Determination of fish gender using fractal analysis of ultrasound images

DEFF Research Database (Denmark)

McEvoy, Fintan J.; Tomkiewicz, Jonna; Støttrup, Josianne

2009-01-01

The gender of cod Gadus morhua can be determined by considering the complexity in their gonadal ultrasonographic appearance. The fractal dimension (DB) can be used to describe this feature in images. B-mode gonadal ultrasound images in 32 cod, where gender was known, were collected. Fractal...... by subjective analysis alone. The mean (and standard deviation) of the fractal dimension DB for male fish was 1.554 (0.073) while for female fish it was 1.468 (0.061); the difference was statistically significant (P=0.001). The area under the ROC curve was 0.84 indicating the value of fractal analysis in gender...... result. Fractal analysis is useful for gender determination in cod. This or a similar form of analysis may have wide application in veterinary imaging as a tool for quantification of complexity in images...

Infrastructural Fractals

DEFF Research Database (Denmark)

Bruun Jensen, Casper

2007-01-01

. Instead, I outline a fractal approach to the study of space, society, and infrastructure. A fractal orientation requires a number of related conceptual reorientations. It has implications for thinking about scale and perspective, and (sociotechnical) relations, and for considering the role of the social...... and a fractal social theory....

Fractals and spectra related to fourier analysis and function spaces

CERN Document Server

Triebel, Hans

1997-01-01

Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...

Dimensional analysis, scaling and fractals

International Nuclear Information System (INIS)

Timm, L.C.; Reichardt, K.; Oliveira Santos Bacchi, O.

2004-01-01

Dimensional analysis refers to the study of the dimensions that characterize physical entities, like mass, force and energy. Classical mechanics is based on three fundamental entities, with dimensions MLT, the mass M, the length L and the time T. The combination of these entities gives rise to derived entities, like volume, speed and force, of dimensions L 3 , LT -1 , MLT -2 , respectively. In other areas of physics, four other fundamental entities are defined, among them the temperature θ and the electrical current I. The parameters that characterize physical phenomena are related among themselves by laws, in general of quantitative nature, in which they appear as measures of the considered physical entities. The measure of an entity is the result of its comparison with another one, of the same type, called unit. Maps are also drawn in scale, for example, in a scale of 1:10,000, 1 cm 2 of paper can represent 10,000 m 2 in the field. Entities that differ in scale cannot be compared in a simple way. Fractal geometry, in contrast to the Euclidean geometry, admits fractional dimensions. The term fractal is defined in Mandelbrot (1982) as coming from the Latin fractus, derived from frangere which signifies to break, to form irregular fragments. The term fractal is opposite to the term algebra (from the Arabic: jabara) which means to join, to put together the parts. For Mandelbrot, fractals are non topologic objects, that is, objects which have as their dimension a real, non integer number, which exceeds the topologic dimension. For the topologic objects, or Euclidean forms, the dimension is an integer (0 for the point, 1 for a line, 2 for a surface, and 3 for a volume). The fractal dimension of Mandelbrot is a measure of the degree of irregularity of the object under consideration. It is related to the speed by which the estimate of the measure of an object increases as the measurement scale decreases. An object normally taken as uni-dimensional, like a piece of a

Fractal Analysis of Rock Joint Profiles

Science.gov (United States)

Audy, Ondřej; Ficker, Tomáš

2017-10-01

Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.

Pulmonary vasculature in dogs assessed by three-dimensional fractal analysis and chemometrics

DEFF Research Database (Denmark)

Müller, Anna V; Marschner, Clara B; Kristensen, Annemarie T

2017-01-01

Fractal analysis of canine pulmonary vessels could allow quantification of their space-filling properties. Aims of this prospective, analytical, cross-sectional study were to describe methods for reconstructing three dimensional pulmonary arterial vascular trees from computed tomographic pulmonary...... angiogram, applying fractal analyses of these vascular trees in dogs with and without diseases that are known to predispose to thromboembolism, and testing the hypothesis that diseased dogs would have a different fractal dimension than healthy dogs. A total of 34 dogs were sampled. Based on computed...... for each dog using a semiautomated segmentation technique. Vascular three-dimensional reconstructions were then evaluated using fractal analysis. Fractal dimensions were analyzed, by group, using analysis of variance and principal component analysis. Fractal dimensions were significantly different among...

Characterisation of human non-proliferativediabetic retinopathy using the fractal analysis

Directory of Open Access Journals (Sweden)

Carmen Alina Lupaşcu

2015-08-01

Full Text Available AIM:To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method.METHODS:This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images and pathological (148 images states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software.RESULTS:It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions is slightly lower than the corresponding values of mild non-proliferative DR (NPDR images (segmented and skeletonized versions. The average of fractal dimensions D for the normal images (segmented and skeletonized versions is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions. The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions.CONCLUSION:The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with

Fractal vector optical fields.

Science.gov (United States)

Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2016-07-15

We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

Fractals: Giant impurity nonlinearities in optics of fractal clusters

International Nuclear Information System (INIS)

Butenko, A.V.; Shalaev, V.M.; Stockman, M.I.

1988-01-01

A theory of nonlinear optical properties of fractals is developed. Giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal. This enhancement occurs if the exciting radiation frequency lies within the absorption band of the fractal. The giant optical nonlinearities are due to existence of high local electric fields in the sites of impurity locations. Such fields are due to the inhomogeneously broadened character of a fractal spectrum, i.e. partial conservation of individuality of fractal-forming particles (monomers). The field enhancement is proportional to the Q-factor of the resonance of a monomer. The effects of coherent anti-Stokes Raman scattering (CARS) and phase conjugation (PC) of light waves are enhanced to a much greater degree than generation of higher harmonics. In a general case the susceptibility of a higher-order is enhanced in the maximum way if the process includes ''subtraction'' of photons (at least one of the strong field frequencies enters the susceptibility with the minus sign). Alternatively, enhancement for the highest-order harmonic generation (when all the photons are ''accumulated'') is minimal. The predicted phenomena bear information on spectral properties of both impurity molecules and a fractal. In particular, in the CARS spectra a narrow (with the natural width) resonant structure, which is proper to an isolated monomer of a fractal, is predicted to be observed. (orig.)

Fractal Dimension Analysis of Texture Formation of Whey Protein-Based Foods

Directory of Open Access Journals (Sweden)

Robi Andoyo

2018-01-01

Full Text Available Whey protein in the form of isolate or concentrate is widely used in food industries due to its functionality to form gel under certain condition and its nutritive value. Controlling or manipulating the formation of gel aggregates is used often to evaluate food texture. Many researchers made use of fractal analysis that provides the quantitative data (i.e., fractal dimension for fundamentally and rationally analyzing and designing whey protein-based food texture. This quantitative analysis is also done to better understand how the texture of whey protein-based food is formed. Two methods for fractal analysis were discussed in this review: image analysis (microscopy and rheology. These methods, however, have several limitations which greatly affect the accuracy of both fractal dimension values and types of aggregation obtained. This review therefore also discussed problem encountered and ways to reduce the potential errors during fractal analysis of each method.

Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.

Science.gov (United States)

Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K

2014-08-01

Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.

Assessment of Textural Differentiations in Forest Resources in Romania Using Fractal Analysis

Directory of Open Access Journals (Sweden)

Ion Andronache

2017-02-01

Full Text Available Deforestation and forest degradation have several negative effects on the environment including a loss of species habitats, disturbance of the water cycle and reduced ability to retain CO2, with consequences for global warming. We investigated the evolution of forest resources from development regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis. We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested and compact organization in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters. Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby enabling quantification of the uniformity, fragmentation, heterogeneity and homogeneity of forests.

Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

Science.gov (United States)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

Fractal differential equations and fractal-time dynamical systems

Indian Academy of Sciences (India)

like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation ... involving scaling and memory effects. But most of ..... begin by recalling the definition of the Riemann integral in ordinary calculus [33]. Let g: [a ...

Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review

Energy Technology Data Exchange (ETDEWEB)

Michallek, Florian; Dewey, Marc [Humboldt-Universitaet zu Berlin, Freie Universitaet Berlin, Charite - Universitaetsmedizin Berlin, Medical School, Department of Radiology, Berlin (Germany)

2014-01-15

To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)

Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review

International Nuclear Information System (INIS)

Michallek, Florian; Dewey, Marc

2014-01-01

To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)

Insulator Contamination Forecasting Based on Fractal Analysis of Leakage Current

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Bing Luo

2012-07-01

Full Text Available In this paper, an artificial pollution test is carried out to study the leakage current of porcelain insulators. Fractal theory is adopted to extract the characteristics hidden in leakage current waveforms. Fractal dimensions of the leakage current for the security, forecast and danger zones are analyzed under four types of degrees of contamination. The mean value and the standard deviation of the fractal dimension in the forecast zone are calculated to characterize the differences. The analysis reveals large differences in the fractal dimension of leakage current under different contamination discharge stages and degrees. The experimental and calculation results suggest that the fractal dimension of a leakage current waveform can be used as a new indicator of the discharge process and contamination degree of insulators. The results provide new methods and valid indicators for forecasting contamination flashovers.

Conference on Fractals and Related Fields III

CERN Document Server

Seuret, Stéphane

2017-01-01

This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

Fractal analysis of cervical intraepithelial neoplasia.

Directory of Open Access Journals (Sweden)

Markus Fabrizii

Full Text Available INTRODUCTION: Cervical intraepithelial neoplasias (CIN represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. METHODS: Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods. RESULTS: Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. CONCLUSION: Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.

Fractal analysis of bone architecture at distal radius

International Nuclear Information System (INIS)

Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Sone, Teruki; Fukunaga, Masao

2005-01-01

Bone strength depends on bone quality (architecture, turnover, damage accumulation, and mineralization) as well as bone mass. In this study, human bone architecture was analyzed using fractal image analysis, and the clinical relevance of this method was evaluated. The subjects were 12 healthy female controls and 16 female patients suspected of having osteoporosis (age range, 22-70 years; mean age, 49.1 years). High-resolution CT images of the distal radius were acquired and analyzed using a peripheral quantitative computed tomography (pQCT) system. On the same day, bone mineral densities of the lumbar spine (L-BMD), proximal femur (F-BMD), and distal radius (R-BMD) were measured by dual-energy X-ray absorptiometry (DXA). We examined the correlation between the fractal dimension and six bone mass indices. Subjects diagnosed with osteopenia or osteoporosis were divided into two groups (with and without vertebral fracture), and we compared measured values between these two groups. The fractal dimension correlated most closely with L-BMD (r=0.744). The coefficient of correlation between the fractal dimension and L-BMD was very similar to the coefficient of correlation between L-BMD and F-BMD (r=0.783) and the coefficient of correlation between L-BMD and R-BMD (r=0.742). The fractal dimension was the only measured value that differed significantly between both the osteopenic and the osteoporotic subjects with and without vertebral fracture. The present results suggest that the fractal dimension of the distal radius can be reliably used as a bone strength index that reflects bone architecture as well as bone mass. (author)

Electromagnetic fields in fractal continua

Energy Technology Data Exchange (ETDEWEB)

Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Mena, Baltasar [Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F. (Mexico); Patiño, Julián [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Morales, Daniel [Instituto Mexicano del Petróleo, México D.F., 07730 Mexico (Mexico)

2013-04-01

Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum Φ{sub D}{sup 3}⊂E{sup 3} 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{sup α} 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.

Comparison of two fractal interpolation methods

Science.gov (United States)

Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo

2017-03-01

As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has

Fractal analysis of rainfall occurrence observed in the synoptic ...

African Journals Online (AJOL)

Fractal analysis is important for characterizing and modeling rainfall's space-time variations in hydrology. The purpose of this study consists on determining, in a mono-fractal framework, the scale invariance of rainfall series in Benin synopticstations located in two main geographical area: Cotonou, Bohicon , Savè in a sub ...

Passenger flow analysis of Beijing urban rail transit network using fractal approach

Science.gov (United States)

Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia

2018-04-01

To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.

Fractal Metrology for biogeosystems analysis

Directory of Open Access Journals (Sweden)

V. Torres-Argüelles

2010-11-01

Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.

Fractals everywhere

CERN Document Server

Barnsley, Michael F

2012-01-01

""Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs."" - Alan E. Wessel, Santa Clara University""The style of writing is technically excellent, informative, and entertaining."" - Robert McCartyThis new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of

Pre-Service Teachers' Concept Images on Fractal Dimension

Science.gov (United States)

Karakus, Fatih

2016-01-01

The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…

Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects

Science.gov (United States)

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

2013-04-01

This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to

Fractal apertures in waveguides, conducting screens and cavities analysis and design

CERN Document Server

Ghosh, Basudeb; Kartikeyan, M V

2014-01-01

This book deals with the design and analysis of fractal apertures in waveguides, conducting screens and cavities using numerical electromagnetics and field-solvers. The aim is to obtain design solutions with improved accuracy for a wide range of applications. To achieve this goal, a few diverse problems are considered. The book is organized with adequate space dedicated for the design and analysis of fractal apertures in waveguides, conducting screens, and cavities, microwave/millimeter wave applications followed by detailed case-study problems to infuse better insight and understanding of the subject. Finally, summaries and suggestions are given for future work. Fractal geometries were widely used in electromagnetics, specifically for antennas and frequency selective surfaces (FSS). The self-similarity of fractal geometry gives rise to a multiband response, whereas the  space-filling nature of the fractal geometries makes it an efficient element in antenna and FSS unit cell miniaturization. Until now, no e...

A fractal analysis of the public transportation system of Paris

OpenAIRE

L Benguigui

1995-01-01

An analysis of the railway networks of the public transportation system of Paris, based on the notion of fractals, is presented. The two basic networks, (metropolitan and suburban) which have different functions, have also a different fractal dimension: 1.8 for the metropolitan network, and 1.5 for the suburban network. By means of computer simulation, it is concluded that the true dimension of the metro network is probably 2.0. A fractal model of the suburban network, with the same features ...

Steady laminar flow of fractal fluids

Energy Technology Data Exchange (ETDEWEB)

Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)

2017-02-12

We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.

Design of LTCC Based Fractal Antenna

KAUST Repository

AdbulGhaffar, Farhan

2010-09-01

The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.

THE FRACTAL MARKET HYPOTHESIS

Directory of Open Access Journals (Sweden)

FELICIA RAMONA BIRAU

2012-05-01

Full Text Available In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and of course, the manner in which they interpret that information may be different. Also, Fractal Market Hypothesis refers to the way that liquidity and investment horizons influence the behaviour of financial investors.

THE FRACTAL MARKET HYPOTHESIS

OpenAIRE

FELICIA RAMONA BIRAU

2012-01-01

In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and...

An enhanced fractal image denoising algorithm

International Nuclear Information System (INIS)

Lu Jian; Ye Zhongxing; Zou Yuru; Ye Ruisong

2008-01-01

In recent years, there has been a significant development in image denoising using fractal-based method. This paper presents an enhanced fractal predictive denoising algorithm for denoising the images corrupted by an additive white Gaussian noise (AWGN) by using quadratic gray-level function. Meanwhile, a quantization method for the fractal gray-level coefficients of the quadratic function is proposed to strictly guarantee the contractivity requirement of the enhanced fractal coding, and in terms of the quality of the fractal representation measured by PSNR, the enhanced fractal image coding using quadratic gray-level function generally performs better than the standard fractal coding using linear gray-level function. Based on this enhanced fractal coding, the enhanced fractal image denoising is implemented by estimating the fractal gray-level coefficients of the quadratic function of the noiseless image from its noisy observation. Experimental results show that, compared with other standard fractal-based image denoising schemes using linear gray-level function, the enhanced fractal denoising algorithm can improve the quality of the restored image efficiently

Fractal analytical approach of urban form based on spatial correlation function

International Nuclear Information System (INIS)

Chen, Yanguang

2013-01-01

Highlights: ► Many fractal parameter relations of cities can be derived by scaling analysis. ► The area-radius scaling of cities suggests a spatial correlation function. ► Spectral analysis can be used to estimate fractal dimension values of urban form. ► The valid range of fractal dimension of urban form comes between 1.5 and 2. ► The traditional scale concept will be replaced by scaling concept in geography. -- Abstract: Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning

Fractal Analysis of Stealthy Pathfinding Aesthetics

Directory of Open Access Journals (Sweden)

Ron Coleman

2009-01-01

Full Text Available This paper uses a fractal model to analyze aesthetic values of a new class of obstacle-prone or “stealthy” pathfinding which seeks to avoid detection, exposure, openness, and so forth in videogames. This study is important since in general the artificial intelligence literature has given relatively little attention to aesthetic outcomes in pathfinding. The data we report, according to the fractal model, suggests that stealthy paths are statistically significantly unique in relative aesthetic value when compared to control paths. We show furthermore that paths generated with different stealth regimes are also statistically significantly unique. These conclusions are supported by statistical analysis of model results on experimental trials involving pathfinding in randomly generated, multiroom virtual worlds.

Fractal characteristics of an asphaltene deposited heterogeneous surface

International Nuclear Information System (INIS)

Amin, J. Sayyad; Ayatollahi, Sh.; Alamdari, A.

2009-01-01

Several methods have been employed in recent years to investigate homogeneous surface topography based on image analysis, such as AFM (atomic force microscopy) and SEM (scanning electron microscopy). Fractal analysis of the images provides fractal dimension of the surface which is used as one of the most common surface indices. Surface topography has generally been considered to be mono-fractal. On the other hand, precipitation of organic materials on a rough surface and its irregular growth result in morphology alteration and converts a homogeneous surface to a heterogeneous one. In this case a mono-fractal description of the surface does not completely describe the nature of the altered surface. This work aims to investigate the topography alteration of a glass surface as a result of asphaltene precipitation and its growth at various pressures using a bi-fractal approach. The experimental results of the deposited surfaces were clearly indicating two regions of micro- and macro-asperities namely, surface types I and II, respectively. The fractal plots were indicative of bi-fractal behavior and for each surface type one fractal dimension was calculated. The topography information of the surfaces was obtained by two image analyses, AFM and SEM imaging techniques. Results of the bi-fractal analysis demonstrated that topography alteration in surface type II (macro-asperities) is more evident than that in surface type I (micro-asperities). Compared to surface type II, a better correlation was observed between the fractal dimensions inferred from the AFM images (D A ) and those of the SEM images (D S ) in surface type I.

Fractal analysis of polar bear hairs

Directory of Open Access Journals (Sweden)

Wang Qing-Li

2015-01-01

Full Text Available Hairs of a polar bear (Ursus maritimus are of superior properties such as the excellent thermal protection. Why do polar bears can resist such cold environment? The paper concludes that its fractal porosity plays an important role, and its fractal dimensions are very close to the golden mean, 1.618, revealing the possible optimal structure of polar bear hair.

Bony change of apical lesion healing process using fractal analysis

Energy Technology Data Exchange (ETDEWEB)

Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo [Yonsei University College of Medicine, Seoul (Korea, Republic of)

2005-06-15

To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L{sub 0}) is 0.940 {+-} 0.361 and that of normal area (N{sub 0}) is 1.186 {+-} 0.727 (p<0.05). Fractal dimension at apical lesion of 6 months after endodontic treatment (L{sub 1}) is 1.076 {+-} 0.069 and that of normal area (N{sub 1}) is 1.192 {+-} 0.055 (p<0.05). Fractal dimension at apical lesion of 1 year after endodontic treatment (L{sub 2}) is 1.163 {+-} 0.074 and that of normal area (N{sub 2}) is 1.225 {+-} 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.

Fractal structures and fractal functions as disease indicators

Science.gov (United States)

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

1995-01-01

Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.

Fractal analysis for heat extraction in geothermal system

Directory of Open Access Journals (Sweden)

Shang Xiaoji

2017-01-01

Full Text Available Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy’s velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.

Fractal description of fractures

International Nuclear Information System (INIS)

Lung, C.W.

1991-06-01

Recent studies on the fractal description of fractures are reviewed. Some problems on this subject are discussed. It seems hopeful to use the fractal dimension as a parameter for quantitative fractography and to apply fractal structures to the development of high toughness materials. (author). 28 refs, 7 figs

Fractals and foods.

Science.gov (United States)

Peleg, M

1993-01-01

Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.

Fractal dust grains in plasma

International Nuclear Information System (INIS)

Huang, F.; Peng, R. D.; Liu, Y. H.; Chen, Z. Y.; Ye, M. F.; Wang, L.

2012-01-01

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

A fractal-based image encryption system

KAUST Repository

Abd-El-Hafiz, S. K.; Radwan, Ahmed Gomaa; Abdel Haleem, Sherif H.; Barakat, Mohamed L.

2014-01-01

single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved

Fractal analysis of Xylella fastidiosa biofilm formation

Science.gov (United States)

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

2009-07-01

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.

Evaluation of peri-implant bone using fractal analysis

International Nuclear Information System (INIS)

Jung, Yun Hoa

2005-01-01

The purpose of this study was to investigate whether the fractal dimension of successive panoramic radiographs of bone after implant placement is useful in the characterization of structural change in alveolar bone. Twelve subjects with thirty-five implants were retrospectively followed-up from one week to six months after implantation. Thirty-six panoramic radiographs from twelve patients were classified into 1 week. 1-2 months and 3-6 months after implantation and digitized. The windows of bone apical and mesial or distal to the implant were defined as peri apical region of interest (ROI) and inter dental ROI; the fractal dimension of the image was calculated. There was not a statistically significant difference in fractal dimensions during the period up to 6 months after implantation. The fractal dimensions were higher in 13 and 15 mm than 10 and 11.5 mm implant length at inter dental ROIs in 3-6 months after implantation (p<0.01). Longer fixtures showed the higher fractal dimension of bone around implant. This investigation needs further exploration with large numbers of implants for longer follow-up periods.

Fractal nature of hydrocarbon deposits. 2. Spatial distribution

International Nuclear Information System (INIS)

Barton, C.C.; Schutter, T.A; Herring, P.R.; Thomas, W.J.; Scholz, C.H.

1991-01-01

Hydrocarbons are unevenly distributed within reservoirs and are found in patches whose size distribution is a fractal over a wide range of scales. The spatial distribution of the patches is also fractal and this can be used to constrain the design of drilling strategies also defined by a fractal dimension. Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. The authors have performed fractal analyses on the spatial distribution of producing and showing wells combined and of dry wells in 1,600-mi 2 portions of the Denver and Powder River basins that were nearly completely drilled on quarter-mile square-grid spacings. They have limited their analyses to wells drilled to single stratigraphic intervals so that the map pattern revealed by drilling is representative of the spatial patchiness of hydrocarbons at depth. The fractal dimensions for the spatial patchiness of hydrocarbons in the two basins are 1.5 and 1.4, respectively. The fractal dimension for the pattern of all wells drilled is 1.8 for both basins, which suggests a drilling strategy with a fractal dimension significantly higher than the dimensions 1.5 and 1.4 sufficient to efficiently and economically explore these reservoirs. In fact, the fractal analysis reveals that the drilling strategy used in these basins approaches a fractal dimension of 2.0, which is equivalent to random drilling with no geologic input. Knowledge of the fractal dimension of a reservoir prior to drilling would provide a basis for selecting and a criterion for halting a drilling strategy for exploration whose fractal dimension closely matches that of the spatial fractal dimension of the reservoir, such a strategy should prove more efficient and economical than current practice

Discovery of cosmic fractals

CERN Document Server

Baryshev, Yuri

2002-01-01

This is the first book to present the fascinating new results on the largest fractal structures in the universe. It guides the reader, in a simple way, to the frontiers of astronomy, explaining how fractals appear in cosmic physics, from our solar system to the megafractals in deep space. It also offers a personal view of the history of the idea of self-similarity and of cosmological principles, from Plato's ideal architecture of the heavens to Mandelbrot's fractals in the modern physical cosmos. In addition, this invaluable book presents the great fractal debate in astronomy (after Luciano Pi

Fractals in Power Reactor Noise

International Nuclear Information System (INIS)

Aguilar Martinez, O.

1994-01-01

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 signals from random neutron noise signals and processing for diagnosis purposes. The advantages of a fractal analysis approach in the power reactor noise are commented in details

Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions

CERN Document Server

Lapidus, Michel L; Žubrinić, Darko

2017-01-01

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the f...

Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions

CERN Document Server

Lapidus, Michael L

1999-01-01

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo­ metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di­ mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref­ erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap­ pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...

Quantitative evaluation of fluctuation error in X-ray diffraction profiles with fractal analysis

International Nuclear Information System (INIS)

Kurose, Masashi; Hirose, Yukio; Sasaki, Toshihiko; Yoshioka, Yasuo.

1995-01-01

A method of the fractal analysis was applied to the diffraction profiles for its quantitative evaluation. The fractal dimension was analyzed according to both Box counting method and FFT method. The relationship between the fractal dimension and the measurement criteria in X-ray diffraction analysis was discussed with diffraction data obtained under various conditions of the measurement. It was concluded that the fractal analysis is effective for the quantitative evaluation of diffraction data. Box counting method is suitable for evaluation of a whole profile, and FFT method is for that of a fundamental profile. The range of desirable condition of measurement is 1.0≤D≤1.2, where D is a fractal dimension. The appropriate range of measurement becomes 0.01≤Sw/HVB≤0.03, where Sw is the step width and the HVB is the half-value breadth. Stresses with higher precision were obtained from measurements under this new criteria. (author)

Fractal Characteristics Analysis of Blackouts in Interconnected Power Grid

DEFF Research Database (Denmark)

Wang, Feng; Li, Lijuan; Li, Canbing

2018-01-01

The power failure models are a key to understand the mechanism of large scale blackouts. In this letter, the similarity of blackouts in interconnected power grids (IPGs) and their sub-grids is discovered by the fractal characteristics analysis to simplify the failure models of the IPG. The distri......The power failure models are a key to understand the mechanism of large scale blackouts. In this letter, the similarity of blackouts in interconnected power grids (IPGs) and their sub-grids is discovered by the fractal characteristics analysis to simplify the failure models of the IPG....... The distribution characteristics of blackouts in various sub-grids are demonstrated based on the Kolmogorov-Smirnov (KS) test. The fractal dimensions (FDs) of the IPG and its sub-grids are then obtained by using the KS test and the maximum likelihood estimation (MLE). The blackouts data in China were used...

Quantum Fractal Eigenstates

OpenAIRE

Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L.

1997-01-01

We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.

Electromagnetism on anisotropic fractal media

Science.gov (United States)

Ostoja-Starzewski, Martin

2013-04-01

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.

Inkjet-Printed Ultra Wide Band Fractal Antennas

KAUST Repository

Maza, Armando Rodriguez

2012-05-01

In this work, Paper-based inkjet-printed Ultra-wide band (UWB) fractal antennas are presented. Three new designs, a combined UWB fractal monopole based on the fourth order Koch Snowflake fractal which utilizes a Sierpinski Gasket fractal for ink reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics. It is shown that fractals prove to be a successful method of reducing fabrication cost in inkjet printed antennas while retaining or enhancing printed antenna performance.

Fractal-Based Analysis of the Influence of Music on Human Respiration

Science.gov (United States)

Reza Namazi, H.

An important challenge in respiration related studies is to investigate the influence of external stimuli on human respiration. Auditory stimulus is an important type of stimuli that influences human respiration. However, no one discovered any trend, which relates the characteristics of the auditory stimuli to the characteristics of the respiratory signal. In this paper, we investigate the correlation between auditory stimuli and respiratory signal from fractal point of view. We found out that the fractal structure of respiratory signal is correlated with the fractal structure of the applied music. Based on the obtained results, the music with greater fractal dimension will result in respiratory signal with smaller fractal dimension. In order to verify this result, we benefit from approximate entropy. The results show the respiratory signal will have smaller approximate entropy by choosing the music with smaller approximate entropy. The method of analysis could be further investigated to analyze the variations of different physiological time series due to the various types of stimuli when the complexity is the main concern.

Random walk through fractal environments

OpenAIRE

Isliker, H.; Vlahos, L.

2002-01-01

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...

Fractals in several electrode materials

Energy Technology Data Exchange (ETDEWEB)

Zhang, Chunyong, E-mail: zhangchy@njau.edu.cn [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); Wu, Jingyu [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Fu, Degang [Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); State Key Laboratory of Bioelectronics, Southeast University, Nanjing 210096 (China)

2014-09-15

Highlights: • Fractal geometry was employed to characterize three important electrode materials. • The surfaces of all studied electrodes were proved to be very rough. • The fractal dimensions of BDD and ACF were scale dependent. • MMO film was more uniform than BDD and ACF in terms of fractal structures. - Abstract: In the present paper, the fractal properties of boron-doped diamond (BDD), mixed metal oxide (MMO) and activated carbon fiber (ACF) electrode have been studied by SEM imaging at different scales. Three materials are self-similar with mean fractal dimension in the range of 2.6–2.8, confirming that they all exhibit very rough surfaces. Specifically, it is found that MMO film is more uniform in terms of fractal structure than BDD and ACF. As a result, the intriguing characteristics make these electrodes as ideal candidates for high-performance decontamination processes.

Fractals via iterated functions and multifunctions

International Nuclear Information System (INIS)

Singh, S.L.; Prasad, Bhagwati; Kumar, Ashish

2009-01-01

Fractals have wide applications in biology, computer graphics, quantum physics and several other areas of applied sciences (see, for instance [Daya Sagar BS, Rangarajan Govindan, Veneziano Daniele. Preface - fractals in geophysics. Chaos, Solitons and Fractals 2004;19:237-39; El Naschie MS. Young double-split experiment Heisenberg uncertainty principles and cantorian space-time. Chaos, Solitons and Fractals 1994;4(3):403-09; El Naschie MS. Quantum measurement, information, diffusion and cantorian geodesics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 191-205; El Naschie MS. Iterated function systems, information and the two-slit experiment of quantum mechanics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 185-9; El Naschie MS, Rossler OE, Prigogine I. Forward. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995; El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 2004;19:209-36; El Naschie MS. Fractal black holes and information. Chaos, Solitons and Fractals 2006;29:23-35; El Naschie MS. Superstring theory: what it cannot do but E-infinity could. Chaos, Solitons and Fractals 2006;29:65-8). Especially, the study of iterated functions has been found very useful in the theory of black holes, two-slit experiment in quantum mechanics (cf. El Naschie, as mentioned above). The intent of this paper is to give a brief account of recent developments of fractals arising from IFS. We also discuss iterated multifunctions.

Vibration modes of 3n-gaskets and other fractals

Energy Technology Data Exchange (ETDEWEB)

Bajorin, N; Chen, T; Dagan, A; Emmons, C; Hussein, M; Khalil, M; Mody, P; Steinhurst, B; Teplyaev, A [Department of Mathematics, University of Connecticut, Storrs CT 06269 (United States)

2008-01-11

We rigorously study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals, which include the Sierpinski gasket and other 3n-gaskets. We consider the classical Laplacian on fractals which generalizes the usual one-dimensional second derivative, is the generator of the self-similar diffusion process, and has possible applications as the quantum Hamiltonian. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations. Our analysis, in particular, allows the computation of the spectral zeta function on fractals and the limiting distribution of eigenvalues (i.e., integrated density of states). We consider such examples as the level-3 Sierpinski gasket, a fractal 3-tree, and the diamond fractal.

Fractal Electrochemical Microsupercapacitors

KAUST Repository

Hota, Mrinal Kanti

2017-08-17

The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.

Fractal Electrochemical Microsupercapacitors

KAUST Repository

Hota, Mrinal Kanti; Jiang, Qiu; Mashraei, Yousof; Salama, Khaled N.; Alshareef, Husam N.

2017-01-01

The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.

FRACTAL ANALYSIS OF PHYSICAL ADSORPTION ON SURFACES OF ACID ACTIVATED BENTONITES FROM SERBIA

Directory of Open Access Journals (Sweden)

Ljiljana Rožić

2008-11-01

Full Text Available Solid surfaces are neither ideally regular, that is, morphological and energeticcally homogeneous, nor are they fully irregular or fractal. Instead, real solid surfaces exhibit a limited degree of organization quantified by the fractal dimension, D. Fractal analysis was applied to investigate the effect of concentrations of HCl solutions on the structural and textural properties of chemically activated bentonite from southern Serbia. Acid treatment of bentonites is applied in order to remove impurities and various exchangeable cations from bentonite clay. Important physical changes in acid-activated smectite are the increase of the specific surface area and of the average pore volume, depending on acid strength, time and temperature of a treatment. On the basis of the sorption-structure analysis, the fractal dimension of the bentonite surfaces was determined by Mahnke and Mögel method. The fractal dimension evaluated by this method was 2.11 for the AB3 and 1.94 for the AB4.5 sample. The estimation of the values of the fractal dimension of activated bentonites was performed in the region of small pores, 0.5 nm < rp < 2 nm.

