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1

Fractal Dimensions  

NSDL National Science Digital Library

Determine the fractal dimensions of several line-deformation fractals. Input the scale factor and number of similar copies, and the dimension will be calculated. Fractal Dimensions is one of the Interactivate assessment explorers.

2

T-Matrix Optical Scattering Calculations for Atmospheric Aerosol Fractal Soot Aggregates Over a Wide Range of Fractal Dimension  

NASA Astrophysics Data System (ADS)

Carbonaceous soot aerosols formed in flames exhibit radiative forcing effects that are currently known only with significant uncertainty [IPCC AR4]. Better understanding of the soot aerosol range of structures, including coatings by other atmospheric constituents, and their scattering of optical radiation in relevant wavelength ranges will help constrain climate models. Numerical studies of diffusion-limited aggregation (DLA) and diffusion-limited cluster aggregation (DLCA) processes in 3D have since the 1980s indicated that the fractal dimension Df of soot aggregates is typically in the range 1.7-1.8. Multiple experimental studies, often attempting to calculate a 3D fractal dimension from electron micrograph 2D images, are in general agreement with this soot aggregate fractal dimension range. However, recent experiments find a much-wider range (with some aggregates having Df between 1.2 and 1.5) of soot aggregate fractal dimension from real combustion processes [Chakrabarty et al., Phys. Rev. Lett. 102, 235504 (2009)]. In addition, aged soot aggregates in the atmosphere may reach a fractal dimension Df substantially above 2 as they lose their filamentous nature. Several other studies have focused on the range Df from 1.7 to 1.8. We report results from undergraduate research using the T-Matrix technique to compute the optical scattering matrix elements for fractal soot aggregates over a wide range of fractal dimension (1.2 to 2.4). We generate these model aggegates using DLCA algorithms.

Boness, D. A.; Canion, B.

2009-12-01

3

Effect of Image Processing of a Leaf Photograph on the Calculated Fractal Dimension of Leaf Veins  

Microsoft Academic Search

Digital photography is a promised method for estimating the fractal characteristics of leaf veins. In this study, the effects\\u000a of different threshold levels and image processing methods using Adobe Photoshop software on the fractal dimension values\\u000a were examined from a digital photo of nectarine leaf. The results showed that the nectarine leaf vein has typical fractal\\u000a characteristics and its fractal

Yun Kong; Shaohui Wang; Chengwei Ma; Baoming Li; Yuncong Yao

2007-01-01

4

Explicitly accounting for pixel dimension in calculating classical and fractal landscape shape metrics.  

PubMed

Different summarized shape indices, like mean shape index (MSI) and area weighted mean shape index (AWMSI) can change over multiple size scales. This variation is important to describe scale heterogeneity of landscapes, but the exact mathematical form of the dependence is rarely known. In this paper, the use of fractal geometry (by the perimeter and area Hausdorff dimensions) made us able to describe the scale dependence of these indices. Moreover, we showed how fractal dimensions can be deducted from existing MSI and AWMSI data. In this way, the equality of a multiscale tabulated MSI and AWMSI dataset and two scale-invariant fractal dimensions has been demonstrated. PMID:19184455

Imre, Attila R; Rocchini, Duccio

2009-01-29

5

Modeling of three-dimensional groundwater flow using the method to calculate fractal dimension  

Microsoft Academic Search

A three-dimensional finite-difference groundwater flow model was developed by the use of fractal theory. The model developed\\u000a in this study can simulate the groundwater flow in fractured aquifers as well as in porous aquifers. The model was designed\\u000a to be able to use other parameters, such as permeability, hydraulic conductivity, porosity and fractal dimension besides hydraulic\\u000a parameters which are used

Bohyun Chon; Yong-Suk Choi

2001-01-01

6

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

7

Box-covering algorithm for fractal dimension of weighted networks.  

PubMed

Box-covering algorithm is a widely used method to measure the fractal dimension of complex networks. Existing researches mainly deal with the fractal dimension of unweighted networks. Here, the classical box covering algorithm is modified to deal with the fractal dimension of weighted networks. Box size length is obtained by accumulating the distance between two nodes connected directly and graph-coloring algorithm is based on the node strength. The proposed method is applied to calculate the fractal dimensions of the "Sierpinski" weighted fractal networks, the E.coli network, the Scientific collaboration network, the C.elegans network and the USAir97 network. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks. We find that the fractal property is influenced by the edge-weight in weighted networks. The possible variation of fractal dimension due to changes in edge-weights of weighted networks is also discussed. PMID:24157896

Wei, Dai-Jun; Liu, Qi; Zhang, Hai-Xin; Hu, Yong; Deng, Yong; Mahadevan, Sankaran

2013-10-25

8

Correcting for ¢nite spatial scales of self-similarity when calculating the fractal dimensions of real-world structures  

Microsoft Academic Search

SUMMARY Fractal geometry is a potentially valuable tool for quantitatively characterizing complex structures. The fractal dimension (D) canbe used as a simple, single index for summarizing properties of real and abstract structures in space and time. Applications in the ¢elds of biology and ecology range from neurobiology to plant architecture, landscape structure, taxonomy and species diversity. However, methods to estimate

G. M. BERNTSON; P. STOLL

9

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.

10

Fractal dimension of metallic fracture surface  

Microsoft Academic Search

In this study, a complete method of determination of the fractal dimension for fracture surfaces of ferrous alloys has been\\u000a proposed. This dimension is determined for the vertical profile obtained by the profile technique cross-section. The image\\u000a of the profile, seen through the microscope coupled with a camera, is recorded in a computer, where numerical processing is\\u000a performed. For calculation

Piotr Kotowski

2006-01-01

11

Information dimension in fractal structures  

NASA Astrophysics Data System (ADS)

We derive an exact formula for the recently introduced information dimension DI for random-walk processes in terms of the V(r,n) function, the function that gives the number of sites that have exactly r visits during a random walk on a lattice after n steps. This form is general, and it pertains both to regular lattices and fractal structures. The controlling parameter is Sn, the number of sites visited at least once in an n-step walk. We perform computer simulations on regular lattices and on fractal structures: the Sierpinski gasket, two-dimensional, and three-dimensional percolation clusters exactly at criticality. It is found that DI has the same numerical value as the spectral dimension as n-->?, but it takes unusually long times to reach such behavior.

Pitsianis, N.; Bleris, G. L.; Argyrakis, P.

1989-04-01

12

Introduction on background medium theory about celestial body motion orbit and foundation of fractional-dimension calculus about self-similar fractal measure calculation  

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

13

Fractal dimension of cerebral surfaces using magnetic resonance images  

SciTech Connect

The calculation of the fractal dimension of the surface bounded by the grey matter in the normal human brain using axial, sagittal, and coronal cross-sectional magnetic resonance (MR) images is presented. The fractal dimension in this case is a measure of the convolutedness of this cerebral surface. It is proposed that the fractal dimension, a feature that may be extracted from MR images, may potentially be used for image analysis, quantitative tissue characterization, and as a feature to monitor and identify cerebral abnormalities and developmental changes.

Majumdar, S.; Prasad, R.R.

1988-11-01

14

A Novel Tool of Measuring Fractal Dimension or Complexity  

Microsoft Academic Search

The fractal dimension or complexity of physiological signal is calculated with a novel tool, dot counting dimension (DCD) in this paper. The definition and algorithm of DCD are given out. DCD of nine arrhythmia records are calculated and linear result of DCD is achieved. The algorithm of DCD is useful for processing physiological signal because of its implementing easy with

Li Zhi-min; Chen Qiang; Gou Xian-tai; Jin Wei-dong

2008-01-01

15

Fractal dimensions for rainfall time series  

Microsoft Academic Search

Fractals are objects which have a similar appearance when viewed at different scales. Such objects have detail at arbitrarily small scales, making them too complex to be represented by Euclidean space. They are assigned a dimension which is non-integer. Some natural phenomena have been modelled as fractals with success; examples include geologic deposits, topographical surfaces and seismic activity. In particular,

M. C. Breslin; J. A. Belward

1999-01-01

16

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

17

Crack detection in plates using fractal dimension  

Microsoft Academic Search

An effective method for detecting cracks in plate structures based on fractal dimension analysis is presented in this paper. The method is applied to the simulated fundamental vibration mode of a simply supported rectangular plate containing a crack parallel to one of its edges of arbitrary length, depth and location. The analyzed spatial response by exhibiting abrupt changes at the

L. J. Hadjileontiadis; E. Douka

2007-01-01

18

Estimation of fractal dimensions from transect data  

SciTech Connect

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

19

On time-series analysis and signal classification - part I: fractal dimensions  

Microsoft Academic Search

Time series analysis is becoming an increasingly reliable tool for the study of complicated dynamics in measurements across many fields of science and engineering. This paper explores the applications of nonlinear time series analysis for digital communication signal classification. In particular, the fractal dimension was investigated as a tool for signal classification. Primarily, the fractal dimension was calculated for a

Ralph Hippenstiel; H. El-Kishky; P. Radev

2004-01-01

20

Twoband Infrared Data Fusion Method Based-on Fractal Dimension  

Microsoft Academic Search

Researches indicate that the gray-scale images mapped from most nature objects accord to the fractal Brown stochastic field which has a foundation of self-similarity, meaning the image is made up of copies of itself in a reduced scale. The fractal dimension can quantifiably depict the fractal character and the property of an image. Therefore, a new method based-on fractal dimension

Yuqui Sun; Jinwen Tian; Jian Liu

2005-01-01

21

Fractal Dimension of Particle Aggregates in Magnetic Fields  

Microsoft Academic Search

Particle flocculation plays a major role in water treatment processes. In flocculation kinetics models it is usually assumed that spherical particles collide and form spherical aggregates. Real aggregates, however, are of irregular shapes and can be considered as fractal objects. The structure of fractal objects can be described by a fractal dimension number that plays an important role in aggregation

Sotira Yiacoumi; Costas Tsouris

2004-01-01

22

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

23

Uncertainty in fractal dimension estimated from power spectra and variograms  

Microsoft Academic Search

The reliability of using fractal dimension (D) as a quantitative parameter to describe geological variables is dependent mainly\\u000a on the accuracy of estimated D values from observed data. Two widely used methods for the estimation of fractal dimensions\\u000a are based on fitting a fractal model to experimental variograms or power-spectra on a log-log plot. The purpose of this paper\\u000a is

Renjun Wen; Richard Sinding-Larsen

1997-01-01

24

A fully distributed clustering algorithm based on fractal dimension  

NASA Astrophysics Data System (ADS)

Clustering or grouping of similar objects is one of the most widely used procedures in data mining, which has received enormous attentions and many methods have been proposed in these recent decades. However these traditional clustering algorithms require all the data objects to be located at one single site where it is analyzed. And such limitation cannot face the challenge as nowadays monstrous sizes of data sets are often stored on different independently working computers connected to each other via local or wide area networks instead of one single site. Therefore in this paper, we propose a fully distributed clustering algorithm, called a fully distributed clustering based on fractal dimension (FDCFD), which enables each site to collaborate in forming a global clustering model with low communication cost. The main idea behind FDCFD is via calculating fractal dimension to group points in a cluster in such a way that none of the points in the cluster changes the cluster's fractal dimension radically. In our theoretical analysis, we will demonstrate that our approach can work very well for clustering data that is inherently distributed, collect information spread over several local sites to form a global clustering meanwhile without communication costs and delays for transmitting.

Xiong, Xiao; Zhang, Jie; Shi, Qingwei

2007-09-01

25

Time evolution of the fractal dimension of a mixing front  

Microsoft Academic Search

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

26

Nipah Virus Classification via Fractal Dimension & Shannon Entropy  

Microsoft Academic Search

Nipah virus glycoprotein and nucleoprotein sequences were studied using fractal dimension and Shannon entropy. The nucleotide atomic number fluctuation forms the basis of the phylogeny study. The classification reproduces the main results of traditional phylogeny analysis, but with better ability to distinguish closely related strains. The fractal dimension correlation with the GC pair content in the glycoprotein sequence and di-nucleotide

T. Holden; N. Gadura; E. Cheung; P. Schneider; G. Tremberger; N. Elham; D. Sunil; D. Lieberman; T. Cheung

2010-01-01

27

On the fractal dimension of invariant sets: Applications to Navier-Stokes equations  

Microsoft Academic Search

A semigroup St of continuous operators in a Hilbert space H is considered. It is shown that the fractal dimension of a compact strictly invariant set X (Xb H; StX = X) admits the same estimate as the Hausdor dimension, namely, both are bounded from above by the Lyapunov dimension calculated in terms of the global Lyapunov exponents. Applications of

V. V. Chepyzhov; A. A. Ilyin

2003-01-01

28

A set of formulae on fractal dimension relations and its application to urban form  

NASA Astrophysics Data System (ADS)

The area-perimeter scaling can be employed to evaluate the fractal dimension of urban boundaries. However, the formula in common use seems to be not correct. By means of mathematical method, a new formula of calculating the boundary dimension of cities is derived from the idea of box-counting measurement and the principle of dimensional consistency in this paper. Thus, several practical results are obtained as follows. First, I derive the hyperbolic relation between the boundary dimension and form dimension of cities. Using the relation, we can estimate the form dimension through the boundary dimension and vice versa. Second, I derive the proper scales of fractal dimension: the form dimension comes between 1.5 and 2, and the boundary dimension comes between 1 and 1.5. Third, I derive three form dimension values with special geometric meanings. The first is 4/3, the second is 3/2, and the third is about 1.7071. The fractal dimension relation formulae are applied to China's cities and the cities of the United Kingdom, and the computations are consistent with the theoretical expectation. The formulae are useful in the fractal dimension estimation of urban form, and the findings about the fractal parameters are revealing for future city planning and the spatial optimization of cities.

Chen, Yanguang

2013-09-01

29

Fractal dimension and mechanism of aggregation of apple juice particles.  

PubMed

Turbidity of freshly squeezed apple juice is produced by a polydisperse suspension of particles coming from the cellular tissue. After precipitation of coarse particles by gravity, only fine-colloidal particles remain in suspension. Aggregation of colloidal particles leads to the formation of fractal structures. The fractal dimension is a measure of the internal density of these aggregates and depends on their mechanism of aggregation. Digitized images of primary particles and aggregates of depectinized, diafiltered cloudy apple juice were obtained by scanning electron microscopy (SEM). Average radius of the primary particles was found to be a = 40 ± 11 nm. Maximum radius of the aggregates, R(L), ranged between 250 and 7750 nm. Fractal dimension of the aggregates was determined by analyzing SEM images with the variogram method, obtaining an average value of D(f) = 2.3 ± 0.1. This value is typical of aggregates formed by rapid flocculation or diffusion limited aggregation. Diafiltration process was found to reduce the average size and polydispersity of the aggregates, determined by photon correlation spectroscopy. Average gyration radius of the aggregates before juice diafiltration was found to be R(g) = 629 ± 87 nm. Average number of primary particles per aggregate was calculated to be N = 1174. PMID:21339133

Benítez, E I; Lozano, J E; Genovese, D B

2010-04-01

30

Performance Optimization of Fractal Dimension Based Feature Selection Algorithm  

Microsoft Academic Search

\\u000a Feature selection is a key issue in the advanced application fields like data mining, multi-dimensional statistical analysis,\\u000a multimedia index and document classification. It is a novel method to exploit fractal dimension to reduce dimension of feature\\u000a spaces. The most famous one is the fractal dimension based feature selection algorithm FDR proposed by Traina Jr et al. This paper proposes an

Yubin Bao; Ge Yu; Huanliang Sun; Daling Wang

2004-01-01

31

Breast Cancer Diagnosis using MultiFractal Dimension Spectra  

Microsoft Academic Search

The research presented in this paper was aimed to develop a classification system of breast tumors tissues using histopathological images. The paper focuses on using the advantages of fractal geometry texture analysis. The developed approach consists of two main steps: (i) the extraction of the fractal dimension spectra for the regions of interest, and (ii) using a classifier that automatically

L. E. George; K. H. Sager

2007-01-01

32

The Casimir Effect for Parallel Plates in the Spacetime with a Fractal Extra Compactified Dimension  

NASA Astrophysics Data System (ADS)

The Casimir effect for massless scalar fields satisfying Dirichlet boundary conditions on the parallel plates in the presence of one fractal extra compactified dimension is analyzed. We obtain the Casimir energy density by means of the regularization of multiple zeta function with one arbitrary exponent. We find a limit on the scale dimension like to keep the negative sign of the renormalized Casimir energy which is the difference between the regularized energy for two parallel plates and the one with no plates. We derive and calculate the Casimir force relating to the influence from the fractal additional compactified dimension between the parallel plates. The larger scale dimension leads to the greater revision on the original Casimir force. The two kinds of curves of Casimir force in the case of integer-numbered extra compactified dimension or fractal one are not superposition, which means that the Casimir force show whether the dimensionality of additional compactified space is integer or fraction.

Cheng, Hongbo

2013-09-01

33

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

34

First determination of the fractal perimeter dimension of noctilucent clouds  

NASA Astrophysics Data System (ADS)

We report on the first determination of the fractal perimeter dimension of noctilucent clouds using satellite images of cloud fields taken with the CIPS (Cloud Imaging and Particle Size) experiment on NASA's AIM (Aeronomy of Ice in the Mesosphere) spacecraft. The area and perimeter of individual clouds exceeding a certain albedo threshold are used to infer the fractal perimeter dimension. We find scaling behavior of cloud area as a function of cloud perimeter over more than 2 orders of magnitude. The cloud perimeters are fractals and the derived fractal perimeter dimensions decrease slightly with increasing NLC albedo threshold from DNLC = 1.35 ± 0.04 for an albedo threshold of 20 × 10-6 sr-1 to DNLC = 1.23 ± 0.05 for an albedo threshold of 60 × 10-6 sr-1. The fractal dimension for the lower albedo thresholds is in remarkably good agreement with the fractal perimeter dimension of tropospheric clouds and rain fields, possibly suggesting that similar physical processes govern the distribution and shape of both tropospheric and noctilucent clouds.

von Savigny, Christian; Brinkhoff, Lena A.; Bailey, Scott M.; Randall, Cora E.; Russell, James M.

2011-01-01

35

Relationship between the fractal dimension and the width to length ratio of mass movements  

NASA Astrophysics Data System (ADS)

Mass movements have some typical geometrical dimensions. One of these typical geometrical dimensions is the width to length ratio. Also, the fractal dimensions of mass movements from the inventory maps of natural mass movements can be used for their geometrical description and characterization. For this reason, in the present study, development of a computer programme for digitizing and determining the fractal dimensions of mass movements, and investigation of the relationship between the fractal dimensions and the width to length (W/L) tario of the mass movements are aimed. For the purpose of the study, a computer programme namely FRACEK for determination of fractal dimensions of amorphous areas is developed by using the JAVA computer language at first. Secondly, a database including the shapes of the mass movements was compiled from the literature and digitized. Then, their width to length ratios and fractal dimensions were calculated. Finally, a series of simple statistical analyses were performed on the data obtained and the results were interpreted. To investigate the relationships between the fractal dimensions and W/L ratios of the mass movements, a series of simple regression analysis is performed. During the regression analyses, linear, power, logarithmic and exponential functions are employed. According to the results obtained, there are some correlations between the D and the W/L ratio. When considering only debris flow data, a power relationship between the D and the W/L ratio was found and its coefficient of correlation was obtained as 0.85. The lowest coefficient of correlations were obtained from the rotational failure data. The coefficients of correlations of the power and exponential funtions were same, 0.53. A similar result was obtained for the translational failure data. Their coefficient of correlations was 0.74. When all data is evaluated together, a relatively strong correlation between the D and the W/L ratio was obtained. These results revealed that to make a differantiation among the mass movements using the fractal dimension is possible.

Sezer, Ebru

2009-04-01

36

Fractal dimensions of niobium oxide films probed by protons and lithium ions  

SciTech Connect

Cyclic voltammetry (CV) and atomic force microscopy (AFM) were used to determine fractal surface dimensions of sputter deposited niobium pentoxide films. Peak currents were determined by CV measurements. Power spectral densities obtained from AFM measurements of the films were used for calculating length scale dependent root mean square roughness. In order to compare the effect of Li and H ion intercalation at the fractal surfaces, LiClO{sub 4} based as well as propionic acid electrolytes were used. The CV measurements gave a fractal dimension of 2.36 when the films were intercalated by Li ions and 1.70 when the films were intercalated by protons. AFM measurements showed that the former value corresponds to the fractal surface roughness of the films, while the latter value is close to the dimensionality of the distribution of hillocks on the surface. We conclude that the protons are preferentially intercalated at such sites.

Pehlivan, Esat; Niklasson, Gunnar A. [Department of Physics, Faculty of Arts and Sciences, Istanbul Technical University, Maslak, 34469 Istanbul, Turkey and Angstroem Laboratory, Department of Engineering Sciences, Uppsala University, P.O. Box 534, SE-751 21 Uppsala (Sweden); Angstroem Laboratory, Department of Engineering Sciences, Uppsala University, P.O. Box 534, SE-751 21 Uppsala (Sweden)

2006-09-01

37

Some fractal properties of the percolating backbone in two dimensions  

SciTech Connect

A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that fractal dimensionality of the backbone is d/sub f//sup BB/ = 1.61 +/- 0.01, the chemical dimensionality is d/sub t/ = 1.40 +/- 0.01, and the fractal dimension of the minimum path d/sub min/ = 1.15 +/- 0.02 for the two-dimensional triangular lattice.

Laidlaw, D.; MacKay, G.; Jan, N.

1987-02-01

38

Sub-optimal MCV Cover Based Method for Measuring Fractal Dimension  

SciTech Connect

A new method for calculating fractal dimension is developed in this paper. The method is based on the box dimension concept; however, it involves direct estimation of a suboptimal covering of the data set of interest. By finding a suboptimal cover, this method is better able to estimate the required number of covering elements for a given cover size than is the standard box counting algorithm. Moreover, any decrease in the error of the covering element count directly increases the accuracy of the fractal dimension estimation. In general, our method represents a mathematical dual to the standard box counting algorithm by not solving for the number of boxes used to cover a data set given the size of the box. Instead, the method chooses the number of covering elements and then proceeds to find the placement of smallest hyperellipsoids that fully covers the data set. This method involves a variant of the Fuzzy-C Means clustering algorithm, as well as the use of the Minimum Cluster Volume clustering algorithm. A variety of fractal dimension estimators using this suboptimal covering method are discussed. Finally, these methods are compared to the standard box counting algorithm and wavelet-decomposition methods for calculating fractal dimension by using one-dimensional cantor dust sets and a set of standard Brownian random fractal images.

Tolle, Charles Robert; McJunkin, Timothy R; Gorsich, D. I.

2003-01-01

39

Relationship between Fractal Dimension and Agreeability of Facial Imagery  

NASA Astrophysics Data System (ADS)

Why do people feel happy and good or equivalently empathize more, with smiling face imageries than with ones of expressionless face? To understand what the essential factors are underlying imageries in relating to the feelings, we conducted an experiment by 84 subjects asked to estimate the degree of agreeability about expressionless and smiling facial images taken from 23 young persons to whom the subjects were no any pre-acquired knowledge. Images were presented one at a time to each subject who was asked to rank agreeability on a scale from 1 to 10. Fractal dimensions of facial images were obtained in order to characterize the complexity of the imageries by using of two types of fractal analysis methods, i.e., planar and cubic analysis methods, respectively. The results show a significant difference in the fractal dimension values between expressionless faces and smiling ones. Furthermore, we found a well correlation between the degree of agreeability and fractal dimensions, implying that the fractal dimension optically obtained in relation to complexity in imagery information is useful to characterize the psychological processes of cognition and awareness.

Oyama-Higa, Mayumi; Miao, Tiejun; Ito, Tasuo

2007-11-01

40

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

41

Estimating the fractal dimension and the predictability of the atmosphere  

SciTech Connect

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

42

Fractal dimension and mechanical properties of human cortical bone.  

PubMed

Fractal dimension (FD) can be used to characterize microstructure of porous media, particularly bone tissue. The porous microstructure of cortical bone is observable in micro-CT (?CT) images. Estimations of fractal dimensions of ?CT images of coupons of human cortical bone are obtained. The same samples were tested on a tensile test machine and Young's modulus (YM) and Failure stress were obtained. When both types of measures were compared, a clear correlation was found (R=-81%, P<0.01). Young's modulus of each sample and the FD of its ?CT images are correlated. From the assumption that cortical bone is approximately a fractal set, a non-linear constitutive relation involving FD is obtained for YM. Experimental results show good agreement with this constitutive relation. Additional parameters in the non-linear relation between YM and FD have been estimated from experimental results and related to physical parameters. PMID:22835437

Sanchez-Molina, David; Velazquez-Ameijide, Juan; Quintana, Víctor; Arregui-Dalmases, Carlos; Crandall, Jeff R; Subit, Damien; Kerrigan, Jason R

2012-07-24

43

Fractal dimension of surface EMG and its determinants  

Microsoft Academic Search

The fractal dimension (FD) has been proposed as a useful measure for the characterization of EMG interference patterns. This paper studies the relationship between the FD and the properties of EMG signals, such as recruitment number, firing rate and motor unit action potentials (MUAPs). The study is based on simulated surface EMG signals from a volume conductor computation. The FD

Zhengquan Xu; Shaojun Xiao

1997-01-01

44

Fractal Dimension and Maximum Sunspot Number in Solar Cycle  

Microsoft Academic Search

The fractal dimension is a quantitative parameter describing the characteristics of irregular time series. In this study, we use this parameter to analyze the irregular aspects of solar activity and to predict the maximum sunspot number in the following solar cycle by examining time series of the sunspot number. For this, we considered the daily sunspot number since 1850 from

R.-S. Kim; Y. Yi; K.-S. Cho; Y.-J. Moon; S. W. Kim

2006-01-01

45

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

PubMed

Electroencephalogram (EEG) traces corresponding to different physiopathological conditions can be characterized by their fractal dimension, which is a measure of the signal complexity. Generally this dimension is evaluated in the phase space by means of the attractor dimension or other correlated parameters. Nevertheless, to obtain reliable values, long duration intervals are needed and consequently only long-term events can be analysed; also much calculation time is required. To analyse events of brief duration in real-time mode and to apply the results obtained directly in the time domain, thus providing an easier interpretation of fractal dimension behaviour, in this work we optimize and propose a new method for evaluating the fractal dimension. Moreover, we study the robustness of this evaluation in the presence of white or line noises and compare the results with those obtained with conventional spectral methods. The non-linear analysis carried out allows us to investigate relevant EEG events shorter than those detectable by means of other linear and non-linear techniques, thus achieving a better temporal resolution. An interesting link between the spectral distribution and the fractal dimension value is also pointed out. PMID:9418215

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

1997-11-01

46

Effect of pouring temperature on fractal dimension of primary phase morphology in semi-solid A356 alloy  

Microsoft Academic Search

The fractal dimensions of primary phase morphology in semi-solid A356 alloy prepared by low superheat pouring and slightly electromagnetic stirring were calculated, and the effect of pouring temperature on fractal dimension of primary phase morphology in semi-solid A356 alloy was researched. The results indicate that it is feasible to prepare semisolid A356 alloy slurry by low superheat pouring and slightly

Zheng LIU; Wei-min MAO; Xiao-mei LIU

2009-01-01

47

Changes in soil surface fractal dimension due to accumulation of soil organic matter as resulting from the analysis of water vapor adsorption isotherms  

Microsoft Academic Search

The objective of this work is to perform studies aiming at the investigations of the dependence between the content of organic matter and the surface fractal dimension of samples. The values of the surface fractal dimension are calculated from the adsorption isotherms of water vapor. We start with the studies of model systems, containing controlled amount of organic matter. Two

Z. Sokolowska; P. Warchulska; S. Sokolowski

2009-01-01

48

Correlation between the scale-dependent fractal dimension of fracture surfaces and the fracture toughness  

NASA Astrophysics Data System (ADS)

Usually, a negative correlation between the fractal dimension and the fracture toughness of fracture surfaces is obtained experimentally with the slit-island method (SIM). We studied the application of the perimeter-area relation (the basis of the SIM) theoretically and with computer simulations. The conditions under which the fractal dimension obtained by SIM depends on a standard length are found, and we studied the dependence of the fractal dimension on that length. A technique is presented to estimate the fractal dimension of fracture surfaces more accurately. We predict self-similarity, in that the substructure of the fractal has the same dimension as the fractal. In a unified framework, the negative correlation found in experiments can be explained systematically. It is emphasized that before a correlation can be claimed to exist, it is essential to examine the real fractal dimension of fracture surfaces. Our investigation also uncovers additional characteristics of fracture surfaces that can be described by a parameter.

Shi, Duan Wen; Jiang, Jian; Lung, Chi Wei

1996-12-01

49

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

50

Classification of surface EMG signal with fractal dimension  

Microsoft Academic Search

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

51

Effect of mobile phone radiation on brain using EEG analysis by Higuichi's fractal dimension method  

NASA Astrophysics Data System (ADS)

venient window on the mind, revealing synaptic action that is moderately to strongly co-relate with brain state. Fractal dimension, measure of signal complexity can be used to characterize the physiological conditions of the brain. As the EEG signal is non linear, non stationary and noisy, non linear methods will be suitable for the analysis. In this paper Higuichi's fractal method is applied to find the fractal dimension. EEGs of 5 volunteers were recorded at rest and on exposure to radiofrequency (RF) emissions from mobile phones having different SAR values. Mobiles were positioned near the ears and then near the cz position. Fractal dimensions for all conditions are calculated using Higuich's FD estimation algorithm. The result shows that there are some changes in the FD while using mobile phone. The change in FD of the signal varies from person to person. The changes in FD show the variations in EEG signal while using mobile phone, which demonstrate transformation in the activities of brain due to radiation.

Smitha, C. K.; Narayanan, N. K.

2013-01-01

52

Calculation of the small-angle x-ray and neutron scattering from nonrandom (regular) fractals  

NASA Astrophysics Data System (ADS)

The intensity of the small-angle x-ray or neutron scattering has been calculated for two nonrandom (regular) fractals: the Menger sponge and a related fractal, called the fractal jack (a form similar to the metal six-pointed object used in the American children's game). The scatterers are assumed to be systems of independently scattering, randomly oriented identical nonrandom fractals constructed from a material with uniform density. The scattered intensity I(q) can be expressed as a function of qa, where q=4??-1sin(theta/2) ? is the scattered wavelength; theta is the scattering angle, and a is the edge of the cube which is the starting approximant to the fractal. The calculations show that I(q) is a monotonically decreasing function on which maxima and minima are superimposed. For large qa the monotonic decay is proportional to q-D, where D is the fractal dimension. The first maximum for q>0 is a single peak located at q=q1. Groups of maxima are found at q=3kq1, where k is a positive integer greater than 1. The number of maxima within a group becomes greater as k increases. Numerical calculations of I(q) provide no evidence that the maxima and minima are damped and die out as q becomes larger. Thus I(q) for the two nonrandom fractals does not appear to approach the simple power-law scattering proportional to q-D which is characteristic of the small-angle scattering from random fractals. The techniques developed to calculate I(q) for the Menger sponge and the fractal jack can also be employed to find the small-angle scattering from other nonrandom (regular) fractals.

Schmidt, Paul W.; Dacai, Xie

1986-01-01

53

Magnetic ordering of spin systems having fractal dimensions Experimental study  

NASA Astrophysics Data System (ADS)

It is well-known that cooperative properties such as magnetic ordering can depend on the samples' dimensions (Ds) in a qualitative way. However, there have been no samples with well-defined non-integer Ds. The dimension of a given sample has been always discussed on the anisotropy of the electronic/crystal/magnetic structures, which has no definition suitable for quantitative discussion on dimensions vs. properties. On the other hand a particular type of porous samples, i.e. fractal bodies, can have well-defined non-integer Ds dependent exclusively on the geometrical feature of structures, and physical properties of such materials remains unexplored. This paper reports on magnetic ordering in samples covering 2.5 ? D ? 3, in addition to a way of precise control of the fractal dimensions of given samples simply by wax (alkylketene dimer). The results show that the magnetic ordering temperatures, i.e. Néel temperatures (TNs), of CoO depend on D, and rapidly enhance immediately below D = 3. This means that one can control or enhance the critical temperature simply by tuning D with keeping the remaining magnetic properties unchanged. Supplementary material in the form of one pdf file available from the Journal web page at http://dx.doi.org/e2013-40353-3

Naito, T.; Yamamoto, H.; Okuda, K.; Konishi, K.; Mayama, H.; Yamaguchi, D.; Koizumi, S.; Kubo, K.; Nakamura, T.

2013-10-01

54

Comminution, Strain, and Fractal Dimension in Experimental Cataclastic Flow  

NASA Astrophysics Data System (ADS)

Cataclastic flow was produced in Massillon sandstone (92% quartz, porosity 11.4%; average grain-size 300 ? m at room temperature, 15-200 MPa pressure range, and axial strains from 7% to 52%. The transition from faulting to cataclastic flow for the rock occurred at 55-85 MPa pressure range. Cataclastic textures were analyzed using digital optical and SEM images taken at a wide range of magnifications. Strain and pressure dependencies of comminution intensity, fractal dimension (D), and localization anisotropy were determined based on measurements of about 6.2x105 particles in 29 test samples. Comminution intensity, as viewed on 2-D images is defined as C = [1-A/(A0-? A0)], where A is the sectional area of particles with >=10% probability of fracture, A0 is the image area, and ? is the initial porosity. Microscopy supports the assumption that particles with less than 10% probability of fracture, in the order of lower fractal limit and mineral grinding-limit sizes ( ~2-7 ? m), are generated at the lowest experimental strain. Li=1-(Ai/A) gives the degree of anisotropy due to localization, where Ai is A, measured within an area of localized cataclastic deformation (e.g. shear bands and shear fracture zones). Values for Li and C vary between 0 and 1.Within the fractal PSD,A and Ai need not be measured at the same magnification. The mean values of D and C show very little variation as a function of pressure, indicating that pressure does not play a primary role in textural evolution. Fractal dimension and comminution intensity, correlating with a coefficient of 0.794, both increase with strain. Accordingly, variations in comminution intensity with strain (1>= ?repsilon >=0) is defined by power function ?repsilon = C{(D+{?repsilon). Plots of the function, using highest (D=3.69) and lowest (D=2.68) measured 3-D fractal dimension, closely bound the experimental data for the entire range of pressure and strain. The function predicts the emergence of a range of comminution intensities (microbreccia, cataclasite) per strain value at low strains, and a tendency toward textural homogeneity (ultracataclasite) with increasing strain. The localization anisotropy, Li, has its highest value of 0.2 at the lowest pressure, dropping continuously to a steady value of 0.05 at pressures >100 MPa.

Hadizadeh, J.

2001-12-01

55

Measuring the Urban Space-filling Efficiency using Fractal Dimension: The Case of Safranbolu, Turkey  

Microsoft Academic Search

Fractals are spatial entities that are irregular in terms of geometry and independent from scale. Recent research has demonstrated that the urban form can not be fully described by Euclidean geometry, but rather be treated as fractals (Batty and Longley, 1987; Benguigui and Daoud, 1991; Batty and Xie, 1996; 1999; Shen 1997; 2002). Fractal dimension is a quantitative measure of

Ebru CUBUKCU

56

Visual tool for estimating the fractal dimension of images  

NASA Astrophysics Data System (ADS)

This work presents a new Visual Basic 6.0 application for estimating the fractal dimension of images, based on an optimized version of the box-counting algorithm. Following the attempt to separate the real information from “noise”, we considered also the family of all band-pass filters with the same band-width (specified as parameter). The fractal dimension can be thus represented as a function of the pixel color code. The program was used for the study of paintings cracks, as an additional tool which can help the critic to decide if an artistic work is original or not. Catalogue identifier: AEEG_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v1_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.: 29?690 No. of bytes in distributed program, including test data, etc.: 4?967?319 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 30M Classification: 14 Nature of problem: Estimating the fractal dimension of images. Solution method: Optimized implementation of the box-counting algorithm. Use of a band-pass filter for separating the real information from “noise”. User friendly graphical interface. Restrictions: Although various file-types can be used, the application was mainly conceived for the 8-bit grayscale, windows bitmap file format. Running time: In a first approximation, the algorithm is linear.

