Evaluation of disturbed magnetic surfaces with fractal dimensions
International Nuclear Information System (INIS)
Mishimagi, Shigehiro; Yoshii, Keiichi; Kogoshi, Sumio; Maeda, Joji
1998-01-01
For collapsed magnetic surfaces that are produced by overlapping of two magnetic islands, the fractal dimension can effectively estimate the degradation of them. The fractal dimensions of cross sections of regular magnetic surfaces and clear magnetic islands are nearly 1, while that of a collapsed magnetic surface is more than 1.2 in the present study. The Lyapunov exponents and dimensions are also calculated, which suggest the behavior of the field line of the collapsed magnetic surface is chaos. (author)
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 ...
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.
International Nuclear Information System (INIS)
Lin, Naiming; Guo, Junwen; Xie, Faqin; Zou, Jiaojuan; Tian, Wei; Yao, Xiaofei; Zhang, Hongyan; Tang, Bin
2014-01-01
Highlights: • Continuous chromizing coating was synthesized on P110 steel by pack cementation. • The chromizing coating showed better corrosion resistance. • Comparison of surface fractal dimensions can estimate corrosion resistance. - Abstract: In the field of corrosion research, mass gain/loss, electrochemical tests and comparing the surface elemental distributions, phase constitutions as well as surface morphologies before and after corrosion are extensively applied to investigate the corrosion behavior or estimate the corrosion resistance of materials that operated in various environments. Most of the above methods are problem oriented, complex and longer-period time-consuming. However from an object oriented point of view, the corroded surfaces of materials often have self-similar characterization: fractal property which can be employed to efficiently achieve damaged surface analysis. The present work describes a strategy of comparison of the surface fractal dimensions for corrosion resistance estimation: chromizing coating was synthesized on P110 steel surface to improve its performance via pack cementation. Scanning electron microscope (SEM) was used to investigate the surface morphologies of the original and corroded samples. Surface fractal dimensions of the detected samples were calculated by binary images related to SEM images of surface morphologies with box counting algorithm method. The results showed that both surface morphologies and surface fractal dimensions of P110 steel varied greatly before and after corrosion test, but the chromizing coating changed slightly. The chromizing coating indicated better corrosion resistance than P110 steel. Comparison of surface fractal dimensions of original and corroded samples can rapidly and exactly realize the estimation of corrosion resistance
International Nuclear Information System (INIS)
Nishino, Nobuhiro
1997-01-01
The surface structure of the plasma facing materials (PFM) changes due to plasma-surface interaction in a nuclear fusion reactor. Usually B 4 C coated graphite block are used as PFM. In this report, the surface fractal was applied to study the surface structure of plasma-damaged PFM carbon. A convenient flow-type adsorption apparatus was developed to evaluate the surface fractal dimension of materials. Four branched alkanol molecules with different apparent areas were used as the probe adsorbates. The samples used here were B 4 C coated isotopic graphite which were subjected to hydrogen plasma for various periods of exposure. The monolayer capacities of these samples for alkanols were determined by applying BET theory. The surface fractal dimension was calculated using the monolayer capacities and molecular areas for probe molecules and was found to increase from 2 to 3 with the plasma exposure time. (author)
Surface fractal dimensions and textural properties of mesoporous alkaline-earth hydroxyapatites
Energy Technology Data Exchange (ETDEWEB)
Vilchis-Granados, J. [Instituto Nacional de Investigaciones Nucleares, Departamento de Química, A.P. 18-1027, Col. Escandón, Delegación Miguel Hidalgo, C.P. 11801, México, DF (Mexico); Universidad Autónoma del Estado de México, Facultad de Química, Av. Paseo Colón esquina con Paseo Tollocan s/n Toluca, México (Mexico); Granados-Correa, F., E-mail: francisco.granados@inin.gob.mx [Instituto Nacional de Investigaciones Nucleares, Departamento de Química, A.P. 18-1027, Col. Escandón, Delegación Miguel Hidalgo, C.P. 11801, México, DF (Mexico); Barrera-Díaz, C.E. [Universidad Autónoma del Estado de México, Facultad de Química, Av. Paseo Colón esquina con Paseo Tollocan s/n Toluca, México (Mexico)
2013-08-15
This work examines the surface fractal dimensions (D{sub f}) and textural properties of three different alkaline-earth hydroxyapatites. Calcium, strontium and barium hydroxyapatite compounds were successfully synthesized via chemical precipitation method and characterized using X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectrometry, Fourier transform infrared spectroscopy, and N{sub 2}-physisorption measurements. Surface fractal dimensions were determined using single N{sub 2}-adsorption/desorption isotherms method to quantify the irregular surface of as-prepared compounds. The obtained materials were also characterized through their surface hydroxyl group content, determined by the mass titration method. It was found that the D{sub f} values for the three materials covered the range of 0.77 ± 0.04–2.33 ± 0.11; these results indicated that the materials tend to have smooth surfaces, except the irregular surface of barium hydroxyapatite. Moreover, regarding the synthesized calcium hydroxyapatite exhibited better textural properties compared with the synthesized strontium and barium hydroxyapatites for adsorbent purposes. However, barium hydroxyapatite shows irregular surface, indicating a high population of active sites across the surface, in comparison with the others studied hydroxyapatites. Finally, the results showed a linear correlation between the surface hydroxyl group content at the external surface of materials and their surface fractal dimensions.
Construction of fractal surfaces by recurrent fractal interpolation curves
International Nuclear Information System (INIS)
Yun, Chol-hui; O, Hyong-chol; Choi, Hui-chol
2014-01-01
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system (RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible constructions of fractal surfaces
Evaluation de la Qualité de surface par la Dimension Fractale et les ...
African Journals Online (AJOL)
grand diamètre de la bille offre la possibilité de repousser plus de matière permettant le nivellement des aspérités au niveau de la surface traitée, ce qui est constaté sur la cartographie de surface (Fig.7c). En général, la dimension fractale D est comprise entre 2 < D<3, plus D tend vers 2 plus la surface est lisse et régulière ...
Capillary pressure in a porous medium with distinct pore surface and pore volume fractal dimensions.
Deinert, M R; Dathe, A; Parlange, J-Y; Cady, K B
2008-02-01
The relationship between capillary pressure and saturation in a porous medium often exhibits a power-law dependence. The physical basis for this relation has been substantiated by assuming that capillary pressure is directly related to the pore radius. When the pore space of a medium exhibits fractal structure this approach results in a power-law relation with an exponent of 3-D(v), where D(v) is the pore volume fractal dimension. However, larger values of the exponent than are realistically allowed by this result have long been known to occur. Using a thermodynamic formulation for equilibrium capillary pressure we show that the standard result is a special case of the more general exponent (3-D(v))(3-D(s)) where D(s) is the surface fractal dimension of the pores. The analysis reduces to the standard result when D(s)=2, indicating a Euclidean relationship between a pore's surface area and the volume it encloses, and allows for a larger value for the exponent than the standard result when D(s)>2 .
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
International Nuclear Information System (INIS)
Grizzi, Fabio; Russo, Carlo; Colombo, Piergiuseppe; Franceschini, Barbara; Frezza, Eldo E; Cobos, Everardo; Chiriva-Internati, Maurizio
2005-01-01
Modeling the complex development and growth of tumor angiogenesis using mathematics and biological data is a burgeoning area of cancer research. Architectural complexity is the main feature of every anatomical system, including organs, tissues, cells and sub-cellular entities. The vascular system is a complex network whose geometrical characteristics cannot be properly defined using the principles of Euclidean geometry, which is only capable of interpreting regular and smooth objects that are almost impossible to find in Nature. However, fractal geometry is a more powerful means of quantifying the spatial complexity of real objects. This paper introduces the surface fractal dimension (D s ) as a numerical index of the two-dimensional (2-D) geometrical complexity of tumor vascular networks, and their behavior during computer-simulated changes in vessel density and distribution. We show that D s significantly depends on the number of vessels and their pattern of distribution. This demonstrates that the quantitative evaluation of the 2-D geometrical complexity of tumor vascular systems can be useful not only to measure its complex architecture, but also to model its development and growth. Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex form of branched anatomical structures, in an attempt to define more appropriate methods of describing them quantitatively. This knowledge can be used to predict the aggressiveness of malignant tumors and design compounds that can halt the process of angiogenesis and influence tumor growth
Fractal dimension for fractal structures: A Hausdorff approach
Fernández-Martínez, M.; Sánchez-Granero, M.A.
2012-01-01
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a suitable discretization of the Hausdorff theory of fractal dimension. We also find some connections between our definition and the classical ones and also with fractal dimensions I & II (see http://arxiv.org/submit/0080421/pdf). Therefore, we generalize them and ...
The effect of vertical scaling on the estimation of the fractal dimension of randomly rough surfaces
Schouwenaars, Rafael; Jacobo, Víctor H.; Ortiz, Armando
2017-12-01
Fractal analysis of randomly rough surface is an interesting tool to establish relationships between surface geometry and properties. Nonetheless, the observation that different methods to determine the fractal dimension D yield different results has raised questions about its physical meaning. This work shows that such variations are caused by the mathematical details of the methods used, particularly by the effect of vertical scaling. For the triangular prism method (TPM), applied to fractional Brownian motion, the effect of vertical scaling on the numerical estimation of D can be addressed through analytic calculations. The analytic approach was compared to simulations of surface topography obtained by the random midpoint algorithm (RMA) using TPM, box count method (BCM), differential box count (DBC) and detrended fluctuation analysis (DFA). The effect of scaling for TPM is considerable and coincides with the mathematical predictions. BCM and DBC show no effect of scaling but provide poor estimates at high D. A small effect was found for DFA. It is concluded that TPM provides a precise estimate of D which is independent of vertical scaling for infinite image resolution. At finite resolutions, the estimation error on D can be minimised by choosing an optimal vertical scaling factor.
Impulse exchange at the surface of the ocean and the fractal dimension of drifter trajectories
Directory of Open Access Journals (Sweden)
D. M. Summers
2002-01-01
Full Text Available An impulse-based model is developed to represent a coupling between turbulent flow in the atmosphere and turbulent flow in the ocean. In particular, it is argued that the atmosphere flowing horizontally over the ocean surface generates a velocity fluctuation field in the latter's near-surface flow. The mechanism for this can be understood kinematically in terms of an exchange of tangentially-oriented fluid impulse at the air-sea interface. We represent this exchange numerically through the creation of Lagrangian elements of impulse density. An indication of the efficacy of such a model would lie in its ability to predict the observed fractal dimension of lateral trajectories of submerged floats set adrift in the ocean. To this end, we examine the geometry of lateral tracer-paths determined from the present model.
Zuo, Xue; Zhu, Hua; Zhou, Yuankai; Ding, Cong; Sun, Guodong
2016-08-01
Relationships between material hardness, turning parameters (spindle speed and feed rate) and surface parameters (surface roughness Ra, fractal dimension D and characteristic roughness τ∗) are studied and modeled using response surface methodology (RSM). The experiments are carried out on a CNC lathe for six carbon steel material AISI 1010, AISI 1020, AISI 1030, AISI 1045, AISI 1050 and AISI 1060. The profile of turned surface and the surface roughness value are measured by a JB-5C profilometer. Based on the profile data, D and τ∗ are computed through the root-mean-square method. The analysis of variance (ANOVA) reveals that spindle speed is the most significant factors affecting Ra, while material hardness is the most dominant parameter affecting τ∗. Material hardness and spindle speed have the same influence on D. Feed rate has less effect on three surface parameters than spindle speed and material hardness. The second-order models of RSM are established for estimating Ra, D and τ∗. The validity of the developed models is approximately 80%. The response surfaces show that a surface with small Ra and large D and τ∗ can be obtained by selecting a high speed and a large hardness material. According to the established models, Ra, D and τ∗ of six carbon steels surfaces can be predicted under cutting conditions studied in this paper. The results have an instructive meaning to estimate the surface quality before turning.
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 characterization of the coal surface
Directory of Open Access Journals (Sweden)
Miklúová Viera
1998-09-01
Full Text Available The aim of this paper is to point up to the characterization of the brown coal using the fractal theory. On the base of BET measurements on the adsorption surface, the surface fractal dimension of crushed and milled coal samples have been determined. These values of the fractal dimension are used in the estimation of the processes by the energy input.
Fractal Dimension and the Cantor Set
Indian Academy of Sciences (India)
IAS Admin
1000. RESONANCE ⎜ November 2014. GENERAL ⎜ ARTICLE. Fractal Dimension and the Cantor Set. Shailesh A Shirali. Keywords. Dimension, topological dimen- sion, Hausdorff–Besicovitch di- mension, fractal dimension, fractal, Cantor set, Sierpinski triangle, Koch curve. Shailesh Shirali is. Director of Sahyadri School.
Mossotti, Victor G.; Eldeeb, A. Raouf
2000-01-01
Turcotte, 1997, and Barton and La Pointe, 1995, have identified many potential uses for the fractal dimension in physicochemical models of surface properties. The image-analysis program described in this report is an extension of the program set MORPH-I (Mossotti and others, 1998), which provided the fractal analysis of electron-microscope images of pore profiles (Mossotti and Eldeeb, 1992). MORPH-II, an integration of the modified kernel of the program MORPH-I with image calibration and editing facilities, was designed to measure the fractal dimension of the exposed surfaces of stone specimens as imaged in cross section in an electron microscope.