A TUTORIAL INTRODUCTION TO ADAPTIVE FRACTAL ANALYSIS

Directory of Open Access Journals (Sweden)

Michael A Riley

2012-09-01

Full Text Available The authors present a tutorial description of adaptive fractal analysis (AFA. AFA utilizes an adaptive detrending algorithm to extract globally smooth trend signals from the data and then analyzes the scaling of the residuals to the fit as a function of the time scale at which the fit is computed. The authors present applications to synthetic mathematical signals to verify the accuracy of AFA and demonstrate the basic steps of the analysis. The authors then present results from applying AFA to time series from a cognitive psychology experiment on repeated estimation of durations of time to illustrate some of the complexities of real-world data. AFA shows promise in dealing with many types of signals, but like any fractal analysis method there are special challenges and considerations to take into account, such as determining the presence of linear scaling regions.

Fractals and chaos

CERN Document Server

Earnshow, R; Jones, H

1991-01-01

This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...

Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study

Science.gov (United States)

Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana

2016-04-01

The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with

The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal

Science.gov (United States)

Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin

2016-05-01

One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.

Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales

Science.gov (United States)

Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei

2017-11-01

Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

Order-fractal transitions in abstract paintings

Energy Technology Data Exchange (ETDEWEB)

Calleja, E.M. de la, E-mail: elsama79@gmail.com [Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS (Brazil); Cervantes, F. [Department of Applied Physics, CINVESTAV-IPN, Carr. Antigua a Progreso km.6, Cordemex, C.P.97310, Mérida, Yucatán (Mexico); Calleja, J. de la [Department of Informatics, Universidad Politécnica de Puebla, 72640 (Mexico)

2016-08-15

In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.

International Conference on Advances of Fractals and Related Topics

CERN Document Server

Lau, Ka-Sing

2014-01-01

This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.   

Positron annihilation near fractal surfaces

International Nuclear Information System (INIS)

Lung, C.W.; Deng, K.M.; Xiong, L.Y.

1991-07-01

A model for positron annihilation in the sub-surface region near a fractal surface is proposed. It is found that the power law relationship between the mean positron implantation depth and incident positron energy can be used to measure the fractal dimension of the fractal surface in materials. (author). 10 refs, 2 figs

Bony change of apical lesion healing process using fractal analysis

International Nuclear Information System (INIS)

Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo

2005-01-01

To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L 0 ) is 0.940 ± 0.361 and that of normal area (N 0 ) is 1.186 ± 0.727 (p 1 ) is 1.076 ± 0.069 and that of normal area (N 1 ) is 1.192 ± 0.055 (p 2 ) is 1.163 ± 0.074 and that of normal area (N 2 ) is 1.225 ± 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.

Fractal-based exponential distribution of urban density and self-affine fractal forms of cities

International Nuclear Information System (INIS)

Chen Yanguang; Feng Jian

2012-01-01

Highlights: ► The model of urban population density differs from the common exponential function. ► Fractal landscape influences the exponential distribution of urban density. ► The exponential distribution of urban population suggests a self-affine fractal. ► Urban space can be divided into three layers with scaling and non-scaling regions. ► The dimension of urban form with characteristic scale can be treated as 2. - Abstract: Urban population density always follows the exponential distribution and can be described with Clark’s model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark’s model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark’s model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.

Fractal Dimension analysis for seismicity spatial and temporal ...

Indian Academy of Sciences (India)

23

The research can further promote the application of fractal theory in the study ... spatial-temporal propagation characteristics of seismic activities, fractal theory is not ... provide a theoretical basis for the prevention and control of earthquakes. 2. ... random self-similar structure of the earthquake in the time series and the spatial.

Multirate diversity strategy of fractal modulation

International Nuclear Information System (INIS)

Yuan Yong; Shi Si-Hong; Luo Mao-Kang

2011-01-01

Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters are unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment. (general)

Encounters with chaos and fractals

CERN Document Server

Gulick, Denny

2012-01-01

Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.

Investigation into How 8th Grade Students Define Fractals

Science.gov (United States)

Karakus, Fatih

2015-01-01

The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

Fractal Structures For Fixed Mems Capacitors

KAUST Repository

Elshurafa, Amro M.

2014-08-28

An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.

Enhanced Graphene Photodetector with Fractal Metasurface

DEFF Research Database (Denmark)

Fan, Jieran; Wang, Di; DeVault, Clayton

2016-01-01

We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure.......We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure....

Fractal Structures For Fixed Mems Capacitors

KAUST Repository

Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.

2014-01-01

An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.

Psicodiagnóstico fractal

OpenAIRE

Moghilevsky, Débora Estela

2011-01-01

A lo largo de los últimos años del siglo veinte se ha desarrollado la teoría de la complejidad. Este modelo relaciona las ciencias duras tales como la matemática, la teoría del caos, la física cuántica y la geometría fractal con las llamadas seudo ciencias. Dentro de este contexto podemos definir la Psicología Fractal como la ciencia que estudia los aspectos psíquicos como dinámicamente fractales.

A transfer matrix method for the analysis of fractal quantum potentials

International Nuclear Information System (INIS)

Monsoriu, Juan A; Villatoro, Francisco R; Marin, Maria J; UrchueguIa, Javier F; Cordoba, Pedro Fernandez de

2005-01-01

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 distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function

A transfer matrix method for the analysis of fractal quantum potentials

Energy Technology Data Exchange (ETDEWEB)

Monsoriu, Juan A [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Villatoro, Francisco R [Departamento de Lenguajes y Ciencias de la Computacion, Universidad de Malaga, E-29071 Malaga (Spain); Marin, Maria J [Departamento de Termodinamica, Universitat de Valencia, E-46100 Burjassot (Spain); UrchueguIa, Javier F [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Cordoba, Pedro Fernandez de [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain)

2005-07-01

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 distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function.

Shower fractal dimension analysis in a highly-granular calorimeter

CERN Document Server

Ruan, M

2014-01-01

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

2-D Fractal Carpet Antenna Design and Performance

Science.gov (United States)

Barton, C. C.; Tebbens, S. F.; Ewing, J. J.; Peterman, D. J.; Rizki, M. M.

2017-12-01

A 2-D fractal carpet antenna uses a fractal (self-similar) pattern to increase its perimeter by iteration and can receive or transmit electromagnetic radiation within its perimeter-bounded surface area. 2-D fractals are shapes that, at their mathematical limit (infinite iterations) have an infinite perimeter bounding a finite surface area. The fractal dimension describes the degree of space filling and lacunarity which quantifies the size and spatial distribution of open space bounded by a fractal shape. A key aspect of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that are very compact, wideband and multiband. As the number of iterations increases, the antenna operates at higher and higher frequencies. Manifestly different from traditional antenna designs, a fractal antenna can operate at multiple frequencies simultaneously. We have created a MATLAB code to generate deterministic and stochastic modes of Sierpinski carpet fractal antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, number of iterations, and lacunarities have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance

Constructing and applying the fractal pied de poule (houndstooth)

NARCIS (Netherlands)

Feijs, L.M.G.; Toeters, M.J.; Hart, G.; Sarhangi, R.

2013-01-01

Time is ready for a fractal version of pied de poule; it is almost "in the air". Taking inspiration from the Cantor set, and using the analysis of the classical pattern, we obtain a family of elegant new fractal Pied de Poules. We calculate the fractal dimension and develop an attractive fashion

2-D Fractal Wire Antenna Design and Performance

Science.gov (United States)

Tebbens, S. F.; Barton, C. C.; Peterman, D. J.; Ewing, J. J.; Abbott, C. S.; Rizki, M. M.

2017-12-01

A 2-D fractal wire antenna uses a fractal (self-similar) pattern to increase its length by iteration and can receive or transmit electromagnetic radiation. 2-D fractals are shapes that, at their mathematical limit (of infinite iterations) have an infinite length. The fractal dimension describes the degree of space filling. A fundamental property of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that can be very compact, wideband and multiband. As the number of iterations increases, the antenna tends to have additional frequencies that minimize far field return loss. This differs from traditional antenna designs in that a single fractal antenna can operate well at multiple frequencies. We have created a MATLAB code to generate deterministic and stochastic modes of fractal wire antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, and number of iterations have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance.

Bouguer correction density determination from fractal analysis using ...

African Journals Online (AJOL)

In this work, Bouguer density is determined using the fractal approach. This technique was applied to the gravity data of the Kwello area of the Basement Complex, north-western Nigeria. The density obtained using the fractal approach is 2500 kgm which is lower than the conventional value of 2670 kgm used for average ...

Fractal characterization of brain lesions in CT images

International Nuclear Information System (INIS)

Jauhari, Rajnish K.; Trivedi, Rashmi; Munshi, Prabhat; Sahni, Kamal

2005-01-01

Fractal Dimension (FD) is a parameter used widely for classification, analysis, and pattern recognition of images. In this work we explore the quantification of CT (computed tomography) lesions of the brain by using fractal theory. Five brain lesions, which are portions of CT images of diseased brains, are used for the study. These lesions exhibit self-similarity over a chosen range of scales, and are broadly characterized by their fractal dimensions

Neutron scattering from fractals

DEFF Research Database (Denmark)

Kjems, Jørgen; Freltoft, T.; Richter, D.

1986-01-01

The scattering formalism for fractal structures is presented. Volume fractals are exemplified by silica particle clusters formed either from colloidal suspensions or by flame hydrolysis. The determination of the fractional dimensionality through scattering experiments is reviewed, and recent small...

FONT DISCRIMINATIO USING FRACTAL DIMENSIONS

Directory of Open Access Journals (Sweden)

S. Mozaffari

2014-09-01

Full Text Available One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dimension was introduced in this paper for the first time. Our feature extraction methods which consider font recognition as texture identification are independent of document content. Experimental results on different pages written by several font types show that fractal geometry can overcome the complexities of font recognition problem.

Radiologic assessment of bone healing after orthognathic surgery using fractal analysis

Energy Technology Data Exchange (ETDEWEB)

Park, Kwang Soo; Heo, Min Suk; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won [College of Dentistry, Seoul National University, Seoul (Korea, Republic of); Jeon, In Seong [Department of Dentistry, Inje University Sanggyepaik Hospital, Seoul (Korea, Republic of); Kim, Jong Dae [Division of Information and Communication Engineering, Hallym university, Chuncheon (Korea, Republic of)

2002-12-15

To evaluate the radiographic change of operation sites after orthognathic surgery using the digital image processing and fractal analysis. A series of panoramic radiographs of thirty-five randomly selected patients who had undergone mandibular orthognathic surgery (bilateral sagittal split ramus osteotomy) without clinical complication for osseous healing, were taken. The panoramic radiographs of each selected patient were taken at pre-operation (stage 0), 1 or 2 days after operation (stage 1), 1 month after operation (stage 2), 6 months after operation (stage 3), and 12 months after operation (stage 4). The radiographs were digitized at 600 dpi, 8 bit, and 256 gray levels. The region of interest, centered on the bony gap area of the operation site, was selected and the fractal dimension was calculated by using the tile-counting method. The mean values and standard deviations of fractal dimension for each stage were calculated and the differences among stage 0, 1, 2, 3, and 4 were evaluated through repeated measures of the ANOVA and paired t-test. The mean values and standard deviations of the fractal dimensions obtained from stage 0, 1, 2, 3, and 4 were 1.658 {+-} 0.048, 1.580 {+-} 0.050, 1.607 {+-} 0.046, 1.624 {+-} 0.049, and 1.641 {+-} 0.061, respectively. The fractal dimensions from stage 1 to stage 4 were shown to have a tendency to increase (p<0.05). The tendency of the fractal dimesion to increase relative to healing time may be a useful means of evaluating post-operative bony healing of the osteotomy site.

Radiologic assessment of bone healing after orthognathic surgery using fractal analysis

International Nuclear Information System (INIS)

Park, Kwang Soo; Heo, Min Suk; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won; Jeon, In Seong; Kim, Jong Dae

2002-01-01

To evaluate the radiographic change of operation sites after orthognathic surgery using the digital image processing and fractal analysis. A series of panoramic radiographs of thirty-five randomly selected patients who had undergone mandibular orthognathic surgery (bilateral sagittal split ramus osteotomy) without clinical complication for osseous healing, were taken. The panoramic radiographs of each selected patient were taken at pre-operation (stage 0), 1 or 2 days after operation (stage 1), 1 month after operation (stage 2), 6 months after operation (stage 3), and 12 months after operation (stage 4). The radiographs were digitized at 600 dpi, 8 bit, and 256 gray levels. The region of interest, centered on the bony gap area of the operation site, was selected and the fractal dimension was calculated by using the tile-counting method. The mean values and standard deviations of fractal dimension for each stage were calculated and the differences among stage 0, 1, 2, 3, and 4 were evaluated through repeated measures of the ANOVA and paired t-test. The mean values and standard deviations of the fractal dimensions obtained from stage 0, 1, 2, 3, and 4 were 1.658 ± 0.048, 1.580 ± 0.050, 1.607 ± 0.046, 1.624 ± 0.049, and 1.641 ± 0.061, respectively. The fractal dimensions from stage 1 to stage 4 were shown to have a tendency to increase (p<0.05). The tendency of the fractal dimesion to increase relative to healing time may be a useful means of evaluating post-operative bony healing of the osteotomy site.

Fractal analysis of the surgical treatment of ligature-induced peri-implantitis in dogs

International Nuclear Information System (INIS)

Kim, Hak Kun; Kim, Jin Soo

2010-01-01

To evaluate the effect of surgical treatment of ligature-induced peri-implantitis in dogs using fractal analysis. Also, the capabilities of fractal analysis as bone analysis techniques were compared with those of histomorphometric analysis. A total of 24 implants were inserted in 6 dogs. After a 3-months, experimental periimplantitis characterized by a bone loss of about 3 mm was established by inducing with wires. Surgical treatment involving flap procedure, debridement of implants surface with chlorhexidine and saline (group 1), guided bone regeneration (GBR) with absorbable collagen membrane and mineralized bone graft (group 2), and CO2 laser application with GBR (group 3) were performed. After animals were sacrificed in 8 and 16 weeks respectively, bone sections including implants were made. Fractal dimensions were calculated by box-counting method on the skeletonized images, made from each region of interest, including five screws at medial and distal aspects of implant, were selected. Statistically significant differences in the fractal dimensions between the group 1 (0.9340 ± 0.0126) and group 3 (0.9783 ± 0.0118) at 16 weeks were found (P<0.05). The fractal dimension was statistically significant different between 8 (0.9395 ± 0.0283) and 16 weeks in group 3 (P<0.05). These results were similar with the result of the evaluation of new bone formation in histomorphometric analysis. Treatment of experimental peri-implantitis by using CO2 laser with GBR is more useful than other treatments in the formation of new bone and also the tendency of fractal dimension to increase relative to healing time may be a useful means of evaluating.

Fractal analysis of the surgical treatment of ligature-induced peri-implantitis in dogs

Energy Technology Data Exchange (ETDEWEB)

Kim, Hak Kun; Kim, Jin Soo [School of Dentisity, Chosun University, Gwangju (Korea, Republic of)

2010-09-15

To evaluate the effect of surgical treatment of ligature-induced peri-implantitis in dogs using fractal analysis. Also, the capabilities of fractal analysis as bone analysis techniques were compared with those of histomorphometric analysis. A total of 24 implants were inserted in 6 dogs. After a 3-months, experimental periimplantitis characterized by a bone loss of about 3 mm was established by inducing with wires. Surgical treatment involving flap procedure, debridement of implants surface with chlorhexidine and saline (group 1), guided bone regeneration (GBR) with absorbable collagen membrane and mineralized bone graft (group 2), and CO2 laser application with GBR (group 3) were performed. After animals were sacrificed in 8 and 16 weeks respectively, bone sections including implants were made. Fractal dimensions were calculated by box-counting method on the skeletonized images, made from each region of interest, including five screws at medial and distal aspects of implant, were selected. Statistically significant differences in the fractal dimensions between the group 1 (0.9340 {+-} 0.0126) and group 3 (0.9783 {+-} 0.0118) at 16 weeks were found (P<0.05). The fractal dimension was statistically significant different between 8 (0.9395 {+-} 0.0283) and 16 weeks in group 3 (P<0.05). These results were similar with the result of the evaluation of new bone formation in histomorphometric analysis. Treatment of experimental peri-implantitis by using CO2 laser with GBR is more useful than other treatments in the formation of new bone and also the tendency of fractal dimension to increase relative to healing time may be a useful means of evaluating.

Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.

Science.gov (United States)

Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A

2017-11-28

We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

Fractal analysis as a potential tool for surface morphology of thin films

Science.gov (United States)

Soumya, S.; Swapna, M. S.; Raj, Vimal; Mahadevan Pillai, V. P.; Sankararaman, S.

2017-12-01

Fractal geometry developed by Mandelbrot has emerged as a potential tool for analyzing complex systems in the diversified fields of science, social science, and technology. Self-similar objects having the same details in different scales are referred to as fractals and are analyzed using the mathematics of non-Euclidean geometry. The present work is an attempt to correlate fractal dimension for surface characterization by Atomic Force Microscopy (AFM). Taking the AFM images of zinc sulphide (ZnS) thin films prepared by pulsed laser deposition (PLD) technique, under different annealing temperatures, the effect of annealing temperature and surface roughness on fractal dimension is studied. The annealing temperature and surface roughness show a strong correlation with fractal dimension. From the regression equation set, the surface roughness at a given annealing temperature can be calculated from the fractal dimension. The AFM images are processed using Photoshop and fractal dimension is calculated by box-counting method. The fractal dimension decreases from 1.986 to 1.633 while the surface roughness increases from 1.110 to 3.427, for a change of annealing temperature 30 ° C to 600 ° C. The images are also analyzed by power spectrum method to find the fractal dimension. The study reveals that the box-counting method gives better results compared to the power spectrum method.

Study of heart rate variability in driving situation by fractal analysis; Fractal kaiseki ni yoru untenchu no shinpaku hendo no bunseki

Energy Technology Data Exchange (ETDEWEB)

Hirata, Y; Nagaoka, M [Mazda Motor Corp., Hiroshima (Japan)

1997-10-01

This paper will explain method of fractal analysis for heart rate variability, as measuring method of mental stress in vehicle driving. In the previous, although there was a measuring method of mental stress by RSA, a issue arise such as reliability of analysis, because driver`s heart rate affect by respiration and muscle motion as well. We have established a method to measure mental stress by fractal dimension. And tried it is the proving ground and public road driving. We have confident that it is more reliable than RSA to quantify driver`s mental stress and fatigue. 9 refs., 9 figs., 1 tab.

Delay Bound: Fractal Traffic Passes through Network Servers

Directory of Open Access Journals (Sweden)

Ming Li

2013-01-01

Full Text Available Delay analysis plays a role in real-time systems in computer communication networks. This paper gives our results in the aspect of delay analysis of fractal traffic passing through servers. There are three contributions presented in this paper. First, we will explain the reasons why conventional theory of queuing systems ceases in the general sense when arrival traffic is fractal. Then, we will propose a concise method of delay computation for hard real-time systems as shown in this paper. Finally, the delay computation of fractal traffic passing through severs is presented.

Bilipschitz embedding of homogeneous fractals

OpenAIRE

Lü, Fan; Lou, Man-Li; Wen, Zhi-Ying; Xi, Li-Feng

2014-01-01

In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.

Fractal and multifractal analysis of LiF thin film surface

International Nuclear Information System (INIS)

Yadav, R.P.; Dwivedi, S.; Mittal, A.K.; Kumar, M.; Pandey, A.C.

2012-01-01

Highlights: ► Fractal and multifractal analysis of surface morphologies of the LiF thin films. ► Complexity and roughness of the LiF thin films increases as thickness increases. ► LiF thin films are multifractal in nature. ► Strength of the multifractality increases with thickness of the film. - Abstract: Fractal and multifractal analysis is performed on the atomic force microscopy (AFM) images of the surface morphologies of the LiF thin films of thickness 10 nm, 20 nm, and 40 nm, respectively. Autocorrelation function, height–height correlation function, and two-dimensional multifractal detrended fluctuation analysis (MFDFA) are used for characterizing the surface. It is found that the interface width, average roughness, lateral correlation length, and fractal dimension of the LiF thin film increase with the thickness of the film, whereas the roughness exponent decreases with thickness. Thus, the complexity and roughness of the LiF thin films increases as thickness increases. It is also demonstrated that the LiF thin films are multifractal in nature. Strength of the multifractality increases with thickness of the film.

Fractal dimension analysis in a highly granular calorimeter

CERN Document Server

Ruan, M; Brient, J.C; Jeans, D; Videau, H

2015-01-01

The concept of “particle flow” has been developed to optimise the jet energy resolution by distinguishing the different jet components. A highly granular calorimeter designed for the particle flow algorithm provides an unprecedented level of detail for the reconstruction of calorimeter showers and enables new approaches to shower analysis. In this paper the measurement and use of the fractal dimension of showers is described. The fractal dimension is a characteristic number that measures the global compactness of the shower. It is highly dependent on the primary particle type and energy. Its application in identifying particles and estimating their energy is described in the context of a calorimeter designed for the International Linear Collider.

Recognition of fractal graphs

NARCIS (Netherlands)

Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM

1999-01-01

Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems

Random walk through fractal environments

International Nuclear Information System (INIS)

Isliker, H.; Vlahos, L.

2003-01-01

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

Heritability of Retinal Vascular Fractals

DEFF Research Database (Denmark)

Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line

2017-01-01

Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0.......0002) in monozygotic twins than in dizygotic twins (0.108, P = 0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, dominant genetic effects explained 54% of the variation and 46% was individually environmentally determined. Conclusions: In young adult twins...

Chaos and fractals. Applications to nuclear engineering; Caos y fractales. Aplicaciones en ingenieria nuclear

Energy Technology Data Exchange (ETDEWEB)

Clausse, A; Delmastro, D F

1991-12-31

This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author). [Espanol] En este trabajo se presenta una descripcion de las lineas de investigacion que los autores estan llevando a cabo en teoria de caos y fractales orientadas al campo nuclear. Es de especial importancia las posibilidades que se abren en el area de la seguridad nuclear, en donde la informacion proveniente de las tecnicas de caos y fractales pueden ayudar al desarrollo de mejores criterios y disenos mas confiables. (Autor).

A fractal-based image encryption system

KAUST Repository

Abd-El-Hafiz, S. K.

2014-12-01

This study introduces a novel image encryption system based on diffusion and confusion processes in which the image information is hidden inside the complex details of fractal images. A simplified encryption technique is, first, presented using a single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved through several parameters: feedback delay, multiplexing and independent horizontal or vertical shifts. The effect of each parameter is studied separately and, then, they are combined to illustrate their influence on the encryption quality. The encryption quality is evaluated using different analysis techniques such as correlation coefficients, differential attack measures, histogram distributions, key sensitivity analysis and the National Institute of Standards and Technology (NIST) statistical test suite. The obtained results show great potential compared to other techniques.

Fractal analysis of heart rate variability and mortality after an acute myocardial infarction

DEFF Research Database (Denmark)

Tapanainen, Jari M; Thomsen, Poul Erik Bloch; Køber, Lars

2002-01-01

The recently developed fractal analysis of heart rate (HR) variability has been suggested to provide prognostic information about patients with heart failure. This prospective multicenter study was designed to assess the prognostic significance of fractal and traditional HR variability parameters...... in a large, consecutive series of survivors of an acute myocardial infarction (AMI). A consecutive series of 697 patients were recruited to participate 2 to 7 days after an AMI in 3 Nordic university hospitals. The conventional time-domain and spectral parameters and the newer fractal scaling indexes of HR...... variability were analyzed from 24-hour RR interval recordings. During the mean follow-up of 18.4 +/- 6.5 months, 49 patients (7.0%) died. Of all the risk variables, a reduced short-term fractal scaling exponent (alpha(1)

Fractal geometry mathematical foundations and applications

CERN Document Server

Falconer, Kenneth

2013-01-01

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applica

Fractal characteristics investigation on electromagnetic scattering from 2-D Weierstrass fractal dielectric rough surface

International Nuclear Information System (INIS)

Ren Xincheng; Guo Lixin

2008-01-01

A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)

Heterogeneity of cerebral blood flow: a fractal approach

International Nuclear Information System (INIS)

Kuikka, J.T.; Hartikainen, P.

2000-01-01

Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and single-photon emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (=coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17±0.05 (mean±SD) for the left hemisphere and 1.15±0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04±0.03 than in healthy controls. (orig.) [de

Fractal electrodynamics via non-integer dimensional space approach

Science.gov (United States)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

Multi-fractal analysis of highway traffic data

Institute of Scientific and Technical Information of China (English)

Shang Peng-Jian; Shen Jin-Sheng

2007-01-01

The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwise H(o)lder exponent of a function is calculated by developing an algorithm for the numerical evaluation of H(o)lder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.

FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY

Directory of Open Access Journals (Sweden)

Hynek Lauschmann

2011-05-01

Full Text Available The morphology of fatigue fracture surface (caused by constant cycle loading is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness. Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.

A Double-Minded Fractal

Science.gov (United States)

Simoson, Andrew J.

2009-01-01

This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)

Pore Structure and Fractal Characteristics of Niutitang Shale from China

Directory of Open Access Journals (Sweden)

Zhaodong Xi

2018-04-01

Full Text Available A suite of shale samples from the Lower Cambrian Niutitang Formation in northwestern Hunan Province, China, were investigated to better understand the pore structure and fractal characteristics of marine shale. Organic geochemistry, mineralogy by X-ray diffraction, porosity, permeability, mercury intrusion and nitrogen adsorption and methane adsorption experiments were conducted for each sample. Fractal dimension D was obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH model. The relationships between total organic carbon (TOC content, mineral compositions, pore structure parameters and fractal dimension are discussed, along with the contributions of fractal dimension to shale gas reservoir evaluation. Analysis of the results showed that Niutitang shale samples featured high TOC content (2.51% on average, high thermal maturity (3.0% on average, low permeability and complex pore structures, which are highly fractal. TOC content and mineral compositions are two major factors affecting pore structure but they have different impacts on the fractal dimension. Shale samples with higher TOC content had a larger specific surface area (SSA, pore volume (PV and fractal dimension, which enhanced the heterogeneity of the pore structure. Quartz content had a relatively weak influence on shale pore structure, whereas SSA, PV and fractal dimension decreased with increasing clay mineral content. Shale with a higher clay content weakened pore structure heterogeneity. The permeability and Langmuir volume of methane adsorption were affected by fractal dimension. Shale samples with higher fractal dimension had higher adsorption capacity but lower permeability, which is favorable for shale gas adsorption but adverse to shale gas seepage and diffusion.

Heritability of Retinal Vascular Fractals

DEFF Research Database (Denmark)

Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line

2017-01-01

, the retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficients. Falconer's formula and quantitative genetic models were used to determine the genetic component of variation. Results: The mean...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0...

Fractal physiology and the fractional calculus: a perspective.

Science.gov (United States)

West, Bruce J

2010-01-01

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a

Inkjet-Printed Ultra Wide Band Fractal Antennas

KAUST Repository

Maza, Armando Rodriguez

2012-01-01

reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics

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

Science.gov (United States)

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

2001-01-01

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

Categorization of new fractal carpets

International Nuclear Information System (INIS)

Rani, Mamta; Goel, Saurabh

2009-01-01

Sierpinski carpet is one of the very beautiful fractals from the historic gallery of classical fractals. Carpet designing is not only a fascinating activity in computer graphics, but it has real applications in carpet industry as well. One may find illusionary delighted carpets designed here, which are useful in real designing of carpets. In this paper, we attempt to systematize their generation and put them into categories. Each next category leads to a more generalized form of the fractal carpet.

On the Lipschitz condition in the fractal calculus

International Nuclear Information System (INIS)

Golmankhaneh, Alireza K.; Tunc, Cemil

2017-01-01

In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.

Fractal dimension of turbulent black holes

Science.gov (United States)

Westernacher-Schneider, John Ryan

2017-11-01

We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.

Fractals as objects with nontrivial structures at all scales

International Nuclear Information System (INIS)

Lacan, Francis; Tresser, Charles

2015-01-01

Toward the middle of 2001, the authors started arguing that fractals are important when discussing the operational resilience of information systems and related computer sciences issues such as artificial intelligence. But in order to argue along these lines it turned out to be indispensable to define fractals so as to let one recognize as fractals some sets that are very far from being self similar in the (usual) metric sense. This paper is devoted to define (in a loose sense at least) fractals in ways that allow for instance all the Cantor sets to be fractals and that permit to recognize fractality (the property of being fractal) in the context of the information technology issues that we had tried to comprehend. Starting from the meta-definition of a fractal as an “object with non-trivial structure at all scales” that we had used for long, we ended up taking these words seriously. Accordingly we define fractals in manners that depend both on the structures that the fractals are endowed with and the chosen sets of structure compatible maps, i.e., we approach fractals in a category-dependent manner. We expect that this new approach to fractals will contribute to the understanding of more of the fractals that appear in exact and other sciences than what can be handled presently

Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

Science.gov (United States)

Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-01-22

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

Fractal Structures For Mems Variable Capacitors

KAUST Repository

Elshurafa, Amro M.

2014-08-28

In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape separated by a vertical distance from a lower first metal plate with a complementary fractal shape; and a substrate above which the capacitor body is suspended.

Fractal THz metamaterials

DEFF Research Database (Denmark)

Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.

2010-01-01

applications. THz radiation can be employed for various purposes, among them the study of vibrations in biological molecules, motion of electrons in semiconductors and propagation of acoustic shock waves in crystals. We propose here a new THz fractal MTM design that shows very high transmission in the desired...... frequency range as well as a clear differentiation between one polarisation and another. Based on theoretical predictions we fabricated and measured a fractal based THz metamaterial that shows more than 60% field transmission at around 1THz for TE polarized light while the TM waves have almost 80% field...... transmission peak at 0.6THz. One of the main characteristics of this design is its tunability by design: by simply changing the length of the fractal elements one can choose the operating frequency window. The modelling, fabrication and characterisation results will be presented in this paper. Due to the long...

Fractal characterization of acupuncture-induced spike trains of rat WDR neurons

International Nuclear Information System (INIS)

Chen, Yingyuan; Guo, Yi; Wang, Jiang; Hong, Shouhai; Wei, Xile; Yu, Haitao; Deng, Bin

2015-01-01

Highlights: •Fractal analysis is a valuable tool for measuring MA-induced neural activities. •In course of the experiments, the spike trains display different fractal properties. •The fractal properties reflect the long-term modulation of MA on WDR neurons. •The results may explain the long-lasting effects induced by acupuncture. -- Abstract: The experimental and the clinical studies have showed manual acupuncture (MA) could evoke multiple responses in various neural regions. Characterising the neuronal activities in these regions may provide more deep insights into acupuncture mechanisms. This paper used fractal analysis to investigate MA-induced spike trains of Wide Dynamic Range (WDR) neurons in rat spinal dorsal horn, an important relay station and integral component in processing acupuncture information. Allan factor and Fano factor were utilized to test whether the spike trains were fractal, and Allan factor were used to evaluate the scaling exponents and Hurst exponents. It was found that these two fractal exponents before and during MA were different significantly. During MA, the scaling exponents of WDR neurons were regulated in a small range, indicating a special fractal pattern. The neuronal activities were long-range correlated over multiple time scales. The scaling exponents during and after MA were similar, suggesting that the long-range correlations not only displayed during MA, but also extended to after withdrawing the needle. Our results showed that fractal analysis is a useful tool for measuring acupuncture effects. MA could modulate neuronal activities of which the fractal properties change as time proceeding. This evolution of fractal dynamics in course of MA experiments may explain at the level of neuron why the effect of MA observed in experiment and in clinic are complex, time-evolutionary, long-range even lasting for some time after stimulation

Categorization of fractal plants

International Nuclear Information System (INIS)

Chandra, Munesh; Rani, Mamta

2009-01-01

Fractals in nature are always a result of some growth process. The language of fractals which has been created specifically for the description of natural growth process is called L-systems. Recently, superior iterations (essentially, investigated by Mann [Mann WR. Mean value methods in iteration. Proc Am Math Soc 1953;4:506-10 [MR0054846 (14,988f)

Morphometric relations of fractal-skeletal based channel network model

Directory of Open Access Journals (Sweden)

B. S. Daya Sagar

1998-01-01

Full Text Available A fractal-skeletal based channel network (F-SCN model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F-SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.