Grossu, I. V.; Besliu, C.; Rusu, M. V.; Jipa, Al.; Bordeianu, C. C.; Felea, D.

2009-10-01

57

Cosmology in one dimension: fractal geometry, power spectra and correlation  

NASA Astrophysics Data System (ADS)

Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter distribution may not exist. A point of controversy is whether the distribution is fractal and, if so, over what range of scales. One-dimensional models demonstrate that the important dynamics for cluster formation occur in the position-velocity plane. Here the development of scaling behavior and multifractal geometry is investigated for a family of one-dimensional models for three different, scale-free, initial conditions. The methodology employed includes: (1) the derivation of explicit solutions for the gravitational potential and field for a one-dimensional system with periodic boundary conditions (Ewald sums for one dimension); (2) the development of a procedure for obtaining scale-free initial conditions for the growing mode in phase space for an arbitrary power-law index; (3) the evaluation of power spectra, correlation functions, and generalized fractal dimensions at different stages of the system evolution. It is shown that a simple analytic representation of the power spectra captures the main features of the evolution, including the correct time dependence of the crossover from the linear to nonlinear regime and the transition from regular to fractal geometry. A possible physical mechanism for understanding the self-similar evolution is introduced. It is shown that hierarchical cluster formation depends both on the model and on the initial power spectrum. Under special circumstances a simple relation between the power spectrum, correlation function, and correlation dimension in the highly nonlinear regime is confirmed.

Miller, Bruce N.; Rouet, Jean-Louis

2010-12-01

58

Cosmology in One Dimension: Fractal Geometry, Power Spectra and Correlation  

NASA Astrophysics Data System (ADS)

Concentrations of matter, such as galaxies and galactic clusters, originated as very small density fluctuations in the early universe. The existence of galaxy clusters and super-clusters suggests that a natural scale for the matter distribution may not exist. A point of controversy is whether the distribution is fractal and, if so, over what range of scales. Here the development of scaling behavior and multifractal geometry is investigated for a family of one-dimensional models for three different, scale-free, initial conditions. The methodology employed includes: 1) The derivation of explicit solutions for the gravitational potential and field for a one-dimensional system with periodic boundary conditions (Ewald sums for one dimension); 2) The development of a procedure for obtaining scale-free initial conditions for the growing mode in phase space for an arbitrary power-law index; 3) The evaluation of power spectra, correlation functions, and generalized fractal dimensions at different stages of the system evolution. A possible physical mechanism for understanding the self-similar evolution is introduced. It is shown that hierarchical cluster formation depends both on the model and the initial power spectrum. Under special circumstances a simple relation between the power spectrum, correlation function, and correlation dimension in the highly nonlinear regime is confirmed.

Miller, Bruce; Rouet, Jean-Louis

2010-10-01

59

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

60

Quantification of Collagen Organization Using Fractal Dimensions and Fourier Transforms  

PubMed Central

Summary The structure of the collagen fibers that composes tendon and ligament are disrupted or damaged during injury and healing. Quantification of these changes is traditionally a laborious and subjective task. In this work we apply two automated techniques, Fourier transformation (FFT) and fractal dimension analysis (FA) to quantify the organization of collagen fibrils. Using multi-photon images we show that for healing ligament FA differentiates more clearly between the different time-points during healing. Using scanning electron microcopy images of overstretched tendon we show that combining FFT and FA measures separates the damaged and undamaged groups more clearly than either method individually.

Frisch, Kayt E.; Duenwald-Kuehl, Sarah E.; Lakes, Roderic S.; Vanderby, Ray

2011-01-01

61

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

NASA Astrophysics Data System (ADS)

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 angle-scattering light dispersion. Electrophoretic measurements show a similar variation of the zeta potential ( ? potential) for EYPC and DPPC, with a small increase of initial positive values. However, the ? potential of DMPC changes from a initial negative value to near zero with increasing La3+ concentration. The evolution of the aggregate sizes was followed by light scattering. DPPC and DMPC show a RLCA regimen growth at low La3+ concentrations and a DLCA regimen at higher concentrations. In the case of EYPC, the final size of aggregation strongly depends on La3+ concentration. The calculated fractal dimension is in the range 1.8 to 2.1.

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

2007-07-01

62

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

63

Fractal Dimension in Butterflies’ Wings: a novel approach to understanding wing patterns ?  

Microsoft Academic Search

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

2005-01-01

64

The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model  

PubMed Central

The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM.

Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.

2010-01-01

65

The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model  

SciTech Connect

The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski-Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM.

Wang Xujing [Department of Physics, University of Alabama at Birmingham, Birmingham, Alabama 35294 (United States); Becker, Frederick F.; Gascoyne, Peter R. C. [Department of Molecular Pathology, University of Texas M. D. Anderson Cancer Center, Houston, Texas 77030 (United States)

2010-12-15

66

Ruling out the uncertainty of the box-counting method for estimating the fractal dimension of river networks  

NASA Astrophysics Data System (ADS)

The natural river networks are usually featured by a self-similar tree-like structure which represents a deep sense statistical symmetry and can be described by the fractal geometry theory in a decent way (Rodriguez-Iturbe and Rinaldo, 1997). This self-similarity provides a basis to investigate the scale invariance of many hydrological phenomena and has received extensive attention. Many researchers use box-counting method to estimate the fractal dimension of river networks due to now widely available DEM data and easy-to-use river network extraction packages from DEM such as in ESRI’s ArcGIS software package. Zhou et al.’s (2008) study, however, shows that the box-counting dimension is subject to considerable degree of uncertainty, which depends strongly on: 1) the threshold area used to delineate the river network; 2) the range of calculated box sizes to overlay and intersect the river network. This study is devoted to examine the sources of this uncertainty and develop an improved procedure to calculate the box-counting dimension. The calculation based on real world DEMs and theoretical analysis on the mathematical definition of box-counting dimension show that the uncertainty is evoked by the upper bound of range of calculated box sizes, i.e., given the larger upper bound the box-counting dimension varies with the threshold area while given an appropriate upper bound is the unique value of box-counting dimension could be obtained. A more rigorous procedure is finally proposed to calculate the fractal dimension of river networks with the box-counting method. This procedure effectively eliminates the uncertainties of the box-counting method, and thus gives the fractal dimension with higher confidence.

Tian, F.; Wang, B.; Hu, H.

2009-12-01

67

Surface fractal dimension: An indicator to characterize the microstructure of cement-based porous materials  

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

68

Dose Verification in Intensity Modulation Radiation Therapy: A Fractal Dimension Characteristics Study  

PubMed Central

Purpose. This study describes how to identify the coincidence of desired planning isodose curves with film experimental results by using a mathematical fractal dimension characteristic method to avoid the errors caused by visual inspection in the intensity modulation radiation therapy (IMRT). Methods and Materials. The isodose curves of the films delivered by linear accelerator according to Plato treatment planning system were acquired using Osiris software to aim directly at a single interested dose curve for fractal characteristic analysis. The results were compared with the corresponding planning desired isodose curves for fractal dimension analysis in order to determine the acceptable confidence level between the planning and the measurement. Results. The film measured isodose curves and computer planning curves were deemed identical in dose distribution if their fractal dimensions are within some criteria which suggested that the fractal dimension is a unique fingerprint of a curve in checking the planning and film measurement results. The dose measured results of the film were presumed to be the same if their fractal dimension was within 1%. Conclusions. This quantitative rather than qualitative comparison done by fractal dimension numerical analysis helps to decrease the quality assurance errors in IMRT dosimetry verification.

Wu, Jia-Ming; Kuo, Chung-Ming; Chen, Ching-Jiang

2013-01-01

69

Beyond uniformity and independence: analysis of R-trees using the concept of fractal dimension  

Microsoft Academic Search

We propose the concept of fractal dimension of a set of points, in order to quantify the deviation from the uniformity distribution. Using measurements on real data sets (road intersections of U.S. counties, star coordinates from NASA's Infrared-Ultraviolet Explorer etc.) we provide evidence that real data indeed are skewed, and, moreover, we show that they behave as mathematical fractals, with

Christos Faloutsos; Ibrahim Kamel

1994-01-01

70

Oil-spills detection in SAR images by fractal dimension estimation  

Microsoft Academic Search

The paper describes a multi-resolution algorithm based on fractal geometry for texture analysis and detection of oil spills in SAR images. The multi-resolution approach reduces the problems of speckle and sea clutter and preserves subtle variations of oil slicks. The use of fractal dimension as a feature for classification improves the oil spill detection, since enhances texture discrimination. The proposed

Giuliano Benelli; Andrea Garzelli

1999-01-01

71

On the use of spectral methods for the determination of fractal dimension  

SciTech Connect

This paper discusses the use of fractal theory for quantitative analysis of profiles from two-dimensional surfaces. The theoretical relationship between spectral parameters and fractal dimension is examined, including the conditions under which the derived relationship between spectral parameters and fractal dimension by Voss (1985) is valid, and the limitations in making inferences from spectral parameters. Applications of fractal theory to geophysical data are also discussed. In particular, it is shown that an amplitude spectrum with a decay corresponding to a fractal dimension of 1.5 can result from the concatenation of time series with decays corresponding to different fractal dimensions. It has been shown that the spectral density of a fractal distribution will be characterized by a power-law decay, but this paper illustrates that a power-law decay is not sufficient to identify a fractal distribution. Although this paper discusses applications to the study of Earth topography, the results are applicable to the study of any one-dimensional profile.

Hough, S.E. (Columbia Univ., Palisades, NY (USA))

1989-07-01

72

Autonomic control of heart rate during physical exercise and fractal dimension of heart rate variability.  

PubMed

The objectives of the present study were to investigate autonomic nervous system influence on heart rate during physical exercise and to examine the relationship between the fractal component in heart rate variability (HRV) and the system's response. Ten subjects performed incremental exercise on a cycle ergometer, consisting of a 5-min warm-up period followed by a ramp protocol, with work rate increasing at a rate of 2.0 W/min until exhaustion. During exercise, alveolar gas exchange, plasma norepinephrine (NE) and epinephrine (E) responses, and beat-to-beat HRV were monitored. HRV data were analyzed by "coarse-graining spectral analysis" (Y. Yamamoto and R. L. Hughson. J. Appl. Physiol. 71: 1143-1150, 1991) to break down their total power (Pt) into harmonic and nonharmonic (fractal) components. The harmonic component was further divided into low-frequency (0.0-0.15 Hz) and high-frequency (0.15-0.8 Hz) components, from which low-frequency and high-frequency power (Pl and Ph, respectively) were calculated. Parasympathetic (PNS) and sympathetic (SNS) nervous system activity indicators were evaluated by Ph/Pt and Pl/Ph, respectively. From the fractal component, the fractal dimension (DF) and the spectral exponent (beta) were calculated. The PNS indicator decreased significantly (P < 0.05) when exercise intensity exceeded 50% of peak oxygen uptake (VO2 peak). Conversely, the SNS indicator initially increased at 50-60% VO2peak (P < 0.05) and further increased significantly (P < 0.05) at > 60% VO2peak when there were also more pronounced increases in NE and E.(ABSTRACT TRUNCATED AT 250 WORDS) PMID:8458809

Nakamura, Y; Yamamoto, Y; Muraoka, I

1993-02-01

73

Fractal Dimension as a Feature for Adaptive Electroencephalogram Segmentation in Epilepsy.  

National Technical Information Service (NTIS)

In previous studies the fractal dimension (FD) has been shown to be a useful tool to detect non-stationarities and transients in biomedical signals like electroencephalogram (EEG) and electrocardiogram (ECG). The changes in FD are shown to characterise al...

M. E. Kirlangic D. Perez S. Kudryavtseva G. Griessbach G. Henning

2001-01-01

74

Implication of fractal dimension in hydrogeology and rock mechanics. Version 1.1.  

National Technical Information Service (NTIS)

Since much of geology and hydrogeology is controlled by the geometry of geologic features such as faults, fractures and stratigraphy, many researchers have proposed the use of fractal dimension as an index for comparing hydrogeologic environments. This re...

W. Dershowitz K. Redus P. Wallmann P. LaPointe C. L. Axelsson

1992-01-01

75

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence  

Microsoft Academic Search

We present estimates of the Hausdorff fractal dimension of a planar section of the interfaces on the sides of a thin curtain of heavy gas (SF6) embedded in air and accelerated with a planar shock wave at Mach 1.2. As the Richtmyer–Meshkov instability develops, eventually leading to a transition to turbulence in the curtain, the fractal dimension of the interfaces

Peter Vorobieff; Paul M Rightley; Robert F Benjamin

1999-01-01

76

Shock-driven gas curtain: fractal dimension evolution in transition to turbulence  

Microsoft Academic Search

We present estimates of the Hausdorff fractal dimension of a planar section of the interfaces on the sides of a thin curtain of heavy gas (SF6) embedded in air and accelerated with a planar shock wave at Mach 1.2. As the Richtmyer-Meshkov instability develops, eventually leading to a transition to turbulence in the curtain, the fractal dimension of the interfaces

Peter Vorobieff; Paul M. Rightley; Robert F. Benjamin

1999-01-01

77

Exact eigenstates on a two-dimensional Penrose lattice and their fractal dimensions  

NASA Astrophysics Data System (ADS)

Exact eigenstates of a tight-binding model on a two-dimensional Penrose lattice are investigated. Several exact eigenfunctions are found for certain transfer matrices, and a method to obtain more general exact solutions is proposed. The fractal dimension of self-similar non-normalizable eigenfunctions is defined, and the characteristic of wave functions is analyzed successfully in terms of the fractal dimension.

Tokihiro, Tetsuji; Fujiwara, Takeo; Arai, Masao

1988-09-01

78

Fractal Dimension Analysis of Gustatory Electroencephalograms in Humans  

NASA Astrophysics Data System (ADS)

To quantify the neural dynamics of the brain responsible for gustatory recognition and discrimination, fractal dimensions (FDs) of electroencephalograms (EEGs), which were measured under resting and three gustatory stimulation states, were investigated. The seven normal subjects sat on a chair with the chin resting on a frame made of plaster bandage and eyes closed. Distilled water (DW), high concentrated taste (HCT) solution (300 mM NaCl, 1 mM quinine-HCl, 40 mM acetic acid and 500 mM sucrose) and low concentrated taste (LCT) solution (51 mM NaCl, 0.026 mM quinine-HCl, 3 mM acetic acid and 14 mM sucrose) were randomly delivered to the anterior region of the tongue which was protruded slightly out of the mouth. FDs of EEGs from Cz in the resting and in the DW stimulation state were 5.43±1.01 and 4.94±1.03, respectively. In the HCT stimulation state, FD significantly decreased to 4.20±1.08 as compared with that in the resting (P<0.001). While, in the LCT stimulation state, FD significantly increased to 5.77±1.02 as compared with that in the HCT stimulation state (P<0.001). These results suggest that information processing of the brain is relatively simple when easily recognized tastes are applied.

Igasaki, Tomohiko; Murayama, Nobuki

79

Discriminating between elderly and young using a fractal dimension analysis of centre of pressure  

PubMed Central

The aim of this project was to evaluate the use of a new analysis technique, fractal dimension analysis, for quantification of quiet stance centre of pressure (COP). By using a fractal dimension analysis of COP, it might be possible to gain more information about control during quiet stance than traditional analyses have previously allowed. The current project considered a group of young healthy participants and a group of elderly healthy participants to compare traditional measures of COP against a fractal dimension analysis of COP. Results indicated that both types of analyses are able to distinguish between eyes open and eyes closed in the elderly group. However, the fractal dimension analysis more accurately detected differences between the participant groups when standing with their eyes closed. Based on these results it is suggested that fractal dimension analysis is more informative about posture control than traditional measures. It is suggested that a fractal dimension type of analysis can be incorporated into clinical testing to identify patients with pathologies.

2004-01-01

80

Fractal-feature distance analysis of contrast-detail phantom image and meaning of pseudo fractal dimension and complexity  

Microsoft Academic Search

The purposes of our studies are to examine whether or not fractal-feature distance deduced from virtual volume method can\\u000a simulate observer performance indices and to investigate the physical meaning of pseudo fractal dimension and complexity.\\u000a Contrast-detail (C-D) phantom radiographs were obtained at various mAs values (0.5-4.0 mAs) and 140 kVp with a computed radiography\\u000a system, and the reference image was

K. Imai; M. Ikeda; Y. Enchi; T. Niimi

2009-01-01

81

Fractal dimensions of silica gels generated using reactive molecular dynamics simulations  

SciTech Connect

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

82

Maximum entropy, fractal dimension and lacunarity in quantification of cellular rejection in myocardial biopsy of patients submitted to heart transplantation  

NASA Astrophysics Data System (ADS)

This paper presents a method for the quantification of cellular rejection in endomyocardial biopsies of patients submitted to heart transplant. The model is based on automatic multilevel thresholding, which employs histogram quantification techniques, histogram slope percentage analysis and the calculation of maximum entropy. The structures were quantified with the aid of the multi-scale fractal dimension and lacunarity for the identification of behavior patterns in myocardial cellular rejection in order to determine the most adequate treatment for each case.

Neves, L. A.; Oliveira, F. R.; Peres, F. A.; Moreira, R. D.; Moriel, A. R.; de Godoy, M. F.; Murta Junior, L. O.

2011-03-01

83

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

PubMed

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. PMID:11502481

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

2001-08-01

84

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

Microsoft Academic Search

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

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

2001-01-01

85

The Use of Fractal Dimension in Characterizing Tree Growth in Filled Epoxy Resin under Humid Condition  

NASA Astrophysics Data System (ADS)

The structural response of tree growth in epoxy resin blended with silica filler has been investigated. The physical properties of the resin were varied by changing its filler content and exposing to humid air. The fractal dimension of the electrical tree and its relationship with filler content and humidity were determined. The damaged area of tree in various contents of filler was also estimated. It is considered that the filler would create such an obstruction to the tree growth both in humid and dry conditions. At the ambient condition, the more filler content, the more obstruction would be generated, leading to the significant suppression of tree growth. Likewise, the introduction of filler brought a rise in fractal dimension due to the increase of branches. It is concluded that the existence of filler makes the tree structure more complicated by introducing obstacles to tree propagation, leading to the high fractal dimension of the tree. In addition, it was found that the fractal dimension of the tree was very relational to the fractal dimension of the composite material including filler particles.

Kurnianto, Rudi; Murakami, Yoshinobu; Hozumi, Naohiro; Nagao, Masayuki

86

A new way of describing meiosis that uses fractal dimension to predict metaphase I  

PubMed Central

Meiosis, the reductive nuclear division, is a continuum, but for purposes of communication, is described in stages. In sexually-reproducing organisms, including the dwarf mistletoe Arceuthobium americanum, prophase I of meiosis is prolonged (8 months for female A. americanum). Conversely, metaphase I, where chromosome pairs line up along a dividing cell's "equator", is relatively brief, difficult to predict, but critical regarding the random distribution of the paternal and maternal chromosomes in sexual organisms. However, descriptions of meiosis as either a continuum or stages are limited to qualitative observations. A quantification of meiosis can provide mathematical descriptors and allow for the prediction of when chromosomes reach the equator; this will not only be useful to researchers of cell division, but also to those requiring a large sample of metaphase I materials. Here, the probability-density function was used to calculate the fractal dimension of A. americanum nuclei undergoing early meiosis, and it predicted the onset of metaphase I by 2 days.

2005-01-01

87

Fractal dimension of the grain boundaries in ceramics with nanodispersed additions  

NASA Astrophysics Data System (ADS)

The fractal dimension of the grain boundaries in Al2O3-MgO-SiO2 corundum ceramic is measured. It is shown for the first time that a similarity exists between the aggregation of solid disperse particles and the grain formation in the ceramic and that this similarity can be used to reveal grain formation mechanisms. The fractal dimension of the grain boundaries is found to be 1.68 and 1.42 at sintering temperatures of 1200 and 1600°C, respectively. These values correspond to primary recrystallization and normal grain growth in the ceramic. A relationship between the fractal dimension of the grain boundaries and the sintering temperature of the corundum ceramic is obtained.

Nomoev, A. V.; Vikulina, L. S.

2012-12-01

88

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

Microsoft Academic Search

.  ?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

89

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

PubMed

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

2004-12-20

90

Application of atomic force microscopy in determining the fractal dimension of the mirror, mist, and hackle region of silica glass  

SciTech Connect

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

91

Use of sEMG in identification of low level muscle activities: Features based on ICA and fractal dimension  

Microsoft Academic Search

This paper has experimentally verified and compared features of sEMG (Surface Electromyogram) such as ICA (Independent Component Analysis) and Fractal Dimension (FD) for identification of low level forearm muscle activities. The fractal dimension was used as a feature as reported in the literature. The normalized feature values were used as training and testing vectors for an artificial neural network (ANN),

Ganesh R Naik; Dinesh K Kumar; Sridhar Arjunan

2009-01-01

92

The Use of Fractal Dimension in Characterizing Tree Growth in Filled Epoxy Resin under Humid Condition  

Microsoft Academic Search

The structural response of tree growth in epoxy resin blended with silica filler has been investigated. The physical properties of the resin were varied by changing its filler content and exposing to humid air. The fractal dimension of the electrical tree and its relationship with filler content and humidity were determined. The damaged area of tree in various contents of

Rudi Kurnianto; Yoshinobu Murakami; Naohiro Hozumi; Masayuki Nagao

2006-01-01

93

Complete Devil's Staircase, Fractal Dimension, and Universality of Mode Locking Structure in the Circle Map  

Microsoft Academic Search

It is shown numerically that the stability intervals for limit cycles of the circle map form a complete devil's staircase at the onset of chaos. The complementary set to the stability intervals is a Cantor set of fractal dimension D=0.87. This exponent is found to be universal for a large class of functions.

M. Høgh Jensen; Per Bak; Tomas Bohr

1983-01-01

94

The strength and fractal dimension characteristics of alum–kaolin flocs  

Microsoft Academic Search

Flocs generated by various shear forces exhibit different characteristics of size, strength and structure. These properties were investigated by employing a continuous optical monitoring and a microscope with CCD camera to directly monitor aggregation under six different shear intensities. The floc structure was characterized by the fractal dimension. The results showed that the flocculation index (FI) decreased from 1.16 at

Tao Li; Zhe Zhu; Dongsheng Wang; Chonghua Yao; Hongxiao Tang

2007-01-01

95

Box fractal dimension as a measure of statistical homogeneity of jointed rock masses  

Microsoft Academic Search

A written computer programme to estimate the box fractal dimension (DB) is verified by estimating DB of the triadic Koch curve for which the theoretical D is known. The influence of a number of input parameters of the box-counting method on the accuracy of estimated DB is evaluated using the same Koch curve. The employed size range of the applied

Pinnaduwa H. S. W. Kulatilake; Reno Fiedler; Bibhuti B. Panda

1997-01-01

96

Estimating Mass Fractal Dimension of Soil Water Retention Curve using Neural Networks  

Microsoft Academic Search

Soil water retention curve (SWRC) representing the relationship between soil water content and matric potential, is one of the most important soil hydraulic properties which its direct measurement is time consuming and expensive. The objective of this study was to develop an Artificial Neural Networks (ANNs) model to estimate the mass fractal dimension of SWRC from readily available parameters such

B. Ghanbarian-Alavijeh; G. Huang; A. M. Liaghat; R. Taghizadeh-Mehrjerdi

2009-01-01

97

Changes in fractal dimension and lacunarity as early markers of UV-induced apoptosis.  

PubMed

The aim of our study was to employ fractal analysis for evaluation of ultrastructural changes during early stages of apoptosis. Apoptosis was induced in U251 human glioma cell line by exposure to UVB light. The cells were visualized by optical phase-contrast microscopy and photographed before the UV treatment, immediately after the treatment, as well as at 30 min intervals during 5h observation period. For each of the 32 cells analyzed, cellular and nuclear fractal dimension, as well as nuclear lacunarity, were determined at each time point. Our data demonstrate that cellular ultrastructural complexity determined by fractal dimension and lacunarity significantly decreases after the UV irradiation, with the nuclear lacunarity being a particularly sensitive parameter in detecting early apoptosis. Importantly, fractal analysis was able to detect cellular apoptotic changes earlier than conventional flow cytometric analysis of phosphatidylserine exposure, DNA fragmentation and cell membrane permeabilization. These results indicate that fractal analysis might be a powerful and affordable method for non-invasive early identification of apoptosis in cell cultures. PMID:22763132

Pantic, Igor; Harhaji-Trajkovic, Ljubica; Pantovic, Aleksandar; Milosevic, Nebojsa T; Trajkovic, Vladimir

2012-03-21

98

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

USGS Publications Warehouse

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

99

The Application of Identification Method of Ground Surfacesusing Fractal Dimension to Millimeter Wave Radar Altimeter  

NASA Astrophysics Data System (ADS)

Data of scattering coefficient on vertical incidence against ground surface at U-band are obtained by Millimeter Wave Radar Altimeter using FM-CW ranging. Noise suppression by wavelet shrinkage can be utilized to extract feature parameter in high spatial frequency band, in which level of fractal noise is dominated by that of white noise. We propose approximate algorithm for estimation of local fractal dimension in high spatial frequency band which is the most effective parameter for identification for classification of ground surfaces such as vegetation, town area and rice field.

Araki, Kan

100

Scale-dependent fractal dimensions of topographic surfaces: An empirical investigation, with applications in geomorphology and computer mapping  

Microsoft Academic Search

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

101

The influence of the growth conditions of the plague microbe vaccine strain colonies on the fractal dimension of biospeckles  

Microsoft Academic Search

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

A S Ulyanov; A M Lyapina; O V Ulianova; V A Fedorova; S S Uianov

2011-01-01

102

Transition of fractal dimension in a latticed dynamical system  

SciTech Connect

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

103

Fractal dimension of debris-avalanche deposits in the Hawaiian submarine landslide deposits  

NASA Astrophysics Data System (ADS)

17 landslide deposits on the flanks of the southern Hawaiian Ridge have been classified into two major types: SLUMPS, which moved slowly as a coherent mass, and DEBRIS AVALANCHES, which moved quickly.The debris-avalanche deposits are predominant on submarine flanks of volcanic ocean islands elsewhere in the world. Such huge landslides are considered to produce giant tsunamis and megaturbidites covering large areas of abyssal plains. Based on the small scale topographic elements, we reinvestigated the distribution areas and emplacement styles of the debris-avalanche deposits, which differ from those previously proposed from GLORIA images without benefit of detailed bathymetric data or direct seafloor observations. There are several types of small scale topographic elements in the debris-avalanche deposits previously proposed: source amphitheater, toppled blocks, marginal levee, slide-emplaced blocks, chute, mud wave, hummocky terrain. They are very similar to those appeared in subaerial volcanic debris-avalanche fields. However, no correlation between the collapse height and runout distance are observed in the submarine debris-avalanche deposits. The hummocky terrains can be classified into two types: FLAT-TYPE, which is distributed in the nearly flat abyssal plain, less than 0.5 degree, and SLOPE-TYPE, which located on the lower part of the submarine flanks, greater than 1 degree. The size of hummocks in a slope-type hummocky terrain have an unimodal distribution pattern with a broad peak in the number of hummocks versus height category diagram. On the contrary, the size of hummocks in flat-type hummocky terrains have a power law distribution pattern in the same diagram. The fractal dimensions calculated from these diagrams are 1.19 (Nuuanu landslide), 2.32 (Ka Lae landslide) and 2.96 (Alika 2 debris-avalanche), respectively. They are expected to reflect the processes and degree of fragmentation. Therefore, among the debris_]avalanche deposits proposed previously around Hawaiian ridge, only three debris-avalanche deposits, Nuuanu, Alika 2, Ka Lae, could be a huge landslide deposits accompanied with huge tsunamis. Because fractal dimension indicates degree of the fragmentation, Alika 2 debris flow could be the most powerful turbulent flow among others. The bending trend in the power law distribution pattern of the Nuuanu landslide imply that the hummocks were produced by two different fragmentation: turbulent flows at the toe of the debris-avalanche and translational disruption at proximal part. The hummocks without a power law distribution in the terrain have been produced by a overlapping of small scale debris flow deposits rather than a huge landslide failure. Unimodal size distribution with a broad peak may be interpreted as a gravel-rich submarine fans rather than a huge landslide deposit.

Yokose, H.; Yamato, S.

2005-12-01

104

Can one hear the dimension of a fractal?  

Microsoft Academic Search

We consider the spectrum of the Laplacian in a bounded open domain of Rn with a rough boundary (i.e. with possibly non-integer dimension) and we discuss a conjecture by M. V. Berry generalizing Weyl's conjecture. Then using ideas Mark Kac developed in his famous study of the drum, we give upper and lower bounds for the second term of the

Jean Brossard; René Carmona

1986-01-01

105

Repair, Evaluation, Maintenance and Rehabilitation Research Program. Surface Roughness Characterization of Rock Masses Using the Fractal Dimension and the Variogram.  

National Technical Information Service (NTIS)

Fractal dimension analysis, a branch of mathematical topology, and the variogram construction from the theory of regionalized variables were applied to geologic rock surface descriptive data. The purpose was to determine the technique's applicability to c...

J. R. Carr

1990-01-01

106

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

107

Correlation of mass fractal dimension and cluster size of silica in styrene butadiene rubber composites  

NASA Astrophysics Data System (ADS)

The morphology of the precipitated silica VN3 filled in styrene butadiene rubber was studied as a function of the volume fraction ? by means of small-angle X-ray scattering experiments. The wide q-range of 0.008 nm-1fractal dimension does not depend on ?, and by that means experimentally proving that there is not necessarily a correlation between the mass fractal dimension and the cluster size.

Schneider, Gerald Johannes; Vollnhals, V.; Brandt, K.; Roth, S. V.; Göritz, D.

2010-09-01

108

Correlation of mass fractal dimension and cluster size of silica in styrene butadiene rubber composites.  

PubMed

The morphology of the precipitated silica VN3 filled in styrene butadiene rubber was studied as a function of the volume fraction ? by means of small-angle X-ray scattering experiments. The wide q-range of 0.008?nm(-1)fractal dimension does not depend on ?, and by that means experimentally proving that there is not necessarily a correlation between the mass fractal dimension and the cluster size. PMID:20831333

Schneider, Gerald Johannes; Vollnhals, V; Brandt, K; Roth, S V; Göritz, D

2010-09-01

109

Quadratic self-correlation: An improved method for computing local fractal dimension in remote sensing imagery  

NASA Astrophysics Data System (ADS)

We present a new method for computing the local fractal dimension in remote sensing imagery. It is based on a novel way of estimating the quadratic self correlation (or 2D Hurst coefficient) of the pixel values. The method is thoroughly tested with a set of synthetic images an also with remote sensing imagery to assess the usefulness of the techniques for unsupervised image segmentation. We make a comparison with other estimators of the local fractal dimension. Quadratic self-correlation methods provide more accurate results with synthetic images, and also produce more robust and fit segmentations in remote sensing imagery. Even with very small computation windows, the methods prove to be able to detect borders and details precisely.

Silvetti, Andrea F.; Delrieux, Claudio A.

2013-10-01

110

Relationship between retinal fractal dimensions and retinal circulation in patients with type 2 diabetes mellitus.  

PubMed

Abstract Purpose: To investigate the relationship between retinal fractal dimensions (Dfs) and retinal circulation, which is impaired in early-stage diabetic retinopathy (DR) in patients with type 2 diabetes mellitus (DM). Methods: Using a laser Doppler velocimetry system, we measured the retinal vessel diameter (D) and blood velocity (V) and calculated the retinal blood flow (RBF) in the retinal arterioles and venules in 106 eyes (106 patients, mean age?±?standard deviation, 58.7?±?9.8 years). Patients with type 2 DM had no (n?=?86) or mild nonproliferative DR (n?=?20). The Dfs were measured on the retinal photographs using a semiautomatic computer-based program. Results: The average D, V, and RBF in the retinal arterioles and venules were, respectively, 107.9?±?13.3 and 139.4?±?20.1?µm, 33.2?±?7.0 and 22.6?±?6.1?mm/s and 9.3?±?2.9 and 10.4?±?3.8?µl/min. The average Df was 1.4276?±?0.0193. There was no association between the Df and any retinal circulatory parameters of the retinal arterioles. In contrast, we found significant correlations between the Df and the vessel D (r?=?0.37, p?=?0.0002) and RBF (r?=?0.22, p?=?0.026) in the retinal venules. Conclusion: The Df might be associated with changes in the retinal circulation in patients with type 2 DM. PMID:23885750

Nagaoka, Taiji; Yoshida, Akitoshi

2013-07-25

111

A new way of describing meiosis that uses fractal dimension to predict metaphase I.  

PubMed

Meiosis, the reductive nuclear division, is a continuum, but for purposes of communication, is described in stages. In sexually-reproducing organisms, including the dwarf mistletoe Arceuthobium americanum, prophase I of meiosis is prolonged (8 months for female A. americanum). Conversely, metaphase I, where chromosome pairs line up along a dividing cell's "equator", is relatively brief, difficult to predict, but critical regarding the random distribution of the paternal and maternal chromosomes in sexual organisms. However, descriptions of meiosis as either a continuum or stages are limited to qualitative observations. A quantification of meiosis can provide mathematical descriptors and allow for the prediction of when chromosomes reach the equator; this will not only be useful to researchers of cell division, but also to those requiring a large sample of metaphase I materials. Here, the probability-density function was used to calculate the fractal dimension of A. americanum nuclei undergoing early meiosis, and it predicted the onset of metaphase I by 2 days. PMID:16094465

Ross, Cynthia M

2005-08-05

112

Investigation of statistical relationships between quantities describing bone architecture, its fractal dimensions and mechanical properties.  

PubMed

The paper presents linear, logarithmic and exponential regression tabecular bone indices, fractal dimensions and strength. The analysis of the above parameters was supported by determining non-parametric correlation coefficients: Spearman's ?, gamma and Kendall's ?. The principal components' analysis (PCA) was also performed in order to reduce the number of indices describing the variance in the data set. The analysis showed the most independent indices: lacunarity (?m, ?min, ?max), BMD, Conn.D., SMI, DA, ?A and age. PMID:21361259

Cicha?ski, Artur; Nowicki, Krzysztof; Mazurkiewicz, Adam; Topoli?ski, Tomasz

2010-01-01

113

The change of the fractal dimension of the stochastic system with colored multiplicative noise (in Ukrainian)  

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.

114

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

115

Fractal dimension and surface topography on the diamond deposition of seeded WC-Co substrates  

NASA Astrophysics Data System (ADS)

Diamond thin films were deposited on WC-Co substrates by hot filament chemical vapor deposition to improve the tribological performance. The influence of the substrate surface topography was found to play an important role during the nucleation stage and the later growth rate as well. In this study, we systematically investigated the relation between substrate surface irregularity, which was evaluated by fractal dimension as well as statistical roughness parameters and the quality of the later deposited diamond film. Preseeding processes, in diamond acetone suspensions with two particle diameters, by supersonic vibrator were also implemented to investigate the effect of particular size on diamond nucleation. The original surfaces were measured with a stylus profiler and contact-mode atomic force microscopy. The diamond deposited substrates were examined by scanning electron microscopy, x-ray diffractometry, Raman spectroscopy, and Rockwell-C indentation to study substrate topography, crystalline structure of the coating, the composition of diamond films, and adhesion between deposited layers and substrates, respectively. The synergetic influence of the substrate's fractal dimension and the particular size of pre-seeding diamond suspension were studied and addressed. The deposited film of a WC-Co substrate with higher surface fractal dimension (>2.50), preseeded by fine diamond suspension (4-12 nm particle size) in advance, has a high diamond-rich composition and adhesion strength.

Chou, C.-C.; Lin, H.-H.

2010-04-01

116

Quantitative Estimation of the Amount of Fibrosis in the Rat Liver Using Fractal Dimension of the Shape of Power Spectrum  

NASA Astrophysics Data System (ADS)

This paper describes the quantitative measurement of the amount of fibrosis in the rat liver using the fractal dimension of the shape of power spectrum. The shape of the power spectrum of the scattered echo from biotissues is strongly affected by its internal structure. The fractal dimension, which is one of the important parameters of the fractal theory, is useful to express the complexity of shape of figures such as the power spectrum. From in vitro experiments using rat liver, it was found that this method can be used to quantitatively measure the amount of fibrosis in the liver, and has the possibility for use in the diagnosis of human liver cirrhosis.

