin University, Darwin NT 0909 (Australia)

2006-03-15

272

Edge detection and image segmentation of space scenes using fractal analyses

NASA Technical Reports Server (NTRS)

A method was developed for segmenting images of space scenes into manmade and natural components, using fractal dimensions and lacunarities. Calculations of these parameters are presented. Results are presented for a variety of aerospace images, showing that it is possible to perform edge detections of manmade objects against natural background such as those seen in an aerospace environment.

Cleghorn, Timothy F.; Fuller, J. J.

1992-01-01

273

Fractal dynamics of bioconvective patterns

NASA Technical Reports Server (NTRS)

Biologically generated cellular patterns, sometimes called bioconvective patterns, are found to cluster into aggregates which follow fractal growth dynamics akin to diffusion-limited aggregation (DLA) models. The pattern formed is self-similar with fractal dimension of 1.66 +/-0.038. Bioconvective DLA branching results from thermal roughening which shifts the balance between ordering viscous forces and disordering cell motility and random diffusion. The phase diagram for pattern morphology includes DLA, boundary spokes, random clusters, and reverse clusters.

Noever, David A.

1991-01-01

274

WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent ?, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent ? of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators ([Formula: see text] power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series. PMID:22586408

Stadnitski, Tatjana

2012-01-01

275

ERIC Educational Resources Information Center

Explores the subject of fractal geometry focusing on the occurrence of fractal-like shapes in the natural world. Topics include iterated functions, chaos theory, the Lorenz attractor, logistic maps, the Mandelbrot set, and mini-Mandelbrot sets. Provides appropriate computer algorithms, as well as further sources of information. (JJK)

Dewdney, A. K.

1991-01-01

276

NASA Astrophysics Data System (ADS)

Two methods for analyzing OCT images of arterial tissues are tested. These methods are applied toward two types of samples: segments of arteries collected from atherosclerosis-prone Watanabe heritable hyper-lipidemic rabbits and pieces of porcine left descending coronary arteries without atherosclerosis. The first method is based on finding the attenuation coefficients for the OCT signal that propagates through various regions of the tissue. The second method involves calculating the fractal dimensions of the OCT signal textures in the regions of interest identified within the acquired images. A box-counting algorithm is used for calculating the fractal dimensions. Both parameters, the attenuation coefficient as well as the fractal dimension correlate very well with the anatomical features of both types of samples.

Popescu, Dan P.; Flueraru, Costel; Mao, Youxin; Chang, Shoude; Sowa, Michael G.

2010-02-01

277

Segmentation of textured images using fractal transformations

NASA Astrophysics Data System (ADS)

This paper presents an approach to textured image segmentation based on a combination of fractal features. The traditionally fractal dimension obtained from the original and pre-processed images and is combined with fractal transformation coefficients. The latter are extracted using methodologies from image compression using Iterated Function Systems (IFS). Experiments have shown that coefficients used in IFS for image reconstruction can also be used as segmentation and classification features. Experimental results with various natural texture measures will be presented.

Kasparis, Takis; Pongratananukul, Nattorn

2000-07-01

278

National Technical Information Service (NTIS)

Image analysis is performed by defining segmentation boundaries within an image by using wavelet theory or some other suitable method. Such boundaries can be incomplete, irregular, and/or multi-valued. The segmentation boundaries are then incorporated int...

G. W. Rogers C. E. Priebe J. L. Solka R. A. Lorey E. G. Julin

1994-01-01

279

Kinetics of Solid State Reactions With Fractal Reagent

In the present research we theoretically studied the kinetics of nucleation-limited solid state reactions as influenced by the fractal properties of solid reagent. We consider the model of equal-sized primary particles assembled in fractal cluster. The geometry of such an object is assumed to be described solely by its fractal dimension D and by upper (Rmax) and lower (Rmin) cutoffs

S. V. Kalinin; A. A. Vertegel; N. N. Oleynikov; Yu. D. Tretyakov

1998-01-01

280

A Model to Describe the Settling Behavior of Fractal Aggregates

A model to predict fractal dimension from sedimentating fractal aggregates has been successfully developed. This model was developed using the settling rate and size data of fractal aggregates. In order to test the validity of the model, a purpose-built settling rig, equipped with lens with magnification of 1200×, which can capture images of particles\\/flocs down to 2 ?m in diameter

P. Tang; J. Greenwood; J. A. Raper

2002-01-01

281

Fractal analysis is a method of characterizing complex shapes such as the trabecular structure of bone. Numerous algorithms for estimating fractal dimension have been described, but the Fourier power spectrum method is particularly applicable to self-affine fractals, and facilitates corrections for the effects of noise and blurring in an image. We found that it provided accurate estimates of fractal dimension

Geoffrey Dougherty; Geoffrey M. Henebry

2001-01-01

282

FRACTAL ANTENNA FOR PASSIVE UHF RFID APPLICATIONS

This paper addresses the design of fractal antennas placed onto dielectric object in the UHF RFID band and introduces a tag antenna conflguration of simple geometry having impedance tuning capability. Through the paper, the dimensions of the fractal antenna are optimized to improve the impedance matching with the chip impedance. The tag performance changes are studied when it is placed

Saber Helmy Zainud-Deen; Hend Abd El-Azem Malhat; Kamal Hassan Awadalla

2009-01-01

283

NASA Astrophysics Data System (ADS)

Fractal packing and highly irregular shaped particles increase the mechanical properties of rocks and building materials. This suggests that fractal methods are good tools for modeling particle mixes with efficient properties like maximum strength and maximum surface area or minimum porosity and minimum permeability. However gradings and packings are calculated by ``Euclidean'' disk models and sphere models. Surprisingly even the simplest models are far more complex than they appear. The fractal ``Appolonian packing model'' is proposed as the most universal two-dimensional packing model. However the inhomogeneity of gradings and the irregularity of natural grain shapes and surfaces are not reflected by these models. Consequently calculations are often far from empirical observations and experimental results. A thorough quantification of packings and gradings is important for many reasons and still a matter of intense investigation and controversial discussion. This study concentrates on fractal models for densely packed non-cohesive rocks, crushed mineral assemblages, concrete and asphalt mixtures. A summary of fractal grain size distributions with linear cumulative curves on log-log plots is presented for these mixtures. It is shown that fractal two-dimensional and three-dimensional models for dense packings reflect different physical processes of material mixing or geological deposition. The results from shear-box experiments on materials with distinct grain size distributions show a remarkable increase of the mechanical strength from non-fractal to fractal mixtures. It is suggested that fractal techniques need more systematical application and correlation with results from material testing experiments in engineering geology. The purpose of future work should lead towards the computability of dense packings of angular particles in three dimensions.

Hecht, C. A.

284

Fractal universe and quantum gravity.

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed. PMID:20867360

Calcagni, Gianluca

2010-06-25

285

Fractal Universe and Quantum Gravity

We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.

Calcagni, Gianluca [Max Planck Institute for Gravitational Physics (Albert Einstein Institute) Am Muehlenberg 1, D-14476 Golm (Germany)

2010-06-25

286

Random walk through fractal environments.

We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D(F) of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D(F)< or =2 can thus be considered as defective Levy walks. The distribution of jump increments for D(F)>2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D(F)<2, the diffusion is dominated by the finite escape rate. Diffusion for D(F)>2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations. PMID:12636828

Isliker, H; Vlahos, L

2003-02-01

287

Fractal signatures in the aperiodic Fibonacci grating.

The Fibonacci grating (FbG) is an archetypal example of aperiodicity and self-similarity. While aperiodicity distinguishes it from a fractal, self-similarity identifies it with a fractal. Our paper investigates the outcome of these complementary features on the FbG diffraction profile (FbGDP). We find that the FbGDP has unique characteristics (e.g., no reduction in intensity with increasing generations), in addition to fractal signatures (e.g., a non-integer fractal dimension). These make the Fibonacci architecture potentially useful in image forming devices and other emerging technologies. PMID:24784044

Verma, Rupesh; Banerjee, Varsha; Senthilkumaran, Paramasivam

2014-05-01

288

NSDL National Science Digital Library

This webpage is dedicated to all things fractals, and is organized and updated by Professor Paul Bourke. Visitors will find all kinds of useful tools for discovering and learning about fractals including: Fractal forms found by using Google Earth, Natural Fractals in Grand Canyon National Park, Introduction to fractals, a gallery of fractals, and much, much more.

Bourke, Paul

2007-08-15

289

The fractal aggregation of asphaltenes.

This paper discusses time-resolved small-angle neutron scattering results that were used to investigate asphaltene structure and stability with and without a precipitant added in both crude oil and model oil. A novel approach was used to isolate the scattering from asphaltenes that are insoluble and in the process of aggregating from those that are soluble. It was found that both soluble and insoluble asphaltenes form fractal clusters in crude oil and the fractal dimension of the insoluble asphaltene clusters is higher than that of the soluble clusters. Adding heptane also increases the size of soluble asphaltene clusters without modifying the fractal dimension. Understanding the process of insoluble asphaltenes forming fractals with higher fractal dimensions will potentially reveal the microscopic asphaltene destabilization mechanism (i.e., how a precipitant modifies asphaltene-asphaltene interactions). It was concluded that because of the polydisperse nature of asphaltenes, no well-defined asphaltene phase stability envelope exists and small amounts of asphaltenes precipitated even at dilute precipitant concentrations. Asphaltenes that are stable in a crude oil-precipitant mixture are dispersed on the nanometer length scale. An asphaltene precipitation mechanism is proposed that is consistent with the experimental findings. Additionally, it was found that the heptane-insoluble asphaltene fraction is the dominant source of small-angle scattering in crude oil and the previously unobtainable asphaltene solubility at low heptane concentrations was measured. PMID:23808932

Hoepfner, Michael P; Fávero, Cláudio Vilas Bôas; Haji-Akbari, Nasim; Fogler, H Scott

2013-07-16

290

NASA Technical Reports Server (NTRS)

The concept of fractal mapping is introduced and applied to digitized topography of Arizona. It is shown that the fractal statistics satisfy the topography of the state to a good approximation. The fractal dimensions and roughness amplitudes from subregions are used to construct maps of these quantities. It is found that the fractal dimension of actual two-dimensional topography is not affected by the adding unity to the fractal dimension of one-dimensional topographic tracks. In addition, consideration is given to the production of fractal maps from synthetically derived topography.

Huang, J.; Turcotte, D. L.

1989-01-01

291

Applications of fractal analysis to physiology

This review describes approaches to the analysis of fractal properties of physiological observations. Fractals are useful to describe the natural irregularity of physiological systems because their irregularity is not truly random and can be demonstrated to have spatial or temporal correlation. The concepts of fractal analysis are introduced from intuitive, visual, and mathematical perspectives. The regional heterogeneities of pulmonary and myocardial flows are discussed as applications of spatial fractal analysis, and methods for estimating a fractal dimension from physiological data are presented. Although the methods used for fractal analyses of physiological data are still under development and will require additional validation, they appear to have great potential for the study of physiology at scales of resolution ranging from the microcirculation to the intact organism.

Glenny, Robb W.; Robertson, H. Thomas; Yamashiro, Stanley; Bassingthwaighte, James B.

2010-01-01

292

Fractals and cosmological large-scale structure

NASA Technical Reports Server (NTRS)

Observations of galaxy-galaxy and cluster-cluster correlations as well as other large-scale structure can be fit with a 'limited' fractal with dimension D of about 1.2. This is not a 'pure' fractal out to the horizon: the distribution shifts from power law to random behavior at some large scale. If the observed patterns and structures are formed through an aggregation growth process, the fractal dimension D can serve as an interesting constraint on the properties of the stochastic motion responsible for limiting the fractal structure. In particular, it is found that the observed fractal should have grown from two-dimensional sheetlike objects such as pancakes, domain walls, or string wakes. This result is generic and does not depend on the details of the growth process.

Luo, Xiaochun; Schramm, David N.

1992-01-01

293

10 retinal vessel patterns with neovascularisation at or near the optic disk (NVD) from eyes of patients with diabetic retinopathy were compared with vascular patterns from 14 normal eyes. The vascular patterns were taken from low angle fundus photographs. After digitizing, the fractal dimensions were calculated by means of the density-density correlation function method. The fractal dimension was found to be significantly higher for vessel patterns with NVD [D = 1.845 +/- 0.056 (m +/- sd)] as compared with the normal control group (D = 1.708 +/- 0.073) (p < 0.001). The fractal dimension of 1.8 appears to be a cutoff value. Higher values may indicate proliferative changes. Under these conditions the sensitivity of the method for the detection of NVD > or = Grade 3 in the Early Treatment Diabetic Retinopathy Study (ETDRS) grading system is 90%. The presence of such NVD in an eye is a "high risk characteristic" for severe visual loss, which requires panretinal laser treatment. Fractal analysis is therefore a possible new strategy for computer assisted "automated" detection and quantification of proliferative diabetic retinopathy. The fractal dimension of the new vessels suggests possible mechanisms involved in retinal vasculogenesis. PMID:8137633

Daxer, A

1993-12-01

294

Fractal analysis of climatic data: Annual precipitation records in Spain

The rescaled range analysis was applied to the annual precipitation series from 10 weather stations in Spain for the period 1901–1989. The analysis reveals that the series of precipitations fits a fractal distribution, with a mean fractal dimension of 1.32 ± 0.01. This lies in the same order of magnitude as the fractal dimensions obtained from other macrometeorological and paleoclimatic

J. J. Ofiate Rubalcaba

1997-01-01

295

Fractal statistics of cloud fields

NASA Technical Reports Server (NTRS)

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.; Joseph, Joachim H.