A random walk through fractal dimensions

CERN Document Server

Kaye, Brian H

2008-01-01

Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science.From reviews of the first edition:''...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.'' MRS Bulletin

Fractal Geometry and Stochastics V

CERN Document Server

Falconer, Kenneth; Zähle, Martina

2015-01-01

This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott,  Michał Rams, Pablo Shmerkin, and András Te...

Effects of fractal pore on coal devolatilization

Energy Technology Data Exchange (ETDEWEB)

Chen, Yongli; He, Rong [Tsinghua Univ., Beijing (China). Dept. of Thermal Engineering; Wang, Xiaoliang; Cao, Liyong [Dongfang Electric Corporation, Chengdu (China). Centre New Energy Inst.

2013-07-01

Coal devolatilization is numerically investigated by drop tube furnace and a coal pyrolysis model (Fragmentation and Diffusion Model). The fractal characteristics of coal and char pores are investigated. Gas diffusion and secondary reactions in fractal pores are considered in the numerical simulations of coal devolatilization, and the results show that the fractal dimension is increased firstly and then decreased later with increased coal conversions during devolatilization. The mechanisms of effects of fractal pores on coal devolatilization are analyzed.

A fractal analysis of protein to DNA binding kinetics using biosensors.

Science.gov (United States)

Sadana, Ajit

2003-08-01

A fractal analysis of a confirmative nature only is presented for the binding of estrogen receptor (ER) in solution to its corresponding DNA (estrogen response element, ERE) immobilized on a sensor chip surface [J. Biol. Chem. 272 (1997) 11384], and for the cooperative binding of human 1,25-dihydroxyvitamin D(3) receptor (VDR) to DNA with the 9-cis-retinoic acid receptor (RXR) [Biochemistry 35 (1996) 3309]. Ligands were also used to modulate the first reaction. Data taken from the literature may be modeled by using a single- or a dual-fractal analysis. Relationships are presented for the binding rate coefficient as a function of either the analyte concentration in solution or the fractal dimension that exists on the biosensor surface. The binding rate expressions developed exhibit a wide range of dependence on the degree of heterogeneity that exists on the surface, ranging from sensitive (order of dependence equal to 1.202) to very sensitive (order of dependence equal to 12.239). In general, the binding rate coefficient increases as the degree of heterogeneity or the fractal dimension of the surface increases. The predictive relationships presented provide further physical insights into the reactions occurring on the biosensor surface. Even though these reactions are occurring on the biosensor surface, the relationships presented should assist in understanding and in possibly manipulating the reactions occurring on cellular surfaces.

Measurement of heterogeneous distribution on technegas SPECT images by three-dimensional fractal analysis

International Nuclear Information System (INIS)

Nagao, Michinobu; Murase, Kenya

2002-01-01

This review article describes a method for quantifying heterogeneous distribution on Technegas ( 99m Tc-carbon particle radioaerosol) SPECT images by three-dimensional fractal analysis (3D-FA). Technegas SPECT was performed to quantify the severity of pulmonary emphysema. We delineated the SPECT images by using five cut-offs (15, 20, 25, 30 and 35% of the maximal voxel radioactivity), and measured the total number of voxels in the areas surrounded by the contours obtained with each cut-off level. We calculated fractal dimensions from the relationship between the total number of voxels and the cut-off levels transformed into natural logarithms. The fractal dimension derived from 3D-FA is the relative and objective measurement, which can assess the heterogeneous distribution on Technegas SPECT images. The fractal dimension strongly correlate pulmonary function in patients with emphysema and well documented the overall and regional severity of emphysema. (author)

Closed contour fractal dimension estimation by the Fourier transform

International Nuclear Information System (INIS)

Florindo, J.B.; Bruno, O.M.

2011-01-01

Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.

Fractal analysis: A new tool in transient volcanic ash plume characterization.

Science.gov (United States)

Tournigand, Pierre-Yves; Peña Fernandez, Juan Jose; Taddeucci, Jacopo; Perugini, Diego; Sesterhenn, Jörn

2017-04-01

Transient volcanic plumes are time-dependent features generated by unstable eruptive sources. They represent a threat to human health and infrastructures, and a challenge to characterize due to their intrinsic instability. Plumes have been investigated through physical (e.g. visible, thermal, UV, radar imagery), experimental and numerical studies in order to provide new insights about their dynamics and better anticipate their behavior. It has been shown experimentally that plume dynamics is strongly dependent to source conditions and that plume shape evolution holds key to retrieve these conditions. In this study, a shape evolution analysis is performed on thermal high-speed videos of volcanic plumes from three different volcanoes Sakurajima (Japan), Stromboli (Italy) and Fuego (Guatemala), recorded with a FLIR SC655 thermal camera during several field campaigns between 2012 and 2016. To complete this dataset, three numerical gas-jet simulations at different Reynolds number (2000, 5000 and 10000) have been used in order to set reference values to the natural cases. Turbulent flow shapes are well known to feature scale-invariant structures and a high degree of complexity. For this reason we characterized the bi-dimensional shape of natural and synthetic plumes by using a fractal descriptor. Such method has been applied in other studies on experimental turbulent jets as well as on atmospheric clouds and have shown promising results. At each time-step plume contour has been manually outlined and measured using the box-counting method. This method consists in covering the image with squares of variable sizes and counting the number of squares containing the plume outline. The negative slope of the number of squares in function of their size in a log-log plot gives the fractal dimension of the plume at a given time. Preliminary results show an increase over time of the fractal dimension for natural volcanic plume as well as for the numerically simulated ones, but at

Band structures in fractal grading porous phononic crystals

Science.gov (United States)

Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin

2018-05-01

In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.

Classification of radar echoes using fractal geometry

International Nuclear Information System (INIS)

Azzaz, Nafissa; Haddad, Boualem

2017-01-01

Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.

Investigation of diamond wheel topography in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire using fractal analysis method.

Science.gov (United States)

Wang, Qiuyan; Zhao, Wenxiang; Liang, Zhiqiang; Wang, Xibin; Zhou, Tianfeng; Wu, Yongbo; Jiao, Li

2018-03-01

The wear behaviors of grinding wheel have significant influence on the work-surface topography. However, a comprehensive and quantitative method is lacking for evaluating the wear conditions of grinding wheel. In this paper, a fractal analysis method is used to investigate the wear behavior of resin-bonded diamond wheel in Elliptical Ultrasonic Assisted Grinding (EUAG) of monocrystal sapphire, and a series of experiments on EUAG and conventional grinding (CG) are performed. The results show that the fractal dimension of grinding wheel topography is highly correlated to the wear behavior, i.e., grain fracture, grain pullout, and wheel loading. An increase in cutting edge density on the wheel surface results in an increase of the fractal dimension, but an increase in the grain pullout and wheel loading results in a decrease in the fractal dimension. The wheel topography in EUAG has a higher fractal dimension than that in CG before 60 passes due to better self-sharpening behavior, and then has a smaller fractal dimension because of more serious wheel loadings after 60 passes. By angle-dependent distribution analysis of profile fractal dimensions, the wheel surface topography is transformed from isotropic to anisotropic. These indicated that the fractal analysis method could be further used in monitoring of a grinding wheel performance in EUAG. Copyright © 2017 Elsevier B.V. All rights reserved.

Thermodynamics for Fractal Statistics

OpenAIRE

da Cruz, Wellington

1998-01-01

We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.

A new numerical approximation of the fractal ordinary differential equation

Science.gov (United States)

Atangana, Abdon; Jain, Sonal

2018-02-01

The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

Evaluation of 3D Printer Accuracy in Producing Fractal Structure.

Science.gov (United States)

Kikegawa, Kana; Takamatsu, Kyuuichirou; Kawakami, Masaru; Furukawa, Hidemitsu; Mayama, Hiroyuki; Nonomura, Yoshimune

2017-01-01

Hierarchical structures, also known as fractal structures, exhibit advantageous material properties, such as water- and oil-repellency as well as other useful optical characteristics, owing to its self-similarity. Various methods have been developed for producing hierarchical geometrical structures. Recently, fractal structures have been manufactured using a 3D printing technique that involves computer-aided design data. In this study, we confirmed the accuracy of geometrical structures when Koch curve-like fractal structures with zero to three generations were printed using a 3D printer. The fractal dimension was analyzed using a box-counting method. This analysis indicated that the fractal dimension of the third generation hierarchical structure was approximately the same as that of the ideal Koch curve. These findings demonstrate that the design and production of fractal structures can be controlled using a 3D printer. Although the interior angle deviated from the ideal value, the side length could be precisely controlled.

Fractal analysis reveals reduced complexity of retinal vessels in CADASIL.

Directory of Open Access Journals (Sweden)

Michele Cavallari

2011-04-01

Full Text Available The Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy (CADASIL affects mainly small cerebral arteries and leads to disability and dementia. The relationship between clinical expression of the disease and progression of the microvessel pathology is, however, uncertain as we lack tools for imaging brain vessels in vivo. Ophthalmoscopy is regarded as a window into the cerebral microcirculation. In this study we carried out an ophthalmoscopic examination in subjects with CADASIL. Specifically, we performed fractal analysis of digital retinal photographs. Data are expressed as mean fractal dimension (mean-D, a parameter that reflects complexity of the retinal vessel branching. Ten subjects with genetically confirmed diagnosis of CADASIL and 10 sex and age-matched control subjects were enrolled. Fractal analysis of retinal digital images was performed by means of a computer-based program, and the data expressed as mean-D. Brain MRI lesion volume in FLAIR and T1-weighted images was assessed using MIPAV software. Paired t-test was used to disclose differences in mean-D between CADASIL and control groups. Spearman rank analysis was performed to evaluate potential associations between mean-D values and both disease duration and disease severity, the latter expressed as brain MRI lesion volumes, in the subjects with CADASIL. The results showed that mean-D value of patients (1.42±0.05; mean±SD was lower than control (1.50±0.04; p = 0.002. Mean-D did not correlate with disease duration nor with MRI lesion volumes of the subjects with CADASIL. The findings suggest that fractal analysis is a sensitive tool to assess changes of retinal vessel branching, likely reflecting early brain microvessel alterations, in CADASIL patients.

Turbulent wakes of fractal objects

NARCIS (Netherlands)

Staicu, A.D.; Mazzi, B.; Vassilicos, J.C.; Water, van de W.

2003-01-01

Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are

Fractal characteristics of fracture morphology of steels irradiated with high-energy ions

Energy Technology Data Exchange (ETDEWEB)

Xian, Yongqiang; Liu, Juan [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); University of Chinese Academy of Science, Beijing 100049 (China); Zhang, Chonghong, E-mail: c.h.zhang@impcas.ac.cn [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); Chen, Jiachao [Paul Scherrer Institute, Villigen PSI (Switzerland); Yang, Yitao; Zhang, Liqing; Song, Yin [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China)

2015-06-15

Highlights: • Fractal dimensions of fracture surfaces of steels before and after irradiation were calculated. • Fractal dimension can effectively describe change of fracture surfaces induced by irradiation. • Correlation of change of fractal dimension with embrittlement of irradiated steels is discussed. - Abstract: A fractal analysis of fracture surfaces of steels (a ferritic/martensitic steel and an oxide-dispersion-strengthened ferritic steel) before and after the irradiation with high-energy ions is presented. Fracture surfaces were acquired from a tensile test and a small-ball punch test (SP). Digital images of the fracture surfaces obtained from scanning electron microscopy (SEM) were used to calculate the fractal dimension (FD) by using the pixel covering method. Boundary of binary image and fractal dimension were determined with a MATLAB program. The results indicate that fractal dimension can be an effective parameter to describe the characteristics of fracture surfaces before and after irradiation. The rougher the fracture surface, the larger the fractal dimension. Correlation of the change of fractal dimension with the embrittlement of the irradiated steels is discussed.

Fractal geometry and computer graphics

CERN Document Server

Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele

1992-01-01

Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...

Integrated quantitative fractal polarimetric analysis of monolayer lung cancer cells

Science.gov (United States)

Shrestha, Suman; Zhang, Lin; Quang, Tri; Farrahi, Tannaz; Narayan, Chaya; Deshpande, Aditi; Na, Ying; Blinzler, Adam; Ma, Junyu; Liu, Bo; Giakos, George C.

2014-05-01

Digital diagnostic pathology has become one of the most valuable and convenient advancements in technology over the past years. It allows us to acquire, store and analyze pathological information from the images of histological and immunohistochemical glass slides which are scanned to create digital slides. In this study, efficient fractal, wavelet-based polarimetric techniques for histological analysis of monolayer lung cancer cells will be introduced and different monolayer cancer lines will be studied. The outcome of this study indicates that application of fractal, wavelet polarimetric principles towards the analysis of squamous carcinoma and adenocarcinoma cancer cell lines may be proved extremely useful in discriminating among healthy and lung cancer cells as well as differentiating among different lung cancer cells.

Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus

DEFF Research Database (Denmark)

Broe, Rebecca; Rasmussen, Malin L; Frydkjaer-Olsen, Ulrik

2014-01-01

: We included 180 patients with type 1 diabetes in a 16 year follow-up study. In baseline retinal photographs (from 1995), all vessels in a zone 0.5-2.0 disc diameters from the disc margin were traced using Singapore Institute Vessel Assessment-Fractal image analysis software. Artefacts were removed......AIMS/HYPOTHESIS: Fractal analysis of the retinal vasculature provides a global measure of the complexity and density of retinal vessels summarised as a single variable: the fractal dimension. We investigated fractal dimensions as long-term predictors of microvasculopathy in type 1 diabetes. METHODS....... Retinal fractal analysis therefore is a potential tool for risk stratification in type 1 diabetes....

Synergetics and fractals in tribology

CERN Document Server

Janahmadov, Ahad Kh

2016-01-01

This book examines the theoretical and practical aspects of tribological process using synergy, fractal and multifractal methods, and the fractal and multifractal models of self-similar tribosystems developed on their basis. It provides a comprehensive analysis of their effectiveness, and also considers the method of flicker noise spectroscopy with detailed parameterization of surface roughness friction. All models, problems and solutions are taken and tested on the set of real-life examples of oil-gas industry. The book is intended for researchers, graduate students and engineers specialising in the field of tribology, and also for senior students of technical colleges.

Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...

African Journals Online (AJOL)

In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...

Fractal characteristic in the wearing of cutting tool

Science.gov (United States)

Mei, Anhua; Wang, Jinghui

1995-11-01

This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.

Factorial moment and fractal analysis of γ families

International Nuclear Information System (INIS)

Kalmakhelidze, M.Eh.; Roinishvili, N.N.; Svanidze, M.S.; Khizanishvili, L.A.; Chadranyan, L.Kh.

1997-01-01

Factorial and fractal methods were applied to nuclear-electromagnetic cascades in the atmosphere (γ families) to find sensitivity of these methods to multiparticle fluctuations in γ families. Averaged parameters of factorial and fractal methods of the real families were compared with the same quantities for the statistical set of random families. The correlations between the same parameters for families divided into sectors and into rings are studied. The correlations between different parameters for the same families divided into sectors are investigated

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

Science.gov (United States)

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

2010-01-01

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. PMID:21198103

Poiseuille equation for steady flow of fractal fluid

Science.gov (United States)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volume 1 of Eric Hammel's Fractal Dimensions, Volume 2 is filled wit

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1, 2, and 3 of Eric Hammel's Fractal Dimensions, Volume 4 is

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1 and 2 of Eric Hammel's Fractal Dimensions, Volume 3 is fil

Short-term prediction method of wind speed series based on fractal interpolation

International Nuclear Information System (INIS)

Xiu, Chunbo; Wang, Tiantian; Tian, Meng; Li, Yanqing; Cheng, Yi

2014-01-01

Highlights: • An improved fractal interpolation prediction method is proposed. • The chaos optimization algorithm is used to obtain the iterated function system. • The fractal extrapolate interpolation prediction of wind speed series is performed. - Abstract: In order to improve the prediction performance of the wind speed series, the rescaled range analysis is used to analyze the fractal characteristics of the wind speed series. An improved fractal interpolation prediction method is proposed to predict the wind speed series whose Hurst exponents are close to 1. An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed. The chaos optimization algorithm is used to optimize the function to resolve the optimal vertical scaling factors. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Simulation results show that the fractal interpolation prediction method can get better prediction result than others for the wind speed series with the fractal characteristic, and the prediction performance of the proposed method can be improved further because the fractal characteristic of its iterated function system is similar to that of the predicted wind speed series

Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA

Directory of Open Access Journals (Sweden)

Hamidreza Namazi

2015-01-01

Full Text Available Cancer starts when cells in a part of the body start to grow out of control. In fact cells become cancer cells because of DNA damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to study the cancer genes, DNA walk plots of genomes of patients with lung cancer were generated using a program written in MATLAB language. The data so obtained was checked for fractal property by computing the fractal dimension using a program written in MATLAB. Also, the correlation of damaged DNA was studied using the Hurst exponent measure. We have found that the damaged DNA sequences are exhibiting higher degree of fractality and less correlation compared with normal DNA sequences. So we confirmed this method can be used for early detection of lung cancer. The method introduced in this research not only is useful for diagnosis of lung cancer but also can be applied for detection and growth analysis of different types of cancers.

AFM imaging and fractal analysis of surface roughness of AlN epilayers on sapphire substrates

Energy Technology Data Exchange (ETDEWEB)

Dallaeva, Dinara, E-mail: dinara.dallaeva@yandex.ru [Brno University of Technology, Faculty of Electrical Engineering and Communication, Physics Department, Technická 8, 616 00 Brno (Czech Republic); Ţălu, Ştefan [Technical University of Cluj-Napoca, Faculty of Mechanical Engineering, Department of AET, Discipline of Descriptive Geometry and Engineering Graphics, 103-105 B-dul Muncii Street, Cluj-Napoca 400641, Cluj (Romania); Stach, Sebastian [University of Silesia, Faculty of Computer Science and Materials Science, Institute of Informatics, Department of Biomedical Computer Systems, ul. Będzińska 39, 41-205 Sosnowiec (Poland); Škarvada, Pavel; Tománek, Pavel; Grmela, Lubomír [Brno University of Technology, Faculty of Electrical Engineering and Communication, Physics Department, Technická 8, 616 00 Brno (Czech Republic)

2014-09-01

Graphical abstract: - Highlights: • We determined the complexity of 3D surface roughness of aluminum nitride layers. • We used atomic force microscopy and analyzed their fractal geometry. • We determined the fractal dimension of surface roughness of aluminum nitride layers. • We determined the dependence of layer morphology on substrate temperature. - Abstract: The paper deals with AFM imaging and characterization of 3D surface morphology of aluminum nitride (AlN) epilayers on sapphire substrates prepared by magnetron sputtering. Due to the effect of temperature changes on epilayer's surface during the fabrication, a surface morphology is studied by combination of atomic force microscopy (AFM) and fractal analysis methods. Both methods are useful tools that may assist manufacturers in developing and fabricating AlN thin films with optimal surface characteristics. Furthermore, they provide different yet complementary information to that offered by traditional surface statistical parameters. This combination is used for the first time for measurement on AlN epilayers on sapphire substrates, and provides the overall 3D morphology of the sample surfaces (by AFM imaging), and reveals fractal characteristics in the surface morphology (fractal analysis)

Fractional hydrodynamic equations for fractal media

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2005-01-01

We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered

Ghost quintessence in fractal gravity

Indian Academy of Sciences (India)

In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density.

Growth of fractal structures in flames with silicon admixture

NARCIS (Netherlands)

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.

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

The fractal nature of vacuum arc cathode spots

International Nuclear Information System (INIS)

Anders, Andre

2005-01-01

Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Several points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f 2 , where f is frequency, supporting a fractal spot model associated with Brownian motion

Variability of fractal dimension of solar radio flux

Science.gov (United States)

Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om

2018-04-01

In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).

Undergraduate experiment with fractal diffraction gratings

International Nuclear Information System (INIS)

Monsoriu, Juan A; Furlan, Walter D; Pons, Amparo; Barreiro, Juan C; Gimenez, Marcos H

2011-01-01

We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics laboratories and compared with those obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. Good agreement is obtained between experimental and numerical results.

On the arithmetic of fractal dimension using hyperhelices

International Nuclear Information System (INIS)

Toledo-Suarez, Carlos D.

2009-01-01

A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension

Fractal analysis of visual search activity for mass detection during mammographic screening.

Science.gov (United States)

Alamudun, Folami; Yoon, Hong-Jun; Hudson, Kathleen B; Morin-Ducote, Garnetta; Hammond, Tracy; Tourassi, Georgia D

2017-03-01

The objective of this study was to assess the complexity of human visual search activity during mammographic screening using fractal analysis and to investigate its relationship with case and reader characteristics. The study was performed for the task of mammographic screening with simultaneous viewing of four coordinated breast views as typically done in clinical practice. Eye-tracking data and diagnostic decisions collected for 100 mammographic cases (25 normal, 25 benign, 50 malignant) from 10 readers (three board certified radiologists and seven Radiology residents), formed the corpus for this study. The fractal dimension of the readers' visual scanning pattern was computed with the Minkowski-Bouligand box-counting method and used as a measure of gaze complexity. Individual factor and group-based interaction ANOVA analysis was performed to study the association between fractal dimension, case pathology, breast density, and reader experience level. The consistency of the observed trends depending on gaze data representation was also examined. Case pathology, breast density, reader experience level, and individual reader differences are all independent predictors of the complexity of visual scanning pattern when screening for breast cancer. No higher order effects were found to be significant. Fractal characterization of visual search behavior during mammographic screening is dependent on case properties and image reader characteristics. © 2017 American Association of Physicists in Medicine.

A fractal model of effective stress of porous media and the analysis of influence factors

Science.gov (United States)

Li, Wei; Zhao, Huan; Li, Siqi; Sun, Wenfeng; Wang, Lei; Li, Bing

2018-03-01

The basic concept of effective stress describes the characteristics of fluid and solid interaction in porous media. In this paper, based on the theory of fractal geometry, a fractal model was built to analyze the relationship between the microstructure and the effective stress of porous media. From the microscopic point of view, the influence of effective stress on pore structure of porous media was demonstrated. Theoretical analysis and experimental results show that: (i) the fractal model of effective stress can be used to describe the relationship between effective stress and the microstructure of porous media; (ii) a linear increase in the effective stress leads to exponential increases in fractal dimension, porosity and pore number of the porous media, and causes a decreasing trend in the average pore radius.

FRACTAL DIMENSIONALITY ANALYSIS OF MAMMARY GLAND THERMOGRAMS

Directory of Open Access Journals (Sweden)

Yu. E. Lyah

2016-06-01

Full Text Available Thermography may enable early detection of a cancer tumour within a mammary gland at an early, treatable stage of the illness, but thermogram analysis methods must be developed to achieve this goal. This study analyses the feasibility of applying the Hurst exponent readings algorithm for evaluation of the high dimensionality fractals to reveal any possible difference between normal thermograms (NT and malignant thermograms (MT.

Fractal and mechanical micro- and nanorange properties of sylvite and halite crystals

Directory of Open Access Journals (Sweden)

Valery N. Aptukov

2017-09-01

Full Text Available This article involves the treatment of micro- and nanorange scanning and indentation data for salt rock crystals obtained with help of the scanning microscope Dimension Icon using the mathematical models. It also describes the basic methods of fractal analysis. It shows the effectiveness of the method of minimal covering which is chosen to research the fractal properties of salt rock crystal surfaces. The article includes the algorithm of this method and the description of its generalization for the two-dimensional case. The values of fractal index and multifractal parameters have been calculated on the basis of the minimal covering method. The article also involves the anisotropy effects for fractal properties, comparison of fractal behavior on different scale levels. It gives the values of hardness for different parts of the crystals and studies the correlation between hardness and fractal index and describes the character of the influence of fractal dimension on roughness.

Fractal Dimension and Maximum Sunspot Number in Solar Cycle

Directory of Open Access Journals (Sweden)

R.-S. Kim

2006-09-01

Full Text Available 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 SIDC (Solar Influences Data analysis Center and then estimated cycle variation of the fractal dimension by using Higuchi's method. We examined the relationship between this fractal dimension and the maximum monthly sunspot number in each solar cycle. As a result, we found that there is a strong inverse relationship between the fractal dimension and the maximum monthly sunspot number. By using this relation we predicted the maximum sunspot number in the solar cycle from the fractal dimension of the sunspot numbers during the solar activity increasing phase. The successful prediction is proven by a good correlation (r=0.89 between the observed and predicted maximum sunspot numbers in the solar cycles.

Design of LTCC Based Fractal Antenna

KAUST Repository

AdbulGhaffar, Farhan

2010-01-01

The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array

Fractal physiology and the fractional calculus: a perspective

Directory of Open Access Journals (Sweden)

Bruce J West

2010-10-01

Full Text Available This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. We review the allometric aggregation approach to the processing of physiologic time series as a way of determining the fractal character of the underlying phenomena. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. Fractional operators acting on fractal functions yield fractal functions, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine. Allometric control incorporates long-time memory, inverse power-law (IPL correlations, and long-range interactions in complex phenomena as manifest by IPL distributions. We hypothesize that allometric control, rather than homeostatic control, maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can be described using the fractional calculus to capture the dynamics of complex physiologic networks. This hypothesis is supported by a number of physiologic time series data.

Fractal Structures For Mems Variable Capacitors

KAUST Repository

Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.

2014-01-01

In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape

Model of fractal aggregates induced by shear

Directory of Open Access Journals (Sweden)

Wan Zhanhong

2013-01-01

Full Text Available It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.

Fractal Structure and Entropy Production within the Central Nervous System

Directory of Open Access Journals (Sweden)

Andrew J. E. Seely

2014-08-01

Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.

a Fractal Network Model for Fractured Porous Media

Science.gov (United States)

Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung

2016-04-01

The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

Fractal characterization for noise signal validation in power reactors

International Nuclear Information System (INIS)

Aguilar Martinez, Omar

2003-01-01

Up to now, a great variety of methods is used for the dynamical characterization of different components of Nuclear Power Plants (NPPs). With this aim, time and spectral analysis are usually considered, and different tools of non-stationary and non-gaussian analysis are also presented. When applying non-lineal dynamics theory for noise signal validation purposes in power reactors, the extraction of fractal echoes plays a main role. Fractal characterization for noise signal validation purposes can be integrated to the task of processing and acquisition of time signals in noise (fluctuation parameters) analysis systems. The possibility of discrimination between deterministic chaotic signals and pure noise signals has been incorporated, as a complement; to noise signals analysis in normal and anomalous operational conditions in NPPs using a fractal approach. In this work the detailed analysis of a neutronic sensor response is considered and the fractal characterization of its dynamics state (i.e. sensor line) for noise signal classification, it is presented. The experiment from where the time series (signals) were obtained, was carried out at the Research Reactor of the Technical University of Budapest, Hungary, during a model experiment for ageing process study of in-core neutron detectors (author)

Semiflexible crossing-avoiding trails on plane-filling fractals

International Nuclear Information System (INIS)

Živić, I.; Elezović-Hadžić, S.; Milošević, S.

2015-01-01

We have studied the statistics of semiflexible polymer chains modeled by crossing-avoiding trails (CAT) situated on the family of plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension d_f is equal to 2 for all members of the fractal family. By applying the exact and Monte Carlo real-space renormalization group method we have calculated the critical exponent ν, which governs the scaling behavior of the end-to-end distance of the polymer, as well as the entropic critical exponent γ, for a large set of fractals, and various values of polymer flexibility. Our results, obtained for CAT model on PF fractals, show that both critical exponents depend on the polymer flexibility, in such a way that less flexible polymer chains display enlarged values of ν, and diminished values of γ. We have compared the obtained results for CAT model with the known results for the self-avoiding walk and self-avoiding trail models and discussed the influence of excluded volume effect on the values of semiflexible polymer critical exponents, for a large set of studied compact fractals.

Generalized Warburg impedance on realistic self-affine fractals ...

Indian Academy of Sciences (India)

2016-08-26

Aug 26, 2016 ... We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals.

Fractals and multifractals in physics

International Nuclear Information System (INIS)

Arcangelis, L. de.

1987-01-01

We present a general introduction to the world of fractals. The attention is mainly devoted to stress how fractals do indeed appear in the real world and to find quantitative methods for characterizing their properties. The idea of multifractality is also introduced and it is presented in more details within the framework of the percolation problem

An investigation of fractal characteristics of mesoporous carbon electrodes with various pore structures

International Nuclear Information System (INIS)

Pyun, Su-Il; Rhee, Chang-Kyu

2004-01-01

Fractal characteristics of mesoporous carbon electrodes were investigated with various pore structures using the N 2 gas adsorption method and the transmission electron microscopy (TEM) image analysis method. The mesoporous carbons with various pore structures were prepared by imprinting mesophase pitch used as a carbonaceous precursor with different colloidal silica particles. All imprinted mesoporous carbons were composed of two groups of pores produced from the carbonisation of mesophase pitch and from the silica imprinting. The overall surface fractal dimensions of the carbon specimens were determined from the analyses of the N 2 gas adsorption isotherms. In order to distinguish the surface fractal dimension of the carbonisation-induced pore surface from that fractal dimension of the silica-imprinted pore surface, the individual surface fractal dimensions were determined from the image analyses of the TEM images. From the comparison of the overall surface fractal dimension with the individual surface fractal dimensions, it was recognised that the overall surface fractal dimension is crucially influenced by the individual surface fractal dimension of the silica-imprinted pore surface. Moreover, from the fact that the silica-imprinted pore surface with broad relative pore size distribution (PSD) gave lower value of the individual surface fractal dimension than that pore surface with narrow relative PSD, it is concluded that as the silica-imprinted pores comprising the carbon specimen agglomerate, the individual surface fractal dimension of that pore surface decreases

Inverted fractal analysis of TiO{sub x} thin layers grown by inverse pulsed laser deposition

Energy Technology Data Exchange (ETDEWEB)

Égerházi, L., E-mail: egerhazi.laszlo@gmail.com [University of Szeged, Faculty of Medicine, Department of Medical Physics and Informatics, Korányi fasor 9., H-6720 Szeged (Hungary); Smausz, T. [University of Szeged, Faculty of Science, Department of Optics and Quantum Electronics, Dóm tér 9., H-6720 Szeged (Hungary); Bari, F. [University of Szeged, Faculty of Medicine, Department of Medical Physics and Informatics, Korányi fasor 9., H-6720 Szeged (Hungary)

2013-08-01

Inverted fractal analysis (IFA), a method developed for fractal analysis of scanning electron microscopy images of cauliflower-like thin films is presented through the example of layers grown by inverse pulsed laser deposition (IPLD). IFA uses the integrated fractal analysis module (FracLac) of the image processing software ImageJ, and an objective thresholding routine that preserves the characteristic features of the images, independently of their brightness and contrast. IFA revealed f{sub D} = 1.83 ± 0.01 for TiO{sub x} layers grown at 5–50 Pa background pressures. For a series of images, this result was verified by evaluating the scaling of the number of still resolved features on the film, counted manually. The value of f{sub D} not only confirms the fractal structure of TiO{sub x} IPLD thin films, but also suggests that the aggregation of plasma species in the gas atmosphere may have only limited contribution to the deposition.

Fractal analysis and nonlinear forecasting of indoor 222Rn time series

International Nuclear Information System (INIS)

Pausch, G.; Bossew, P.; Hofmann, W.; Steger, F.

1998-01-01

Fractal analyses of indoor 222 Rn time series were performed using different chaos theory based measurements such as time delay method, Hurst's rescaled range analysis, capacity (fractal) dimension, and Lyapunov exponent. For all time series we calculated only positive Lyapunov exponents which is a hint to chaos, while the Hurst exponents were well below 0.5, indicating antipersistent behaviour (past trends tend to reverse in the future). These time series were also analyzed with a nonlinear prediction method which allowed an estimation of the embedding dimensions with some restrictions, limiting the prediction to about three relative time steps. (orig.)

Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals

OpenAIRE

Steinhurst, Benjamin; Teplyaev, Alexander

2012-01-01

We show that if a Barlow-Evans Markov process on a vermiculated space is symmetric, then one can study the spectral properties of the corresponding Laplacian using projective limits. For some examples, such as the Laakso spaces and a Spierpinski P\\^ate \\`a Choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. Also, one can construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhu...

Generalized Warburg impedance on realistic self-affine fractals

Indian Academy of Sciences (India)

We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals. The information about the ...

International Conference and Workshop on Fractals and Wavelets

CERN Document Server

Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod

2014-01-01

Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.

Computation of complexity measures of morphologically significant zones decomposed from binary fractal sets via multiscale convexity analysis

International Nuclear Information System (INIS)

Lim, Sin Liang; Koo, Voon Chet; Daya Sagar, B.S.