Kikuchi, Tsuneo; Nakazawa, Toshihiro; Furukawa, Tetsuo; Higuchi, Toshiyuki; Maruyama, Yukio; Sato, Sojun

1995-05-01

117

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

PubMed

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

118

A Brief Historical Introduction to Fractals and Fractal Geometry  

ERIC Educational Resources Information Center

|This paper deals with a brief historical introduction to fractals, fractal dimension and fractal geometry. Many fractals including the Cantor fractal, the Koch fractal, the Minkowski fractal, the Mandelbrot and Given fractal are described to illustrate self-similar geometrical figures. This is followed by the discovery of dynamical systems and…

Debnath, Lokenath

2006-01-01

119

Fractal dimension values of cerebral and cerebellar activity in rats loaded with aluminium.  

PubMed

Aluminium interferes with a variety of cellular metabolic processes in the mammalian nervous system and its intake might increase a risk of developing Alzheimer's disease (AD). While cerebral involvement even at the early stages of intoxication is well known, the role of cerebellum is underestimated. Our aim was to investigate cerebral and cerebellar electrocortical activity in adult male rats exposed to chronic aluminium treatment by nonlinear analytic tools. The adult rats in an aluminium-treated group were injected by AlCl(3), intraperitoneally (2 mg Al/kg, daily for 4 weeks). Fractal analysis of brain activity was performed off-line using Higuchi's algorithm. The average fractal dimension of electrocortical activity in aluminium-treated animals was lower than the average fractal dimension of electrocortical activity in the control rats, at cerebral but not at cerebellar level. The changes in the stationary and nonlinear properties of time series were more expressed in cerebral electrocortical activity than in cerebellar activity. This can be useful for developing effective diagnostic and therapeutic strategies in neurodegenerative diseases. PMID:20424923

Kekovic, Goran; Culic, Milka; Martac, Ljiljana; Stojadinovic, Gordana; Capo, Ivan; Lalosevic, Dusan; Sekulic, Slobodan

2010-04-28

120

The minimal spanning tree method for calculating seismic multi-fractal  

NASA Astrophysics Data System (ADS)

There are many methods to calculate seismic fractal at present. However, there are still more or less questions to every method. In this paper, we introduce a new way to calculate seismic fractal — the minimal spanning tree. We make an important improvement for this method. By studying some seismic events of four regions including Wushi, Wusu, Tangshan and Haicheng, we obtain that, before the strong earthquake occurrence, the multi-fractal spectrum of the space-time distribution of earthquakes changes from centralized to loose. The result shows that the complexity of fractal structure and the inhomogeneity of the space-time distribution of earthquakes are both increasing. By studying the numerical simulation of point sets, we draw the conclusion that the physical essence of multi-fractal spectrums before and after a strong earthquake occurrence is a changing process from homogeneous to inhomogeneous, from simple to complex.

Ling-Ren, Zhu; Hai-Ying, Long

2000-07-01

121

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

122

The influence of edge detection algorithms on the estimation of the fractal dimension of binary digital images  

NASA Astrophysics Data System (ADS)

The boundary of a fractal object, represented in a two-dimensional space, is theoretically a line with an infinitely small width. In digital images this boundary or contour is limited to the pixel resolution of the image and the width of the line commonly depends on the edge detection algorithm used. The Minkowski dimension was evaluated by using three different edge detection algorithms (Sobel, Roberts, and Laplace operator). These three operators were investigated because they are very widely used and because their edge detection result is very distinct concerning the line width. Very common fractals (Sierpinski carpet and Koch islands) were investigated as well as the binary images from a cancer invasion assay taken with a confocal laser scanning microscope. The fractal dimension is directly proportional to the width of the contour line and the fact, that in practice very often the investigated objects are fractals only within a limited resolution range is considered too.

Ahammer, Helmut; Devaney, Trevor T. J.

2004-03-01

123

Improving Spatial Adaptivity of Nonlocal Means in Low-Dosed CT Imaging Using Pointwise Fractal Dimension  

PubMed Central

NLMs is a state-of-art image denoising method; however, it sometimes oversmoothes anatomical features in low-dose CT (LDCT) imaging. In this paper, we propose a simple way to improve the spatial adaptivity (SA) of NLMs using pointwise fractal dimension (PWFD). Unlike existing fractal image dimensions that are computed on the whole images or blocks of images, the new PWFD, named pointwise box-counting dimension (PWBCD), is computed for each image pixel. PWBCD uses a fixed size local window centered at the considered image pixel to fit the different local structures of images. Then based on PWBCD, a new method that uses PWBCD to improve SA of NLMs directly is proposed. That is, PWBCD is combined with the weight of the difference between local comparison windows for NLMs. Smoothing results for test images and real sinograms show that PWBCD-NLMs with well-chosen parameters can preserve anatomical features better while suppressing the noises efficiently. In addition, PWBCD-NLMs also has better performance both in visual quality and peak signal to noise ratio (PSNR) than NLMs in LDCT imaging.

Zheng, Xiuqing; Hu, Shaoxiang; Li, Ming; Zhou, Jiliu

2013-01-01

124

Measuring the fractal dimensions of ideal and actual objects: implications for application in geology and geophysics  

NASA Astrophysics Data System (ADS)

The box-counting algorithm is the most commonly used method for evaluating the fractal dimension D of natural images. However, its application may easily lead to erroneous results. In a previous paper (Gonzato et al. 1998) we demonstrated that a crucial bias is introduced by insufficient sampling and/or by uncritical application of the regression technique. This bias turns out to be common in many practical applications. Here it is shown that an equally important additional bias is introduced by the orientation, placement and length of the digitized object relative to that of the initial box. Some additional problems are introduced by objects containing unconnected parts, since the discontinuities may or may not be indicative of a fractal pattern. Last, but certainly not least in magnitude, the thickness of the digitized profile, which is implicitly controlled by the scanner resolution versus the image line thickness, plays a fundamental role. All of these factors combined introduce systematic errors in determining D, the magnitudes of which are found to exceed 50 per cent in some cases, crucially affecting classification. To study these errors and minimize them, a program that accounts for image digitization, zooming and automatic box counting has been developed and tested on images of known dimension. The code automatically extracts the unconnected parts from a digitized shape given as input, zooms each part as optimally as possible, and performs the box-counting algorithm on a virtual screen. The size of the screen can be set to meet the sampling requirement needed to produce stable and reliable results. However, this code does not provide image vectorization, which must be performed prior to running this program. A number of image vectorizing codes are available that successfully reduce the thickness of the image parts to one pixel. Image vectorization applied prior to the application of our code reduces the sampling bias for objects with known fractal dimension to around 10-20 per cent. Since this bias is always positive, this effect can be readily compensated by a multiplying factor, and estimates of the fractal dimension accurate to about 10 per cent are effectively possible.

Gonzato, Guido; Mulargia, Francesco; Ciccotti, Matteo

2000-07-01

125

Network-Growth Rule Dependence of Fractal Dimension of Percolation Cluster on Square Lattice  

NASA Astrophysics Data System (ADS)

To investigate the network-growth rule dependence of certain geometric aspects of percolation clusters, we propose a generalized network-growth rule introducing a generalized parameter q and we study the time evolution of the network. The rule we propose includes a rule in which elements are randomly connected step by step and the rule recently proposed by Achlioptas et al. [Science 323 (2009) 1453]. We consider the q-dependence of the dynamics of the number of elements in the largest cluster. As q increases, the percolation step is delayed. Moreover, we also study the q-dependence of the roughness and the fractal dimension of the percolation cluster.

Tanaka, Shu; Tamura, Ryo

2013-05-01

126

Fractal analysis of the uterine contractions.  

PubMed

The fractal dimension D may be calculated in many ways, since its strict definition, the Hausdorff definition is too complicated for practical estimation. In this paper we perform a comparative study often methods of fractal analysis of time series. In Benoit, a commercial program for fractal analysis, five methods of computing fractal dimension of time series (rescaled range analysis, power spectral analysis, roughness-length, variogram methods and wavelet method) are available. We have implemented some other algorithms for calculating D: Higuchi's fractal dimension, relative dispersion analysis, running fractal dimension, method based on mathematical morphology and method based on intensity differences. For biomedical signals results obtained by means of different algorithms are different, but consistent. PMID:15754597

Oczeretko, Edward; Kitlas, Agnieszka; Swiatecka, Jolanta; Lauda?ski, Tadeusz

127

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: The Fractal Dimensions of Complex Networks  

NASA Astrophysics Data System (ADS)

It is shown that many real complex networks share distinctive features, such as the small-world effect and the heterogeneous property of connectivity of vertices, which are different from random networks and regular lattices. Although these features capture the important characteristics of complex networks, their applicability depends on the style of networks. To unravel the universal characteristics many complex networks have in common, we study the fractal dimensions of complex networks using the method introduced by Shanker. We find that the average 'density' (?(r)) of complex networks follows a better power-law function as a function of distance r with the exponent df, which is defined as the fractal dimension, in some real complex networks. Furthermore, we study the relation between df and the shortcuts Nadd in small-world networks and the size N in regular lattices. Our present work provides a new perspective to understand the dependence of the fractal dimension df on the complex network structure.

Guo, Long; Cai, XU

2009-08-01

128

Fractal Dimension Analysis in Self-Assembled Poly(dA)·poly(dT) DNA Network on Mica Surface  

NASA Astrophysics Data System (ADS)

Characteristics of the self-assembled poly(dA)·poly(dT) DNA network adhered on the mica substrate are experimentally investigated based on the AFM observations and the fractal dimension analysis. Artificial B-type double stranded DNA, which consists of 50 base pairs of adenine and thymine, is specially prepared for the experiment. The manufacturing process of DNA network is done in the aqueous solution of poly(dA)·poly(dT) DNA, and the systematical experimental runs are made for various concentration of the solution. It is found that the 2D fractal dimension strongly depends on the fabrication process of the DNA network.

Kawano, Satoyuki

129

Stress assessment of argan ( Argania spinosa (L.) Skeels) in response to land uses across an aridity gradient: Translational asymmetry and branch fractal dimension  

Microsoft Academic Search

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

130

Discriminating at-risk post-MI patients by fractal dimension analysis of the late potential attractor  

Microsoft Academic Search

A novel and reliable approach which quantifies the degree of complexity of late potential (LP) activity in the time domain is presented. By defining the LP attractor in the microvoltage, 3-dimensional space, and then computing the fractal dimension (?) of the attractor's trajectory, the degree of complexity of LP can be quantified with a single parameter. ? may indicate the

R. H. Mitchell; O. Escalona

1998-01-01

131

Global fractal dimension of human DNA sequences treated as pseudorandom walks  

NASA Astrophysics Data System (ADS)

We used a pseudorandom-walk representation in a four-dimensional embedding to estimate the global fractal dimension D of 164 sequences from GenBank and generated length-matched control sequences of three types: random, matched in base content, and matched in dimer content. The mean D of the sequences was 1.631+/-0.137. This D was significantly lower than the D's for all three control types, indicating the presence of significant information content in DNA sequences not explained by base or dimer frequencies. This variation was due largely to nonuniform distribution of bases and dimers within DNA sequences. The D of genomic DNA sequences was different from the D of messenger RNA sequences.

Berthelsen, Cheryl L.; Glazier, James A.; Skolnick, Mark H.

1992-06-01

132

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

PubMed Central

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

133

Nonlinear Geoscience: Fractals  

NSDL National Science Digital Library

This site, from the Earth Monitoring Station at the University of North Carolina, provides an examination of self-similarity and fractals in geoscience. The generation of artificial fractals, fractal dimensions and definitions, and fractal geometry are explained. The site also contains examples such as river basins, coastlines, and lightening that exhibit fractal characteristics.

2007-03-30

134

Fractal dimension approach in postural control of subjects with Prader-Willi Syndrome  

PubMed Central

Background Static posturography is user-friendly technique suitable for the study of the centre of pressure (CoP) trajectory. However, the utility of static posturography in clinical practice is somehow limited and there is a need for reliable approaches to extract physiologically meaningful information from stabilograms. The aim of this study was to quantify the postural strategy of Prader-Willi patients with the fractal dimension technique in addition to the CoP trajectory analysis in time and frequency domain. Methods 11 adult patients affected by Prader-Willi Syndrome (PWS) and 20 age-matched individuals (Control group: CG) were included in this study. Postural acquisitions were conducted by means of a force platform and the participants were required to stand barefoot on the platform with eyes open and heels at standardized distance and position for 30 seconds. Platform data were analysed in time and frequency domain. Fractal Dimension (FD) was also computed. Results The analysis of CoP vs. time showed that in PWS participants all the parameters were statistically different from CG, with greater displacements along both the antero-posterior and medio-lateral direction and longer CoP tracks. As for frequency analysis, our data showed no significant differences between PWS and CG. FD evidenced that PWS individuals were characterized by greater value in comparison with CG. Conclusions Our data showed that while the analysis in the frequency domain did not seem to explain the postural deficit in PWS, the FD method appears to provide a more informative description of it and to complement and integrate the time domain analysis.

2011-01-01

135

Quantification of fractal dimension and Shannon's entropy in histological diagnosis of prostate cancer  

PubMed Central

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

136

Simulated fractal permeability for porous membranes  

Microsoft Academic Search

Fractal permeability model for bi-dispersed porous media is developed based on the fractal characteristics of pores in the membrane. The fractal permeability model is found to be a function of the tortuosity fractal dimension, pore area fractal dimension, sizes of particles and clusters, micro-porosity inside clusters, and the effective porosity of a medium. The pore area fractal dimension and the

M. R. Othman; Z. Helwani; Martunus

2010-01-01

137

Multiscale differential fractal feature with application to target detection  

NASA Astrophysics Data System (ADS)

A multiscale differential fractal feature of an image is proposed and a small target detection method from complex nature clutter is presented. Considering the speciality that the fractal features of man-made objects change much more violently than that of nature's when the scale is varied, fractal features at multiple scales used for distinguishing man-made target from nature clutter should have more advantages over standard fractal dimensions. Multiscale differential fractal dimensions are deduced from typical fractal model and standard covering-blanket method is improved and used to estimate multiscale fractal dimensions. A multiscale differential fractal feature is defined as the variation of fractal dimensions between two scales at a rational scale range. It can stand out the fractal feature of man-made object from natural clutters much better than the fractal dimension by standard covering-blanket method. Meanwhile, the calculation and the storage amount are reduced greatly, they are 4/M and 2/M that of the standard covering-blanket method respectively (M is scale). In the image of multiscale differential fractal feature, local gray histogram statistical method is used for target detection. Experiment results indicate that this method is suitable for both kinds background of land and sea. It also can be appropriate in both kinds of infrared and TV images, and can detect small targets from a single frame correctly. This method is with high speed and is easy to be implemented.

Shi, Zelin; Wei, Ying; Huang, Shabai

2004-07-01

138

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

139

FUNDAMENTAL AREAS OF PHENOMENOLOGY (INCLUDING APPLICATIONS): Sprout Branching of Tumour Capillary Network Growth: Fractal Dimension and Multifractal Structure  

NASA Astrophysics Data System (ADS)

A tumour vascular network, characterized as an irregularly stochastic growth, is different from the normal vascular network. We systematically analyse the dependence of the branching. It is found that anastomosis of tumour on time is according to a number of tumour images, and both the fractal dimensions and multifractal spectra of the tumours are obtained. In the cases studied, the fractal dimensions of the tumour vascular network increase with time and the multifractal spectrum not only rises entirely but also shifts right. In addition, the best drug delivery stage is discussed according to the difference of the singularity exponent ??(?? = ?max — ?min), which shows some change in the growth process of the tumour vascular network. A common underlying principle is obtained from our analysis along with previous results.

Kou, Jian-Long; Lu, Hang-Jun; Wu, Feng-Min; Xu, You-Sheng

2008-05-01

140

Fractal analysis of high-resolution rainfall time series  

Microsoft Academic Search

Two-year series of 1-min rainfall intensities observed by rain gages at six different points are analyzed to obtain information about the fractal behavior of the rainfall distribution in time. First, the rainfall time series are investigated using a monodimensional fractal approach (simple scaling) by calculating the box and correlation dimensions, respectively. The results indicate scaling but with different dimensions for

Jonas Olsson; Janusz Niemczynowicz; Ronny Berndtsson

1993-01-01

141

Fractal Dimension Analysis in Self-Assembled Poly(dA)·poly(dT) DNA Network on Mica Surface  

Microsoft Academic Search

Characteristics of the self-assembled poly(dA)·poly(dT) DNA network adhered on the mica substrate are experimentally investigated based on the AFM observations and the fractal dimension analysis. Artificial B-type double stranded DNA, which consists of 50 base pairs of adenine and thymine, is specially prepared for the experiment. The manufacturing process of DNA network is done in the aqueous solution of poly(dA)·poly(dT)

Satoyuki Kawano

2005-01-01

142

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

PubMed Central

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

143

Gene entropy-fractal dimension informatics with application to mouse-human translational medicine.  

PubMed

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. PMID:23586047

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

2013-03-17

144

A Robust Algorithm for Optimisation and Customisation of Fractal Dimensions of Time Series Modified by Nonlinearly Scaling Their Time Derivatives: Mathematical Theory and Practical Applications  

PubMed Central

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.

2013-01-01

145

Fractal analysis of turbulent mixing in fractal-generated turbulence by planar laser-induced fluorescence  

NASA Astrophysics Data System (ADS)

The fractal geometry of turbulent mixing of high-Schmidt-number scalars in multiscale, fractal-generated turbulence (FGT) is experimentally investigated. The difference between the fractal geometry in FGT and that in classical grid turbulence (CGT) generated by a biplane, single-scale grid is also investigated. Nondimensional concentration fields are measured by a planar laser-induced fluorescence technique whose accuracy has recently been improved by our research group, and the fractal dimensions are calculated by using the box-counting method. The mesh Reynolds number is 2500 for both CGT and FGT. The Schmidt number is about 2100. It is found that the threshold width ?Cth, when applying the box-counting method, does not affect the evaluation of the fractal dimension at large scales; therefore, the fractal dimensions at large scales have been investigated in this study. The results show that the fractal dimension in FGT is larger than that in CGT. In addition, the fractal dimension in FGT monotonically increases with the onset of time (or with the downstream direction), whereas that in CGT is almost constant with time. The investigation of the number of counted boxes in a unit area, together with the above results, suggests that turbulent mixing is more enhanced in FGT from the viewpoints of fractal geometry and expansion of the mixing interface.

Suzuki, Hiroki; Nagata, Kouji; Sakai, Yasuhiko; Hasegawa, Yutaka

2013-07-01

146

Aggregation rate and fractal dimension of fullerene nanoparticles via simultaneous multiangle static and dynamic light scattering measurement.  

PubMed

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

2012-11-08

147

Archean Earth Atmosphere Fractal Haze Aggregates: Light Scattering Calculations and the Faint Young Sun Paradox  

NASA Astrophysics Data System (ADS)

As part of an ongoing undergraduate research project of light scattering calculations involving fractal carbonaceous soot aggregates relevant to current anthropogenic and natural sources in Earth's atmosphere, we have read with interest a recent paper [E.T. Wolf and O.B Toon,Science 328, 1266 (2010)] claiming that the Faint Young Sun paradox discussed four decades ago by Carl Sagan and others can be resolved without invoking heavy CO2 concentrations as a greenhouse gas warming the early Earth enough to sustain liquid water and hence allow the origin of life. Wolf and Toon report that a Titan-like Archean Earth haze, with a fractal haze aggregate nature due to nitrogen-methane photochemistry at high altitudes, should block enough UV light to protect the warming greenhouse gas NH3 while allowing enough visible light to reach the surface of the Earth. To test this hypothesis, we have employed a rigorous T-Matrix arbitrary-particle light scattering technique, to avoid the simplifications inherent in Mie-sphere scattering, on haze fractal aggregates at UV and visible wavelenths of incident light. We generate these model aggregates using diffusion-limited cluster aggregation (DLCA) algorithms, which much more closely fit actual haze fractal aggregates than do diffusion-limited aggregation (DLA) algorithms.

Boness, D. A.; Terrell-Martinez, B.

2010-12-01

148

Microstructure of Ag2BI4 (B = Ag, Cd) superionics studied by SEM, impedance spectroscopy and fractal dimension analysis  

NASA Astrophysics Data System (ADS)

Two silver ion conducting solid electrolytes, Ag2HgI4 and Ag2CdI4, representing a wide class of AgI-based halogenide superionics have been the subjects of study by means of electrical impedance spectroscopy, SEM, porosity measurements and fractal dimension analysis. Even though both materials have been obtained by the same method under strictly identical conditions they were found to exhibit certain differences at the microstructural level. Thus, by the direct measurements of porosity and density it was found that the grain boundaries are better developed in silver mercuric iodide. On the assumption that pore geometry in the materials under study displays fractal character it was shown that the fractal dimension of the pore contours is larger in the case of Ag2HgI4. These results are in agreement with electrical studies which indicated that the grain boundary capacitance in Ag2CdI4 is two orders of magnitude smaller than that of the silver mercuric iodide.

Bellucci, S.; Bolesta, I.; Karbovnyk, I.; Hrytskiv, R.; Fafilek, G.; Popov, A. I.

2008-11-01

149

Comparison of fractal dimension estimation algorithms for epileptic seizure onset detection  

NASA Astrophysics Data System (ADS)

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 of the accuracy of the different algorithms and assessment of their robustness in the presence of noise were performed based on synthetic signals of known FD. When applied to scalp EEG data, Katz's and Higuchi's algorithms were found to be incapable of producing consistent changes of a single type (either a drop or an increase) during seizures. On the other hand, the k-NN algorithm produced a drop, starting close to the seizure onset, in most seizures of all patients. The k-NN algorithm outperformed both Katz's and Higuchi's algorithms in terms of robustness in the presence of noise and seizure onset detection ability. The seizure detection methodology, based on the k-NN algorithm, yielded in the training data set a sensitivity of 100% with 10.10 s mean detection delay and a false positive rate of 0.27 h-1, while the corresponding values in the testing data set were 100%, 8.82 s and 0.42 h-1, respectively. The above detection results compare favourably to those of other seizure onset detection methodologies applied to scalp EEG in the literature. The methodology described, based on the k-NN algorithm, appears to be promising for the detection of the onset of epileptic seizures based on scalp EEG.

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

2010-08-01

150

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

PubMed

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. PMID:24040000

Rajagopalan, Venkateswaran; Liu, Zao; Allexandre, Didier; Zhang, Luduan; Wang, Xiao-Feng; Pioro, Erik P; Yue, Guang H

2013-09-09

151

An Application of Fractal Box Dimension to the Recognition of Mesoscale Cloud Patterns in Infrared Satellite Images.  

NASA Astrophysics Data System (ADS)

Mesoscale cloud patterns are analyzed through the application of fractal box dimensions. Verification of fractal properties in satellite infrared images is carried out by computing box dimensions with two different methods and by computing the fraction of cloudy pixels for two sets of images: 174 are considered the `control series,' and 178 (for verification) are considered the `test series.' The main instabilities in the behavior of such dimensions are investigated from the simulation of circles filling space in several spatial distributions. It is shown that the box dimensions are sensitive to the increase of the area covered and to the spatial organization-that is, the number of cells, the spatial clustering, and the isotropy of the distribution of pixels. From a principal components analysis, the authors find six main patterns in the cloudiness for the control series. The three main patterns related to enhanced convection are the massive noncircular spread cloudiness, the highly isotropic distribution of cloud in several cells, and the most circular pattern associated with mesoscale convective complexes. The six patterns are separated into a cluster analysis, and the properties of each cluster are averaged and verified for the test series. This method is a simple and skillful procedure to recognize mesoscale cloud patterns in satellite infrared images.

Carvalho, Leila M. V.; Silva Dias, Maria A. F.

1998-10-01

152

A Model of void distribution in collapsed zone based on fractal theory  

Microsoft Academic Search

In order to calculate the grout volume in the collapsed zone in coal mine after mining, the fractal theory is used to study the feature of the void distribution in collapsed zone, and a fractal model forecasting the voidage in collapsed zone is put forward. The fractal dimension of block particles, pile size of rock block, pore, porosity in the

Li Xing-shang; Xu Jia-lin

2009-01-01

153

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

Microsoft Academic Search

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

154

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, S. R.; Tuovila, Susan M.

1995-06-01

155

Critical electronic wave functions on quasiperiodic lattices: Exact calculation of fractal measures  

NASA Astrophysics Data System (ADS)

We examine two wave functions which have recently been found for electrons in quasiperiodic systems, and which can be shown to satisfy an exact self-similarity relation-closely related to the self-similarity of the quasiperiodic lattice itself. The first wave function is for the ground state of an electron on a two-dimensional Penrose lattice, and the second is for the center of the spectrum of the Hamiltonian for an electron on a one-dimensional Fibonacci lattice. We calculate exactly the fractal measure of the singularities of these wave functions, as reflected in the exponent ?(?), defined by J||x||<=R||?(x)||?~R?(?). .AE

Sutherland, Bill

1987-06-01

156

Exploring Fractals  

NSDL National Science Digital Library

Dr. Mary Ann Connors, a faculty member in the Department of Mathematics and Statistics at University of Massachusetts Amherst has developed this website based on a curriculum project previously funded by the National Science Foundation. Exploring Fractals provides an introduction to fractals, explores concepts such as shape and dimension, provides some classroom investigations, demonstrates how to create simple fractals, and offers some additional information for teachers. Diagrams and pictures are used as part of the explanations. Other Internet resources for further investigation are also provided.

2007-12-12

157

Exploring Fractals  

NSDL National Science Digital Library

Dr. Mary Ann Connors, a faculty member in the Department of Mathematics and Statistics at University of Massachusetts Amherst has developed this website based on a curriculum project previously funded by the National Science Foundation. Exploring Fractals provides an introduction to fractals, explores concepts such as shape and dimension, provides some classroom investigations, demonstrates how to create simple fractals, and offers some additional information for teachers. Diagrams and pictures are used as part of the explanations. Other Internet resources for further investigation are also provided.

2006-01-19

158

Fractal analysis of motor imagery recognition in the BCI research  

NASA Astrophysics Data System (ADS)

A fractal approach is employed for the brain motor imagery recognition and applied to brain computer interface (BCI). The fractal dimension is used as feature extraction and SVM (Support Vector Machine) as feature classifier for on-line BCI applications. The modified Inverse Random Midpoint Displacement (mIRMD) is adopted to calculate the fractal dimensions of EEG signals. The fractal dimensions can effectively reflect the complexity of EEG signals, and are related to the motor imagery tasks. Further, the SVM is employed as the classifier to combine with fractal dimension for motor-imagery recognition and use mutual information to show the difference between two classes. The results are compared with those in the BCI 2003 competition and it shows that our method has better classification accuracy and mutual information (MI).

Chang, Chia-Tzu; Huang, Han-Pang; Huang, Tzu-Hao

2011-08-01

159

Dual Fractal Dimension and Long-Range Correlation of Chinese Stock Prices  

NASA Astrophysics Data System (ADS)

The recently developed modified inverse random midpoint displacement (mIRMD) and conventional detrended fluctuation analysis (DFA) algorithms are used to analyze the tick-by-tick high-frequency time series of Chinese A-share stock prices and indexes. A dual-fractal structure with a crossover at about 10 min is observed. The majority of the selected time series show visible persistence within this time threshold, but approach a random walk on a longer time scale. The phenomenon is found to be industry-dependent, i.e., the crossover is much more prominent for stocks belonging to cyclical industries than for those belonging to noncyclical (defensive) industries. We have also shown that the sign series show a similar dual-fractal structure, while like generally found, the magnitude series show a much longer time persistence.

Chen, Chaoshi; Wang, Lei

2012-03-01

160

Determination of fractal dimensions of digital elevation models for the watershed of Lake Jocasse, South Carolina  

SciTech Connect

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

161

Properties of Fractals  

NSDL National Science Digital Library

This lesson is designed to develop students' understanding of fractals and fractal dimension. This lesson provides links to discussions and activities related to fractals as well as suggested ways to integrate them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

2010-01-01

162

Electromagnetic time-domain calculations in two and three dimensions  

SciTech Connect

For some time, computer codes have been available for time-domain calculations of the beam-induced electromagnetic fields in axially symmetric structures (two dimensions). Recently, these codes have been extended to three-dimensional geometries. Time-domain calculations are complementary to frequency-domain calculations in accelerator designs and represent a better approach in some areas. Some of these areas will be reviewed in this paper and an introduction to the computer codes will be given.

Chan, K.C.D.

1988-01-01

163

Electromagnetic time-domain calculations in two and three dimensions  

NASA Astrophysics Data System (ADS)

For some time, computer codes have been available for time-domain calculations of the beam-induced electromagnetic fields in axially symmetric structures (two dimensions). Recently, these codes have been extended to three-dimensional geometries. Time-domain calculations are complementary to frequency-domain calculations in accelerator designs and represent a better approach in some areas. Some of these areas will be reviewed in this paper and an introduction to the computer codes will be given.

Chan, K. C. D.

164

Electromagnetic Fields on Fractals  

Microsoft Academic Search

Fractals are measurable metric sets with non-integer Hausdorff dimensions. If\\u000aelectric and magnetic fields are defined on fractal and do not exist outside of\\u000afractal in Euclidean space, then we can use the fractional generalization of\\u000athe integral Maxwell equations. The fractional integrals are considered as\\u000aapproximations of integrals on fractals. We prove that fractal can be described\\u000aas a

Vasily E. Tarasov

2007-01-01

165

Estimating the fractal dimension of the atmosphere and the predictability via Lyapunov exponents for the Caribbean region  

NASA Astrophysics Data System (ADS)

The fractal dimension, Lyapunov-exponent spectrum, and predictability are analyzed for chaotic attractors in the atmosphere by analyzing the time series of daily wind speeds over the Caribbean region. It can be shown that this dimension is greater than 8. However, the number of data points may be too small to obtain a reliable estimate of the Grassberger-Procaccia (1983a) correlation dimension because of the limitations discussed by Ruelle (1990). These results lead us 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 (1983b) are sensitive to the selection of the time delay and are thus unreliable. 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. (1991). Using this method, it is found that the error-doubling time is 2-3 days for time series over the Caribbean region. This is comparable to the predictability time found by Waelbrock (1995) for a single station in Mexico. The predictability time over land is slightly less than that over ocean which tends to have higher climatic signal-to-noise ratio. This analysis impacts on the selection of prediction tools (deterministic chaotic linear and non-linear maps or linear stochastic modeling) for wind speeds in the short term for wind energy farm resource planning and management. We conclude that short term wind predictions in the Caribbean region, for a few days ahead, may be best done with a stochastic model instead of a deterministic chaotic model. References Grassberger, P., and I. Procaccia. 1983a. Measuring the strangeness of attractors. Physica D 9: 189-208. Grassberger, P., and I. Procaccia. 1983b. Estimating the Kolmogorov entropy from a chaotic signal. Phys. Rev. A. 28: 2591-2593. Ruelle, D. 1990. Deterministic chaos: the science and the fiction. Proc. Royal Soc. Lond. A 427: 241-248. Waelbrock, H. 1995. Deterministic chaos in tropical atmospheric dynamics. J. Atmos. Sci. 52: 2404-2415. Zeng, X., R. Eykholt, and R. A. Pielke. 1991. Estimating the Lyapunov-exponent spectrum from short time series of low precision. Phys. Rev. Lett. 66: 3229-3232.

Chadee, X. T.

2007-05-01

166

Hierarchical fractal structure of perfect single-layer graphene  

NASA Astrophysics Data System (ADS)

The atomic lattice structure of perfect singlelayer graphene that can actually be regarded as a kind of hierarchical fractal structure from the perspective of fractal geometry was studied for the first time. Three novel and special discoveries on hierarchical fractal structure and sets were unveiled upon examination of the regular crystal lattices of the single-layer graphene. The interior fractaltype structure was discovered to be the fifth space-filling curve from physical realm. Two efficient methods for calculating the fractal dimension of this fresh member was also provided. The outer boundary curve had a fractal dimension equal to one, and a multi-fractal structure from a naturally existing material was found for the first time. A series of strict self-similar hexagons comprised a rotating fractal set. These hexagons slewed at a constant counterclockwise angle ? of 19.1° when observed from one level to the next higher level. From the perspective of fractal geometry, these pioneering discoveries added three new members to the existing regular fractal structures and sets. A fundamental example of a multi-fractal structure was also presented.

Zhang, T.; Ding, K.

2013-10-01

167

Nonlinear anomalous diffusion equation and fractal dimension: exact generalized Gaussian solution.  

PubMed

In this work we incorporate, in a unified way, two anomalous behaviors, the power law and stretched exponential ones, by considering the radial dependence of the N-dimensional nonlinear diffusion equation partial differential rho/ partial differential t=nabla.(Knablarho(nu))-nabla.(muFrho)-alpharho, where K=Dr(-theta), nu, theta, mu, and D are real parameters, F is the external force, and alpha is a time-dependent source. This equation unifies the O'Shaughnessy-Procaccia anomalous diffusion equation on fractals (nu=1) and the spherical anomalous diffusion for porous media (theta=0). An exact spherical symmetric solution of this nonlinear Fokker-Planck equation is obtained, leading to a large class of anomalous behaviors. Stationary solutions for this Fokker-Planck-like equation are also discussed by introducing an effective potential. PMID:12005807

Pedron, I T; Mendes, R S; Malacarne, L C; Lenzi, E K

2002-04-10

168

The Quasi-Fractal Structure of Fish Brain Neurons  

Microsoft Academic Search

The box-counting method for calculating the fractal dimension (D) with the ImageJ 1.20s software is used as a tool for quantitative analysis of the neuronal morphology in the fish brain. The fractal dimension was determined for several types of neurons in the brain of two teleost species, Pholidapus dybowskii and Oncorhynchus keta. These results were compared with those obtained for

V. V. Isaeva; E. V. Pushchina; Yu. A. Karetin

2004-01-01

169

Fractal aggregates in Titan's atmosphere  

NASA Astrophysics Data System (ADS)

The cluster structure of Titan's atmosphere was modeled by using an Eulerian microphysical model with the specific formulation of microphysical laws applying to fractal particles. The growth of aggregates in the settling phase was treated by introducing the fractal dimension as a parameter of the model. The model was used to obtain a vertical distribution of size and number density of the aggregates for different production altitudes. Results confirm previous estimates of the formation altitude of photochemical aerosols. The vertical profile of the effective radius of aggregates was calculated as a function of the visible optical depth.

Cabane, M.; Rannou, P.; Chassefiere, E.; Israel, G.

1993-04-01

170

Fractal Analysis of Brittle Fracture.  

National Technical Information Service (NTIS)

Fractal geometry provides a tool for the description of irregular objects. While Euclidean geometry allows for only integer dimensions, fractal geometry admits to the existence of a dimensional continuum. Thus, geometric shapes can be classified according...

T. J. Mackin J. J. Mecholsky

1987-01-01

171

Fractal structure of digital speckle patterns produced by rough surfaces  

NASA Astrophysics Data System (ADS)

We report on the fractal analysis of digital speckle patterns experimentally generated using an optical setup to record the light scattered from metallic rough surfaces in the normal direction. Using the differential box counting technique, we have calculated the fractal dimension of digital speckle patterns for six samples with different roughness. Our results show a quadratic dependence between the surface roughness and the fractal dimension of the corresponding digital speckle pattern. As an application a method to determine the surface roughness of metallic surfaces is proposed.

Corrêa, R. D.; Meireles, J. B.; Huguenin, J. A. O.; Caetano, D. P.; da Silva, L.