1989-01-01

296

Efficient Desalination with Fractal Absorbers

A class of Ramified graphs (RG) is introduced as Iterated Function Systems (IFS) to optimally design networks for efficient reverse osmosis desalination in deep seawater. Different forms of the IFS are presented, along with a corresponding contractivity factor sc, in order to identify the attractors of the systems and their fractal dimension. Using the analogy to electrostatics, the diffusion equation

Martin Singleton; Gregor Heiss; Alfred Hubler

2008-01-01

297

Internal fields of soot fractal aggregates.

This work uses the discrete dipole approximation (DDA) to examine the internal electric field within a simulated carbon soot fractal aggregate in fixed and random orientations. For fixed orientations, deviations of the internal field magnitude up to ±50% from that assumed by the Rayleigh-Debye-Gans Approximation (RDGA) are found. Given the refractive index of the aggregate monomers and conditions for the validity of the approximation, such large deviations are no surprise. Yet despite this deviation, the far-field scattered intensity from such aggregates agrees surprisingly well with that described by the RDGA. Moreover, if the average over an ensemble of many random aggregate-orientations is calculated, both the DDA and RDGA scattered intensities obey the well-known power-law functionality in terms of the scattering wave vector and show a forward-angle intensity-maximum proportional to the square of the number of monomers. The explanation for this lies in the over and under estimations made by the approximation of the internal field, which apparently mostly cancel upon integration to yield the scattered intensity. It is shown that this error cancellation is related to the fractal structure of the aggregate and that the agreement between the DDA and RDGA improves with aggregates of increasing size provided the fractal dimension is less than two. Overall, the analysis suggests that both the special fractal character of the aggregate and its orientational averaging is important to account for the experimentally observed validity of the RDGA despite its poor description of the internal fields. PMID:24322849

Berg, Matthew J; Sorensen, Christopher M

2013-10-01

298

A fractal analysis of CT liver images for the discrimination of hepatic lesions: a comparative study

A quantitative study for the discrimination of different hepatic lesions is presented in this paper. The study is based on the fractal analysis of CT liver images in order to estimate their fractal dimension and to differentiate normal liver parenchyma from hepatocellular carcinoma. Four fractal dimension estimators have been implemented throughout this work; three well-established methods and a novel implementation

C.-P. A. Sariyanni; P. Asvestas; G. K. Matsopoulos; K. S. Nikita; A. S. Nikita; D. Kelekis

2001-01-01

299

The Possible Role of Fractal Geometry in Tribology

Fractal geometry, in which infinite numbers of fractional dimensions are permitted in contradistinction to the three integer dimensions in Euclidean geometry, has been applied to the study of surface roughness. A tentative conclusion is that fractal geometry offers yet another vehicle for the physical chemist to meet the mechanical engineer on solving problems in the boundary lubrication regime of tribology.

Frederick F. Ling

1989-01-01

300

Fractal Theory for Permeability Prediction, Venezuelan and USA Wells

NASA Astrophysics Data System (ADS)

Inferring petrophysical parameters such as permeability, porosity, water saturation, capillary pressure, etc, from the analysis of well logs or other available core data has always been of critical importance in the oil industry. Permeability in particular, which is considered to be a complex parameter, has been inferred using both empirical and theoretical techniques. The main goal of this work is to predict permeability values on different wells using Fractal Theory, based on a method proposed by Pape et al. (1999). This approach uses the relationship between permeability and the geometric form of the pore space of the rock. This method is based on the modified equation of Kozeny-Carman and a fractal pattern, which allows determining permeability as a function of the cementation exponent, porosity and the fractal dimension. Data from wells located in Venezuela and the United States of America are analyzed. Employing data of porosity and permeability obtained from core samples, and applying the Fractal Theory method, we calculated the prediction equations for each well. At the beginning, this was achieved by training with 50% of the data available for each well. Afterwards, these equations were tested inferring over 100% of the data to analyze possible trends in their distribution. This procedure gave excellent results in all the wells in spite of their geographic distance, generating permeability models with the potential to accurately predict permeability logs in the remaining parts of the well for which there are no core samples, using even porority logs. Additionally, empirical models were used to determine permeability and the results were compared with those obtained by applying the fractal method. The results indicated that, although there are empirical equations that give a proper adjustment, the prediction results obtained using fractal theory give a better fit to the core reference data.

Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana

2014-05-01

301

NASA Astrophysics Data System (ADS)

This study is an attempt of a semi-automatic geomorphological GIS analysis based on morphometric indices. In the study, 10-m-resolution Digital Elevation Models (DEMs) are used to assess the neotectonic signals regarding the recent topographic developments and to attach additional significance to active tectonics in the Bingöl basin area. The methodology incorporates the determination of the structural similarities of the faults in the basins using fractal concepts and the application of four morphometric indices (Stream Power Index (SP), Multi-resolution Index of Valley Bottom Flatness (MRVBF), Terrain Ruggedness Index (TRI) and Valley Width-to-Height Ratio (Vf)). In order to detect the deviation from spatial randomness of the applied indices, the weighted correlation coefficient Moran’s I is used and the results are interpreted at a confidence interval of 99%. The spatial distribution of integrated index values is evaluated with the tectonically active fault zones in order to determine the probable activity and the structural deformation in the basin. The applied methodology reveals that the fractal analysis of the fault lines and the spatial analysis of the morphometric indices proved to be effective tools in analyzing the tectonic influence of the fault system on the basin area. Within the basin area, a relatively lesser degree of tectonic activity is observed, in contrast with the high tectonic activity outside the basin.

Sarp, Gulcan

2014-07-01

302

Multi-Scale Fractal Analysis of Image Texture and Pattern

NASA Technical Reports Server (NTRS)

Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images is the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimension-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.

Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.

1999-01-01

303

Fractals and fractal scaling in fracture mechanics

A review of modern fractal models of fracture in brittle and quasibrittle materials is given. The difference between mathematical\\u000a and physical fractal approaches is emphasized. The scaling for both a fractal solitary crack and a fractal pattern of microcracks\\u000a surrounding the main fracture is considered. Some concepts appropriate for fractal description of fracture are discussed.\\u000a It is shown that if

Feodor M. Borodich

1999-01-01

304

NSDL National Science Digital Library

This website from the Department of Physics and Astronomy at Johns Hopkins University introduces chaos and describes how it appears in animal populations and weather models. The site also describes fractals and explains the butterfly effect. Images provide representations of chaotic behavior.

Bradley, Larry

2009-06-15

305

Fractal patterns formed by growth of radial viscous fingers*

NASA Astrophysics Data System (ADS)

We examine fractal patterns formed by the injection of air into oil in a thin (0.13 mm) layer contained between two cylindrical glass plates of 288 mm diameter (a Hele-Shaw cell) [1]. The resultant radially grown patterns are similar to those formed in Diffusion Limited Aggregation (DLA), but the relation between the continuum limit of DLA and continuum (Laplacian) growth remains an open question. Our viscous fingering patterns in the limit of very high pressure difference reach an asymptotic state in which they exhibit a fractal dimension of 1.70± 0.02, in good agreement with a calculation of the fractal dimension of a DLA cluster, 1.713± 0.003 [2]. The generalized dimensions are also computed and show that the observed pattern is self-similar with Dq = 1.70 for all q. Further, the probability density function of shielding angles suggests the existence of a critical angle close to 75 degrees. This result is in accord with numerical and analytical evidence of a critical angle in DLA [3]. Thus fractal viscous fingering patterns and Diffusion Limited Aggregation clusters have a similar geometrical structure. *Work conducted in collaboration with H.L. Swinney, M.G. Moore and Eran Sharon [1] E. Sharon, M. G. Moore, W. D. McCormick, and H. L. Swinney, Phys. Rev. Lett. 91, 205504 (2003). [2] B.Davidovitch et A. Levermann and I. Procaccia, Phys. Rev. E 62, 5919 (2000). [3] D. A. Kessler et al., Phys. Rev. E 57, 6913 (1998).

Praud, Olivier

2004-03-01

306

A fractal description of grain boundaries in a sintered powder metallurgical sample

In this paper, the authors have presented the concept of using the fractal dimension as a descriptor for the tortuosity of a grain boundary. The implication of fractal concepts in reality is not fully understood. But in their view, estimation of the fractal dimension of the grain boundaries might be beneficial to quantify the surface area related parameters. This would be of importance in materials where the surface properties play a dominant role such as in catalysis. In the synthesis of powder particles, an idea about the fractal dimension might also help in optimizing process parameters to produce powder particles having large values of fractal dimensions. This in turn could ensure better sinterability and surface activity of powders. The grain boundary traces of sintered YBa[sub 2]Cu[sub 3]O[sub 7] high [Tc] superconductor showed fractal structure and the fractal dimension was found to be dependent on grain orientation.

Ramakrishnan, K.N.; Venkadesan, S.; Murthy, K.P.N. (Indira Gandhi Centre for Atomic Research, Tamilnadu (India). Metallurgy and Materials Group)

1995-03-01

307

Multi-Scale Fractal Analysis of Image Texture and Pattern

NASA Technical Reports Server (NTRS)

Analyses of the fractal dimension of Normalized Difference Vegetation Index (NDVI) images of homogeneous land covers near Huntsville, Alabama revealed that the fractal dimension of an image of an agricultural land cover indicates greater complexity as pixel size increases, a forested land cover gradually grows smoother, and an urban image remains roughly self-similar over the range of pixel sizes analyzed (10 to 80 meters). A similar analysis of Landsat Thematic Mapper images of the East Humboldt Range in Nevada taken four months apart show a more complex relation between pixel size and fractal dimension. The major visible difference between the spring and late summer NDVI images of the absence of high elevation snow cover in the summer image. This change significantly alters the relation between fractal dimension and pixel size. The slope of the fractal dimensional-resolution relation provides indications of how image classification or feature identification will be affected by changes in sensor spatial resolution.

Emerson, Charles W.; Lam, Nina Siu-Ngan; Quattrochi, Dale A.

1999-01-01

308

Computerized analysis of mammographic parenchymal patterns using fractal analysis

NASA Astrophysics Data System (ADS)

Mammographic parenchymal patterns have been shown to be associated with breast cancer risk. Fractal-based texture analyses, including box-counting methods and Minkowski dimension, were performed within parenchymal regions of normal mammograms of BRCA1/BRCA2 gene mutation carriers and within those of women at low risk for developing breast cancer. Receiver Operating Characteristic (ROC) analysis was used to assess the performance of the computerized radiographic markers in the task of distinguishing between high and low-risk subjects. A multifractal phenomenon was observed with the fractal analyses. The high frequency component of fractal dimension from the conventional box-counting technique yielded an Az value of 0.84 in differentiating between two groups, while using the LDA to estimate the fractal dimension yielded an Az value of 0.91 for the high frequency component. An Az value of 0.82 was obtained with fractal dimensions extracted using the Minkowski algorithm.

Li, Hui; Giger, Maryellen L.; Huo, Zhimin; Olopade, Olufunmilayo I.; Chinander, Michael R.; Lan, Li; Bonta, Ioana R.

2003-05-01

309

Diffusion on fractals with interacting internal boundaries

NASA Astrophysics Data System (ADS)

We studied random walks interacting with the internal boundaries (borders of lacunas) of Sierpinski carpets (SC), which are infinitely ramified fractals with fractal dimensions DF between 1 and 2. The probability of steps along the borders is u=exp(-E/kBT) times the probability of steps in the bulk, where E<0 represents attraction and E>0 represents repulsion. The mean-square displacement

Aara~O Reis, F. D. A.

1999-07-01

310

Microtopographic Inspection and Fractal Analysis of Skin Neoplasia

NASA Astrophysics Data System (ADS)

Early detection of skin cancer is fundamental to a successful treatment. Changes in the shape, including the relief, of skin lesions are an indicator of a possible malignity. Optical microtopographic inspection of skin lesions can be used to identify diagnostic patterns of benign and malign skin' lesions. Statistical parameters like the mean roughness (Ra) may allow the discrimination between different types of lesions and degree of malignity. Fractal analysis of bi-dimensional and 3D images of skin lesions can validate or complement that assessment by calculation of its fractal dimensions (FD). On the study herein reported the microtopographic inspection of the skin lesions were performed using the optical triangulation based microtopographer developed at the Physics Department of the University of Minho, MICROTOP.03.MFC. The patients that participated in this research work were men and women older than 15 years with the clinical and histopathology diagnoses of: melanoma, basocellular carcinoma, epidermoide carcinoma, actinic keratosis, keratoacantosis and benign nevus. Latex impressions of the lesions were taken and microtopographically analyzed. Characteristic information for each type of studied lesion was obtained. For melanoma it was observed that on the average these tumors present an increased roughness of around 67 percent compared to the roughness of the healthy skin. This feature allows the distinction from other tumors as basocellular carcinoma (were the roughness increase was in the average of 49 percent) and benign lesions as the epidermoide cyst (37 percent) or the seborrhea keratosis (4 percent). Tumor size and roughness are directly proportional to the grade of malignality. The characterization of the fractal geometry of 2D (histological slides) and 3D images of skin lesions was performed by obtaining its FD evaluated by means of the Box counting method. Results obtained showed that the average fractal dimension of histological slide images (FDh) corresponding to some neoplasia is higher (1.334+/-0.072) than those for healthy skin (1.091+/-0.082). A significant difference between the fractal dimensions of neoplasia and healhty skin (>0.001) was registered. The FD of microtopography maps (FDm) can also distinguish between healthy and malignant tissue in general (2.277+/-0.070 to 2.309+/-0.040), but not discriminate the different types of skin neoplasias. The combination of the rugometric evaluation and fractal geometry characterization provides valuable information about the malignity of skin lesions and type of lesion.