FRACTAL DIMENSIONING OF SAND GRAINS USING IMAGE ANALYSIS SYSTEM
Directory of Open Access Journals (Sweden)
Suat AKBULUT
2002-03-01
Full Text Available Engineers and earth scientists have successfully used the concept of fractal theory to better analyze the roughness of soil and/or rock particles, and how it affects the permeability, structure and distribution of pores in sedimentary rocks and their influence on strength. Use of fractals as a way to describe irregular or rough objects has been highlighted in articles by researchers working in fields such as powder mechanics, rock and soil mechanics, sedimentary petrography and geoenvironmental applications. Fractal scaling has been found appropriate to express such scale independence for collection of soil particles and aggregates. In many aspects, soil is a fractal medium and fractal models are available for the fragmentation of aggregates with fractal pore space, and with fractal surface. Applications of fractal concepts encompass description of soil physical properties such as pore-size distribution, pore surface area, and grain-size distribution. The roughness of particulate soils is an important characteristic that affects the mass behavior of the soil. The area-perimeter technique was used to predict the fractal dimension using image analysis system. This paper presents the effects of the roughness and sorting of the sand patterns with different shapes on fractal dimension. Results confirmed the significance of the roughness effect on fractal dimension.
Fractal dimension of bioconvection patterns
Noever, David A.
1990-01-01
Shallow cultures of the motile algal strain, Euglena gracilis, were concentrated to 2 x 10 to the 6th organisms per ml and placed in constant temperature water baths at 24 and 38 C. Bioconvective patterns formed an open two-dimensional structure with random branches, similar to clusters encountered in the diffusion-limited aggregation (DLA) model. When averaged over several example cultures, the pattern was found to have no natural length scale, self-similar branching, and a fractal dimension (d about 1.7). These agree well with the two-dimensional DLA.
Shi, Binkai; Qiao, Pizhong
2018-03-01
Vibration-based nondestructive testing is an area of growing interest and worthy of exploring new and innovative approaches. The displacement mode shape is often chosen to identify damage due to its local detailed characteristic and less sensitivity to surrounding noise. Requirement for baseline mode shape in most vibration-based damage identification limits application of such a strategy. In this study, a new surface fractal dimension called edge perimeter dimension (EPD) is formulated, from which an EPD-based window dimension locus (EPD-WDL) algorithm for irregularity or damage identification of plate-type structures is established. An analytical notch-type damage model of simply-supported plates is proposed to evaluate notch effect on plate vibration performance; while a sub-domain of notch cases with less effect is selected to investigate robustness of the proposed damage identification algorithm. Then, fundamental aspects of EPD-WDL algorithm in term of notch localization, notch quantification, and noise immunity are assessed. A mathematical solution called isomorphism is implemented to remove false peaks caused by inflexions of mode shapes when applying the EPD-WDL algorithm to higher mode shapes. The effectiveness and practicability of the EPD-WDL algorithm are demonstrated by an experimental procedure on damage identification of an artificially-induced notched aluminum cantilever plate using a measurement system of piezoelectric lead-zirconate (PZT) actuator and scanning laser Doppler vibrometer (SLDV). As demonstrated in both the analytical and experimental evaluations, the new surface fractal dimension technique developed is capable of effectively identifying damage in plate-type structures.
Fractal dimension of wind speed time series
International Nuclear Information System (INIS)
Chang, Tian-Pau; Ko, Hong-Hsi; Liu, Feng-Jiao; Chen, Pai-Hsun; Chang, Ying-Pin; Liang, Ying-Hsin; Jang, Horng-Yuan; Lin, Tsung-Chi; Chen, Yi-Hwa
2012-01-01
Highlights: ► Fractal dimension of wind speeds in Taiwan is studied considering climate factors. ► Relevant algorithms for the calculation of fractal dimension are presented graphically. ► Fractal dimension reveals negative correlation with mean wind speed. ► Fractal dimension is not lower even wind distribution is well described by Weibull pdf. - Abstract: The fluctuation of wind speed within a specific time period affects a lot the energy conversion rate of wind turbine. In this paper, the concept of fractal dimension in chaos theory is applied to investigate wind speed characterizations; numerical algorithms for the calculation of the fractal dimension are presented graphically. Wind data selected is observed at three wind farms experiencing different climatic conditions from 2006 to 2008 in Taiwan, where wind speed distribution can be properly classified to high wind season from October to March and low wind season from April to September. The variations of fractal dimensions among different wind farms are analyzed from the viewpoint of climatic conditions. The results show that the wind speeds studied are characterized by medium to high values of fractal dimension; the annual dimension values lie between 1.61 and 1.66. Because of monsoon factor, the fluctuation of wind speed during high wind months is not as significant as that during low wind months; the value of fractal dimension reveals negative correlation with that of mean wind speed, irrespective of wind farm considered. For a location where the wind distribution is well described by Weibull function, its fractal dimension is not necessarily lower. These findings are useful to wind analysis.
Fractal dimension of turbulent black holes
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.
1000 Fractal Dimension and the Cantor Set
Indian Academy of Sciences (India)
IAS Admin
. GENERALARTICLES. 977 How did Cantor Discover Set Theory and Topology? S M Srivastava. 1000 Fractal Dimension and the Cantor Set. Shailesh A Shirali. 1005 Biofilms: Community Behavior by Bacteria. Vinita Shivakumar and ...
Fractal Dimension in Epileptic EEG Signal Analysis
Uthayakumar, R.
Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include
Pre-Service Teachers' Concept Images on Fractal Dimension
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…
The effect of crack propagation mechanism on the fractal dimension of fracture surfaces in steels
Czech Academy of Sciences Publication Activity Database
Dlouhý, Ivo; Strnadel, B.
2008-01-01
Roč. 75, č. 3-4 (2008), s. 726-738 ISSN 0013-7944 R&D Projects: GA ČR(CZ) GA106/06/0646; GA AV ČR IAA200410502 Institutional research plan: CEZ:AV0Z20410507 Keywords : low-alloyed steel * fracture surface * fractography Subject RIV: JL - Materials Fatigue, Friction Mechanics Impact factor: 1.713, year: 2008
The fractal dimension of architecture
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...
Electromagnetic field computation at fractal dimensions
Zubair, M.; Ang, Y. S.; Ang, L. K.
According to Mandelbrot's work on fractals, many objects are in fractional dimensions that the traditional calculus or differential equations are not sufficient. Thus fractional models solving the relevant differential equations are critical to understand the physical dynamics of such objects. In this work, we develop computational electromagnetics or Maxwell equations in fractional dimensions. For a given degree of imperfection, impurity, roughness, anisotropy or inhomogeneity, we consider the complicated object can be formulated into a fractional dimensional continuous object characterized by an effective fractional dimension D, which can be calculated from a self-developed algorithm. With this non-integer value of D, we develop the computational methods to design and analyze the EM scattering problems involving rough surfaces or irregularities in an efficient framework. The fractional electromagnetic based model can be extended to other key differential equations such as Schrodinger or Dirac equations, which will be useful for design of novel 2D materials stacked up in complicated device configuration for applications in electronics and photonics. This work is supported by Singapore Temasek Laboratories (TL) Seed Grant (IGDS S16 02 05 1).
Fractal dimensions of spatial digital noise by scintillation camera
International Nuclear Information System (INIS)
Iwata, Kazuro; Hamada, Nobuo; Sumita, Mitsugu; Ueda, Suguru
1987-01-01
The fractal dimensions of the spatial digital noise by scintillation camera were measured under the various conditions. It was found that fractal dimension decreases with increasing total counts, and that fractal dimension by the point source is larger than that by the collimated plane source. When a simple pattern is added to the spatial noise, the fractal dimension decreases and is separated into two components. (Auth.)
Hong, Wang Xu; Huijie, Qin; Zhe, Zhang; Fei, Li
2014-03-01
Remote sensing images are highly structured, and contiguous pixels of space domain have strong correlations that contain abundant information on land surface structure features and land surface electromagnetic radiation features. The information capacity model, which is a quality evaluation model based on a multi-dimensional histogram, includes local correlations within different pixels. Thus, the information capacity can illustrate land surface structural information more objectively and effectively than other single-pixel calculation models. Our results reveal that the information capacity value correlates well with the meaningful grey level of remote sensing imagery. This high correlation is related to the complexity of terrestrial surface landscapes. Therefore, information capacity, as applied to geoscience, is introduced in this study to demonstrate the spatial differentiation of information capacity of different landform regions. Generally, the information capacity of a mountain is large and is followed in decreasing order by those of the hills and the plains. Moreover, the correlation between information capacity and the fractal dimension is analysed. Based on the results of this study, it can be concluded that the level of correlation for information capacity and the fractal dimension is high, and the correlation coefficient for the basic landform areas and the loess landform areas is 0.874 and 0.825, respectively. Finally, this paper proposes that information capacity be used as a new reference index for geoscientific analysis in quantitative research on the characteristics of land surface complexity.
Tumor cells diagnostic through fractal dimensions
International Nuclear Information System (INIS)
Timbo, Christiano dos Santos
2004-01-01
This method relies on the application of an algorithm for the quantitative and statistic differentiation of a sample of cells stricken by a certain kind of pathology and a sample of healthy cells. This differentiation is made by applying the principles of fractal dimension to digital images of the cells. The algorithm was developed using the the concepts of Object- Oriented Programming, resulting in a simple code, divided in 5 distinct procedures, and a user-friendly interface. To obtain the fractal dimension of the images of the cells, the program processes the image, extracting its border, and uses it to characterize the complexity of the form of the cell in a quantitative way. In order to validate the code, it was used a digitalized image found in an article by W. Bauer, developer of an analog method. The result showed a difference of 6% between the value obtained by Bauer and the value obtained the algorithm developed in this work. (author)
Arctic sea ice melt pond fractal dimension - explained
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.
Directory of Open Access Journals (Sweden)
Alexander J. Bies
2016-07-01
Full Text Available Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D and power spectrum decay rate (β. Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. Here, we determine the relationship between D and β for 1- and 2-dimensional fractals. We find that for 1-dimensional fractals, measurements of D and β obey the derived relationship. Similarly, in 2-dimensional fractals, measurements along any straight-line path across the fractal’s surface obey the mathematically derived relationship. However, the standard approach of vision researchers is to measure β of the surface after 2-dimensional Fourier decomposition rather than along a straight-line path. This surface technique provides measurements of β that do not obey the mathematically derived relationship with D. Instead, this method produces values of β that imply that the fractal’s surface is much smoother than the measurements along the straight lines indicate. To facilitate communication across disciplines, we provide empirically derived equations for relating each measure of β to D. Finally, we discuss implications for future research on topics including stress reduction and the perception of motion in the context of a generalized equation relating β to D.
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.
Relationship between the anomalous diffusion and the fractal dimension of the environment
Zhokh, Alexey; Trypolskyi, Andrey; Strizhak, Peter
2018-03-01
In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.
Electroencephalographic fractal dimension in healthy ageing and Alzheimer's disease
Smits, Fenne Margreeth; Porcaro, Camillo; Cottone, Carlo; Cancelli, Andrea; Rossini, Paolo Maria; Tecchio, Franca
2016-01-01
Brain activity is complex; a reflection of its structural and functional organization. Among other measures of complexity, the fractal dimension is emerging as being sensitive to neuronal damage secondary to neurological and psychiatric diseases. Here, we calculated Higuchi's fractal dimension (HFD)
Variability of fractal dimension of solar radio flux
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).
Fractal dimension analysis of complexity in Ligeti piano pieces
Bader, Rolf
2005-04-01
Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.
Fractal dimensions the digital art of Eric Hammel
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
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
Fractal dimensions the digital art of Eric Hammel
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
The influence of frequency on fractal dimension of adsorbed layers
International Nuclear Information System (INIS)
Gasparovic, B.; Risovic, D.; Cosovic, B.; Nelson, A.
2007-01-01
Alternating current (AC) voltammetry and electrochemical impedance spectroscopy are often the methods of choice for use in study of adsorption of organic molecules. The adsorption of organic molecules on interface may result in the formation of fractal structures, whose fractal dimension can be estimated using the method of scaling the hanging mercury drop electrode (HMDE). The aim of present study was to check whether the estimated fractal dimension, D (or for that matter the fractal ordering of the adsorbed layer) shows any correlation (dependence) with change of applied frequency, and second, to check the possibility to extend the method to broad frequency spectrum compatible with impedance spectroscopy. The investigation included two surfactants nonionic Triton-X-100 (T-X-100) and anionic sodium dodecyl sulfate (SDS) and alcohol tert-butanol. All measurements were performed on HMDE at thermodynamic equilibrium employing broad frequency spectrum. The validity of the approach was checked by measurements on pure electrolyte and by comparison with previously obtained results for fractal layers. The results of the investigations show that: (1) the method of scaling the HMDE to obtain the fractal dimension of adsorbed layer is compatible with impedance spectroscopy and the combination of these methods can be used as a powerful tool to investigate fractal aspect of adsorption of organic molecules; (2) fractal ordering of adsorbed layer and the value of fractal dimension is not influenced by the frequency of applied sinusoidal voltage perturbations
Shower fractal dimension analysis in a highly-granular calorimeter
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.
Fractal dimensions and porosities of Zoogloea ramigera and Saccharomyces cerevisae aggregates.
Logan, B E; Wilkinson, D B
1991-08-05
The fractal nature microbial aggregates is a function of the type of microorganism and mixing conditions used to develop aggregates. We determined fractal dimensions from length-projected area (D(2)) and length-number scaling (D(3)) relationships. Aggregates of Zoogloea ramigera developed in rotating test tubes were both surface and mass fractals, with fractal dimensions of D(2) = 1.69 +/- 0.11 and D(3)= 1.79 +/- 0.28 (+/-standard deviation), respectively. When we grew this bacteria in a bench-top fermentor, aggregates maintained their surface fractal characteristics (D(2) = 1.78 +/- 0.11) but lost their mass fractal characteristics (D(3) = 2.99 +/- 0.36). Yeast aggregates (Saccharomyces cerevisae) grown in rotating tests tubes had higher average fractal dimensions than bacterial aggregates grown under physically identical conditions, and were also considered fractal (D(2) = 1.92 +/- 0.08 and D(3) = 2.66 +/- 0.34). Aggregates porosity can be expressed in term of a fractal dimensions, but average porosities are higher than expected. The porosities of yeast aggregates (0.9250-0.9966) were similar to porosities of bacterial aggregates (0.9250-0.9966) cultured under the same physical conditions, although bacterial aggregates developed in the reactor had higher average porosities (0.9857-0.9980). These results suggest that that scaling relationships based on fractal geometry may be more useful than equations derived from Euclidean geometry for quantifying the effects of different fluid mechanical environments on aggregates morphology and characteristics such as density, porosity, and projected surface area.