2013-02-01

172

A correlation between the b -value and the fractal dimension from the aftershock sequence of the 1999 Chi-Chi, Taiwan, earthquake  

Microsoft Academic Search

SUMMARY We analyse large number of aftershock events from the 1999 Chi-Chi, Taiwan, earthquake (M L 7.3) recorded around the epicentre area of the main shock in central Taiwan where events can be precisely located, due to dense coverage of modern seismometers. The seismicity is characterized by the b-value of the Gutenberg-Richter relation and the fractal (correlation) dimension D of

Chien-Chih Chen; Wei-Chien Wang; Young-Fo Chang; Yih-Min Wu; Yuan-Hsi Lee

2006-01-01

173

Clinical relevance of the fractal dimension of F0 perturbations computed by the box-counting method.  

PubMed

The box-counting method for determining the fractal dimension (Dfj) was applied to the fundamental frequency (F0) perturbations in normal and pathological voices in order to assess its clinical value. The upper limit of these Dfj values was similar for both groups, but the distribution for pathological voices extended to lower values than for the normal voices. However, these lower values were most probably the result of one or a few outlying frequency points due to incorrect determination of the vocal period. The Dfj of normal voices were within the range of values found for randomly varying F0 values. It was concluded, that the vocal perturbations in pathological voices are also more or less randomly distributed. So, the Dfj, at that least determined with the box-counting method, do not contain clinically relevant information in addition to the traditional measures for the extent of the vocal period perturbations. An exception is special perturbation types like diplophonia. The result of the computation is very sensitive for voice breaks and vibrato and depends on the number of periods. PMID:9422278

Boek, W; Wieneke, G H; Dejonckere, P H

1997-12-01

174

The Use of Fractal Dimension Analysis in Estimation of Blood Vessels Shape in Transplantable Mammary Adenocarcinoma in Wistar Rats after Photodynamic Therapy Combined with Cysteine Protease Inhibitors  

PubMed Central

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

175

Fractal pharmacokinetics.  

PubMed

Pharmacokinetics (PK) has been traditionally dealt with under the homogeneity assumption. However, biological systems are nowadays comprehensively understood as being inherently fractal. Specifically, the microenvironments where drug molecules interact with membrane interfaces, metabolic enzymes or pharmacological receptors, are unanimously recognized as unstirred, space-restricted, heterogeneous and geometrically fractal. Therefore, classical Fickean diffusion and the notion of the compartment as a homogeneous kinetic space must be revisited. Diffusion in fractal spaces has been studied for a long time making use of fractional calculus and expanding on the notion of dimension. Combining this new paradigm with the need to describe and explain experimental data results in defining time-dependent rate constants with a characteristic fractal exponent. Under the one-compartment simplification this strategy is straightforward. However, precisely due to the heterogeneity of the underlying biology, often at least a two-compartment model is required to address macroscopic data such as drug concentrations. This simple modelling step-up implies significant analytical and numerical complications. However, a few methods are available that make possible the original desideratum. In fact, exploring the full range of parametric possibilities and looking at different drugs and respective biological concentrations, it may be concluded that all PK modelling approaches are indeed particular cases of the fractal PK theory. PMID:20461596

Pereira, Luis M

2010-06-01

176

The surface fractal investigation on carbon nanotubes modified by the adsorption of poly(acrylic acid)  

Microsoft Academic Search

In this paper, surface fractal analysis is carried out to study the surface of carbon nanotubes after the adsorption of poly(acrylic acid) (PAA) using the thermodynamic method. The fractal dimension (dSF ) of a fractal surface, BET surface area (SBET) and pore size distribution (PSD) are calculated from low-temperature nitrogen adsorption isotherms. The value of dSF declines as the adsorption

Qing-Feng Hou; Xian-Cai Lu; Xian-Dong Liu; Bai-Xing Hu; Ju-Qing Cui; Jian Shen

2005-01-01

177

Image segmentation using fractal coding  

Microsoft Academic Search

Applying fractal coding to image segmentation was attempted as its new application. The encoding method is the same as the conventional fractal coding method, and the fractal-code is used for image segmentation. An image can be segmented by calculating basins on a dynamical system parametrized by the fractal-code. It is shown that the new method has the ability to segment

T. Ida; Y. Sambonsugi

1995-01-01

178

Fractal organisation in biological macromolecular lattices.  

PubMed

Macromolecular solutions of proteic, glycoproteic or polysaccharidic nature in the presence of salt gave rise (when slowly dried) to dendritic-like fractal patterns. A fractal dimension D = 1.79 +/- 0.018 was obtained for dendritic patterns of a sonicated ovomucin gel (40% ovomucin-60% ovalbumin) in the presence of 0.1 M NaCl. The calculated D is similar to that described in percolation clusters. The appearance of fractal patterns was dependent upon the protein:salt ratio with an optimum in the range 0.75-1.25. Patterns disappeared at either lower or higher ratios. We conclude that the salt percolates through the macromolecular lattice and precipitates in fractal clusters during the drying process. Dendritic-like fractal patterns with similar D and morphologies were obtained with solutions of fetuin, ovalbumin, albumin or starch suggesting that fractal patterning is a general property of biological polymers. That cellular polymers would also aggregate in a fractal way was implied from the analysis of cellular cytoskeleton and microtrabecular lattices. PMID:1524703

Rabouille, C; Cortassa, S; Aon, M A

1992-04-01

179

Three implementations of fractal analysis of particle outlines  

NASA Astrophysics Data System (ADS)

Three methods of calculating the stride (perimeter step-off) for determining the fractal (Hausdorff-Besicovitch) dimension from Richardson Plots are described. The initial input of two-dimensional projections of grains or of micrographs is from a videodigitizer which supplies coordinates of the particle outline. The three algorithms give differences in the speed and accuracy of the calculated fractal dimension according to the way in which the stride is calculated from the coordinate (pixel) information. Although the FAST method may be suitable for some types of (grain) outline, it is considered best to standardize on either the EXACT or HYBRID algorithms for all outline roughness assessments.

Hayward, Janette; Orford, Julian D.; Brian Whalley, W.

180

Fractal theory based Non-linear analysis of sEMG  

Microsoft Academic Search

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

181

Fractal theory based Non-linear analysis of sEMG  

Microsoft Academic Search

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. Experimental results demonstrate that the combination of fractal dimension and maximum fractal length of sEMG recordings

Sridhar P Arjunan; Dinesh K Kumar

2007-01-01

182

Aperture correlation of a fractal fracture  

Microsoft Academic Search

A rough-walled facture is modeled by fractal geometry. In the fractal fracture model, the rock surfaces are characterized by a fractal dimension D between 2 and 3, with lower D for smoother surfaces and higher D for rougher surfaces. The mismatch due to shear displacement between two mirror-image fractal surfaces determines the fracture aperture distribution. An analytic equation is derived

J. S. Y. Wang; T. N. Narasimhan; C. H. Scholz

1988-01-01

183

Calculation of unsaturated hydraulic conductivity using a fractal model for the pore-size distribution  

Microsoft Academic Search

The hydraulic conductivity of unsaturated soils with constant volume is a function of the saturation degree or matric suction, and can be obtained based on currently available procedures. However, each procedure has its limitations and consequently cares should be taken in the selection of a proper procedure. Fractal approach seems to be a potentially useful tool to describe hierarchical systems

Yongfu Xu

2004-01-01

184

Body-force linear elastic stress intensity factor calculation using fractal two level finite element method  

Microsoft Academic Search

Fractal two level finite element method (F2LFEM) for the analysis of linear fracture problems subjected to body force loading is presented. The main objective here is to show that by employing the F2LFEM a highly accurate and an efficient linear analysis of fracture bodies subjected to internal loading can be obtained as it is hard to find any analytical and

A. Y. T. Leung; R. K. L. Su

1995-01-01

185

Discrimination of walking patterns using wavelet-based fractal analysis.  

PubMed

In this paper, we attempted to classify the acceleration signals for walking along a corridor and on stairs by using the wavelet-based fractal analysis method. In addition, the wavelet-based fractal analysis method was used to evaluate the gait of elderly subjects and patients with Parkinson's disease. The triaxial acceleration signals were measured close to the center of gravity of the body while the subject walked along a corridor and up and down stairs continuously. Signal measurements were recorded from 10 healthy young subjects and 11 elderly subjects. For comparison, two patients with Parkinson's disease participated in the level walking. The acceleration signal in each direction was decomposed to seven detailed signals at different wavelet scales by using the discrete wavelet transform. The variances of detailed signals at scales 7 to 1 were calculated. The fractal dimension of the acceleration signal was then estimated from the slope of the variance progression. The fractal dimensions were significantly different among the three types of walking for individual subjects (p < 0.01) and showed a high reproducibility. Our results suggest that the fractal dimensions are effective for classifying the walking types. Moreover, the fractal dimensions were significantly higher for the elderly subjects than for the young subjects (p < 0.01). For the patients with Parkinson's disease, the fractal dimensions tended to be higher than those of healthy subjects. These results suggest that the acceleration signals change into a more complex pattern with aging and with Parkinson's disease, and the fractal dimension can be used to evaluate the gait of elderly subjects and patients with Parkinson's disease. PMID:12503784

Sekine, Masaki; Tamura, Toshiyo; Akay, Metin; Fujimoto, Toshiro; Togawa, Tatsuo; Fukui, Yasuhiro

2002-09-01

186

A spectrum fractal feature classification algorithm for agriculture crops with hyper spectrum image  

NASA Astrophysics Data System (ADS)

A fractal dimension feature analysis method in spectrum domain for hyper spectrum image is proposed for agriculture crops classification. Firstly, a fractal dimension calculation algorithm in spectrum domain is presented together with the fast fractal dimension value calculation algorithm using the step measurement method. Secondly, the hyper spectrum image classification algorithm and flowchart is presented based on fractal dimension feature analysis in spectrum domain. Finally, the experiment result of the agricultural crops classification with FCL1 hyper spectrum image set with the proposed method and SAM (spectral angle mapper). The experiment results show it can obtain better classification result than the traditional SAM feature analysis which can fulfill use the spectrum information of hyper spectrum image to realize precision agricultural crops classification.

Su, Junying

2011-11-01

187

A fractal model for heat transfer of nanofluids by convection in a pool  

NASA Astrophysics Data System (ADS)

Based on the fractal distribution of nanoparticles, a fractal model for heat transfer of nanofluids is presented in the Letter. Considering heat convection between nanoparticles and liquids due to the Brownian motion of nanoparticles in fluids, the formula of calculating heat flux of nanofluids by convection is given. The proposed model is expressed as a function of the average size of nanoparticle, concentration of nanoparticle, fractal dimension of nanoparticle, temperature and properties of fluids. It is shown that the fractal model is effectual according to a good agreement between the model predictions and experimental data.

Xiao, Boqi; Yu, Boming; Wang, Zongchi; Chen, Lingxia

2009-11-01

188

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

PubMed

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 d(s) 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. PMID:23004869

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2012-05-30

189

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

190

Divine proportion shape preservation and the fractal nature of cluster-cluster aggregates  

NASA Astrophysics Data System (ADS)

We present a restricted hierarchial model of cluster-cluster aggregation which allows for an analytical calculation of the fractal dimensions in excellent agreement with those found in Nature and simulations. We argue that this agreement is a consequence of the self-preserving cluster shape common to all models and Nature. This shape determines the fractal dimension and in our model is described by d-dimensional generalizations of the Fibonacci series and the divine proportion.

Sorensen, C. M.; Oh, C.

1998-12-01

191

Fractal dynamics in chaotic quantum transport  

NASA Astrophysics Data System (ADS)

Despite several experiments on chaotic quantum transport, corresponding ab initio quantum simulations have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. Applying a large set of magnetic fields yields a complete picture of the magnetoconductance that indicates fractal scaling on intermediate time scales. Two methods that originate from different fields of physics are used to analyze the scaling exponent and the fractal dimension. They lead to consistent results that, in turn, qualitatively agree with the previous experimental data.

Rasanen, Esa; Kotimaki, Ville; Hennig, Holger; Heller, Eric

2013-03-01

192

Fractal dynamics in chaotic quantum transport  

NASA Astrophysics Data System (ADS)

Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis—a widely used method in time-series analysis—and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.

Kotimäki, V.; Räsänen, E.; Hennig, H.; Heller, E. J.

2013-08-01

193

Fractal Dimension of Soil Particle Size Distribution Along an Altitudinal Gradient in the Alxa Rangeland, Western Inner Mongolia  

Microsoft Academic Search

The Alxa Plateau of Inner Mongolia exhibits vast differences in vertical distribution in vegetation and soil types. The plant communities range from the alpine meadows at the top of the Helan Mountain (3500 m) to the shrub desert at the foothills (1360 m). This type of ecosystem is common in the northwestern China, yet limited research has been conducted.We studied the fractal

Hua Fu; Shifang Pei; Changgui Wan; Ronald E. Sosebee

2009-01-01

194

Dimension of chaotic attractors  

SciTech Connect

Dimension is perhaps the most basic property of an attractor. In this paper we discuss a variety of different definitions of dimension, compute their values for a typical example, and review previous work on the dimension of chaotic attractors. The relevant definitions of dimension are of two general types, those that depend only on metric properties, and those that depend on probabilistic properties (that is, they depend on the frequency with which a typical trajectory visits different regions of the attractor). Both our example and the previous work that we review support the conclusion that all of the probabilistic dimensions take on the same value, which we call the dimension of the natural measure, and all of the metric dimensions take on a common value, which we call the fractal dimension. Furthermore, the dimension of the natural measure is typically equal to the Lyapunov dimension, which is defined in terms of Lyapunov numbers, and thus is usually far easier to calculate than any other definition. Because it is computable and more physically relevant, we feel that the dimension of the natural measure is more important than the fractal dimension.

Farmer, J.D.; Ott, E.; Yorke, J.A.

1982-09-01

195

Fractal Geometry of Architecture  

NASA Astrophysics Data System (ADS)

In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.

Lorenz, Wolfgang E.

196

Self-affine fractal features of earthquake time series before and after moderate earthquakes  

NASA Astrophysics Data System (ADS)

In this paper we calculate the local fractal dimension values D of the self-affine feature of earthquake time series by RMS (root-mean-square) error method, and express the fractal dimensionality by the normalized correlation coefficient R. The fractal dimension values are given for earthquakes occurred in Tangshan, Haicheng, Songpan, Longling, Changshu, Liyang in China and its vicinity by the moving scanning method with different magnitude thresholds and the fixed-window length (100 events). The results show the D values are characterized by decreasing, continued low level in values or by decreasing first and then increasing before moderate earthquakes.

Liu, Chang-Hai; Liu, Yi-Gao; Zhang, Jun

1994-08-01

197

The Use of Fractals for the Study of the Psychology of Perception:  

NASA Astrophysics Data System (ADS)

The present article deals with perception of time (subjective assessment of temporal intervals), complexity and aesthetic attractiveness of visual objects. The experimental research for construction of functional relations between objective parameters of fractals' complexity (fractal dimension and Lyapunov exponent) and subjective perception of their complexity was conducted. As stimulus material we used the program based on Sprott's algorithms for the generation of fractals and the calculation of their mathematical characteristics. For the research 20 fractals were selected which had different fractal dimensions that varied from 0.52 to 2.36, and the Lyapunov exponent from 0.01 to 0.22. We conducted two experiments: (1) A total of 20 fractals were shown to 93 participants. The fractals were displayed on the screen of a computer for randomly chosen time intervals ranging from 5 to 20 s. For each fractal displayed, the participant responded with a rating of the complexity and attractiveness of the fractal using ten-point scale with an estimate of the duration of the presentation of the stimulus. Each participant also answered the questions of some personality tests (Cattell and others). The main purpose of this experiment was the analysis of the correlation between personal characteristics and subjective perception of complexity, attractiveness, and duration of fractal's presentation. (2) The same 20 fractals were shown to 47 participants as they were forming on the screen of the computer for a fixed interval. Participants also estimated subjective complexity and attractiveness of fractals. The hypothesis on the applicability of the Weber-Fechner law for the perception of time, complexity and subjective attractiveness was confirmed for measures of dynamical properties of fractal images.

Mitina, Olga V.; Abraham, Frederick David

198

Fractal Aggregate Structure and the Divine Proportion  

NASA Astrophysics Data System (ADS)

We show that the morphology of diffusion limited cluster aggregation (DLCA) aggregates is determined by the shape preserving nature of the aggregation process. We demonstrate this in the idealized case of equally sized clusters (the Hierarchical Model) on a square 2d lattice. Ramified fractals only result when the end of one aggregate sticks to the side of the other, where end and side are the shortest and longest dimensions of a rectangle circumscribing the cluster. A series of side-to-end aggregations yields an invariant cluster shape with an aspect ratio (side/end) of ?_2=1.618.... This number is the Divine Proportion of the ancients. It occurs in clusters because during binary aggregation in the Hierarchical Model, the end and side both grow in accord with the Fibonacci series, 1, 1, 2, 3, 5, 8, 13..., for which the ratio of any two consecutive series members limits to the Divine Proportion. Moreover, since during binary aggregation the number of monomers per cluster doubles while the cluster's dimensions increase by ?_2, the fractal dimension can be calculated simply as D_2=log2/log ?_2=1.44, a value in excellent agreement with simulation. Remarkably, these concepts can be generalized to any spatial dimension. We define a d-dimensional Fibonacci series and a d-dimensional Divine Proportion from which the d-dimensional fractal dimension can be calculated with excellent numerical agreement with simulation.

Sorensen, C. M.; Oh, C.

1998-03-01

199

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

200

Mountains of Fractals  

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

201

Thermodynamics of Photons on Fractals  

NASA Astrophysics Data System (ADS)

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PVs=U/ds, where ds is the spectral dimension and Vs defines the “spectral volume.” For regular manifolds, Vs coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

Akkermans, Eric; Dunne, Gerald V.; Teplyaev, Alexander

2010-12-01

202

Fractal Analysis of the Maternal Surface of the Placenta: Preliminary Report  

Microsoft Academic Search

Aims: The objective of this study was to determine whether the maternal surface of the placenta is fractal, and whether the mean fractal dimension differs according to the gestational age and clinically or pathologically different conditions. Methods: Using digitized images of the maternal surface of 75 placentas, fractal dimensions were measured with a fractal analysis software. Results: The mean fractal

Masahiro Shiba; Akihiko Kikuchi; Kikue Hara; Sorahiro Sunagawa; Shiro Yoshida; Kimiyo Takagi; Yoshifumi Ogiso

2007-01-01

203

Vibrational characteristics of cracks in two-dimensional annular networks: numerical study of spectral dimensions  

NASA Astrophysics Data System (ADS)

The spectral dimensions of vibrations of cracks in an annular geometry were computed. The numerical cracks used here were calculated using the Random Fuse Model with a given disorder in the fuse burnout thresholds. Like the Hurst exponents, and hence the fractal dimension of these fractures, which depend on the imposed disorders in the fuse's burnout threshold, the spectral dimensions are different for each case. This allows the experimental analysis of the fractal features of cracks via their vibrational emissions.

Olivi-Tran, N.

2003-01-01

204

Detection of architectural distortion in prior screening mammograms using Gabor filters, phase portraits, fractal dimension, and texture analysis  

Microsoft Academic Search

Objective  Mammography is a widely used screening tool for the early detection of breast cancer. One of the commonly missed signs of\\u000a breast cancer is architectural distortion. The purpose of this study is to explore the application of fractal analysis and\\u000a texture measures for the detection of architectural distortion in screening mammograms taken prior to the detection of breast\\u000a cancer.\\u000a \\u000a \\u000a \\u000a Materials

Rangaraj M. Rangayyan; Shormistha Prajna; Fábio J. Ayres; J. E. Leo Desautels

2008-01-01

205

LETTER: Conformal curves in the Potts model: numerical calculation  

NASA Astrophysics Data System (ADS)

We calculated numerically the fractal dimension of the boundaries of the Fortuin-Kasteleyn clusters of the q-state Potts model for integer and non-integer values of q on the square lattice. In addition we calculated with high accuracy the fractal dimension of the boundary points of the same clusters on the square domain. Our calculation confirms that these curves can be described in terms of SLE?.

Gliozzi, F.; Rajabpour, M. A.

2010-05-01

206

Fractal analysis of narwhal space use patterns.  

PubMed

Quantifying animal movement in response to a spatially and temporally heterogeneous environment is critical to understanding the structural and functional landscape influences on population viability. Generalities of landscape structure can easily be extended to the marine environment, as marine predators inhabit a patchy, dynamic system, which influences animal choice and behavior. An innovative use of the fractal measure of complexity, indexing the linearity of movement paths over replicate temporal scales, was applied to satellite tracking data collected from narwhals (Monodon monoceros) (n = 20) in West Greenland and the eastern Canadian high Arctic. Daily movements of individuals were obtained using polar orbiting satellites via the ARGOS data location and collection system. Geographic positions were filtered to obtain a daily good quality position for each whale. The length of total pathway was measured over seven different temporal length scales (step lengths), ranging from one day to one week, and a seasonal mean was calculated. Fractal dimension (D) was significantly different between seasons, highest during summer (D = 1.61, SE 0.04) and winter (D = 1.69, SE 0.06) when whales made convoluted movements in focal areas. Fractal dimension was lowest during fall (D = 1.34, SE 0.03) when whales were migrating south ahead of the forming sea ice. There were no significant effects of size category or sex on fractal dimension by season. The greater linearity of movement during the migration period suggests individuals do not intensively forage on patchy resources until they arrive at summer or winter sites. The highly convoluted movements observed during summer and winter suggest foraging or searching efforts in localized areas. Significant differences between the fractal dimensions on two separate wintering grounds in Baffin Bay suggest differential movement patterns in response to the dynamics of sea ice. PMID:16351924

Laidre, Kristin L; Heide-Jørgensen, Mads P; Logsdon, Miles L; Hobbs, Roderick C; Dietz, Rune; VanBlaricom, Glenn R

2004-01-01

207

Implementation of a diffusion-limited aggregation model in the simulation of fractals in PVDF-HFP/PEMA-NH4CF3SO3-Cr2O3 nanocomposite polymer electrolyte films  

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

208

Fractal EEG analysis with Higuchi's algorithm of low-frequency noise exposition on humans  

NASA Astrophysics Data System (ADS)

Authors used methods based on fractal analysis of EEG signal to assess the influence of low-frequency sound field on the human brain electro-potentials. The relations between LFN (low-frequency noise) and change in fractal dimension EEG signal were measured with stimulations tones. Three types of LFN stimuli were presented; each specified dominant frequency and sound-pressure levels (7 Hz at 120 dB, 18 Hz at 120 dB, and 40 Hz at 110 dB). Standard EEG signal was recorded before, during, and after subject's exposure for 35 min. LFN. Applied to the analysis fractal dimension of EEG-signal Higuchis algorithm. Experiments show LFN influence on complexity of EEG-signal with calculated Higuchi's algorithm. Observed increase of mean value of Higuchi's fractal dimension during exposition to LFN.

Panuszka, Ryszard; Damijan, Zbigniew; Kasprzak, Cezary

2001-05-01

209

Photoreceptor rearrangement and vision restoration in eyes with outer retinopathy: Quantitative assessment by fractal analysis  

NASA Astrophysics Data System (ADS)

The differentiation between normal and abnormal photoreceptor rearrangement before and after treatments may improve understanding on the sequence of events involved in the visual field defects. In this study, we evaluated a fractal analysis approach to quantify photoreceptor rearrangement and vision restoration. We analyzed Optical Coherence Tomography (OCT) data from an individual with outer retinopathy before and after treatment. The outer nuclear layer (ONL) was delineated from the rest of the retinal structure by using a custom-built segmentation algorithm. We then determined the fractal box dimension of the ONL's outline using the box counting method. Thickness and reflectance of the ONL were also calculated. Our results showed that the ONL's fractal dimension, thickness and relative reflectivity decreased after treatment. These early results showed that ONL's fractal dimension could be used as an index of photoreceptor rearrangement, which might lead to a more effective approach to therapy and improved diagnosis.

Cabrera Debuc, Delia; Tchitnga, Robert

2009-03-01

210

Light-scattering properties of fractal aggregates: numerical calculations by a superposition technique and the discrete-dipole approximation  

Microsoft Academic Search

Dust particles in space often grow by mutual collisions and appear to be an agglomeration of individual grains, the morphology of which can be described by the concept of fractals. In this paper, we study light scattering by fractal aggregates of identical spheres (monomers) using the superposition technique incorporated into the T-matrix method where the orientationally averaged scattering matrix is

Hiroshi Kimura

2001-01-01

211

Flocculation control study based on fractal theory*  

PubMed Central

A study on flocculation control based on fractal theory was carried out. Optimization test of chemical coagulant dosage confirmed that the fractal dimension could reflect the flocculation degree and settling characteristics of aggregates and the good correlation with the turbidity of settled effluent. So that the fractal dimension can be used as the major parameter for flocculation system control and achieve self-acting adjustment of chemical coagulant dosage. The fractal dimension flocculation control system was used for further study carried out on the effects of various flocculation parameters, among which are the dependency relationship among aggregates fractal dimension, chemical coagulant dosage, and turbidity of settled effluent under the conditions of variable water quality and quantity. And basic experimental data were obtained for establishing the chemical coagulant dosage control model mainly based on aggregates fractal dimension.

Chang, Ying; Liu, Qian-jun; Zhang, Jin-song

2005-01-01

212

Comparison of image features calculated in different dimensions for computer-aided diagnosis of lung nodules  

Microsoft Academic Search

Features calculated from different dimensions of images capture quantitative information of the lung nodules through one or multiple image slices. Previously published computer-aided diagnosis (CADx) systems have used either twodimensional (2D) or three-dimensional (3D) features, though there has been little systematic analysis of the relevance of the different dimensions and of the impact of combining different dimensions. The aim of

Ye Xu; Michael C. Lee; Lilla Boroczky; Aaron D. Cann; Alain C. Borczuk; Steven M. Kawut; Charles A. Powell

2009-01-01

213

African Fractals  

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

214

An Appraisal of the 2001 Bhuj Earthquake (Mw 7.7, India) Source Zone: Fractal Dimension and b Value Mapping of the Aftershock Sequence  

NASA Astrophysics Data System (ADS)

We examined seismic characteristics, b value and fractal dimension of the aftershock sequence of the January 26, 2001 Bhuj earthquake (Mw 7.7) that occurred in the Kutch failed rift basin, western margin of the Stable Continental Region (SCR) of India. A total of about 2,000 events (M ? 2.0) were recorded within two and a half months, immediately after the main shock. Some 795 events were precisely relocated by simultaneous inversion. These relocated events are used for mapping the frequency-magnitude relation ( b value) and fractal correlation dimension (Dc) to understand the seismic characteristics of the aftershocks and the source zone of the main shock. The surface maps of the b value and Dc reveal two distinct tectonic arms or zones of the V-shaped aftershock area, western zone and eastern zone. The b value is relatively higher (~1.6) in the western zone compared to a lower value (~1.4) in the eastern zone. The Dc map also shows a higher value (1.2-1.35) in the western zone compared to a lower Dc (0.80-1.15) in the eastern zone; this implies a positive correlation between Dc and b value. Two cross sections, E-W and N-S, are examined. The E-W sections show similar characteristics, higher b value and higher Dc in the western zone and lower in the eastern zone with depth. The N-S sections across the fault zones, however, show unique features; it imaged both the b and Dc characteristics convincingly to identify two known faults, the Kutch Mainland fault and the South Wagad fault (SWF), one stepping over the other with a seismogenic source zone at depth (20-35 km). The source zone at depth is imaged with a relatively lower b and higher Dc at the `fault end' of the SWF showing a negative correlation. These observations, corroborated with the seismic tomography as well as with the proposed geological/tectonic model, shed a new light to our understanding on seismogenesis of the largest SCR earthquake in India in the recent years.

Kayal, J. R.; Das, Vishal; Ghosh, Uma

2012-12-01

215

Fractal Tool  

NSDL National Science Digital Library

Using this tool, students build these classic fractals: the Koch snowflake, a fractal tree, a reduced square, and the Sierpinksi triangle. As these shapes grow and change using an iterative process, students can observe patterns in the images created and in the table of values as the fractals progress through several stages.

Mathematics, National C.

2009-01-01

216

“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

217

Two-Dimensional Fractal Characteristics of the Martian Surface  

NASA Astrophysics Data System (ADS)

We present global maps of two-dimensional fractal statistics for Mars topography calculated by applying the two-dimensional Fourier spectral approach to MOLA altimetry measurements over spatial scales extending from approximately 450 meters to 15 kilometers. Three global maps were generated: 1) surface (two-dimensional) fractal dimension, 2) roughness amplitude at a scale of one kilometer, and 3) linear model fit error in the log-log relation of mean power spectral density to radial wavenumber. The linear model fit error is a convenient way to judge the appropriateness of the fractal model. Examination of the fractal dimension and model error maps reveals that a majority of the surface is well modeled by fractal geometry. This is evidenced by minimal systematic spatial variation in fractal dimension and low model fit errors, with the northern plains exhibiting slightly higher overall error than the cratered highlands. There are also several spatially coherent regions in the fractal dimension map that have enhanced values. These regions include Amazonis Planitia and southeast Elysium Planitia. On the other hand, Isidis Planitia and portions of the Olympus Mons aureole exhibit high model fit errors which imply a lower applicability of fractal geometry to these terrains. The one kilometer roughness amplitude map exhibits a tremendous amount of spatial detail and clearly delineates differing roughness terrains. The portions of Amazonis Planitia and southeast Elysium Planitia with enhanced fractal dimension have roughness amplitudes significantly below the global mean, while the Valles Marineris system, the circum-Argyre region, and the chaotic and heavily eroded terrains located along the crustal dichotomy boundary exhibit elevated roughness values. The Tharsis region is particularly rich in detail, displaying a wide range of spatially contiguous roughness provinces that are traceable to known surface units. Comparison of the roughness amplitude map to the MOLA pulse width-derived roughness data (75 meter baseline) reveals a strong correlation with a few notable exceptions. The circum-polar debris mantle located 30 to 45 degrees bilaterally from the equator and a small yet distinct terrain located northwest of Olympus Mons are both evident in the 75 m pulse width data but are not expressed in the longer wavelength roughness amplitude map. This implies that the surface processes responsible for producing these terrains are dominant only at shorter length scales.

Seelos, F. P.; Deal, K. S.; Arvidson, R. E.; Neumann, G. A.

2003-12-01

218

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

219

Fractal Scattering of Microwaves from Soils  

NASA Astrophysics Data System (ADS)

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.

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

2002-10-01

220

Fractal and Multiresolution Techniques for the Understanding of Geo-Information  

Microsoft Academic Search

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

221

The elastic problem for fractal media: basic theory and finite element formulation  

Microsoft Academic Search

In a previous paper [Comput. Methods Appl. Mech. Eng. 190 (2001) 6053], the framework for the mechanics of solids, deformable over fractal subsets, was outlined. Anomalous mechanical quantities with fractal dimensions were introduced, i.e., the fractal stress [??], the fractal strain [??] and the fractal work of deformation W?. By means of the local fractional operators, the static and kinematic

A. Carpinteri; B. Chiaia; P. Cornetti

2004-01-01

222

Fractal analysis in studies of mycelium in soil  

Microsoft Academic Search

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

223

Fractal analysis of foliage distribution in loblolly pine crowns  

Microsoft Academic Search

A new method for estimating fractal characteristics (fractal dimension and foliage density) of a single crown or its portions is developed. The proposed method operates with volume and mass of natural units of the crown, such as shoots and branches, rather than with numbers of regular cubes. Fractal dimension alone is not sufficient to describe foliage distribution in the crown

Boris Zeide

1998-01-01

224

Clustering in stock market based on fractal theory  

Microsoft Academic Search

The K-line, which reflects the trend of stock, is fractal graphics with a stable fractal dimension; we use the stable fractal dimension as an important parameter in the research of stock cluster analysis. We have made an empirical research on the A-stock market of Shanghai. And the result shows that the same kind of stocks, which is clustered by the

Zeng Xiu; Peng Hong; Zeng Zhen

2009-01-01

225

High-frequency spectral falloff of earthquakes, fractal dimension of complex rupture, b value, and the scaling of strength on faults  

USGS Publications Warehouse

The high-frequency falloff ??-y of earthquake displacement spectra and the b value of aftershock sequences are attributed to the character of spatially varying strength along fault zones. I assume that the high frequency energy of a main shock is produced by a self-similar distribution of subevents, where the number of subevents with radii greater than R is proportional to R-D, D being the fractal dimension. In the model, an earthquake is composed of a hierarchical set of smaller earthquakes. The static stress drop is parameterized to be proportional to R??, and strength is assumed to be proportional to static stress drop. I find that a distribution of subevents with D = 2 and stress drop independent of seismic moment (?? = 0) produces a main shock with an ??-2 falloff, if the subevent areas fill the rupture area of the main shock. By equating subevents to "islands' of high stress of a random, self-similar stress field on a fault, I relate D to the scaling of strength on a fault, such that D = 2 - ??. Thus D = 2 corresponds to constant stress drop scaling (?? = 0) and scale-invariant fault strength. A self-similar model of aftershock rupture zones on a fault is used to determine the relationship between the b value, the size distribution of aftershock rupture zones, and the scaling of strength on a fault. -from Author

Frankel, A.

1991-01-01

226

A program for fractal and multifractal analysis of two-dimensional binary images: Computer algorithms versus mathematical theory  

Microsoft Academic Search

In this paper we present a tool to carry out the multifractal analysis of binary, two-dimensional images through the calculation of the Rényi D(q) dimensions and associated statistical regressions. The estimation of a (mono)fractal dimension corresponds to the special case where the moment order is q=0.

Edith Perrier; Ana M. Tarquis; Annette Dathe

2006-01-01

227

Segmentation of histological structures for fractal analysis  

NASA Astrophysics Data System (ADS)

Pathologists examine histology sections to make diagnostic and prognostic assessments regarding cancer based on deviations in cellular and/or glandular structures. However, these assessments are subjective and exhibit some degree of observer variability. Recent studies have shown that fractal dimension (a quantitative measure of structural complexity) has proven useful for characterizing structural deviations and exhibits great potential for automated cancer diagnosis and prognosis. Computing fractal dimension relies on accurate image segmentation to capture the architectural complexity of the histology specimen. For this purpose, previous studies have used techniques such as intensity histogram analysis and edge detection algorithms. However, care must be taken when segmenting pathologically relevant structures since improper edge detection can result in an inaccurate estimation of fractal dimension. In this study, we established a reliable method for segmenting edges from grayscale images. We used a Koch snowflake, an object of known fractal dimension, to investigate the accuracy of various edge detection algorithms and selected the most appropriate algorithm to extract the outline structures. Next, we created validation objects ranging in fractal dimension from 1.3 to 1.9 imitating the size, structural complexity, and spatial pixel intensity distribution of stained histology section images. We applied increasing intensity thresholds to the validation objects to extract the outline structures and observe the effects on the corresponding segmentation and fractal dimension. The intensity threshold yielding the maximum fractal dimension provided the most accurate fractal dimension and segmentation, indicating that this quantitative method could be used in an automated classification system for histology specimens.

Dixon, Vanessa; Kouznetsov, Alexei; Tambasco, Mauro

2009-02-01

228

Electromagnetism on anisotropic fractal media  

NASA Astrophysics Data System (ADS)

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

Ostoja-Starzewski, Martin

2013-04-01

229

Fractal mapping of digitized images - Application to the topography of Arizona and comparisons with synthetic images  

Microsoft Academic Search

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

230

Fractal Geometry  

NSDL National Science Digital Library

This is a web site to support a first course in fractal geometry for students without a strong mathematical background. It covers a wide range of topics in fractals, modern dynamics, and chaos. Each of the topics contains examples of fractals in the arts, humanities, or social sciences. The site also contains lesson plans and software that can be used for a broad range of classes.