Costa, Manuel F. M.; Hipolito, Alberto Valencia; Gutierrez, Gustavo Fidel; Chanona, Jorge; Gallegos, Eva Ramón

2008-04-01

311

Random walks of oriented particles on fractals

NASA Astrophysics Data System (ADS)

Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features.

Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko

2014-04-01

312

NASA Astrophysics Data System (ADS)

The impossibility of observing magma migration inside the crust obliges us to rely on geophysical data and mathematical modelling to interpret precursors and to forecast volcanic eruptions. Of the geophysical signals that may be recorded before and during an eruption, deformation and seismicity are two of the most relevant as they are directly related to its dynamic. The final phase of the unrest episode that preceded the 2011-2012 eruption on El Hierro (Canary Islands) was characterized by local and accelerated deformation and seismic energy release indicating an increasing fracturing and a migration of the magma. Application of time varying fractal analysis to the seismic data and the characterization of the seismicity pattern and the strain and the stress rates allow us to identify different stages in the source mechanism and to infer the geometry of the path used by the magma and associated fluids to reach the Earth's surface. The results obtained illustrate the relevance of such studies to understanding volcanic unrest and the causes that govern the initiation of volcanic eruptions.

López, Carmen; Martí, Joan; Abella, Rafael; Tarraga, Marta

2014-05-01

313

NASA Astrophysics Data System (ADS)

The impossibility of observing magma migration inside the crust obliges us to rely on geophysical data and mathematical modelling to interpret precursors and to forecast volcanic eruptions. Of the geophysical signals that may be recorded before and during an eruption, deformation and seismicity are two of the most relevant as they are directly related to its dynamic. The final phase of the unrest episode that preceded the 2011-2012 eruption on El Hierro (Canary Islands) was characterized by local and accelerated deformation and seismic energy release indicating an increasing fracturing and a migration of the magma. Application of time varying fractal analysis to the seismic data and the characterization of the seismicity pattern and the strain and the stress rates allow us to identify different stages in the source mechanism and to infer the geometry of the path used by the magma and associated fluids to reach the Earth's surface. The results obtained illustrate the relevance of such studies to understanding volcanic unrest and the causes that govern the initiation of volcanic eruptions.

López, Carmen; Martí, Joan; Abella, Rafael; Tarraga, Marta

2014-05-01

314

Scaling properties of multilayer fractal structures

Multilayer fractal structures, being a subclass of nonperiodic yet deterministic media are studied in relation to the problem of classical wave propagation. A general case of fractal multilayers is considered. Numerical calculations reveal that the geometry and optical spectra of such structures are directly connected. Namely, it has been found that structures and spectra exhibit exactly the same scaling relations,

S. V. Zhurkovsky; Andrei V. Lavrinenko; Sergey V. Gaponenko

2002-01-01

315

Fractal and multifractal analysis: a review.

Over the last years, fractal and multifractal geometries were applied extensively in many medical signal (1D, 2D or 3D) analysis applications like pattern recognition, texture analysis and segmentation. Application of this geometry relies heavily on the estimation of the fractal features. Various methods were proposed to estimate the fractal dimension or multifractal spectral of a signal. This article presents an overview of these algorithms, the way they work, their benefits and their limits. The aim of this review is to explain and to categorize the various algorithms into groups and their application in the field of medical signal analysis. PMID:19535282

Lopes, R; Betrouni, N

2009-08-01

316

Characterization of branch complexity by fractal analyses

The comparison between complexity in the sense of space occupancy (box-counting fractal dimension D(c) and information dimension D1) and heterogeneity in the sense of space distribution (average evenness index f and evenness variation coefficient J(cv)) were investigated in mathematical fractal objects and natural branch structures. In general, increased fractal dimension was paired with low heterogeneity. Comparisons between branch architecture in Anthyllis cytisoides under different slope exposure and grazing impact revealed that branches were more complex and more homogeneously distributed for plants on northern exposures than southern, while grazing had no impact during a wet year. Developmental instability was also investigated by the statistical noise of the allometric relation between internode length and node order. In conclusion, our study demonstrated that fractal dimension of branch structure can be used to analyze the structural organization of plants, especially if we consider not only fractal dimension but also shoot distribution within the canopy (lacunarity). These indexes together with developmental instability analyses are good indicators of growth responses to the environment.

Alados, C. L.; Escos, J.; Emlen, J. M.; Freeman, D. C.

1999-01-01

317

Fractal nature of humic materials

Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this disorder within disorder.'' Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fraction has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis.

Rice, J.A. (South Dakota State Univ., Brookings, SD (United States). Dept. of Chemistry); Lin, J.S. (Oak Ridge National Lab., TN (United States))

1992-01-01

318

Fractal nature of humic materials

Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this ``disorder within disorder.`` Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fraction has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis.

Rice, J.A. [South Dakota State Univ., Brookings, SD (United States). Dept. of Chemistry; Lin, J.S. [Oak Ridge National Lab., TN (United States)

1992-03-01

319

Chaos vs linear instability in the Vlasov equation: A fractal analysis characterization

In this paper we discuss the most recent results concerning the Vlasov dynamics inside the spinodal region. The chaotic behavior which follows an initial regular evolution is characterized through the calculation of the fractal dimension of the distribution of the final modes excited. The ambiguous role of the largest Lyapunov exponent for unstable systems is also critically reviewed. This investigation seems to confirm the crucial role played by deterministic chaos in nuclear multifragmentation. {copyright} {ital 1996 The American Physical Society.}

Atalmi, A.; Baldo, M.; Burgio, G.F.; Rapisarda, A. [Centro Siciliano di Fisica Nucleare e Struttura della Materia, c.so Italia 57, I-95129 Catania (Italy)] [Centro Siciliano di Fisica Nucleare e Struttura della Materia, c.so Italia 57, I-95129 Catania (Italy); [Dipartimento di Fisica Universita di Catania, c.so Italia 57, I-95129 Catania (Italy); [I.N.F.N. Sezione di Catania, c.so Italia 57, I-95129 Catania (Italy)

1996-05-01

320

NASA Astrophysics Data System (ADS)

Pore structure is one of important factors affecting the properties of porous media, but it is difficult to describe the complexity of pore structure exactly. Fractal theory is an effective and available method for quantifying the complex and irregular pore structure. In this paper, the fractal dimension calculated by box-counting method based on fractal theory was applied to characterize the pore structure of artificial cores. The microstructure or pore distribution in the porous material was obtained using the nuclear magnetic resonance imaging (MRI). Three classical fractals and one sand packed bed model were selected as the experimental material to investigate the influence of box sizes, threshold value, and the image resolution when performing fractal analysis. To avoid the influence of box sizes, a sequence of divisors of the image was proposed and compared with other two algorithms (geometric sequence and arithmetic sequence) with its performance of partitioning the image completely and bringing the least fitted error. Threshold value selected manually and automatically showed that it plays an important role during the image binary processing and the minimum-error method can be used to obtain an appropriate or reasonable one. Images obtained under different pixel matrices in MRI were used to analyze the influence of image resolution. Higher image resolution can detect more quantity of pore structure and increase its irregularity. With benefits of those influence factors, fractal analysis on four kinds of artificial cores showed the fractal dimension can be used to distinguish the different kinds of artificial cores and the relationship between fractal dimension and porosity or permeability can be expressed by the model of D = a - bln(x + c).

Wang, Heming; Liu, Yu; Song, Yongchen; Zhao, Yuechao; Zhao, Jiafei; Wang, Dayong

2012-11-01

321

A Fractal Approach to Assess the Risks of Nitroamine Explosives

To the best of our knowledge, this work represents the first thermal conductivity theory for fractal energetic particle groups to combine fractal and hot-spot theories. We considered the influence of the fractal dimensions of particles on their thermal conductivity and even on the sensitivity of the explosive. Based on this theory, two types of nitroamine explosives (hexahydro-1,3,5-trinitro-1,3,5-triazine [RDX] and hexanitrohexaazaisowurtzitane

Xiaolan Song; Fengsheng Li; Yi Wang; Chongwei An; Jingyu Wang; Jinglin Zhang

2012-01-01

322

We have created a second-order finite-difference solution to the anisotropic elastic wave equation in three dimensions and implemented the solution as an efficient Matlab script. This program allows the user to generate synthetic seismograms for three-dimensional anisotropic earth structure. The code was written for teleseismic wave propagation in the 1 0.1 Hz frequency range but is of general utility and

Oliver S. Boyd

2006-01-01

323

SLIC (simple line interface calculation). [Usable in 1, 2, or 3 space dimensions

SLIC is an alternating-direction method for the geometric approximation of fluid interfaces. It may be used in one, two, or three space dimensions, and it is characterized by the following features: Fluid surfaces are represented locally for each mixed-fluid zone, and these surfaces are defined as a composition of one-space-dimensional components, one for each coordinate direction. These one-dimensional components are

W. F. Noh; P. Woodward

1976-01-01

324

Fractal properties of quantum spacetime.

We show that, in general, a spacetime having a quantum group symmetry has also a scale-dependent fractal dimension which deviates from its classical value at short scales, a phenomenon that resembles what is observed in some approaches to quantum gravity. In particular, we analyze the cases of a quantum sphere and of kappa-Minkowski spacetime, the latter being relevant in the context of quantum gravity. PMID:19392189

Benedetti, Dario

2009-03-20

325

Fractality of eroded coastlines of correlated landscapes.

Using numerical simulations of a simple sea-coast mechanical erosion model, we investigate the effect of spatial long-range correlations in the lithology of coastal landscapes on the fractal behavior of the corresponding coastlines. In the model, the resistance of a coast section to erosion depends on the local lithology configuration as well as on the number of neighboring sea sides. For weak sea forces, the sea is trapped by the coastline and the eroding process stops after some time. For strong sea forces erosion is perpetual. The transition between these two regimes takes place at a critical sea force, characterized by a fractal coastline front. For uncorrelated landscapes, we obtain, at the critical value, a fractal dimension D=1.33, which is consistent with the dimension of the accessible external perimeter of the spanning cluster in two-dimensional percolation. For sea forces above the critical value, our results indicate that the coastline is self-affine and belongs to the Kardar-Parisi-Zhang universality class. In the case of landscapes generated with power-law spatial long-range correlations, the coastline fractal dimension changes continuously with the Hurst exponent H, decreasing from D=1.34 to 1.04, for H=0 and 1, respectively. This nonuniversal behavior is compatible with the multitude of fractal dimensions found for real coastlines. PMID:21867252

Morais, P A; Oliveira, E A; Araújo, N A M; Herrmann, H J; Andrade, J S

2011-07-01

326

Novel design of star shaped circular fractal antenna

This paper presents the design of a star shaped circular microstrip fractal antenna. This star shaped circular microstrip fractal antenna has been designed on substrate with dielectric constant epsivr = 4.3 and thickness h = 1.53 mm. The antenna has been simulated using FDTD technique with dimension a = 40 mm. The simulated result shows the multiple resonances at 0.81

Raj Kumar; Yogesh B. Thakare; M. Bhattacharya

2008-01-01

327

Fractal image analysis - Application to the topography of Oregon and synthetic images.

NASA Technical Reports Server (NTRS)

Digitized topography for the state of Oregon has been used to obtain maps of fractal dimension and roughness amplitude. The roughness amplitude correlates well with variations in relief and is a promising parameter for the quantitative classification of landforms. The spatial variations in fractal dimension are low and show no clear correlation with different tectonic settings. For Oregon the mean fractal dimension from a two-dimensional spectral analysis is D = 2.586, and for a one-dimensional spectral analysis the mean fractal dimension is D = 1.487, which is close to the Brown noise value D = 1.5. Synthetic two-dimensional images have also been generated for a range of D values. For D = 2.6, the synthetic image has a mean one-dimensional spectral fractal dimension D = 1.58, which is consistent with the results for Oregon. This approach can be easily applied to any digitzed image that obeys fractal statistics.

Huang, Jie; Turcotte, Donald L.

1990-01-01

328

Spectral and fractal measures of cerebellar and cerebral activity in various types of anesthesia.

The features of rat cerebral and cerebellar electrocortical activity (ECoG) under different types of anaesthesia (nembutal, ketamine or zoletil) were examined by the distribution of spectral entropy across frequency bands of ECoG and by calculation of fractal dimension determined on the basis of Higuchi's algorithm. Spectral entropy, as a measure of activity, in the case of cerebrum had greater values than the spectral entropy of cerebellum in low frequency ranges, regardless of the type of applied anesthetic. Various anesthetics evoked different effects on spectral entropy of electrocortical activity: spectral entropy of delta range greatly dominated under nembutal anesthesia, while ketamine or zoletil appeared to affect the spectral entropy of higher frequency ranges. The pronounced effect of ketamine or zoletil anesthesia on spectral entropy of higher frequency was confirmed by the higher values of Higucihi's fractal dimension (FD) of ECoGs, with a tendency of higher FD values in cerebellar activity than cerebral activity. PMID:20407488

Kekovic, Goran; Stojadinovic, Gordana; Martac, Ljiljana; Podgorac, Jelena; Sekulic, Slobodan; Culic, Milka

2010-01-01

329

Fractal characterization of neural correlates of consciousness

NASA Astrophysics Data System (ADS)

In this work we present a novel experimental paradigm, based on binocular rivalry, to address the study of internally and externally generated conscious percepts. Assuming the nonlinear nature of the EEG signals, we propose the use of fractal dimension to characterize the complexity of the EEG associated with each percept. Data analysis showed significant differences in complexity between the internally and externally generated percepts. Moreover, EEG complexity of auditory and visual percepts was unequal. These results support fractal dimension analyses as a new tool to characterize conscious perception.

Ibañez-Molina, A. J.; Iglesias-Parro, S.