A random walk through fractal dimensions
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
Generating one-column grids with fractal flow dimension
Doughty, Christine
2017-11-01
The grid generation capability built into the numerical simulator TOUGH for multi-phase fluid and heat flow through geologic media can create one-column grids with linear or radial geometry, corresponding to one-dimensional or two-dimensional radial flow, respectively. The integral-finite-difference-method that TOUGH employs for spatial discretization makes it very simple to generalize the grid-generation algorithm from integer to non-integer (fractal) flow dimension. Here the grid-generation algorithm is generalized to create one-column grids with fractal flow dimension ranging from less than 1 to 3. The fractal grid generation method is verified by comparing numerical simulation results to an analytical solution for a generalized Theis solution for integer and non-integer flow dimensions between 0.4 and 3. It is then applied to examine gas production decline curves from hydraulically fractured shale that is modeled as a fractal-dimensioned fracture network with flow dimensions between 0.25 and 3. Grids with fractal flow dimension are useful for representing flow through fracture networks or highly heterogeneous geologic media with fractal geometry, and may be particularly useful for inverse methods.
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.
The Role of Resolution in the Estimation of Fractal Dimension Maps From SAR Data
Directory of Open Access Journals (Sweden)
Gerardo Di Martino
2017-12-01
Full Text Available This work is aimed at investigating the role of resolution in fractal dimension map estimation, analyzing the role of the different surface spatial scales involved in the considered estimation process. The study is performed using a data set of actual Cosmo/SkyMed Synthetic Aperture Radar (SAR images relevant to two different areas, the region of Bidi in Burkina Faso and the city of Naples in Italy, acquired in stripmap and enhanced spotlight modes. The behavior of fractal dimension maps in the presence of areas with distinctive characteristics from the viewpoint of land-cover and surface features is discussed. Significant differences among the estimated maps are obtained in the presence of fine textural details, which significantly affect the fractal dimension estimation for the higher resolution spotlight images. The obtained results show that if we are interested in obtaining a reliable estimate of the fractal dimension of the observed natural scene, stripmap images should be chosen in view of both economic and computational considerations. In turn, the combination of fractal dimension maps obtained from stripmap and spotlight images can be used to identify areas on the scene presenting non-fractal behavior (e.g., urban areas. Along this guideline, a simple example of stripmap-spotlight data fusion is also presented.
Fractal dimensions of rampart impact craters on Mars
Ching, Delwyn; Taylor, G. Jeffrey; Mouginis-Mark, Peter; Bruno, Barbara C.
1993-01-01
Ejecta blanket morphologies of Martian rampart craters may yield important clues to the atmospheric densities during impact, and the nature of target materials (e.g., hard rock, fine-grained sediments, presence of volatiles). In general, the morphologies of such craters suggest emplacement by a fluidized, ground hugging flow instead of ballistic emplacement by dry ejecta. We have quantitatively characterized the shape of the margins of the ejecta blankets of 15 rampart craters using fractal geometry. Our preliminary results suggest that the craters are fractals and are self-similar over scales of approximately 0.1 km to 30 km. Fractal dimensions (a measure of the extent to which a line fills a plane) range from 1.06 to 1.31. No correlations of fractal dimension with target type, elevation, or crater size were observed, though the data base is small. The range in fractal dimension and lack of correlation may be due to a complex interplay of target properties (grain size, volatile content), atmospheric pressure, and crater size. The mere fact that the ejecta margins are fractals, however, indicates that viscosity and yield strength of the ejecta were at least as low as those of basalts, because silicic lava flows are not generally fractals.
Surface fractals in liposome aggregation.
Roldán-Vargas, Sándalo; Barnadas-Rodríguez, Ramon; Quesada-Pérez, Manuel; Estelrich, Joan; Callejas-Fernández, José
2009-01-01
In this work, the aggregation of charged liposomes induced by magnesium is investigated. Static and dynamic light scattering, Fourier-transform infrared spectroscopy, and cryotransmission electron microscopy are used as experimental techniques. In particular, multiple intracluster scattering is reduced to a negligible amount using a cross-correlation light scattering scheme. The analysis of the cluster structure, probed by means of static light scattering, reveals an evolution from surface fractals to mass fractals with increasing magnesium concentration. Cryotransmission electron microscopy micrographs of the aggregates are consistent with this interpretation. In addition, a comparative analysis of these results with those previously reported in the presence of calcium suggests that the different hydration energy between lipid vesicles when these divalent cations are present plays a fundamental role in the cluster morphology. This suggestion is also supported by infrared spectroscopy data. The kinetics of the aggregation processes is also analyzed through the time evolution of the mean diffusion coefficient of the aggregates.
Risović, Dubravko; Pavlović, Zivko
2013-01-01
Processing of gray scale images in order to determine the corresponding fractal dimension is very important due to widespread use of imaging technologies and application of fractal analysis in many areas of science, technology, and medicine. To this end, many methods for estimation of fractal dimension from gray scale images have been developed and routinely used. Unfortunately different methods (dimension estimators) often yield significantly different results in a manner that makes interpretation difficult. Here, we report results of comparative assessment of performance of several most frequently used algorithms/methods for estimation of fractal dimension. To that purpose, we have used scanning electron microscope images of aluminum oxide surfaces with different fractal dimensions. The performance of algorithms/methods was evaluated using the statistical Z-score approach. The differences between performances of six various methods are discussed and further compared with results obtained by electrochemical impedance spectroscopy on the same samples. The analysis of results shows that the performance of investigated algorithms varies considerably and that systematically erroneous fractal dimensions could be estimated using certain methods. The differential cube counting, triangulation, and box counting algorithms showed satisfactory performance in the whole investigated range of fractal dimensions. Difference statistic is proved to be less reliable generating 4% of unsatisfactory results. The performances of the Power spectrum, Partitioning and EIS were unsatisfactory in 29%, 38%, and 75% of estimations, respectively. The results of this study should be useful and provide guidelines to researchers using/attempting fractal analysis of images obtained by scanning microscopy or atomic force microscopy. © Wiley Periodicals, Inc.
A simple method for estimating the fractal dimension from digital images: The compression dimension
International Nuclear Information System (INIS)
Chamorro-Posada, Pedro
2016-01-01
The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored as digital image files. The computational scheme can be implemented using readily available free software. Its simplicity also makes it very interesting for introductory elaborations of basic concepts of fractal geometry, complexity, and information theory. A test of the computational scheme using limited-quality images of well-defined fractal sets obtained from the Internet and free software has been performed. Also, a systematic evaluation of the proposed method using computer generated images of the Weierstrass cosine function shows an accuracy comparable to those of the methods most commonly used to estimate the dimension of fractal data sequences applied to the same test problem.
International Nuclear Information System (INIS)
Smitha, K A; Gupta, A K; Jayasree, R S
2015-01-01
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades. (paper)
Smitha, K A; Gupta, A K; Jayasree, R S
2015-09-07
Glioma, the heterogeneous tumors originating from glial cells, generally exhibit varied grades and are difficult to differentiate using conventional MR imaging techniques. When this differentiation is crucial in the disease prognosis and treatment, even the advanced MR imaging techniques fail to provide a higher discriminative power for the differentiation of malignant tumor from benign ones. A powerful image processing technique applied to the imaging techniques is expected to provide a better differentiation. The present study focuses on the fractal analysis of fluid attenuation inversion recovery MR images, for the differentiation of glioma. For this, we have considered the most important parameters of fractal analysis, fractal dimension and lacunarity. While fractal analysis assesses the malignancy and complexity of a fractal object, lacunarity gives an indication on the empty space and the degree of inhomogeneity in the fractal objects. Box counting method with the preprocessing steps namely binarization, dilation and outlining was used to obtain the fractal dimension and lacunarity in glioma. Statistical analysis such as one-way analysis of variance and receiver operating characteristic (ROC) curve analysis helped to compare the mean and to find discriminative sensitivity of the results. It was found that the lacunarity of low and high grade gliomas vary significantly. ROC curve analysis between low and high grade glioma for fractal dimension and lacunarity yielded 70.3% sensitivity and 66.7% specificity and 70.3% sensitivity and 88.9% specificity, respectively. The study observes that fractal dimension and lacunarity increases with an increase in the grade of glioma and lacunarity is helpful in identifying most malignant grades.
Fractal dimension of interfaces in Edwards-Anderson spin glasses for up to six space dimensions
Wang, Wenlong; Moore, M. A.; Katzgraber, Helmut G.
2018-03-01
The fractal dimension of domain walls produced by changing the boundary conditions from periodic to antiperiodic in one spatial direction is studied using both the strong-disorder renormalization group algorithm and the greedy algorithm for the Edwards-Anderson Ising spin-glass model for up to six space dimensions. We find that for five or fewer space dimensions, the fractal dimension is lower than the space dimension. This means that interfaces are not space filling, thus implying that replica symmetry breaking is absent in space dimensions fewer than six. However, the fractal dimension approaches the space dimension in six dimensions, indicating that replica symmetry breaking occurs above six dimensions. In two space dimensions, the strong-disorder renormalization group results for the fractal dimension are in good agreement with essentially exact numerical results, but the small difference is significant. We discuss the origin of this close agreement. For the greedy algorithm there is analytical expectation that the fractal dimension is equal to the space dimension in six dimensions and our numerical results are consistent with this expectation.
Gap sequence, Lipschitz equivalence and box dimension of fractal sets
International Nuclear Information System (INIS)
Rao Hui; Yang Yamin; Ruan Huojun
2008-01-01
We introduce a notion of gap sequences for compact sets E subset of R d , which is a generalization of the gap sequences of compact sets on the real line. We show that if the gap sequences of two fractal sets are not equivalent, then these two sets cannot be Lipschitz equivalent, where the latter fact is usually very hard to verify. Finally, we show that for some typical fractal sets, the gap sequences characterize the upper box dimension
Fractal analysis as a potential tool for surface morphology of thin films
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.
Effect of exposure time and image resolution on fractal dimension
Energy Technology Data Exchange (ETDEWEB)
An, Byung Mo; Heo, Min Suk; Lee, Seung Pyo; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won [College of Dentistry, Seoul National University, Seoul (Korea, Republic of); Kim, Jong Dae [Division of Information and Communication Engineering, Hallym University, Chuncheon (Korea, Republic of)
2002-06-15
To evaluate the effect of exposure time and image resolution on fractal dimension calculations for determining the optimal range of these two variances. Thirty-one radiographs of the mandibular angle area of sixteen human dry mandibles were taken at different exposure times (0.01, 0.08, 0.16, 0.25, 0.40, 0.64, and 0.80 s). Each radiograph was digitized at 1200 dpi, 8 bit, 256 gray level using a film scanner. We selected an Region of Interest (ROI) that corresponded to the same region as in each radiograph, but the resolution of ROI was degraded to 1000, 800, 600, 500, 400, 300, 200, and 100 dpi. The fractal dimension was calculated by using the tile-counting method for each image, and the calculated values were then compared statistically. As the exposure time and the image resolution increased, the mean value of the fractal dimension decreased, except the case where exposure time was set at 0.01 seconds (alpha = 0.05). The exposure time and image resolution affected the fractal dimension by interaction (p<0.001). When the exposure time was set to either 0.64 seconds or 0.80 seconds, the resulting fractal dimensions were lower, irrespective of image resolution, than at shorter exposure times (alpha = 0.05). The optimal range for exposure time and resolution was determined to be 0.08-0.40 seconds and from 400-1000 dpi, respectively. Adequate exposure time and image resolution is essential for acquiring the fractal dimension using tile-counting method for evaluation of the mandible.
Effect of exposure time and image resolution on fractal dimension
International Nuclear Information System (INIS)
An, Byung Mo; Heo, Min Suk; Lee, Seung Pyo; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won; Kim, Jong Dae
2002-01-01
To evaluate the effect of exposure time and image resolution on fractal dimension calculations for determining the optimal range of these two variances. Thirty-one radiographs of the mandibular angle area of sixteen human dry mandibles were taken at different exposure times (0.01, 0.08, 0.16, 0.25, 0.40, 0.64, and 0.80 s). Each radiograph was digitized at 1200 dpi, 8 bit, 256 gray level using a film scanner. We selected an Region of Interest (ROI) that corresponded to the same region as in each radiograph, but the resolution of ROI was degraded to 1000, 800, 600, 500, 400, 300, 200, and 100 dpi. The fractal dimension was calculated by using the tile-counting method for each image, and the calculated values were then compared statistically. As the exposure time and the image resolution increased, the mean value of the fractal dimension decreased, except the case where exposure time was set at 0.01 seconds (alpha = 0.05). The exposure time and image resolution affected the fractal dimension by interaction (p<0.001). When the exposure time was set to either 0.64 seconds or 0.80 seconds, the resulting fractal dimensions were lower, irrespective of image resolution, than at shorter exposure times (alpha = 0.05). The optimal range for exposure time and resolution was determined to be 0.08-0.40 seconds and from 400-1000 dpi, respectively. Adequate exposure time and image resolution is essential for acquiring the fractal dimension using tile-counting method for evaluation of the mandible.
Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions
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...