Frame, Michael; Mandelbrot, Benoit

2004-11-30

231

Comparison in fractal dimension between those obtained from structure factor and viscoelasticity of gel networks of 1,3:2,4-bis-O-(p-methylbenzylidene)-D-sorbitol in polystyrene melt at gel point  

NASA Astrophysics Data System (ADS)

We investigated time evolution of shear moduli in the physical gelation process of 1,3:2,4-bis-O-(p-methylbenzylidene)-D-sorbitol in polystyrene melt. At the gel point, storage and loss shear moduli, G' and G'', were described by the power law of frequency ?, G'~G''~?n, with the critical exponent n being nearly equal to 2/3, in agreement with the value predicted by the percolation theory. We also investigated the structure factor over two decades in length scale at gel point by using ultra-small-angle X-ray scattering, and small-angle X-ray scattering. We found the power-law behavior in low-q region, indicating that the gel network forms the self-similar structure with mass-fractal dimension. Comparison between the exponent of mass-fractal dimension from structure factor and that from viscoelasticity indicates that hydrodynamic interactions are completely screened out and the excluded volume effects are dominant in the gel. The gel strength was found to increase with the decrease in the lower limit length scale of fractality.

Takenaka, Mikihito; Kobayashi, Toshiaki; Saijo, Kenji; Tanaka, Hirokazu; Iwase, Naoki; Hashimoto, Takeji; Takahashi, Masaoki

2004-08-01

232

Fractals, Chaos  

NSDL National Science Digital Library

Paul Bourke of the Astrophysics and Supercomputing department at Swinburne University of Technology is the author of this massive resource on fractals and chaos. He gives examples of many different kinds and classes of fractals, including the Mandelbrot set and various attractors; and brief explanations accompany each one. A substantial introduction to fractals covers the underlying principles and connection to chaos theory. Many stunning, high resolution fractal image galleries show elaborate patterns and colors. Examples of C and PovRay code used to create the remarkable images are provided. Bourke's homepage has many other sections of tutorials, papers, and notes on a diverse range of subjects.

2003-01-01

233

Fractal Analysis of Optical Coherence Tomography of Normal and Malignant Breast Tissue  

NASA Astrophysics Data System (ADS)

Optical coherence tomography (OCT) provides real-time imaging of tissue several mean free photon paths into tissue by heterodyne detection of backscattered light. OCT can potentially be used to rapidly assess tumor margins during breast cancer resection, however, currently it is difficult to differentiate between normal and malignant tissues with OCT. Because cancer is characterized morphologically by increasing disorder, we investigated the fractal dimension of OCT images of normal and cancerous breast tissue. 3D OCT images of 44 specimens were collected, then tissues were histologically processed to independently determine distinct regions of adipose, stroma and cancer. The fractal dimension of each tissue type was then calculated with a one-dimensional box-counting algorithm applied to the OCT axial scans. We found that the fractal dimensions of stromal tissues were significantly higher than those of cancer (P<10-6), while those of adipose tissue were significantly lower than those of cancer (P<10-4).

Sullivan, Amanda C.; Hunt, John P.; Oldenburg, Amy L.

2011-03-01

234

Performance bounds for fractal coding  

Microsoft Academic Search

Reports on investigations concerning the performance of fractal transforms. Emerging from the structural constraints of fractal coding schemes, lower bounds for the reconstruction error are given without regarding quantization noise. This implies finding an at least locally optimal transformation matrix. A full search approach is by definition optimal but also intractable for practical implementations. In order to simplify the calculation

Bernd Hiirtgen; Rwth Aachen

1995-01-01

235

Fractal dynamics of earthquakes  

NASA Astrophysics Data System (ADS)

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.

1995-03-01

236

Thermodynamics of Photons on Fractals  

SciTech Connect

A thermodynamical treatment of a massless scalar field (a photon) confined to a fractal spatial manifold leads to an equation of state relating pressure to internal energy, PV{sub s}=U/d{sub s}, where d{sub s} is the spectral dimension and V{sub s} defines the 'spectral volume'. For regular manifolds, V{sub s} coincides with the usual geometric spatial volume, but on a fractal this is not necessarily the case. This is further evidence that on a fractal, momentum space can have a different dimension than position space. Our analysis also provides a natural definition of the vacuum (Casimir) energy of a fractal. We suggest ways that these unusual properties might be probed experimentally.

Akkermans, Eric [Department of Physics, Technion Israel Institute of Technology, 32000 Haifa (Israel); Dunne, Gerald V. [Department of Physics, University of Connecticut, Storrs, Connecticut 06269 (United States); Teplyaev, Alexander [Department of Mathematics, University of Connecticut, Storrs, Connecticut 06269 (United States)

2010-12-03

237

FLIP: A method for adaptively zoned, particle-in-cell calculations of fluid in two dimensions  

Microsoft Academic Search

A method is presented for calculating fluid flow in two dimensions using a full particle-in-cell representation on an adaptively zoned grid. The method has many interesting properties, among them an almost total absence of numerical dissipation and the ability to represent large variations in the data. The method is described using a standard formalism and its properties are illustrated by

J. U. Brackbill; H. M. Ruppel

1986-01-01

238

Assessing the Use of Graphing Calculators in College Algebra: Reflecting on Dimensions of Teaching and Learning.  

ERIC Educational Resources Information Center

Considers various aspects of teaching and learning stemming from the integration of graphing calculator use in a semester-long college algebra course. Argues that technology use has had a positive impact on various dimensions of student learning. (Author/CCM)

Smith, Karan B.; Shotsberger, Paul G.

1997-01-01

239

Measuring Fractality  

PubMed Central

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 (d^ML, 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.

Stadnitski, Tatjana

2012-01-01

240

Measuring fractality.  

PubMed

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

2012-05-07

241

Nature's Fractals  

NSDL National Science Digital Library

Nature is full of fractals, that is, things that have the same general shape from their tiniest details to their broadest form.This radio broadcast reports on the work of one scientist who is using mathematical equations to model the fractal nature of flowing water such as in river basins and streams. The clip is 2 minutes in length.

242

Comparison of image features calculated in different dimensions for computer-aided diagnosis of lung nodules  

NASA Astrophysics Data System (ADS)

Features calculated from different dimensions of images capture quantitative information of the lung nodules through one or multiple image slices. Previously published computer-aided diagnosis (CADx) systems have used either twodimensional (2D) or three-dimensional (3D) features, though there has been little systematic analysis of the relevance of the different dimensions and of the impact of combining different dimensions. The aim of this study is to determine the importance of combining features calculated in different dimensions. We have performed CADx experiments on 125 pulmonary nodules imaged using multi-detector row CT (MDCT). The CADx system computed 192 2D, 2.5D, and 3D image features of the lesions. Leave-one-out experiments were performed using five different combinations of features from different dimensions: 2D, 3D, 2.5D, 2D+3D, and 2D+3D+2.5D. The experiments were performed ten times for each group. Accuracy, sensitivity and specificity were used to evaluate the performance. Wilcoxon signed-rank tests were applied to compare the classification results from these five different combinations of features. Our results showed that 3D image features generate the best result compared with other combinations of features. This suggests one approach to potentially reducing the dimensionality of the CADx data space and the computational complexity of the system while maintaining diagnostic accuracy.

Xu, Ye; Lee, Michael C.; Boroczky, Lilla; Cann, Aaron D.; Borczuk, Alain C.; Kawut, Steven M.; Powell, Charles A.

2009-02-01

243

Formation of fractal structures from silicon dioxide nanoparticles synthesized by RF atmospheric pressure plasma enhanced chemical vapor deposition.  

PubMed

Fractal structures were formed on silicon substrates from SiO2 nanoparticles homogeneously synthesized in low temperature atmospheric pressure plasma from tetraethoxysilane (TEOS). RF discharge (power absorbed was about 10 W) sustained between two parallel mesh electrodes was used to generate plasma. The average size of nanoparticles was in the range of 8-20 nm and was determined by process parameters. The obtained products were analyzed by SEM (scanning electron microscopy) and XPS (X-ray photoelectron spectroscopy). Values of fractal dimension parameter of bidimensionals agglomerates formed on the substrate surface from nanoparticles were calculated with the use of Gwyddion and others. It was found that values of this parameter of the deposited structures varied in the range of 1.48-2 and were determined by combination of the process parameters. An empirical model explaining mechanism of the fractal structures formation and variation of the fractal dimension parameter with the process parameters was proposed. PMID:22097514

Alexandrov, S E; Kretusheva, I V; Mishin, M V; Yasenovets, G M

2011-09-01

244

Fractal Infiltration Model using Bundle Tubes  

NASA Astrophysics Data System (ADS)

A fractal infiltration model is proposed in this paper to describe the penetration of wetting front from ponded water in the unsaturated zone. The proposed model describes the pore space of the soil as by a bundle tubes which have a fractal distribution of pore sizes. Penetration of wetting front is studies in a one-dimensional semi-infinite domain with a constant pressure head at upper boundary. Infiltration process is simplified as the wetting front uniformly moving downward. The effective travel distance of the wetting front at a specific time is calculated based on the mass conservation for the movement of wetting front in fractal distributed tubes. A connection between the effective travel distance and the arrival time is analytically derived. Also the effectively arrival time is used to describe the spatial location of the wetting front. Results indicate that the effective travel distance advances with respect to the square root of arrival time. The total flux is then used to inverse the soil pore geometric properties, i.e. the maximum pore radius, the minimum pore radius and fractal dimension. The estimated values of soil pore properties from inverse approach show excellent agreement with the valves assigned in the method. To illustrate the use of the model, a sandbox experiment was conducted in the laboratory. Results of sandbox experiment demonstrate that the fractal infiltration model works well under for the experimental results. Among the soil properties, the minimum pore radius show the most insensitive in the inverse process but in the forward process. The proposed model can be applied for soil characterization and for studying hydrological issues related to infiltration.

Chen, C.; Hsu, K.

2009-12-01

245

Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line  

NASA Astrophysics Data System (ADS)

A discontinuous media can be described by fractal dimensions. Fractal objects has special geometric properties, which are discrete and discontinuous structure. A fractal-time diffusion equation is a model for subdiffusive. In this work, we have generalized the Hamiltonian and Lagrangian dynamics on fractal using the fractional local derivative, so one can use as a new mathematical model for the motion in the fractal media. More, Poisson bracket on fractal subset of real line is suggested.

Golmankhaneh, Alireza Khalili; Golmankhaneh, Ali Khalili; Baleanu, Dumitru

2013-07-01

246

Lagrangian and Hamiltonian Mechanics on Fractals Subset of Real-Line  

NASA Astrophysics Data System (ADS)

A discontinuous media can be described by fractal dimensions. Fractal objects has special geometric properties, which are discrete and discontinuous structure. A fractal-time diffusion equation is a model for subdiffusive. In this work, we have generalized the Hamiltonian and Lagrangian dynamics on fractal using the fractional local derivative, so one can use as a new mathematical model for the motion in the fractal media. More, Poisson bracket on fractal subset of real line is suggested.

Golmankhaneh, Alireza Khalili; Golmankhaneh, Ali Khalili; Baleanu, Dumitru

2013-11-01

247

Fractal Geometry  

NSDL National Science Digital Library

This is one of the best online resources about fractals, and is "meant to support a first course in fractal geometry for students without especially strong mathematical preparation." The site is incredibly deep, providing everything from the most basic definitions and non-technical discussions to involved mathematical formulations. Interactive Java applets, downloadable software for the PC and Macintosh, and laboratory activities are also presented. A particularly interesting section of the site explores about 100 places in nature and society where fractals are found.

Frame, Michael; Mandelbrot, Benoit; Neger, Nial

248

Fractal network model for contact conductance  

Microsoft Academic Search

The topography of rough surfaces strongly influences the conduction of heat and electricity between two surfaces in contact. Roughness measurements on a variety of surfaces have shown that their structure follows a fractal geometry whereby similar images of the surface appear under repeated magnification. Such a structure is characterized by the fractal dimension D, which lies between 2 and 3

A. Majumdar; C. L. Tien

1991-01-01

249

Fractal capacitors  

Microsoft Academic Search

A linear capacitor structure using fractal geometries is described. This capacitor exploits both lateral and vertical electric fields to increase the capacitance per unit area. Compared to standard parallel-plate capacitors, the parasitic bottom-plate capacitance is reduced. Unlike conventional metal-to-metal capacitors, the capacitance density increases with technology scaling. A classic fractal structure is implemented with 0.6-?m metal spacing, and a factor

H. Samavati; A. Hajimiri; A. R. Shahani; G. N. Nasserbakht; T. H. Lee

1998-01-01

250

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

251

An Introduction to Fractals  

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

252

Fractal generation of surface area of porous media  

Microsoft Academic Search

Many natural porous geological rock formations, as well as engineered porous structures, have fractal properties, i.e., they\\u000a are self-similar over several length scales. While there have been many experimental and theoretical studies on how to quantify\\u000a a fractal porous medium and on how to determine its fractal dimension, the numerical generation of a fractal pore structure\\u000a with predefined statistical and

Hongbing Sun; Manfred Koch

1998-01-01

253

The fractal aggregation of asphaltenes.  

PubMed

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

2013-06-28

254

Quantitative Description of Soil Microstructure Using Fractals.  

National Technical Information Service (NTIS)

This Phase 2 SBIR report presents the results of experimental studies to determine the fractal dimension associated with soil microstructure. This was accomplished by obtaining images of samples of real soils scanned directly at 3000 dpi and 256 level of ...

C. Moore

1992-01-01

255

Multiparton correlations and fractal structure in QCD jets  

NASA Astrophysics Data System (ADS)

Angular correlation functions for an arbitrary number of partons are derived from a recursive scheme in the double log approximation. For partons in a sideways cone we calculate the normalised multiplicity moments and obtain the fractal dimension Dq = [(q+1)/q]?0 where ?0 = ?6?s/? is the anomalous dimension controlling the energy dependence of the total multiplicity. At very high energies these observables scale according to a known function of a single variable. A systematic approach to finite energies is presented. On leave from the Jagellonian University, Cracow, Poland.

Ochs, Wolfgang; Wosiek, Jacek

1993-05-01

256

Constraints on Titan’s topography through fractal analysis of shorelines  

NASA Astrophysics Data System (ADS)

Titan’s north polar hydrocarbon lakes offer a unique opportunity to indirectly characterize the statistical properties of Titan’s landscape. The complexity of a shoreline can be related to the complexity of the landscape it is embedded in through fractal theory. We mapped the shorelines of 290 of the north polar titanian lakes in the Cassini synthetic aperture radar dataset. Out of these, we used a subset of 190 lake shorelines for our analysis. The fractal dimensions of the shorelines were calculated via two methods: the divider/ruler method and the box-counting method, at length scales of (1-10) km and found to average 1.27 and 1.32, respectively. The inferred power-spectral exponent of Titan’s topography (?) from theoretical and empirical relations is found to be ?2, which is lower than the values obtained from the global topography of the Earth or Venus. Some of the shorelines exhibit multi-fractal behavior (different fractal dimensions at different scales), which we interpret to signify a transition from one set of dominant surface processes to another. We did not observe any spatial variation in the fractal dimension with latitude; however we do report significant spatial variation of the fractal dimension with longitude. A systematic difference between the dimensions of orthogonal sections of lake shorelines is also noted, which signifies possible anisotropy in Titan’s topography. The topographic information thus gleaned can be used to constrain landscape evolution modeling to infer the dominant surface processes that sculpt the landscape of Titan.

Sharma, Priyanka; Byrne, Shane

2010-10-01

257

Fractal trace of earthworms  

NASA Astrophysics Data System (ADS)

We investigate a process of random walks of a point particle on a two-dimensional square lattice of size n×n with periodic boundary conditions. A fraction p?20% of the lattice is occupied by holes (p represents macroporosity). A site not occupied by a hole is occupied by an obstacle. Upon a random step of the walker, a number of obstacles, M, can be pushed aside. The system approaches equilibrium in (nlnn)2 steps. We determine the distribution of M pushed in a single move at equilibrium. The distribution F(M) is given by M? where ?=?1.18 for p=0.1, decreasing to ?=?1.28 for p=0.01. Irrespective of the initial distribution of holes on the lattice, the final equilibrium distribution of holes forms a fractal with fractal dimension changing from a=1.56 for p=0.20 to a=1.42 for p=0.001 (for n=4,000). The trace of a random walker forms a distribution with expected fractal dimension 2.

Burdzy, Krzysztof; Ho?yst, Robert; Pruski, ?ukasz

2013-05-01

258

Cavity dimensions for high velocity penetration events: A comparison of calculational results with data  

SciTech Connect

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

259

On the fractal nature of cytoplasm.  

PubMed

On the basis of a quantification of the fractal dimension, D, in micrographs of cytoskeleton components or microtrabecular lattice, we propose that the cellular cytoplasm can be described as a percolation cluster, a sort of 'random fractal'. Our hypothesis deals with: (i) the existence of the percolation threshold--a remarkable property of percolation processes; and (ii) the reactivity increase--when enzymes, or targets, and substrates, or effectors, coexist in the same topological dimension. PMID:8181555

Aon, M A; Cortassa, S

1994-05-01

260

Fractons and Fractal Statistics  

NASA Astrophysics Data System (ADS)

Fractons are anyons classified into equivalence classes and they obey specific fractal statistics. The equivalence classes are labeled by a fractal parameter or Hausdorff dimension h. We consider this approach in the context of the fractional quantum Hall effect (FQHE) and the concept of duality between such classes, defined by ~ {h}=3-h shows us that the filling factors for which the FQHE were observed just appear into these classes. A connection between equivalence classes h and the modular group for the quantum phase transitions of the FQHE is also obtained. A ?-function is defined for a complex conductivity which embodies the classes h. The thermodynamics is also considered for a gas of fractons (h,?) with a constant density of states and an exact equation of state is obtained at low-temperature and low-density limits. We also prove that the Farey sequences for rational numbers can be expressed in terms of the equivalence classes h.

da Cruz, Wellington

261

Harmonization and homogenization on fractals  

Microsoft Academic Search

This paper suggests a direct approach to define the Laplacian, the spectral dimension of nested fractals and the pre-Sierpinski carpet conductivity. We find a geometric construction of the harmonic functions on the gasket and therefore can describe effectively the dense set of functions having finite energy. The paper is mostly aimed at the homogenization on the pre-Sierpinski gasket, whose horizontal

Serguei M. Kozlov

1993-01-01

262

Fractal analysis of surface EMG signals from the biceps  

Microsoft Academic Search

Nonlinear analysis techniques are necessary to understand the complexity of the EMG. The purpose of the present study was to determine the fractal dimension of surface EMO obtained from the biceps brachii of normal subjects during isokinetic flexion-extension of the arm. The measurements were obtained with different loading conditions on the arm and for various rates of flexion-extension. Fractal dimensions

Vineet Gupta; Srikanth Suryanarayanan; Narender P. Reddy

1997-01-01

263

The Possible Role of Fractal Geometry in Tribology  

Microsoft Academic Search

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

264

Riemann zeros, prime numbers, and fractal potentials.  

PubMed

Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one dimension. We also investigate the fractal properties of the reconstructed potentials and estimate the fractal dimensions to be D=1.5 for the Riemann zeros and D=1.8 for the prime numbers. This result is somewhat surprising since the nearest-neighbor spacings of the Riemann zeros are known to be chaotically distributed, whereas the primes obey almost Poissonlike statistics. Our findings show that the fractal dimension is dependent on both level statistics and spectral rigidity, Delta(3), of the energy levels. PMID:16241330

van Zyl, Brandon P; Hutchinson, David A W

2003-06-23

265

Chaos & Fractals  

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

266

Fractal Images  

NSDL National Science Digital Library

Fractal images made for the most part using a software application called Flarium24. Galleries contain about 15 images each and should be viewed in hi-color or truecolor settings. Tilable images that can be downloaded?for wallpaper are also available.

Forum, Math; Webb, Sharon

2000-01-01

267

Microbial growth patterns described by fractal geometry.  

PubMed Central

Fractal geometry has made important contributions to understanding the growth of inorganic systems in such processes as aggregation, cluster formation, and dendritic growth. In biology, fractal geometry was previously applied to describe, for instance, the branching system in the lung airways and the backbone structure of proteins as well as their surface irregularity. This investigation applies the fractal concept to the growth patterns of two microbial species, Streptomyces griseus and Ashbya gossypii. It is a first example showing fractal aggregates in biological systems, with a cell as the smallest aggregating unit and the colony as an aggregate. We find that the global structure of sufficiently branched mycelia can be described by a fractal dimension, D, which increases during growth up to 1.5. D is therefore a new growth parameter. Two different box-counting methods (one applied to the whole mass of the mycelium and the other applied to the surface of the system) enable us to evaluate fractal dimensions for the aggregates in this analysis in the region of D = 1.3 to 2. Comparison of both box-counting methods shows that the mycelial structure changes during growth from a mass fractal to a surface fractal. Images FIG. 1

Obert, M; Pfeifer, P; Sernetz, M

1990-01-01

268

On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: A review.  

PubMed

Fractals have been very successful in quantifying nature's geometrical complexity, and have captured the imagination of scientific community. The development of fractal dimension and its applications have produced significant results across a wide variety of biomedical applications. This review deals with the application of fractals in pharmaceutical sciences and attempts to account the most important developments in the fields of pharmaceutical technology, especially of advanced Drug Delivery nano Systems and of biopharmaceutics and pharmacokinetics. Additionally, fractal kinetics, which has been applied to enzyme kinetics, drug metabolism and absorption, pharmacokinetics and pharmacodynamics are presented. This review also considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain information and more realistic description on different parts of pharmaceutical sciences. As a conclusion, the purpose of the present work is to highlight the presence of fractal geometry in almost all fields of pharmaceutical research. PMID:24025993

Pippa, Natassa; Dokoumetzidis, Aristides; Demetzos, Costas; Macheras, Panos

2013-09-08

269

Intrasolid Interfacial Fractality of a Less-Crystalline Solid.  

PubMed

Small angle X-ray scattering (SAXS) measurements have been carried out on pitch (PIT) and cellulose (CEL)-based activated carbon fibers (ACFs). In the higher angle region, the scattering intensity did not obey the classical Porod's law. This suggests that ACFs have a rough surface and their roughness is expressed by the concept of surface fractal. The surface fractal dimension was determined from SAXS for each ACF. ACFs were treated at high temperature in argon in order to control the nanographitic crystallinity. PIT and CEL lost their microporosity upon heat treatment above 1773 and 2073 K, respectively. These nonporous ACFs showed also a strong SAXS caused by the electron density difference at the interface between microcrystalline and amorphous phase. This interface also had a fractal dimension, which was defined as the interfacial fractal dimension. The surface or interfacial fractal dimension of ACF depended on the heating temperature. As the treating temperature increased, the surface or interfacial fractal dimension decreased from 2.8 to 2.0. Both PIT and CEL showed a similar temperature dependence on each other. The surface or interfacial fractal dimension was reduced with the growth of nanographites, and upon heating at 3173 K, the intrasolid interfacial fractal dimension became 2. Copyright 1998 Academic Press. PMID:9792780

Ruike; Murase; Imai; Ishii; Suzuki; Kaneko

1998-11-15

270

Spanky Fractal Database  

NSDL National Science Digital Library

Spanky Fractal Database: fractal images, programs, documents, papers, code examples, and other fractal related material. Submitted by contributors or hunted down from various nooks and crannies on the net. Enjoy and discover.

271

Sprott's Fractal Gallery  

NSDL National Science Digital Library

This site displays a new fractal image every day. It also includes images of many types of fractals, such as strange attractors and Julia sets, and it also has a section on the fractals found in nature.

Sprott, Julien

2011-08-02

272

Menger Sponge-Like Fractal Body Created with a Designed Template Method  

NASA Astrophysics Data System (ADS)

Fractal body, a porous silica with cross-sectional fractal dimension Dcs = 1.87 was created by a sol-gel reaction of tetramethyl orthosilicate (TMOS) using unique template particles. Dcs was maintained over ca. three decades in pore size from 0.05 - 30 ?m and its density ? = 0.35 g·cm-3. Based on the obtained Dcs, pore size distribution and ?, it was concluded that its fractal geometry was closer to Menger sponge (fractal dimension D = 2.73) at the 7th generation, a mathematical model of fractal body. Our experimental strategy would allow us to design fractality of porous materials in real space.

Mayama, H.; Tsujii, K.

2007-07-01

273

Extremum and variational principles for elastic and inelastic media with fractal geometries  

Microsoft Academic Search

This paper further continues the recently begun extension of continuum mechanics and thermodynamics to fractal porous media\\u000a which are specified by a mass (or spatial) fractal dimension D, a surface fractal dimension d, and a resolution lengthscale R. The focus is on pre-fractal media (i.e., those with lower and upper cut-offs) through a theory based on dimensional regularization,\\u000a in which

Martin Ostoja-Starzewski

2009-01-01

274

MORPH-I (Version 1.0): A Software Package for the Analysis of Scanning Electron Micrograph (Binary Formatted) Images for the Assessment of the Fractal Dimension of Enclosed Pore Surfaces.  

National Technical Information Service (NTIS)

In recent years, fractal mathematics has provided an alternative to Euclidian mathematics as an approach to the problem of modeling the complex microstructure of porous geological materials (Turcotte, 1992). Our interest in this report is in the fractal a...

V. G. Mossotti A. R. Eldeeb R. Oscarson

1998-01-01

275

Fractal features based technique to identify subtle forearm movements and to measure alertness using physiological signals (sEMG, EEG)  

Microsoft Academic Search

This research paper reports the use of fractal features based technique in physiological signals like surface electromyogram (sEMG), electroencephalogram (EEG) which has gained increasing attention in biosignal processing for medical and healthcare applications. This research reports the use of fractal dimension, a fractal complexity measure in physiological signals and also reports identification of a new feature of sEMG, maximum fractal

Sridhar Poosapadi Arjunan; Dinesh Kant Kumar

2008-01-01

276

Image segmentation and contour detection using fractal coding  

Microsoft Academic Search

Fractal coding was applied to image segmentation and contour detection. The encoding method was the same as in conventional fractal coding, and the compressed code, which we call the fractal code, was used for image segmentation and contour detection instead of image reconstruction. An image can be segmented by calculating the basin of attraction on a mapping that is a

Takashi Ida; Yoko Sambonsugi

1998-01-01

277

Fractal characterization of impact fracture surface of steel  

NASA Astrophysics Data System (ADS)

The fracture surfaces have self-similar properties and are mostly expressed in the form of two-dimensional digital image. In this paper, a pixel-covering method is applied and an improvement is made to research the fractal characterization of the steel impact fracture surface. The results show that taking boundary to the feature parts of the gray image can increase the accuracy of the fractal dimension. The linearity of the fractal dimension curves of impact fractures is obvious, indicating the impact fractures have fractal properties and the pixel-covering method can describe it. Fractal dimension can be a parameter reflecting the roughness of the impact fracture surface. Rougher the surface is, the higher is the fractal dimension. There is a positive correlation between the fractal dimension of the impact fracture and the toughness of the material. It would be possible to establish a quantitative correlation between fractal dimension, surface roughness, impact toughness, and fracture mechanism, which presents a good potential to material and failure analysis of material.

Tang, Wei; Wang, Yong

2012-03-01

278

Random sequential adsorption on fractals  

NASA Astrophysics Data System (ADS)

Irreversible adsorption of spheres on flat collectors having dimension d < 2 is studied. Molecules are adsorbed on Sierpinski's triangle and carpet-like fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.

Ciesla, Michal; Barbasz, Jakub

2012-07-01

279

The fractal shape of riparian forest patches  

Microsoft Academic Search

Remnant patches of a forest corridor were examined along the Iowa and Cedar Rivers, Iowa. A fractal dimension was found for these patches which was incorporated with the perimeter:area ratio in an index of shape. This index was then regressed on 5 hydrogeomorphic variables hypothesized to represent processes which might control patch dimensions, plus a variable to represent human impact.

K. D. Rex; George P. Malanson

1990-01-01

280

Fractal Analysis of DNA Sequence Data  

NASA Astrophysics Data System (ADS)

DNA sequence databases are growing at an almost exponential rate. New analysis methods are needed to extract knowledge about the organization of nucleotides from this vast amount of data. Fractal analysis is a new scientific paradigm that has been used successfully in many domains including the biological and physical sciences. Biological growth is a nonlinear dynamic process and some have suggested that to consider fractal geometry as a biological design principle may be most productive. This research is an exploratory study of the application of fractal analysis to DNA sequence data. A simple random fractal, the random walk, is used to represent DNA sequences. The fractal dimension of these walks is then estimated using the "sandbox method." Analysis of 164 human DNA sequences compared to three types of control sequences (random, base -content matched, and dimer-content matched) reveals that long-range correlations are present in DNA that are not explained by base or dimer frequencies. The study also revealed that the fractal dimension of coding sequences was significantly lower than sequences that were primarily noncoding, indicating the presence of longer-range correlations in functional sequences. The multifractal spectrum is used to analyze fractals that are heterogeneous and have a different fractal dimension for subsets with different scalings. The multifractal spectrum of the random walks of twelve mitochondrial genome sequences was estimated. Eight vertebrate mtDNA sequences had uniformly lower spectra values than did four invertebrate mtDNA sequences. Thus, vertebrate mitochondria show significantly longer-range correlations than do invertebrate mitochondria. The higher multifractal spectra values for invertebrate mitochondria suggest a more random organization of the sequences. This research also includes considerable theoretical work on the effects of finite size, embedding dimension, and scaling ranges.

Berthelsen, Cheryl Lynn

281

Growth of fractal structures in flames with silicon admixture  

NASA Astrophysics Data System (ADS)

Transmission electron microscopy (TEM) measurements and theoretical analysis are combined to construct the physical picture of formation of SiO2 fractal aggregates in a methane/hexamethyldisiloxane/air atmospheric pressure flame. The formation of SiO2 fractal aggregates is described as a multistage process. The first stage is combustion of fuel in a narrow flame front region with formation of main combustion products including SiO2 molecules. Further downstream SiO2 molecules join in liquid nanoclusters. After cooling combustion products due to heat losses to surroundings, the nanoclusters become solid in a cold flame region and join in fractal aggregates there. Along with growth of fractal aggregates, the restructuring process proceeds in a cold flame region that leads to the decrease of the fractal dimension of fractal aggregates. The measured parameters of fractal aggregates are in accord with those followed from theoretical models.

Smirnov, B. M.; Dutka, M.; van Essen, V. M.; Gersen, S.; Visser, P.; Vainchtein, D.; De Hosson, J. Th. M.; Levinsky, H. B.; Mokhov, A. V.

2012-06-01

282

A transfer matrix method for the analysis of fractal quantum potentials  

Microsoft Academic Search

The scattering properties of quantum particles on a sequence of potentials converging towards a fractal one are obtained by means of the transfer matrix method. The reflection coefficients for both the fractal potential and finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal potential has a self-similar structure associated with the fractal

Juan A Monsoriu; Francisco R Villatoro; Mar ´ õa J; Mar ´ õn; Javier F Urchuegu ´ õa; Pedro Fern ´

283

A Fractal Approach to Assess the Risks of Nitroamine Explosives  

Microsoft Academic Search

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

284

Fuzzy fractals, chaos, and noise  

SciTech Connect

To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.

Zardecki, A.

1997-05-01

285

Comparison of ictal and interictal EEG signals using fractal features.  

PubMed

The feature analysis of epileptic EEG is very significant in diagnosis of epilepsy. This paper introduces two nonlinear features derived from fractal geometry for epileptic EEG analysis. The features of blanket dimension and fractal intercept are extracted to characterize behavior of EEG activities, and then their discriminatory power for ictal and interictal EEGs are compared by means of statistical methods. It is found that there is significant difference of the blanket dimension and fractal intercept between interictal and ictal EEGs, and the difference of the fractal intercept feature between interictal and ictal EEGs is more noticeable than the blanket dimension feature. Furthermore, these two fractal features at multi-scales are combined with support vector machine (SVM) to achieve accuracies of 97.58% for ictal and interictal EEG classification and 97.13% for normal, ictal and interictal EEG classification. PMID:24156671

Wang, Yu; Zhou, Weidong; Yuan, Qi; Li, Xueli; Meng, Qingfang; Zhao, Xiuhe; Wang, Jiwen

2013-09-18

286

Quantitative characterization of the regressive ecological succession by fractal analysis of plant spatial patterns  

Microsoft Academic Search

We studied the effect of grazing on the degree of regression of successional vegetation dynamic in a semi-arid Mediterranean matorral. We quantified the spatial distribution patterns of the vegetation by fractal analyses, using the fractal information dimension and spatial autocorrelation measured by detrended fluctuation analyses (DFA). It is the first time that fractal analysis of plant spatial patterns has been

C. L. Alados; Y. Pueyo; M. L. Giner; T. Navarro; J. Escos; F. Barroso; B. Cabezudo; J. M. Emlen

2003-01-01

287

The Fractal Model of Specific Resistance of Filtration  

Microsoft Academic Search

A fractal model of specific resistance of filtration (SRF) was deduced based on the traditional micro-model of SRF as well as the relationship between fractal dimension, porosity, particle size and density, etc. Additionally the influencing factors and the way of improving sludge filtration were discussed.

Min Xie; Xiao-bo Liu; Dan Gao; Fang Li

2010-01-01

288

Fractal and geostatistical methods for modeling of a fracture network  

Microsoft Academic Search

The modeling of fracture networks is useful for fluid flow and rock mechanics studies. About 6600 fracture traces were recorded on drifts of a uranium mine in a granite massif. The traces have an extension of 0.20–20 m. The network was studied by fractal and by geostatistical methods but can be considered neither as a fractal with a constant dimension

J. P. Chilès

1988-01-01

289

Fractal and geostatistical methods for modeling of a fracture network  

Microsoft Academic Search

The modeling of fracture networks is useful for fluid flow and rock mechanics studies. About 6600 fracture traces were recorded on drifts of a uranium mine in a granite massif. The traces have an extension of 0.20-20 m. The network was studied by fractal and by geostatistical methods but can be considered neither as a fractal with a constant dimension

J. P. Chiles

1988-01-01

290

Fractal characterization of electromagnetic scattering waves from rough sea surfaces  

Microsoft Academic Search

Based on the sea power spectrum, a fractal model of equilibrium gravity waves is founded. The analytical closed-form formulation of the scattering coefficient is also presented. Then the fractal dimension of the backscattered wave is extracted by the box-counting technique, and its relation with the parameters of the sea surface and radar system are discussed. The results obtained are useful

Jihuan Yao; Yidong Fang; Jingming Xiao; Debiao Ge

1998-01-01

291

Three-Dimensional Fractal Mountains.  

National Technical Information Service (NTIS)

This study provides a guide to a series of systematic techniques used to create fractal mountains. The fractal mountains are created through an Interactive System for Fractal Mountains (ISFM). To create the fractal mountains in ISFM a modified midpoint di...

P. J. Collins

1988-01-01

292

Fractal analysis of yeast cell optical speckle  

NASA Astrophysics Data System (ADS)

Steady state laser light propagation in diffuse media such as biological cells generally provide bulk parameter information, such as the mean free path and absorption, via the transmission profile. The accompanying optical speckle can be analyzed as a random spatial data series and its fractal dimension can be used to further classify biological media that show similar mean free path and absorption properties, such as those obtained from a single population. A population of yeast cells can be separated into different portions by centrifuge, and microscope analysis can be used to provide the population statistics. Fractal analysis of the speckle suggests that lower fractal dimension is associated with higher cell packing density. The spatial intensity correlation revealed that the higher cell packing gives rise to higher refractive index. A calibration sample system that behaves similar as the yeast samples in fractal dimension, spatial intensity correlation and diffusion was selected. Porous silicate slabs with different refractive index values controlled by water content were used for system calibration. The porous glass as well as the yeast random spatial data series fractal dimension was found to depend on the imaging resolution. The fractal method was also applied to fission yeast single cell fluorescent data as well as aging yeast optical data; and consistency was demonstrated. It is concluded that fractal analysis can be a high sensitivity tool for relative comparison of cell structure but that additional diffusion measurements are necessary for determining the optimal image resolution. Practical application to dental plaque bio-film and cam-pill endoscope images was also demonstrated.

Flamholz, A.; Schneider, P. S.; Subramaniam, R.; Wong, P. K.; Lieberman, D. H.; Cheung, T. D.; Burgos, J.; Leon, K.; Romero, J.