2009-01-01

Multiscale convexity analysis of certain fractal binary objects-like 8-segment Koch quadric, Koch triadic, and random Koch quadric and triadic islands-is performed via (i) morphologic openings with respect to recursively changing the size of a template, and (ii) construction of convex hulls through half-plane closings. Based on scale vs convexity measure relationship, transition levels between the morphologic regimes are determined as crossover scales. These crossover scales are taken as the basis to segment binary fractal objects into various morphologically prominent zones. Each segmented zone is characterized through normalized morphologic complexity measures. Despite the fact that there is no notably significant relationship between the zone-wise complexity measures and fractal dimensions computed by conventional box counting method, fractal objects-whether they are generated deterministically or by introducing randomness-possess morphologically significant sub-zones with varied degrees of spatial complexities. Classification of realistic fractal sets and/or fields according to sub-zones possessing varied degrees of spatial complexities provides insight to explore links with the physical processes involved in the formation of fractal-like phenomena.

Convergence of trajectories in fractal interpolation of stochastic processes

International Nuclear Information System (INIS)

MaIysz, Robert

2006-01-01

The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation

Fractal Dimension Of CT Images Of Normal Parotid Glands

International Nuclear Information System (INIS)

Lee, Sang Jin; Heo, Min Suk; You, Dong Soo

1999-01-01

This study was to investigate the age and sex differences of the fractal dimension of the normal parotid glands in the digitized CT images. The six groups, which were composed of 42 men and women from 20's, 40's and 60's and over were picked. Each group contained seven people of the same sex. The normal parotid CT images were digitized, and their fractal dimensions were calculated using Scion Image PC program. The mean of fractal dimensions in males was 1.7292 (+/-0.0588) and 1.6329 (+/-0.0425) in females. The mean of fractal dimensions in young males was 1.7617, 1.7328 in middle males, and 1.6933 in old males. The mean of fractal dimensions in young females was 1.6318, 1.6365 in middle females, and 1.6303 in old females. There was no statistical difference in fractal dimension between left and right parotid gland of the same subject (p>0.05). Fractal dimensions in male were decreased in older group (p 0.05). The fractal dimension of parotid glands in the digitized CT images will be useful to evaluate the age and sex differences.

Chaos and fractals an elementary introduction

CERN Document Server

Feldman, David P

2012-01-01

For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.

Ga-doped ZnO thin film surface characterization by wavelet and fractal analysis

Energy Technology Data Exchange (ETDEWEB)

Jing, Chenlei; Tang, Wu, E-mail: tang@uestc.edu.cn

2016-02-28

Graphical abstract: - Highlights: • Multi-resolution signal decomposition of wavelet transform is applied to Ga-doped ZnO thin films with various thicknesses. • Fractal properties of GZO thin films are investigated by box counting method. • Fractal dimension is not in conformity with original RMS roughness. • Fractal dimension mainly depends on the underside diameter (grain size) and distance between adjacent grains. - Abstract: The change in roughness of various thicknesses Ga-doped ZnO (GZO) thin films deposited by magnetron reactive sputtering on glass substrates at room temperature was measured by atomic force microscopy (AFM). Multi-resolution signal decomposition based on wavelet transform and fractal geometry was applied to process surface profiles, to evaluate the roughness trend of relevant frequency resolution. The results give a six-level decomposition and the results change with deposited time and surface morphology. Also, it is found that fractal dimension is closely connected to the underside diameter (grain size) and the distance between adjacent grains that affect the change rate of surface and the increase of the defects such as abrupt changes lead to a larger value of fractal dimension.

A fractal-like resistive network

International Nuclear Information System (INIS)

Saggese, A; De Luca, R

2014-01-01

The equivalent resistance of a fractal-like network is calculated by means of approaches similar to those employed in defining the equivalent resistance of an infinite ladder. Starting from an elementary triangular circuit, a fractal-like network, named after Saggese, is developed. The equivalent resistance of finite approximations of this network is measured, and the didactical implications of the model are highlighted. (paper)

Electro-chemical manifestation of nanoplasmonics in fractal media

Science.gov (United States)

Baskin, Emmanuel; Iomin, Alexander

2013-06-01

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

FAST TRACK COMMUNICATION: Weyl law for fat fractals

Science.gov (United States)

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

2010-10-01

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.

Paper-based inkjet-printed ultra-wideband fractal antennas

KAUST Repository

Maza, Armando Rodriguez

2012-01-01

For the first time, paper-based inkjet-printed ultra-wideband (UWB) fractal antennas are presented. Two new designs, a miniaturised UWB monopole, which utilises a fractal matching network and is the smallest reported inkjet-printed UWB printed antenna to date, and a fourth-order Koch Snowflake monopole, which utilises a Sierpinski gasket fractal for ink reduction, are demonstrated. It is shown that fractals prove to be a successful method of reducing fabrication costs in inkjet-printed antennas, while retaining or enhancing printed antenna performance. © 2012 The Institution of Engineering and Technology.

Effective degrees of freedom of a random walk on a fractal

Science.gov (United States)

Balankin, Alexander S.

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation

Directory of Open Access Journals (Sweden)

ELNAZ Rezaei abajelu

2017-03-01

Full Text Available Introduction: Soil Hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. In recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (Ks. Fractal models with two subset of two (solid and pore and three phases (solid, pore and soil fractal (PSF are used to estimate the fractal dimension of soil particles. The PSF represents a generalization of the solid and pore mass fractal models. The PSF characterizes both the solid and pore phases of the porous material. It also exhibits self-similarity to some degree, in the sense that where local structure seems to be similar to the whole structure.PSF models can estimate interface fractal dimension using soil pore size distribution data (PSD and soil moisture retention curve (SWRC. The main objective of this study was to evaluate different fractal models to estimate the Ksparameter. Materials and Methods: The Schaapetal data was used in this study. The complex consists of sixty soil samples. Soil texture, soil bulk density, soil saturated hydraulic conductivity and soil particle size distribution curve were measured by hydrometer method, undistributed soil sample, constant head method and wet sieve method, respectively for all soil samples.Soil water retention curve were determined by using pressure plates apparatus.The Ks parameter could be estimated by Ralws model as a function of fractal dimension by seven fractal models. Fractal models included Fuentes at al. (1996, Hunt and Gee (2002, Bird et al. (2000, Huang and Zhang (2005, Tyler and Wheatcraft (1990, Kutlu et al. (2008, Sepaskhah and Tafteh (2013.Therefore The Ks parameter can be estimated as a function of the DS (fractal dimension by seven fractal models (Table 2.Sensitivity analysis of Rawls model was assessed by making changes±10%, ±20% and±30%(in input parameters

Power Load Prediction Based on Fractal Theory

OpenAIRE

Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song

2015-01-01

The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...

Naturaleza fractal en redes de cristales de grasas

Directory of Open Access Journals (Sweden)

Gómez Herrera, C.

2004-06-01

Full Text Available The determination of the mechanical and rheological characteris­tics of several plastic fats requires a detailed understanding of the microstructure of the fat crystal network aggregates. The (or A fractal approach is useful for the characterization of this micros­tructure. This review begins with information on fractality and statistical self-similar structure. Estimations for fractal dimension by means of equations relating the volume fraction of solid fat to shear elastic modulus G' in linear region are described. The influence of interesterification on fractal dimension decrease (from 2, 46 to 2 ,15 for butterfat-canola oil blends is notable . This influence is not significant for fat blends without butterfat. The need for an increase in research concerning the relationship between fractality and rheology in plastic fats is emphasized.La determinación de las características mecánicas y reológicas de ciertas grasas plásticas requiere conocimientos detallados sobre las microestructuras de los agregados que forman la red de cristales grasos. El estudio de la naturaleza fractal de estas microestructuras resulta útil para su carac­terización. Este artículo de información se inicia con descripciones de la dimensión fractal y de la "autosimilitud estadística". A continuación se describe el cálculo de la dimensión fractal mediante ecuaciones que relacionan la fracción en volumen de grasa sólida con el módulo de recuperación (G' dentro de un comportamiento viscoelástico lineal. Se destaca la influencia que la interesterificación ejerce sobre la dimensión fractal de una mezcla de grasa láctea y aceite de canola (que pasa de 2,64 a 2,15. Esta influencia no se presenta en mezclas sin grasa láctea. Se insiste sobre la necesidad de incrementar las investi­gaciones sobre la relación entre reología y estructura fractal en grasas plásticas.

Fractal analysis of the effect of particle aggregation distribution on thermal conductivity of nanofluids

Energy Technology Data Exchange (ETDEWEB)

Wei, Wei, E-mail: weiw2015@gmail.com [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Cai, Jianchao, E-mail: caijc@cug.edu.cn [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Hu, Xiangyun, E-mail: xyhu@cug.edu.cn [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Han, Qi, E-mail: hanqi426@gmail.com [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Liu, Shuang, E-mail: lius@cug.edu.cn [Hubei Subsurface Multi-scale Imaging Key Laboratory, Institute of Geophysics and Geomatics, China University of Geosciences, Wuhan 430074 (China); Zhou, Yingfang, E-mail: yingfang.zhou@abdn.ac.uk [School of Engineering, University of Aberdeen, FN 264, King' s College, Aberdeen, AB24 3UE (United Kingdom)

2016-08-26

A theoretical effective thermal conductivity model for nanofluids is derived based on fractal distribution characteristics of nanoparticle aggregation. Considering two different mechanisms of heat conduction including particle aggregation and convention, the model is expressed as a function of the fractal dimension and concentration. In the model, the change of fractal dimension is related to the variation of aggregation shape. The theoretical computations of the developed model provide a good agreement with the experimental results, which may serve as an effective approach for quantitatively estimating the effective thermal conductivity of nanofluids. - Highlights: • A thermal conductivity model is derived based on fractal aggregation distribution. • The relationship between aggregation shape and fractal dimension is analyzed. • Predictions of the proposed model show good agreement with experimental data.

Trabecular morphometry by fractal signature analysis is a novel marker of osteoarthritis progression.

Science.gov (United States)

Kraus, Virginia Byers; Feng, Sheng; Wang, ShengChu; White, Scott; Ainslie, Maureen; Brett, Alan; Holmes, Anthony; Charles, H Cecil

2009-12-01

To evaluate the effectiveness of using subchondral bone texture observed on a radiograph taken at baseline to predict progression of knee osteoarthritis (OA) over a 3-year period. A total of 138 participants in the Prediction of Osteoarthritis Progression study were evaluated at baseline and after 3 years. Fractal signature analysis (FSA) of the medial subchondral tibial plateau was performed on fixed flexion radiographs of 248 nonreplaced knees, using a commercially available software tool. OA progression was defined as a change in joint space narrowing (JSN) or osteophyte formation of 1 grade according to a standardized knee atlas. Statistical analysis of fractal signatures was performed using a new model based on correlating the overall shape of a fractal dimension curve with radius. Fractal signature of the medial tibial plateau at baseline was predictive of medial knee JSN progression (area under the curve [AUC] 0.75, of a receiver operating characteristic curve) but was not predictive of osteophyte formation or progression of JSN in the lateral compartment. Traditional covariates (age, sex, body mass index, knee pain), general bone mineral content, and joint space width at baseline were no more effective than random variables for predicting OA progression (AUC 0.52-0.58). The predictive model with maximum effectiveness combined fractal signature at baseline, knee alignment, traditional covariates, and bone mineral content (AUC 0.79). We identified a prognostic marker of OA that is readily extracted from a plain radiograph using FSA. Although the method needs to be validated in a second cohort, our results indicate that the global shape approach to analyzing these data is a potentially efficient means of identifying individuals at risk of knee OA progression.

Fractal nature of humic materials

International Nuclear Information System (INIS)

Rice, J.A.

1992-01-01

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

Node insertion in Coalescence Fractal Interpolation Function

International Nuclear Information System (INIS)

Prasad, Srijanani Anurag

2013-01-01

The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed

Exploring the relationship between fractal features and bacterial essential genes

International Nuclear Information System (INIS)

Yu Yong-Ming; Yang Li-Cai; Zhao Lu-Lu; Liu Zhi-Ping; Zhou Qian

2016-01-01

Essential genes are indispensable for the survival of an organism in optimal conditions. Rapid and accurate identifications of new essential genes are of great theoretical and practical significance. Exploring features with predictive power is fundamental for this. Here, we calculate six fractal features from primary gene and protein sequences and then explore their relationship with gene essentiality by statistical analysis and machine learning-based methods. The models are applied to all the currently available identified genes in 27 bacteria from the database of essential genes (DEG). It is found that the fractal features of essential genes generally differ from those of non-essential genes. The fractal features are used to ascertain the parameters of two machine learning classifiers: Naïve Bayes and Random Forest. The area under the curve (AUC) of both classifiers show that each fractal feature is satisfactorily discriminative between essential genes and non-essential genes individually. And, although significant correlations exist among fractal features, gene essentiality can also be reliably predicted by various combinations of them. Thus, the fractal features analyzed in our study can be used not only to construct a good essentiality classifier alone, but also to be significant contributors for computational tools identifying essential genes. (paper)

Transport properties of electrons in fractal magnetic-barrier structures

Science.gov (United States)

Sun, Lifeng; Fang, Chao; Guo, Yong

2010-09-01

Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.

Analysis of MRI by fractals for prediction of sensory attributes: A case study in loin

DEFF Research Database (Denmark)

Caballero, Daniel; Antequera, Teresa; Caro, Andrés

2018-01-01

This study investigates the use of fractal algorithms to analyse MRI of meat products, specifically loin, in order to determine sensory parameters of loin. For that, the capability of different fractal algorithms was evaluated (Classical Fractal Algorithm, CFA; Fractal Texture Algorithm, FTA...... was analysed. Results on this study firstly demonstrate the capability of fractal algorithms to analyse MRI from meat product. Different combinations of the analysed techniques can be applied for predicting most sensory attributes of loins adequately (R > 0.5). However, the combination of SE, OPFTA and MLR...... offered the most appropriate results. Thus, it could be proposed as an alternative to the traditional food technology methods....

Temporal fractals in seabird foraging behaviour: diving through the scales of time

Science.gov (United States)

Macintosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan

2013-05-01

Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (216 data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.

Towards thermomechanics of fractal media

Science.gov (United States)

Ostoja-Starzewski, Martin

2007-11-01

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.

Undergraduate Experiment with Fractal Diffraction Gratings

Science.gov (United States)

Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.

2011-01-01

We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…

Quantum mechanical analysis of fractal conductance fluctuations: a picture using self-similar periodic orbits

International Nuclear Information System (INIS)

Ogura, Tatsuo; Miyamoto, Masanori; Budiyono, Agung; Nakamura, Katsuhiro

2007-01-01

Fractal magnetoconductance fluctuations are often observed in experiments on ballistic quantum dots. Although the analysis of the exact self-affine fractal has been given by the semiclassical theory using self-similar periodic orbits in systems with a soft-walled potential with a saddle, there has been no corresponding quantum mechanical investigation. We numerically calculate the quantum conductance with use of the recursive Green's function method applied to open cavities characterized by a Henon-Heiles type potential. The conductance fluctuations show exact self-affinity just as in some of the experimental observations. The enlargement factor for the horizontal axis can be explained by the scaling factor of the area of self-similar periodic orbits, and therefore be attributed to the curvature of the saddle in the cavity potential. The fractal dimension obtained through the box counting method agrees with those evaluated with use of the Hurst exponent, and coincides with the semiclassical prediction. We further investigate the variation of the fractal dimension by changing the control parameters between the classical and quantum domains. (fast track communication)

Effect of noise on fractal structure

Energy Technology Data Exchange (ETDEWEB)

Serletis, Demitre [Division of Neurosurgery, Hospital for Sick Children, 1504-555 University Avenue, Toronto, Ont., M5G 1X8 (Canada)], E-mail: demitre.serletis@utoronto.ca

2008-11-15

In this paper, I investigate the effect of dynamical noise on the estimation of the Hurst exponent and the fractal dimension of time series. Recently, Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on estimation of Lyapunov exponents from a time series. Chaos, Solitons and Fractals, forthcoming] have shown that dynamical noise can make the detection of chaotic dynamics very difficult, and Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on the bifurcation behavior of dynamical systems. Chaos, Solitons and Fractals, forthcoming] have shown that dynamical noise can also shift bifurcation points and produce noise-induced transitions, making the determination of bifurcation boundaries difficult. Here I apply the detrending moving average (DMA) method, recently developed by Alessio et al. [Alessio E, Carbone A, Castelli G, Frappietro V. Second-order moving average and scaling of stochastic time series. The Eur Phys J B 2002;27:197-200] and Carbone et al. [Carbone A, Castelli G, Stanley HE. Time-dependent Hurst exponent in financial time series. Physica A 2004;344:267-71; Carbone A, Castelli G, Stanley HE. Analysis of clusters formed by the moving average of a long-range correlated time series. Phys Rev E 2004;69:026105], to estimate the Hurst exponent of a Brownian walk with a Hurst exponent of 0.5, coupled with low and high intensity noise, and show that dynamical noise has no effect on fractal structure.

Fractal actors and infrastructures

DEFF Research Database (Denmark)

Bøge, Ask Risom

2011-01-01

-network-theory (ANT) into surveillance studies (Ball 2002, Adey 2004, Gad & Lauritsen 2009). In this paper, I further explore the potential of this connection by experimenting with Marilyn Strathern’s concept of the fractal (1991), which has been discussed in newer ANT literature (Law 2002; Law 2004; Jensen 2007). I...... under surveillance. Based on fieldwork conducted in 2008 and 2011 in relation to my Master’s thesis and PhD respectively, I illustrate fractal concepts by describing the acts, actors and infrastructure that make up the ‘DNA surveillance’ conducted by the Danish police....

Random walks of oriented particles on fractals

International Nuclear Information System (INIS)

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

2014-01-01

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

Using Peano Curves to Construct Laplacians on Fractals

Science.gov (United States)

Molitor, Denali; Ott, Nadia; Strichartz, Robert

2015-12-01

We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

ABC of multi-fractal spacetimes and fractional sea turtles

Energy Technology Data Exchange (ETDEWEB)

Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)

2016-04-15

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)

ABC of multi-fractal spacetimes and fractional sea turtles

International Nuclear Information System (INIS)

Calcagni, Gianluca

2016-01-01

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)

ABC of multi-fractal spacetimes and fractional sea turtles

Science.gov (United States)

Calcagni, Gianluca

2016-04-01

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

NATO Advanced Study Institute and Séminaire de mathématiques supérieures on Fractal Geometry and Analysis

CERN Document Server

Dubuc, Serge

1991-01-01

This ASI- which was also the 28th session of the Seminaire de mathematiques superieures of the Universite de Montreal - was devoted to Fractal Geometry and Analysis. The present volume is the fruit of the work of this Advanced Study Institute. We were fortunate to have with us Prof. Benoit Mandelbrot - the creator of numerous concepts in Fractal Geometry - who gave a series of lectures on multifractals, iteration of analytic functions, and various kinds of fractal stochastic processes. Different foundational contributions for Fractal Geometry like measure theory, dy­ namical systems, iteration theory, branching processes are recognized. The geometry of fractal sets and the analytical tools used to investigate them provide a unifying theme of this book. The main topics that are covered are then as follows. Dimension Theory. Many definitions of fractional dimension have been proposed, all of which coincide on "regular" objects, but often take different values for a given fractal set. There is ample discussion ...

Towards Video Quality Metrics Based on Colour Fractal Geometry

Directory of Open Access Journals (Sweden)

Richard Noël

2010-01-01

Full Text Available Vision is a complex process that integrates multiple aspects of an image: spatial frequencies, topology and colour. Unfortunately, so far, all these elements were independently took into consideration for the development of image and video quality metrics, therefore we propose an approach that blends together all of them. Our approach allows for the analysis of the complexity of colour images in the RGB colour space, based on the probabilistic algorithm for calculating the fractal dimension and lacunarity. Given that all the existing fractal approaches are defined only for gray-scale images, we extend them to the colour domain. We show how these two colour fractal features capture the multiple aspects that characterize the degradation of the video signal, based on the hypothesis that the quality degradation perceived by the user is directly proportional to the modification of the fractal complexity. We claim that the two colour fractal measures can objectively assess the quality of the video signal and they can be used as metrics for the user-perceived video quality degradation and we validated them through experimental results obtained for an MPEG-4 video streaming application; finally, the results are compared against the ones given by unanimously-accepted metrics and subjective tests.

A fractal derivative constitutive model for three stages in granite creep

Directory of Open Access Journals (Sweden)

R. Wang

Full Text Available In this paper, by replacing the Newtonian dashpot with the fractal dashpot and considering damage effect, a new constitutive model is proposed in terms of time fractal derivative to describe the full creep regions of granite. The analytic solutions of the fractal derivative creep constitutive equation are derived via scaling transform. The conventional triaxial compression creep tests are performed on MTS 815 rock mechanics test system to verify the efficiency of the new model. The granite specimen is taken from Beishan site, the most potential area for the China’s high-level radioactive waste repository. It is shown that the proposed fractal model can characterize the creep behavior of granite especially in accelerating stage which the classical models cannot predict. The parametric sensitivity analysis is also conducted to investigate the effects of model parameters on the creep strain of granite. Keywords: Beishan granite, Fractal derivative, Damage evolution, Scaling transformation

An Investigation of Fractal Characteristics of Marine Shales in the Southern China from Nitrogen Adsorption Data

Directory of Open Access Journals (Sweden)

Jian Xiong

2015-01-01

Full Text Available We mainly focus on the Permian, Lower Cambrian, Lower Silurian, and Upper Ordovician Formation; the fractal dimensions of marine shales in southern China were calculated using the FHH fractal model based on the low-pressure nitrogen adsorption analysis. The results show that the marine shales in southern China have the dual fractal characteristics. The fractal dimension D1 at low relative pressure represents the pore surface fractal characteristics, whereas the fractal dimension D2 at higher relative pressure describes the pore structure fractal characteristics. The fractal dimensions D1 range from 2.0918 to 2.718 with a mean value of 2.4762, and the fractal dimensions D2 range from 2.5842 to 2.9399 with a mean value of 2.8015. There are positive relationships between fractal dimension D1 and specific surface area and total pore volume, whereas the fractal dimensions D2 have negative correlation with average pore size. The larger the value of the fractal dimension D1 is, the rougher the pore surface is, which could provide more adsorption sites, leading to higher adsorption capacity for gas. The larger the value of the fractal dimension D2 is, the more complicated the pore structure is, resulting in the lower flow capacity for gas.

Pulse regime in formation of fractal fibers

Energy Technology Data Exchange (ETDEWEB)

Smirnov, B. M., E-mail: bmsmirnov@gmail.com [Joint Institute for High Temperatures (Russian Federation)

2016-11-15

The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gas flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.

Fractal characterization of the compaction and sintering of ferrites

NARCIS (Netherlands)

Glass, H.J.; With, de G.

2001-01-01

A novel parameter, the fractal exponent DE, is derived using the concept of fractal scaling. The fractal exponent DE relates the development of a feature within a material to the development of the size of the material. As an application, structural changes during the compaction and sintering of

Correlation of optical properties with the fractal microstructure of black molybdenum coatings

Energy Technology Data Exchange (ETDEWEB)

Barrera, Enrique; Gonzalez, Federico [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Rodriguez, Eduardo [Area de Computacion y Sistemas, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Alvarez-Ramirez, Jose, E-mail: jjar@xanum.uam.mx [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico)

2010-01-01

Coating is commonly used for improving the optical properties of surfaces for solar collector applications. The coating morphology depends on the deposition conditions, and this determines the final optical characteristics. Coating morphologies are irregular and of fractal nature, so a suitable approach for its characterization should use methods borrowed from fractal analysis. The aim of this work is to study the fractal characteristics of black molybdenum coatings on copper and to relate the fractal parameters to the optical properties. To this end, coating surfaces were prepared via immersion in a solution of ammonium paramolybdate for different deposition periods. The fractal analysis was carried out for SEM and AFM images of the coating surface and the fractal properties were obtained with a recently developed high-dimensional extension of the well-known detrended fluctuation analysis (DFA). The most salient parameter drawn from the application of the DFA is the Hurst index, a parameter related to the roughness of the coating surface, and the multifractality index, which is related to the non-linearity features of the coating morphology. The results showed that optical properties, including absorptance and emittance, are decreasing functions of the Hurst and multifractality indices. This suggests that coating surfaces with high absorptance and emittance values are related to complex coating morphologies conformed within a non-linear structure.

Labelling Of Coolant Flow Anomaly Using Fractal Structure

International Nuclear Information System (INIS)

Djainal, Djen Djen

1996-01-01

This research deals with the instrumentation of the detection and characterization of vertical two-phase flow coolant. This type of work is particularly intended to find alternative method for the detection and identification of noise in vertical two-phase flow in a nuclear reactor environment. Various new methods have been introduced in the past few years, an attempt to developed an objective indicator off low patterns. One of new method is Fractal analysis which can complement conventional methods in the description of highly irregular fluctuations. In the present work, Fractal analysis was applied to analyze simulated boiling coolant signal. This simulated signals were built by sum random elements in small subchannels of the coolant channel. Two modes are defined and both are characterized by their void fractions. In the case of uni modal -PDF signals, the difference between these modes is relatively small. On other hand, bimodal -PDF signals have relative large range. In this research, Fractal dimension can indicate the characters of that signals simulation

A Tutorial Review on Fractal Spacetime and Fractional Calculus

Science.gov (United States)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Site effect classification based on microtremor data analysis using concentration-area fractal model

Science.gov (United States)

Adib, A.; Afzal, P.; Heydarzadeh, K.

2014-07-01

The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Fractal based modelling and analysis of electromyography (EMG) to identify subtle actions.

Science.gov (United States)

Arjunan, Sridhar P; Kumar, Dinesh K

2007-01-01

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 demonstrate that the feature set consisting of bias values and fractal dimension of the recordings is suitable for classification of sEMG against the different hand gestures. The scatter plots demonstrate the presence of simple relationships of these features against the four hand gestures. The results indicate that there is small inter-experimental variation but large inter-subject variation. This may be due to differences in the size and shape of muscles for different subjects. The possible applications of this research include use in developing prosthetic hands, controlling machines and computers.

Fractal Image Coding with Digital Watermarks

Directory of Open Access Journals (Sweden)

Z. Klenovicova

2000-12-01

Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.

Biometric feature extraction using local fractal auto-correlation

International Nuclear Information System (INIS)

Chen Xi; Zhang Jia-Shu

2014-01-01

Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme: (i) using two-dimensional Gabor filter to extract the texture features of biometric images; (ii) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and (iii) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach. (condensed matter: structural, mechanical, and thermal properties)

Fractal dimension of cantori

International Nuclear Information System (INIS)

Li, W.; Bak, P.

1986-01-01

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

Fractal characteristic study of shearer cutter cutting resistance curves

Energy Technology Data Exchange (ETDEWEB)

Liu, C. [Heilongjiang Scientific and Technical Institute, Haerbin (China). Dept of Mechanical Engineering

2004-02-01

The cutting resistance curve is the most useful tool for reflecting the overall cutting performance of a cutting machine. The cutting resistance curve is influenced by many factors such as the pick structure and arrangement, the cutter operation parameters, coal quality and geologic conditions. This paper discusses the use of fractal geometry to study the properties of the cutting resistance curve, and the use of fractal dimensions to evaluate cutting performance. On the basis of fractal theory, the general form and calculation method of fractal characteristics are given. 4 refs., 3 figs., 1 tab.

Fractality and the law of the wall

Science.gov (United States)

Xu, Haosen H. A.; Yang, X. I. A.

2018-05-01

Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.

Fractal dynamics of heartbeat time series of young persons with metabolic syndrome

Science.gov (United States)

Muñoz-Diosdado, A.; Alonso-Martínez, A.; Ramírez-Hernández, L.; Martínez-Hernández, G.

2012-10-01

Many physiological systems have been in recent years quantitatively characterized using fractal analysis. We applied it to study heart variability of young subjects with metabolic syndrome (MS); we examined the RR time series (time between two R waves in ECG) with the detrended fluctuation analysis (DFA) method, the Higuchi's fractal dimension method and the multifractal analysis to detect the possible presence of heart problems. The results show that although the young persons have MS, the majority do not present alterations in the heart dynamics. However, there were cases where the fractal parameter values differed significantly from the healthy people values.

Analysis of a Model for the Morphological Structure of Renal Arterial Tree: Fractal Structure

Directory of Open Access Journals (Sweden)

Aurora Espinoza-Valdez

2013-01-01

experimental data measurements of the rat kidneys. The fractal dimension depends on the probability of sprouting angiogenesis in the development of the arterial vascular tree of the kidney, that is, of the distribution of blood vessels in the morphology generated by the analytical model. The fractal dimension might determine whether a suitable renal vascular structure is capable of performing physiological functions under appropriate conditions. The analysis can describe the complex structures of the development vasculature in kidney.

Morphometrical differences between resectable and non-resectable pancreatic cancer: a fractal analysis.

Science.gov (United States)

Vasilescu, Catalin; Giza, Dana Elena; Petrisor, Petre; Dobrescu, Radu; Popescu, Irinel; Herlea, Vlad

2012-01-01

Pancreatic cancer is a highly aggressive cancer with a rising incidence and poor prognosis despite active surgical treatment. Candidates for surgical resection should be carefully selected. In order to avoid unnecessary laparotomy it is useful to identify reliable factors that may predict resectability. Nuclear morphometry and fractal dimension of pancreatic nuclear features could provide important preoperative information in assessing pancreas resectability. Sixty-one patients diagnosed with pancreatic cancer were enrolled in this retrospective study between 2003 and 2005. Patients were divided into two groups: one resectable cancer group and one with non-resectable pancreatic cancer. Morphometric parameters measured were: nuclear area, length of minor axis and length of major axis. Nuclear shape and chromatin distribution of the pancreatic tumor cells were both estimated using fractal dimension. Morphometric measurements have shown significant differences between the nuclear area of the resectable group and the non-resectable group (61.9 ± 19.8µm vs. 42.2 ± 15.6µm). Fractal dimension of the nuclear outlines and chromatin distribution was found to have a higher value in the non-resectable group (p<0.05). Objective measurements should be performed to improve risk assessment and therapeutic decisions in pancreatic cancer. Nuclear morphometry of the pancreatic nuclear features can provide important pre-operative information in resectability assessment. The fractal dimension of the nuclear shape and chromatin distribution may be considered a new promising adjunctive tool for conventional pathological analysis.

Optical diffraction from fractals with a structural transition

International Nuclear Information System (INIS)

Perez Rodriguez, F.; Canessa, E.

1994-04-01

A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and biharmonic equations and are compared to more 'regular' irreversible clusters such as diffusion limited and Laplacian aggregates. The optical diffraction method enables to identify a decrease of the fractal dimension above the structural point. (author). 19 refs, 6 figs

An integral time series on simulated labeling using fractal structure

International Nuclear Information System (INIS)

Djainal, D.D.

1997-01-01

This research deals with the detection of time series of vertical two-phase flow, in attempt to developed an objective indicator of time series flow patterns. One of new method is fractal analysis which can complement conventional methods in the description of highly irregular fluctuations. in the present work, fractal analysis applied to analyze simulated boiling coolant signal. this simulated signals built by sum random elements in small subchannels of the coolant channel. Two modes are defined and both modes are characterized by their void fractions. in the case of unimodal-PDF signals, the difference between these modes is relative small. on other hand, bimodal-PDF signals have relative large range. in this research, fractal dimension can indicate the characters of that signals simulation

Classification of diabetic retinopathy using fractal dimension analysis of eye fundus image

Science.gov (United States)

Safitri, Diah Wahyu; Juniati, Dwi

2017-08-01

Diabetes Mellitus (DM) is a metabolic disorder when pancreas produce inadequate insulin or a condition when body resist insulin action, so the blood glucose level is high. One of the most common complications of diabetes mellitus is diabetic retinopathy which can lead to a vision problem. Diabetic retinopathy can be recognized by an abnormality in eye fundus. Those abnormalities are characterized by microaneurysms, hemorrhage, hard exudate, cotton wool spots, and venous's changes. The diabetic retinopathy is classified depends on the conditions of abnormality in eye fundus, that is grade 1 if there is a microaneurysm only in the eye fundus; grade 2, if there are a microaneurysm and a hemorrhage in eye fundus; and grade 3: if there are microaneurysm, hemorrhage, and neovascularization in the eye fundus. This study proposed a method and a process of eye fundus image to classify of diabetic retinopathy using fractal analysis and K-Nearest Neighbor (KNN). The first phase was image segmentation process using green channel, CLAHE, morphological opening, matched filter, masking, and morphological opening binary image. After segmentation process, its fractal dimension was calculated using box-counting method and the values of fractal dimension were analyzed to make a classification of diabetic retinopathy. Tests carried out by used k-fold cross validation method with k=5. In each test used 10 different grade K of KNN. The accuracy of the result of this method is 89,17% with K=3 or K=4, it was the best results than others K value. Based on this results, it can be concluded that the classification of diabetic retinopathy using fractal analysis and KNN had a good performance.