2013-01-01

330

Antenna Miniaturization Using Koch Snowflake Fractal Geometry

NASA Astrophysics Data System (ADS)

The Wireless Industry is witnessing an volatile emergence today in present era. Also requires the performance over several frequency bands or are reconfigurable as the demands on the system changes. This Paper Presents Rectangular, Koch Fractal Patch Antennas on Single and Multilayer Substrate With and Without Air-Gap using Advanced Design System Simulator (ADS). Fractal Antenna provides Miniaturization over conventional microstrip Antennas. The Antennas Have Been Designed on FR4 substrate with ? = 4.2, h = 1.53 and the initial Dimension of the simple Rectangular Patch is 36.08 * 29.6 mm. The experimental Resonant Frequencies of the Fractal Patch with 1st, 2nd & 3rd are observed 2.22, 2.14 & 2.02 GHz Respectively in comparison to Rectangular Patch with 2.43 GHz. The reduced Impedance bandwidth of the Fractal Patch has been improved by designing the patch over multilayer substrate with varying Air-gap between two Substrate. As we increase the air- gap between the two substrate layer further enhancement in impedance bandwidth of Fractal antenna has been Obtained. The Radiation pattern of Koch Fractal antenna is as similar to rectangular patch antenna but with better H-plane Cross Polarization for fractal patch. The all simulated Results are in close Agreement with experimental Results.

Minal; Dhama, Nitin

2010-11-01

331

There is ongoing research directed towards the development of cheap and reliable decision support systems for the detection and prediction of osteoarthritis (OA) in knee joints. Fractal analysis of trabecular bone texture X-ray images is one of the most promising approaches. It is cheap and non-invasive. However, difficulties arise when the fractal signature methods are used to quantify bone roughness and anisotropy on individual scales. This is because the fractal methods are able to quantify bone texture only in the vertical and horizontal directions, and previous studies showed that OA bone changes can occur in any direction. To address these difficulties, three directional fractal signature methods were developed in this study, i.e. a fractal signature Hurst orientation transform (FSHOT) method, a variance orientation transform (VOT) method, and a blanket with rotating-grid (BRG) method. These methods were tested and the best performing method was selected. Unlike other methods, the newly developed techniques are able to calculate fractal dimensions (FDs) on individual scales (i.e. fractal signature) in all possible directions. The accuracy of the methods developed in measuring texture roughness and anisotropy on individual scales was evaluated. The effects of imaging conditions such as image noise, blur, exposure, magnification, and projection angle and the effects of translation of the bone region of interest on texture parameters were also evaluated. Computer-generated fractal surface images with known FDs and X-ray images obtained for a human tibia head were used. Results obtained show that the VOT method performs better than the FSHOT and BRG methods. PMID:19278198

Wolski, M; Podsiadlo, P; Stachowiak, G W

2009-02-01

332

Comments on the Riemann conjecture and index theory on Cantorian fractal space-time

An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbert. A discrete\\/fractal derivative self adjoint operator whose spectrum may contain the nontrivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show using generalized index-theory arguments, corresponding to the (fractal) spectral dimensions of fractal branes living in Cantorian-fractal

Carlos Castro; Jorge Mahecha

2000-01-01

333

Comments on the Riemann conjecture and index theory on Cantorian fractal space-time

An heuristic proof of the Riemann conjecture is proposed. It is based on the old idea of Polya–Hilbert. A discrete\\/fractal derivative self-adjoint operator whose spectrum may contain the non-trivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show using generalized index-theory arguments, corresponding to the (fractal) spectral dimensions of fractal branes living in Cantorian-fractal space-time,

Carlos Castro; Jorge Mahecha

2002-01-01

334

Deterministic fractals: extracting additional information from small-angle scattering data.

The small-angle scattering curves of deterministic mass fractals are studied and analyzed in momentum space. In the fractal region, the curve I(q)q(D) is found to be log-periodic with good accuracy, and the period is equal to the scaling factor of the fractal. Here, D and I(q) are the fractal dimension and the scattering intensity, respectively. The number of periods of this curve coincides with the number of fractal iterations. We show that the log-periodicity of I(q)q(D) in the momentum space is related to the log-periodicity of the quantity g(r)r(3-D) in the real space, where g(r) is the pair distribution function. The minima and maxima positions of the scattering intensity are estimated explicitly by relating them to the pair distance distribution in real space. It is shown that the minima and maxima are damped with increasing polydispersity of the fractal sets; however, they remain quite pronounced even at sufficiently large values of polydispersity. A generalized self-similar Vicsek fractal with controllable fractal dimension is introduced, and its scattering properties are studied to illustrate the above findings. In contrast with the usual methods, the present analysis allows us to obtain not only the fractal dimension and the edges of the fractal region, but also the fractal iteration number, the scaling factor, and the number of structural units from which the fractal is composed. PMID:22060471

Cherny, A Yu; Anitas, E M; Osipov, V A; Kuklin, A I

2011-09-01

335

[Physical and fractal properties of polyaluminum chloride-humic acid (PACl-HA) flocs].

The powder of polyaluminum chloride-humic acid (PACl-HA) flocs was prepared by cryo-freezing-vacuum-drying method. These flocs were characterized by X-ray diffractometry, FTIR spectroscopy, elementary analysis and surface area determination. The results show that these flocs are amorphous, mainly composed by elements of C, O, Al, and reserve some characteristic functional groups from PACl, HA or Kaolin. The N2 absorption-desorption data determined the microstructure of PACl-HA flocs: 130 - 161 m2 x g(-1) of BET specific surface area, 0.38 - 0.52 cm3 x g(-1) of BJH cumulative absorbed volume and 7.7 - 9.6nm of BJH desorption average pore diameter. The peak values of pore size distribution (PSD) curves were found at 8.4 - 11.2nm of pore diameter. The self-similar and rough surface was observed in SEM images of PACl-HA flocs. The surface fractal dimensions D(s) of the flocs determined from both SEM images method and N2 absorption-desorption one were 2.03 - 2.26 and 2.24 - 2.37, respectively. The correspondent fractal scale for the former method was 23 - 390nm, mainly belonging to exterior surface scales, and the lowest limit of the fractal scale for the latter method was 0.2nm and fell in pore surface scales. This demonstrated that the flocs surface had multi-scale fractal properties. Furthermore, some difference was given between the pore surface fractal dimensions D(s) calculated from N2 absorption data and desorption data. The calculated pore surface D(s) values of much more than three through thermodynamic model had discrepancy from Sahouli et al's results. PMID:17326433

Wang, Yi-Li; Liu, Jie; Du, Bai-Yu

2006-11-01

336

Fractal structure of porous solids characterized by adsorption

NASA Astrophysics Data System (ADS)

The fractal dimensions of porous solids, zeolites A, X, and Dowex MSC-1 were determined by physical adsorption and the values were 2.57, 2.37, and 2.92, respectively. In fact, it is counting the coverages of the adsorbate on the adsorbent. The solids can be visualized and simulated by a reducing similarity transformation. The resulting difference and significance of using the volume and area of the adsorbate to obtain the fractal dimensions are discussed.

Sze, S. J.; Lee, T. Y.

1995-04-01

337

Fractal symmetry of protein interior: what have we learned?

The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept\\u000a of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim\\u000a of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially,\\u000a there

Anirban Banerji; Indira Ghosh

2011-01-01

338

Rapid calculation method for Frenkel-type two-exciton states in one to three dimensions.

Biexciton and two-exciton dissociated states of Frenkel-type excitons are well described by a tight-binding model with a nearest-neighbor approximation. Such two-exciton states in a finite-size lattice are usually calculated by numerical diagonalization of the Hamiltonian, which requires an increasing amount of computational time and memory as the lattice size increases. I develop here a rapid, memory-saving method to calculate the energies and wave functions of two-exciton states by employing a bisection method. In addition, an attractive interaction between two excitons in the tight-binding model can be obtained directly so that the biexciton energy agrees with the observed energy, without the need for the trial-and-error procedure implemented in the numerical diagonalization method. PMID:25053304

Ajiki, Hiroshi

2014-07-21

339

The bending and torsional degrees of freedom in S1 acetylene, C2H2, are subject to strong vibrational resonances and rovibrational interactions, which create complex vibrational polyad structures even at low energy. As the internal energy approaches that of the barrier to cis-trans isomerization, these energy level patterns undergo further large-scale reorganization that cannot be satisfactorily treated by traditional models tied to local minima of the potential energy surface for nuclear motion. Experimental spectra in the region near the cis-trans transition state have revealed these complicated new patterns. In order to understand near-barrier spectroscopic observations and to predict the detailed effects of cis-trans isomerization on the rovibrational energy level structure, we have performed reduced dimension rovibrational variational calculations of the S1 state. In this paper, we present the methodological details, several of which require special care. Our calculation uses a high accuracy ab initio potential surface and a fully symmetrized extended complete nuclear permutation inversion group theoretical treatment of a multivalued internal coordinate system that is appropriate for large amplitude bending and torsional motions. We also discuss the details of the rovibrational basis functions and their symmetrization, as well as the use of a constrained reduced dimension rovibrational kinetic energy operator. PMID:24437882

Changala, P Bryan

2014-01-14

340

NASA Astrophysics Data System (ADS)

The bending and torsional degrees of freedom in S1 acetylene, C2H2, are subject to strong vibrational resonances and rovibrational interactions, which create complex vibrational polyad structures even at low energy. As the internal energy approaches that of the barrier to cis-trans isomerization, these energy level patterns undergo further large-scale reorganization that cannot be satisfactorily treated by traditional models tied to local minima of the potential energy surface for nuclear motion. Experimental spectra in the region near the cis-trans transition state have revealed these complicated new patterns. In order to understand near-barrier spectroscopic observations and to predict the detailed effects of cis-trans isomerization on the rovibrational energy level structure, we have performed reduced dimension rovibrational variational calculations of the S1 state. In this paper, we present the methodological details, several of which require special care. Our calculation uses a high accuracy ab initio potential surface and a fully symmetrized extended complete nuclear permutation inversion group theoretical treatment of a multivalued internal coordinate system that is appropriate for large amplitude bending and torsional motions. We also discuss the details of the rovibrational basis functions and their symmetrization, as well as the use of a constrained reduced dimension rovibrational kinetic energy operator.

Changala, P. Bryan

2014-01-01

341

Fraunhofer diffraction by Cantor fractals: study of their lacunarity

NASA Astrophysics Data System (ADS)

The optical diffraction by fractal openings is increasingly being studied, because it allows to determine the properties and parameters that characterize these objects. Allain and Cloitre published the first results showing that the resulting analysis of the distribution of intensity obtained for diffraction experiments through fractal deterministic pupils permits the direct objection of the Hausdorff dimension an of other geometrical characteristic of these structures. In this work are studied, solved analytically, and characterized the lacunarity effect (epsilon) , dimension d and stage of growth k of Cantor fractal about he distribution of intensities of the diffraction pattern. In particular we make notice in the influence of lacunarity because this is one of the first works in which this geometric fractal parameter is being into consideration. The result of this study allow to say that an intimate relation exists between the distribution of the diffracted waves and the parameters that describe this kind of fractal geometry.

Zunino, Luciano; Garavaglia, Mario

2001-08-01

342

Chaos, Fractals, and Polynomials.

ERIC Educational Resources Information Center

Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)

Tylee, J. Louis; Tylee, Thomas B.

1996-01-01

343

Fractal structure of the interplanetary magnetic field

NASA Technical Reports Server (NTRS)

Under some conditions, time series of the interplanetary magnetic field strength and components have the properties of fractal curves. Magnetic field measurements made near 8.5 AU by Voyager 2 from June 5 to August 24, 1981 were self-similar over time scales from approximately 20 sec to approximately 3 x 100,000 sec, and the fractal dimension of the time series of the strength and components of the magnetic field was D = 5/3, corresponding to a power spectrum P(f) approximately f sup -5/3. Since the Kolmogorov spectrum for homogeneous, isotropic, stationary turbulence is also f sup -5/3, the Voyager 2 measurements are consistent with the observation of an inertial range of turbulence extending over approximately four decades in frequency. Interaction regions probably contributed most of the power in this interval. As an example, one interaction region is discussed in which the magnetic field had a fractal dimension D = 5/3.

Burlaga, L. F.; Klein, L. W.

1986-01-01

344

Wavelet and fractal analysis of ground-vehicle images

NASA Astrophysics Data System (ADS)

A large number of terrain images were taken at Aberdeen Proving Grounds, some containing ground vehicles. Is it possible to screen the images for possible targets in a short amount of time using the fractal dimension to detect texture variations. The fractal dimension is determined using the wavelet transform for these visual images. The vehicles are positioned within the grass and in different locations. Since it has been established that natural terrain exhibits a statistical l/f self-similarity property and the psychophysical perception of roughness can be quantified by the same self-similarity, fractal dimensions estimates should vary only at texture boundaries and breaks in the tree and grass patterns. Breaks in the patterns are found using contour plots of the dimension estimates and are considered as perceptual texture variations. Variation in the dimension estimate is considered more important than the accuracy of the actual dimensions number. Accurate variation estimates are found even with low resolution images.

Gorsich, David J.; Tolle, Charles R.; Karlsen, Robert E.; Gerhart, Grant R.

1996-10-01

345

NSDL National Science Digital Library

This first website offers a collection of fractal music using images created by G.W.F. Albrecht. The technology and mathematics which this presentation draws on is described on the second website. The second website, developed by David Strohbeen, offers some basic information about fractals and fractal music. He has also posted some samples of his music and invites visitors to download software for creating fractal music and to submit their own compositions.

346

Emergence of fractals in aggregation with stochastic self-replication.