2006-03-01

293

Fractal parameters and vascular networks: facts & artifacts  

PubMed Central

Background Several fractal and non-fractal parameters have been considered for the quantitative assessment of the vascular architecture, using a variety of test specimens and of computational tools. The fractal parameters have the advantage of being scale invariant, i.e. to be independent of the magnification and resolution of the images to be investigated, making easier the comparison among different setups and experiments. Results The success of several commercial and/or free codes in computing the fractal parameters has been tested on well known exact models. Based on such a preliminary study, we selected the code Frac-lac in order to analyze images obtained by visualizing the angiogenetic process occurring in chick Chorio Allontoic Membranes (CAM), assumed to be paradigmatic of a realistic 2D vascular network. Among the parameters investigated, the fractal dimension Df proved to be the most robust estimator for CAM vascular networks. Moreover, only Df was able to discriminate between effective and elusive increases in vascularization after drug-induced angiogenic stimulations on CAMs. Conclusion The fractal dimension Df is likely to be the most promising tool for monitoring the effectiveness of anti-angiogenic therapies in various clinical contexts.

Mancardi, Daniele; Varetto, Gianfranco; Bucci, Enrico; Maniero, Fabrizio; Guiot, Caterina

2008-01-01

294

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

295

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

PubMed

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

296

Fractal study for the fractured surface of Nd-Fe-B permanent magnets  

NASA Astrophysics Data System (ADS)

Fractal study was used to the analysis of the fractured surface of commercial N50-type Nd-Fe-B sintered magnets. The strain-stress properties of the specimens indicate that the elastic and plastic deformations occur simultaneously during intergranual cracking. The microfractography of the specimens exhibits typical brittle fracture pattern with some toughness dimples, indicating that plastic deformation has happened in some local areas. A ``line-measuring dimension'' Dline was selected to discuss the fracture behavior. The calculated Dline is about 1.28 and 1.29 for the specimens with c-axis parallel and perpendicular to the applied force direction, respectively. The line-measuring dimension analysis indicates that the fracture feature may be isotropic for our studied specimens, which is a bit inconsistent with previous report on the fracture characterization of Nd-Fe-B sintered magnets. More comprehensive fractal study is further needed to confirm the fracture behavior in detail in the future.

Zhu, Minggang; Li, Wei; Fang, Yikun; Zhang, Wenchen; Zhao, Rui; Wang, Jingdai; Li, Anhua; Feng, Haibo; Guo, Zhaohui; Zhou, Mingge; Li, Yanfeng

2011-04-01

297

First order calculation of the inclusive cross section pp?ZZ by graviton exchange in large extra dimensions  

NASA Astrophysics Data System (ADS)

We calculate the inclusive cross section of double Z-boson production within large extra dimensions at the Large Hadron Collider (LHC). Using perturbatively quantized gravity in the ADD (Arkani-Hamed, Dvali, Dimopoulos) model we perform a first order calculation of the graviton mediated contribution to the pp?ZZ+x cross section. At low energies (e.g. Tevatron) this additional contribution is very small, making it virtually unobservable, for a fundamental mass scale above 2500 GeV. At LHC energies, however, the calculation indicates that the ZZ-production rate within the ADD model should differ significantly from the standard model if the new fundamental mass scale would be below 15000 GeV. A comparison with the observed production rate at the LHC might therefore provide direct hints on the number and structure of the extra dimensions.

Kober, Martin; Koch, Benjamin; Bleicher, Marcus

2007-12-01

298

Fractal plate reconstructions with spreading asymmetry  

NASA Astrophysics Data System (ADS)

Information theory and fractal analysis are the basis of a novel fitting criterion for simultaneous plate tectonic reconstructions of magnetic isochrons and fracture zone crossings of a range of ages, rather than a single isochron age. Accretionary boundaries are modeled as two-dimensional fractal structures including both contemporary spreading boundaries and reconstructed magnetic isochron and fracture zone crossings. Each model incorporates reconstruction parameters which describe the full accretionary history, including asymmetry. The reconstruction parameters are derived by spline interpolation in time of trial rotation pseudovectors, including variable asymmetric spreading between ridge segments. Iterative algorithms, without partial derivative constraints, converge on a nominally optimal model by minimizing the sum of two-dimensional fractal bins, over the range of bin-spacings, and produce thereby progressively refined fractal spectra. The new method can incorporate all isochron identifications from the selected plates and age range in the iterative calculation set. The solution set also provides continuous instantaneous rotation parameters, including asymmetries. An example data set illustrates the methodology and model results. The rationale for an optimal fractal criterion is rooted in recent developments in information theory: fractal structures maximize Shannon information entropy distributed over a range of scales. The fractal measure is the sum of bins occupied by reconstructed data points for each bin spacing. The fitting criterion utilized in this work is, in turn, the grand sum of the fractal measures over all calculated bin spacings. The optimal fractal measure for the grand sum has minimal integrated "fractality" relative to non-optimal sets while maximizing entropy for the optimal parameters for each bin spacing.

Pilger, Rex H.

2012-06-01

299

FAST TRACK COMMUNICATION: Weyl law for fat fractals  

NASA Astrophysics Data System (ADS)

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

2010-10-01

300

Fractal simulation of the resistivity and capacitance of arsenic selenide  

SciTech Connect

The temperature dependences of the ac resistivity R and ac capacitance C of arsenic selenide were measured more than four decades ago [V. I. Kruglov and L. P. Strakhov, in Problems of Solid State Electronics, Vol. 2 (Leningrad Univ., Leningrad, 1968)]. According to these measurements, the frequency dependences are R {proportional_to} {omega}{sup -0.80{+-}0.01} and {Delta}C {proportional_to} {omega}{sup -0.120{+-}0.006} ({omega} is the circular frequency and {Delta}C is measured from the temperature-independent value C{sub 0}). According to fractal-geometry methods, R {proportional_to} {omega}{sup 1-3/h} and {Delta}C {proportional_to} {omega}{sup -2+3/h}, where h is the walk dimension of the electric current in arsenic selenide. Comparison of the experimental and theoretical results indicates that the walk dimensions calculated from the frequency dependences of resistivity and capacitance are h{sub R} = 1.67 {+-} 0.02 and h{sub C} = 1.60 {+-} 0.08, which are in agreement with each other within the measurement errors. The fractal dimension of the distribution of conducting sections is D = 1/h = 0.6. Since D < 1, the conducting sections are spatially separated and form a Cantor set.

Balkhanov, V. K., E-mail: ballar@yandex.ru; Bashkuev, Yu. B. [Russian Academy of Sciences, Division of Physical Problems, Buryat Scientific Center, Siberian Branch (Russian Federation)

2010-03-15

301

Fractal analysis of bone structure with applications to osteoporosis and microgravity effects  

NASA Astrophysics Data System (ADS)

We characterize the trabecular structure with the aid of fractal dimension. We use alternating sequential filters (ASF) to generate a nonlinear pyramid for fractal dimension computations. We do not make any assumptions of the statistical distributions of the underlying fractal bone structure. The only assumption of our scheme is the rudimentary definition of self-similarity. This allows us the freedom of not being constrained by statistical estimation schemes. With mathematical simulations, we have shown that the ASF methods outperform other existing methods for fractal dimension estimation. We have shown that the fractal dimension remains the same when computed with both the x-ray images and the MRI images of the patella. We have shown that the fractal dimension of osteoporotic subjects is lower than that of the normal subjects. In animal models, we have shown that the fractal dimension of osteoporotic rats was lower than that of the normal rats. In a 17 week bedrest study, we have shown that the subject's prebedrest fractal dimension is higher than that of the postbedrest fractal dimension.

Acharya, Raj S.; Leblanc, Adrian; Shackelford, Linda; Swarnakar, Vivek; Krishnamurthy, Ram; Hausman, E.; Lin, C.

1995-05-01

302

Dynamical symmetry breaking in fractal space  

SciTech Connect

We formulate field theories in fractal space and show the phase diagrams of the coupling versus the fractal dimension for dynamical symmetry breaking. We first consider the four-dimensional Gross-Neveu (GN) model in (4{minus}d)-dimensional randomized Cantor space where the fermions are restricted to a fractal space by the high potential barrier of the Cantor fractal shape. By the statistical treatment of this potential, we obtain an effective action depending on the fractal dimension. Solving the 1/N leading Schwinger-Dyson (SD) equation, we get the phase diagram of dynamical symmetry breaking with a critical line similar to that of the d-dimensional (2{lt}d{le}4) GN model except for the system-size dependence. We also consider four-dimensional QED with only the fermions formally compactified to d dimensions. Solving the ladder SD equation, we obtain the phase diagram of dynamical chiral symmetry breaking with a linear critical line, which is consistent with the known results for d=4 (the Maskawa-Nakajima case) and d=2 (the case with the external magnetic field). {copyright} {ital 1997} {ital The American Physical Society}

Nagatani, Y. [Department of Physics, Nagoya University, Nagoya 464-01 (Japan)

1997-07-01

303

Imaging of Fractal Surfaces.  

National Technical Information Service (NTIS)

We examine the imaging of standard Brownian Fractal surfaces, and find that given certain assumptions, a Fractal surface with power spectrum proportional to f-Beta has an image with power spectrum proportional to f squared -Beta.

A. Pentland P. Kube

1986-01-01

304

Fractal symmetry of protein interior: what have we learned?  

Microsoft Academic Search

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

305

On the relation between correlation dimension, approximate entropy and sample entropy parameters, and a fast algorithm for their calculation  

NASA Astrophysics Data System (ADS)

We explore the relation between correlation dimension, approximate entropy and sample entropy parameters, which are commonly used in nonlinear systems analysis. Using theoretical considerations we identify the points which are shared by all these complexity algorithms and show explicitly that the above parameters are intimately connected and mutually interdependent. A new geometrical interpretation of sample entropy and correlation dimension is provided and the consequences for the interpretation of sample entropy, its relative consistency and some of the algorithms for parameter selection for this quantity are discussed. To get an exact algorithmic relation between the three parameters we construct a very fast algorithm for simultaneous calculations of the above, which uses the full time series as the source of templates, rather than the usual 10%. This algorithm can be used in medical applications of complexity theory, as it can calculate all three parameters for a realistic recording of 104 points within minutes with the use of an average notebook computer.

Zurek, Sebastian; Guzik, Przemyslaw; Pawlak, Sebastian; Kosmider, Marcin; Piskorski, Jaroslaw

2012-12-01

306

Fractal structure of the interplanetary magnetic field  

SciTech Connect

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.

1985-05-01

307

Fractals in the Classroom  

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

308

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

309

Surface fractal analysis of pore structure of high-volume fly-ash cement pastes  

NASA Astrophysics Data System (ADS)

The surface fractal dimensions of high-volume fly-ash cement pastes are evaluated for their hardening processes on the basis of mercury intrusion porosimetry (MIP) data. Two surface fractal models are retained: Neimark's model with cylindrical pore hypothesis and Zhang's model without pore geometry assumption. From both models, the logarithm plots exhibit the scale-dependent fractal properties and three distinct fractal regions (I, II, III) are identified for the pore structures. For regions I and III, corresponding to the large (capillary) and small (C-S-H inter-granular) pore ranges respectively, the pore structure shows strong fractal property and the fractal dimensions are evaluated as 2.592-2.965 by Neimark's model and 2.487-2.695 by Zhang's model. The fractal dimension of region I increases with w/ b ratio and hardening age but decreases with fly-ash content by its physical filling effect; the fractal dimension of region III does not evolve much with these factors. The region II of pore size range, corresponding to small capillary pores, turns out to be a transition region and show no clear fractal properties. The range of this region is much influenced by fly-ash content in the pastes. Finally, the correlation between the obtained fractal dimensions and pore structure evolution is discussed in depth.

Zeng, Qiang; Li, Kefei; Fen-Chong, Teddy; Dangla, Patrick

2010-11-01

310

Fractal properties of landforms in the Ordos Block and surrounding areas, China  

NASA Astrophysics Data System (ADS)

This paper investigates the fractal properties of landforms in the Ordos Block and surrounding areas within China and discusses their geological and geomorphological implications. The Ordos Block is tectonically stable, but the surrounding areas are much more active and are affected by shear-extensional structures. We utilized the variogram method and the cellular fractal model to estimate parameters such as the fractal dimension (D), ordinate intercept (?), and range (R) from the SRTM3 DEM using a moving window operation. We suggest that the fractal dimension reflects the frequency of variation in elevation, while the ordinate intercept reflects the amplitude of relief. The fractal properties range from 90 m to 30 km. Geomorphological zones can be delineated using the fractal dimension and ordinate intercept. These zones are consistent with known qualitative types of topography. Some basins are characterized by high fractal dimensions and low ordinate intercepts, in contrast to mountainous areas with low fractal dimensions and high ordinate intercepts. Other areas such as the Loess Plateau and deserts also have unique values of fractal properties. The effects of geological and geomorphological processes on the fractal properties are also discussed.

Bi, Lisi; He, Honglin; Wei, Zhanyu; Shi, Feng

2012-11-01

311

Fractal Based Modelling and Analysis of Electromyography (EMG) To Identify Subtle Actions  

Microsoft Academic Search

The paper reports the use of fractal theory and fractal dimension to study the non-linear properties of surface electromyogram (sEMG) and to use these properties to classify subtle hand actions. The paper reports identifying a new feature of the fractal dimension, the bias that has been found to be useful in modelling the muscle activity and of sEMG. Experimental results

Sridhar P Arjunan; Dinesh K Kumar

2007-01-01

312

Fractal aggregates induced by liposome-liposome interaction in the presence of Ca2+  

NASA Astrophysics Data System (ADS)

We present a study of the fractal dimension of clusters of large unilamellar vesicles (LUVs) formed by egg yolk phosphatidylcholine (EYPC), dimyristoylphosphocholine (DMPC) and dipalmitoylphosphocholine (DPPC) induced by Ca2+ . Fractal dimensions were calculated by application of two methods, measuring the angular dependency of the light scattered by the clusters and following the evolution of the cluster size. In all cases, the fractal dimensions fell in the range from 2.1 to 1.8, corresponding to two regimes: diffusion-limited cluster aggregation (DLCA) and reaction-limited cluster aggregation (RLCA). Whereas DMPC clusters showed a typical transition from the RLCA to the DLCA aggregation, EYPC exhibited an unusual behaviour, since the aggregation was limited for a higher concentration than the critical aggregation concentration. The behaviour of DPPC was intermediate, with a transition from the RLCA to the DLCA regimes with cluster sizes depending on Ca2+ concentration. Studies on the reversibility of the aggregates show that EYPC and DPPC clusters can be re-dispersed by dilution with water. DMPC does not present reversibility. Reversibility is evidence of the existence of secondary minima in the DLVO potential between two liposomes. To predict these secondary minima, a correction of the DLVO model was necessary taking into account a repulsive force of hydration.

Sab?n, J.; Prieto, G.; Ruso, J. M.; Sarmiento, F.

2007-10-01

313

Fractal Analysis on Human Behaviors Dynamics  

Microsoft Academic Search

The study of human dynamics has attracted much interest from many fields\\u000arecently. In this paper, the fractal characteristic of human behaviors is\\u000ainvestigated from the perspective of time series constructed with the amount of\\u000alibrary loans. The Hurst exponents and length of non-periodic cycles calculated\\u000athrough Rescaled Range Analysis indicate that the time series of human\\u000abehaviors is fractal

Chao Fan; Jin-Li Guo; Yi-Long Zha

2010-01-01

314

Morphological decomposition of sandstone pore–space: fractal power-laws  

Microsoft Academic Search

Morphological decomposition procedure is applied to estimate fractal dimension of a pore–space, which is isolated from a sandstone microphotograph. The fractal dimensions that have been computed by considering various probing rules have precisely followed the universal power-law relationships proposed elsewhere. These results are derived by considering structuring elements such as octagon, square and rhombus that have been used to decompose

Teo Lay Lian; P. Radhakrishnan; B. S. Daya Sagar

2004-01-01

315

Enhancing the beauty of fractals  

Microsoft Academic Search

Fractals are famous for their beauty and fractal techniques are employed for smaller storage space requirements when storing images. Fractal geometry has gradually established its importance in the study of image characteristics. The concept of multiple reduction copy machine (MRCM) has been used for creating fractals for a long time. A modified MRCM has been designed to generate fractal patterns.

Ajay Kumar Bisoi; Jibitesh Mishra

1999-01-01

316

Fractal analysis and graph theory applied to the spatial and temporal variability of soil water content  

NASA Astrophysics Data System (ADS)

Spatial and temporal variability of soil moisture content has been frequently evaluated using statistical and geostatistical methods for several issues. For example, the statistical study of the temporal persistence or temporal stability in spatial patterns of soil moisture content has found interest to improve soil water monitoring strategies and to correct the average soil water content for missing data. Fractal analysis and graph theory are additional tools that can provide information and further insight to assess and to model indirect or hidden interactions in soil moisture content. In fractal analysis the fractal dimension (D) is an indicator of the pattern and extent of spatial and/or temporal variability. Large D values indicate the importance of short-range variation, while small D values reflect the importance of long-range variation when spatial and temporal data sets are analyzed. Moreover, for spatial and temporal variability, D can range from 1 to 2 for a profile and from 2 to 3 for a two dimensional network. Moreover, as the fractal dimension value increases the degree of roughness also increases. Graph theory tools take into account network structure by modelling pair wise relations between objects, which allow considering explicitly spatial-temporal connectivity of a given data set. The objective of this study was to use fractal analysis and graph theory to characterize the pattern of spatial and temporal variability of soil moisture content. The experimental field was located at Ottawa, Canada. Volumetric water content was monitored using Time Domain Reflectometry (TDR) during 34 dates at 164 locations per date. The depth of the TDR probes was 20 cm. The first and last measurements were 21 month apart and no data were taken in winter when the soil was covered by snow. The fractal dimension, D, was estimated from the slope of the regression line of log semivariogram versus distance for each of studied data sets. Using graph theory various parameters were calculated from the data measured in the 164 experimental vertices including edges, disconnected pair's number, average degree and clustering, etc.; calculations were performed for 21 groups of sets measured during three successive dates. Fractal dimension, D, ranged from 2.589 to 2.910, so that the smallest and the largest values indicate domination of long- and short-range variation respectively. Interestingly there was no correlation between fractal dimension, D, and coefficient of variation. Highest D values were recorded in spring and summer time. Parameters derived from graphs also allowed discrimination of the structure corresponding to successive data sets measured in three successive dates. For example, clustering varied from 0.406 to 0.836, given a correlation coefficient of 0.995. Different degrees of connectivity corresponded to different seasons. Parameters derived from fractal analysis and graph theory were useful to characterize the pattern and extent of spatial and temporal variability of soil moisture content. Acknowledgement: This work was partly supported by Spanish Ministry of Education (Project PHB2009-0094-PC.)

Vieira, Sidney R.; Vidal Vázquez, Eva; Miranda, José G. V.; Paz Ferreiro, Jorge; Topp, George C.

2010-05-01

317

Rheological and fractal characteristics of unconditioned and conditioned water treatment residuals.  

PubMed

The rheological and fractal characteristics of raw (unconditioned) and conditioned water treatment residuals (WTRs) were investigated in this study. Variations in morphology, size, and image fractal dimensions of the flocs/aggregates in these WTR systems with increasing polymer doses were analyzed. The results showed that when the raw WTRs were conditioned with the polymer CZ8688, the optimum polymer dosage was observed at 24 kg/ton dry sludge. The average diameter of irregularly shaped flocs/aggregates in the WTR suspensions increased from 42.54 ?m to several hundred micrometers with increasing polymer doses. Furthermore, the aggregates in the conditioned WTR system displayed boundary/surface and mass fractals. At the optimum polymer dosage, the aggregates formed had a volumetric average diameter of about 820.7 ?m, with a one-dimensional fractal dimension of 1.01 and a mass fractal dimension of 2.74 on the basis of the image analysis. Rheological tests indicated that the conditioned WTRs at the optimum polymer dosage showed higher levels of shear-thinning behavior than the raw WTRs. Variations in the limiting viscosity (?(?)) of conditioned WTRs with sludge content could be described by a linear equation, which were different from the often-observed empirical exponential relationship for most municipal sludge. With increasing temperature, the ?(?) of the raw WTRs decreased more rapidly than that of the raw WTRs. Good fitting results for the relationships between lg?(?)?T using the Arrhenius equation indicate that the WTRs had a much higher activation energy for viscosity of about 17.86-26.91 J/mol compared with that of anaerobic granular sludge (2.51 J/mol) (Mu and Yu, 2006). In addition, the Bingham plastic model adequately described the rheological behavior of the conditioned WTRs, whereas the rheology of the raw WTRs fit the Herschel-Bulkley model well at only certain sludge contents. Considering the good power-law relationships between the limiting viscosity and sludge content of the conditioned WTRs, their mass fractal dimensions were calculated through the models proposed by Shih et al. (1990), which were 2.48 for these conditioned WTR aggregates. The results demonstrate that conditioned WTRs behave like weak-link flocs/aggregates. PMID:21609849

Dong, Y J; Wang, Y L; Feng, J

2011-05-04

318

Fractal analysis of Pollock's drip paintings  

NASA Astrophysics Data System (ADS)

Scientific objectivity proves to be an essential tool for determining the fundamental content of the abstract paintings produced by Jackson Pollock in the late 1940s. Pollock dripped paint from a can onto vast canvases rolled out across the floor of his barn. Although this unorthodox technique has been recognized as a crucial advancement in the evolution of modern art, the precise quality and significance of the patterns created are controversial. Here we describe an analysis of Pollock's patterns which shows, first, that they are fractal, reflecting the fingerprint of nature, and, second, that the fractal dimensions increased during Pollock's career.

Taylor, Richard P.; Micolich, Adam P.; Jonas, David

1999-06-01

319

A difference-fractal model for the permeability of fibrous porous media  

NASA Astrophysics Data System (ADS)

In this Letter, a difference-fractal model for the permeability of viscous flow through fibrous porous media is proposed. Since fractal objects have well-defined geometric properties, and are discrete and discontinuous, we apply the difference approach to developing the fractal model. The model of non-dimensional permeability is expressed as a function of porosity and fractal dimension. To verify the validity of the proposed model, the predicted permeability values are compared with those of experimental measurements. A good agreement between the prediction of the fractal model and the existing experimental data from the literature is found.

Shou, Dahua; Fan, Jintu; Ding, Feng

2010-02-01

320

Improved techniques to calculate two-loop anomalous dimensions in QCD  

NASA Astrophysics Data System (ADS)

In this thesis, the calculation of the full flavour non- singlet Altarelli-Parisi splitting functions as well as the Nc2-part of the gluon-gluon splitting functions in next-to-leading order is presented. The calculation has been performed by employing the method of Curci, Furmanski and Petronzio (CFP), which is based on the light-cone gauge. In previous calculations relying on the CFP method, the spurious poles of the gluon propagator in light-cone gauge always had been regularized by using the 'principal value' (PV) prescription. As the PV prescription is formally unsatisfactory in several respects, it entails the application of some 'phenomenological rules', whose working principles are not really understood, to obtain the correct result. The calculation presented here has been done by applying the Mandelstam-Leibbrandt (ML) prescription, which has a solid field-theoretical foundation, to regulate the gauge induced poles. As a consequence, the phenomenological rules needed in the PV case became obsolete. On the other hand, the use of the ML prescription increased the complexity of the calculation mainly due to the fact that unitarity requires the inclusion of so-called 'axial ghost' degrees of freedom. The calculation can be organized by studying gauge invariant subparts defined by a certain colour structure. The part proportional to CF2, being of Abelian nature, constitutes an opportunity to study the effects of the ML prescription in isolation from other complications. The non-Abelian part proportional to CFNc turned out to be much more involved, revealing new features concerning the cancellation mechanism of the spurious poles. For colour structure CFTf, the calculation of the two-loop quark selfenergy has been included, thus being able to extract the full endpoint contribution at x = 1. In this way it was possible to check the consistency with the sum rules expressing fermion number conservation, which constitutes a new test not only of the ML prescription, but also of the CFP method itself. In order to investigate the viability of the ML prescription in all possible one-loop structures of QCD, the Nc2-part of the gluon-gluon splitting function, which contains the highly nontrivial one-loop three-gluon vertex, also has been calculated. Using the methods developed for the CFNc-part, the usefulness and reliability of the ML prescription in this context again could be confirmed. In summary, having established the CFP method with ML prescription as a method without conceptual loopholes, this work might serve as a powerful tool to extend the calculation to three loops.

Heinrich, Gudrun Marlen

321

Self-organized one-atom thick fractal nanoclusters via field-induced atomic transport  

NASA Astrophysics Data System (ADS)

We report on the growth of a monolayer thick fractal nanostructures of Ag on flat-top Ag islands, grown on Si(111). Upon application of a voltage pulse at an edge of the flat-top Ag island from a scanning tunneling microscope tip, Ag atoms climb from the edge onto the top of the island. These atoms aggregate to form precisely one-atom thick nanostructures of fractal nature. The fractal (Hausdorff) dimension, DH = 1.75 +/- 0.05, of this nanostructure has been determined by analyzing the morphology of the growing nanocluster, imaged by scanning tunneling microscopy, following the application of the voltage pulse. This value of the fractal dimension is consistent with the diffusion limited aggregation (DLA) model. We also determined two other fractal dimensions based on perimeter-radius-of-gyration (DP) and perimeter-area (D'P) relationship. Simulations of the DLA process, with varying sticking probability, lead to different cluster morphologies [P. Meakin, Phys. Rev. A 27, 1495 (1983)] however, the value of DH is insensitive to this difference in morphology. We suggest that the morphology can be characterized by additional fractal dimension(s) DP and/or D'P, besides DH. We also show that within the DLA process DP = DH [C. Amitrano et al., Phys. Rev. A 40, 1713 (1989)] is only a special case; in general, DP and DH can be unequal. Characterization of fractal morphology is important for fractals in nanoelectronics, as fractal morphology would determine the electron transport behavior.

Batabyal, R.; Mahato, J. C.; Das, Debolina; Roy, Anupam; Dev, B. N.

2013-08-01

322

Fractals and Wavelets  

NASA Astrophysics Data System (ADS)

In the first chapters, which cover fractals, I study an unusual mathematical structure. Snowflakes, bridges, and trees all have some fractal pattern. I try to give meaning to a calculus problem on a fractal structure by attempting to find the vibration frequency spectrum for one particular fractal. Wavelets are an analytical tool that can be used to study fractals. In the middle chapters, I have applied wavelets to the fractal structure with which I began. Fourier analysis applies to the frequency spectrum of some objects. I tried to use wavelet analysis to express the solution I constructed in the previous section. In the final chapters, I study wavelets themselves and apply wavelet analysis to some of the Proton Decay Experiment photomultiplier patterns. The primary goals are to construct useful wavelets and to use wavelets to detect patterns obscured by noise.

Lulofs, Edward Ray

323

Theoretical calculation of SSNTD response for radon measurements and optimum diffusion chambers dimensions  

Microsoft Academic Search

The response of some SSNTDs was calculated theoretically taking into consideration the major parameters that affect them. These parameters are related to the behavior of alpha emitters, the detectors types and the used diffusion chambers. The obtained results showed that the response of the filtered CR-39 detector is about 5 times higher than that of the LR-115 detector and more

M. Mansy; M. A. Sharaf; H. M. Eissa; S. U. El-Kamees; M. Abo-Elmagd

2006-01-01

324

Flash Fractal Maker  

NSDL National Science Digital Library

While some may know fractals primarily from their use in abstract painting and African art, fractals are important elements within the world of mathematics. For those who seek to learn more about the construction of fractals and their uses, this very nice Flash-enabled feature from Daniel Gries at Merrimack College will definitely come in handy. This particular Flash applet draws fractals by means of a recursive algorithm, using a simple "generator" that users draw in the space that it is provided. Before using the application, users may wish read the overview offered online, and also take the time to read the instructions thoroughly.

Gries, Daniel

325

An efficient Matlab script to calculate heterogeneous anisotropically elastic wave propagation in three dimensions  

USGS Publications Warehouse

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 can be used at all scales of space and time. This program was created to help distinguish among various types of lithospheric structure given the uneven distribution of sources and receivers commonly utilized in passive source seismology. Several successful implementations have resulted in a better appreciation for subduction zone structure, the fate of a transform fault with depth, lithospheric delamination, and the effects of wavefield focusing and defocusing on attenuation. Companion scripts are provided which help the user prepare input to the finite-difference solution. Boundary conditions including specification of the initial wavefield, absorption and two types of reflection are available. ?? 2005 Elsevier Ltd. All rights reserved.

Boyd, O. S.

2006-01-01

326

Higuchi Fractal Properties of Onset Epilepsy Electroencephalogram  

PubMed Central

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

327

Fractal and Multifractal Analysis of Human Gait  

NASA Astrophysics Data System (ADS)

We carried out a fractal and multifractal analysis of human gait time series of young and old individuals, and adults with three illnesses that affect the march: The Parkinson's and Huntington's diseases and the amyotrophic lateral sclerosis (ALS). We obtained cumulative plots of events, the correlation function, the Hurst exponent and the Higuchi's fractal dimension of these time series and found that these fractal markers could be a factor to characterize the march, since we obtained different values of these quantities for youths and adults and they are different also for healthy and ill persons and the most anomalous values belong to ill persons. In other physiological signals there is complexity lost related with the age and the illness, in the case of the march the opposite occurs. The multifractal analysis could be also a useful tool to understand the dynamics of these and other complex systems.

Muñoz-Diosdado, A.; Del Río Correa, J. L.; Angulo-Brown, F.

2003-09-01

328

Stabilogram diffusion analysis algorithm to estimate the Hurst exponent of high-dimensional fractals  

NASA Astrophysics Data System (ADS)

We suggest an algorithm for the estimation of the Hurst exponent that is based on the results of the well-known stabilogram diffusion analysis method of Hurst exponent estimation for one-dimensional fractals. Our algorithm can be applied to Hurst exponent estimation for fractals with two or more dimensions. To assess the efficiency of this algorithm, we compare its calculation results to those of the well-known Hurst exponent estimation detrending moving average analysis algorithm. In this paper, the computation of the Hurst exponent has been performed for two-dimensional domains of various sizes, which were generated by the Cholesky-Levinson factorization algorithm. The surrogate surfaces have Hurst exponents of H = 0.1, 0.5, and 0.9. It has been established that the detrending moving average analysis algorithm is more sensitive to high-frequency components, while the stabilogram diffusion analysis tends to be sensitive to low-frequency components.

Gorshkov, Oleg

2012-04-01

329

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

330

Calculation of the transfer matrix T in six dimensions for an rf-deflector element  

SciTech Connect

One possible element for funneling two beams together is a deflector with a constant or time-varying electric-field strength. With such an element, arbitrary beams can be brought together and maintained on the axis, if the appropriate combination of deflector parameters is chosen. A parallel beam can be handled only with a time-varying voltage of the deflector. The six-dimensional transfer matrices are calculated for constant or time-varying fields; all the results are correct in first-order approximation.

Bongardt, K.

1981-01-01

331

Calculation of grey level co-occurrence matrix-based seismic attributes in three dimensions  

NASA Astrophysics Data System (ADS)

Seismic interpretation can be supported by seismic attribute analysis. Common seismic attributes use mathematical relationships based on the geometry and the physical properties of the subsurface to reveal features of interest. But they are mostly not capable of describing the spatial arrangement of depositional facies or reservoir properties. Textural attributes such as the grey level co-occurrence matrix (GLCM) and its derived attributes are able to describe the spatial dependencies of seismic facies. The GLCM – primary used for 2D data – is a measure of how often different combinations of pixel brightness values occur in an image. We present in this paper a workflow for full three-dimensional calculation of GLCM-based seismic attributes that also consider the structural dip of the seismic data. In our GLCM workflow we consider all 13 possible space directions to determine GLCM-based attributes. The developed workflow is applied onto various seismic datasets and the results of GLCM calculation are compared to common seismic attributes such as coherence.

Eichkitz, Christoph Georg; Amtmann, Johannes; Schreilechner, Marcellus Gregor

2013-10-01

332

Fractal dimension based neurofeedback in serious games  

Microsoft Academic Search

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

333

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

334

Fractal Dimension and Localization of DNA Knots  

Microsoft Academic Search

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak binding, that permits (partial) relaxation on the surface. In (i) the radius of

Erika Ercolini; Francesco Valle; Jozef Adamcik; Guillaume Witz; Ralf Metzler; Paolo de Los Rios; Joaquim Roca; Giovanni Dietler

2007-01-01

335

Fractal dimension and localization of DNA knots.  

PubMed

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak binding, that permits (partial) relaxation on the surface. In (i) the radius of gyration of the adsorbed DNA knot scales with the 3D Flory exponent nu approximately 0.60 within error. In (ii), we find nu approximately 0.66, a value between the 3D and 2D (nu=3/4) exponents. Evidence is also presented for the localization of knot crossings in 2D under weak adsorption conditions. PMID:17358904

Ercolini, Erika; Valle, Francesco; Adamcik, Jozef; Witz, Guillaume; Metzler, Ralf; De Los Rios, Paolo; Roca, Joaquim; Dietler, Giovanni

2007-01-29

336

Fractal Dimension and Localization of DNA Knots  

NASA Astrophysics Data System (ADS)

The scaling properties of DNA knots of different complexities were studied by atomic force microscope. Following two different protocols DNA knots are adsorbed onto a mica surface in regimes of (i) strong binding, that induces a kinetic trapping of the three-dimensional (3D) configuration, and of (ii) weak binding, that permits (partial) relaxation on the surface. In (i) the radius of gyration of the adsorbed DNA knot scales with the 3D Flory exponent ??0.60 within error. In (ii), we find ??0.66, a value between the 3D and 2D (?=3/4) exponents. Evidence is also presented for the localization of knot crossings in 2D under weak adsorption conditions.

Ercolini, Erika; Valle, Francesco; Adamcik, Jozef; Witz, Guillaume; Metzler, Ralf; de Los Rios, Paolo; Roca, Joaquim; Dietler, Giovanni

2007-02-01

337

Fractal diffraction elements with variable transmittance and phase shift  

NASA Astrophysics Data System (ADS)

The new type of diffraction fractal elements is presented and optical fields properties, obtained from these elements are discussed. Fractal diffraction elements based on well-known fractals, possess exact or statistical selfsimilarity, but have managed amplitude transmittance and phase shift, which are correlated with fractal spatial characteristics. The fractal dimension is not enough for these objects description, and the correlation coefficient between phase/amplitude and spatial characteristic is needed. For this reason the fractal objects were called multifractal structures (MFS). It is shown that the MFS diffraction spectrum possess prevailing power of high frequencies in comparison with spectra of regular two-dimensional or fractal structures with binary transmittance and phase shift. This property could be applied for spatial filtering and transparent objects phase heterogeneities detection. Modeling results for different MFS types are presented and it is shown that MFS application allows detecting the value of initial object distortion with high accuracy. The description of fractal zone plates (FraZP) with variable transmittance and/or phase shift is also presented. The results of Fresnel diffraction modeling from FraZPs with MFS show that the correlation coefficient value has influence on the focal point position.

Muzychenko, Ya. B.; Zinchik, A. A.; Stafeev, S. C.; Tomilin, M. G.