Proteins in solution: Fractal surfaces in solutions
Directory of Open Access Journals (Sweden)
R. Tscheliessnig
2016-02-01
Full Text Available The concept of the surface of a protein in solution, as well of the interface between protein and 'bulk solution', is introduced. The experimental technique of small angle X-ray and neutron scattering is introduced and described briefly. Molecular dynamics simulation, as an appropriate computational tool for studying the hydration shell of proteins, is also discussed. The concept of protein surfaces with fractal dimensions is elaborated. We finish by exposing an experimental (using small angle X-ray scattering and a computer simulation case study, which are meant as demonstrations of the possibilities we have at hand for investigating the delicate interfaces that connect (and divide protein molecules and the neighboring electrolyte solution.
Fractal-like dimension of nanometer Diesel soot particles
Energy Technology Data Exchange (ETDEWEB)
Skillas, G.; Baltensperger, U. [Paul Scherrer Inst. (PSI), Villigen (Switzerland); Siegmann, K. [Eidgenoessische Technische Hochschule, Zurich (Switzerland)
1997-11-01
Measurements with a low-pressure impactor and a differential mobility analyser were conducted for Diesel soot at various engine loads. By means of these measurements a fractal-like dimension of Diesel soot particles, with diameters ranging from 55 up to 260 nm, was established. (author) 2 figs., 7 refs.
Solar Cycle Phase Dependence of Supergranular Fractal Dimension
Indian Academy of Sciences (India)
We study the complexity of supergranular cells using the intensity patterns obtained from the Kodaikanal Solar Observatory during the 23rd solar cycle. Our data consists of visually identified supergranular cells, from which a fractal dimension for supergranulation is obtained according to the relation ∝ /2, where is ...
Fractal dimension at the phase transition of inhomogeneous cellular automata
International Nuclear Information System (INIS)
da Silva, L.R.
1988-01-01
For random binary mixtures of cellular automata in the square lattice, calculations are made of the fractal dimensions associated with the damage spreading and the propagation time of damage at the transition to chaos. Two rules are mixed and universalities of these quantities are sought with respect to change of the rules
A simpler and elegant algorithm for computing fractal dimension in ...
Indian Academy of Sciences (India)
A simpler and elegant algorithm for computing fractal dimension in higher dimensional state space. S GHORUI, A K DAS and N VENKATRAMANI. Laser and Plasma Technology Division, Power Plasma Devices Section, Bhabha Atomic Research. Centre, Mumbai 400 085, India. MS received 26 November 1999. Abstract.
Effect of 3D fractal dimension on contact area and asperity interactions in elastoplastic contact
Directory of Open Access Journals (Sweden)
Abdeljalil Jourani
2016-05-01
Full Text Available Few models are devoted to investigate the effect of 3D fractal dimension Ds on contact area and asperity interactions. These models used statistical approaches or two-dimensional deterministic simulations without considering the asperity interactions and elastic–plastic transition regime. In this study, a complete 3D deterministic model is adopted to simulate the contact between fractal surfaces which are generated using a modified two-variable Weierstrass–Mandelbrot function. This model incorporates the asperity interactions and considers the different deformation modes of surface asperities which range from entirely elastic through elastic-plastic to entirely plastic contact. The simulations reveal that the elastoplastic model is more appropriate to calculate the contact area ratio and pressure field. It is also shown that the influence of the asperity interactions cannot be neglected, especially at lower fractal dimension Ds and higher load.
Damage Identification of Beam with Breathing Crack under Fractal Dimension
Zhao, Ying; Ren, Yi Chun
2018-03-01
Damage identification has been more urgent in engineering, especially beam structure which is often damaged by ambient excitation. It is based on time-frequency domain analysis of beam with breathing crack under fractal dimension in this paper. An equivalent cantilever beam model is constructed. The stiffness cosine model with time as parameter is used to simulate the opening and closing process of crack. The most widely used box dimension in fractal dimension is selected to calculate and analyze the displacement response of beam structure. The results show that the changes of box dimensional of beam structure displacement response can determine whether there is damage or not and identify the damage degree intuitively. It is more practical for damage identification in actual engineering.
Heat diffusion in fractal geometry cooling surface
Directory of Open Access Journals (Sweden)
Ramšak Matjaz
2012-01-01
Full Text Available In the paper the numerical simulation of heat diffusion in the fractal geometry of Koch snowflake is presented using multidomain mixed Boundary Element Method. The idea and motivation of work is to improve the cooling of small electronic devices using fractal geometry of surface similar to cooling ribs. The heat diffusion is assumed as the only principle of heat transfer. The results are compared to the heat flux of a flat surface. The limiting case of infinite small fractal element is computed using Richardson extrapolation.
Fractals and universal spaces in dimension theory
Lipscomb, Stephen
2009-01-01
Historically, for metric spaces the quest for universal spaces in dimension theory spanned approximately a century of mathematical research. The history breaks naturally into two periods - the classical (separable metric) and the modern (not-necessarily separable metric). This book unifies the modern theory from 1960-2007.
The Extraction of Vegetation Points from LiDAR Using 3D Fractal Dimension Analyses
Directory of Open Access Journals (Sweden)
Haiquan Yang
2015-08-01
Full Text Available Light Detection and Ranging (LiDAR, a high-precision technique used for acquiring three-dimensional (3D surface information, is widely used to study surface vegetation information. Moreover, the extraction of a vegetation point set from the LiDAR point cloud is a basic starting-point for vegetation information analysis, and an important part of its further processing. To extract the vegetation point set completely and to describe the different spatial morphological characteristics of various features in a LiDAR point cloud, we have used 3D fractal dimensions. We discovered that every feature has its own distinctive 3D fractal dimension interval. Based on the 3D fractal dimensions of tall trees, we propose a new method for the extraction of vegetation using airborne LiDAR. According to this method, target features can be distinguished based on their morphological characteristics. The non-ground points acquired by filtering are processed by region growing segmentation and the morphological characteristics are evaluated by 3D fractal dimensions to determine the features required for the determination of the point set for tall trees. Avon, New York, USA was selected as the study area to test the method and the result proves the method’s efficiency. Thus, this approach is feasible. Additionally, the method uses the 3D coordinate properties of the LiDAR point cloud and does not require additional information, such as return intensity, giving it a larger scope of application.
Effect of surfaces similarity on contact resistance of fractal rough surfaces under cyclic loading
Gao, Yuanwen; Liu, Limei; Ta, Wurui; Song, Jihua
2018-03-01
Although numerous studies have shown that contact resistance depends significantly on roughness and fractal dimension, it remains elusive how they affect contact resistance between rough surfaces. The interface similarity index is first proposed to describe the similarity of the contact surfaces, which gives a good indication of the actual contact area between surfaces. We reveal that the surfaces' similarity be an origin of contact resistance variation. The cyclic loading can increase the contact stiffness, and the contact stiffness increases with the increase of the interface similarity index. These findings explain the mechanism of surface roughness and fractal dimension on contact resistance, and also provide reference for the reliability design of the electrical connection.
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)
Fractal Dimension and the Cantor Set
Indian Academy of Sciences (India)
IAS Admin
S Smith. dimension'). We now give two examples of such objects to show that this notion is not vacuous. Cantor Set. Start with the unit interval [0, 1]. Delete the open mid- dle third of the segment, leaving behind two closed seg- ments: [0, 1/3] and [2/3, 1]. Note that, each has length. 1/3. Repeat the same construction for each ...
Predicting beauty: fractal dimension and visual complexity in art.
Forsythe, A; Nadal, M; Sheehy, N; Cela-Conde, C J; Sawey, M
2011-02-01
Visual complexity has been known to be a significant predictor of preference for artistic works for some time. The first study reported here examines the extent to which perceived visual complexity in art can be successfully predicted using automated measures of complexity. Contrary to previous findings the most successful predictor of visual complexity was Gif compression. The second study examined the extent to which fractal dimension could account for judgments of perceived beauty. The fractal dimension measure accounts for more of the variance in judgments of perceived beauty in visual art than measures of visual complexity alone, particularly for abstract and natural images. Results also suggest that when colour is removed from an artistic image observers are unable to make meaningful judgments as to its beauty. ©2010 The British Psychological Society.
Fractal dimension analysis in a highly granular calorimeter
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.
Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia.
Directory of Open Access Journals (Sweden)
Guihu Zhao
Full Text Available A failure of adaptive inference-misinterpreting available sensory information for appropriate perception and action-is at the heart of clinical manifestations of schizophrenia, implicating key subcortical structures in the brain including the hippocampus. We used high-resolution, three-dimensional (3D fractal geometry analysis to study subtle and potentially biologically relevant structural alterations (in the geometry of protrusions, gyri and indentations, sulci in subcortical gray matter (GM in patients with schizophrenia relative to healthy individuals. In particular, we focus on utilizing Fractal Dimension (FD, a compact shape descriptor that can be computed using inputs with irregular (i.e., not necessarily smooth surfaces in order to quantify complexity (of geometrical properties and configurations of structures across spatial scales of subcortical GM in this disorder. Probabilistic (entropy-based information FD was computed based on the box-counting approach for each of the seven subcortical structures, bilaterally, as well as the brainstem from high-resolution magnetic resonance (MR images in chronic patients with schizophrenia (n = 19 and age-matched healthy controls (n = 19 (age ranges: patients, 22.7-54.3 and healthy controls, 24.9-51.6 years old. We found a significant reduction of FD in the left hippocampus (median: 2.1460, range: 2.07-2.18 vs. median: 2.1730, range: 2.15-2.23, p<0.001; Cohen's effect size, U3 = 0.8158 (95% Confidence Intervals, CIs: 0.6316, 1.0, the right hippocampus (median: 2.1430, range: 2.05-2.19 vs. median: 2.1760, range: 2.12-2.21, p = 0.004; U3 = 0.8421 (CIs: 0.5263, 1, as well as left thalamus (median: 2.4230, range: 2.40-2.44, p = 0.005; U3 = 0.7895 (CIs: 0.5789, 0.9473 in schizophrenia patients, relative to healthy individuals. Our findings provide in-vivo quantitative evidence for reduced surface complexity of hippocampus, with reduced FD indicating a less complex, less regular GM surface detected in
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
Fractal dimension and image statistics of anal intraepithelial neoplasia
Energy Technology Data Exchange (ETDEWEB)
Ahammer, H., E-mail: helmut.ahammer@medunigraz.a [Institute of Biophysics, Center of Physiological Medicine, Medical University of Graz, Harrachgasse 21, A-8010 Graz (Austria); Kroepfl, J.M. [Human Performance Research Graz (HPR Graz), Karl-Franzens and Medical University of Graz, Max-Mell Allee 11, A-8010 Graz (Austria); Hackl, Ch. [Research Group of Applied Theoretical Pathology, Department of Pathology, Country Medical Centre St.Poelten, Propst Fuehrer Strasse 4, A-3100 St.Poelten (Austria); Sedivy, R. [Research Group of Applied Theoretical Pathology, Department of Pathology, Country Medical Centre St.Poelten, Propst Fuehrer Strasse 4, A-3100 St.Poelten (Austria); Department of Pathology, Country Medical Centre St.Poelten, Propst Fuehrer Strasse 4, A-3100 St.Poelten (Austria)
2011-01-15
Research Highlights: Human papillomaviruses cause anal intraepithelial neoplasia (AIN). Digital image processing was carried out to classify the grades of AIN quantitatively. The fractal dimension as well as grey value statistics was calculated. Higher grades of AIN yielded higher values of the fractal dimension. An automatic detection system is feasible. - Abstract: It is well known that human papillomaviruses (HPV) induce a variety of tumorous lesions of the skin. HPV-subtypes also cause premalignant lesions which are termed anal intraepithelial neoplasia (AIN). The clinical classification of AIN is of growing interest in clinical practice, due to increasing HPV infection rates throughout human population. The common classification approach is based on subjective inspections of histological slices of anal tissues with all the drawbacks of depending on the status and individual variances of the trained pathologists. Therefore, a nonlinear quantitative classification method including the calculation of the fractal dimension and first order as well as second order image statistical parameters was developed. The absolute values of these quantitative parameters reflected the distinct grades of AIN very well. The quantitative approach has the potential to decrease classification errors significantly and it could be used as a widely applied screening technique.
Fractal Dimension in Eeg Signals during Muscle Fatigue
Huang, Haibin; Yao, Bin; Yue, Guang; Brown, Robert; Jing, Liu
2003-10-01
Fractal dimension (FD) has been successfully used to characterize signals in the format of time series. In this study, we calculated FD of EEG signals recorded during human muscle fatigue as a measure of changes in the EEG signal complexity along fatigue. Subjects performed 200 intermittent handgrip contractions at 100contraction level. Each contraction lasted 2 s, followed by a 5-s rest. EEG data were recorded from the scalp along with handgrip force and muscle EMG signals. The FD computation was based on measurements of the length (Lk) of the signal at 6 different temporal resolutions (k = 1, 2, ¡, 6). FD was determined from the relationship between Lk and k using the least square fit. The results showed that: (1) EEG fractal dimension associated with the motor performance was significantly higher than that during the rest period; (2) changes in the fractal dimension along the process of fatigue showed a significant correlation with the decline in force and EMG signals.
Fractal analysis of AFM images of the surface of Bowman's membrane of the human cornea.