We propose and investigate a simple model which describes the kinetics of aggregation of Brownian particles with stochastic self-replication. An exact solution and the scaling theory are presented alongside numerical simulation which fully support all theoretical findings. In particular, we show analytically that the particle size distribution function exhibits dynamic scaling and we verify it numerically using the idea of data collapse. Furthermore, the conditions under which the resulting system emerges as a fractal are found, the fractal dimension of the system is given, and the relationship between this fractal dimension and a conserved quantity is pointed out. PMID:24229145

Hassan, Md Kamrul; Hassan, Md Zahedul; Islam, Nabila

2013-10-01

347

Fractal properties of lysozyme: A neutron scattering study

NASA Astrophysics Data System (ADS)

The spatial structure and dynamics of hen egg white lysozyme have been investigated by small-angle and inelastic neutron scattering. Analysis of the results was carried using the fractal approach, which allowed determination of the fractal and fracton dimensions of lysozyme, i.e., consideration of the protein structure and dynamics by using a unified approach. Small-angle neutron scattering studies of thermal denaturation of lysozyme have revealed changes in the fractal dimension in the vicinity of the thermal denaturation temperature that reflect changes in the spatial organization of protein.

Lushnikov, S. G.; Svanidze, A. V.; Gvasaliya, S. N.; Torok, G.; Rosta, L.; Sashin, I. L.

2009-03-01

348

Multi-Scale Fractal Analysis of Image Texture and Pattern

NASA Technical Reports Server (NTRS)

Fractals embody important ideas of self-similarity, in which the spatial behavior or appearance of a system is largely independent of scale. Self-similarity is defined as a property of curves or surfaces where each part is indistinguishable from the whole, or where the form of the curve or surface is invariant with respect to scale. An ideal fractal (or monofractal) curve or surface has a constant dimension over all scales, although it may not be an integer value. This is in contrast to Euclidean or topological dimensions, where discrete one, two, and three dimensions describe curves, planes, and volumes. Theoretically, if the digital numbers of a remotely sensed image resemble an ideal fractal surface, then due to the self-similarity property, the fractal dimension of the image will not vary with scale and resolution. However, most geographical phenomena are not strictly self-similar at all scales, but they can often be modeled by a stochastic fractal in which the scaling and self-similarity properties of the fractal have inexact patterns that can be described by statistics. Stochastic fractal sets relax the monofractal self-similarity assumption and measure many scales and resolutions in order to represent the varying form of a phenomenon as a function of local variables across space. In image interpretation, pattern is defined as the overall spatial form of related features, and the repetition of certain forms is a characteristic pattern found in many cultural objects and some natural features. Texture is the visual impression of coarseness or smoothness caused by the variability or uniformity of image tone or color. A potential use of fractals concerns the analysis of image texture. In these situations it is commonly observed that the degree of roughness or inexactness in an image or surface is a function of scale and not of experimental technique. The fractal dimension of remote sensing data could yield quantitative insight on the spatial complexity and information content contained within these data. A software package known as the Image Characterization and Modeling System (ICAMS) was used to explore how fractal dimension is related to surface texture and pattern. The ICAMS software was verified using simulated images of ideal fractal surfaces with specified dimensions. The fractal dimension for areas of homogeneous land cover in the vicinity of Huntsville, Alabama was measured to investigate the relationship between texture and resolution for different land covers.

Emerson, Charles W.

1998-01-01

349

Fractal fluctuations in human respiration.

The present study was designed to characterize respiratory fluctuations in awake, healthy adult humans under resting conditions. For this purpose, we recorded respiratory movements with a strain-gauge pneumograph in 20 subjects. We then used Allan factor, Fano factor, and dispersional analysis to test whether the fluctuations in the number of breaths, respiratory period, and breath amplitude were fractal (i.e., time-scale-invariant) or random in occurrence. Specifically, we measured the slopes of the power laws in the Allan factor, Fano factor, and dispersional analysis curves for original time series and compared these with the slopes of the curves for surrogates (randomized data sets). In addition, the Hurst exponent was calculated from the slope of the power law in the Allan factor curve to determine whether the long-range correlations among the fluctuations in breath number were positively or negatively correlated. The results can be summarized as follows. Fluctuations in all three parameters were fractal in nine subjects. There were four subjects in whom only the fluctuations in number of breaths and breath amplitude were fractal, three subjects in whom only the fluctuations in number of breaths were fractal, and two subjects in whom only fluctuations in breath number and respiratory period were fractal. Time-scale-invariant behavior was absent in the two remaining subjects. The results indicate that, in most cases, apparently random fluctuations in respiratory pattern are, in fact, correlated over more than one time scale. Moreover, the data suggest that fractal fluctuations in breath number, respiratory period, and breath amplitude are controlled by separate processes. PMID:15286051

Fadel, Paul J; Barman, Susan M; Phillips, Shaun W; Gebber, Gerard L

2004-12-01

350

Segmentation of natural microtextures by joining local and global fractal model parameters

NASA Astrophysics Data System (ADS)

This paper deals with the problematic of the segmentation of natural images based on the fractal models. These models are based on the concept of measure of random sets and its self- similarity, and lead to the estimation of a single parameter for a natural texture: its fractal dimension. Different approaches to the implementation of the fractal geometry to the texture study are described and their properties stressed in order to obtain a close relationship between the humans point of view and the estimated fractal variables: the fractal dimension and the fractal density. The Hausdorff geometry of the measure in connection with the fractional Brownian model allowed to correlate the fractal dimension with the short range values of the autocorrelation function of properly transformed natural images, and the local definition of fractal dimensions of natural surfaces. The box counting and the covering blanket methods and algorithms were implemented and applied to estimate the fractal dimension, the lacunarity and the fractal signature of images of paper sheet and cork agglomerate surfaces. Results were statistically validated using the Kolmogorov-Smirnoff test statistics.

Limas Serafim, Antonio F.

1997-08-01

351

ERIC Educational Resources Information Center

Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…

Fraboni, Michael; Moller, Trisha

2008-01-01

352

Abelian Manna model on two fractal lattices

NASA Astrophysics Data System (ADS)

We analyze the avalanche size distribution of the Abelian Manna model on two different fractal lattices with the same dimension dg=ln3/ln2 , with the aim to probe for scaling behavior and to study the systematic dependence of the critical exponents on the dimension and structure of the lattices. We show that the scaling law D(2-?)=dw generalizes the corresponding scaling law on regular lattices, in particular hypercubes, where dw=2 . Furthermore, we observe that the lattice dimension dg , the fractal dimension of the random walk on the lattice dw , and the critical exponent D form a plane in three-dimensional parameter space, i.e., they obey the linear relationship D=0.632(3)dg+0.98(1)dw-0.49(3) .

Huynh, Hoai Nguyen; Chew, Lock Yue; Pruessner, Gunnar

2010-10-01

353

The fractal structure of equine articular cartilage.

The naturally occurring structure of articular cartilage has proven to be an effective means for the facilitation of motion and load support in equine and other animal joints. Cartilage has been found to be a complex and dynamic medium, which has led to an incomplete understanding of the nature and operating mechanisms acting within a joint. Although cartilage has biphasic and triphasic properties, it is believed that the performance of equine articular joints is influenced by the surface roughness of the joint cartilage (Ateshian et al., '98; Chan et al., 2011; Yao and Unsworth, '93). Various joint types with different motions and regimes of lubrication have altered demands on the articular surface that may affect cartilage surface properties. In research performed on freshly harvested samples, equine articular cartilage has been shown to possess a multiscale structure and a fractal dimension. It is thought that by determining the fractal dimension (D) of articular cartilage, a better understanding of the friction, wear, and lubrication mechanisms for biomechanic surfaces can eventually be reached. This study looks at the fractal dimensions of three different articular cartilage surfaces in the equine carpus: the radiocarpal, midcarpal, and carpometacarpal surfaces. The three surfaces provide an ideal comparison of fractal dimensions for a different range of motion, geometry, and loading. In each sample, identical treatment was performed during measurement by a stylus profilometer. PMID:22753326

Smyth, Patrick A; Rifkin, Rebecca E; Jackson, Robert L; Reid Hanson, R

2012-01-01

354

Generalized Mandelbrot Rule for Fractal Sections.

National Technical Information Service (NTIS)

Mandelbrot's rule for sections is generalized to apply to the Hentschel and Procaccia fractal dimension at arbitrary q and on arbitrary sections. It is shown that for almost all (n-m)-dimensional sections, Dn(q) = Dn-m(q) + m, where the Dr(q) are box-coun...

L. V. Meisel

1993-01-01

355

Full dimension Rb2He ground triplet potential energy surface and quantum scattering calculations.

We have developed a three-dimensional potential energy surface for the lowest triplet state of the Rb(2)He complex. A global analytic fit is provided as in the supplementary material [see supplementary material at http://dx.doi.org/10.1063/1.4709433 for the corresponding Fortran code]. This surface is used to perform quantum scattering calculations of (4)He and (3)He colliding with (87)Rb(2) in the partial wave J = 0 at low and ultralow energies. For the heavier helium isotope, the computed vibrational relaxation probabilities show a broad and strong shape resonance for a collisional energy of 0.15 K and a narrow Feshbach resonance at about 17 K for all initial Rb(2) vibrational states studied. The broad resonance corresponds to an efficient relaxation mechanism that does not occur when (3)He is the colliding partner. The Feshbach resonance observed at higher collisional energy is robust with respect to the isotopic substitution. However, its effect on the vibrational relaxation mechanism is faint for both isotopes. PMID:22583230

Guillon, Grégoire; Viel, Alexandra; Launay, Jean-Michel

2012-05-01

356

FORTRAN programs for calculating nonlinear seismic ground response in two dimensions

The programs described here were designed for calculating the nonlinear seismic response of a two-dimensional configuration of soil underlain by a semi-infinite elastic medium representing bedrock. There are two programs. One is for plane strain motions, that is, motions in the plane perpendicular to the long axis of the structure, and the other is for antiplane strain motions, that is motions parallel to the axis. The seismic input is provided by specifying what the motion of the rock-soil boundary would be if the soil were absent and the boundary were a free surface. This may be done by supplying a magnetic tape containing the values of particle velocity for every boundary point at every instant of time. Alternatively, a punch card deck may be supplied giving acceleration values at every instant of time. In the plane strain program it is assumed that the acceleration values apply simultaneously to every point on the boundary; in the antiplane strain program it is assumed that the acceleration values characterize a plane shear wave propagating upward in the underlying elastic medium at a specified angle with the vertical. The nonlinear hysteretic behavior of the soil is represented by a three-dimensional rheological model. A boundary condition is used which takes account of finite rigidity in the elastic substratum. The computations are performed by an explicit finite-difference scheme that proceeds step by step in space and time. Computations are done in terms of stress departures from an unspecified initial state. Source listings are provided here along with instructions for preparing the input. A more detailed discussion of the method is presented elsewhere.

Joyner, W. B.

1978-01-01

357

Probing the Fractal Nature of Long GRBs

NASA Astrophysics Data System (ADS)

We interrogated Swift Long GRBs using a Fast Wavelet technique to probe the observed variability for fractal (or self-affine) behavior. Self-affine behavior for a time-series implies a statistical similarity after a particular rescaling transformation from the Affine Group, X(jt) = j-(?-1)/2X(t). It is straightforward to associate the slope parameter, ?, with the Hurst exponent, H, and the fractal dimension, D. These measures may hold a key to a better understanding of GRB variability and provide constraints for theoretical models.

MacLachlan, G. A.; Ukwatta, T. N.; Dhuga, K. S.; Morris, D. C.; Cobb, B.; Parke, W. C.; Maximon, L. C.; Eskandarian, A.; Shenoy, A.; Coyne, R.; Ghauri, J.; Guo, S.

2011-08-01

358

Fractal dimension based neurofeedback in serious games

EEG-based technology is widely used in serious game design since more wireless headsets that meet consumer criteria for wearability,\\u000a price, portability, and ease-of-use are coming to the market. Originally, such technologies were mostly used in different\\u000a medical applications, Brain Computer Interfaces (BCI) and neurofeedback games. The algorithms adopted in such applications\\u000a are mainly based on power spectrum analysis, which may

Qiang Wang; Olga Sourina; Minh Khoa Nguyen

2011-01-01

359

Trabecular Bone Mechanical Properties and Fractal Dimension.

National Technical Information Service (NTIS)

Countermeasures for reducing bone loss and muscle atrophy due to extended exposure to the microgravity environment of space are continuing to be developed and improved. An important component of this effort is finite element modeling of the lower extremit...

H. A. Hogan

1996-01-01

360

Respiratory Onset Detection Using Variance Fractal Dimension.

National Technical Information Service (NTIS)

Recently a non-invasive acoustical method has been developed to detect respiratory phases without airflow measurement, in which the average power of tracheal breath sounds is used to detect the onset of breaths 1. We improved the accuracy of the breath on...

Y. L. Yap Z. Moussavi

2001-01-01

361

A fractal model for crustal deformation

NASA Technical Reports Server (NTRS)

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.

1986-01-01

362

The three-loop contribution to the anomalous dimension of the diffusion coefficient of the model of a random walk in a potential random field with long-range correlations is calculated. Contrary to earlier conjectures, the result is not zero for logarithmic growth of the correlations, but vanishes only in one and two dimensions, in which the one-loop contribution yields the exact value

S. E. Derkachov; J. Honkonen; Y. M. Pis'mak

1990-01-01

363

NASA Technical Reports Server (NTRS)

Fractals are geometric or data structures which do not simplify under magnification. Fractal Image Compression is a technique which associates a fractal to an image. On the one hand, the fractal can be described in terms of a few succinct rules, while on the other, the fractal contains much or all of the image information. Since the rules are described with less bits of data than the image, compression results. Data compression with fractals is an approach to reach high compression ratios for large data streams related to images. The high compression ratios are attained at a cost of large amounts of computation. Both lossless and lossy modes are supported by the technique. The technique is stable in that small errors in codes lead to small errors in image data. Applications to the NASA mission are discussed.