Using fractal analysis of thermal signatures for thyroid disease evaluation

Science.gov (United States)

Gavriloaia, Gheorghe; Sofron, Emil; Gavriloaia, Mariuca-Roxana; Ghemigean, Adina-Mariana

2010-11-01

The skin is the largest organ of the body and it protects against heat, light, injury and infection. Skin temperature is an important parameter for diagnosing diseases. Thermal analysis is non-invasive, painless, and relatively inexpensive, showing a great potential research. Since the thyroid regulates metabolic rate it is intimately connected to body temperature, more than, any modification of its function generates a specific thermal image on the neck skin. The shapes of thermal signatures are often irregular in size and shape. Euclidean geometry is not able to evaluate their shape for different thyroid diseases, and fractal geometry is used in this paper. Different thyroid diseases generate different shapes, and their complexity are evaluated by specific mathematical approaches, fractal analysis, in order to the evaluate selfsimilarity and lacunarity. Two kinds of thyroid diseases, hyperthyroidism and papillary cancer are analyzed in this paper. The results are encouraging and show the ability to continue research for thermal signature to be used in early diagnosis of thyroid diseases.

Fractal tomography and its application in 3D vision

Science.gov (United States)

Trubochkina, N.

2018-01-01

A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.

Wetting characteristics of 3-dimensional nanostructured fractal surfaces

Science.gov (United States)

Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy

2017-01-01

This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.

Teaching about Fractals.

Science.gov (United States)

Willson, Stephen J.

1991-01-01

Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)

A short history of fractal-Cantorian space-time

International Nuclear Information System (INIS)

Marek-Crnjac, L.

2009-01-01

The article attempts to give a short historical overview of the discovery of fractal-Cantorian space-time starting from the 17th century up to the present. In the last 25 years a great number of scientists worked on fractal space-time notably Garnet Ord in Canada, Laurent Nottale in France and Mohamed El Naschie in England who gave an exact mathematical procedure for the derivation of the dimensionality and curvature of fractal space-time fuzzy manifold.

Enhancement of critical temperature in fractal metamaterial superconductors

Energy Technology Data Exchange (ETDEWEB)

Smolyaninov, Igor I., E-mail: smoly@umd.edu [Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 (United States); Smolyaninova, Vera N. [Department of Physics Astronomy and Geosciences, Towson University, 8000 York Road, Towson, MD 21252 (United States)

2017-04-15

Fractal metamaterial superconductor geometry has been suggested and analyzed based on the recently developed theoretical description of critical temperature increase in epsilon near zero (ENZ) metamaterial superconductors. Considerable enhancement of critical temperature has been predicted in such materials due to appearance of large number of additional poles in the inverse dielectric response function of the fractal. Our results agree with the recent observation (Fratini et al. Nature 466, 841 (2010)) that fractal defect structure promotes superconductivity.

The fractal dimension of architecture

CERN Document Server

Ostwald, Michael J

2016-01-01

Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along...

Connotations of pixel-based scale effect in remote sensing and the modified fractal-based analysis method

Science.gov (United States)

Feng, Guixiang; Ming, Dongping; Wang, Min; Yang, Jianyu

2017-06-01

Scale problems are a major source of concern in the field of remote sensing. Since the remote sensing is a complex technology system, there is a lack of enough cognition on the connotation of scale and scale effect in remote sensing. Thus, this paper first introduces the connotations of pixel-based scale and summarizes the general understanding of pixel-based scale effect. Pixel-based scale effect analysis is essentially important for choosing the appropriate remote sensing data and the proper processing parameters. Fractal dimension is a useful measurement to analysis pixel-based scale. However in traditional fractal dimension calculation, the impact of spatial resolution is not considered, which leads that the scale effect change with spatial resolution can't be clearly reflected. Therefore, this paper proposes to use spatial resolution as the modified scale parameter of two fractal methods to further analyze the pixel-based scale effect. To verify the results of two modified methods (MFBM (Modified Windowed Fractal Brownian Motion Based on the Surface Area) and MDBM (Modified Windowed Double Blanket Method)); the existing scale effect analysis method (information entropy method) is used to evaluate. And six sub-regions of building areas and farmland areas were cut out from QuickBird images to be used as the experimental data. The results of the experiment show that both the fractal dimension and information entropy present the same trend with the decrease of spatial resolution, and some inflection points appear at the same feature scales. Further analysis shows that these feature scales (corresponding to the inflection points) are related to the actual sizes of the geo-object, which results in fewer mixed pixels in the image, and these inflection points are significantly indicative of the observed features. Therefore, the experiment results indicate that the modified fractal methods are effective to reflect the pixel-based scale effect existing in remote sensing

Fractal Dimension of Fracture Surface in Rock Material after High Temperature

Directory of Open Access Journals (Sweden)

Z. Z. Zhang

2015-01-01

Full Text Available Experiments on granite specimens after different high temperature under uniaxial compression were conducted and the fracture surfaces were observed by scanning electron microscope (SEM. The fractal dimensions of the fracture surfaces with increasing temperature were calculated, respectively. The fractal dimension of fracture surface is between 1.44 and 1.63. Its value approximately goes up exponentially with the increase of temperature. There is a quadratic polynomial relationship between the rockburst tendency and fractal dimension of fracture surface; namely, a fractal dimension threshold can be obtained. Below the threshold value, a positive correlativity shows between rockburst tendency and fractal dimension; when the fractal dimension is greater than the threshold value, it shows an inverse correlativity.

MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS

NARCIS (Netherlands)

VOGELAAR, MGR; WAKKER, BP; SCHWARZ, UJ

1991-01-01

To study the structure of interstellar clouds we used the so-called perimeter-area relation to estimate fractal dimensions. We studied the reliability of the method by applying it to artificial fractals and discuss some of the problems and pitfalls. Results for two different cloud types

On uses, misuses and potential abuses of fractal analysis in zooplankton behavioral studies: A review, a critique and a few recommendations

Science.gov (United States)

Seuront, Laurent

2015-08-01

Fractal analysis is increasingly used to describe, and provide further understanding to, zooplankton swimming behavior. This may be related to the fact that fractal analysis and the related fractal dimension D have the desirable properties to be independent of measurement scale and to be very sensitive to even subtle behavioral changes that may be undetectable to other behavioral variables. As early claimed by Coughlin et al. (1992), this creates "the need for fractal analysis" in behavioral studies, which has hence the potential to become a valuable tool in zooplankton behavioral ecology. However, this paper stresses that fractal analysis, as well as the more elaborated multifractal analysis, is also a risky business that may lead to irrelevant results, without paying extreme attention to a series of both conceptual and practical steps that are all likely to bias the results of any analysis. These biases are reviewed and exemplified on the basis of the published literature, and remedial procedures are provided not only for geometric and stochastic fractal analyses, but also for the more complicated multifractal analysis. The concept of multifractals is finally introduced as a direct, objective and quantitative tool to identify models of motion behavior, such as Brownian motion, fractional Brownian motion, ballistic motion, Lévy flight/walk and multifractal random walk. I finally briefly review the state of this emerging field in zooplankton behavioral research.

Elasticity of fractal materials using the continuum model with non-integer dimensional space

Science.gov (United States)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

Application of fractal theory to top-coal caving

International Nuclear Information System (INIS)

Xie, H.; Zhou, H.W.

2008-01-01

The experiences of underground coal mining in China show that coal in a thick hard coal seam with a hard roof, the so-called 'double hard coal seam', is difficult to be excavated by top-coal caving technique. In order to solve the problem, a top-coal weakening technique is proposed in this paper. In the present study, fractal geometry provides a new description of the fracture mechanism for blasting. By means of theoretical analysis of the relationship between the fractal dimension of blasting fragments and the dynamite specific energy, a mechanical model for describing the size distribution of top-coal and the dissipation of blasting energy is proposed. The theoretical results are in agreement with laboratory and in situ test results. Moreover, it is shown that the fractal dimension of coal fragments can be used as an index for optimizing the blasting parameters for a top-coal weakening technique

Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method

Science.gov (United States)

Zhu, Fanglong; Li, Kejing

2010-03-01

In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.

Fractal systems of central places based on intermittency of space-filling

International Nuclear Information System (INIS)

Chen Yanguang

2011-01-01

Highlights: → The idea of intermittency is introduced into central place model. → The revised central place model suggests incomplete space filling. → New central place fractals are presented for urban analysis. → The average nearest distance is proposed to estimate the fractal dimension. → The concept of distance-based space is replaced by that of dimension-based space. - Abstract: The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d = 2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D < d = 2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to explain the real patterns of urban places very well. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.

Fractales y series de datos geofísicos

Directory of Open Access Journals (Sweden)

Montes Vides Luis Alfredo

1993-10-01

Full Text Available

There is a new Geometry which provides a potentially tool for the characterization of geophysical data: The Fractal Geometry. Generally, Geophysical data consist of records in time or data series, for example yearly records of temperature, and they show a random behavior or variation on both a short and a long-term time scale. The trace of a record is a curve with a fractal dimension D, and it is characterized by an exponent H. In this paper, the Hurt's rescaled range analysis method is used to determine the fractal dimension of a geophysical data serie D and H, his self-affinity measure.

La geometría de fractales ha surgido como una herramienta potencialmente útil para la caracterización de datos en Geofísica. Comúnmente, los datos geofísicos conforman series de tiempo, que exhiben un comportamiento aleatorio o variación a corto y a largo plazo. Un ejemplo típico son los registros anuales de temperatura. La traza de un registro es una curva con una dimensión fractal D, caracterizada por un exponente H.

En el presente trabajo se utiliza el método de análisis de rango en cambios de escala, creado por H. E. Hurst, para determinar la dimensión fractal de una serie de datos geofísicos, y su medida de auto-afinidad.

Fractal analysis of striatal dopamine re-uptake sites

International Nuclear Information System (INIS)

Kuikka, J.T.; Bergstroem, K.A.; Tiihonen, J.; Raesaenen, P.; Karhu, J.

1997-01-01

Spatial variation in regional blood flow, metabolism and receptor density within the brain and in other organs is measurable even with a low spatial resolution technique such as emission tomography. It has been previously shown that the observed variance increases with increasing number of subregions in the organ/tissue studied. This resolution-dependent variance can be described by fractal analysis. We studied striatal dopamine re-uptake sites in 39 healthy volunteers with high-resolution single-photon emission tomography using iodine-123 labelled 2β-carbomethoxy-3β-(4-iodophenyl)tropane ([ 123 I]β-CIT). The mean fractal dimension was 1.15±0.07. The results indicate that regional striatal dopamine re-uptake sites involve considerable spatial heterogeneity which is higher than the uniform density (dimension=1.00) but much lower than complete randomness (dimension=1.50). There was a gender difference, with females having a higher heterogeneity in both the left and the right striatum. In addition, we found striatal asymmetry (left-to-right heterogeneity ratio of 1.19±0.15; P<0.001), suggesting functional hemispheric lateralization consistent with the control of motor behaviour and integrative functions. (orig.). With 5 figs., 1 tab

Fractal analysis of striatal dopamine re-uptake sites

Energy Technology Data Exchange (ETDEWEB)

Kuikka, J.T.; Bergstroem, K.A. [Department of Clinical Physiology, Kuopio University Hospital, Kuopio (Finland); Tiihonen, J.; Raesaenen, P. [Department of Forensic Psychiatry, University of Kuopio and Niuvanniemi Hospital, Kuopio (Finland); Karhu, J. [Department of Clinical Neurophysiology, Kuopio University Hospital, Kuopio (Finland)

1997-09-01

Spatial variation in regional blood flow, metabolism and receptor density within the brain and in other organs is measurable even with a low spatial resolution technique such as emission tomography. It has been previously shown that the observed variance increases with increasing number of subregions in the organ/tissue studied. This resolution-dependent variance can be described by fractal analysis. We studied striatal dopamine re-uptake sites in 39 healthy volunteers with high-resolution single-photon emission tomography using iodine-123 labelled 2{beta}-carbomethoxy-3{beta}-(4-iodophenyl)tropane ([{sup 123}I]{beta}-CIT). The mean fractal dimension was 1.15{+-}0.07. The results indicate that regional striatal dopamine re-uptake sites involve considerable spatial heterogeneity which is higher than the uniform density (dimension=1.00) but much lower than complete randomness (dimension=1.50). There was a gender difference, with females having a higher heterogeneity in both the left and the right striatum. In addition, we found striatal asymmetry (left-to-right heterogeneity ratio of 1.19{+-}0.15; P<0.001), suggesting functional hemispheric lateralization consistent with the control of motor behaviour and integrative functions. (orig.). With 5 figs., 1 tab.

MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS

NARCIS (Netherlands)

VOGELAAR, MGR; WAKKER, BP

To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We

MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS

NARCIS (Netherlands)

VOGELAAR, MGR; WAKKER, BP

1994-01-01

To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We

Site effect classification based on microtremor data analysis using a concentration-area fractal model

Science.gov (United States)

Adib, A.; Afzal, P.; Heydarzadeh, K.

2015-01-01

The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modelling reveal that proper soil types are located around the central city. The results derived via the fractal modelling were utilized to improve the Nogoshi and Igarashi (1970, 1971) classification results in the Meybod city. The resulting categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.

Heritability of retinal vascular fractals: a twin study

DEFF Research Database (Denmark)

Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line

. The retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficents. Falconer´s formula and quantitative genetic models were used to determine the genetic component of variation. Results: The retinal...... for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, p=0.0002) in monozygotic twins than in dizygotic twins (0.108, p=0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, 54% of the variation was explained...

Fractal Theory for Permeability Prediction, Venezuelan and USA Wells

Science.gov (United States)

Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana

2014-05-01

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

From dendrimers to fractal polymers and beyond

Directory of Open Access Journals (Sweden)

Charles N. Moorefield

2013-01-01

Full Text Available The advent of dendritic chemistry has facilitated materials research by allowing precise control of functional component placement in macromolecular architecture. The iterative synthetic protocols used for dendrimer construction were developed based on the desire to craft highly branched, high molecular weight, molecules with exact mass and tailored functionality. Arborols, inspired by trees and precursors of the utilitarian macromolecules known as dendrimers today, were the first examples to employ predesigned, 1 → 3 C-branched, building blocks; physical characteristics of the arborols, including their globular shapes, excellent solubilities, and demonstrated aggregation, combined to reveal the inherent supramolecular potential (e.g., the unimolecular micelle of these unique species. The architecture that is a characteristic of dendritic materials also exhibits fractal qualities based on self-similar, repetitive, branched frameworks. Thus, the fractal design and supramolecular aspects of these constructs are suggestive of a larger field of fractal materials that incorporates repeating geometries and are derived by complementary building block recognition and assembly. Use of terpyridine-M2+-terpyridine (where, M = Ru, Zn, Fe, etc connectivity in concert with mathematical algorithms, such as forms the basis for the Seirpinski gasket, has allowed the beginning exploration of fractal materials construction. The propensity of the fractal molecules to self-assemble into higher order architectures adds another dimension to this new arena of materials and composite construction.

Persistent fluctuations in stride intervals under fractal auditory stimulation.

Science.gov (United States)

Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J; Daffertshofer, Andreas

2014-01-01

Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.

Paper-based inkjet-printed ultra-wideband fractal antennas

KAUST Repository

Maza, Armando Rodriguez; Cook, Benjamin Stassen; Jabbour, Ghassan E.; Shamim, Atif

2012-01-01

For the first time, paper-based inkjet-printed ultra-wideband (UWB) fractal antennas are presented. Two new designs, a miniaturised UWB monopole, which utilises a fractal matching network and is the smallest reported inkjet-printed UWB printed

Detecting Springs in the Coastal Area of the Gunungsewu Karst Terrain, Yogyakarta Special Province, Indonesia, Analysis using Fractal Geometry

Directory of Open Access Journals (Sweden)

Sari Bahagiarti Kusumayudha

2009-11-01

Full Text Available The Gunungsewu area is a karst terrain with water scarcity, located in the Yogyakarta Special Province, adjacent to the open sea of Indian Ocean in the South. Shorelines of the Gunungsewu southern parts show fractal geometry phenomenon, and there can be found some groundwater outlets discharging to the Indian Ocean. One of the coastal outlets exists at the Baron Beach.The amount of water discharge from this spring reaches 20,000 l/sec in wet season, and approximately 9000 in dry season. In order to find other potential coastal springs, shoreline of the south coast is divided into some segments. By applying fractal analysis utilizing air photo of 1 : 30,000 scale, the fractal dimension of every shore line segment is determined, and then the fractal dimension value is correlated to the existence of spring in the segment being analyzed. The results inform us that shoreline segments having fractal dimension (D > 1.300 are potential for the occurrence of coastal springs.

Applications of fractals in ecology.

Science.gov (United States)

Sugihara, G; M May, R

1990-03-01

Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.

Fractal geometry of two-dimensional fracture networks at Yucca Mountain, southwestern Nevada: proceedings

International Nuclear Information System (INIS)

Barton, C.C.; Larsen, E.

1985-01-01

Fracture traces exposed on three 214- to 260-m 2 pavements in the same Miocene ash-flow tuff at Yucca Mountain, southwestern Nevada, have been mapped at a scale of 1:50. The maps are two-dimensional sections through the three-dimensional network of strata-bound fractures. All fractures with trace lengths greater than 0.20 m were mapped. The distribution of fracture-trace lengths is log-normal. The fractures do not exhibit well-defined sets based on orientation. Since fractal characterization of such complex fracture-trace networks may prove useful for modeling fracture flow and mechanical responses of fractured rock, an analysis of each of the three maps was done to test whether such networks are fractal. These networks proved to be fractal and the fractal dimensions (D) are tightly clustered (1.12, 1.14, 1.16) for three laterally separated pavements, even though visually the fracture networks appear quite different. The fractal analysis also indicates that the network patterns are scale independent over two orders of magnitude for trace lengths ranging from 0.20 to 25 m. 7 refs., 7 figs

Asymmetric multi-fractality in the U.S. stock indices using index-based model of A-MFDFA

International Nuclear Information System (INIS)

Lee, Minhyuk; Song, Jae Wook; Park, Ji Hwan; Chang, Woojin

2017-01-01

Highlights: • ‘Index-based A-MFDFA’ model is proposed to assess the asymmetric multi-fractality. • The asymmetric multi-fractality in the U.S. stock indices are investigated using ‘Index-based’ and ‘Return-based’ A-MFDFA. • The asymmetric feature is more significantly identified by ‘Index-based’ model than ‘return-based’ model. • Source of multi-fractality and time-varying features are analyzed. - Abstract: We detect the asymmetric multi-fractality in the U.S. stock indices based on the asymmetric multi-fractal detrended fluctuation analysis (A-MFDFA). Instead using the conventional return-based approach, we propose the index-based model of A-MFDFA where the trend based on the evolution of stock index rather than stock price return plays a role for evaluating the asymmetric scaling behaviors. The results show that the multi-fractal behaviors of the U.S. stock indices are asymmetric and the index-based model detects the asymmetric multi-fractality better than return-based model. We also discuss the source of multi-fractality and its asymmetry and observe that the multi-fractal asymmetry in the U.S. stock indices has a time-varying feature where the degree of multi-fractality and asymmetry increase during the financial crisis.

Band structures in Sierpinski triangle fractal porous phononic crystals

International Nuclear Information System (INIS)

Wang, Kai; Liu, Ying; Liang, Tianshu

2016-01-01

In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.

Band structures in Sierpinski triangle fractal porous phononic crystals

Energy Technology Data Exchange (ETDEWEB)

Wang, Kai; Liu, Ying, E-mail: yliu5@bjtu.edu.cn; Liang, Tianshu

2016-10-01

In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.

Proliferative diabetic retinopathy characterization based on fractal features: Evaluation on a publicly available dataset.

Science.gov (United States)

Orlando, José Ignacio; van Keer, Karel; Barbosa Breda, João; Manterola, Hugo Luis; Blaschko, Matthew B; Clausse, Alejandro

2017-12-01

Diabetic retinopathy (DR) is one of the most widespread causes of preventable blindness in the world. The most dangerous stage of this condition is proliferative DR (PDR), in which the risk of vision loss is high and treatments are less effective. Fractal features of the retinal vasculature have been previously explored as potential biomarkers of DR, yet the current literature is inconclusive with respect to their correlation with PDR. In this study, we experimentally assess their discrimination ability to recognize PDR cases. A statistical analysis of the viability of using three reference fractal characterization schemes - namely box, information, and correlation dimensions - to identify patients with PDR is presented. These descriptors are also evaluated as input features for training ℓ1 and ℓ2 regularized logistic regression classifiers, to estimate their performance. Our results on MESSIDOR, a public dataset of 1200 fundus photographs, indicate that patients with PDR are more likely to exhibit a higher fractal dimension than healthy subjects or patients with mild levels of DR (P≤1.3×10-2). Moreover, a supervised classifier trained with both fractal measurements and red lesion-based features reports an area under the ROC curve of 0.93 for PDR screening and 0.96 for detecting patients with optic disc neovascularizations. The fractal dimension of the vasculature increases with the level of DR. Furthermore, PDR screening using multiscale fractal measurements is more feasible than using their derived fractal dimensions. Code and further resources are provided at https://github.com/ignaciorlando/fundus-fractal-analysis. © 2017 American Association of Physicists in Medicine.

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

International Nuclear Information System (INIS)

Rangayyan, Rangaraj M.; Prajna, Shormistha; Ayres, Fabio J.; Desautels, J.E.L.

2008-01-01

Mammography is a widely used screening tool for the early detection of breast cancer. One of the commonly missed signs of breast cancer is architectural distortion. The purpose of this study is to explore the application of fractal analysis and texture measures for the detection of architectural distortion in screening mammograms taken prior to the detection of breast cancer. A method based on Gabor filters and phase portrait analysis was used to detect initial candidates for sites of architectural distortion. A total of 386 regions of interest (ROIs) were automatically obtained from 14 ''prior mammograms'', including 21 ROIs related to architectural distortion. From the corresponding set of 14 ''detection mammograms'', 398 ROIs were obtained, including 18 related to breast cancer. For each ROI, the fractal dimension and Haralick's texture features were computed. The fractal dimension of the ROIs was calculated using the circular average power spectrum technique. The average fractal dimension of the normal (false-positive) ROIs was significantly higher than that of the ROIs with architectural distortion (p = 0.006). For the ''prior mammograms'', the best receiver operating characteristics (ROC) performance achieved, in terms of the area under the ROC curve, was 0.80 with a Bayesian classifier using four features including fractal dimension, entropy, sum entropy, and inverse difference moment. Analysis of the performance of the methods with free-response receiver operating characteristics indicated a sensitivity of 0.79 at 8.4 false positives per image in the detection of sites of architectural distortion in the ''prior mammograms''. Fractal dimension offers a promising way to detect the presence of architectural distortion in prior mammograms. (orig.)

Terahertz response of fractal meta-atoms based on concentric rectangular square resonators

Energy Technology Data Exchange (ETDEWEB)

Song, Zhiqiang; Zhao, Zhenyu, E-mail: zyzhao@shnu.edu.cn; Shi, Wangzhou [Department of Physics, Shanghai Normal University, Shanghai 200234 (China); Peng, Wei [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050 (China)

2015-11-21

We investigate the terahertz electromagnetic responses of fractal meta-atoms (MAs) induced by different mode coupling mechanisms. Two types of MAs based on concentric rectangular square (CRS) resonators are presented: independent CRS (I-CRS) and junctional-CRS (J-CRS). In I-CRS, each resonator works as an independent dipole so as to result in the multiple resonance modes when the fractal level is above 1. In J-CRS, however, the generated layer is rotated by π/2 radius to the adjacent CRS in one MA. The multiple resonance modes are coupled into a single mode resonance. The fractal level increasing induces resonance modes redshift in I-CRS while blueshift in J-CRS. When the fractal level is below 4, the mode Q factor of J-CRS is in between the two modes of I-CRS; when the fractal level is 4 or above, the mode Q factor of J-CRS exceeds the two modes of I-CRS. Furthermore, the modulation depth (MD) decreases in I-CRS while it increases in J-CRS with the increase in fractal levels. The surface currents analysis reveals that the capacitive coupling of modes in I-CRS results in the modes redshift, while the conductive coupling of modes in J-CRS induces the mode blueshift. A high Q mode with large MD can be achieved via conductive coupling between the resonators of different scales in a fractal MA.

Fractal studies on the positron annihilation in metals

International Nuclear Information System (INIS)

Lung, C.W.

1994-06-01

Traditionally, the Euclidean lines, circles and spheres have served as the basis of the intuitive understanding of the geometry of nature. Recently, the concept of fractals has caught the imagination of scientists in many fields. This paper is to continue our previous work on position annihilation near fractal surfaces to demonstrate that the concept of fractals provides a powerful tool for understanding the structure and properties of defects and rough surfaces in relation to positron annihilation studies. Some problems on Berry geometrical phase have also been discussed. (author). 15 refs, fig., 1 tab

Using fractal analysis in modeling the dynamics of forest areas and economic impact assessment

DEFF Research Database (Denmark)

Pintilii, Radu Daniel; Andronache, Ion; Diaconu, Daniel Constantin

2017-01-01

This study uses fractal analysis to quantify the spatial changes of forest resources caused by an increase of deforested areas. The method introduced contributes to the evaluation of forest resources being under significant pressure from anthropogenic activities. The pressure on the forest...... resources has been analyzed for Maramures, County, one of the most deforested counties in Romania. In order to evaluate this, the deforested areas were calculated for the period of 2001-2014, by using the Global Forest Change 2000-2014 database. The Fractal Fragmentation Index (FFI) and Fixed Grid 2D...

Mechanical test and fractal analysis on anisotropic fracture of cortical bone

International Nuclear Information System (INIS)

Yin, Dagang; Chen, Bin; Ye, Wei; Gou, Jihua; Fan, Jinghong

2015-01-01

Highlights: • The mechanical properties of the cortical bone of fresh bovine femora along three different directions are tested through four-point bending experiments. • SEM observation shows that the roughness of the fracture surfaces of the three different directions of the bone are remarkably different. • The fractal dimensions of the different fracture surfaces of the bone are calculated by box-counting method in MATLAB. • The fracture energies of the different fracture directions are calculated based on their fractal models. - Abstract: The mechanical properties of the cortical bone of fresh bovine femora along three different directions are tested through four-point bending experiments. It is indicated that the fracture energy along the transversal direction of the bone is distinctly larger than those of the longitudinal and radial directions. The fracture surfaces of the three different directions are observed by scanning electron microscope (SEM). It is shown that the roughness of the fracture surface of the transversal direction is obviously larger than those of the fracture surfaces of the longitudinal and radial directions. It is also revealed that the osteons in the bone are perpendicular to the fracture surface of the transversal direction and parallel to the fracture surfaces of the longitudinal and radial directions. Based on these experimental results, the fractal dimensions of the fracture surfaces of different directions are calculated by box-counting method in MATLAB. The calculated results show that the fractal dimension of the fracture surface of the transversal direction is remarkably larger than those of the fracture surfaces of the longitudinal and radial directions. The fracture energies of different directions are also calculated based on their fractal models. It is denoted that the fracture energy of the transversal direction is remarkably larger than those of the longitudinal and radial directions. The calculated results are in

Mechanical test and fractal analysis on anisotropic fracture of cortical bone

Energy Technology Data Exchange (ETDEWEB)

Yin, Dagang [State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044 (China); College of Aerospace Engineering, Chongqing University, Chongqing 400044 (China); Chen, Bin, E-mail: bchen@cqu.edu.cn [State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044 (China); College of Aerospace Engineering, Chongqing University, Chongqing 400044 (China); Ye, Wei [College of Aerospace Engineering, Chongqing University, Chongqing 400044 (China); Gou, Jihua [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 (United States); Fan, Jinghong [Division of Mechanical Engineering, Alfred University, Alfred, NY 14802 (United States)

2015-12-01

Highlights: • The mechanical properties of the cortical bone of fresh bovine femora along three different directions are tested through four-point bending experiments. • SEM observation shows that the roughness of the fracture surfaces of the three different directions of the bone are remarkably different. • The fractal dimensions of the different fracture surfaces of the bone are calculated by box-counting method in MATLAB. • The fracture energies of the different fracture directions are calculated based on their fractal models. - Abstract: The mechanical properties of the cortical bone of fresh bovine femora along three different directions are tested through four-point bending experiments. It is indicated that the fracture energy along the transversal direction of the bone is distinctly larger than those of the longitudinal and radial directions. The fracture surfaces of the three different directions are observed by scanning electron microscope (SEM). It is shown that the roughness of the fracture surface of the transversal direction is obviously larger than those of the fracture surfaces of the longitudinal and radial directions. It is also revealed that the osteons in the bone are perpendicular to the fracture surface of the transversal direction and parallel to the fracture surfaces of the longitudinal and radial directions. Based on these experimental results, the fractal dimensions of the fracture surfaces of different directions are calculated by box-counting method in MATLAB. The calculated results show that the fractal dimension of the fracture surface of the transversal direction is remarkably larger than those of the fracture surfaces of the longitudinal and radial directions. The fracture energies of different directions are also calculated based on their fractal models. It is denoted that the fracture energy of the transversal direction is remarkably larger than those of the longitudinal and radial directions. The calculated results are in

Experimental study of circle grid fractal pattern on turbulent intensity in pipe flow

International Nuclear Information System (INIS)

Manshoor, B; Zaman, I; Othman, M F; Khalid, Amir

2013-01-01

Fractal turbulence is deemed much more efficient than grid turbulence in terms of a turbulence generation. In this paper, the hotwire experimental results for the circle grids fractal pattern as a turbulent generator will be presented. The self-similar edge characteristic of the circle grid fractal pattern is thought to play a vital role in the enhancement of turbulent intensity. Three different beta ratios of perforated plates based on circle grids fractal pattern were used in the experimental work and each paired with standard circle grids with similar porosity. The objectives were to study the fractal scaling influence on the flow and also to explore the potential of the circle grids fractal pattern in enhancing the turbulent intensity. The results provided an excellent insight of the fractal generated turbulence and the fractal flow physics. Across the circle grids fractal pattern, the pressure drop was lower but the turbulent intensity was higher than those across the paired standard circle grids

An efficient fractal image coding algorithm using unified feature and DCT

International Nuclear Information System (INIS)

Zhou Yiming; Zhang Chao; Zhang Zengke

2009-01-01

Fractal image compression is a promising technique to improve the efficiency of image storage and image transmission with high compression ratio, however, the huge time consumption for the fractal image coding is a great obstacle to the practical applications. In order to improve the fractal image coding, efficient fractal image coding algorithms using a special unified feature and a DCT coder are proposed in this paper. Firstly, based on a necessary condition to the best matching search rule during fractal image coding, the fast algorithm using a special unified feature (UFC) is addressed, and it can reduce the search space obviously and exclude most inappropriate matching subblocks before the best matching search. Secondly, on the basis of UFC algorithm, in order to improve the quality of the reconstructed image, a DCT coder is combined to construct a hybrid fractal image algorithm (DUFC). Experimental results show that the proposed algorithms can obtain good quality of the reconstructed images and need much less time than the baseline fractal coding algorithm.

Fractal analysis of mandibular trabecular bone: optimal tile sizes for the tile counting method.

Science.gov (United States)

Huh, Kyung-Hoe; Baik, Jee-Seon; Yi, Won-Jin; Heo, Min-Suk; Lee, Sam-Sun; Choi, Soon-Chul; Lee, Sun-Bok; Lee, Seung-Pyo

2011-06-01

This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characteristics of the trabecular bone were calculated. The fractal dimensions of the processed images were analyzed in various tile sizes by the tile counting method. The optimal range of tile size was 0.132 mm to 0.396 mm for the fractal dimension using the tile counting method. The sizes were closely related to the morphometric parameters. The fractal dimension of mandibular trabecular bone, as calculated with the tile counting method, can be best characterized with a range of tile sizes from 0.132 to 0.396 mm.