Ţălu, Ştefan; Stach, Sebastian; Sueiras, Vivian; Ziebarth, Noël Marysa
2015-04-01
The objective of this study is to further investigate the ultrastructural details of the surface of Bowman's membrane of the human cornea, using atomic force microscopy (AFM) images. One representative image acquired of Bowman's membrane of a human cornea was investigated. The three-dimensional (3-D) surface of the sample was imaged using AFM in contact mode, while the sample was completely submerged in optisol solution. Height and deflection images were acquired at multiple scan lengths using the MFP-3D AFM system software (Asylum Research, Santa Barbara, CA), based in IGOR Pro (WaveMetrics, Lake Oswego, OR). A novel approach, based on computational algorithms for fractal analysis of surfaces applied for AFM data, was utilized to analyze the surface structure. The surfaces revealed a fractal structure at the nanometer scale. The fractal dimension, D, provided quantitative values that characterize the scale properties of surface geometry. Detailed characterization of the surface topography was obtained using statistical parameters, in accordance with ISO 25178-2: 2012. Results obtained by fractal analysis confirm the relationship between the value of the fractal dimension and the statistical surface roughness parameters. The surface structure of Bowman's membrane of the human cornea is complex. The analyzed AFM images confirm a fractal nature of the surface, which is not taken into account by classical surface statistical parameters. Surface fractal dimension could be useful in ophthalmology to quantify corneal architectural changes associated with different disease states to further our understanding of disease evolution.
Mapping soil fractal dimension in agricultural fields with GPR
Oleschko, K.; Korvin, G.; Muñoz, A.; Velazquez, J.; Miranda, M. E.; Carreon, D.; Flores, L.; Martínez, M.; Velásquez-Valle, M.; Brambila, F.; Parrot, J.-F.; Ronquillo, G.
2008-09-01
We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM) accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H, the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging) in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean HR/S=0.15), significantly different to Andosol under conventional tillage (HR/S=0.47).
Mapping soil fractal dimension in agricultural fields with GPR
Directory of Open Access Journals (Sweden)
K. Oleschko
2008-09-01
Full Text Available We documented that the mapping of the fractal dimension of the backscattered Ground Penetrating Radar traces (Fractal Dimension Mapping, FDM accomplished over heterogeneous agricultural fields gives statistically sound combined information about the spatial distribution of Andosol' dielectric permittivity, volumetric and gravimetric water content, bulk density, and mechanical resistance under seven different management systems. The roughness of the recorded traces was measured in terms of a single number H, the Hurst exponent, which integrates the competitive effects of volumetric water content, pore topology and mechanical resistance in space and time. We showed the suitability to combine the GPR traces fractal analysis with routine geostatistics (kriging in order to map the spatial variation of soil properties by nondestructive techniques and to quantify precisely the differences under contrasting tillage systems. Three experimental plots with zero tillage and 33, 66 and 100% of crop residues imprinted the highest roughness to GPR wiggle traces (mean H_{R/S}=0.15, significantly different to Andosol under conventional tillage (H_{R/S}=0.47.
Fractal Dimension of Geologically Constrained Crater Populations of Mercury
Mancinelli, Paolo; Pauselli, Cristina; Perugini, Diego; Lupattelli, Andrea; Federico, Costanzo
2015-07-01
Data gathered during the Mariner10 and MESSENGER missions are collated in this paper to classify craters into four geo-chronological units constrained to the geological map produced after MESSENGER's flybys. From the global catalogue, we classify craters, constraining them to the geological information derived from the map. We produce a size frequency distribution (SFD) finding that all crater classes show fractal behaviour: with the number of craters inversely proportional to their diameter, the exponent of the SFD (i.e., the fractal dimension of each class) shows a variation among classes. We discuss this observation as possibly being caused by endogenic and/or exogenic phenomena. Finally, we produce an interpretative scenario where, assuming a constant flux of impactors, the slope variation could be representative of rheological changes in the target materials.
Fractal dimension and energetic heterogeneity of gold-modified Al-Fe-Ce pilc's
International Nuclear Information System (INIS)
Carriazo, J.G.; Molina, R.; Moreno, S.
2008-01-01
This paper studies the energetic and topographical changes that occur on the surface of a series of clays pillared with the mixed Al-Fe-Ce system and on the surface of solids synthesized by the deposition of gold nanoparticles over these pillared clays. The energetic heterogeneity of the solids was analyzed by means of the distribution of the adsorption potential, while the variations in the fractal dimension were determined from the nitrogen adsorption isotherms at 77 K, using the equation proposed by Avnir-Jaroniec. Results show the generation of microporous structures with important topographical modifications indicating an increase in the roughness (fractal geometry) of the surface of the solids as a consequence of the pillaring, revealing a positive effect of cerium addition in the synthesis process and the possible formation of nanoparticles of iron species and gold on the surface of pillared clays. The solids were also analyzed by transmission electron microscopy (TEM), confirming the formation of nanoparticles on the surface.
Molecularly-Limited Fractal Surface Area of Mineral Powders
Directory of Open Access Journals (Sweden)
Petr Jandacka
2016-05-01
Full Text Available The topic of the specific surface area (SSA of powders is not sufficiently described in the literature in spite of its nontrivial contribution to adsorption and dissolution processes. Fractal geometry provides a way to determine this parameter via relation SSA ~ x(D − 3s(2 − D, where x (m is the particle size and s (m is a scale. Such a relation respects nano-, micro-, or macro-topography on the surface. Within this theory, the fractal dimension 2 ≤ D < 3 and scale parameter s plays a significant role. The parameter D may be determined from BET or dissolution measurements on several samples, changing the powder particle sizes or sizes of adsorbate molecules. If the fractality of the surface is high, the SSA does not depend on the particle size distribution and vice versa. In this paper, the SSA parameter is analyzed from the point of view of adsorption and dissolution processes. In the case of adsorption, a new equation for the SSA, depending on the term (2 − D∙(s2 − sBET/sBET, is derived, where sBET and s2 are effective cross-sectional diameters for BET and new adsorbates. Determination of the SSA for the dissolution process appears to be very complicated, since the fractality of the surface may change in the process. Nevertheless, the presented equations have good application potential.
Nanoformation in doped silicate glass and its fractal dimensions
International Nuclear Information System (INIS)
Bulavyin, L.A.; Samojlenko, S. O.; Kyichanov, S.E.; Kozlenko, D.P.; Yivan'kov, O.I.; Yislamov, A.Kh.; Savenko, B.N.; Guryin, V.S.; Rachkovs'ka, G.E.; Zaharevych, G.B.
2015-01-01
PbS nanostructures in silicate glasses under different conditions of heat treatment were investigated using small- angle neutron scattering. It was found that spherical nanoparticles with radii of 3.0 nm to 3.9 nm are forming in these glasses. The increase of the average size of nanoparticles and changes in the fractal dimension of glass samples under increasing heat treatment time are observed. The structural model of the formation mechanism of PbS nanoparticles in a glass matrix during its thermal treatment is discussed
Nanoformation in doped silicate glass and its fractal dimensions
Directory of Open Access Journals (Sweden)
L. A. Bulavin
2015-07-01
Full Text Available PbS nanostructures in silicate glasses under different conditions of heat treatment were investigated using small-angle neutron scattering. It was found that spherical nanoparticles with radii of 3.0 nm to 3.9 nm are forming in these glasses. The increase of the average size of nanoparticles and changes in the fractal dimension of glass samples under increasing heat treatment time are observed. The structural model of the formation mechanism of PbS nanoparticles in a glass matrix during its thermal treatment is discussed.
Fractal Dimension of Particle Showers Measured in a Highly Granular Calorimeter
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.
Mossotti, Victor G.; Eldeeb, A. Raouf; Oscarson, Robert
1998-01-01
MORPH-I is a set of C-language computer programs for the IBM PC and compatible minicomputers. The programs in MORPH-I are used for the fractal analysis of scanning electron microscope and electron microprobe images of pore profiles exposed in cross-section. The program isolates and traces the cross-sectional profiles of exposed pores and computes the Richardson fractal dimension for each pore. Other programs in the set provide for image calibration, display, and statistical analysis of the computed dimensions for highly complex porous materials. Requirements: IBM PC or compatible; minimum 640 K RAM; mathcoprocessor; SVGA graphics board providing mode 103 display.
Collisions of ideal gas molecules with a rough/fractal surface. A computational study.
Panczyk, Tomasz
2007-02-01
The frequency of collisions of ideal gas molecules (argon) with a rough surface has been studied. The rough/fractal surface was created using random deposition technique. By applying various depositions, the roughness of the surface was controlled and, as a measure of the irregularity, the fractal dimensions of the surfaces were determined. The surfaces were next immersed in argon (under pressures 2 x 10(3) to 2 x 10(5) Pa) and the numbers of collisions with these surfaces were counted. The calculations were carried out using a simplified molecular dynamics simulation technique (only hard core repulsions were assumed). As a result, it was stated that the frequency of collisions is a linear function of pressure for all fractal dimensions studied (D = 2, ..., 2.5). The frequency per unit pressure is quite complex function of the fractal dimension; however, the changes of that frequency with the fractal dimension are not strong. It was found that the frequency of collisions is controlled by the number of weakly folded sites on the surfaces and there is some mapping between the shape of adsorption energy distribution functions and this number of weakly folded sites. The results for the rough/fractal surfaces were compared with the prediction given by the Langmuir-Hertz equation (valid for smooth surface), generally the departure from the Langmuir-Hertz equation is not higher than 48% for the studied systems (i.e. for the surfaces created using the random deposition technique).
Static friction between rigid fractal surfaces.
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.
Porosity-dependent fractal nature of the porous silicon surface
Energy Technology Data Exchange (ETDEWEB)
Rahmani, N.; Dariani, R. S., E-mail: dariani@alzahra.ac.ir [Department of Physics, Alzahra University, Tehran, 1993893973 (Iran, Islamic Republic of)
2015-07-15
Porous silicon films with porosity ranging from 42% to 77% were fabricated by electrochemical anodization under different current density. We used atomic force microscopy and dynamic scaling theory for deriving the surface roughness profile and processing the topography of the porous silicon layers, respectively. We first compared the topography of bare silicon surface with porous silicon and then studied the effect of the porosity of porous silicon films on their scaling behavior by using their self-affinity nature. Our work demonstrated that silicon compared to the porous silicon films has the highest Hurst parameter, indicating that the formation of porous layer due to the anodization etching of silicon surface leads to an increase of its roughness. Fractal analysis revealed that the evolution of the nanocrystallites’ fractal dimension along with porosity. Also, we found that both interface width and Hurst parameter are affected by the increase of porosity.
Lu, Xiao-long; Zheng, Qin; Yin, Xian-zhen; Xiao, Guang-qing; Liao, Zu-hua; Yang, Ming; Zhang, Ji-wen
2015-06-01
The shape and structure of granules are controlled by the granulation process, which is one of the main factors to determine the nature of the solid dosage forms. In this article, three kinds of granules of a traditional Chinese medicine for improving appetite and promoting digestion, namely, Jianwei Granules, were prepared using granulation technologies as pendular granulation, high speed stirring granulation, and fluidized bed granulation and the powder properties of them were investigated. Meanwhile, synchrotron radiation X-ray computed micro tomography (SR-µCT) was applied to quantitatively determine the irregular internal structures of the granules. The three-dimensional (3D) structure models were obtained by 3D reconstruction, which were more accurately to characterize the three-dimensional structures of the particles through the quantitative data. The models were also used to quantitatively compare the structural differences of granules prepared by different granulation processes with the same formula, so as to characterize how the production process plays a role in the pharmaceutical behaviors of the granules. To focus on the irregularity of the particle structure, the box counting method was used to calculate the fractal dimensions of the granules. The results showed that the fractal dimension is more sensitive to reflect the minor differences in the structure features than the conventional parameters, and capable to specifically distinct granules in structure. It is proved that the fractal dimension could quantitatively characterize the structural information of irregular granules. It is the first time suggested by our research that the fractal dimension difference (Df,c) between two fractal dimension parameters, namely, the volume matrix fractal dimension and the surface matrix fractal dimension, is a new index to characterize granules with irregular structures and evaluate the effects of production processes on the structures of granules as a new
Analysis of fractal dimensions of rat bones from film and digital images
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.
Texture segmentation of non-cooperative spacecrafts images based on wavelet and fractal dimension
Wu, Kanzhi; Yue, Xiaokui
2011-06-01
With the increase of on-orbit manipulations and space conflictions, missions such as tracking and capturing the target spacecrafts are aroused. Unlike cooperative spacecrafts, fixing beacons or any other marks on the targets is impossible. Due to the unknown shape and geometry features of non-cooperative spacecraft, in order to localize the target and obtain the latitude, we need to segment the target image and recognize the target from the background. The data and errors during the following procedures such as feature extraction and matching can also be reduced. Multi-resolution analysis of wavelet theory reflects human beings' recognition towards images from low resolution to high resolution. In addition, spacecraft is the only man-made object in the image compared to the natural background and the differences will be certainly observed between the fractal dimensions of target and background. Combined wavelet transform and fractal dimension, in this paper, we proposed a new segmentation algorithm for the images which contains complicated background such as the universe and planet surfaces. At first, Daubechies wavelet basis is applied to decompose the image in both x axis and y axis, thus obtain four sub-images. Then, calculate the fractal dimensions in four sub-images using different methods; after analyzed the results of fractal dimensions in sub-images, we choose Differential Box Counting in low resolution image as the principle to segment the texture which has the greatest divergences between different sub-images. This paper also presents the results of experiments by using the algorithm above. It is demonstrated that an accurate texture segmentation result can be obtained using the proposed technique.
FRACTAL DIMENSION OF URBAN EXPANSION BASED ON REMOTE SENSING IMAGES
Directory of Open Access Journals (Sweden)
IACOB I. CIPRIAN
2012-11-01
Full Text Available Fractal Dimension of Urban Expansion Based on Remote Sensing Images: In Cluj-Napoca city the process of urbanization has been accelerated during the years and implication of local authorities reflects a relevant planning policy. A good urban planning framework should take into account the society demands and also it should satisfy the natural conditions of local environment. The expansion of antropic areas it can be approached by implication of 5D variables (time as a sequence of stages, space: with x, y, z and magnitude of phenomena into the process, which will allow us to analyse and extract the roughness of city shape. Thus, to improve the decision factor we take a different approach in this paper, looking at geometry and scale composition. Using the remote sensing (RS and GIS techniques we manage to extract a sequence of built-up areas (from 1980 to 2012 and used the result as an input for modelling the spatialtemporal changes of urban expansion and fractal theory to analysed the geometric features. Taking the time as a parameter we can observe behaviour and changes in urban landscape, this condition have been known as self-organized – a condition which in first stage the system was without any turbulence (before the antropic factor and during the time tend to approach chaotic behaviour (entropy state without causing an disequilibrium in the main system.