Barnsley, Michael F.; Sloan, Alan D.

1989-01-01

364

NASA Astrophysics Data System (ADS)

The fractal analysis is carried out to study the influence of adsorption of polyoxyethylene sorbitan monooleate (Tween 80) on the surface properties of graphite. The surface fractal dimension ( d), BET surface area ( S) and pore size distribution (PSD) are calculated from low temperature nitrogen adsorption isotherms. The decline in the d of graphite surface is found as the adsorption amount of Tween 80 increases, which suggests that the adsorbed Tween 80 smoothes the graphite surface. Additionally, the observation of atomic force microscopy (AFM) proves that the original slit pores in pure graphite are blocked up and the step defect sites are screened by Tween 80, which may result in the reduction of graphite roughness. The PSD pattern of graphite changes after the adsorption due to the pore blocking effect. S of the graphite decreases as the adsorption amount of Tween 80 increases, which is attributed to both pore blocking effect and surface screening effect.

Qing-Feng, Hou; Xian-Cai, Lu; Xian-Dong, Liu; Bai-Xing, Hu; Zhi-Jun, Lu; Jian, Shen

2005-02-01

365

Analysis of permeability for transient two-phase flow in fractal porous media

NASA Astrophysics Data System (ADS)

A relative permeability model for transient two-phase flow in fractal porous media is derived based on the fractal characteristics of pore size distribution and the assumption that porous media consists of capillary bundles. The functions in this model are tortuosity fractal dimension, pore fractal dimension, and maximum and minimum pore diameters. Every parameter has clear physical meaning without the use of empirical constants. Good agreement between model predictions and experimental data is obtained, the sensitive parameters that influence the relative permeability are specified and their effects on relative permeability are discussed.

Tan, Xiao-Hua; Li, Xiao-Ping; Liu, Jian-Yi; Zhang, Guang-Dong; Zhang, Lie-Hui

2014-03-01

366

Higuchi Fractal Properties of Onset Epilepsy Electroencephalogram

Epilepsy is a medical term which indicates a common neurological disorder characterized by seizures, because of abnormal neuronal activity. This leads to unconsciousness or even a convulsion. The possible etiologies should be evaluated and treated. Therefore, it is necessary to concentrate not only on finding out efficient treatment methods, but also on developing algorithm to support diagnosis. Currently, there are a number of algorithms, especially nonlinear algorithms. However, those algorithms have some difficulties one of which is the impact of noise on the results. In this paper, in addition to the use of fractal dimension as a principal tool to diagnose epilepsy, the combination between ICA algorithm and averaging filter at the preprocessing step leads to some positive results. The combination which improved the fractal algorithm become robust with noise on EEG signals. As a result, we can see clearly fractal properties in preictal and ictal period so as to epileptic diagnosis.

Khoa, Truong Quang Dang; Ha, Vo Quang; Toi, Vo Van

2012-01-01

367

Fractals and the analysis of waveforms.

Waveforms are planar curves--ordered collections of (x, y) point pairs--where the x values increase monotonically. One technique for numerically classifying waveforms assesses their fractal dimensionality, D. For waveforms: D = log(n)/(log(n) + log(d/L], with n = number of steps in the waveform (one less than the number of (x, y) point pairs), d = planar extent (diameter) of the waveform, and L = total length of the waveform. Under this formulation, fractal dimensions range from D = 1.0, for straight lines through approximately D = 1.15 for random-walk waveforms, to D approaching 1.5 for the most convoluted waveforms. The fractal characterization may be especially useful for analyzing and comparing complex waveforms such as electroencephalograms (EEGs). PMID:3396335

Katz, M J

1988-01-01

368

Fractal structures in casting films from chlorophyll

NASA Astrophysics Data System (ADS)

Chlorophyll (Chl) molecules are important because they can act as natural light-harvesting devices during the photosynthesis. In addition, they have potential for application as component of solar cell. In this work, we have prepared casting films from chlorophyll (Chl) and demonstrated the occurrence of fractal structures when the films were submitted to different concentrations. By using optical microscopy and the box-count method, we have found that the fractal dimension is Df = 1.55. This value is close to predicted by the diffusion-limited aggregation (DLA) model. This suggests that the major mechanism – which determines the growth of the fractal structures from Chl molecules – is the molecular diffusion. Since the efficiencies of solar cells depend on the morphology of their interfaces, these finds can be useful to improve this kind of device.

Pedro, G. C.; Gorza, F. D. S.; de Souza, N. C.; Silva, J. R.

2014-04-01

369

Dimension increase in filtered chaotic signals

An increase in fractal dimension is shown to occur in filtered chaotic signals. The dependence of the Liapunov dimension on the filter parameters is used to predict the behavior of the information dimension which is directly evaluated for two experimental systems: the NMR laser and Rayleigh-Benard convection. Good quantitative agreement with the theoretical predictions is found. The understanding of the

R. Badii; G. Broggi; B. Derighetti; M. Ravani; S. Ciliberto; A. Politi; M. Rubio

1988-01-01

370

NASA Astrophysics Data System (ADS)

In this paper, a new concept of integration of fractal and the butterfly effect is proposed and implemented. A new fractal program was designed and developed to perform such integration. Among many existing fractal and chaos software programs, none of them allow us to achieve the resulting patterns demonstrated in this paper. Moreover, it is the first time that a fractal program provides functional concepts of overlapping results in 3D space and sequential transformations, which allow us to generate a wider variety of patterns. Therefore, potentially an artist can use this program to create 2D digital artworks.

Chang, Yin-Wei; Huang, Fay

371

Fractales en el ruido de reactores de potencia. (Fractals in Power Reactor Noise).

National Technical Information Service (NTIS)

In this work the non- lineal dynamic problem of power reactor is analyzed using classic concepts of fractal analysis as: attractors, Hausdorff-Besikovics dimension, phase space, etc. A new non-linear problem is also analyzed: the discrimination of chaotic...

O. Aguilar Martinez

1994-01-01

372

Fourier transforms and fractals in the food and agricultural industry

NASA Astrophysics Data System (ADS)

Links between the fractal Hausdorff-dimension, the Fourier transform of 2D scenes and image segmentation by texture are discussed. It is shown that the fractal Hausdorff-dimension can be derived by integration of the intensity of the spatial frequency domain (i.e. the Fourier plane) over a set of different band-limited spatial filters. The difference between a computational and optical approach to determine the Hausdorff-dimension are shown, with advantages of both methods discussed. Possible future directions of research/improvements are mentioned. Natural and simulated scenes are considered which apply to a wide range of situations in the agricultural and food industry.

Zwiggelaar, Reyer; Bull, Christine R.

1994-11-01

373

Role of surface roughness characterized by fractal geometry on laminar flow in microchannels.

A three-dimensional model of laminar flow in microchannels is numerically analyzed incorporating surface roughness effects as characterized by fractal geometry. The Weierstrass-Mandelbrot function is proposed to characterize the multiscale self-affine roughness. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all investigated and discussed. The results indicate that unlike flow in smooth microchannels, the Poiseuille number in rough microchannels increases linearly with the Reynolds number, Re, and is larger than what is typically observed in smooth channels. For these situations, the flow over surfaces with high relative roughness induces recirculation and flow separation, which play an important role in single-phase pressure drop. More specifically, surfaces with the larger fractal dimensions yield more frequent variations in the surface profile, which result in a significantly larger incremental pressure loss, even though at the same relative roughness. The accuracy of the predicted Poiseuille number as calculated by the present model is verified using experimental data available in the literature. PMID:19792243

Chen, Yongping; Zhang, Chengbin; Shi, Mingheng; Peterson, G P

2009-08-01

374

Role of surface roughness characterized by fractal geometry on laminar flow in microchannels

NASA Astrophysics Data System (ADS)

A three-dimensional model of laminar flow in microchannels is numerically analyzed incorporating surface roughness effects as characterized by fractal geometry. The Weierstrass-Mandelbrot function is proposed to characterize the multiscale self-affine roughness. The effects of Reynolds number, relative roughness, and fractal dimension on laminar flow are all investigated and discussed. The results indicate that unlike flow in smooth microchannels, the Poiseuille number in rough microchannels increases linearly with the Reynolds number, Re, and is larger than what is typically observed in smooth channels. For these situations, the flow over surfaces with high relative roughness induces recirculation and flow separation, which play an important role in single-phase pressure drop. More specifically, surfaces with the larger fractal dimensions yield more frequent variations in the surface profile, which result in a significantly larger incremental pressure loss, even though at the same relative roughness. The accuracy of the predicted Poiseuille number as calculated by the present model is verified using experimental data available in the literature.

Chen, Yongping; Zhang, Chengbin; Shi, Mingheng; Peterson, G. P.

2009-08-01

375

Evaluation of Two Fractal Methods for Magnetogram Image Analysis

NASA Technical Reports Server (NTRS)

Fractal and multifractal techniques have been applied to various types of solar data to study the fractal properties of sunspots as well as the distribution of photospheric magnetic fields and the role of random motions on the solar surface in this distribution. Other research includes the investigation of changes in the fractal dimension as an indicator for solar flares. Here we evaluate the efficacy of two methods for determining the fractal dimension of an image data set: the Differential Box Counting scheme and a new method, the Jaenisch scheme. To determine the sensitivity of the techniques to changes in image complexity, various types of constructed images are analyzed. In addition, we apply this method to solar magnetogram data from Marshall Space Flight Centers vector magnetograph.

Stark, B.; Adams, M.; Hathaway, D. H.; Hagyard, M. J.

1997-01-01

376

Comparison of fractal and profilometric methods for surface topography characterization

NASA Astrophysics Data System (ADS)

In this study microstructural and roughness characterization of surface of aluminium foils used in lithographic printing process was performed by contact and non-contact profilometric methods and fractal analysis. Significant differences in roughness parameters values inferred from stylus method in respect to those inferred from the non-contact measurements were observed. The investigation of correlation between various fractal dimensions obtained from gray-scale SEM micrographs and binary images resulting from median filtering of the original SEM micrographs as well as selected relevant roughness parameters shows that there is a strong correlation between certain roughness parameters and particular fractal dimensions. This correlations permit better physical understanding of fractal characteristics and interpretation of the dynamics of surface roughness change through processing. Generally these correlations are more suitable for parameters obtained by stylus method than those inferred from the laser-based measurements.

Mahovic Poljacek, S.; Risovic, D.; Furic, K.; Gojo, M.

2008-03-01

377

High precision boundary fractal analysis for shape characterization

NASA Astrophysics Data System (ADS)

Numerous kinds of particles in geological and environmental sciences may be characterized by their boundary fractal dimension. Several methods are available: structured walk, box-counting, dilation and euclidean distance mapping (EDM). The precision and stability of these techniques is variable and usually low precision fractal dimensions are obtained (±0.1). Validation on mathematical fractals and tests of the effects of pixelization, size, resolution and topology were performed with three computer-derived methods (box-counting, dilation and EDM), using mathematical objects and fragments coming from impact and ore deposits breccias. Tests demonstrate that high precision results can be yielded with the right technique and caution. EDM showed the highest precision (±0.01) and strongest reliability with less sensitivity to size and resolution, with reproducible results for fragments as small as 10,000 pixels of area. It was also the most accurate for mathematical fractals.

Bérubé, Dominique; Jébrak, Michel

1999-11-01

378

Global first-passage times of fractal lattices

NASA Astrophysics Data System (ADS)

The global first passage time density of a network is the probability that a random walker released at a random site arrives at an absorbing trap at time T . We find simple expressions for the mean global first passage time ?T? for five fractals: the d -dimensional Sierpinski gasket, T fractal, hierarchical percolation model, Mandelbrot-Given curve, and a deterministic tree. We also find an exact expression for the second moment ?T2? and show that the variance of the first passage time, Var(T) , scales with the number of nodes within the fractal N such that Var(T)˜N4/ dmacr , where dmacr is the spectral dimension.

Haynes, C. P.; Roberts, A. P.

2008-10-01

379

Fractal behavior of nanocrystalline ceria-yttria solid solution

NASA Astrophysics Data System (ADS)

The fractal characteristics of nano-sized powders of CeO 2-YO 1.5 solid solutions, prepared by combustion synthesis and calcined at various temperatures, have been investigated by small angle X-ray scattering technique. Results show a mass-fractal behavior for the powders with mass-fractal dimension Dm in the range 2.2-2.6. The estimated particle radii are in the range of 4-15 nm, which is in close agreement with TEM results. For the powders calcined at higher temperatures, the particle interface has a tendency to become rough with a significant growth in the particle size and polydispersity.

Sastry, P. U.; Sen, D.; Mazumder, S.; Chavan, S. V.; Tyagi, A. K.

2003-11-01

380

Study of fractality of optical fields scattered by Brownian particles

NASA Astrophysics Data System (ADS)

Light-scattering by the ensemble of Brownian particles is simulated and experimentally modeled. It has been shown that temporal stochastization of the scattered radiation field keeps the fractal properties of the particles movement. Empirical diagnostics interconnections have been found between the fractal dimension and fluctuations of the scattered radiation intensity, on the one hand, and the parameters of light-scattering medium, on the other.

Maksimyak, Alexander P.; Shlamp, Katerina I.

2013-12-01

381

Fractal geometry of some Martian lava flow margins: Alba Patera

NASA Technical Reports Server (NTRS)

Fractal dimension for a few lava flow margins on the gently sloping flanks of Alba Patera were measured using the structured walk method. Fractal behavior was observed at scales ranging from 20 to 100 pixels. The upper limit of the linear part of log(margin length) vs. log(scale) profile correlated well to the margin length. The lower limit depended on resolution and flow properties.