A study of complexity of oral mucosa using fractal geometry

Directory of Open Access Journals (Sweden)

S R Shenoi

2017-01-01

Full Text Available Background: The oral mucosa lining the oral cavity is composed of epithelium supported by connective tissue. The shape of the epithelial-connective tissue interface has traditionally been used to describe physiological and pathological changes in the oral mucosa. Aim: The aim is to evaluate the morphometric complexity in normal, dysplastic, well-differentiated, and moderately differentiated squamous cell carcinoma (SCC of the oral mucosa using fractal geometry. Materials and Methods: A total of 80 periodic acid–Schiff stained histological images of four groups: normal mucosa, dysplasia, well-differentiated SCC, and moderately differentiated SCC were verified by the gold standard. These images were then subjected to fractal analysis. Statistical Analysis: ANOVA and post hoc test: Bonferroni was applied. Results: Fractal dimension (FD increases as the complexity increases from normal to dysplasia and then to SCC. Normal buccal mucosa was found to be significantly different from dysplasia and the two grades of SCC (P < 0.05. ANOVA of fractal scores of four morphometrically different groups of buccal mucosa was significantly different with F (3,76 = 23.720 and P< 0.01. However, FD of dysplasia was not significantly different from well-differentiated and moderately differentiated SCC (P = 1.000 and P = 0.382, respectively. Conclusion: This study establishes FD as a newer tool in differentiating normal tissue from dysplastic and neoplastic tissue. Fractal geometry is useful in the study of both physiological and pathological changes in the oral mucosa. A new grading system based on FD may emerge as an adjuvant aid in cancer diagnosis.

Persistent fluctuations in stride intervals under fractal auditory stimulation.

Directory of Open Access Journals (Sweden)

Vivien Marmelat

Full Text Available Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.

The fractal nature materials microstructure influence on electrochemical energy sources

Directory of Open Access Journals (Sweden)

Mitić V.V.

2015-01-01

Full Text Available With increasing of the world energy crisis, research for new, renewable and alternative energy sources are in growth. The focus is on research areas, sometimes of minor importance and applications, where the different synthesis methods and microstructure properties optimization, performed significant improvement of output materials’ and components’ electro-physical properties, which is important for higher energy efficiency and in the electricity production (batteries and battery systems, fuel cells and hydrogen energy contribution. Also, the storage tanks capacity improvement, for the energy produced on such way, which is one of the most important development issues in the energy sphere, represents a very promising research and application area. Having in mind, the results achieved in the electrochemical energy sources field, especially electrolyte development, these energy sources, materials fractal nature optimization analysis contribution, have been investigated. Based on materials fractal structure research field, particularly electronic materials, we have performed microstructure influence parameters research in electrochemistry area. We have investigated the Ho2O3 concentration influence (from 0.01wt% to 1wt% and sintering temperature (from 1320°C to 1380°C, as consolidation parameters, and thus, also open the electrochemical function fractalization door and in the basic thermodynamic parameters the fractal correction introduced. The fractal dimension dependence on additive concentration is also investigated. [Projekat Ministarstva nauke Republike Srbije, br. 172057: Directed synthesis, structure and properties of multifunctional materials

Fractal dimension evolution and spatial replacement dynamics of urban growth

International Nuclear Information System (INIS)

Chen Yanguang

2012-01-01

Highlights: ► The fractal dimension growth can be modeled by Boltzmann’s equation. ► Boltzmann’s model suggests urban spatial replacement dynamics. ► If the rate of urban growth is too high, periodic oscillations or chaos will arise. ► Chaos is associated with fractals by the fractal dimension evolution model. ► The fractal dimension of urban form implies the space-filling ratio of a city. - Abstract: This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to interpret the fractal dimension of urban form. The fractal dimension evolution of urban growth can be empirically modeled with Boltzmann’s equation. For the normalized data, Boltzmann’s equation is just equivalent to the logistic function. The logistic equation can be transformed into the well-known 1-dimensional logistic map, which is based on a 2-dimensional map suggesting spatial replacement dynamics of city development. The 2-dimensional recurrence relations can be employed to generate the nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is thus made in this article that, for the fractal dimension growth following the logistic curve, the normalized dimension value is the ratio of space filling. If the rate of spatial replacement (urban growth) is too high, the periodic oscillations and chaos will arise. The spatial replacement dynamics can be extended to general replacement dynamics, and bifurcation and chaos mirror a process of complex replacement.

Fractal and multifractal analyses of bipartite networks

Science.gov (United States)

Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

2017-03-01

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

Vortex-ring-fractal Structure of Atom and Molecule

International Nuclear Information System (INIS)

Osmera, Pavel

2010-01-01

This chapter is an attempt to attain a new and profound model of the nature's structure using a vortex-ring-fractal theory (VRFT). Scientists have been trying to explain some phenomena in Nature that have not been explained so far. The aim of this paper is the vortex-ring-fractal modeling of elements in the Mendeleev's periodic table, which is not in contradiction to the known laws of nature. We would like to find some acceptable structure model of the hydrogen as a vortex-fractal-coil structure of the proton and a vortex-fractal-ring structure of the electron. It is known that planetary model of the hydrogen atom is not right, the classical quantum model is too abstract. Our imagination is that the hydrogen is a levitation system of the proton and the electron. Structures of helium, oxygen, and carbon atoms and a hydrogen molecule are presented too.

The effect of ventricular assist devices on cerebral blood flow and blood pressure fractality

International Nuclear Information System (INIS)

Bellapart, Judith; Fraser, John F; Chan, Gregory S H; Tzeng, Yu-Chieh; Ainslie, Philip N; Dunster, Kimble R; Barnett, Adrian G; Boots, Rob

2011-01-01

Biological signals often exhibit self-similar or fractal scaling characteristics which may reflect intrinsic adaptability to their underlying physiological system. This study analysed fractal dynamics of cerebral blood flow in patients supported with ventricular assist devices (VAD) to ascertain if sustained modifications of blood pressure waveform affect cerebral blood flow fractality. Simultaneous recordings of arterial blood pressure and cerebral blood flow velocity using transcranial Doppler were obtained from five cardiogenic shock patients supported by VAD, five matched control patients and five healthy subjects. Computation of a fractal scaling exponent (α) at the low-frequency time scale by detrended fluctuation analysis showed that cerebral blood flow velocity exhibited 1/f fractal scaling in both patient groups (α = 0.95 ± 0.09 and 0.97 ± 0.12, respectively) as well as in the healthy subjects (α = 0.86 ± 0.07). In contrast, fluctuation in blood pressure was similar to non-fractal white noise in both patient groups (α = 0.53 ± 0.11 and 0.52 ± 0.09, respectively) but exhibited 1/f scaling in the healthy subjects (α = 0.87 ± 0.04, P < 0.05 compared with the patient groups). The preservation of fractality in cerebral blood flow of VAD patients suggests that normal cardiac pulsation and central perfusion pressure changes are not the integral sources of cerebral blood flow fractality and that intrinsic vascular properties such as cerebral autoregulation may be involved. However, there is a clear difference in the fractal scaling properties of arterial blood pressure between the cardiogenic shock patients and the healthy subjects

Nonlinear dynamics, fractals, cardiac physiology and sudden death

Science.gov (United States)

Goldberger, Ary L.

1987-01-01

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Speculations on self-avoiding surfaces in fractals. A mean field treatment

International Nuclear Information System (INIS)

Pandey, R.B.; Kumar, N.; Stauffer, D.

1984-08-01

We estimate the exponents characterizing the self-avoiding surfaces using an approximation in the framework of a Flory-type theory. We find for planar self-avoiding surfaces embedded randomly in a fractal of dimensionality D':theta=3/(4+D'); for random surfaces of fractal dimension D embedded in a Euclidian space of dimensionality d:theta=3/(2D+d-2); and for fractal surfaces embedded in a structure of fractal dimensionality D':theta=3/(2D+D'-2). (author)

Ulam method and fractal Weyl law for Perron-Frobenius operators

Science.gov (United States)

Ermann, L.; Shepelyansky, D. L.

2010-06-01

We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.

Taylor dispersion on a fractal

International Nuclear Information System (INIS)

Mazo, R.M.

1998-01-01

Taylor dispersion is the greatly enhanced diffusion in the direction of a fluid flow caused by ordinary diffusion in directions orthogonal to the flow. It is essential that the system be bounded in space in the directions orthogonal to the flow. We investigate the situation where the medium through which the flow occurs has fractal properties so that diffusion in the orthogonal directions is anomalous and non-Fickian. The effective diffusion in the flow direction remains normal; its width grows proportionally with the time. However, the proportionality constant depends on the fractal dimension of the medium as well as its walk dimension. (author)

Fractal universe and quantum gravity.

Science.gov (United States)

Calcagni, Gianluca

2010-06-25

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

Fractals control in particle's velocity

International Nuclear Information System (INIS)

Zhang Yongping; Liu Shutang; Shen Shulan

2009-01-01

Julia set, a fractal set of the literature of nonlinear physics, has significance for the engineering applications. For example, the fractal structure characteristics of the generalized M-J set could visually reflect the change rule of particle's velocity. According to the real world requirement, the system need show various particle's velocity in some cases. Thus, the control of the nonlinear behavior, i.e., Julia set, has attracted broad attention. In this work, an auxiliary feedback control is introduced to effectively control the Julia set that visually reflects the change rule of particle's velocity. It satisfies the performance requirement of the real world problems.

Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation

Directory of Open Access Journals (Sweden)

Zhen Yao

2004-12-01

Full Text Available A hybrid 3D compression scheme which combines fractal coding with neighbourhood vector quantisation for video and volume data is reported. While fractal coding exploits the redundancy present in different scales, neighbourhood vector quantisation, as a generalisation of translational motion compensation, is a useful method for removing both intra- and inter-frame coherences. The hybrid coder outperforms most of the fractal coders published to date while the algorithm complexity is kept relatively low.

a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

Science.gov (United States)

Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin

Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.

Fractal aspects and convergence of Newton`s method

Energy Technology Data Exchange (ETDEWEB)

Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)

1996-12-31

Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.

Electron spin-lattice relaxation in fractals

International Nuclear Information System (INIS)

Shrivastava, K.N.

1986-08-01

We have developed the theory of the spin-fracton interaction for paramagnetic ions in fractal structures. The interaction is exponentially damped by the self-similarity length of the fractal and by the range dimensionality d Φ . The relaxation time of the spin due to the absorption and emission of the fracton has been calculated for a general dimensionality called the Raman dimensionality d R , which for the fractons differs from the Hausdorff (fractal) dimensionality, D, as well as from the Euclidean dimensionality, d. The exponent of the energy level separation in the relaxation rate varies with d R d Φ /D. We have calculated the spin relaxation rate due to a new type of Raman process in which one fracton is absorbed to affect a spin transition from one electronic level to another and later another fracton is emitted along with a spin transition such that the difference in the energies of the two fractons is equal to the electronic energy level separation. The temperature and the dimensionality dependence of such a process has been found in several approximations. In one of the approximations where the van Vleck relaxation rate for a spin in a crystal is known to vary with temperature as T 9 , our calculated variation for fractals turns out to be T 6.6 , whereas the experimental value for Fe 3+ in frozen solutions of myoglobin azide is T 6.3 . Since we used d R =4/3 and the fracton range dimensionality d Φ =D/1.8, we expect to measure the dimensionalities of the problem by measuring the temperature dependence of the relaxation times. We have also calculated the shift of the paramagnetic resonance transition for a spin in a fractal for general dimensionalities. (author)

Launching the chaotic realm of iso-fractals: A short remark

Energy Technology Data Exchange (ETDEWEB)

O' Schmidt, Nathan [Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725 (United States); Katebi, Reza [Department of Physics, California State University in Fullerton, 800 North State College Boulevard, Fullerton, CA 92831 (United States); Corda, Christian [Institute for Theoretical Physics and Advanced Mathematics Einstein-Galilei (IFM), Via Santa Gonda 14, 59100 Prato (Italy)

2015-03-10

In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete case examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.

[Features of fractal dynamics EEG of alpha-rhythm in patients with neurotic and neurosis-like disorders].

Science.gov (United States)

Shul'ts, E V; Baburin, I N; Karavaeva, T A; Karvasarskiĭ, B D; Slezin, V B

2011-01-01

Fifty-five patients with neurotic and neurosis-like disorders and 20 healthy controls, aged 17-64 years, have been examined. The basic research method was electroencephalography (EEG) with the fractal analysis of alpha power fluctuations. In patients, the changes in the fractal structure were of the same direction: the decrease of fractal indexes of low-frequency fluctuations and the increase of fractal indexes of mid-frequency fluctuations. Patients with neurosis-like disorders, in comparison to those with neurotic disorders, were characterized by more expressed (quantitative) changes in fractal structures of more extended character. It suggests the presence of deeper pathological changes in patients with neurosis-like disorders.

Fractals as macroscopic manifestation of squeezed coherent states and brain dynamics

International Nuclear Information System (INIS)

Vitiello, Giuseppe

2012-01-01

Recent results on the relation between self-similarity and squeezed coherent states are presented. I consider fractals which are generated iteratively according to a prescribed recipe, the so-called deterministic fractals. Fractal properties are incorporated in the framework of the theory of the entire analytical functions and deformed coherent states. Conversely, fractal properties of squeezed coherent states are recognized. This sheds some light on the understanding of the dynamical origin of fractals and their global nature emerging from local deformation processes. The self-similarity in brain background activity suggested by laboratory observations of power-law distributions of power spectral densities of electrocorticograms is also discussed and accounted in the frame of the dissipative many-body model of brain.

Chaos and fractals. Applications to nuclear engineering

International Nuclear Information System (INIS)

Clausse, A.; Delmastro, D.F.

1990-01-01

This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es

Fractal analysis of the hydraulic conductivity on a sandy porous media reproduced in a laboratory facility.

Science.gov (United States)

de Bartolo, S.; Fallico, C.; Straface, S.; Troisi, S.; Veltri, M.

2009-04-01

The complexity characterization of the porous media structure, in terms of the "pore" phase and the "solid" phase, can be carried out by means of the fractal geometry which is able to put in relationship the soil structural properties and the water content. It is particularly complicated to describe analytically the hydraulic conductivity for the irregularity of the porous media structure. However these can be described by many fractal models considering the soil structure as the distribution of particles dimensions, the distribution of the solid aggregates, the surface of the pore-solid interface and the fractal mass of the "pore" and "solid" phases. In this paper the fractal model of Yu and Cheng (2002) and Yu and Liu (2004), for a saturated bidispersed porous media, was considered. This model, using the Sierpinsky-type gasket scheme, doesn't contain empiric constants and furnishes a well accord with the experimental data. For this study an unconfined aquifer was reproduced by means of a tank with a volume of 10 Ã- 7 Ã- 3 m3, filled with a homogeneous sand (95% of SiO2), with a high percentage (86.4%) of grains between 0.063mm and 0.125mm and a medium-high permeability. From the hydraulic point of view, 17 boreholes, a pumping well and a drainage ring around its edge were placed. The permeability was measured utilizing three different methods, consisting respectively in pumping test, slug test and laboratory analysis of an undisturbed soil cores, each of that involving in the measurement a different support volume. The temporal series of the drawdown obtained by the pumping test were analyzed by the Neuman-type Curve method (1972), because the saturated part above the bottom of the facility represents an unconfined aquifer. The data analysis of the slug test were performed by the Bouwer & Rice (1976) method and the laboratory analysis were performed on undisturbed saturated soil samples utilizing a falling head permeameter. The obtained values either of the

Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

Science.gov (United States)

Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P

2015-01-01

Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.

Theoretical study of fractal growth and stability on surface

DEFF Research Database (Denmark)

Dick, Veronika V.; Solov'yov, Ilia; Solov'yov, Andrey V.

2009-01-01

We perform a theoretical study of the fractal growing process on surface by using the deposition, diffusion, aggregation method. We present a detailed analysis of the post-growth processes occurring in a nanofractal on surface. For this study we developed a method which describes the internal...... dynamics of particles in a fractal and accounts for their diffusion and detachment. We demonstrate that these kinetic processes are responsible for the formation of the final shape of the islands on surface after the post-growth relaxation....

Fractal analysis of the ULF geomagnetic data obtained at Izu Peninsula, Japan in relation to the nearby earthquake swarm of June–August 2000

Directory of Open Access Journals (Sweden)

K. Gotoh

2003-01-01

Full Text Available In our recent papers we applied fractal methods to extract the earthquake precursory signatures from scaling characteristics of the ULF geomagnetic data, obtained in a seismic active region of Guam Island during the large earthquake of 8 August 1993. We found specific dynamics of their fractal characteristics (spectral exponents and fractal dimensions before the earthquake: appearance of the flicker-noise signatures and increase of the time series fractal dimension. Here we analyze ULF geomagnetic data obtained in a seismic active region of Izu Peninsula, Japan during a swarm of the strong nearby earthquakes of June–August 2000 and compare the results obtained in both regions. We apply the same methodology of data processing using the FFT procedure, Higuchi method and Burlaga-Klein approach to calculate the spectral exponents and fractal dimensions of the ULF time series. We found the common features and specific peculiarities in the behavior of fractal characteristics of the ULF time series before Izu and Guam earthquakes. As a common feature, we obtained the same increase of the ULF time series fractal dimension before the earthquakes, and as specific peculiarity – this increase appears to be sharp for Izu earthquake in comparison with gradual increase of the ULF time series fractal dimension for Guam earthquake. The results obtained in both regions are discussed on the basis of the SOC (self-organized criticality concept taking into account the differences in the depths of the earthquake focuses. On the basis of the peculiarities revealed, we advance methodology for extraction of the earthquake precursory signatures. As an adjacent step, we suggest the combined analysis of the ULF time series in the parametric space polarization ratio – fractal dimension. We reason also upon the advantage of the multifractal approach with respect to the mono-fractal analysis for study of the earthquake preparation dynamics.

Fractal character of structural control on uranium mineralization in south china

International Nuclear Information System (INIS)

Zhou Quanyu; Tan Kaixuan; Xie Yanshi

2009-01-01

South China is the most important uranium producer in the country. Most uranium ore deposits in south China are strictly controlled by NE-NNE trending regional fracture structure. Fractal analyses on spatial distribution of uranium ore deposits and regional fracture structure in south China have been done in this paper. It indicates that the spatial distribution of both uranium ore deposits and regional fracture structure in south China show fractal character. The fractal dimension D=1.414 2 for the spatial distribution of regional fracture structure in the whole area indicate a higher ripening degree in the fracture structure evolution and an advantages to fluid flow and uranium mineralization. The fractal dimension D=1.052 7 for the spatial distribution of uranium ore deposits in south China show a lower complexity than regional fracture structure. The fractal dimensions in three sub-areas in south China on spatial distribution of uranium ore deposits show a positive correlation to which of regional fracture structure. The fractal spatial distribution of uranium ore deposits in south China is the result of the evolution of the fractal fracture structure system. (authors)

Anisotropic fractal media by vector calculus in non-integer dimensional space

Energy Technology Data Exchange (ETDEWEB)

Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)

2014-08-15

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Anisotropic fractal media by vector calculus in non-integer dimensional space

Science.gov (United States)

Tarasov, Vasily E.

2014-08-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

Anisotropic fractal media by vector calculus in non-integer dimensional space

International Nuclear Information System (INIS)

Tarasov, Vasily E.

2014-01-01

A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media

Design of silicon-based fractal antennas

KAUST Repository

Ghaffar, Farhan A.

2012-11-20

This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.

Design of silicon-based fractal antennas

KAUST Repository

Ghaffar, Farhan A.; Shamim, Atif

2012-01-01

This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.

Fractal dimension of microbead assemblies used for protein detection.

Science.gov (United States)

Hecht, Ariel; Commiskey, Patrick; Lazaridis, Filippos; Argyrakis, Panos; Kopelman, Raoul

2014-11-10

We use fractal analysis to calculate the protein concentration in a rotating magnetic assembly of microbeads of size 1 μm, which has optimized parameters of sedimentation, binding sites and magnetic volume. We utilize the original Forrest-Witten method, but due to the relatively small number of bead particles, which is of the order of 500, we use a large number of origins and also a large number of algorithm iterations. We find a value of the fractal dimension in the range 1.70-1.90, as a function of the thrombin concentration, which plays the role of binding the microbeads together. This is in good agreement with previous results from magnetorotation studies. The calculation of the fractal dimension using multiple points of reference can be used for any assembly with a relatively small number of particles. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.

Return to axi-symmetry for pipe flows generated after a fractal orifice

Energy Technology Data Exchange (ETDEWEB)

Nicolleau, F C G A, E-mail: F.Nicolleau@Sheffield.ac.uk [SFMG, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD (United Kingdom)

2013-12-15

We present experimental results obtained from pipe flows generated by fractal shaped orifices or openings. We compare different fractal orifices and their efficiencies to re-generate axi-symmetric flows and to return to the standard flow generated by a perforated plate or a circular orifice plate. We consider two families of fractal openings: mono-orifice and complex orifice and emphasize the differences between the two fractal families. For the Reynolds number we used, we found that there is an optimum iteration for the fractal level above which no improvement for practical applications such as flowmetering is to be expected. The main parameters we propose for the characterization of the fractal orifice are the connexity parameter, the symmetry angle and the gap to the wall {delta}*{sub g}. The results presented here are among the first for flows forced through fractal openings and will serve as a reference for future studies and benchmarks for numerical applications. (paper)

Return to axi-symmetry for pipe flows generated after a fractal orifice

International Nuclear Information System (INIS)

Nicolleau, F C G A

2013-01-01

We present experimental results obtained from pipe flows generated by fractal shaped orifices or openings. We compare different fractal orifices and their efficiencies to re-generate axi-symmetric flows and to return to the standard flow generated by a perforated plate or a circular orifice plate. We consider two families of fractal openings: mono-orifice and complex orifice and emphasize the differences between the two fractal families. For the Reynolds number we used, we found that there is an optimum iteration for the fractal level above which no improvement for practical applications such as flowmetering is to be expected. The main parameters we propose for the characterization of the fractal orifice are the connexity parameter, the symmetry angle and the gap to the wall δ* g . The results presented here are among the first for flows forced through fractal openings and will serve as a reference for future studies and benchmarks for numerical applications. (paper)

Boundary Fractal Analysis of Two Cube-oriented Grains in Partly Recrystallized Copper

DEFF Research Database (Denmark)

Sun, Jun; Zhang, Yubin; Dahl, Anders Bjorholm

2015-01-01

The protrusions and retrusions observed on the recrystallizing boundaries affect the migration kinetics during recrystallization. Characterization of the boundary roughness is necessary in order to evaluate their effects. This roughness has a structure that can be characterized by fractal analysis...

Turbulent premixed flames on fractal-grid-generated turbulence

Energy Technology Data Exchange (ETDEWEB)

Soulopoulos, N; Kerl, J; Sponfeldner, T; Beyrau, F; Hardalupas, Y; Taylor, A M K P [Mechanical Engineering Department, Imperial College London, London SW7 2AZ (United Kingdom); Vassilicos, J C, E-mail: ns6@ic.ac.uk [Department of Aeronautics, Imperial College London, London SW7 2AZ (United Kingdom)

2013-12-15

A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area. (paper)

Wetting characteristics of 3-dimensional nanostructured fractal surfaces

Energy Technology Data Exchange (ETDEWEB)

Davis, Ethan, E-mail: ethan.davis4@huskers.unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States); Liu, Ying; Jiang, Lijia; Lu, Yongfeng [Laser Assisted Nano Engineering Lab, Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, 209N Scott Engineering Center, Lincoln, NE 68588-0511 (United States); Ndao, Sidy, E-mail: sndao2@unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States)

2017-01-15

Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.

Wetting characteristics of 3-dimensional nanostructured fractal surfaces

International Nuclear Information System (INIS)

Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy

2017-01-01

Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.

Fractal scale-free networks resistant to disease spread

International Nuclear Information System (INIS)

Zhang, Zhongzhi; Zhou, Shuigeng; Zou, Tao; Chen, Guisheng

2008-01-01

The conventional wisdom is that scale-free networks are prone to epidemic propagation; in the paper we demonstrate that, on the contrary, disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show that it simultaneously has the following rich topological properties: scale-free degree distribution, tunable clustering coefficient, 'large-world' behavior, and fractal scaling. Existing network models do not display these characteristics. Then, we investigate the susceptible–infected–removed (SIR) model of the propagation of diseases in our fractal scale-free networks by mapping it to the bond percolation process. We establish the existence of non-zero tunable epidemic thresholds by making use of the renormalization group technique, which implies that power law degree distribution does not suffice to characterize the epidemic dynamics on top of scale-free networks. We argue that the epidemic dynamics are determined by the topological properties, especially the fractality and its accompanying 'large-world' behavior

Self-stabilized Fractality of Sea-coasts Through Damped Erosion

Science.gov (United States)

Sapoval, B.; Baldassari, A.; Gabrielli, A.

2004-05-01

Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).

Association between stride time fractality and gait adaptability during unperturbed and asymmetric walking.

Science.gov (United States)

Ducharme, Scott W; Liddy, Joshua J; Haddad, Jeffrey M; Busa, Michael A; Claxton, Laura J; van Emmerik, Richard E A

2018-04-01

Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5-10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50-100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking

Fractal Geometry in the Arts: AN Overview across the Different Cultures

Science.gov (United States)

Sala, Nicoletta

Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. The word "fractal" was coined less than thirty years ago by one of history's most creative and mathematicians, Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision of the geometry. Although other mathematical thinkers like Georg Cantor (1845-1918), Felix Hausdorff (1868-1942), Gaston Julia (1893-1978), Helge von Koch (1870-1924), Giuseppe Peano (1858-1932), Lewis Richardson (1891-1953), Waclaw Sierpinski (1882-1969) and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fascinating discipline. Fractal geometry is applied in different field now: engineering, physics, chemistry, biology, and architecture. The aim of this paper is to introduce an approach where the arts are analysed using a fractal point of view.

A variational principle for the Hausdorff dimension of fractal sets

DEFF Research Database (Denmark)

Olsen, Lars; Cutler, Colleen D.

1994-01-01

Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)......Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)...

Fractal and probability analysis of creep crack growth behavior in 2.25Cr–1.6W steel incorporating residual stresses

Energy Technology Data Exchange (ETDEWEB)

Xu, Mengjia; Xu, Jijin, E-mail: xujijin_1979@sjtu.edu.cn; Lu, Hao; Chen, Jieshi; Chen, Junmei; Wei, Xiao

2015-12-30

Graphical abstract: - Highlights: • Statistical and fractal analysis is applied to study the creep fracture surface. • The tensile residual stresses promote the initiation of creep crack. • The fractal dimension of a mixed mode fracture surface shows a wavy variation. • The fractal dimension increases with increasing intergranular fracture percentage. • Height coordinates of intergranular fracture surface fit Gaussian distribution. - Abstract: In order to clarify creep crack growth behavior in 2.25Cr–1.6W steel incorporating residual stresses, creep crack tests were carried out on the tension creep specimens, in which the residual stresses were generated by local remelting and cooling. Residual stresses in the specimens were measured using Synchrotron X-ray diffraction techniques. The fracture surface of the creep specimen was analyzed using statistical methods and fractal analysis. The relation between fractal dimension of the fracture surface and fracture mode of the creep specimen was discussed. Due to different fracture mechanisms, the probability density functions of the height coordinates vary with the intergranular crack percentage. Good fitting was found between Gaussian distribution and the probability function of height coordinates of the high percentage intergranular crack surface.

Fractal and probability analysis of creep crack growth behavior in 2.25Cr–1.6W steel incorporating residual stresses

International Nuclear Information System (INIS)

Xu, Mengjia; Xu, Jijin; Lu, Hao; Chen, Jieshi; Chen, Junmei; Wei, Xiao

2015-01-01

Graphical abstract: - Highlights: • Statistical and fractal analysis is applied to study the creep fracture surface. • The tensile residual stresses promote the initiation of creep crack. • The fractal dimension of a mixed mode fracture surface shows a wavy variation. • The fractal dimension increases with increasing intergranular fracture percentage. • Height coordinates of intergranular fracture surface fit Gaussian distribution. - Abstract: In order to clarify creep crack growth behavior in 2.25Cr–1.6W steel incorporating residual stresses, creep crack tests were carried out on the tension creep specimens, in which the residual stresses were generated by local remelting and cooling. Residual stresses in the specimens were measured using Synchrotron X-ray diffraction techniques. The fracture surface of the creep specimen was analyzed using statistical methods and fractal analysis. The relation between fractal dimension of the fracture surface and fracture mode of the creep specimen was discussed. Due to different fracture mechanisms, the probability density functions of the height coordinates vary with the intergranular crack percentage. Good fitting was found between Gaussian distribution and the probability function of height coordinates of the high percentage intergranular crack surface.

Fractal based curves in musical creativity: A critical annotation

Science.gov (United States)

Georgaki, Anastasia; Tsolakis, Christos

In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.

Fractal dimension analysis of malignant and benign endobronchial ultrasound nodes

International Nuclear Information System (INIS)

Fiz, José Antonio; Monte-Moreno, Enrique; Andreo, Felipe; Auteri, Santiago José; Sanz-Santos, José; Serra, Pere; Bonet, Gloria; Castellà, Eva; Manzano, Juan Ruiz

2014-01-01

Endobronchial ultrasonography (EBUS) has been applied as a routine procedure for the diagnostic of hiliar and mediastinal nodes. The authors assessed the relationship between the echographic appearance of mediastinal nodes, based on endobronchial ultrasound images, and the likelihood of malignancy. The images of twelve malignant and eleven benign nodes were evaluated. A previous processing method was applied to improve the quality of the images and to enhance the details. Texture and morphology parameters analyzed were: the image texture of the echographies and a fractal dimension that expressed the relationship between area and perimeter of the structures that appear in the image, and characterizes the convoluted inner structure of the hiliar and mediastinal nodes. Processed images showed that relationship between log perimeter and log area of hilar nodes was lineal (i.e. perimeter vs. area follow a power law). Fractal dimension was lower in the malignant nodes compared with non-malignant nodes (1.47(0.09), 1.53(0.10) mean(SD), Mann–Whitney U test p < 0.05)). Fractal dimension of ultrasonographic images of mediastinal nodes obtained through endobronchial ultrasound differ in malignant nodes from non-malignant. This parameter could differentiate malignat and non-malignat mediastinic and hiliar nodes

Study on Conversion Between Momentum and Contrarian Based on Fractal Game

Science.gov (United States)

Wu, Xu; Song, Guanghui; Deng, Yan; Xu, Lin

2015-06-01

Based on the fractal game which is performed by the majority and the minority, the fractal market theory (FMT) is employed to describe the features of investors' decision-making. Accordingly, the process of fractal games is formed in order to analyze the statistical features of conversion between momentum and contrarian. The result shows that among three fractal game mechanisms, the statistical feature of simulated return rate series is much more similar to log returns on actual series. In addition, the conversion between momentum and contrarian is also extremely similar to real situation, which can reflect the effectiveness of using fractal game in analyzing the conversion between momentum and contrarian. Moreover, it also provides decision-making reference which helps investors develop effective investment strategy.

Arctic sea ice melt pond fractal dimension - explained

Science.gov (United States)

Popovic, Predrag

As Arctic sea ice starts to melt in the summer, pools of melt water quickly form on its surface, significantly changing its albedo, and impacting its subsequent evolution. These melt ponds often form complex geometric shapes. One characteristic of their shape, the fractal dimension of the pond boundaries, D, when plotted as a function of pond size, has been shown to transition between the two fundamental limits of D = 1 and D = 2 at some critical pond size. Here, we provide an explanation for this behavior. First, using aerial photographs, we show how this fractal transition curve changes with time, and show that there is a qualitative difference in the pond shape as ice transitions from impermeable to permeable. Namely, while ice is impermeable, maximum fractal dimension is less than 2, whereas after it becomes permeable, maximum fractal dimension becomes very close to 2. We then show how the fractal dimension of a collection of overlapping circles placed randomly on a plane also transitions from D = 1 to D = 2 at a size equal to the average size of a single circle. We, therefore, conclude that this transition is a simple geometric consequence of regular shapes connecting. The one physical parameter that can be extracted from the fractal transition curve is the length scale at which transition occurs. We provide a possible explanation for this length scale by noting that the flexural wavelength of the ice poses a fundamental limit on the size of melt ponds on permeable ice. If this is true, melt ponds could be used as a proxy for ice thickness.

Fractal fluctuations and quantum-like chaos in the brain by analysis of variability of brain waves: A new method based on a fractal variance function and random matrix theory: A link with El Naschie fractal Cantorian space-time and V. Weiss and H. Weiss golden ratio in brain

International Nuclear Information System (INIS)

Conte, Elio; Khrennikov, Andrei; Federici, Antonio; Zbilut, Joseph P.