Multi-Focus Image Fusion Using the Local Fractal Dimension
Directory of Open Access Journals (Sweden)
Qingping Li
2013-05-01
Full Text Available Abstract With the development of sensor and image-processing technology, image fusion has become a promising research field. Multi-focus image fusion is an important issue in multi-sensor image fusion. To make full use of the texture features of an image and take into account the inherent advantages of fractal theory in multi-focus image fusion, a new image fusion algorithm using the local fractal dimension (LFD is proposed. The algorithm first calculates the LFD of each source image pixel-wise by using a blanket method and generates LFD maps of the source images. Then the local energy of each LFD is calculated to generate a decision map, in order to decide pixels of the fused image are from which source image. Finally, the fused image is reconstructed from the source images according to the decision map. Experimental results show that the proposed algorithm outperforms classic LP-based and DWT-based methods according to both visual and objective evaluations.
Design and application of quick computation program on fractal dimension of land-use types
Mei, Xin; Wang, Quanfang; Wang, Qian; Liu, Junyi
2009-07-01
Now the fractal dimension of Land Use Types is often calculated by using raster data as the raw data, but quite a number of spatial data is stored as vector data in fact. If these data are converted to images to calculate fractal dimension, perhaps some pixels with inaccurate grey value will result from the "GRID" structure of raster data. And the precision of fractal dimension calculated on raster Data is closely related to the size of pixel and Grid image.In view of this, In this paper, a computation program of the fractal dimension for 2D vector data based on Windows platform has been designed by using Visual Csharp. This program has been successfully applied to land-use data of the middle Qinling Mountains and the southeast of Hubei Province in China.in the 1990s. The results show that the program is a convenient, reliable and precise method of fractal dimension for 2D Vector Data.
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)
Dependence of fractal dimension of DLCA clusters on size of primary particles.
Wu, Hua; Lattuada, Marco; Morbidelli, Massimo
2013-07-01
It is well known that clusters generated from colloidal aggregation driven by Brownian motion are typical fractal objects with the fractal dimension in the range of 1.75-1.85 under the diffusion-limited cluster aggregation (DLCA) conditions. In this work, we review and analyze the values of the fractal dimension for DLCA clusters experimentally determined in the literature. It is found that the value of the fractal dimension decreases significantly as the primary particle radius increases. Then, we have properly designed the DLCA experiments, using different radii of the primary particles, and determined the fractal dimensions of the generated clusters. Our results have well confirmed that the fractal dimension indeed decreases as the particle radius increases. To explore the mechanism leading to such dependence, we have performed intense computations through the full T-Matrix theory, and we conclude that this is not related to the effect of the intra-cluster multiple scattering on the slope of the scattering structure factor. The large fractal dimensions of the clusters generated by very small nanoparticles could be explained by thermal restructuring due to their low bonding energies, but no clear explanation can be given for the small fractal dimensions of the clusters made of large particles. Copyright © 2013 Elsevier B.V. All rights reserved.
Effect of Fractal Geometry on the Energy Balance at the Ground Surface
Sakai, S.; Iizawa, I.; Onishi, M.; Nakamura, M.; Kobayashi, K.; Mitsunaga, M.; Furuya, K.
2008-12-01
The surfaces of the urban areas are covered by large flat surfaces such as roads and walls of buildings while those of the rural areas are covered by many plants which have fractal structures. This difference in the surface geometry has great impact on the energy balance at the ground surface. A small leaf has large thermal conductivity to the surrounding air flow comparing with a anthropogenic large flat surface in an urban area even when the transpiration effect is ignored. For a cluster of many small leaves, the conductivity can be reduced by the interference, but trees have a structure to minimize its effect. We have conducted 3-dimensional laser measurements and analyzed their fractal dimensions. The analysis revealed that the trees have a fractal dimension of 2 although they are spread in a 3-dimensional space. Mathematically speaking, it means that the trees have 2-dimensional areas but do not have volume, in the limit of infinite self similarity. This geometry is favorable to absorb the sunlight using 2-dimensional area with minimum interruption of the 3-dimensional air flow. Being motivated by the results above, we have constructed a fractal sun roof consists of Sierpinski"fs tetrahedrons which have fractal dimension of 2. The roof covers an area of 100m2. The result shows that the surface temperature of the fractal roof is lower than the large flat surface with same material by more than 10 degrees.
Lee, Bum Han; Lee, Sung Keun
2013-07-01
Despite the importance of understanding and quantifying the microstructure of porous networks in diverse geologic settings, the effects of the specific surface area and porosity on the key structural parameters of the networks have not been fully understood. We performed cube-counting fractal dimension (Dcc) and lacunarity analyses of 3D porous networks of model sands and configurational entropy analysis of 2D cross sections of model sands using random packing simulations and nuclear magnetic resonance (NMR) micro-imaging. We established relationships among porosity, specific surface area, structural parameters (Dcc and lacunarity), and the corresponding macroscopic properties (configurational entropy and permeability). The Dcc of the 3D porous networks increases with increasing specific surface area at a constant porosity and with increasing porosity at a constant specific surface area. Predictive relationships correlating Dcc, specific surface area, and porosity were also obtained. The lacunarity at the minimum box size decreases with increasing porosity, and that at the intermediate box size (∼0.469 mm in the current model sands) was reproduced well with specific surface area. The maximum configurational entropy increases with increasing porosity, and the entropy length of the pores decreases with increasing specific surface area and was used to calculate the average connectivity among the pores. The correlation among porosity, specific surface area, and permeability is consistent with the prediction from the Kozeny-Carman equation. From the relationship between the permeability and the Dcc of pores, the permeability can be expressed as a function of the Dcc of pores and porosity. The current methods and these newly identified correlations among structural parameters and properties provide improved insights into the nature of porous media and have useful geophysical and hydrological implications for elasticity and shear viscosity of complex composites of rock
Electroencephalographic Fractal Dimension in Healthy Ageing and Alzheimer's Disease.
Directory of Open Access Journals (Sweden)
Fenne Margreeth Smits
Full Text Available Brain activity is complex; a reflection of its structural and functional organization. Among other measures of complexity, the fractal dimension is emerging as being sensitive to neuronal damage secondary to neurological and psychiatric diseases. Here, we calculated Higuchi's fractal dimension (HFD in resting-state eyes-closed electroencephalography (EEG recordings from 41 healthy controls (age: 20-89 years and 67 Alzheimer's Disease (AD patients (age: 50-88 years, to investigate whether HFD is sensitive to brain activity changes typical in healthy aging and in AD. Additionally, we considered whether AD-accelerating effects of the copper fraction not bound to ceruloplasmin (also called "free" copper are reflected in HFD fluctuations. The HFD measure showed an inverted U-shaped relationship with age in healthy people (R2 = .575, p < .001. Onset of HFD decline appeared around the age of 60, and was most evident in central-parietal regions. In this region, HFD decreased with aging stronger in the right than in the left hemisphere (p = .006. AD patients demonstrated reduced HFD compared to age- and education-matched healthy controls, especially in temporal-occipital regions. This was associated with decreasing cognitive status as assessed by mini-mental state examination, and with higher levels of non-ceruloplasmin copper. Taken together, our findings show that resting-state EEG complexity increases from youth to maturity and declines in healthy, aging individuals. In AD, brain activity complexity is further reduced in correlation with cognitive impairment. In addition, elevated levels of non-ceruloplasmin copper appear to accelerate the reduction of neural activity complexity. Overall, HDF appears to be a proper indicator for monitoring EEG-derived brain activity complexity in healthy and pathological aging.
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.
Hu, Kang-Bo; Wang, Yi-Li; Li, Jun-Qing; Gui, Ping; Jiang, Yan-Ling
2011-07-01
Surface morphology and pore surface fractal characteristics of the sediment in the desilting basin of Queshan Reservoir were studied. Six sediment samples were collected and particle size, morphology, pore structure and fractal characteristics, surface elements distribution were analyzed as well. The objectives of this study were to investigate the reason for the differences among the pore surface fractal dimensions and fractal scales on the basis of different models, and discuss the effect of surface morphology of these sediment particles on their surface elements distribution. The results showed that these sediment particles with average diameter of 18-83 microm were mainly composed of clay, silt and fine sand. Their complex surface morphology and pore size distribution were reflected by wide range of the BET surface area (8.248-31.60 m2/g), average pore diameter (3.977-7.850 nm) and pore-size distribution (1.870-60.78 nm). Although the pore surface fractal dimensions (D(s)), based on fractal FHH or thermodynamic models, were 2.67-2.89, and their fractal scales generally ranged from several nanometers to tens of nanometers, the differences were still observed in D(s) values calculated from above two models because of inhomogeneity in surface pore size distribution. Therefore, the D(s) based on pore-size distribution were 2.12-2.60, these values close to D(s) calculated from fractal FHH models revealed that pore-size distribution could contribute significantly to D(s) calculation. In addition, the heterogeneous surface adsorption sites of these sediment particles caused by much complex surface morphology had strong influence on the each element distribution on the particle surface.
Tumor growth in the space-time with temporal fractal dimension
International Nuclear Information System (INIS)
Molski, Marcin; Konarski, Jerzy
2008-01-01
An improvement of the Waliszewski and Konarski approach [Waliszewski P, Konarski J. The Gompertzian curve reveals fractal properties of tumor growth. Chaos, Solitons and Fractals 2003;16:665-74] to determination of the time-dependent temporal fractal dimension b t (t) and the scaling factor a t (t) for the tumor formation in the fractal space-time is presented. The analytical formulae describing the time-dependence of b t (t) and a t (t), which take into account appropriate boundary conditions for t → 0 and t → ∞, are derived. Their validity is tested on the experimental growth curve obtained by Laird for the Flexner-Jobling rat's tumor. A hypothesis is formulated that tumorigenesis has a lot in common with the neuronal differentiation and synapse formation. These processes are qualitatively described by the same Gompertz function of growth and take place in the fractal space-time whose mean temporal fractal dimension is lost during progression
Surface areas of fractally rough particles studied by scattering
International Nuclear Information System (INIS)
Hurd, A.J.; Schaefer, D.W.; Smith, D.M.; Ross, S.B.; Le Mehaute, A.; Spooner, S.
1989-01-01
The small-angle scattering from fractally rough surfaces has the potential to give information on the surface area at a given resolution. By use of quantitative neutron and x-ray scattering, a direct comparison of surface areas of fractally rough powders was made between scattering and adsorption techniques. This study supports a recently proposed correction to the theory for scattering from fractal surfaces. In addition, the scattering data provide an independent calibration of molecular adsorbate areas
Directory of Open Access Journals (Sweden)
Gautam Rawat
2016-11-01
Full Text Available Ultra-low frequency (ULF geomagnetic data recorded during 1 January 2010 to 31 December 2010 at multi-parametric geophysical observatory (30.53°N, 78.74°E in Garhwal Himalaya region of Uttarakhand, India, are analyzed. From the temporal variation of polarization ratio, the presence of seismo-magnetic disturbances superposed upon background geomagnetic variations are inferred. Considering earthquake process as a self-organized critical system based on flicker noise characteristics, fractal dimension for each day is estimated using two methods namely power spectral (FFT method and Higuchi method. Variability in fractal dimension is studied in the background of local earthquakes (M ≥ 3.5 within a zone of radius 150 km from observing station multi-parametric geophysical observatory (MPGO, Ghuttu. Fractal dimension variability indicates that average fractal dimension for first half of the year is increased as compared to average fractal dimension of second half of the year and there is gradual increase in the fractal dimension before earthquakes. It is also observed that during the first half of the year, there is seismic activity within zone of 150 Km radius centred at around MPGO, Ghuttu. There are no earthquakes during the second half of the year. Gradual increase in the fractal dimension before earthquakes, observed elsewhere in the world, is considered precursory signature of seismo-electromagnetic field emissions.
Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures
Directory of Open Access Journals (Sweden)
Runbo Bai
2012-01-01
Full Text Available Fractal dimension analysis is an emerging method for vibration-based structural damage identification. An unresolved problem in this method is its incapability of identifying damage by higher-order mode shapes. The natural inflexions of higher-order mode shapes may cause false peaks of high-magnitude estimates of fractal dimension, largely masking any signature of damage. In the situation of a scanning laser vibrometer (SLV providing a chance to reliably acquire higher-order (around tenth-order mode shapes, an improved fractal dimension method that is capable of treating higher-order mode shapes for damage detection is of important significance. This study proposes a sophisticated fractal dimension method with the aid of a specially designed affine transformation that is able to obviate natural inflexions of a higher-order mode shape while preserving its substantial damage information. The affine transformed mode shape facilitates the fractal dimension analysis to yield an effective damage feature: fractal dimension trajectory, in which an abruptly risking peak clearly characterizes the location and severity of the damage. This new fractal dimension method is demonstrated on multiple cracks identification in numerically simulated damage scenarios. The effectiveness of the method is experimentally validated by using a SLV to acquire higher-order mode shapes of a cracked cantilever beam.
Fractal Dimension Analysis of Transient Visual Evoked Potentials: Optimisation and Applications.