Kauhanen, K.

1993-01-01

382

Robust fractal characterization of 1D and 2D signals

NASA Astrophysics Data System (ADS)

Fractal characterization of signals is well suited in analysis of some time series data and in classification of natural shapes and textures. A maximum likelihood estimator is used to measure the parameter H which is directly related to the fractal dimension. The robustness of the estimator and the performance of the method are demonstrated on datasets generated using a variety of techniques. Finally the characterization is used in segmentation of composite images of natural textures.

Avadhanam, Niranjan; Mitra, Sunanda

1993-10-01

383

Linear chains and chain-like fractals from electrostatic heteroaggregation.

The internal structure of materials prepared by aggregation of oppositely charged polystyrene spheres (electrostatic heteroaggregation) is investigated by static light scattering, optical microscopy, and Brownian dynamics simulation. Light scattering indicates ultralow mass fractal dimensions, as low as 1.2. Such low fractal dimensions, approaching the theoretical limit of a linear object, imply a chaining mechanism. Optical micrographs reveal linear chains with the particle charge alternating down the chains. Brownian dynamics simulation gives additional support for a chaining mechanism. For the polystyrene system (120-nm primary particle diameters), the fractal dimension is found to increase from 1.2 to 1.7 as the background electrolyte is increased. In terms of electrostatic screening, the results match those reported recently for larger polystyrene spheres. The low fractal dimensions appear to represent a crossover from linear chains to a structure of diffusion-limited aggregates; however, experiments under density-neutral conditions imply that sedimentation plays an important role in the formation of ultralow fractal dimensions. The practical implication is that microcomposites with a locally uniform distribution of starting materials and almost any degree of branching can be prepared from oppositely charged particles. PMID:12742045

Kim, Anthony Y; Hauch, Kip D; Berg, John C; Martin, James E; Anderson, Robert A

2003-04-01

384

A brief outline of the application of fractals to porous solids is given. The variation of porosity and surface area as functions of particle size and pore size are discussed. For F-20 Alcoa alumina most of the surface is contained in pores of radius near 20 Å. However, fractal behavior is observed if probe molecules are used that are too

Carroll O. Bennett; W. Curtis Conner

1995-01-01

385

Observation of two different fractal structures in nanoparticle, protein and surfactant complexes

NASA Astrophysics Data System (ADS)

Small angle neutron scattering has been carried out from a complex of nanoparticle, protein and surfactant. Although all the components are similarly (anionic) charged, we have observed strong interactions in their complex formation. It is characterized by the coexistence of two different mass fractal structures. The first fractal structure is originated from the protein and surfactant interaction and second from the depletion effect of first fractal structure leading the nanoparticle aggregation. The fractal structure of protein-surfactant complex represents to bead necklace structure of micelle-like clusters of surfactant formed along the unfolded protein chain. Its fractal dimension depends on the surfactant to protein ratio (r) and decreases with the increase in r. However, fractal dimension of nanoparticle aggregates in nanoparticle-protein complex is found to be independent of protein concentration and governed by the diffusion limited aggregation like morphology.

Mehan, Sumit; Kumar, Sugam; Aswal, V. K.

2014-04-01

386

Fractal Segmentation and Clustering Analysis for Seismic Time Slices

NASA Astrophysics Data System (ADS)

Fractal analysis has become part of the standard approach for quantifying texture on gray-tone or colored images. In this research we introduce a multi-stage fractal procedure to segment, classify and measure the clustering patterns on seismic time slices from a 3-D seismic survey. Five fractal classifiers (c1)-(c5) were designed to yield standardized, unbiased and precise measures of the clustering of seismic signals. The classifiers were tested on seismic time slices from the AKAL field, Cantarell Oil Complex, Mexico. The generalized lacunarity (c1), fractal signature (c2), heterogeneity (c3), rugosity of boundaries (c4) and continuity resp. tortuosity (c5) of the clusters are shown to be efficient measures of the time-space variability of seismic signals. The Local Fractal Analysis (LFA) of time slices has proved to be a powerful edge detection filter to detect and enhance linear features, like faults or buried meandering rivers. The local fractal dimensions of the time slices were also compared with the self-affinity dimensions of the corresponding parts of porosity-logs. It is speculated that the spectral dimension of the negative-amplitude parts of the time-slice yields a measure of connectivity between the formation's high-porosity zones, and correlates with overall permeability.

Ronquillo, G.; Oleschko, K.; Korvin, G.; Arizabalo, R. D.

2002-05-01

387

Landscape roughness analysis of Mt. Etna volcanic complex detected via fractal geometry

NASA Astrophysics Data System (ADS)

During the last years several aspects relevant to volcanic activity have been analyzed in fractal context. These studies have been aimed at identifying the power laws that govern the magma fragmentation processes and/or the classification of different geological processes. In this work we exploit the algorithm proposed by Di Martino et al. (2012) that allows retrieving the fractal dimension of a natural surface starting from its corresponding Synthetic Aperture Radar (SAR) image. Such an algorithm is based on an analytical model that links the stochastic characterization of a single SAR amplitude image to the fractal dimension of the observed surface, modeled via a fractional Brownian motion (fBm) process. The considered SAR image processing provides - as an output product - the pixel by pixel map of the fractal dimension of the scene observed by the sensor. Previous works demonstrated that the fractal dimension of lava flows is strictly connected to the natural surface roughness. Moreover, Pepe et al. (2012) showed the possibility of characterizing the single volcanic structures by means of the fractal dimension values retrieved from the corresponding SAR images. In the present work we consider a data-set of Cosmo-SkyMed high resolution images acquired over the Mt. Etna volcanic complex (South Italy), spanning the 2009 - 2011 time period. Starting from the SAR amplitude images of the considered data-set, we generated the corresponding fractal dimension maps that were subsequently co-registered each other, thus retrieving the fractal dimension time-series of the Mt. Etna volcano. Then, by averaging the so-computed fractal dimension maps with respect to time we generated a map of the mean fractal dimension of the investigated area. This procedure allows significantly improving the quality of the final fractal dimension map, as the average operation reduces the noise (due to the speckle effect on SAR images) present on each fractal map. Besides, the so-obtained mean fractal dimension map was quantized in order to identify and aggregate areas that are homogeneous from a fractal viewpoint, i.e., areas having a similar surface roughness. The comparison with the geological map of Mt. Etna volcanic complex reveals that the level of roughness is strictly connected with the lava flow age. More specifically, the roughness of lava flows, which is measured by the fractal dimension, decreases with the increasing of time. In other words, our analysis demonstrates that the volcanic depositional processes of the lava flows produce surfaces with high fractal dimension (roughness), whereas the exogenous phenomena, as the erosion processes, significantly reduce the fractal dimension associated with eruptive mechanisms. The COSMO-SkyMed and ALOS data used in this study have been processed at REA-CNR within the SAR4Volcanoes project under Italian Space Agency agreement n. I/034/11/0. G. Di Martino, D. Riccio, I. Zinno, "SAR Imaging of Fractal Surfaces," IEEE Trans. Geosci. Remote Sens., vol.50, no.2, pp. 630-644, Feb. 2012. S. Pepe, G. Di Martino, A. Iodice, M. Manzo, A. Pepe, D. Riccio, G. Ruello, E. Sansosti, P. Tizzani, I. Zinno; "Analysis of the fractal dimension of volcano geomorphology through Synthetic Aperture Radar (SAR) amplitude images acquired in C and X band", Geophysical Research Abstracts Vol. 14, EGU2012-6573-1, 2012, EGU General Assembly 2012.

De Luca, Claudio; Bonfante, Antonello; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Antonio; Pepe, Susi; Riccio, Daniele; Sansosti, Eugenio; Tizzani, Pietro; Zinno, Ivana

2013-04-01

388

Fractal aggregates in tennis ball systems

NASA Astrophysics Data System (ADS)

We present a new practical exercise to explain the mechanisms of aggregation of some colloids which are otherwise not easy to understand. We have used tennis balls to simulate, in a visual way, the aggregation of colloids under reaction-limited colloid aggregation (RLCA) and diffusion-limited colloid aggregation (DLCA) regimes. We have used the images of the cluster of balls, following Forrest and Witten's pioneering studies on the aggregation of smoke particles, to estimate their fractal dimension.

Sabin, J.; Bandín, M.; Prieto, G.; Sarmiento, F.

2009-09-01

389

Single- and dual-fractal analysis of hydridization binding kinetics: Biosensor applications

The diffusion-limited hybridization kinetics of analyte in solution to a receptor immobilized on a biosensor or immunosensor surface is analyzed within a fractal framework. The data may be analyzed by a single- or a dual-fractal analysis. This was indicated by the regression analysis provided by sigmaplot. It is of interest to note that the binding rate coefficient and the fractal dimension both exhibit changes in the same direction for both the single-fractal and the dual-fractal analysis examples presented. For example, for a single-fractal analysis and for the hybridization of 10 nM 16*CFl (oligonucleotide) to 16*B immobilized via sulfosuccinimidyl-6-(biotinamido)-hexanoate and streptavidin using chemical and thermal regeneration, an increase in the fractal dimension, D{sub f} from 1.211 to 1.394, leads to an increase in the binding rate coefficient, k, from 86.53 to 100.0. An increase in the degree of heterogeneity on the biosensor surface leads to an increase in the binding rate coefficient. When a dual-fractal analysis was utilized, an increase in the fractal dimension value from D{sub f1} to D{sub f2} leads to an increase in the binding rate coefficient value from k{sub 1} to k{sub 2}.

Sadana, A. [Univ. of Mississippi, University, MS (United States). Chemical Engineering Dept.] [Univ. of Mississippi, University, MS (United States). Chemical Engineering Dept.; Vo-Dinh, T. [Oak Ridge National Lab., TN (United States). Advanced Monitoring Development Group] [Oak Ridge National Lab., TN (United States). Advanced Monitoring Development Group

1998-09-01

390

Fractal structures of three-dimensional simplicial gravity

NASA Astrophysics Data System (ADS)

Phases and fractal structures of three-dimensional simplicial quantum gravity are studied by the Monte-Carlo method. After measuring the surface area distribution (SAD) which is the three-dimensional analog of the loop length distribution (LLD) in two-dimensional quantum gravity, we classify the fractal structures into three types: (i) a crumpled manifold in the strong coupling (hot) phase with a large Hausdorff dimension d H ? 5 . (ii) a pseudo-fractal manifold at the critical point with a Hausdorff dimension d H ? 4 . We observe some scaling behaviors for the cross-sections of the manifold. (iii) a branched-polymer structure in the weak coupling (cold) phase with a small Hausdorff dimension d H ? 2 .

Hagura, H.; Tsuda, N.; Yukawa, T.

1997-02-01

391

Tissue as a self-organizing system with fractal dynamics

NASA Astrophysics Data System (ADS)

Cell is a supramolecular dynamic network. Screening of tissue-specific cDNA library and results of Relative RT-PCR indicate that the relationship between genotype, (i.e., dynamic network of genes and their protein regulatory elements) and phenotype is non-bijective, and mendelian inheritance is a special case only. This implies non-linearity, complexity, and quasi-determinism, (i.e., co-existence of deterministic and non-deterministic events) of dynamic cellular network; prerequisite conditions for the existence of fractal structure. Indeed, the box counting method reveals that morphological patterns of the higher order, such as gland-like structures or populations of differentiating cancer cells possess fractal dimension and self-similarity. Since fractal space is not filled out randomly, a variety of morphological patterns of functional states arises. The expansion coefficient characterizes evolution of fractal dynamics. The coefficient indicates what kind of interactions occurs between cells, and how far from the limiting integer dimension of the Euclidean space the expanding population of cells is. We conclude that cellular phenomena occur in the fractal space; aggregation of cells is a supracollective phenomenon (expansion coefficient > 0), and differentiation is a collective one (expansion coefficient < 0). Fractal dimension or self-similarity are lost during tumor progression. The existence of fractal structure in a complex tissue system denotes that dynamic cellular phenomena generate an attractor with the appropriate organization of space-time. And vice versa, this attractor sets up physical limits for cellular phenomena during their interactions with various fields. This relationship can help to understand the emergence of extraterrestial forms of life. Although those forms can be composed of non-carbon molecules, fractal structure appears to be the common feature of all interactive biosystems.

Waliszewski, P.; Konarski, J.