2011-08-01

338

Evolution of fractal particles in systems with conserved order parameter  

PubMed

Computer simulations of the evolution of fractal aggregates in systems with conserved order parameter are described in this work. The aggregates are generated by diffusion-limited aggregation. This model describes such important processes as annealing of dendrite inclusions in solids, healing of cracks in ceramics, temperature-induced transformations in composites, relaxation of rough surfaces, aging of colloid particles, etc. It is shown that the evolution in fractal media differs significantly from that occurring in initially homogeneous systems and leads to different values of the scaling exponent. A relationship between the fractal dimension, mechanism of relaxation, and scaling exponent was also derived. PMID:11046393

Kalinin; Gorbachev; Borisevich; Tomashevitch; Vertegel; Markworth; Tretyakov

2000-02-01

339

UHF fractal antennas  

Microsoft Academic Search

The use of fractal antenna techniques to reduce the size of a UHF linear dipole is investigated and discussed. Fractal designs are derived using an empirical method and a genetic algorithm based method. While both achieve size reduction, the latter design shows the most promise from a size reduction and design methodology standpoint, since simulation is inherent in the design

S. D. Eason; R. Libonati; J. W. Culver; D. H. Werner; P. L. Werner; S. Mummareddy

2001-01-01

340

Design of modified Sierpinski fractal antenna for multiband application  

Microsoft Academic Search

A modified Sierpinski fractal broadband antenna for multiband application is investigated, simulated, and measured in this paper. The perturbed fractal patch and the modified groundplane are employed to obtain the wider bandwidth at the resonance frequencies. The implemented antenna, with nearly omnidirectional radiation pattern, has been designed with a total dimension of 50.8??69??1.6 mm3. According to the measured results, it

Zhang Hu; Guobin Wan; Changjie Sun; Huiling Zhao

2009-01-01

341

Iterated Function Systems and the Global Construction of Fractals  

Microsoft Academic Search

Iterated function systems (i.f.ss) are introduced as a unified way of generating a broad class of fractals. These fractals are often attractors for i.f.ss and occur as the supports of probability measures associated with functional equations. The existence of certain `p-balanced' measures for i.f.ss is established, and these measures are uniquely characterized for hyperbolic i.f.ss. The Hausdorff-Besicovitch dimension for some

M. F. Barnsley; S. Demko

1985-01-01

342

Thermal properties of bodies in fractal and cantorian physics  

Microsoft Academic Search

Fundamental laws describing the heat diffusion in fractal environment are discussed. It is shown that for the three-dimensional space the heat radiation process occur in structures with fractal dimension D??0,1), whereas in structures with D?(1,3? heat conduction and convection have the upper hand (generally in the real gases).To describe the heat diffusion a new law has been formulated. Its validity

Oldrich Zmeskal; Miroslav Buchnicek; Martin Vala

2005-01-01

343

Quantum Physics and Fractal Space Time  

Microsoft Academic Search

We argue for a new fractal space-time which is different from that of Nottale, Ord and El Naschie. The fractal here is a deterministic fractal, where a fractal seed on an M+1 th scale, let us say, is about 1040 times the diameter of the fractal seed on the M th fractal scale. At each scale, the fractal seed is

David Maker

1999-01-01

344

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

PubMed

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

345

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

346

FORTRAN programs for calculating nonlinear seismic ground response in two dimensions  

USGS Publications Warehouse

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

347

Electromagnetic fields in fractal continua  

NASA Astrophysics Data System (ADS)

Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum ?D3?E3 with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space F? accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.

Balankin, Alexander S.; Mena, Baltasar; Patiño, Julián; Morales, Daniel

2013-04-01

348

A Multi-Fractal Spectrum Analysis of Turbulence Data and the DNA of Worms  

NASA Astrophysics Data System (ADS)

This paper discusses the physical meanings of various parameters in multi-fractal spectrum and offers the thermo-mechanical formula in calculating the multi-fractal spectrum. Besides it works out the sets of multi-fractal Cantor, the multi-fractal spectrum of turbulence data of Rayleigh-Benard convection and DNA series by means of wavelet transform maximum modulus (WTMM). In the end, it arrives at the conclusions that the means of WTMM is plausible on the application of multi-fractal research, multi-fractal spectrum offers function ?~f(?), which describes all the sub-collections' characters. So it gives specific information of a system. Turbulence is similar to DNA's multi-fractal character. The latter is more uneven and complex. Multi-fractal spectrum analysis can reveal the uneven overall distribution information of the series (or sets). But it has a limited description of the local position information of signal singularity and concrete local structure.

Fu, Q.; Chen, Z. F.; Zhou, Y. H.; Wang, L.

2011-09-01

349

Intelligent control of aircraft dynamic systems with a new hybrid neuro-fuzzy-fractal approach  

Microsoft Academic Search

We describe in this paper a hybrid method for adaptive model-based control of non-linear dynamic systems using Neural Networks, Fuzzy Logic and Fractal Theory. The new neuro–fuzzy–fractal method combines Soft Computing (SC) techniques with the concept of the fractal dimension for the domain of Non-Linear Dynamic System Control. The new method for adaptive model-based control has been implemented as a

Patricia Melin; Oscar Castillo

2002-01-01

350

Intelligent adaptive control of aircraft dynamic systems with a new neuro-fuzzy-fractal approach  

Microsoft Academic Search

We describe a general method for adaptive model-based control of nonlinear dynamic systems using neural networks, fuzzy logic and fractal theory. The new neuro-fuzzy-fractal method combines soft computing techniques with the concept of the fractal dimension for the domain of nonlinear dynamic system control. The new method for adaptive model-based control has been implemented as a computer program to show

Patricia Melin; O. Castillo

1999-01-01

351

Fractal analysis of rat brain activity after injury.  

PubMed

With application of the Higuchi algorithm, fractal dimension (FD) values of the electrocortical activity of the rat parietal cerebral and paravermal cerebellar cortex were calculated, before and after unilateral discrete injury of the left parietal cortex. Immediately following the first acute injury, in a group of six rats, a reversible increase in mean FD was found at the left (ipsilateral side to the injury) cerebral cortex, from 1.38 to 1.59, and at the left cerebellar cortex from 1.51 to 1.73. In addition, an indication of plastic changes after repeated (third) injury was found as an irreversible increase in mean FD: 1.54 on the left and 1.48 on the right side of parietal cortex. PMID:16035222

Spasic, S; Kalauzi, A; Grbic, G; Martac, L; Culic, M

2005-05-01

352

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

SciTech Connect

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.; Vo-Dinh, T. [Oak Ridge National Lab., TN (United States). Advanced Monitoring Development Group

1998-09-01

353

Roughness and fractality of fracture surfaces as indicators of mechanical quantities of porous solids  

NASA Astrophysics Data System (ADS)

The 3D profile surface parameter H q and fractal dimension D were tested as indicators of mechanical properties inferred from fracture surfaces of porous solids. High porous hydrated cement pastes were used as prototypes of porous materials. Both the profile parameter H q and the fractal dimension D showed capability to assess compressive strength from the fracture surfaces of hydrated pastes. From a practical point of view the 3D profile parameter H q seems to be more convenient as an indicator of mechanical properties, as its values suffer much less from statistical scatter than those of fractal dimensions.

Ficker, Tomáš; Martišek, Dalibor

2011-12-01

354

Cynthia Lanius' Fractal Unit  

NSDL National Science Digital Library

Cynthia Lanius, a former mathematics teacher who currently serves as Technology Integration Specialist for Sinton Independent School District in Sinton, Texas, has posted numerous lessons online. This website features a Fractals Unit for elementary and middle school students (although adults are also welcome to enjoy the lesson). The lesson includes a discussion on why one might study fractals and then provides step-by-step explanations on how to make fractals using Java, along with some challenging mathematics questions to consider. Samples of student work are also posted. A section for teachers provides an overview of the unit objectives along with links to other resources and materials to use in the classroom.

2007-12-12

355

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

356

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

SciTech Connect

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

357

Fractal properties of tremor and gas piston events observed at Kilauea Volcano, Hawaii  

Microsoft Academic Search

We study the fractal properties of shallow volcanic tremor and gas piston events associated with magma degassing at Kilauea Volcano, Hawaii, using data from two dense short-baseline arrays of seismographs deployed near the active crater of Puu Oo on the east rift of the volcano. We found an upper bound on the fractal dimension of a strange attractor common to

Bernard Chouet; Herbert R. Shaw

1991-01-01

358

Test of a Mean Field Theory for the Optics of Fractal Clusters  

Microsoft Academic Search

Fractal aggregates such as soot particles are modelled as connected clusters of N spherules of radius a and complex refractive index µ, whose density correlation function p(x) varies like x as x ? 0, where D is the fractal dimension. They scatter scalar or vector waves of wavelength 2?\\/k where ka ? 1. Multiple scattering effects are included using a

Jenny Nelson

1989-01-01

359

Fractal generalized zone plates.  

PubMed

The construction of fractal generalized zone plates from a set of periodic diffractive optical elements with circular symmetry is proposed. This allows us, for instance, to increase the number of foci of a conventional fractal zone plate while keeping the self-similarity property within the axial irradiance. The focusing properties of these fractal diffractive optical elements for points not only along but also in the close vicinity of the optical axis are investigated. In both cases analytical expressions for the irradiance are derived. Numerical simulations of the energetic efficiency of fractal generalized zone plates under plane wave illumination are carried out. In addition, some effects on the axial irradiance caused by variations in the area of their transparent rings are shown. PMID:19412233

Mendoza-Yero, Omel; Fernández-Alonso, Mercedes; Mínguez-Vega, Gladys; Lancis, Jesús; Climent, Vicent; Monsoriu, Juan A

2009-05-01

360

Chaos and fractals  

NSDL National Science Digital Library

This website 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.

2007-07-18

361

Mechanics of Fractal Damage.  

National Technical Information Service (NTIS)

This report describes a preliminary investigation of the applicability of fractal geometry to damage modeling. Microstructural heterogeneity, both the size distribution and spatial distribution of microstructural features, can be modeled simply and compac...

S. Yongqi T. L. Anderson

1992-01-01

362

Fractals : what comes next?  

NSDL National Science Digital Library

This online activity challenges students to explore the relationship between the number of triangles and the sum of the triangle perimeters in each of the first three iterations of the Sierpinski triangle fractal. The activity is one of 80 mathematical challenges featured on the Figure This! web site. In this activity, students are encouraged to use two problem-solving strategies: investigate a simpler problem and make a chart. For other sections of the activity, students find the general rule for determining the amount of paint needed to cover the increasing number of triangles in iterations of the Sierpinski triangle and investigate similar area and perimeter questions with square fractals. The activity includes information about self-similarity, a key characteristic of fractals, and about how fractals can model natural phenomena. Copyright 2005 Eisenhower National Clearinghouse

National Council of Teachers of Mathematics (NCTM)

2002-01-01

363

Patterns in Fractals  

NSDL National Science Digital Library

This lesson is designed to introduce students to the idea of finding patterns in the generation of several different types of fractals. This lesson provides links to discussions and activities related to patterns and fractals as well as suggested ways to work them into the lesson. Finally, the lesson provides links to follow-up lessons designed for use in succession with the current one.

2010-01-01

364

Hydrodynamics of fractal continuum flow.  

PubMed

A model of fractal continuum flow employing local fractional differential operators is suggested. The generalizations of the Green-Gauss divergence and Reynolds transport theorems for a fractal continuum are suggested. The fundamental conservation laws and hydrodynamic equations for an anisotropic fractal continuum flow are derived. Some physical implications of the long-range correlations in the fractal continuum flow are briefly discussed. It is noteworthy to point out that the fractal (quasi)metric defined in this paper implies that the flow of an isotropic fractal continuum obeying the Mandelbrot rule of thumb for intersection is governed by conventional hydrodynamic equations. PMID:22463270

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2012-02-13

365

Spatial log-periodic oscillations of first-passage observables in fractals  

NASA Astrophysics Data System (ADS)

For transport processes in geometrically restricted domains, the mean first-passage time (MFPT) admits a general scaling dependence on space parameters for diffusion, anomalous diffusion, and diffusion in disordered or fractal media. For transport in self-similar fractal structures, we obtain an expression for the source-target distance dependence of the MFPT that exhibits both the leading power-law behavior, depending on the Hausdorff and spectral dimension of the fractal, as well as small log-periodic oscillations that are a clear and definitive signal of the underlying fractal structure. We also present refined numerical results for the Sierpinski gasket that confirm this oscillatory behavior.

Akkermans, Eric; Benichou, Olivier; Dunne, Gerald V.; Teplyaev, Alexander; Voituriez, Raphael

2012-12-01

366

Fractal, wavelet and Fourier analysis for investigation of nanoscale CoSi2 structures in Si produced by ion synthesis  

NASA Astrophysics Data System (ADS)

Ordered and disordered CoSi2 surface structures observed in scanning tunneling microscopy (STM) were investigated by means of wavelet, Fourier and fractal analysis. The relationship between fractal dimensions and degree of surface cobalt disilicide ordering was established and the correlation between Fourier and fractal analysis was shown. Two methods were used for determining fractal dimensions for ordered and disordered structures, and the results, obtained by these methods, were compared. Wavelet analysis of spatially ordered structures and an attempt to determine the form of these structures, depending on wavelet parameters, were performed.

Gerasimenko, N. N.; Pavluchenko, M. N.; Levchenko, V. D.; Djamanbalin, K. K.; Troitskiy, V. Yu.; Skobochkin, A. M.

2003-05-01

367

Fractal aggregation and optical absorption of copper nanoparticles prepared by in situ chemical reduction within a Cu2+-polymer complex  

NASA Astrophysics Data System (ADS)

A polymer-matrix nanocomposite containing copper particles has been prepared by in situ chemical reduction within a Cu2+-poly(itaconic acid-co-acrylic acid) complex solid film. The copper particle size in the order of 10 nm is controlled by the initial content of the metal ions in the complex. Their fractal pattern and the value of the fractal dimension indicate that there exists a cluster-cluster aggregation process in the present system. Optical absorption spectra of copper-polymer nanocomposites show distinct plasma absorption bands and quantum size effect in the samples. The calculated blueshift of the resonance peak based on a quantum-sphere model gives remarkable agreement with the experimental data as the size of copper particles embedded in the polymer becomes smaller.

Huang, C.; Yang, C. Z.

1999-03-01

368

Size effects of exchange cation on the pore structure and surface fractality of montmorillonite  

SciTech Connect

Ca-montmorillonites were exchanged with both metal cations (manganese and copper) and organic cations (tetramethylammonium (TMA) and hexadecyltrimmethylammonium (HDTMA)) to study the cation size effects on the pore structure and surface roughness of montmorillonite based on the classical and fractal analysis of their nitrogen adsorption isotherms. The surface fractal dimension D was calculated from their nitrogen isotherms with the aid of the recently proposed Neimark equation. The decrease of BET surface area of montmorillonite induced by the larger size of exchange cation was interpreted with both the coverture of some surface roughness (surface screening effect) and the inhibition of nitrogen molecule into some pores (pore blocking effect). The pore blocking effect was examined with the changes of mean pore size. Meanwhile, the D value was used to examine whether or not the surface screening effect existed. It was concluded that the combination of classical and fractal analyses of nitrogen isotherms may facilitate understanding of the evolution of pore and surface structures of clay exchanged with different cations.

Lee, J.F.; Lee, C.K.; Juang, L.C.

1999-09-01

369

A Method of Calculating the Second Dimension Retention Index in Comprehensive Two-Dimensional Gas Chromatography Time-of-Flight Mass Spectrometry  

PubMed Central

A method was developed to calculate the second dimension retention index of comprehensive two-dimensional gas chromatography time-of-flight mass spectrometry (GC×GC/TOF-MS) data using n-alkanes as reference compounds. The retention times of the C7-C31 alkanes acquired during 24 isothermal experiments cover the 0 – 6 s retention time area in the second dimension retention time space, which makes it possible to calculate the retention indices of target compounds from the corresponding retention time values without the extension of the retention space of the reference compounds. An empirical function was proposed to show the relationship among the second dimension retention time, the temperature of the second dimension column, and the carbon number of the n-alkanes. The proposed function is able to extend the second dimension retention time beyond the reference n-alkanes by increasing the carbon number. The extension of carbon numbers in reference n-alkanes up to two more carbon atoms introduces less than 10 retention index units (iu) of deviation. The effectiveness of using the proposed method was demonstrated by analyzing a mixture of compound standards in temperature programmed experiments using 6 different initial column temperatures. The standard deviation of the calculated retention index values of the compound standards fluctuated from 1 to 12 iu with a mean standard deviation of 5 iu.

Zhao, Yaping; Zhang, Jun; Wang, Bing; Ho Kim, Seong; Fang, Aiqin; Bogdanov, Bogdan; Zhou, Zhanxiang; McClain, Craig; Zhang, Xiang

2011-01-01

370

Fractal Patterns and Chaos Games  

ERIC Educational Resources Information Center

|Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.|

Devaney, Robert L.

2004-01-01

371

Fractal Patterns and Chaos Games  

ERIC Educational Resources Information Center

Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.

Devaney, Robert L.

2004-01-01

372

Fractal interrelationship in field and seismic data. Fifth quarterly technical report, March 21--June 21, 1996  

SciTech Connect

The primary goal of this study is to evaluate the possibility that the fractal characteristics of reservoir fracture systems might be inferred from the fractal characteristics of the reservoir reflector. Results discussed in the summary below provide support for such a view. The matter will, however, remain unresolved until fracture data acquired from core or FMS logs can be compared to reflection seismic data from the core areas. A series of cross sections along the Middle Mountain syncline and Elkhorn Mountain anticline were evaluated. Near-surface deformation in the Middle Mountain and Elkhorn mountain area of the Valley and Ridge province is significant. In this area the fractal dimension of topography is linearly related to the fractal dimension of underlying structure. Comparison of the fractal variability of Valley and Ridge structures with those observed in seismic data from the Plateau indicate that the increased fractal dimension of reflection events implies greater relative abundance of higher order or smaller wavelength structures. Results from the seismic evaluation suggest that fractal analysis might provide a useful exploration tool in cases where one is interested in locating subtle detached structures or identifying fractured reservoirs. Results from the Valley and a Ridge area suggest that, in active tectonic areas, fractal analysis may provide a means to assess the relative frequency of earthquake activity over time periods that extend beyond the historical record.

Wilson, T.H.; Dominic, J.; Halverson, J.

1996-12-31

373

Fractal-wavelet image denoising  

Microsoft Academic Search

In this paper, we propose a simple yet effective fractal-wavelet scheme for edge-preserving smoothing of noisy images. Over the past decade, there has been significant interest in fractal coding for the purpose of image compression. Fractal-wavelet transforms were introduced in an effort to reduce the blockiness and com- putational complexity that are inherent in fractal image compres- sion. Applications of

Mohsen Ghazel; Edward R. Vrscay; George H. Freeman

2002-01-01

374

New Approach to Spectrum Calculations in Lattice Hamiltonian Field Theories l. Introduction and Application to lambda phi 4 in (1+1) Dimensions.  

National Technical Information Service (NTIS)

The authors developed a finite lattice technique for calculating the spectrum of fluctuating Bose theories in the continuum limit. The method gave the continuum spectrum to an estimated accuracy of about 1% in (1+1) dimensions using available computer mem...

T. Barnes G. J. Daniell

1982-01-01

375

STOSS - A Computer Module Which Can Be Used in Monte-Carlo-Calculation for Determining the Path of a Particle in a Heterogeneous Medium in Three Dimensions.  

National Technical Information Service (NTIS)

The computer program STOSS determines the path of a particle in a heterogenous medium in three dimensions. The program can be used as a module in Monte-Carlo-calculations. The collision can be transferred from the centre-of-mass system into a fixed cartes...

G. Sdouz

1980-01-01

376

Arterial pressure fractality is highly dependent on wave reflection.  

PubMed

Wave reflection is an important factor that influences pressure wave morphology and becomes more significant with aging, when cardiovascular risk increases. A pressure wave, measured at any location in the arterial tree, can be decomposed into its forward and backward components and depends on the corresponding amplitude and shifting time delays. Fractal dimension (FD) quantifies the time series complexity defined by its geometrical representation. Objective: The aim of this study was to evaluate the arterial pressure and diameter time series in order to assess the relationship between wave reflection and arterial pressure fractal dimension (FD). Methods: Simultaneous aortic pressure and diameter were measured in 14 conscious dogs. A pair of ultrasonic crystals, a pressure microtransducer and a pneumatic cuff occluder were positioned in the upper third of the descending aorta. Results: Total reflection induced by the occlusion maneuver decreased FD concomitant to the aortic stiffening. Conclusion: Arterial pressure fractality is highly dependent on wave reflection. PMID:24110099

Armentano, Ricardo L; Cymberknop, Leandro J; Legnani, Walter; Pessana, Franco M; Craiem, Damian; Graf, Sebastian; Barra, Juan G

2013-07-01

377

Stochastic Lagrangian Particle Approach to Fractal Navier-Stokes Equations  

NASA Astrophysics Data System (ADS)

In this article we study the fractal Navier-Stokes equations by using the stochastic Lagrangian particle path approach in Constantin and Iyer (Comm Pure Appl Math LXI:330-345, 2008). More precisely, a stochastic representation for the fractal Navier-Stokes equations is given in terms of stochastic differential equations driven by Lévy processes. Based on this representation, a self-contained proof for the existence of a local unique solution for the fractal Navier-Stokes equation with initial data in {{mathbb W}^{1,p}} is provided, and in the case of two dimensions or large viscosity, the existence of global solutions is also obtained. In order to obtain the global existence in any dimensions for large viscosity, the gradient estimates for Lévy processes with time dependent and discontinuous drifts are proved.

Zhang, Xicheng

2012-04-01

378

The Fractal Geometry of Invention  

Microsoft Academic Search

Fractals are geometric objects of inexhaustible detail. Fractal structures have been found in the contours of mountain ranges, the patterns of veins on a leaf, and the fluctuations of the Dow Jones Industrial Average. The endeavor of inventing new technologies, consisting of a hierarchical network of practical inquiries, exhibits fractal properties as well. Among these are multiplicity, latency, and self-similarity.

Alan L. Durham

2012-01-01

379

Moisture diffusivity in structure of random fractal fiber bed  

NASA Astrophysics Data System (ADS)

A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.

Zhu, Fanglong; Zhou, Yu; Feng, Qianqian; Xia, Dehong

2013-11-01

380

Digital holographic fractal speckle  

NASA Astrophysics Data System (ADS)

It has been shown in previous studies that fractal speckles can be produced in an image plane by using as a pupil filter in the imaging system a spatial light modulator with an intensity transmittance obeying a negative power-law. However, this method has a disadvantage in that the intensity distributions of such speckles are very low due to the pupil filter giving a lower total transmittance. To overcome this disadvantage, we propose here the use of digital holography to generate fractal speckles. The theoretical background is explained briefly, and experimental results are shown.

Funamizu, Hideki; Uozumi, Jun; Aizu, Yoshihisa

2013-03-01

381

Characterization of grain-boundary configuration and fracture surface roughness by fractal geometry and creep-rupture properties of metallic materials  

Microsoft Academic Search

Grain-boundary configuration in heat-treated specimens and fracture surface roughness in creep-ruptured specimens of several kinds of metallic material were quantitatively evaluated on the basis of fractal geometry. Correlations between the fractal dimension of grain boundary, that of fracture surface profile, the creep-rupture properties and the fracture mechanisms of the alloys are discussed. In heat-resistant alloys, the fractal dimension of a

Manabu Tanaka

1992-01-01

382

Perimeter-Yardstick Technique for Fracture Surface Fractal Analysis.  

National Technical Information Service (NTIS)

Local fractal dimensions alpha(Chi, Epsilon), which are closely related to crowding indices of individual islands and lakes formed by sectioning of fracture surfaces produced in Charpy impact testing of a high-strength and high-toughness steel (ASTM A723)...

G. Kendall P. J. Cote L. V. Meisel

1994-01-01

383

Fractal analysis of physical adsorption on material surfaces  

Microsoft Academic Search

In order to find the fractal dimension of rough surfaces, adsorption isotherms are studied. Fripiat Gatineau and Van Damme ‘Langmuir 2 (1986) 562’ extended the BET-Formula ‘J. Am. Chem. Soc. 60 (1938) 309’ which was originally designed for flat surfaces. As far as we are aware, this method has never been practically applied. This is mainly due to a term

M. Mahnke; H. J. Mögel

2003-01-01

384

Comparison between spectral and fractal EEG analyses of sleeping newborns  

Microsoft Academic Search

Spectral parameters (power spectrum in the delta, theta, alpha, beta1 and beta2 bands) and the fractal dimension were estimated for each two seconds frame of the EEG sleep time series at the awake condition or during one of the four EEG sleep states: active sleep (two stages: mixed and low voltage irregular) and quiet sleep (two stages: quiet sleep high

A. P. Accardo; M. Affinito; M. Carrozzi; S. Cisint; F. Bouquet

1998-01-01

385

Application of fractal theory in analysis of human electroencephalographic signals.  

PubMed

In medical discipline, complexity measure is focused on the analysis of nonlinear patterns in processing waveform signals. The complexity measure of such waveform signals is well performed by fractal dimension technique, which is an index for measuring the complexity of an object. Its applications are found in diverse fields like medical, image and signal processing. Several algorithms have been suggested to compute the fractal dimension of waveforms. We have evaluated the performance of the two famous algorithms namely Higuchi and Katz. They contain some problems of determining the initial and final length of scaling factors and their performance with electroencephalogram (EEG) signals did not give better results. In this paper, fractal dimension is proposed as an effective tool for analyzing and measuring the complexity of nonlinear human EEG signals. We have developed an algorithm based on size measure relationship (SMR) method. The SMR algorithm can be used to detect the brain disorders and it locates the affected brain portions by analyzing the behavior of signals. The efficiency of the algorithm to locate the critical brain sites (recurrent seizure portion) is compared to other fractal dimension algorithms. The K-means clustering algorithm is used for grouping of electrode positions. PMID:18234169

Paramanathan, P; Uthayakumar, R

2008-01-29

386

Influence of GSM Microwaves on Fractal Structure of brain tumours  

Microsoft Academic Search

Fractal dimension of C-6 rat glioma tumours growing in microwave field generated by signal simulation of the Global System for Mobile communications (GSM) with frequency 960 MHz was found significantly enhanced as compared with field free tumours growing at different temperatures. The Mandelbrot answer to Richardson question: \\

M. Babincová; P. Sourivong; D. Leszczynska; P. Babinec

2003-01-01

387

Adaptive intelligent control of aircraft systems with a hybrid approach combining neural networks, fuzzy logic and fractal theory  

Microsoft Academic Search

We describe in this paper a hybrid method for adaptive model-based control of nonlinear dynamic systems using neural networks, fuzzy logic and fractal theory. The new neuro-fuzzy-fractal method combines soft computing techniques with the concept of the fractal dimension for the domain of nonlinear dynamic system control. The new method for adaptive model-based control has been implemented as a computer

Patricia Melin; Oscar Castillo

2003-01-01

388

Classification of breast ultrasound images using fractal feature.  

PubMed

Fractal analyses have been applied successfully for the image compression, texture analysis, and texture image segmentation. The fractal dimension could be used to quantify the texture information. In this study, the differences of gray value of neighboring pixels are used to estimate the fractal dimension of an ultrasound image of breast lesion by using the fractal Brownian motion. Furthermore, a computer-aided diagnosis (CAD) system based on the fractal analysis is proposed to classify the breast lesions into two classes: benign and malignant. To improve the classification performances, the ultrasound images are preprocessed by using morphology operations and histogram equalization. Finally, the k-means classification method is used to classify benign tumors from malignant ones. The US breast image databases include only histologically confirmed cases: 110 malignant and 140 benign tumors, which were recorded. All the digital images were obtained prior to biopsy using by an ATL HDI 3000 system. The receiver operator characteristic (ROC) area index AZ is 0.9218, which represents the diagnostic performance. PMID:15967313

Chen, Dar-Ren; Chang, Ruey-Feng; Chen, Chii-Jen; Ho, Ming-Feng; Kuo, Shou-Jen; Chen, Shou-Tung; Hung, Shin-Jer; Moon, Woo Kyung

389

Statistical errors in the fractal analysis of flame boundaries  

SciTech Connect

A high speed tomographic technique is used to evaluate the effect of spatial resolution, and requirements for statistical convergence on the fractal analysis of a turbulent, premixed, stoichiometric methane/air flame at high Damkoehler number. The gas velocity at the nozzle exit is 5 m/s, the turbulence intensity is 7%, the integral length scale 3 mm and hence the turbulence Reynolds number is 70. The light source is a copper vapor laser which produces 20ns, 5 mJ pulses at a 4KHz repetition rate. Cylindrical lenses transform the 38mm circular laser beam to a sheet 50 mm high and 0.6 mm thick. A high speed Fastax camera is used to record the tomographic images formed by the scattering of light from oil droplets seeded in the reactant flow. The films are digitized and the flame front extracted from the images by a thresholding technique. Digitization noise, which appears in the fractal plots at approximately twice the pixel resolution, can obscure the inner cutoff. Simple smoothing can remove this problem if the spatial resolution is sufficient. At insufficient resolution smoothing produces plausible resolutes are produced which in fact erroneous. If the inner cutoff is ambiguous the range over which the fractal dimension is determined will be unclear. The wide distribution of fractal dimensions obtained from the individual images indicates the necessity of ensemble averaging the fractal plots if reliable statistical results are to be obtained. 8 refs., 6 figs.

Shepherd, I.G.; Cheng, R.K.

1990-10-01

390

Fractal analysis of vascular networks: insights from morphogenesis.  

PubMed

Considering their extremely complicated and hierarchical structure, a long standing question in vascular physio-pathology is how to characterize blood vessels patterns, including which parameters to use. Another question is how to define a pertinent taxonomy, with applications to normal development and to diagnosis and/or staging of diseases. To address these issues, fractal analysis has been applied by previous investigators to a large variety of healthy or pathologic vascular networks whose fractal dimensions have been sought. A review of the results obtained on healthy vascular networks first shows that no consensus has emerged about whether normal networks must be considered as fractals or not. Based on a review of previous theoretical work on vascular morphogenesis, we argue that these divergences are the signature of a two-step morphogenesis process, where vascular networks form via progressive penetration of arterial and venous quasi-fractal arborescences into a pre-existing homogeneous capillary mesh. Adopting this perspective, we study the multi-scale behavior of generic patterns (model structures constructed as the superposition of homogeneous meshes and quasi-fractal trees) and of healthy intracortical networks in order to determine the artifactual and true components of their multi-scale behavior. We demonstrate that, at least in the brain, healthy vascular structures are a superposition of two components: at low scale, a mesh-like capillary component which becomes homogeneous and space-filling over a cut-off length of order of its characteristic length; at larger scale, quasi-fractal branched (tree-like) structures. Such complex structures are consistent with all previous studies on the multi-scale behavior of vascular structures at different scales, resolving the apparent contradiction about their fractal nature. Consequences regarding the way fractal analysis of vascular networks should be conducted to provide meaningful results are presented. Finally, consequences for vascular morphogenesis or hemodynamics are discussed, as well as implications in case of pathological conditions, such as cancer. PMID:19913557

Lorthois, Sylvie; Cassot, Francis

2009-11-12

391

Comment on "Fractal analysis of ULF electromagnetic emissions in possible association with earthquakes in China" by Ida et al. (2012)  

NASA Astrophysics Data System (ADS)

Ida et al. (2012) identified anomalous decreases in the fractal dimension of the vertical (Z) component of the geomagnetic field, which they interpreted as precursors to the China earthquake of 1 September 2003. According to Ida et al. (2012), short-term earthquake prediction seems to be possible only by using electromagnetic phenomena. Here, it is shown that the decreases of the fractal dimension documented by Ida et al. (2012) are not really anomalous, but they are part of the normal geomagnetic activity driven by solar-terrestrial interactions. As a consequence, these fractal dimension decreases are not related to the 1 September 2003 earthquake.

Masci, F.; Thomas, J. N.

2013-06-01

392

Renormalization of first-passage times for random walks on deterministic fractals  

NASA Astrophysics Data System (ADS)

The first-passage time density for nearest-neighbor random walks on various deterministic fractal lattices is calculated. The procedure consists of the derivation of a renormalization equation, similar to that derived by Machta for a random walk in one dimension [Phys. Rev. B 24, 5260 (1981)], and in its solution in terms of an auxiliary function, defined by a functional equation. Both the cases of waiting times with finite first moment or with fractal time properties are discussed. By rescaling time and length in the appropriate way, the first-passage time density approaches a ``universal'' asymptotic form ?(?). The scaling properties are consistent with subdiffusive behavior ~t2/dw, with dw>2, as discussed previously in the literature. The overall shape of ?(?) is found to be very similar to that for a random walk in one dimension, except that the small-? behavior is qualitatively different in both cases. The existence of these two time regimes was already suggested by Guyer [Phys. Rev. A 29, 2751 (1984)] and explains why different scaling forms for the Green's function have been proposed in the literature.

van den Broeck, C.

1989-12-01

393

Poisson-to-Wigner crossover transition in the nearest-neighbor statistics of random points on fractals  

Microsoft Academic Search

We show that the nearest-neighbor spacing distribution for a model that consists of random points uniformly distributed on a self-similar fractal is the Brody distribution of random matrix theory. In the usual context of Hamiltonian systems, the Brody parameter does not have a definite physical meaning, but in the model considered here, the Brody parameter is actually the fractal dimension.

Jamal Sakhr; John M. Nieminen

2005-01-01

394

Fractal Characteristics of May-Grünwald-Giemsa Stained Chromatin Are Independent Prognostic Factors for Survival in Multiple Myeloma  

Microsoft Academic Search

BackgroundThe use of computerized image analysis for the study of nuclear texture features has provided important prognostic information for several neoplasias. Recently fractal characteristics of the chromatin structure in routinely stained smears have shown to be independent prognostic factors in acute leukemia. In the present study we investigated the influence of the fractal dimension (FD) of chromatin on survival of

Daniela P. Ferro; Monica A. Falconi; Randall L. Adam; Manoela M. Ortega; Carmen P. Lima; Carmino A. de Souza; Irene Lorand-Metze; Konradin Metze

2011-01-01

395

Fractal analysis of Xylella fastidiosa biofilm formation  

NASA Astrophysics Data System (ADS)

We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73+/-0.06 and 2.68+/-0.06, respectively, while in the maturation stage, Df=2.57+/-0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.

Moreau, A. L. D.; Lorite, G. S.; Rodrigues, C. M.; Souza, A. A.; Cotta, M. A.

2009-07-01

396

Fractal nature of the sea ice draft profile  

NASA Astrophysics Data System (ADS)

The fractal dimension is examined as a descriptor of ice roughness for more than 3000 km of under-ice draft submarine sonar data. The data can be considered to constitute a fractal set within a limited range of scales, as defined by the Hurst parameter H. It was found that 0.55 < H < 0.78 for scales of 3-15 m and 0.15 < H < 0.45 for scales of 15-75 m, beyond which H is near unity. From this it is seen quantitatively that sea ice on the large scale is smooth. The fractal dimension, D=2-H, at the smaller scales is similar to that measured by other investigators for individual ice features such as keels. The fractal dimension did not show any changing spatial pattern across ice regions, indicating that the scaling relationship is similar even when first-order measures such as the mean and variance of ice draft change. Therefore, D does not appear to be useful for partitioning the transect into homogeneous ice areas in the draft data examined.

Key, J.; McLaren, A. S.

397

Fractal Mining - Self Similarity-based Clustering and its Applications  

NASA Astrophysics Data System (ADS)

Self-similarity is the property of being invariant with respect to the scale used to look at the data set. Self-similarity can be measured using the fractal dimension. Fractal dimension is an important charactaristics for many complex systems and can serve as a powerful representation technique. In this chapter, we present a new clustering algorithm, based on self-similarity properties of the data sets, and also its applications to other fields in Data Mining, such as projected clustering and trend analysis. Clustering is a widely used knowledge discovery technique. The new algorithm which we call Fractal Clustering (FC) places points incrementally in the cluster for which the change in the fractal dimension after adding the point is the least. This is a very natural way of clustering points, since points in the same clusterhave a great degree of self-similarity among them (and much less self-similarity with respect to points in other clusters). FC requires one scan of the data, is suspendable at will, providing the best answer possible at that point, and is incremental. We show via experiments that FC effectively deals with large data sets, high-dimensionality and noise and is capable of recognizing clusters of arbitrary shape.

Barbara, Daniel; Chen, Ping

398

Calculations of nonlocal electron energy transport in laser produced plasmas in one and two dimensions using the velocity dependent Krook model  

NASA Astrophysics Data System (ADS)

This paper extends the velocity dependent Krook (VDK) model, developed at NRL over the last 4 years, to two dimensions and presents a variety of calculations. One dimensional spherical calculations presented here investigate shock ignition. Comparing VDK calculations to a flux limit calculation shows that the laser profile has to be retuned and some gain is sacrificed due to preheat of the fuel. However, preheat is by no means a show stopper for laser fusion. The recent foil acceleration experiments at the University of Rochester Laboratory for Laser Energetics are modeled with two-dimensional simulations. The radial loss is very important to consider in modeling the foil acceleration. Once this is done, the VDK model gives the best agreement with the experiment.