Boon, Mei Ying; Henry, Bruce Ian; Chu, Byoung Sun; Basahi, Nour; Suttle, Catherine May; Luu, Chi; Leung, Harry; Hing, Stephen
2016-01-01
The visual evoked potential (VEP) provides a time series signal response to an external visual stimulus at the location of the visual cortex. The major VEP signal components, peak latency and amplitude, may be affected by disease processes. Additionally, the VEP contains fine detailed and non-periodic structure, of presently unclear relevance to normal function, which may be quantified using the fractal dimension. The purpose of this study is to provide a systematic investigation of the key parameters in the measurement of the fractal dimension of VEPs, to develop an optimal analysis protocol for application. VEP time series were mathematically transformed using delay time, τ, and embedding dimension, m, parameters. The fractal dimension of the transformed data was obtained from a scaling analysis based on straight line fits to the numbers of pairs of points with separation less than r versus log(r) in the transformed space. Optimal τ, m, and scaling analysis were obtained by comparing the consistency of results using different sampling frequencies. The optimised method was then piloted on samples of normal and abnormal VEPs. Consistent fractal dimension estimates were obtained using τ = 4 ms, designating the fractal dimension = D2 of the time series based on embedding dimension m = 7 (for 3606 Hz and 5000 Hz), m = 6 (for 1803 Hz) and m = 5 (for 1000Hz), and estimating D2 for each embedding dimension as the steepest slope of the linear scaling region in the plot of log(C(r)) vs log(r) provided the scaling region occurred within the middle third of the plot. Piloting revealed that fractal dimensions were higher from the sampled abnormal than normal achromatic VEPs in adults (p = 0.02). Variances of fractal dimension were higher from the abnormal than normal chromatic VEPs in children (p = 0.01). A useful analysis protocol to assess the fractal dimension of transformed VEPs has been developed.
METHODS OF BIOMONITORING IN URBAN ENVIRONMENT: LEAF AREA AND FRACTAL DIMENSION
Directory of Open Access Journals (Sweden)
Nicoleta IANOVICI
2015-12-01
Full Text Available In urban conditions, we investigated several leaf traits (leaf area, specific leaf area, fractal dimension and specific leaf weight on Taraxacum officinale, Tilia tomentosa, Aesculus hippocastanum and Ambrosia artemisiifolia. The analyzed organs were mature leaves, on the first indications of senescence. This study used an exact, inexpensive and efficient in terms of costs alternative methods for determining the leaf parameters. On the other hand, this paper presents an application of the leaf area and fractal dimension in the analysis of leaf shape. Our results show that leaf area and fractal dimension are sensitive parameters that can be effectively used in biomonitoring.
Brief communication: age and fractal dimensions of human sagittal and coronal sutures
DEFF Research Database (Denmark)
Lynnerup, Niels; Jacobsen, Jens Christian Brings
2003-01-01
The fractal dimensions of human sagittal and coronal sutures were calculated on 31 complete skulls from the Terry Collection. The aim was to investigate whether the fractal dimension, relying on the whole sutural length, might yield a better description of age-related changes in sutural morphology......, as opposed to other methods of quantification, which generally rely on more arbitrary scoring systems. However, the fractal dimension did not yield better age correlations than other previously described methods. At best, the results reflected the general observation that young adults below age 40 years...
Directory of Open Access Journals (Sweden)
Santos Sérgio Francisco dos
2003-01-01
Full Text Available The purpose of this work is to show the correlation between the fractal dimension, D, and mechanical properties such as work of fracture, gammawof, and fracture toughness, K Ic. Alumina-mullite-zirconia composites were characterized by the slit-island method, SIM, to obtain values of D and its fractional part, D*. The fracture surface roughness was also evaluated using a cyclic voltametric method. It will be shown that there is a positive experimental dependency of gammawof on D* and that there is not an evident correlation between K Ic and D*.
Maggi, F.
2007-01-01
While the fractal dimension of suspended flocs of cohesive sediment is known to vary with the shear rate, electrochemical properties of the sediment and environment, geometrical restructuring, and presence of organic matter, experimental data presented in this work suggest changes in fractal
Brinkhoff, L. A.; von Savigny, C.; Randall, C. E.; Burrows, J. P.
2015-05-01
The fractal perimeter dimension is a fundamental property of clouds. It describes the cloud shape and is used to improve the understanding of atmospheric processes responsible for cloud shapes. von Savigny et al. (2011) determined the fractal perimeter dimension of noctilucent clouds (or polar mesospheric clouds) for the first time based on a limited data set of cloud images observed with the CIPS (Cloud Imaging and Particle Size) instrument on board the AIM (Aeronomy of Ice in the Mesosphere) satellite. This paper builds on von Savigny et al. (2011) by first presenting a sensitivity analysis of the determination of the fractal perimeter dimension, and secondly presenting results on the seasonal and interhemispheric differences of the perimeter dimension of noctilucent clouds (NLCs). The same method as in the earlier study is applied to an extended data set of satellite images of noctilucent cloud fields taken with the CIPS experiment. The sensitivity studies reveal that cloud holes play an important role for the area-perimeter method, since excluding clouds with holes reduces the dimension value by up to 3%. The results on the fractal perimeter dimension over six NLC seasons from 2007 to 2009 demonstrate that the dimension values of the NLCs neither show significant differences between the seasons nor between the hemispheres.
Fractal and Lacunarity Analyses: Quantitative Characterization of Hierarchical Surface Topographies.
Ling, Edwin J Y; Servio, Phillip; Kietzig, Anne-Marie
2016-02-01
Biomimetic hierarchical surface structures that exhibit features having multiple length scales have been used in many technological and engineering applications. Their surface topographies are most commonly analyzed using scanning electron microscopy (SEM), which only allows for qualitative visual assessments. Here we introduce fractal and lacunarity analyses as a method of characterizing the SEM images of hierarchical surface structures in a quantitative manner. Taking femtosecond laser-irradiated metals as an example, our results illustrate that, while the fractal dimension is a poor descriptor of surface complexity, lacunarity analysis can successfully quantify the spatial texture of an SEM image; this, in turn, provides a convenient means of reporting changes in surface topography with respect to changes in processing parameters. Furthermore, lacunarity plots are shown to be sensitive to the different length scales present within a hierarchical structure due to the reversal of lacunarity trends at specific magnifications where new features become resolvable. Finally, we have established a consistent method of detecting pattern sizes in an image from the oscillation of lacunarity plots. Therefore, we promote the adoption of lacunarity analysis as a powerful tool for quantitative characterization of, but not limited to, multi-scale hierarchical surface topographies.
Fetal Heart Sounds Detection Using Wavelet Transform and Fractal Dimension.
Koutsiana, Elisavet; Hadjileontiadis, Leontios J; Chouvarda, Ioanna; Khandoker, Ahsan H
2017-01-01
Phonocardiography is a non-invasive technique for the detection of fetal heart sounds (fHSs). In this study, analysis of fetal phonocardiograph (fPCG) signals, in order to achieve fetal heartbeat segmentation, is proposed. The proposed approach (namely WT-FD) is a wavelet transform (WT)-based method that combines fractal dimension (FD) analysis in the WT domain for the extraction of fHSs from the underlying noise. Its adoption in this field stems from its successful use in the fields of lung and bowel sounds de-noising analysis. The efficiency of the WT-FD method in fHS extraction has been evaluated with 19 simulated fHS signals, created for the present study, with additive noise up to (3 dB), along with the simulated fPCGs database available at PhysioBank. Results have shown promising performance in the identification of the correct location and morphology of the fHSs, reaching an overall accuracy of 89% justifying the efficacy of the method. The WT-FD approach effectively extracts the fHS signals from the noisy background, paving the way for testing it in real fHSs and clearly contributing to better evaluation of the fetal heart functionality.
Iris Recognition Using Feature Extraction of Box Counting Fractal Dimension
Khotimah, C.; Juniati, D.
2018-01-01
Biometrics is a science that is now growing rapidly. Iris recognition is a biometric modality which captures a photo of the eye pattern. The markings of the iris are distinctive that it has been proposed to use as a means of identification, instead of fingerprints. Iris recognition was chosen for identification in this research because every human has a special feature that each individual is different and the iris is protected by the cornea so that it will have a fixed shape. This iris recognition consists of three step: pre-processing of data, feature extraction, and feature matching. Hough transformation is used in the process of pre-processing to locate the iris area and Daugman’s rubber sheet model to normalize the iris data set into rectangular blocks. To find the characteristics of the iris, it was used box counting method to get the fractal dimension value of the iris. Tests carried out by used k-fold cross method with k = 5. In each test used 10 different grade K of K-Nearest Neighbor (KNN). The result of iris recognition was obtained with the best accuracy was 92,63 % for K = 3 value on K-Nearest Neighbor (KNN) method.
Fetal Heart Sounds Detection Using Wavelet Transform and Fractal Dimension
Directory of Open Access Journals (Sweden)
Elisavet Koutsiana
2017-09-01
Full Text Available Phonocardiography is a non-invasive technique for the detection of fetal heart sounds (fHSs. In this study, analysis of fetal phonocardiograph (fPCG signals, in order to achieve fetal heartbeat segmentation, is proposed. The proposed approach (namely WT–FD is a wavelet transform (WT-based method that combines fractal dimension (FD analysis in the WT domain for the extraction of fHSs from the underlying noise. Its adoption in this field stems from its successful use in the fields of lung and bowel sounds de-noising analysis. The efficiency of the WT–FD method in fHS extraction has been evaluated with 19 simulated fHS signals, created for the present study, with additive noise up to (3 dB, along with the simulated fPCGs database available at PhysioBank. Results have shown promising performance in the identification of the correct location and morphology of the fHSs, reaching an overall accuracy of 89% justifying the efficacy of the method. The WT–FD approach effectively extracts the fHS signals from the noisy background, paving the way for testing it in real fHSs and clearly contributing to better evaluation of the fetal heart functionality.
Quantitative characteristics of the Indian Ocean seafloor relief using fractal dimension
Digital Repository Service at National Institute of Oceanography (India)
Chakraborty, B.; Mahale, V.; Shashikumar, K.; Srinivas, K.
parameter (S) is computed. Also, computation of Fractal Dimension (D) using spectral exponent parameter was carried out and analyses is presented. Current investigation also includes presentation of scatter plot between the b(beta) and S value for each site...
Some new developments in experimental mechanics using random particles and fractal dimension
Chiang, Fu-Pen
2001-06-01
Recent developments of SIEM for micro/nano measurements are presented including applications to composite interphase, crack tip deformation, heart mechanics, and electronic packaging. A new technique FDS which uses fractal dimensions to assess composite damage is also described.
Estimation of Soil Water Retention Curve Using Fractal Dimension ...
African Journals Online (AJOL)
ADOWIE PERE
2018-02-10
Feb 10, 2018 ... particle size distribution has fractal properties. Hence, fractal model can be used to estimate the soil water retention curve. Thus determining the DSWRC from SWRC experimental data, establishing a relationship among DSWRC and soil readily available characteristics (i.e. clay, silt and sand contents and.
Predicting settling performance of ANAMMOX granular sludge based on fractal dimensions.
Wang, Zhiyao; Zheng, Ping
2017-09-01
The settling performance of ANAMMOX granular sludge determines the biomass retention in reactors, and finally determines the potential reaction capacity. In this paper, Stokes equation was modified by fractal dimensions to describe the settling performance of ANAMMOX granular sludge. A new method was developed to obtain fractal dimensions, and a fractal settling model was established for ANAMMOX granular sludge. The fractal settling model was excellent with only a small deviation of 0.8% from the experimental data. Assuming normal distribution of all Feret diameters, 88% experimental data fell into the 90% confidence interval of settling velocities. Further assuming logarithmic normal distribution, 95% experimental data fell into the 90% confidence interval. The fractal settling model is helpful for the prediction of settling velocities of granular sludge and the optimization of bioreactor performance. Copyright © 2017 Elsevier Ltd. All rights reserved.
Fractal Dimension Analysis of Higher-Order Mode Shapes for Damage Identification of Beam Structures
Bai, Runbo; Cao, Maosen; Su, Zhongqing; Ostachowicz, Wieslaw; Xu, Hao
2012-01-01
Fractal dimension analysis is an emerging method for vibration-based structural damage identification. An unresolved problem in this method is its incapability of identifying damage by higher-order mode shapes. The natural inflexions of higher-order mode shapes may cause false peaks of high-magnitude estimates of fractal dimension, largely masking any signature of damage. In the situation of a scanning laser vibrometer (SLV) providing a chance to reliably acquire higher-order (around tenth-or...
Hydrophobic fractal surface from glycerol tripalmitate and the effects on C6 glioma cell growth.
Zhang, Shanshan; Chen, Xuerui; Yu, Jing; Hong, Biyuan; Lei, Qunfang; Fang, Wenjun
2016-06-01
To provide a biomimic environment for glial cell culture, glycerol tripalmitate (PPP) has been used as a raw material to prepare fractal surfaces with different degrees of hydrophobicity. The spontaneous formation of the hydrophobic fractal surfaces was monitored by differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The surface morphologies were observed by a scanning electron microscope (SEM), and then the fractal dimension (FD) values of the surfaces were determined with the box-counting method. C6 glioma cells were cultured and compared on different hydrophobic PPP surfaces and poly-L-lysine (PLL)-coated surface. The cell numbers as a function of incubation time on different surfaces during the cell proliferation process were measured, and the cell morphologies were observed under a fluorescence microscope. Influences of hydrophobic fractal surfaces on the cell number and morphology were analyzed. The experimental results show that the cell proliferation rates decrease while the cell morphology complexities increase with the growth of the fractal dimensions of the PPP surfaces. Copyright © 2016 Elsevier B.V. All rights reserved.