2009-01-01

We develop a new method for analysis of fundamental brain waves as recorded by the EEG. To this purpose we introduce a Fractal Variance Function that is based on the calculation of the variogram. The method is completed by using Random Matrix Theory. Some examples are given. We also discuss the link of such formulation with H. Weiss and V. Weiss golden ratio found in the brain, and with El Naschie fractal Cantorian space-time theory.

Fractal Nanotechnology

Directory of Open Access Journals (Sweden)

Amato P

2008-01-01

Full Text Available Abstract Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.

Fractal design concepts for stretchable electronics.

Science.gov (United States)

Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A

2014-01-01

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

Fractal design concepts for stretchable electronics

Science.gov (United States)

Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.

2014-02-01

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

Static friction between rigid fractal surfaces.

Science.gov (United States)

Alonso-Marroquin, Fernando; Huang, Pengyu; Hanaor, Dorian A H; Flores-Johnson, E A; Proust, Gwénaëlle; Gan, Yixiang; Shen, Luming

2015-09-01

Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.

Fractal analysis of electrolytically-deposited palladium hydride dendrites

International Nuclear Information System (INIS)

Bursill, L.A.; Julin, Peng; Xudong, Fan.

1990-01-01

The fractal scaling characteristics of the surface profile of electrolytically-deposited palladium hydride dendritic structures have been obtained using conventional and high resolution transmission electron microscopy. The results are in remarkable agreement with the modified diffusion-limited aggregation model. 19 refs., 3 tabs., 13 figs

Linear correlation between fractal dimension of surface EMG signal from Rectus Femoris and height of vertical jump

International Nuclear Information System (INIS)

Ancillao, Andrea; Galli, Manuela; Rigoldi, Chiara; Albertini, Giorgio

2014-01-01

Fractal dimension was demonstrated to be able to characterize the complexity of biological signals. The EMG time series are well known to have a complex behavior and some other studies already tried to characterize these signals by their fractal dimension. This paper is aimed at studying the correlation between the fractal dimension of surface EMG signal recorded over Rectus Femoris muscles during a vertical jump and the height reached in that jump. Healthy subjects performed vertical jumps at different heights. Surface EMG from Rectus Femoris was recorded and the height of each jump was measured by an optoelectronic motion capture system. Fractal dimension of sEMG was computed and the correlation between fractal dimension and eight of the jump was studied. Linear regression analysis showed a very high correlation coefficient between the fractal dimension and the height of the jump for all the subjects. The results of this study show that the fractal dimension is able to characterize the EMG signal and it can be related to the performance of the jump. Fractal dimension is therefore an useful tool for EMG interpretation

Fractal growth in impurity-controlled solidification in lipid monolayers

DEFF Research Database (Denmark)

Fogedby, Hans C.; Sørensen, Erik Schwartz; Mouritsen, Ole G.

1987-01-01

A simple two-dimensional microscopic model is proposed to describe solidifcation processes in systems with impurities which are miscible only in the fluid phase. Computer simulation of the model shows that the resulting solids are fractal over a wide range of impurity concentrations and impurity...... diffusional constants. A fractal-forming mechanism is suggested for impurity-controlled solidification which is consistent with recent experimental observations of fractal growth of solid phospholipid domains in monolayers. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....

Experiencia en el aula de secundaria con fractales

OpenAIRE

Gallardo, Sandra; Martínez-Santaolalla, Manuel José; Molina, Marta; Peñas, María; Cañadas, María C.; Crisóstomo, Edson

2006-01-01

Presentamos una experiencia docente en un aula de 2º ESO en la que trabajamos los fractales mediante el uso de material de carácter manipulativo. La metodología seguida se basa en la construcción de casos particulares con el fin de llegar al concepto de fractal.

A fractal view of Chernobyl fallout in Northern Italy and Europe

International Nuclear Information System (INIS)

Salvadori, G.; Ratti, S.P.; Belli, G.; Quinto, E.

1996-01-01

Fractals are associated with irregularity and represent a powerful tool for investigating phenomena featuring a complex behaviour, as it is the case of the atmospheric processes playing a role in spreading the radioactive pollution of Chernobyl in the environment. The introduction of fractals in environmental sciences is quite recent. Fractals may account for the presence of strong fluctuations and for the high variability characterising the natural events involved in the Chernobyl fallout: the geographical sparseness of pollutant and the presence of 'hot spots' make it advisable to use fractals as a theoretical framework for modelling

Fractal Dimension of Particle Showers Measured in a Highly Granular Calorimeter

CERN Document Server

Ruan, Manqi; Bourdy, Vincent; Brients, Jean-Claude; Videau, Henri

2014-01-01

fractal dimension of showers measured in a high granularity calorimeter designed for a future lepton collider. The shower fractal dimension reveals detailed information of the spatial configuration of the shower. It is found to be characteristic of the type of interaction and highly sensitive to the nature of the incident particle. Using the shower fractal dimension, we demonstrate a particle identification algorithm that can efficiently separate electromagnetic showers, hadronic showers and non-showering tracks. We also find a logarithmic dependence of the shower fractal dimension on the particle energy.

A family of fractal sets with Hausdorff dimension 0.618

Energy Technology Data Exchange (ETDEWEB)

Zhong Ting [Information Management and Engineering Institute, Jishou University, Zhangjiajie 427000, Hunan (China)], E-mail: zhongting_2005@126.com

2009-10-15

In this paper, we introduce a class of fractal sets, which can be recursively constructed by two sequences {l_brace}n{sub k}{r_brace}{sub k{>=}}{sub 1} and {l_brace}c{sub k}{r_brace}{sub k{>=}}{sub 1}. We obtain the exact Hausdorff dimensions of these types of fractal sets using the continued fraction map. Connection of continued fraction with El Naschie's fractal spacetime is also illustrated. Furthermore, we restrict one sequence {l_brace}c{sub k}{r_brace}{sub k{>=}}{sub 1} to make every irrational number {alpha} element of (0, 1) correspond to only one of the above fractal sets called {alpha}-Cantor sets, and we found that almost all {alpha}-Cantor sets possess a common Hausdorff dimension of 0.618, which is also the Hausdorff dimension of the one-dimensional random recursive Cantor set and it is the foundation stone of E-infinity fractal spacetime theory.

Incomplete information and fractal phase space

International Nuclear Information System (INIS)

Wang, Qiuping A.

2004-01-01

The incomplete statistics for complex systems is characterized by a so called incompleteness parameter ω which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of ω on the basis of fractal phase space. ω is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process

Theoretical concepts of fractal geometry semkow by radon emanation in solids

International Nuclear Information System (INIS)

Cruz G, H.

1996-01-01

The objective of this work is to introduce the fractal geometry concept to the study of gaseous emanations in solids, specially with reference to radon emission in mineral grains. The basic elements of fractals theory are developed. A fractal is defined as an auto similar subassembly, which fractal dimension is greater than the topological dimension. Starting from this, and making a brief description of the physicals basis of radon emission in solids, a model between emanation power (E R ) and the ratio s/v (surface to volume), is founded. A Gaussian model is assumed for extent of recoil from alpha decay of Ra-226. Using the results of Pfeifer it is obtained that distribution of pore size is scaled like Br -D-1 , where D: fractal[dimension, B: constant and r: pore radius. After an adequate mathematics expansion, it is found that the expression for emanation power is scaled like r 0 D-3 (r 0 grain radius). We may concluded that if we have a logarithmic graph of E R vs size of grain we can deduce the fractal dimension of the emanation surface. The experimental data of different materials provides an interval into fractal dimension D , between 2.1 to 2.86. (author). 5 refs., 1 tab

Form in the Natural Environment: Fractal Computer Graphics and Wassily Kandinsky.

Science.gov (United States)

Geake, John; Porter, Jim

1992-01-01

Reports on study of use of fractal geometry in a computer graphics program to improve the perception of intermediate grade level students in their paintings. Finds that students are more likely to use changing shapes and colors after viewing slides of fractal computer graphics. Concludes that fractal computer graphics would make highly engaging…

Prediction of pork quality parameters by applying fractals and data mining on MRI

DEFF Research Database (Denmark)

Caballero, Daniel; Pérez-Palacios, Trinidad; Caro, Andrés

2017-01-01

This work firstly investigates the use of MRI, fractal algorithms and data mining techniques to determine pork quality parameters non-destructively. The main objective was to evaluate the capability of fractal algorithms (Classical Fractal algorithm, CFA; Fractal Texture Algorithm, FTA and One...... Point Fractal Texture Algorithm, OPFTA) to analyse MRI in order to predict quality parameters of loin. In addition, the effect of the sequence acquisition of MRI (Gradient echo, GE; Spin echo, SE and Turbo 3D, T3D) and the predictive technique of data mining (Isotonic regression, IR and Multiple linear...... regression, MLR) were analysed. Both fractal algorithm, FTA and OPFTA are appropriate to analyse MRI of loins. The sequence acquisition, the fractal algorithm and the data mining technique seems to influence on the prediction results. For most physico-chemical parameters, prediction equations with moderate...

Fractal markets: Liquidity and investors on different time horizons

Science.gov (United States)

Li, Da-Ye; Nishimura, Yusaku; Men, Ming

2014-08-01

In this paper, we propose a new agent-based model to study the source of liquidity and the “emergent” phenomenon in financial market with fractal structure. The model rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stability and liquidity of the financial market the real world market lacks detailed data to bring it to light since it is difficult to identify and distinguish the investors with different time horizons in the empirical approach. results show that in a relatively short period of time fractal market provides liquidity from investors with different horizons and the market gains stability when the market structure changes from uniformity to diversification. In the real world the fractal structure with the finite of horizons can only stabilize the market within limits. With the finite maximum horizons, the greater diversity of the investors and the fractal structure will not necessarily bring more stability to the market which might come with greater fluctuation in large time scale.

Plot-slope soil erosion using 7Be measurement and rill fractal dimension

International Nuclear Information System (INIS)

Zhang Fengbao; Yang Mingyi

2010-01-01

In this study, we intended to use 7 Be measurement and fractal theory to quantify soil erosion process on slope. The results showed that contribution rate of inter rill erosion was more than that of rill erosion during early stage of rainfall. When it rained, contribution rate of rill erosion began to be higher than inter rill erosion and become the main part of erosion during medium stage of rainfall. The trend of contribution rate of inter rill erosion was growing and the rill erosion was lowering during late stage of rainfall. Rill fractal dimension on the plot slope was almost growing larger during rainfall,growing quickly during early stage of rainfall and slowly during the late stage. Correlations was positive between rill fractal dimension and total erosion amount, also positive between rill fractal dimension and rill erosion. The correlations was positive between rill fractal dimension variation and total erosion amount, also was positive between rill fractal dimension variation and rill erosion amount. The best correlation was observed between rill fractal dimension and rill erosion amount. These results indicated that the rill fractal dimension on the plot slope could represent the development process of rill,the complex degree of rill and the variation of soil erosion intensity on the entire slope. (authors)

Super Water-Repellent Fractal Surfaces of a Photochromic Diarylethene Induced by UV Light

Science.gov (United States)

Izumi, Norikazu; Minami, Takayuki; Mayama, Hiroyuki; Takata, Atsushi; Nakamura, Shinichiro; Yokojima, Satoshi; Tsujii, Kaoru; Uchida, Kingo

2008-09-01

Photochromic diarylethene forms super water-repellent surfaces upon irradiation with UV light. Microfibril-like crystals grow on the solid diarylethene surface after UV irradiation, and the contact angle of water on the surface becomes larger with increasing surface roughness with time. The fractal analysis was made by the box-counting method for the rough surfaces. There are three regions in the roughness size having the fractal dimension of ca. 2.4 (size of roughness smaller than 5 µm), of ca. 2.2 (size of roughness between 5-40 µm), and of ca. 2.0 (size of roughness larger than 40 µm). The fractal dimension of ca. 2.4 was due to the fibril-like structures generated gradually by UV irradiation on diarylethene surfaces accompanied with an increase in the contact angle. The surface structure with larger fractal dimension mainly contributes to realizing the super water-repellency of the diarylethene surfaces. This mechanism of spontaneous formation of fractal surfaces is similar to that for triglyceride and alkylketene dimer waxes.

An approach to study of methods for urban analysis and urban fabric renewal in observation of a city as a multiple fractal structure

Directory of Open Access Journals (Sweden)

Bogdanov Ana

2007-01-01

Full Text Available Urban forms and processes can be observed as fractal structures since in their seemingly chaotic development and complexity it can be noticed an internal order and regularity, which could be quantified and described by the methods of fractal analysis. With determination of fractal dimension it is possible to quantify the level of irregularity, the complexity and hierarchy of the urban structures, as well as the level of urban transformations in various time intersections. The fractal geometry method has been used in analyses of spatial distribution of population, networks and utilities because it corresponds more than deterministic methods to the nature of urban settlements as open, non-linear and dynamic systems. In that sense, fractal geometry becomes the means to grasp a complex morphological urban structure of urban settlements in general, the interrelationships between the inner spatial elements, and to predict future development possibilities. Moreover on the basis of urban pattern analysis by means of fractal geometry, it is possible to evaluate the growth and development process and to perform a comparative analysis of development in spatially and temporarily different settlement settings. Having in view that complex urban fabric presumes tight connections and diversity, which is in contrast to sprawl and monotony which increasingly characterize urban growth and development, this paper is a contribution to research of potential for modern urban settlements to regain the spirit of spontaneity and human dimension through application of development models that are fractal geometry based.

Fractal dimension of the fractured surface of materials

International Nuclear Information System (INIS)

Lung, C.W.; Zhang, S.Z.

1989-05-01

Fractal dimension of the fractured surface of materials is discussed to show that the origin of the negative correlation between D F and toughness lies in the method of fractal dimension measurement with perimeter-area relation and also in the physical mechanism of crack propagation. (author). 8 refs, 4 figs, 1 tab

A variable-order fractal derivative model for anomalous diffusion

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Liu Xiaoting

2017-01-01

Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

Science.gov (United States)

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E.; Bertoldo, Alessandra

2015-02-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

International Nuclear Information System (INIS)

Squarcina, Letizia; Bellani, Marcella; De Luca, Alberto; Bertoldo, Alessandra; Brambilla, Paolo; Turkheimer, Federico E

2015-01-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders. (paper)

Moisture diffusivity in structure of random fractal fiber bed

Energy Technology Data Exchange (ETDEWEB)

Zhu, Fanglong, E-mail: zhufanglong_168@163.com [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); The Chinese People' s Armed Police Forces Academy, Langfan City (China); Zhou, Yu; Feng, Qianqian [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); Xia, Dehong [School of Mechanical Engineering, University of Science and Technology, Beijing (China)

2013-11-08

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.

An Efficient Computational Technique for Fractal Vehicular Traffic Flow

Directory of Open Access Journals (Sweden)

Devendra Kumar

2018-04-01

Full Text Available In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.

Fractal corrections of BaTiO3-ceramic sintering parameters

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Mitić V.V.

2014-01-01

Full Text Available Morphology of ceramics grains and pores as well as Brownian character of particle dynamics inside ceramics specimen contributes to better understanding of the sintering process. BaTiO3-ceramics, studied in this paper, has light fractal form and it is emanated in three aspects. First, the surface of grains, even in starting green body as well as distribution of grains shows fractal behavior. Second, existence of pores and their distribution follow the rules of fractal geometry. Third, movement of particles inside viscous flow underlies the rule of Brownian motion, which is essentially a fractal category. These three elements, each in its domain influence sintering dynamics, and can be described by dimensionless quantitative factors, αs αp and αm, being normalized to the interval [0,1]. Following sintering process, the associate formulae of Frenkel, Scherer and Mackenzie-Shuttleworth are shown from the angle of view of ceramics fractal dimension changing that approaches to 3. Also, it is shown that the energy balance is not violated after applying fractal correction to quasi equilibrium of the energy emanating from surface area reduction ES and energy adopted by viscous flow Ef .[Projekat Ministarstva nauke Republike Srbije, br. 172057: Directed synthesis, structure and properties of multifunctional materials

Flames in fractal grid generated turbulence

Energy Technology Data Exchange (ETDEWEB)

Goh, K H H; Hampp, F; Lindstedt, R P [Department of Mechanical Engineering, Imperial College, London SW7 2AZ (United Kingdom); Geipel, P, E-mail: p.lindstedt@imperial.ac.uk [Siemens Industrial Turbomachinery AB, SE-612 83 Finspong (Sweden)

2013-12-15

Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values {approx}0.1 and {approx}0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration. (paper)

Thermal properties of bodies in fractal and cantorian physics

International Nuclear Information System (INIS)

Zmeskal, Oldrich; Buchnicek, Miroslav; Vala, Martin

2005-01-01

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 element of 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 is more general than the Plank's radiation law based on the quantum heat diffusion theory. The energy density w = f (K, D), where K is the fractal measure and D is the fractal dimension exhibit typical dependency peaking with agreement with Planck's radiation law and with the experimental data for the absolutely black body in the energy interval kT m m kT m ∼ 1.5275. The agreement of the fractal model with the experimental outcomes is documented for the spectral characteristics of the Sun. The properties of stellar objects (black holes, relict radiation, etc.) and the elementary particles fields and interactions between them (quarks, leptons, mesons, baryons, bosons and their coupling constants) will be discussed with the help of the described mathematic apparatus in our further contributions. The general gas law for real gases in its more applicable form than the widely used laws (e.g. van der Waals, Berthelot, Kammerlingh-Onnes) has been also formulated. The energy density, which is in this case represented by the gas pressure p = f (K, D), can gain generally complex value and represents the behaviour of real (cohesive) gas in interval D element of (1,3>. The gas behaves as the ideal one only for particular values of the fractal dimensions (the energy density is real-valued). Again, it is shown that above the critical temperature (kT > K h c) and for fractal dimension D m > 2.0269 the results are comparable to the kinetics theory of real (ideal) gas (van der Waals equation of state, compressibility factor, Boyle's temperature). For the critical temperature (K h c = kT r ) the compressibility

Toward a new “Fractals-General Science”

Directory of Open Access Journals (Sweden)

Hassen Taher Dorrah

2014-09-01

Full Text Available A recent study has shown that everywhere real systems follow common “fractals-general stacking behavior” during their change pathways (or evolutionary life cycles. This fact leads to the emergence of the new discipline “Fractals-General Science” as a mother-discipline (and acting as upper umbrella of existing natural and applied sciences to commonly handle their fractals-general change behavior. It is, therefore, the main targets of this short communication are to present the motives, objectives, relations with other existing sciences, and the development map of such new science. It is discussed that there are many foreseen illustrative applications in geology, archeology, astronomy, life sciences, ecology, environmental science, hydrology, agronomy, engineering, materials sciences, chemistry, nanotechnology, biology, medicine, psychiatry, sociology, humanities, education, and arts that could effectively lead the implementation and experimentation of such new science. It is highlighted that the new “Fractals-General Science” could provide through multi-stacking representations the necessary platforms for investigating interactions and mutual changes between real life systems belonging to several sciences and disciplines. Examples are handling problems of the processing of basic formation and changes of matter and substances, propagation of combined corrosion, creep, fatigue and sedimentation of engineering and industrial systems, and the progressing of humans’ evolutionary life cycles.

Fractal sets generated by chemical reactions discrete chaotic dynamics

International Nuclear Information System (INIS)

Gontar, V.; Grechko, O.

2007-01-01

Fractal sets composed by the parameters values of difference equations derived from chemical reactions discrete chaotic dynamics (DCD) and corresponding to the sequences of symmetrical patterns were obtained in this work. Examples of fractal sets with the corresponding symmetrical patterns have been presented

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

Science.gov (United States)

Papadakis, Giorgos; Vallianatos, Filippos; Sammonds, Peter

2014-05-01

slope of the recurrence curve to forecast earthquakes in Colombia. Earth Sci. Res. J., 8, 3-9. Makropoulos, K., Kaviris, G., Kouskouna, V., 2012. An updated and extended earthquake catalogue for Greece and adjacent areas since 1900. Nat. Hazards Earth Syst. Sci., 12, 1425-1430. Papadakis, G., Vallianatos, F., Sammonds, P., 2013. Evidence of non extensive statistical physics behavior of the Hellenic Subduction Zone seismicity. Tectonophysics, 608, 1037-1048. Papaioannou, C.A., Papazachos, B.C., 2000. Time-independent and time-dependent seismic hazard in Greece based on seismogenic sources. Bull. Seismol. Soc. Am., 90, 22-33. Robertson, M.C., Sammis, C.G., Sahimi, M., Martin, A.J., 1995. Fractal analysis of three-dimensional spatial distributions of earthquakes with a percolation interpretation. J. Geophys. Res., 100, 609-620. Turcotte, D.L., 1997. Fractals and chaos in geology and geophysics. Second Edition, Cambridge University Press. Vallianatos, F., Michas, G., Papadakis, G., Sammonds, P., 2012. A non-extensive statistical physics view to the spatiotemporal properties of the June 1995, Aigion earthquake (M6.2) aftershock sequence (West Corinth rift, Greece). Acta Geophys., 60, 758-768.

Integration of Fractal Biosensor in a Digital Microfluidic Platform

KAUST Repository

Mashraei, Yousof

2016-06-08

The digital microfluidic (DMF) platform introduces many applications in biomedical assays. If it is to be commercially available to the public, it needs to have the essential features of smart sensing and a compact size. In this work, we report on a fractal electrode biosensor that is used for both droplet actuation and sensing C-reactive protein (CRP) concentration levels to assess cardiac disease risk. Our proposed electrode is the first two-terminal electrode design to be integrated into DMF platforms. A simulation of the electrical field distribution shows reduced peak intensities and uniform distribution of the field. When compared to a V-notch square electrode, the fractal electrode shows a superior performance in both aspects, i.e. field uniformity and intensity. These improvements are translated into a successful and responsive actuation of a water droplet with 100V. Likewise, the effective dielectric strength is improved by a 33% increase in the fractal electrode breakdown voltage. Additionally, the capability of the fractal electrode to work as a capacitive biosensor is evaluated with CRP quantification test. Selected fractal electrodes undergo a surface treatment to immobilize anti-CRP antibodies on their surface. The measurement shows a response to the added CRP in capacitance within three minutes. When the untreated electrodes were used for quantification, there was no significant change in capacitance, and this suggested that immobilization was necessary. The electrodes configuration in the fabricated DMF platform allows the fractal electrodes to be selectively used as biosensors, which means the device could be integrated into point-of-care applications.

Fuzzy fractals, chaos, and noise

Energy Technology Data Exchange (ETDEWEB)

Zardecki, A.

1997-05-01

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.

Some fractal properties of the percolating backbone in two dimensions

International Nuclear Information System (INIS)

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

1987-01-01

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

Solving fractal steady heat-transfer problems with the local fractional Sumudu transform

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Wang Yi

2015-01-01

Full Text Available In this paper the linear oscillator problem in fractal steady heat-transfer is studied within the local fractional theory. In particular, the local fractional Sumudu transform (LFST will be used to solve both the homogeneous and the non-homogeneous local fractional oscillator equations (LFOEs under fractal steady heat-transfer. It will be shown that the obtained non-differentiable solutions characterize the fractal phenomena with and without the driving force in fractal steady heat transfer at low excess temperatures.

Evaluation of surface quality by Fractal Dimension and Volume ...

African Journals Online (AJOL)

Experimental and simulation results have enabled to show than the large diameter ball under low loads and medium feed speeds, favors the elimination of peaks and reduction of fractal dimension whence quality improvement of surface. Keywords: burnishing, volume parameters, fractal dimension, experimental designs ...

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

Science.gov (United States)

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

On fractality and chaos in Moroccan family business stock returns and volatility

Science.gov (United States)

Lahmiri, Salim

2017-05-01

The purpose of this study is to examine existence of fractality and chaos in returns and volatilities of family business companies listed on the Casablanca Stock Exchange (CSE) in Morocco, and also in returns and volatility of the CSE market index. Detrended fluctuation analysis based Hurst exponent and fractionally integrated generalized autoregressive conditional heteroskedasticity (FIGARCH) model are used to quantify fractality in returns and volatility time series respectively. Besides, the largest Lyapunov exponent is employed to quantify chaos in both time series. The empirical results from sixteen family business companies follow. For return series, fractality analysis show that most of family business returns listed on CSE exhibit anti-persistent dynamics, whilst market returns have persistent dynamics. Besides, chaos tests show that business family stock returns are not chaotic while market returns exhibit evidence of chaotic behaviour. For volatility series, fractality analysis shows that most of family business stocks and market index exhibit long memory in volatility. Furthermore, results from chaos tests show that volatility of family business returns is not chaotic, whilst volatility of market index is chaotic. These results may help understanding irregularities patterns in Moroccan family business stock returns and volatility, and how they are different from market dynamics.

Fractal effects on excitations in diluted ferromagnets

International Nuclear Information System (INIS)

Kumar, D.

1981-08-01

The low energy spin-wave like excitations in diluted ferromagnets near percolation threshold are studied. For this purpose an explicit use of the fractal model for the backbone of the infinite percolating cluster due to Kirkpatrick is made. Three physical effects are identified, which cause the softening of spin-waves as the percolation point is approached. The importance of fractal effects in the calculation of density of states and the low temperature thermodynamics is pointed out. (author)

Three-dimensional fractal geometry for gas permeation in microchannels

NARCIS (Netherlands)

Malankowska, Magdalena; Schlautmann, Stefan; Berenschot, Erwin J.W.; Tiggelaar, Roald M.; Pina, Maria Pilar; Mallada, Reyes; Tas, Niels R.; Gardeniers, Han

2018-01-01

The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The

On Nonextensive Statistics, Chaos and Fractal Strings

CERN Document Server

Castro, C

2004-01-01

Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics ( with a non-additive $ q$-entropy ) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...

Fractal analysis of fracture increasing spontaneous imbibition in porous media with gas-saturated

KAUST Repository

Cai, Jianchao; Sun, Shuyu

2013-01-01

Spontaneous imbibition (SI) of wetting liquid into matrix blocks due to capillary pressure is regarded as an important recovery mechanism in low permeability fractured reservoir. In this paper, an analytical model is proposed for characterizing SI horizontally from a single plane fracture into gas-saturated matrix blocks. The presented model is based on the fractal character of pores in porous matrix, with gravity force included in the entire imbibition process. The accumulated mass of wetting liquid imbibed into matrix blocks is related to a number of factors such as contact area, pore fractal dimension, tortuosity, maximum pore size, porosity, liquid density and viscosity, surface tension, contact angle, as well as height and tilt angle of the fracture. The mechanism of fracture-enhanced SI is analyzed accordingly. Because of the effect of fracture, the gravity force is positive to imbibition process. Additionally, the farther away from the fracture top of the pore, the more influential the hydrostatic pressure is upon the imbibition action. The presented fractal analysis of horizontal spontaneous imbibition from a single fracture could also shed light on the scaling study of the mass transfer function between matrix and fracture system of fractured reservoirs. © 2013 World Scientific Publishing Company.

Fractal analysis of fracture increasing spontaneous imbibition in porous media with gas-saturated

KAUST Repository

Cai, Jianchao

2013-08-01

Spontaneous imbibition (SI) of wetting liquid into matrix blocks due to capillary pressure is regarded as an important recovery mechanism in low permeability fractured reservoir. In this paper, an analytical model is proposed for characterizing SI horizontally from a single plane fracture into gas-saturated matrix blocks. The presented model is based on the fractal character of pores in porous matrix, with gravity force included in the entire imbibition process. The accumulated mass of wetting liquid imbibed into matrix blocks is related to a number of factors such as contact area, pore fractal dimension, tortuosity, maximum pore size, porosity, liquid density and viscosity, surface tension, contact angle, as well as height and tilt angle of the fracture. The mechanism of fracture-enhanced SI is analyzed accordingly. Because of the effect of fracture, the gravity force is positive to imbibition process. Additionally, the farther away from the fracture top of the pore, the more influential the hydrostatic pressure is upon the imbibition action. The presented fractal analysis of horizontal spontaneous imbibition from a single fracture could also shed light on the scaling study of the mass transfer function between matrix and fracture system of fractured reservoirs. © 2013 World Scientific Publishing Company.

Fractal and Morphological Characteristics of Single Marble Particle Crushing in Uniaxial Compression Tests

Directory of Open Access Journals (Sweden)

Yidong Wang

2015-01-01

Full Text Available Crushing of rock particles is a phenomenon commonly encountered in geotechnical engineering practice. It is however difficult to study the crushing of rock particles using classical theory because the physical structure of the particles is complex and irregular. This paper aims at evaluating fractal and morphological characteristics of single rock particle. A large number of particle crushing tests are conducted on single rock particle. The force-displacement curves and the particle size distributions (PSD of crushed particles are analysed based on particle crushing tests. Particle shape plays an important role in both the micro- and macroscale responses of a granular assembly. The PSD of an assortment of rocks are analysed by fractal methods, and the fractal dimension is obtained. A theoretical formula for particle crushing strength is derived, utilising the fractal model, and a simple method is proposed for predicting the probability of particle survival based on the Weibull statistics. Based on a few physical assumptions, simple equations are derived for determining particle crushing energy. The results of applying these equations are tested against the actual experimental data and prove to be very consistent. Fractal theory is therefore applicable for analysis of particle crushing.

Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors

Science.gov (United States)

Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.

2017-11-01

Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.

Fractal Image Coding Based on a Fitting Surface

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Sheng Bi

2014-01-01

Full Text Available A no-search fractal image coding method based on a fitting surface is proposed. In our research, an improved gray-level transform with a fitting surface is introduced. One advantage of this method is that the fitting surface is used for both the range and domain blocks and one set of parameters can be saved. Another advantage is that the fitting surface can approximate the range and domain blocks better than the previous fitting planes; this can result in smaller block matching errors and better decoded image quality. Since the no-search and quadtree techniques are adopted, smaller matching errors also imply less number of blocks matching which results in a faster encoding process. Moreover, by combining all the fitting surfaces, a fitting surface image (FSI is also proposed to speed up the fractal decoding. Experiments show that our proposed method can yield superior performance over the other three methods. Relative to range-averaged image, FSI can provide faster fractal decoding process. Finally, by combining the proposed fractal coding method with JPEG, a hybrid coding method is designed which can provide higher PSNR than JPEG while maintaining the same Bpp.

The influence of the fractal particle size distribution on the mobility of dry granular materials

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Vallejo Luis E.

2017-01-01

Full Text Available This study presents an experimental analysis on the influence of the particle size distribution (psd on the mobility of dry granular materials. The psd obeys a power law of the form: N(L>d=kd-Df, where N is the number of particles with diameter L greater than a given diameter d, k is a proportionality constant, and Df is the fractal dimension of the psd. No laboratory or numerical study has been conducted to date analysing how a fractal psd influences the mobility of granular flows as in the case of rock avalanches. In this study, the flow characteristics of poly-dispersed granular materials that have a fractal psd were investigated in the laboratory. Granular mixtures having different fractal psd values were placed in a hollow cylinder. The cylinder was lifted and the distance of flow of the mixture was measured with respect to the original position of the cylinder. It was determined that the distance of flow of the mixtures was directly related to their fractal psd values. That is, the larger the distance of flow of the mixture, the larger is the fractal psd of the granular mixture tested. Thus, the fractal psd in dry granular mixtures seems to have a large influence on the easiness by which dry granular mixtures move in the field.

Vector calculus in non-integer dimensional space and its applications to fractal media

Science.gov (United States)

Tarasov, Vasily E.

2015-02-01

We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

Surface structures of equilibrium restricted curvature model on two fractal substrates

International Nuclear Information System (INIS)

Song Li-Jian; Tang Gang; Zhang Yong-Wei; Han Kui; Xun Zhi-Peng; Xia Hui; Hao Da-Peng; Li Yan

2014-01-01

With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature (ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension d f , but possess different dynamic exponents of random walk z rw . The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension d f , but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk z rw . The ERC model growing on the two substrates follows the well-known Family—Vicsek scaling law and satisfies the scaling relations 2α + d f ≍ z ≍ 2z rw . In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins—Herring equation. (general)

Navigation performance in virtual environments varies with fractal dimension of landscape.

Science.gov (United States)

Juliani, Arthur W; Bies, Alexander J; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E

2016-09-01

Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.