Manheimer, Wallace; Colombant, Denis; Schmitt, Andrew J.

2012-05-01

399

Calculations of nonlocal electron energy transport in laser produced plasmas in one and two dimensions using the velocity dependent Krook model  

SciTech Connect

This paper extends the velocity dependent Krook (VDK) model, developed at NRL over the last 4 years, to two dimensions and presents a variety of calculations. One dimensional spherical calculations presented here investigate shock ignition. Comparing VDK calculations to a flux limit calculation shows that the laser profile has to be retuned and some gain is sacrificed due to preheat of the fuel. However, preheat is by no means a show stopper for laser fusion. The recent foil acceleration experiments at the University of Rochester Laboratory for Laser Energetics are modeled with two-dimensional simulations. The radial loss is very important to consider in modeling the foil acceleration. Once this is done, the VDK model gives the best agreement with the experiment.

Manheimer, Wallace; Colombant, Denis; Schmitt, Andrew J. [Laser Plasma Branch, Plasma Physics Division, Naval Research Laboratory, Washington, DC 20375 (United States)

2012-05-15

400

Collapse of loaded fractal trees  

NASA Astrophysics Data System (ADS)

Mandelbrot1 has argued that a wide range of natural objects and phenomena are fractals; examples of fractal trees include actual trees, plants such as a cauliflower, river systems and the cardiovascular system. Here we apply the renormalization group approach2 to the collapse of fractal trees, which may be applicable to a variety of problems including cardiac arrest, failure of bronchial systems, failure of electrical distribution systems and the instability resulting in earthquakes.

Turcotte, D. L.; Smalley, R. F.; Solla, Sara A.

1985-02-01

401

Characterizing attractors using local intrinsic dimensions calculated by singular-value decomposition and information-theoretic criteria  

Microsoft Academic Search

An algorithm to estimate the average local intrinsic dimension () of an attractor using signal versus noise separation methods based on information-theoretic criteria is explored in this work. Using noisy sample data the is computed from an eigenanalysis of local attractor regions, indicating the local orthogonal directions along which the data are clustered. The algorithm requires the separation

T. Hediger; A. Passamante; Mary Eileen Farrell

1990-01-01

402

Temperature induced smoothing of initially fractal grain boundaries  

SciTech Connect

Recently the effect of serrated or rugged grain boundaries on the mechanical properties of alloys and the numerical characterization of such a geometrically irregular microstructure by means of the concept of fractal geometry has attracted great attention. It has been reported that the generation of serrated or rugged grain boundaries, e.g. by cold work or heat treatment, is one of the most effective methods to improve the high-temperature strength of alloys, especially the creep rupture properties. In the present paper, for the first time, measurements of the change in the roughness of initially fractal grain boundaries after annealing are presented. The experimental results are discussed on the basis of a coarsening model for self-similar interfaces, which predicts a dependency of the smoothing kinetics of the grain boundaries on their initially fractal dimension.

Streitenberger, P.; Foerster, D.; Kolbe, G.; Veit, P. [Otto-von-Guericke-Univ. Magdeburg (Germany). Inst. fuer Experimentelle Physik

1996-01-01

403

Darwinian Evolution and Fractals  

NASA Astrophysics Data System (ADS)

Did nature's beauty emerge by chance or was it intelligently designed? Richard Dawkins asserts that evolution is blind aimless chance. Michael Behe believes, on the contrary, that the first cell was intelligently designed. The scientific evidence is that nature's creativity arises from the interplay between chance AND design (laws). Darwin's ``Origin of the Species,'' published 150 years ago in 1859, characterized evolution as the interplay between variations (symbolized by dice) and the natural selection law (design). This is evident in recent discoveries in DNA, Madelbrot's Fractal Geometry of Nature, and the success of the genetic design algorithm. Algorithms for generating fractals have the same interplay between randomness and law as evolution. Fractal statistics, which are not completely random, characterize such phenomena such as fluctuations in the stock market, the Nile River, rainfall, and tree rings. As chaos theorist Joseph Ford put it: God plays dice, but the dice are loaded. Thus Darwin, in discovering the evolutionary interplay between variations and natural selection, was throwing God's dice!

Carr, Paul H.

2009-05-01

404

Eigenfrequencies of fractal drums  

NASA Astrophysics Data System (ADS)

A method for the computation of eigenfrequencies and eigenmodes of fractal drums is presented. The approach involves first conformally mapping the unit disk to a polygon approximating the fractal and then solving a weighted eigenvalue problem on the unit disk by a spectral collocation method. The numerical computation of the complicated conformal mapping was made feasible by the use of the fast multipole method as described in [L. Banjai, L.N. Trefethen, A multipole method for Schwarz-Christoffel mapping of polygons with thousands of sides, SIAM J. Sci. Comput. 25(3) (2003) 1042-1065]. The linear system arising from the spectral discretization is large and dense. To circumvent this problem we devise a fast method for the inversion of such a system. Consequently, the eigenvalue problem is solved iteratively. We obtain eight digits for the first eigenvalue of the Koch snowflake and at least five digits for eigenvalues up to the 20th. Numerical results for two more fractals are shown.

Banjai, Lehel

2007-01-01

405

Improved Integrated Model of Electromagnetic Scattering for Two Dimensional Fractal Sea Surface  

Microsoft Academic Search

In this paper, an improved integrated model of electromagnetic scattering for two dimensional fractal sea surface is built. Both geometrical fractal characteristic and permittivity characteristic of sea water are strictly considered, especially for the effects of salinity and temperature on the electromagnetic field scattered by sea water are added on. Finally, the calculated results from the new model are in

Chonghua Fang; Qian Liu; Xiaonan Zhao

2010-01-01

406

Fractal properties and denoising of lidar signals from cirrus clouds  

NASA Astrophysics Data System (ADS)

Airborne lidar signals of cirrus clouds are analyzed to determine the cloud structure. Climate modeling and numerical weather prediction benefit from accurate modeling of cirrus clouds. Airborne lidar measurements of the European Lidar in Space Technology Experiment (ELITE) campaign were analyzed by combining shots to obtain the backscatter at constant altitude. The signal at high altitude was analyzed for horizontal structure of cirrus clouds. The power spectrum and the structure function show straight lines on a double logarithmic plot. This behavior is characteristic for a Brownian fractal. Wavelet analysis using the Haar wavelet confirms the fractal aspects. It is shown that the horizontal structure of cirrus can be described by a fractal with a dimension of 1.8 over length scales that vary 4 orders of magnitude. We use the fractal properties in a new denoising method. Denoising is required for future lidar measurements from space that have a low signal to noise ratio. Our wavelet denoising is based on the Haar wavelet and uses the statistical fractal properties of cirrus clouds in a method based on the maximum a posteriori (MAP) probability. This denoising based on wavelets is tested on airborne lidar signals from ELITE using added Gaussian noise. Superior results with respect to averaging are obtained.

van den Heuvel, J. C.; Driesenaar, M. L.; Lerou, R. J. L.

2000-02-01

407

Fractal geometry in an expanding, one-dimensional, Newtonian universe.  

PubMed

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure. PMID:17930359

Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel

2007-09-14

408

Arbitrariness in defining fractal basins: Relations between open and closed systems  

Microsoft Academic Search

A discussion about dependences of the (fractal) basin boundary dimension with the definition of the basins and the size of the exits is presented for systems with one or more exits. In particular, it is shown that the dimension is largely independent of the choice of the basins, and decreases with the size of the exits. Considering the limit of

A. E. Motter; P. S. Letelier

2001-01-01

409

Multi-fractal and Wavelet Analysis for Cosmic Ray Mass Composition Studies using the TACTIC Telescope  

NASA Astrophysics Data System (ADS)

We have investigated the efficiency of multifractal and wavelet parameters of the simulated images of atmospheric Cerenkov events, in segregating the events in terms of primary mass. We find that the fractal dimension D6 and the wavelet dimension 6 can be employed effectively for studying cosmic ray mass composition at > 20 TeV energy with the TACTIC array.

Bhat, C. K.; Kaul, R. K.

2003-03-01

410

Hierarchical fractal weyl laws for chaotic resonance States in open mixed systems.  

PubMed

In open chaotic systems the number of long-lived resonance states obeys a fractal Weyl law, which depends on the fractal dimension of the chaotic saddle. We study the generic case of a mixed phase space with regular and chaotic dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of the chaotic phase-space component. This is based on our observation of hierarchical resonance states localizing on these regions. Numerically this is verified for the standard map and a hierarchical model system. PMID:24074090

Körber, M J; Michler, M; Bäcker, A; Ketzmerick, R

2013-09-13

411

Hierarchical Fractal Weyl Laws for Chaotic Resonance States in Open Mixed Systems  

NASA Astrophysics Data System (ADS)

In open chaotic systems the number of long-lived resonance states obeys a fractal Weyl law, which depends on the fractal dimension of the chaotic saddle. We study the generic case of a mixed phase space with regular and chaotic dynamics. We find a hierarchy of fractal Weyl laws, one for each region of the hierarchical decomposition of the chaotic phase-space component. This is based on our observation of hierarchical resonance states localizing on these regions. Numerically this is verified for the standard map and a hierarchical model system.

Körber, M. J.; Michler, M.; Bäcker, A.; Ketzmerick, R.

2013-09-01

412

Hausdorff dimension of a quantum string  

NASA Astrophysics Data System (ADS)

In the path integral formulation of quantum mechanics, Feynman and Hibbs noted that the trajectory of a particle is continuous but nowhere differentiable. We extend this result to the quantum-mechanical path of a relativistic string and find that the ``trajectory,'' in this case, is a fractal surface with Hausdorff dimension three. Depending on the resolution of the detecting apparatus, the extra dimension is perceived as ``fuzziness'' of the string world surface. We give an interpretation of this phenomenon in terms of a new form of the uncertainty principle for strings, and study the transition from the smooth to the fractal phase.

Ansoldi, S.; Aurilia, A.; Spallucci, E.

1997-08-01

413

Fractal Analysis of Trabecular Bone  

NSDL National Science Digital Library

Fractals are unusual geometric structures that can be used to analyze many biologic structures not amenable to conventional analysis. The purpose of this exhibit is to teach some of the fundamentals of fractal analysis, and to show how they can be applied to analysis of trabecular bone.

Richardson, Michael L.; Gillespy, Thurman

2007-03-29

414

Fractal calculus on [0, 1  

Microsoft Academic Search

Ordinary differential equations are generalized to fractal supports with regular or multifractal properties. This can be done by considering the corresponding integral equations with respect to the measure. Closed form solutions of simple differential equations (giving rise to exponential, sine and cosine functions) on fractals are presented and the generalization to arbitrary differential equations discussed. Some applications of this formalism

Massimiliano Giona

1995-01-01

415

Fractal EEG analysis with Higuchi's algorithm of low-frequency noise exposition on humans  

Microsoft Academic Search

Authors used methods based on fractal analysis of EEG signal to assess the influence of low-frequency sound field on the human brain electro-potentials. The relations between LFN (low-frequency noise) and change in fractal dimension EEG signal were measured with stimulations tones. Three types of LFN stimuli were presented; each specified dominant frequency and sound-pressure levels (7 Hz at 120 dB,

Ryszard Panuszka; Zbigniew Damijan; Cezary Kasprzak

2001-01-01

416

Fractality of sooty smoke: implications for the severity of nuclear winter  

Microsoft Academic Search

IT is now recognized that the sooty fraction of the smoke produced by fires in the wake of a nuclear exchange is a critical factor in determining climatic effects1-3. Sooty smoke particles occur as chained aggregates of small spherules which are fractal with a dimension of 1.7-1.9. According to a recently developed mean-field theory4 for the optics of such fractal

Jenny Nelson

1989-01-01

417

A note on the soil-water conductivity of a fractal soil  

Microsoft Academic Search

We show that for a fractal soil the soil-water conductivity, K, is given by \\u000a$$\\\\frac{K}{{K_\\\\varepsilon }} = (\\\\Theta \\/\\\\varepsilon )^{2D\\/3 + 2\\/(3 - D)}$$\\u000a where \\u000a$$K_\\\\varepsilon$$\\u000a is the saturated conductivity, ? the water content, ? its saturated value and D is the fractal dimension obtained from reinterpreting Millington and Quirk's equation for practical values of the porosity ?, as \\u000a$$D

Carlos Fuentes; Michel Vauclin; Jean-Yves Parlange; Randel Haverkamp

1996-01-01

418

Modification of fractal algorithm for oil spill detection from RADARSAT-1 SAR data  

Microsoft Academic Search

This paper introduces a modified formula for the fractal box counting dimension. The method is based on utilization of the probability distribution formula in the fractal box count. The purpose of this method is to use it for the discrimination of oil spill areas from the surrounding features, e.g., sea surface and look-alikes in RADARSAT-1 SAR Wide beam mode (W1)

Maged Marghany; Arthur P. Cracknell; Mazlan Hashim

2009-01-01

419

a Fractal Approach to Spontaneous Imbibition Height in Natural Porous Media  

NASA Astrophysics Data System (ADS)

Spontaneous imbibition of wetting liquids in porous media is of great importance in many fields. In this paper, an analytical model for characterizing spontaneous imbibition height versus time in natural porous media was derived using fractal approach. The average imbibition height in porous media is in terms of porosity, fractal dimensions, maximum pore size and viscosity, surface tension and liquid-solid interactions. The developed model is consistent with previous results and is tested against available experimental data showing fair agreements.

You, Lijun; Cai, Jianchao; Kang, Yili; Luo, Liang

2013-09-01

420

Accuracy of EGSnrc calculations at 60Co energies for the response of ion chambers configured with various wall materials and cavity dimensions.  

PubMed

In this investigation, five experimental data sets are used to evaluate the ability of the EGSnrc Monte Carlo code to calculate the change in chamber response associated with changes in wall material and cavity dimension at 60Co energies. Calculations of the ratios of response per unit mass of air as a function of cavity volume for walls ranging from polystyrene to lead are generally within 1%-3% of experiments. A few exceptions, which are discussed, include 20%-30% discrepancies with experiments involving lead-walled chambers used by Attix et al. [J. Res. Natl. Bur. Stand. 60, 235-243 (1958)] and Cormack and Johns [Radiat. Res. 1, 133-157 (1954)], and 5% discrepancies for the graphite chamber of Attix et al. (relative to data for other wall materials). Simulations of the experiment by Whyte [Radiat. Res. 6, 371-379 (1957)], which varied cavity air pressure in a large cylindrical chamber, are generally within 0.5% (wall/electrode materials ranging from beryllium to copper). In all cases, the agreement between measurements and EGSnrc calculations is much better when the response as a function of cavity height or air pressure is considered for each wall material individually. High-precision measurements [Burns et al., Phys. Med. Biol. 52, 7125-7135 (2007)] of the response per unit mass as a function of cavity height for a graphite chamber are also accurately reproduced, and validate previous tests of the transport mechanics of EGSnrc. Based on the general agreement found in this work between corresponding experimental results and EGSnrc calculations it can be concluded that EGSnrc can reliably be used to calculate changes in response with changes in various wall materials and cavity dimensions at 60Co energies within a accuracy of a few percent or less. PMID:19175120

La Russa, Daniel J; Rogers, D W O

2008-12-01

421

Accuracy of EGSnrc calculations at {sup 60}Co energies for the response of ion chambers configured with various wall materials and cavity dimensions  

SciTech Connect

In this investigation, five experimental data sets are used to evaluate the ability of the EGSnrc Monte Carlo code to calculate the change in chamber response associated with changes in wall material and cavity dimension at {sup 60}Co energies. Calculations of the ratios of response per unit mass of air as a function of cavity volume for walls ranging from polystyrene to lead are generally within 1%-3% of experiments. A few exceptions, which are discussed, include 20%-30% discrepancies with experiments involving lead-walled chambers used by Attix et al. [J. Res. Natl. Bur. Stand. 60, 235-243 (1958)] and Cormack and Johns [Radiat. Res. 1, 133-157 (1954)], and 5% discrepancies for the graphite chamber of Attix et al. (relative to data for other wall materials). Simulations of the experiment by Whyte [Radiat. Res. 6, 371-379 (1957)], which varied cavity air pressure in a large cylindrical chamber, are generally within 0.5% (wall/electrode materials ranging from beryllium to copper). In all cases, the agreement between measurements and EGSnrc calculations is much better when the response as a function of cavity height or air pressure is considered for each wall material individually. High-precision measurements [Burns et al., Phys. Med. Biol. 52, 7125-7135 (2007)] of the response per unit mass as a function of cavity height for a graphite chamber are also accurately reproduced, and validate previous tests of the transport mechanics of EGSnrc. Based on the general agreement found in this work between corresponding experimental results and EGSnrc calculations it can be concluded that EGSnrc can reliably be used to calculate changes in response with changes in various wall materials and cavity dimensions at {sup 60}Co energies within a accuracy of a few percent or less.

La Russa, Daniel J.; Rogers, D. W. O. [Carleton Laboratory for Radiotherapy Physics, Ottawa Carleton Institute of Physics, Carleton University Campus, Ottawa, Ontario K1S 5B6 (Canada)

2008-12-15

422

Numerical calculation of thermal convection in porous media in two dimensions with applications to nuclear repository design  

SciTech Connect

Thermal convection induced by nuclear waste heating could be an important mechanism in the transport of radioactive nuclides to the biosphere. A computer code HP2D was developed to calculate this effect. The code calculates transient and steady state heat and fluid flow in porous media. It allows for anisotropy of hydraulic conductivities, temperature dependent fluid density and viscosity. A heat source and a variety of temperature and flow boundary conditions can be easily employed. The code solves two coupled governing equations. The time dependent heat transport is solved by an alternating direction implicit technique; and the steady state flow of water is solved by a Gauss-Seidel Poisson solver. A sample calculation of thermal convection about a repository is given.

Maiden, D.E.

1980-05-01

423

Dynamic structure factor of vibrating fractals: proteins as a case study.  

PubMed

We study the dynamic structure factor S(k,t) of proteins at large wave numbers k, kR(g)?1, where R(g) is the gyration radius. At this regime measurements are sensitive to internal dynamics, and we focus on vibrational dynamics of folded proteins. Exploiting the analogy between proteins and fractals, we perform a general analytic calculation of the displacement two-point correlation functions, <[u(?>)(i)(t)-u(?>)(j)(0)](2)>. We confront the derived expressions with numerical evaluations that are based on protein data bank (PDB) structures and the Gaussian network model (GNM) for a few proteins and for the Sierpinski gasket as a controlled check. We use these calculations to evaluate S(k,t) with arrested rotational and translational degrees of freedom, and show that the decay of S(k,t) is dominated by the spatially averaged mean-square displacement of an amino acid. The latter has been previously shown to evolve subdiffusively in time, <[u(?>)(i)(t)-u(?>)(i)(0)](2)> ~t(?), where ? is the anomalous diffusion exponent that depends on the spectral dimension d(s) and fractal dimension d(f). As a result, for wave numbers obeying k(2))(2)>?1, S(k,t) effectively decays as a stretched exponential S(k,t)?S(k)e(-(?(k)t)(?)) with ???, where the relaxation rate is ?(k)~(k(B)T/m?(o)(2))(1/?)k(2/?), T is the temperature, and m?(o)(2) the GNM effective spring constant describing the interaction between neighboring amino acids. The static structure factor is dominated by the fractal character of the native fold, S(k)~k(-d(f)), with negligible to marginal influence of vibrations. The analytical expressions are first confronted with numerically based calculations on the Sierpinski gasket, and very good agreement is found between simulations and theory. We then perform PDB-GNM-based numerical calculations for a few proteins, and an effective stretched exponential decay of the dynamic structure factor is found, albeit their relatively small size. However, when rotational and translational diffusion are added, we find that their contribution is never negligible due to finite size effects. While we can still attribute an effective stretching exponent ? to the relaxation profile, this exponent is significantly larger than the anomalous diffusion exponent ?. We compare our theory with recent neutron spin-echo studies of myoglobin and hemoglobin and conclude that experiments in which the rotational and translational degrees of freedom are arrested, e.g., by anchoring the proteins to a surface, will improve the detection of internal vibrational dynamics. PMID:22400590

Reuveni, Shlomi; Klafter, Joseph; Granek, Rony

2012-01-10

424

Dynamic structure factor of vibrating fractals: Proteins as a case study  

NASA Astrophysics Data System (ADS)

We study the dynamic structure factor S(k,t) of proteins at large wave numbers k, kRg?1, where Rg is the gyration radius. At this regime measurements are sensitive to internal dynamics, and we focus on vibrational dynamics of folded proteins. Exploiting the analogy between proteins and fractals, we perform a general analytic calculation of the displacement two-point correlation functions, <[u?i(t)-u?j(0)]2>. We confront the derived expressions with numerical evaluations that are based on protein data bank (PDB) structures and the Gaussian network model (GNM) for a few proteins and for the Sierpinski gasket as a controlled check. We use these calculations to evaluate S(k,t) with arrested rotational and translational degrees of freedom, and show that the decay of S(k,t) is dominated by the spatially averaged mean-square displacement of an amino acid. The latter has been previously shown to evolve subdiffusively in time, <[u?i(t)-u?i(0)]2>˜t?, where ? is the anomalous diffusion exponent that depends on the spectral dimension ds and fractal dimension df. As a result, for wave numbers obeying k2?1, S(k,t) effectively decays as a stretched exponential S(k,t)?S(k)e-(?kt)? with ???, where the relaxation rate is ?k˜(kBT/m?o2)1/?k2/?, T is the temperature, and m?o2 the GNM effective spring constant describing the interaction between neighboring amino acids. The static structure factor is dominated by the fractal character of the native fold, S(k)˜k-df, with negligible to marginal influence of vibrations. The analytical expressions are first confronted with numerically based calculations on the Sierpinski gasket, and very good agreement is found between simulations and theory. We then perform PDB-GNM-based numerical calculations for a few proteins, and an effective stretched exponential decay of the dynamic structure factor is found, albeit their relatively small size. However, when rotational and translational diffusion are added, we find that their contribution is never negligible due to finite size effects. While we can still attribute an effective stretching exponent ? to the relaxation profile, this exponent is significantly larger than the anomalous diffusion exponent ?. We compare our theory with recent neutron spin-echo studies of myoglobin and hemoglobin and conclude that experiments in which the rotational and translational degrees of freedom are arrested, e.g., by anchoring the proteins to a surface, will improve the detection of internal vibrational dynamics.

Reuveni, Shlomi; Klafter, Joseph; Granek, Rony

2012-01-01

425

Transition-path theory calculations on non-uniform meshes in two and three dimensions using finite elements  

NASA Astrophysics Data System (ADS)

Rare events between states in complex systems are fundamental in many scientific fields and can be studied by building reaction pathways. A theoretical framework to analyze reaction pathways is provided by transition-path theory (TPT). The central object in TPT is the committor function, which is found by solution of the backward-Kolmogorov equation on a given potential. Once determined, the committor can be used to calculate reactive fluxes and rates, among other important quantities. We demonstrate here that the committor can be calculated using the method of finite elements on non-uniform meshes. We show that this approach makes it feasible to perform TPT calculations on 3D potentials because it requires many fewer degrees of freedom than a regular-mesh finite-difference approach. In various illustrative 2D and 3D problems, we calculate the committor function and reaction rates at different temperatures, and we discuss effects of temperatures and simple entropic barriers on the structure of the committor and the reaction rate constants.

Lapelosa, Mauro; Abrams, Cameron F.

2013-10-01

426

A new neuro-fuzzy-fractal approach for adaptive model-based control of non-linear dynamic systems: the case of controlling aircraft dynamics  

Microsoft Academic Search

Describes a general method for adaptive model-based control of non-linear dynamic systems using neural networks, fuzzy logic and fractal theory. The new neuro-fuzzy-fractal method combines soft computing (SC) techniques with the concept of the fractal dimension for the domain of non-linear dynamic system control. The new method for adaptive model-based control has been implemented as a computer program to show

Patricia Melin; Oscar Castillo

1999-01-01

427

Fractal-wavelet image denoising revisited  

Microsoft Academic Search

The essence of fractal image denoising is to predict the fractal code of a noiseless image from its noisy observation. From the predicted fractal code, one can generate an estimate of the original image. We show how well fractal-wavelet denoising predicts parent wavelet subtress of the noiseless image. The per- formance of various fractal-wavelet denoising schemes (e.g., fixed partitioning, quadtree

Mohsen Ghazel; George H. Freeman; Edward R. Vrscay

2006-01-01

428

Torus fractalization and intermittency.  

PubMed

The bifurcation transition is studied for the onset of intermittency analogous to the Pomeau-Manneville mechanism of type I, but generalized for the presence of a quasiperiodic external force. The analysis is concentrated on the torus-fractalization (TF) critical point that occurs at some critical amplitude of driving. (At smaller amplitudes the bifurcation corresponds to a collision and subsequent disappearance of two smooth invariant curves, and at larger amplitudes it is a touch of attractor and repeller at some fractal set without coincidence.) For the TF critical point, renormalization group (RG) analysis is developed. For the golden mean rotation number a nontrivial fixed-point solution of the RG equation is found in a class of fractional-linear functions with coefficients depending on the phase variable. Universal constants are computed that are responsible for scaling in phase space (alpha=2.890 053... and beta= -1.618 034...) and in parameter space (delta(1)=3.134 272... and delta(2)=1.618 034...). An analogy with the Harper equation is outlined, which reveals important peculiarities of the transition. For amplitudes of driving less than the critical value the transition leads (in the presence of an appropriate reinjection mechanism) to intermittent chaotic regimes; in the supercritical case it gives rise to a strange nonchaotic attractor. PMID:12188817

Kuznetsov, Sergey P

2002-06-24

429

Intermittency in and the fractal nature of nuclear fragmentation A critical examination  

NASA Astrophysics Data System (ADS)

We discuss the use of factorial moments to search for intermittency in nuclear fragmentation, and relate it to the fractal nature of the fragmenting system. We show thatthe horizontally scaled moments measure the deviation of the fluctuations from a poissonian distribution. The intermittency index is directly related to the anomalous or fractal dimension of the system, and its dependence on the order of the moments is different for mono- and multifractals. We calculate the moments and intermittency indices for the charge distribution from the statistical decay of an equilibrated hot nucleus, which we model by sampling the microcanonical phase space for nuclear fragmentation. The model is used to realistically study the conditions leading to the phenomenon of intermittency in heavy-ion reactions. The results are compared to those measured in 1 GeV/amu 197Au79 on emulsion data. They indicate possible biasing of the experimental data towards events of low multiplicity. We are able to reproduce both the resolution and order scaling as given by the data while generating many more events. We show that order scaling can be related to the form of the fluctuations as well as signal intermittency.

Deangelis, A. R.; Gross, D. H. E.; Heck, R.

1992-02-01

430

Three-dimensional midpoint displacement algorithm for the generation of fractal porous media  

NASA Astrophysics Data System (ADS)

We propose a novel method of generating fractal three-dimensional porous media geometry. The method is an extension of the two-dimensional midpoint displacement method, used to generate realistic looking terrain for graphics applications, to a third dimension. The extended algorithm generates a three-dimensional matrix of scalars and by selecting an appropriate cut-off value to produce the porosity of the resultant media. The specific surface area of the geometry can also be controlled by adjusting the decay of the random component of the midpoint displacement. The geometries generated are fully periodic, which will help to simplify boundary conditions for future simulations. Statistical properties such as the two-point probability function and lineal-path function are calculated for the generated geometries. These properties are shown to have similar features as those of rocks which have been digitized from 2D cross sections of a physical sample. The structures generated by the proposed method do not share the blocky appearance of previous fractal based methods. This gives them a more realistic appearance similar to those produced through an image reconstruction method. In future work the geometries generated using this method will be used to link pore scale properties such as specific surface area to macroscopic permeability and storage capacity.

Jilesen, Jonathan; Kuo, Jim; Lien, Fue-Sang

2012-09-01

431

Coagulation dynamics of fractal-like soot aggregates  

Microsoft Academic Search

How the self-preserving distribution for soot aggregate size evolves as the aerosol passes through the transition regime from free molecule to diffusion limited collision dynamics is experimentally studied over the range of fractal dimension from 1.9?Df?2.5. To isolate coagulation from the nucleation and surface growth processes that normally coexist in the flame, soot from a premixed ethylene flame is rapidly

M. Matti Maricq

2007-01-01

432

Stresses and strains in a deformable fractal medium and in its fractal continuum model  

NASA Astrophysics Data System (ADS)

The model of fractal continuum accounting the topological, metric, and dynamic properties of deformable physical fractal medium is suggested. The kinematics of fractal continuum deformation is developed. The corresponding geometric interpretations are provided. The concept of stresses in the fractal continuum is defined. The conservation of linear and angular momentums is established. The mapping of mechanical problems for physical fractal media into the corresponding problems for fractal continuum is discussed.

Balankin, Alexander S.

2013-11-01

433

Modelling of ceramic matrix composite microstructure using a two-dimensional fractal spatial particle distribution  

NASA Astrophysics Data System (ADS)

Particulate composite reinforcements are good candidates for the fracture toughness of ceramics. In order to predict mechanical response of ceramic matrix composites, an efficient method capable of modelling their complex microstructure is needed. The purpose of this research is the development of such a model using fractal spatial particle distribution. A review of different toughness mechanisms for particulate composites and associated models for deriving their constitutive relationships is presented in chapter 2. These different toughening mechanisms as well constitutive properties depend on particle shape, size and spatial distribution, which lend themselves to a self-similar fractal based modelling approach. A self-similar distribution of particles linked to the fractal geometry is proposed. Fractal geometry provides an ideal tool for describing the randomness and disorder of the system. Its foundations are reviewed in chapter three with emphasis on iterated function systems that are subsequently used to obtain the particle configurations in the proposed model. For the sake of completeness, a review of fractal structure in science is given to illustrate possible applications. Derivation of the volume fraction associated with self similar distributions is provided in chapter 4. This is followed by a description of the numerical model and the boundary conditions. A Finite Element simulation is performed for different volume fractions, generators and number of particles for different displacements (two uniaxial and biaxial cases) and 2-D stress state cases. From these simulations the inverse distribution of the maximum principal stress is computed. Then the self similar models are compared with the model obtained by the Yang Teriari Gokhale (Y.T.G.) method and model obtained by only one iteration. Fractal dimension for real microstructure are computed and microstructure based on the fractal dimension and number of particle is simulated. It can be derived that the fractal dimension can be related to the average radius of circular particle in special cases. General conclusion and recommendation for future work brings this investigation to a close.

Cottet, Arnaud J.

434

Thermal collapse of snowflake fractals  

NASA Astrophysics Data System (ADS)

Snowflakes are thermodynamically unstable structures that would ultimately become ice balls. To investigate their dynamics, we mapped atomistic molecular dynamics simulations of small ice crystals - built as filled von Koch fractals - onto a discrete-time random walk model. Then the walkers explored the thermal evolution of high fractal generations. The in silico experiments showed that the evolution is not entirely random. The flakes step down one fractal generation before forfeiting their architecture. The effect may be used to trace the thermal history of snow.

Gallo, T.; Jurjiu, A.; Biscarini, F.; Volta, A.; Zerbetto, F.

2012-08-01

435

2-dimensional fractally homogeneous distribution of liquid crystalline nuclei in the isotropic melt  

NASA Astrophysics Data System (ADS)

Quenching a system below the isotropic-to-liquid-crystal phase transition, one would intuitively expect a random distribution of liquid crystal nuclei growing in the isotropic melt. By fractal dimensional analysis it is demonstrated that the germ distribution is, in fact, not completely random, but rather fractally homogeneous. The fractal dimension was determined as a function of time as the quench depth and sample dimension were varied. The results show that the germ distribution obtained after completing the short-term nucleus growth process as well as late-time coarsening, is independent of the quench depth and sample dimension, which suggest a spatial correlation of germs due to a direct interaction between nuclei.

Dierking, I.

2001-07-01

436

Chaos and Fractal Analysis of Electroencephalogram Signals during Different Imaginary Motor Movement Tasks  

NASA Astrophysics Data System (ADS)

This paper presents the novel approach to evaluate the effects of different motor activation tasks of the human electroencephalogram (EEG). The applications of chaos and fractal properties that are the most important tools in nonlinear analysis are been presented for four tasks of EEG during the real and imaginary motor movement. Three subjects, aged 23-30 years, participated in the experiment. Correlation dimension (D2), Lyapunov spectrum (?i), and Lyapunov dimension (DL) are been estimated to characterize the movement related EEG signals. Experimental results show that these nonlinear measures are good discriminators of EEG signals. There are significant differences in all conditions of subjective task. The fractal dimension appeared to be higher in movement conditions compared to the baseline condition. It is concluded that chaos and fractal analysis could be powerful methods in investigating brain activities during motor movements.

Soe, Ni Ni; Nakagawa, Masahiro

2008-04-01

437

THE EFFECT OF IONIC MIGRATION AND DIFFUSION ON THE ROUGHNESS DEVELOPMENT OF GROWING ELECTRODEPOSITS. THE USE OF FRACTALS TO COMPARE THEORY WITH EXPERIMENTAL RESULTS  

Microsoft Academic Search

Fractal geometry is used to describe (qualitatively and quantitatively) the surface roughness on electrodes as their surface morphology develops during electrodeposition. The effect of current density on copper deposits is investigated experimentally and the surface roughness of the electrodes found to increase with increasing deposition times and current density, the fractal dimension providing a good measure of this roughnessA comprehensive

S. A. GODORR; B. D. YOUNG; A. W. BRYSON

1992-01-01

438

Fractal properties of active region and flare  

NASA Astrophysics Data System (ADS)

A fractal analysis of narrowband images of the chromosphere and transition layer has been performed in order to study regimes of turbulence and their variations during time-varying processes in active regions. The NOAA 10039 and 10050 activity complexes on July 31, 2002, were observed at Baikal astrophysical observatory of ISZF SO RAN in the H-? line using a chromospheric telescope equipped with a Halle birefringent filter (BF) with a passband of 0.5 Å. Images of the same activity complexes in the spectral band centered at the FeXI 171 Å line, obtained at TRACE space observatory, have been processed using the same technique. The method of structure functions has been used to compute the time series of the scaling parameters. The power spectra of two-dimensional images have been used to compute the time variations in the fractal dimension of the considered activity complex. It has been indicated that the parameters of a multifractal structure (intermittent turbulence) demonstrate jump-like and quasiperiodic time variations correlating with flares. These variations were detected in the H-? and FeXI 171 Å lines of the transition zone, using the ground-based and onboard measurements, which demonstrates that they are of the solar origin.

Golovko, A. A.; Salakhutdinova, I. I.; Khlystova, A. I.

2009-12-01

439

Microfabricated fractal branching networks.  

PubMed

In this article, we demonstrate how a combination of engineering and biological techniques could lead to the realization of branched microstructures that can be used for the repair of damaged vascularized tissue. Recursive "treelike" networks were first generated by using fractal algorithms based on Murray's equation for vascular branching as well as allometric scaling rules. Two- and three-dimensional branching patterns with different levels of complexity were then microfabricated from poly-lactide-co-glycolide (PLGA) by using the pressure-assisted microsyringe (PAM) system developed in our laboratory. Human endothelial cells isolated from umbilical cords were seeded on the microfabricated branched scaffolds to evaluate their effectiveness in supporting site-specific cell adhesion. The results show that cell densities on the networks increase with complexity up to the sixth level and are then constant independent of branching level. The implications of this finding are discussed in terms of contact inhibition of "capillaries." PMID:15376267

Vozzi, G; Previti, A; Ciaravella, G; Ahluwalia, A

2004-11-01

440

Fractality of Hofstadter Butterfly in Specific Heat Oscillation  

Microsoft Academic Search

We calculate thermodynamical properties of the Hofstadter model using a\\u000arecently developed quantum transfer matrix method. We find intrinsic\\u000aoscillation features in specific heat that manifest the fractal structure of\\u000athe Hofstadter butterfly. We also propose experimental approaches which use\\u000aspecific heat as an access to detect the Hofstadter butterfly.

L. P. Yang; W. H. Xu; M. P. Qin; T. Xiang

2010-01-01

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