2001-01-01

392

Fractal analysis of the spatial distribution of earthquakes along the Hellenic Subduction Zone

NASA Astrophysics Data System (ADS)

The Hellenic Subduction Zone (HSZ) is the most seismically active region in Europe. Many destructive earthquakes have taken place along the HSZ in the past. The evolution of such active regions is expressed through seismicity and is characterized by complex phenomenology. The understanding of the tectonic evolution process and the physical state of subducting regimes is crucial in earthquake prediction. In recent years, there is a growing interest concerning an approach to seismicity based on the science of complex systems (Papadakis et al., 2013; Vallianatos et al., 2012). In this study we calculate the fractal dimension of the spatial distribution of earthquakes along the HSZ and we aim to understand the significance of the obtained values to the tectonic and geodynamic evolution of this area. We use the external seismic sources provided by Papaioannou and Papazachos (2000) to create a dataset regarding the subduction zone. According to the aforementioned authors, we define five seismic zones. Then, we structure an earthquake dataset which is based on the updated and extended earthquake catalogue for Greece and the adjacent areas by Makropoulos et al. (2012), covering the period 1976-2009. The fractal dimension of the spatial distribution of earthquakes is calculated for each seismic zone and for the HSZ as a unified system using the box-counting method (Turcotte, 1997; Robertson et al., 1995; Caneva and Smirnov, 2004). Moreover, the variation of the fractal dimension is demonstrated in different time windows. These spatiotemporal variations could be used as an additional index to inform us about the physical state of each seismic zone. As a precursor in earthquake forecasting, the use of the fractal dimension appears to be a very interesting future work. Acknowledgements Giorgos Papadakis wish to acknowledge the Greek State Scholarships Foundation (IKY). References Caneva, A., Smirnov, V., 2004. Using the fractal dimension of earthquake distributions and the slope of the recurrence curve to forecast earthquakes in Colombia. Earth Sci. Res. J., 8, 3-9. Makropoulos, K., Kaviris, G., Kouskouna, V., 2012. An updated and extended earthquake catalogue for Greece and adjacent areas since 1900. Nat. Hazards Earth Syst. Sci., 12, 1425-1430. Papadakis, G., Vallianatos, F., Sammonds, P., 2013. Evidence of non extensive statistical physics behavior of the Hellenic Subduction Zone seismicity. Tectonophysics, 608, 1037-1048. Papaioannou, C.A., Papazachos, B.C., 2000. Time-independent and time-dependent seismic hazard in Greece based on seismogenic sources. Bull. Seismol. Soc. Am., 90, 22-33. Robertson, M.C., Sammis, C.G., Sahimi, M., Martin, A.J., 1995. Fractal analysis of three-dimensional spatial distributions of earthquakes with a percolation interpretation. J. Geophys. Res., 100, 609-620. Turcotte, D.L., 1997. Fractals and chaos in geology and geophysics. Second Edition, Cambridge University Press. Vallianatos, F., Michas, G., Papadakis, G., Sammonds, P., 2012. A non-extensive statistical physics view to the spatiotemporal properties of the June 1995, Aigion earthquake (M6.2) aftershock sequence (West Corinth rift, Greece). Acta Geophys., 60, 758-768.

Papadakis, Giorgos; Vallianatos, Filippos; Sammonds, Peter

2014-05-01

393

Prediction of CEC Using Fractal Parameters by Artificial Neural Networks

NASA Astrophysics Data System (ADS)

The prediction of cation exchange capacity from readily available soil properties remains a challenge. In this study, firstly, we extended the entire particle size distribution curve from limited soil texture data and, at the second step, calculated the fractal parameters from the particle size distribution curve. Three pedotransfer functions were developed based on soil properties, parameters of particle size distribution curve model and fractal parameters of particle size distribution curve fractal model using the artificial neural networks technique. 1 662 soil samples were collected and separated into eight groups. Particle size distribution curve model parameters were estimated from limited soil texture data by the Skaggs method and fractal parameters were calculated by Bird model. Using particle size distribution curve model parameters and fractal parameters in the pedotransfer functions resulted in improvements of cation exchange capacity predictions. The pedotransfer functions that used fractal parameters as predictors performed better than the those which used particle size distribution curve model parameters. This can be related to the non-linear relationship between cation exchange capacity and fractal parameters. Partitioning the soil samples significantly increased the accuracy and reliability of the pedotransfer functions. Substantial improvement was achieved by utilising fractal parameters in the clusters.

Bayat, Hossein; Davatgar, Naser; Jalali, Mohsen

2014-04-01

394

Reinforcement of rubber by fractal aggregates

NASA Astrophysics Data System (ADS)

Rubber is commonly reinforced with colloidal aggregates of carbon or silica, whose structure has the scale invariance of a fractal object. Reinforced rubbers support large stresses, which often grow faster than linearly with the strain. We argue that under strong elongation the stress arises through lateral compression of the aggregates, driven by the large bulk modulus of the rubber. We derive a power-law relationship between stress and elongation ? when ?gg 1. The predicted power p depends on the fractal dimension D and a second structural scaling exponent C. For diffusion-controlled aggregates this power p should lie beween 0.9 and 1.1 ; for reaction-controlled aggregates p should lie between 1.8 and 2.4. For uniaxial compression the analogous powers lie near 4. Practical rubbers filled with fractal aggregates should approach the conditions of validity for these scaling laws. On renforce souvent le caoutchouc avec des agrégats de carbone ou de silice dont la structure a l'invariance par dilatation d'un objet fractal. Les caoutchoucs ainsi renforcés supportent de grandes contraintes qui croissent souvent plus vite que l'élongation. Nous prétendons que, sous élongation forte, cette contrainte apparaît à cause d'une compression latérale des agrégats induite par le module volumique important du caoutchouc. Nous établissons une loi de puissance reliant la contrainte et l'élongation ? quand ?gg 1. Cet exposant p dépend de la dimension fractale D et d'un deuxième exposant structural C. Pour des agrégats dont la cinétique de formation est limitée par diffusion, p vaut entre 0,9 et 1,1. Si la cinétique est limitée par le soudage local des particules, p vaut entre 1,8 et 2,4. Sous compression uniaxiale, les puissances homologues valent environ 4. Des caoutchoucs pratiques chargés de tels agrégats devraient approcher des conditions où ces lois d'échelle sont valables.

Witten, T. A.; Rubinstein, M.; Colby, R. H.

1993-03-01

395

Fractal geometry, developed by B. Mandelbrot, has provided new key concepts necessary to the understanding and quantification of some aspects of pattern and shape randomness, irregularity, complexity and self-similarity. In the field of microscopy, fractals have profound implications in relation to the effects of magnification and scaling on morphology and to the methodological approaches necessary to measure self-similar structures. In this article are reviewed the fundamental concepts on which fractal geometry is based, their relevance to the microscopy field as well as a number of technical details that can help improving the robustness of morphological analyses when applied to microscopy problems. PMID:21118245

Landini, G

2011-01-01

396

Fractal scaling of landslide distribution in the Umbria Region (Italy)

NASA Astrophysics Data System (ADS)

The application of the fractal theory has made a great contribution to the understanding of surface processes governing landscape evolution. In this study we focus on landslide events, which also have critical implications in Natural Hazard assessment. Several works have shown that landslides can be described as processes characterized by self-organized criticality. Based on this, the distribution of landslides in the Umbria Region (Central Italy) was analysed by means of fractal techniques. Statistical self-similarity in space was investigated by applying the box-counting method and the Grassberger-Procaccia algorithm to the inventory map of landslide trigger points. Results showed the existence of fractal scaling and provided an estimate of the Capacity Dimension (D0) and Correlation Dimension (D2) of the sample, the latter expressed as the mean regional value. The characteristic minimum distance of landslides was extrapolated from the lower scaling limit for D0. In order to investigate the spatial pattern of landslides, artificial point maps were generated. Three different distributions were imposed on the points: i) uniform distribution, ii) random distribution and iii) cluster distribution. The box-counting method was applied to each distribution and the calculated Capacity Dimensions were compared with that of the natural sample. Results showed that landslides in the Umbria Region display spatial clustering. In addition, the D0 measured for the uniform distribution, lower than 2, highlights that the statement that a D0 equal to 2 indicates a uniform distribution of points in a 2-dimensional space must be carefully considered on a case by case basis, since the shape of the embedding space strongly affects its value. Additional analyses were carried out to address the problem of the 'edge effect' in the computation of D2, which results in the underestimation of its value and may lead to incorrect interpretations of the statistical distribution of points. We propose a GIS-based approach to estimate correlation among points in terms of density. This approach enables us to efficiently treat also points near the boundaries, thus avoiding the loss of information. By applying this method, a scaling behavior was identified in the variation of the density of landslides in their neighborhoods.

Liucci, Luisa; Melelli, Laura; Ponziani, Francesco

2014-05-01

397

Fractal Analysis of Creutzfeld-Jakob Disease Frontal Horn Brain Magnetic Resonance Image

The Higuchi fractal method on a random series was applied to the study of the brightness fluctuation of Creutzfeld-Jakob disease (CJD) brain magnetic resonance (MR) frontal horn images. The brightness fluctuation along either a horizontal or vertical direction across an image formed a random series suitable for the Higuchi method. The average fractal dimension was found to decrease for the

T. Holden; E. Cheung; R. Subramaniam; R. Sullivan; P. Schneider; A. Flamholz; D. Lieberman; T. Cheung

2009-01-01

398

Modeling of fractal patterns in matrix acidizing and their impact on well performance

This paper describes a model where wormholes, the primary feature of carbonate acidizing, are considered as fractals. The influences of acid volume, injection rate, fractal dimension, porosity, and the ratio of undamaged to damaged permeabilities on well performance are studied. Exact expressions of post-treatment skin effects are developed for vertical and horizontal wells.

Frick, T.P.; Kuermayr, M.; Economides, M.J.

1994-02-01

399

NASA Astrophysics Data System (ADS)

Several studies on earthquake occurrence and associated faulting have demonstrated that both phenomena have a scale-invariant behavior which can be analyzed by means of a set of non-integer dimensions ( D q ) describing their fractal properties and the calculation of multi-fractal spectra. It is the case that the behavior of these spectra is asymptotic at the ends of the variation interval of q, which is a real number that enters into the definition of the partition function of the dataset. The difference between the extreme values, called multi-fractal spectrum slope, is used to investigate the heterogeneity of the spatial distribution of earthquakes and fault systems. In this paper we focus on the Betic Cordillera, southeastern Spain, which is commonly considered the contact between the Eurasian and African plates and has an important seismic activity in the context of the Iberian Peninsula. Some of the most conspicuous Iberian earthquakes, such as the 1829 m b6.3 Torrevieja and the 1884 m b6.1 Alhama de Granada earthquakes occurred in this mountain range and both reached intensity X. The present work implies a new analysis based on the slope of multi-fractal spectra and referred to the historical seismicity of the region, specifically b-value (frequency distribution of earthquakes respect to magnitude), epicentral location, seismic energy and faulting. On this basis we propose a seismotectonic zonation that is contrasted with the stress state and the geodynamical evolution of the Betic Cordillera.

Henares Romero, J.; López Casado, C.; Badal, J.; Peláez, J. A.

2010-08-01

400

Fractal spacetime structure in asymptotically safe gravity

NASA Astrophysics Data System (ADS)

Four-dimensional Quantum Einstein Gravity (QEG) is likely to be an asymptotically safe theory which is applicable at arbitrarily small distance scales. On sub-planckian distances it predicts that spacetime is a fractal with an effective dimensionality of 2. The original argument leading to this result was based upon the anomalous dimension of Newton's constant. In the present paper we demonstrate that also the spectral dimension equals 2 microscopically, while it is equal to 4 on macroscopic scales. This result is an exact consequence of asymptotic safety and does not rely on any truncation. Contact is made with recent Monte Carlo simulations.

Lauscher, Oliver; Reuter, Martin

2005-10-01

401

A fractal transition in the two dimensional shear layer

NASA Technical Reports Server (NTRS)

The dependence of product generation with the Peclet and Reynolds number in a numerically simulated, reacting, two dimensional, temporally growing mixing layer is used to compute the fractal dimension of passive scalar interfaces. A transition from a low dimension of 4/3 to a higher one of 5/3 is identified and shown to be associated to the kinematic distortion on the flow field during the first pairing interaction. It is suggested that the structures responsible for this transition are non-deterministic, non-random, inhomogeneous fractals. Only the large scales are involved. No further transition is found for Reynolds numbers up to 20,000.

Jimenez, Javier; Martel, Carlos

1990-01-01

402

Quantification of the fractal nature of mycelial aggregation in Aspergillus niger submerged cultures

Background Fractal geometry estimates have proven useful in studying the growth strategies of fungi in response to different environments on soil or on agar substrates, but their use in mycelia grown submerged is still rare. In the present study, the effects of certain important fermentation parameters, such as the spore inoculum level, phosphate and manganese concentrations in the medium, on mycelial morphology of the citric acid producer Aspergillus niger were determined by fractal geometry. The value of employing fractal geometry to describe mycelial structures was examined in comparison with information from other descriptors including classic morphological parameters derived from image analysis. Results Fractal analysis of distinct morphological forms produced by fermentation conditions that influence fungal morphology and acid production, showed that the two fractal dimensions DBS (box surface dimension) and DBM (box mass dimension) are very sensitive indexes, capable of describing morphological differences. The two box-counting methods applied (one applied to the whole mass of the mycelial particles and the other applied to their surface only) enabled evaluation of fractal dimensions for mycelial particles in this analysis in the region of DBS = 1.20–1.70 and DBM = 1.20–2.70. The global structure of sufficiently branched mycelia was described by a single fractal dimension D, which did not exceed 1.30. Such simple structures are true mass fractals (DBS = DBM = D) and they could be young mycelia or dispersed forms of growth produced by very dense spore inocula (108–109 spores/ml) or by addition of manganese in the medium. Mycelial clumps and pellets were effectively discriminated by fractal analysis. Fractal dimension values were plotted together with classic morphological parameters derived from image analysis for comparisons. Their sensitivity to treatment was analogous to the sensitivity of classic morphological parameters suggesting that they could be equally used as morphological descriptors. Conclusion Starting from a spore, the mycelium develops as a mass fractal and, depending on culture conditions, it either turns to a surface fractal or remains a mass fractal. Since fractal dimensions give a measure of the degree of complexity and the mass filling properties of an object, it may be possible that a large number of morphological parameters which contribute to the overall complexity of the particles, could be replaced by these indexes effectively.

Papagianni, Maria

2006-01-01

403

National Technical Information Service (NTIS)

Rapid image decompression is crucial for many potential Navy and commercial users of the fractal image compression scheme. The focus of the work was the development of IFS algorithms and computer code for image compression, the refinement of algorithms an...

Y. Fisher A. Lawrence

1992-01-01

404

Coarsening of Fractal Interfaces.

National Technical Information Service (NTIS)

The process of coarse