Quantitative Fractal Evaluation of Herbicide Effects on the Water-Absorbing Capacity of Superabsorbent Polymers

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Renkuan Liao

2014-01-01

Full Text Available The water absorption capacity of superabsorbent polymers (SAPs is important for agricultural drought resistance. However, herbicides may leach into the soil and affect water absorption by damaging the SAP three-dimensional membrane structures. We used 100-mesh sieves, electron microscopy, and fractal theory to study swelling and water absorption in SAPs in the presence of three common herbicides (atrazine, alachlor, and tribenuron-methyl at concentrations of 0.5, 1.0, and 2.0 mg/L. In the sieve experiments it was found that 2.0 mg/L atrazine reduces the capacity by 9.64–23.3% at different swelling points; no significant diminution was observed for the other herbicides or for lower atrazine concentrations. We found that the hydrogel membrane pore distributions have fractal characteristics in both deionized water and atrazine solution. The 2.0 mg/L atrazine destroyed the water-retaining polymer membrane pores and reduced the water-absorbing mass by modifying its three-dimensional membrane structure. A linear correlation was observed between the fractal analysis and the water-absorbing mass. Multifractal analysis characterized the membrane pore distribution by using the range of singularity indexes Δα (relative distinguishing range of 16.54–23.44%, which is superior to single-fractal analysis that uses the fractal dimension D (relative distinguishing range of 2.5–4.0%.

Fractal formation of a Y-Ba-Cu-O thin film on SrTiO3

International Nuclear Information System (INIS)

Chow, L.; Chen, J.; Desai, V.; Sundaram, K.; Arora, S.

1989-01-01

Fractal formation has been observed after thermal annealing of the rf-sputtered Y-Ba-Cu-O thin film on SrTiO 3 substrate. Through energy-dispersive x-ray analysis, it was found that the composition of the fractal was YBa 2 Cu 3 O x and the surrounding film composition wasY 2 Ba 2 Cu 3 O x . The fractal dimensions D ranging from 1.26 to 1.65 were obtained using the standard sandbox method with different thresholds

Fractal and spectroscopic analysis of soot from internal combustion engines

Science.gov (United States)

Swapna, M. S.; Saritha Devi, H. V.; Raj, Vimal; Sankararaman, S.

2018-03-01

Today diesel engines are used worldwide for various applications and very importantly in transportation. Hydrocarbons are the most widespread precursors among carbon sources employed in the production of carbon nanotubes (CNTs). The aging of internal combustion engine is an important parameter in deciding the carbon emission and particulate matter due to incomplete combustion of fuel. In the present work, an attempt has been made for the effective utilization of the aged engines for potential applicationapplications in fuel cells and nanoelectronics. To analyze the impact of aging, the particulate matter rich in carbon content areis collected from diesel engines of different ages. The soot with CNTs is purified by the liquid phase oxidation method and analyzed by Field Emission Scanning Electron Microscopy, High-Resolution Transmission Electron Microscopy, Energy Dispersive Spectroscopy, UV-Visible spectroscopy, Raman spectroscopy and Thermogravimetric analysis. The SEM image contains self-similar patterns probing fractal analysis. The fractal dimensions of the samples are determined by the box counting method. We could find a greater amount of single-walled carbon nanotubes (SWCNTs) in the particulate matter emitted by aged diesel engines and thereby giving information about the combustion efficiency of the engine. The SWCNT rich sample finds a wide range of applicationapplications in nanoelectronics and thereby pointing a potential use of these aged engines.

Fractal behaviour of the seismicity in the Southern Iberian Peninsula

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X. Lana

2005-01-01

Full Text Available The fractal behaviour of the seismicity in the Southern Iberian Peninsula is analysed by considering two different series of data: the distance and the elapsed time between consecutive seismic events recorded by the seismic network of the Andalusian Institute of Geophysics (AIG. The fractal analyses have been repeated by considering four threshold magnitudes of 2.5, 3.0, 3.5 and 4.0. The re-scaled analysis lets to determine if the seismicity shows strong randomness or if it is characterised by time-persistence and the cluster dimension indicates the degree of time and spatial clustering of the seismicity. Another analysis, based on the reconstruction theorem, permits to evaluate the minimum number of nonlinear equations describing the dynamical mechanism of the seismicity, its 'loss of memory', its chaotic character and the instability of a possible predicting algorithm. The results obtained depict some differences depending on distances or elapsed times and the different threshold levels of magnitude also lead to slightly different results. Additionally, only a part of the fractal tools, the re-scaled analysis, have been applied to five seismic crises in the same area.

Designing a fractal antenna of 2400 MHz

International Nuclear Information System (INIS)

Miranda Hamburger, Fabio

2012-01-01

The design of a fractal antenna with 2400 MHz of frequency has been studied. The fractal used is described by Waclaw Spierpi.ski. The initial figure, also known as seed, is divided using equilateral triangles with the aim of obtaining a perimeter similar to a meaningful portion of wave length. The use of λ to establish an ideal perimeter has reduced the radiation resistance. The adequate number of iterations needed to design the antenna is calculated based on λ. (author) [es

Heat kernels and zeta functions on fractals

International Nuclear Information System (INIS)

Dunne, Gerald V

2012-01-01

On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)

Password Authentication Based on Fractal Coding Scheme

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Nadia M. G. Al-Saidi

2012-01-01

Full Text Available Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.

Ag nanoparticles formed by femtosecond pulse laser ablation in water: self-assembled fractal structures

Energy Technology Data Exchange (ETDEWEB)

Santillán, Jesica M. J. [CONICET La Plata-CIC, Centro de Investigaciones Ópticas (CIOp) (Argentina); Fernández van Raap, Marcela B., E-mail: raap@fisica.unlp.edu.ar; Mendoza Zélis, Pedro; Coral, Diego [CONICET, Instituto de Física La Plata (IFLP) (Argentina); Muraca, Diego [Universidade Estadual de Campinas, Instituto de Física “Gleb Wataghin” (IFGW) (Brazil); Schinca, Daniel C.; Scaffardi, Lucía B., E-mail: lucias@ciop.unlp.edu.ar [CONICET La Plata-CIC, Centro de Investigaciones Ópticas (CIOp) (Argentina)

2015-02-15

We report for the first time on the formation of self-assembled fractals of spherical Ag nanoparticles (Nps) fabricated by femtosecond pulse laser ablation of a solid silver target in water. Fractal structures grew both in two and three Euclidean dimensions (d). Ramified-fractal assemblies of 2 nm height and 5–14 μm large, decorated with Ag Nps of 3 nm size, were obtained in a 2d geometry when highly diluted drops of colloidal suspension were dried at a fast heating rate over a mica substrate. When less-diluted drops were dried at slow heating rate, isolated single Nps or rosette-like structures were formed. Fractal aggregates about 31 nm size in 3d geometry were observed in the as-prepared colloidal suspension. Electron diffraction and optical extinction spectroscopy (OES) analyses performed on the samples confirmed the presence of Ag and Ag{sub 2}O. The analysis of the optical extinction spectrum, using the electrostatic approximation of Mie theory for small spheres, showed the existence of Ag bare core, Ag–Ag{sub 2}O and air–Ag core–shell Nps, Ag–Ag{sub 2}O being the most frequent type [69 % relative abundance (r.a.)]. Core-size and shell-thickness distribution was derived from OES. In situ scattering measurements of the Ag colloidal suspension, carried out by small-angle X-ray scattering, indicate a mass fractal composed of packaged 〈D{sub SAXS}〉 = (5 ± 1) nm particles and fractal dimension d{sub f} = 2.5. Ex situ atomic force microscopy imaging displayed well-ramified structures, which, analyzed with box-counting method, yield a fractal dimension d{sub f} = 1.67. The growing behavior of these 2d and 3d self-assembled fractals is consistent with the diffusion-limited aggregation model.

Fractal dimensions of silica gels generated using reactive molecular dynamics simulations

International Nuclear Information System (INIS)

Bhattacharya, Sudin; Kieffer, John

2005-01-01

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

A simple method for estimating the size of nuclei on fractal surfaces

Science.gov (United States)

Zeng, Qiang

2017-10-01

Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.

Fractal analysis of urban environment: land use and sewer system

Science.gov (United States)

Gires, A.; Ochoa Rodriguez, S.; Van Assel, J.; Bruni, G.; Murla Tulys, D.; Wang, L.; Pina, R.; Richard, J.; Ichiba, A.; Willems, P.; Tchiguirinskaia, I.; ten Veldhuis, M. C.; Schertzer, D. J. M.

2014-12-01

Land use distribution are usually obtained by automatic processing of satellite and airborne pictures. The complexity of the obtained patterns which are furthermore scale dependent is enhanced in urban environment. This scale dependency is even more visible in a rasterized representation where only a unique class is affected to each pixel. A parameter commonly analysed in urban hydrology is the coefficient of imperviousness, which reflects the proportion of rainfall that will be immediately active in the catchment response. This coefficient is strongly scale dependent with a rasterized representation. This complex behaviour is well grasped with the help of the scale invariant notion of fractal dimension which enables to quantify the space occupied by a geometrical set (here the impervious areas) not only at a single scale but across all scales. This fractal dimension is also compared to the ones computed on the representation of the catchments with the help of operational semi-distributed models. Fractal dimensions of the corresponding sewer systems are also computed and compared with values found in the literature for natural river networks. This methodology is tested on 7 pilot sites of the European NWE Interreg IV RainGain project located in France, Belgium, Netherlands, United-Kingdom and Portugal. Results are compared between all the case study which exhibit different physical features (slope, level of urbanisation, population density...).

Fractal Globule as a model of DNA folding in eukaryotes

Science.gov (United States)

Imakaev, Maksim; Mirny, Leonid

2012-02-01

A recent study (Lieberman-Aiden et al., Science, 2009) observed that the structure of the genome, on the scale of a few megabases, is consistent with a fractal globule. The fractal globule is a quasi-equilibrium state of a polymer after a rapid collapse. First proposed theoretically in 1988, this structure had never been simulated. Fractal globule was seen as a state, in which each subchain is compact, and doesn't mix with other subchains due to their mutual unentanglement (topological constraints). We use GPU-assisted dynamics to create fractal globules of different sizes and observe their dynamics. Our simulations confirm that a polymer after rapid collapse has compact subchains. We measure the scaling of looping probability of a subchain with it's length, and observe the remarkably robust inverse proportionality. Dynamic simulation of the equilibration of this state show that it exhibits Rose type subdiffusion. Due to diffusion, fractal globule quickly degrades to a quasi-equilibrium state, in which subchains of a polymer are mixed, but topologically unentangled. We propose that separation of spatial and topological equilibration of a polymer chain might have implications in different fields of physics.

Aqueous synthesis of LiFePO4 with Fractal Granularity

Science.gov (United States)

Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro

2016-06-01

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.

Electrical conductivity modeling in fractal non-saturated porous media

Science.gov (United States)

Wei, W.; Cai, J.; Hu, X.; Han, Q.

2016-12-01

The variety of electrical conductivity in non-saturated conditions is important to study electric conduction in natural sedimentary rocks. The electrical conductivity in completely saturated porous media is a porosity-function representing the complex connected behavior of single conducting phases (pore fluid). For partially saturated conditions, the electrical conductivity becomes even more complicated since the connectedness of pore. Archie's second law is an empirical electrical conductivity-porosity and -saturation model that has been used to predict the formation factor of non-saturated porous rock. However, the physical interpretation of its parameters, e.g., the cementation exponent m and the saturation exponent n, remains questionable. On basis of our previous work, we combine the pore-solid fractal (PSF) model to build an electrical conductivity model in non-saturated porous media. Our theoretical porosity- and saturation-dependent models contain endmember properties, such as fluid electrical conductivities, pore fractal dimension and tortuosity fractal dimension (representing the complex degree of electrical flowing path). We find the presented model with non-saturation-dependent electrical conductivity datasets indicate excellent match between theory and experiments. This means the value of pore fractal dimension and tortuosity fractal dimension change from medium to medium and depends not only on geometrical properties of pore structure but also characteristics of electrical current flowing in the non-saturated porous media.

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

Science.gov (United States)

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

2007-09-01

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.

Temperature-induced assembly of semiconductor nanocrystals into fractal architectures and thermoelectric power properties in Au/Ge bilayer films

Energy Technology Data Exchange (ETDEWEB)

Li Quanbao; Wang Jian; Jiao Zheng [Shanghai Applied Radiation Institute, Institute of Nanochemistry and Nanobiology, School of Environmental and Chemical Engineering, Shanghai University, Shanghai 200444 (China); Wu Minghong, E-mail: mhwu@staff.shu.edu.cn [Shanghai Applied Radiation Institute, Institute of Nanochemistry and Nanobiology, School of Environmental and Chemical Engineering, Shanghai University, Shanghai 200444 (China); Shek, Chan-Hung; Lawrence Wu, C.M.; Lai, Joseph K.L. [Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong (Hong Kong); Chen Zhiwen, E-mail: cnzwchen@yahoo.com.cn [Shanghai Applied Radiation Institute, Institute of Nanochemistry and Nanobiology, School of Environmental and Chemical Engineering, Shanghai University, Shanghai 200444 (China); Department of Physics and Materials Science, City University of Hong Kong, Tat Chee Avenue, Kowloon Tong (Hong Kong)

2011-08-15

Highlights: > Ge fractal architectures were achieved by temperature-induced assembly. > The appearance of fractal architectures influences the thermoelectric power. > But it has little effect on the resistivity. > The values of the superlocalization exponent were within 1.22 {<=} {xi} {<=} 1.29. > It was higher than expected for two-dimension fractal system. - Abstract: Fractal architectures of semiconductor nanocrystals were successfully achieved by temperature-induced assembly of semiconductor nanocrystals in gold/germanium (Au/Ge) bilayer films. New assessment strategies of fractal architectures are of fundamental importance in the development of micro/nano-devices. Temperature-dependent properties including resistivity and thermoelectric power (TEP) of Au/Ge bilayer films with self-similar fractal patterns were investigated in detail. Experimental results indicated that the microstructure of Au film plays an important role in the characteristics of Au/Ge bilayer films after annealing and the crystallization processes of amorphous Ge accompany by fractal formation of Ge nanocrystals via temperature-induced assembly. The appearance of fractal architectures has significantly influence on the TEP but little effect on the resistivity of the annealed bilayer film. By analysis of the data, we found that the values of superlocalization exponent are within 1.22 {<=} {xi} {<=} 1.29, which are higher than expected for two-dimension fractal systems. The results provided possible evidence for the superlocalization on fractal architectures in Au/Ge bilayer films. The TEP measurements are considered a more effective method than the conductivity for investigating superlocalization in a percolating system.

Generating hierarchial scale-free graphs from fractals

Energy Technology Data Exchange (ETDEWEB)

Komjathy, Julia, E-mail: komyju@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary); Simon, Karoly, E-mail: simonk@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary)

2011-08-15

Highlights: > We generate deterministic scale-free networks using graph-directed self similar IFS. > Our model exhibits similar clustering, power law decay properties to real networks. > The average length of shortest path and the diameter of the graph are determined. > Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal {Lambda}. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal {Lambda} we generate random graph sequence sharing similar properties.

Computer Security: The dilemma of fractal defence

CERN Multimedia

Stefan Lueders, Computer Security Team

2015-01-01

Aren’t mathematical fractals just beautiful? The Mandelbrot set and the Julia set, the Sierpinski gasket, the Menger sponge, the Koch curve (see here)… Based on very simple mathematical rules, they quickly develop into a mosaic of facets slightly different from each other. More and more features appear the closer you zoom into a fractal and expose similar but not identical features of the overall picture.   Computer security is like these fractals, only much less pretty: simple at first glance, but increasingly complex and complicated when you look more closely at the details. The deeper you dig, the more and more possibilities open up for malicious people as the attack surface grows, just like that of “Koch’s snowflakes”, where the border length grows exponentially. Consequently, the defensive perimeter also increases when we follow the bits and bytes layer by layer from their processing in the CPU, trickling up the software stack thro...

Lectures on fractal geometry and dynamical systems

CERN Document Server

Pesin, Yakov

2009-01-01

Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular "chaotic" motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples o...

Generation of fractals from complex logistic map

International Nuclear Information System (INIS)

Rani, Mamta; Agarwal, Rashi

2009-01-01

Remarkably benign looking logistic transformations x n+1 = r x n (1 - x n ) for choosing x 0 between 0 and 1 and 0 < r ≤ 4 have found a celebrated place in chaos, fractals and discrete dynamics. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck [Beck C. Physical meaning for Mandelbrot and Julia sets. Physica D 1999;125(3-4):171-182. Zbl0988.37060] to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter case. The purpose of this paper is to study the bounded behavior of the complex logistic map using superior iterates and generate fractals from the same. The analysis in this paper shows that many beautiful properties of the logistic map are extendable for a larger value of r.

Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.

Science.gov (United States)

Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter

2014-11-20

An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.

Heterogeneity of Glucose Metabolism in Esophageal Cancer Measured by Fractal Analysis of Fluorodeoxyglucose Positron Emission Tomography Image: Correlation between Metabolic Heterogeneity and Survival.

Science.gov (United States)

Tochigi, Toru; Shuto, Kiyohiko; Kono, Tsuguaki; Ohira, Gaku; Tohma, Takayuki; Gunji, Hisashi; Hayano, Koichi; Narushima, Kazuo; Fujishiro, Takeshi; Hanaoka, Toshiharu; Akutsu, Yasunori; Okazumi, Shinichi; Matsubara, Hisahiro

2017-01-01

Intratumoral heterogeneity is a well-recognized characteristic feature of cancer. The purpose of this study is to assess the heterogeneity of the intratumoral glucose metabolism using fractal analysis, and evaluate its prognostic value in patients with esophageal squamous cell carcinoma (ESCC). 18F-fluorodeoxyglucose positron emission tomography (FDG-PET) studies of 79 patients who received curative surgery were evaluated. FDG-PET images were analyzed using fractal analysis software, where differential box-counting method was employed to calculate the fractal dimension (FD) of the tumor lesion. Maximum standardized uptake value (SUVmax) and FD were compared with overall survival (OS). The median SUVmax and FD of ESCCs in this cohort were 13.8 and 1.95, respectively. In univariate analysis performed using Cox's proportional hazard model, T stage and FD showed significant associations with OS (p = 0.04, p heterogeneity measured by fractal analysis can be a novel imaging biomarker for survival in patients with ESCC. © 2016 S. Karger AG, Basel.

Difference fractal surfaces poured earth floors Tamaulipas / Diferencia fractal en superficies de tierra vertida con suelo de Tamaulipas

Directory of Open Access Journals (Sweden)

Edgardo Jonathan Suárez Dominguez

2013-09-01

Full Text Available Poured earth is a sustainable construction and economically feasible technique to develop in Tamaulipas, by the materials availability and traditional manufacturing procedures uses. There are several variables to be considered in these elements for their properties, among them it can be found roughness and porosity analysis which are important because they are related to material mechanical resistance and durability. This study aimed to characterize solid surfaces using fractal dimension to know its uniformity and porosity, compared with a concrete surface. Solids were obtained from poured earth of two combinations of soils stabilized with cement from the state of Tamaulipas. We found that a surface of a sample, obtained with ground, is more uniform than poured concrete surface, and that fractal dimension is higher while porosity increases; results suggest that this is because of the presence of clay in the poured earth mixtures. La tierra vertida es una técnica constructiva sustentable y económicamente viable para desarrollarse en Tamaulipas, por la disponibilidad de materiales y procedimientos de fabricación similares a los tradicionales. Son diversas las variables que deben estudiarse en estos elementos para conocer sus propiedades, entre las que se encuentran la rugosidad y la porosidad, las cuales son importantes debido a su estrecha relación con la resistencia mecánica y durabilidad del material estudiado. El presente trabajo tuvo por objetivo caracterizar superficies sólidas a partir de la dimensión fractal para conocer su uniformidad y porosidad, comparándola con una superficie de concreto. Los sólidos fueron obtenidos a partir de tierra vertida conformada de dos combinaciones de suelos estabilizadas con cemento provenientes del estado de Tamaulipas. Se encontró que una superficie de tierra vertida es menos irregular que una superficie de concreto además de tener una menor porosidad reflejada en una menor dimensión fractal

Development and application of 3-D fractal reservoir model based on collage theorem

Energy Technology Data Exchange (ETDEWEB)

Kim, I.K.; Kim, K.S.; Sung, W.M. [Hanyang Univ., Seoul (Korea, Republic of)

1995-04-30

Reservoir characterization is the essential process to accurately evaluate the reservoir and has been conducted by geostatistical method, SRA algorithm, and etc. The characterized distribution of heterogeneous property by these methods shows randomly distributed phenomena, and does not present anomalous shape of property variation at discontinued space as compared with the observed shape in nature. This study proposed a new algorithm of fractal concept based on collage theorem, which can virtually present not only geometric shape of irregular and anomalous pore structures or coastlines, but also property variation for discontinuously observed data. With a basis of fractal concept, three dimensional fractal reservoir model was developed to more accurately characterize the heterogeneous reservoir. We performed analysis of pre-predictable hypothetically observed permeability data by using the fractal reservoir model. From the results, we can recognize that permeability distributions in the areal view or the cross-sectional view were consistent with the observed data. (author). 8 refs., 1 tab., 6 figs.

Nonlinear stochastic interacting dynamics and complexity of financial gasket fractal-like lattice percolation

Science.gov (United States)

Zhang, Wei; Wang, Jun

2018-05-01

A novel nonlinear stochastic interacting price dynamics is proposed and investigated by the bond percolation on Sierpinski gasket fractal-like lattice, aim to make a new approach to reproduce and study the complexity dynamics of real security markets. Fractal-like lattices correspond to finite graphs with vertices and edges, which are similar to fractals, and Sierpinski gasket is a well-known example of fractals. Fractional ordinal array entropy and fractional ordinal array complexity are introduced to analyze the complexity behaviors of financial signals. To deeper comprehend the fluctuation characteristics of the stochastic price evolution, the complexity analysis of random logarithmic returns and volatility are preformed, including power-law distribution, fractional sample entropy and fractional ordinal array complexity. For further verifying the rationality and validity of the developed stochastic price evolution, the actual security market dataset are also studied with the same statistical methods for comparison. The empirical results show that this stochastic price dynamics can reconstruct complexity behaviors of the actual security markets to some extent.

Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill.

Science.gov (United States)

Choi, Jin-Seung; Kang, Dong-Won; Seo, Jeong-Woo; Tack, Gye-Rae

2017-12-08

This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation. Copyright © 2017 Elsevier Ltd. All rights reserved.

Experimental modal analysis of fractal-inspired multi-frequency structures for piezoelectric energy converters

International Nuclear Information System (INIS)

Castagnetti, D

2012-01-01

An important issue in the field of energy harvesting through piezoelectric materials is the design of simple and efficient structures which are multi-frequency in the ambient vibration range. This paper deals with the experimental assessment of four fractal-inspired multi-frequency structures for piezoelectric energy harvesting. These structures, thin plates of square shape, were proposed in a previous work by the author and their modal response numerically analysed. The present work has two aims. First, to assess the modal response of these structures through an experimental investigation. Second, to evaluate, through computational simulation, the performance of a piezoelectric converter relying on one of these fractal-inspired structures. The four fractal-inspired structures are examined in the range between 0 and 100 Hz, with regard to both eigenfrequencies and eigenmodes. In the same frequency range, the modal response and power output of the piezoelectric converter are investigated. (paper)

Fractal analysis of SEM images and mercury intrusion porosimetry data for the microstructural characterization of microcrystalline cellulose-based pellets

International Nuclear Information System (INIS)

Gomez-Carracedo, A.; Alvarez-Lorenzo, C.; Coca, R.; Martinez-Pacheco, R.; Concheiro, A.; Gomez-Amoza, J.L.

2009-01-01

The microstructure of theophylline pellets prepared from microcrystalline cellulose, carbopol and dicalcium phosphate dihydrate, according to a mixture design, was characterized using textural analysis of gray-level scanning electron microscopy (SEM) images and thermodynamic analysis of the cumulative pore volume distribution obtained by mercury intrusion porosimetry. Surface roughness evaluated in terms of gray-level non-uniformity and fractal dimension of pellet surface depended on agglomeration phenomena during extrusion/spheronization. Pores at the surface, mainly 1-15 μm in diameter, determined both the mechanism and the rate of theophylline release, and a strong negative correlation between the fractal geometry and the b parameter of the Weibull function was found for pellets containing >60% carbopol. Theophylline mean dissolution time from these pellets was about two to four times greater. Textural analysis of SEM micrographs and fractal analysis of mercury intrusion data are complementary techniques that enable complete characterization of multiparticulate drug dosage forms

Efficiency analysis of diffusion on T-fractals in the sense of random walks.

Science.gov (United States)

Peng, Junhao; Xu, Guoai

2014-04-07

Efficiently controlling the diffusion process is crucial in the study of diffusion problem in complex systems. In the sense of random walks with a single trap, mean trapping time (MTT) and mean diffusing time (MDT) are good measures of trapping efficiency and diffusion efficiency, respectively. They both vary with the location of the node. In this paper, we analyze the effects of node's location on trapping efficiency and diffusion efficiency of T-fractals measured by MTT and MDT. First, we provide methods to calculate the MTT for any target node and the MDT for any source node of T-fractals. The methods can also be used to calculate the mean first-passage time between any pair of nodes. Then, using the MTT and the MDT as the measure of trapping efficiency and diffusion efficiency, respectively, we compare the trapping efficiency and diffusion efficiency among all nodes of T-fractal and find the best (or worst) trapping sites and the best (or worst) diffusing sites. Our results show that the hub node of T-fractal is the best trapping site, but it is also the worst diffusing site; and that the three boundary nodes are the worst trapping sites, but they are also the best diffusing sites. Comparing the maximum of MTT and MDT with their minimums, we find that the maximum of MTT is almost 6 times of the minimum of MTT and the maximum of MDT is almost equal to the minimum for MDT. Thus, the location of target node has large effect on the trapping efficiency, but the location of source node almost has no effect on diffusion efficiency. We also simulate random walks on T-fractals, whose results are consistent with the derived results.

Fractal Analysis of Radiologists Visual Scanning Pattern in Screening Mammography

Energy Technology Data Exchange (ETDEWEB)

Alamudun, Folami T [ORNL; Yoon, Hong-Jun [ORNL; Hudson, Kathy [University of Tennessee, Knoxville (UTK); Morin-Ducote, Garnetta [University of Tennessee, Knoxville (UTK); Tourassi, Georgia [ORNL

2015-01-01

Several investigators have investigated radiologists visual scanning patterns with respect to features such as total time examining a case, time to initially hit true lesions, number of hits, etc. The purpose of this study was to examine the complexity of the radiologists visual scanning pattern when viewing 4-view mammographic cases, as they typically do in clinical practice. Gaze data were collected from 10 readers (3 breast imaging experts and 7 radiology residents) while reviewing 100 screening mammograms (24 normal, 26 benign, 50 malignant). The radiologists scanpaths across the 4 mammographic views were mapped to a single 2-D image plane. Then, fractal analysis was applied on the derived scanpaths using the box counting method. For each case, the complexity of each radiologist s scanpath was estimated using fractal dimension. The association between gaze complexity, case pathology, case density, and radiologist experience was evaluated using 3 factor fixed effects ANOVA. ANOVA showed that case pathology, breast density, and experience level are all independent predictors of the visual scanning pattern complexity. Visual scanning patterns are significantly different for benign and malignant cases than for normal cases as well as when breast parenchyma density changes.

The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction.

Science.gov (United States)

Najafi, Elham; Darooneh, Amir H

2015-01-01

A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.

The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction

Science.gov (United States)

Najafi, Elham; Darooneh, Amir H.

2015-01-01

A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction. PMID:26091207

FDG uptake heterogeneity evaluated by fractal analysis improves the differential diagnosis of pulmonary nodules

Energy Technology Data Exchange (ETDEWEB)

Miwa, Kenta, E-mail: kenta5710@gmail.com [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Division of Medical Quantum Science, Department of Health Sciences, Graduate School of Medical Sciences, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka 812-8582 (Japan); Inubushi, Masayuki, E-mail: inubushi@med.kawasaki-m.ac.jp [Department of Nuclear Medicine, Kawasaki Medical School, 577 Matsushima Kurashiki, Okayama 701-0192 (Japan); Wagatsuma, Kei, E-mail: kei1192@hotmail.co.jp [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Nagao, Michinobu, E-mail: minagao@radiol.med.kyushu-u.ac.jp [Department of Molecular Imaging and Diagnosis, Graduate School of Medical Sciences, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka 812-8582 (Japan); Murata, Taisuke, E-mail: taisuke113@gmail.com [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Koyama, Masamichi, E-mail: masamichi.koyama@jfcr.or.jp [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Koizumi, Mitsuru, E-mail: mitsuru@jfcr.or.jp [Department of Nuclear Medicine, Cancer Institute Hospital of Japanese Foundation for Cancer Research, 3-8-31 Ariake, Koto-ku, Tokyo 135-8550 (Japan); Sasaki, Masayuki, E-mail: msasaki@hs.med.kyushu-u.ac.jp [Division of Medical Quantum Science, Department of Health Sciences, Graduate School of Medical Sciences, Kyushu University, 3-1-1 Maidashi, Higashi-ku, Fukuoka 812-8582 (Japan)

2014-04-15

Purpose: The present study aimed to determine whether fractal analysis of morphological complexity and intratumoral heterogeneity of FDG uptake can help to differentiate malignant from benign pulmonary nodules. Materials and methods: We retrospectively analyzed data from 54 patients with suspected non-small cell lung cancer (NSCLC) who were examined by FDG PET/CT. Pathological assessments of biopsy specimens confirmed 35 and 19 nodules as NSCLC and inflammatory lesions, respectively. The morphological fractal dimension (m-FD), maximum standardized uptake value (SUV{sub max}) and density fractal dimension (d-FD) of target nodules were calculated from CT and PET images. Fractal dimension is a quantitative index of morphological complexity and tracer uptake heterogeneity; higher values indicate increased complexity and heterogeneity. Results: The m-FD, SUV{sub max} and d-FD significantly differed between malignant and benign pulmonary nodules (p < 0.05). Although the diagnostic ability was better for d-FD than m-FD and SUV{sub max}, the difference did not reach statistical significance. Tumor size correlated significantly with SUV{sub max} (r = 0.51, p < 0.05), but not with either m-FD or d-FD. Furthermore, m-FD combined with either SUV{sub max} or d-FD improved diagnostic accuracy to 92.6% and 94.4%, respectively. Conclusion: The d-FD of intratumoral heterogeneity of FDG uptake can help to differentially diagnose malignant and benign pulmonary nodules. The SUV{sub max} and d-FD obtained from FDG-PET images provide different types of information that are equally useful for differential diagnoses. Furthermore, the morphological complexity determined by CT combined with heterogeneous FDG uptake determined by PET improved diagnostic accuracy.

Model to estimate fractal dimension for ion-bombarded materials

Energy Technology Data Exchange (ETDEWEB)

Hu, A., E-mail: hu77@purdue.edu; Hassanein, A.

2014-03-15

Comprehensive fractal Monte Carlo model ITMC-F (Hu and Hassanein, 2012 [1]) is developed based on the Monte Carlo ion bombardment simulation code, i.e., Ion Transport in Materials and Compounds (ITMC) code (Hassanein, 1985 [2]). The ITMC-F studies the impact of surface roughness on the angular dependence of sputtering yield. Instead of assuming material surfaces to be flat or composed of exact self-similar fractals in simulation, we developed a new method to describe the surface shapes. Random fractal surfaces which are generated by midpoint displacement algorithm and support vector machine algorithm are combined with ITMC. With this new fractal version of ITMC-F, we successfully simulated the angular dependence of sputtering yield for various ion-target combinations, with the input surface roughness exponent directly depicted from experimental data (Hu and Hassanein, 2012 [1]). The ITMC-F code showed good agreement with the experimental data. In advanced, we compare other experimental sputtering yield with the results from ITMC-F to estimate the surface roughness exponent for ion-bombarded material in this research.

[Modeling continuous scaling of NDVI based on fractal theory].

Science.gov (United States)

Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng

2013-07-01

Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.

Evolution of fractality in space plasmas of interest to geomagnetic activity

Science.gov (United States)

Muñoz, Víctor; Domínguez, Macarena; Alejandro Valdivia, Juan; Good, Simon; Nigro, Giuseppina; Carbone, Vincenzo

2018-03-01

We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from the Dst data and from a magnetohydrodynamic shell model for turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds, which suggest that it is possible, by means of the fractal dimension, to characterize the complexity of the magnetic cloud structure.

Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems

NARCIS (Netherlands)

Buffle, J.; Leeuwen, van H.P.

2008-01-01

This book aims to provide the scientific community with a novel and valuable approach based on fractal geometry concepts on the important properties and processes of diverse environmental systems. The interpretation of complex environmental systems using modern fractal approaches is compared and

SU-D-BRA-04: Fractal Dimension Analysis of Edge-Detected Rectal Cancer CTs for Outcome Prediction

International Nuclear Information System (INIS)