Approximating the Ising model on fractal lattices of dimension less than two
DEFF Research Database (Denmark)
Codello, Alessandro; Drach, Vincent; Hietanen, Ari
2015-01-01
We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of a zero external magnetic field, based on the combinatorial method of Feynman and Vdovichenko. We show that the procedure is applicable to any fractal obtained...... with, possibly, arbitrary accuracy and paves the way for determination Tc of any fractal of dimension less than two. Critical exponents are more diffcult to determine since the free energy of any periodic approximation still has a logarithmic singularity at the critical point implying α = 0. We also...
Mukherjee, Anika; Chan, Adrian D C; Keating, Sarah; Redline, Raymond W; Fritsch, Michael K; Machin, Geoffrey A; Cornejo-Palma, Daniel; de Nanassy, Joseph; El-Demellawy, Dina; von Dadelszen, Peter; Benton, Samantha J; Grynspan, David
2016-01-01
The distal villous hypoplasia (DVH) pattern is a placental correlate of fetal growth restriction. Because the pattern seems to involve less complexity than do appropriately developed placental villi, we postulated that it may be associated with lower fractal dimension-a mathematical measure of complexity. Our study objectives were to evaluate interobserver agreement related to the DVH pattern among expert pathologists and to determine whether pathologist classification of DVH correlates with fractal dimension. A study set of 30 images of placental parenchyma at ×4 magnification was created by a single pathologist from a digital slide archive. The images were graded for the DVH pattern according to pre-specified definitions and included 10 images graded as "no DVH" (grade = 0), 10 with mild to moderate DVH (grade = 1), and 10 with severe DVH (grade = 2). The images were randomly sorted and shown to a panel of 4 international experts who similarly graded the images for DVH. Weighted kappas were calculated. For each image, fractal dimension was calculated by the Box Counting method. The correlation coefficient between (1) the averaged DVH scores obtained by the 5 pathologists and (2) fractal dimension was calculated. The mean weighted kappa score among the observers was 0.59 (range: 0.42-0.70). The correlation coefficient between fractal dimension and the averaged DVH score was -0.915 (P fractal dimension and represents an objective measure for DVH.
Bearing Fault Detection Using Multi-Scale Fractal Dimensions Based on Morphological Covers
Directory of Open Access Journals (Sweden)
Pei-Lin Zhang
2012-01-01
Full Text Available Vibration signals acquired from bearing have been found to demonstrate complicated nonlinear characteristics in literature. Fractal geometry theory has provided effective tools such as fractal dimension for characterizing the vibration signals in bearing faults detection. However, most of the natural signals are not critical self-similar fractals; the assumption of a constant fractal dimension at all scales may not be true. Motivated by this fact, this work explores the application of the multi-scale fractal dimensions (MFDs based on morphological cover (MC technique for bearing fault diagnosis. Vibration signals from bearing with seven different states under four operations conditions are collected to validate the presented MFDs based on MC technique. Experimental results reveal that the vibration signals acquired from bearing are not critical self-similar fractals. The MFDs can provide more discriminative information about the signals than the single global fractal dimension. Furthermore, three classifiers are employed to evaluate and compare the classification performance of the MFDs with other feature extraction methods. Experimental results demonstrate the MFDs to be a desirable approach to improve the performance of bearing fault diagnosis.
Esbenshade, Donald H., Jr.
1991-01-01
Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)
Bianciardi, Giorgio; Bisogno, Stefania; Bertoldi, Ilaria; Laurini, Lorella; Coviello, Giuseppe; Frediani, Bruno
2013-01-01
We aimed to measure the fractal dimension on x-ray images and ultrasonographic parameters of the os calcis of bone from 4 districts in osteoporotic patients and in control subjects, in order to test the hypothesis that ultrasonographic parameters correlate to the fractal dimension obtained on x-ray images. Fractal analysis on radiological images from 4 bone districts (proximal femur, calcaneus, metacarpus and 3rd phalanx) was performed in a study comparing ultrasonographic evaluation of the os calcis in severe osteoporotic patients and in control cases. We studied 86 x-ray-views from patients with severe reduction of ultrasound Stiffness Index and in healthy women. Ultrasound measurements of left os calcis were performed using the Lunar Achilles-Plus instrument. Fractal analysis was performed using the box-counting method. In healthy subjects, fractal dimension, D, measure of structural complexity, resulted close to the topological dimension (no fractal structure), TD, in femur (1.99±0.03)and phalanx (1.96±0.03), D differed significantly from TD in calcaneus (D=1.90±0.02; pfractal dimension and ultrasound broadband attenuation T-score correlated significantly in calcaneus and metacarpus (pfractal analysis on radiographic images may add useful structural information regarding the patients' skeleton using non invasive procedures.
FRACTAL DIMENSIONING OF SAND GRAINS USING IMAGE ANALYSIS SYSTEM
Suat AKBULUT
2002-01-01
Engineers and earth scientists have successfully used the concept of fractal theory to better analyze the roughness of soil and/or rock particles, and how it affects the permeability, structure and distribution of pores in sedimentary rocks and their influence on strength. Use of fractals as a way to describe irregular or rough objects has been highlighted in articles by researchers working in fields such as powder mechanics, rock and soil mechanics, sedimentary petrography and geoenvironm...
Navigation performance in virtual environments varies with fractal dimension of landscape.
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.
Fractal dimension analysis for spike detection in low SNR extracellular signals.
Salmasi, Mehrdad; Büttner, Ulrich; Glasauer, Stefan
2016-06-01
Many algorithms have been suggested for detection and sorting of spikes in extracellular recording. Nevertheless, it is still challenging to detect spikes in low signal-to-noise ratios (SNR). We propose a spike detection algorithm that is based on the fractal properties of extracellular signals and can detect spikes in low SNR regimes. Semi-intact spikes are low-amplitude spikes whose shapes are almost preserved. The detection of these spikes can significantly enhance the performance of multi-electrode recording systems. Semi-intact spikes are simulated by adding three noise components to a spike train: thermal noise, inter-spike noise, and spike-level noise. We show that simulated signals have fractal properties which make them proper candidates for fractal analysis. Then we use fractal dimension as the main core of our spike detection algorithm and call it fractal detector. The performance of the fractal detector is compared with three frequently used spike detectors. We demonstrate that in low SNR, the fractal detector has the best performance and results in the highest detection probability. It is shown that, in contrast to the other three detectors, the performance of the fractal detector is independent of inter-spike noise power and that variations in spike shape do not alter its performance. Finally, we use the fractal detector for spike detection in experimental data and similar to simulations, it is shown that the fractal detector has the best performance in low SNR regimes. The detection of low-amplitude spikes provides more information about the neural activity in the vicinity of the recording electrodes. Our results suggest using the fractal detector as a reliable and robust method for detecting semi-intact spikes in low SNR extracellular signals.
Fractal dimension of chromatin is an independent prognostic factor for survival in melanoma
Directory of Open Access Journals (Sweden)
Landman Gilles
2010-06-01
Full Text Available Abstract Background Prognostic factors in malignant melanoma are currently based on clinical data and morphologic examination. Other prognostic features, however, which are not yet used in daily practice, might add important information and thus improve prognosis, treatment, and survival. Therefore a search for new markers is desirable. Previous studies have demonstrated that fractal characteristics of nuclear chromatin are of prognostic importance in neoplasias. We have therefore investigated whether the fractal dimension of nuclear chromatin measured in routine histological preparations of malignant melanomas could be a prognostic factor for survival. Methods We examined 71 primary superficial spreading cutaneous melanoma specimens (thickness ≥ 1 mm from patients with a minimum follow up of 5 years. Nuclear area, form factor and fractal dimension of chromatin texture were obtained from digitalized images of hematoxylin-eosin stained tissue micro array sections. Clark's level, tumor thickness and mitotic rate were also determined. Results The median follow-up was 104 months. Tumor thickness, Clark's level, mitotic rate, nuclear area and fractal dimension were significant risk factors in univariate Cox regressions. In the multivariate Cox regression, stratified for the presence or absence of metastases at diagnosis, only the Clark level and fractal dimension of the nuclear chromatin were included as independent prognostic factors in the final regression model. Conclusion In general, a more aggressive behaviour is usually found in genetically unstable neoplasias with a higher number of genetic or epigenetic changes, which on the other hand, provoke a more complex chromatin rearrangement. The increased nuclear fractal dimension found in the more aggressive melanomas is the mathematical equivalent of a higher complexity of the chromatin architecture. So, there is strong evidence that the fractal dimension of the nuclear chromatin texture is a new
Fractal Dimension of Structurally Controlled River Networks of Pinar del Río, Cuba
Robert Ramírez-Hernández; Alina Rodríguez-Infante; Alexis Ordaz-Hernández
2017-01-01
River networks were studied applying the fractal systems approach and based on morphometric parameters. Procedures are applied to Cangre, Los Pozos, Paso Viejo, San Diego, Los Palacios, Santa Cruz and San Cristóbal river basins (Pinar del Río, Cuba). Drainage areas were extracted taking into account isolevel lines configurations and river lengths. For every stream the Euclidian length was also estimated, to calculate the river network fractal dimension. It seems that Takayasu approach is the ...
The number of elementary particles in a fractal M-theory of 11.2360667977 dimensions
International Nuclear Information System (INIS)
He, J.-H.
2007-01-01
It is generally accepted that there are 60 experimentally found particles. The standard model strongly predicts two more hypothetical particles, the Higgs and the graviton. This paper reveals other possible scenario for predicting 69 particles at different energy scales in 11+φ 3 fractal dimensions of a fractal M theory, where φ=(5-1)/2. A modified Newton's law is suggested to experimentally verify our predictions at extremely small quantum scales. The modified Newton's law is in harmony with Heisenberg's uncertainty principle
Meseguer-Ruiz, Oliver; Osborn, Timothy J.; Sarricolea, Pablo; Jones, Philip D.; Cantos, Jorge Olcina; Serrano-Notivoli, Roberto; Martin-Vide, Javier
2018-03-01
Precipitation on the Spanish mainland and in the Balearic archipelago exhibits a high degree of spatial and temporal variability, regardless of the temporal resolution of the data considered. The fractal dimension indicates the property of self-similarity, and in the case of this study, wherein it is applied to the temporal behaviour of rainfall at a fine (10-min) resolution from a total of 48 observatories, it provides insights into its more or less convective nature. The methodology of Jenkinson & Collison which automatically classifies synoptic situations at the surface, as well as an adaptation of this methodology at 500 hPa, was applied in order to gain insights into the synoptic implications of extreme values of the fractal dimension. The highest fractal dimension values in the study area were observed in places with precipitation that has a more random behaviour over time with generally high totals. Four different regions in which the atmospheric mechanisms giving rise to precipitation at the surface differ from the corresponding above-ground mechanisms have been identified in the study area based on the fractal dimension. In the north of the Iberian Peninsula, high fractal dimension values are linked to a lower frequency of anticyclonic situations, whereas the opposite occurs in the central region. In the Mediterranean, higher fractal dimension values are associated with a higher frequency of the anticyclonic type and a lower frequency of the advective type from the east. In the south, lower fractal dimension values indicate higher frequency with respect to the anticyclonic type from the east and lower frequency with respect to the cyclonic type.
Estimating Mass Fractal Dimension of Soil Water Retention Curve using Neural Networks
Ghanbarian-Alavijeh, B.; Huang, G.; Liaghat, A. M.; Taghizadeh-Mehrjerdi, R.
2009-04-01
Soil water retention curve (SWRC) representing the relationship between soil water content and matric potential, is one of the most important soil hydraulic properties which its direct measurement is time consuming and expensive. The objective of this study was to develop an Artificial Neural Networks (ANNs) model to estimate the mass fractal dimension of SWRC from readily available parameters such as clay and sand contents, geometric standard deviation, total porosity and fractal dimension of particle-size distribution. Also, a sensitivity analysis was carried out on the Rieu and Sposito model. The results showed that the most sensitive parameter of the model is the fractal dimension of SWRC whereas this model is less sensitive to air entry value and porosity. To evaluate the developed ANNs model, the estimated mass fractal dimension and measured soil porosity and air entry value were used to determine the water content for each matric potential using Rieu and Sposito model. The calculated RMSE=0.044 showed that the developed ANNs model estimates the mass fractal dimension of SWRC well.
Stankovic, Marija; Pantic, Igor; De Luka, Silvio R; Puskas, Nela; Zaletel, Ivan; Milutinovic-Smiljanic, Sanja; Pantic, Senka; Trbovich, Alexander M
2016-03-01
The aim of the study was to examine alteration and possible application of fractal dimension, angular second moment, and correlation for quantification of structural changes in acutely inflamed tissue. Acute inflammation was induced by injection of turpentine oil into the right and left hind limb muscles of mice, whereas control animals received intramuscular saline injection. After 12 h, animals were anesthetised and treated muscles collected. The tissue was stained by hematoxylin and eosin, digital micrographs produced, enabling determination of fractal dimension of the cells, angular second moment and correlation of studied tissue. Histopathological analysis showed presence of inflammatory infiltrate and tissue damage in inflammatory group, whereas tissue structure in control group was preserved, devoid of inflammatory infiltrate. Fractal dimension of the cells, angular second moment and correlation of treated tissue in inflammatory group decreased in comparison to the control group. In this study, we were first to observe and report that fractal dimension of the cells, angular second moment, and correlation were reduced in acutely inflamed tissue, indicating loss of overall complexity of the cells in the tissue, the tissue uniformity and structure regularity. Fractal dimension, angular second moment and correlation could be useful methods for quantification of structural changes in acute inflammation. © 2015 The Authors Journal of Microscopy © 2015 Royal Microscopical Society.
Pacagnelli, Francis Lopes; Sabela, Ana Karênina Dias de Almeida; Mariano, Thaoan Bruno; Ozaki, Guilherme Akio Tamura; Castoldi, Robson Chacon; Carmo, Edna Maria do; Carvalho, Robson Francisco; Tomasi, Loreta Casquel; Okoshi, Katashi; Vanderlei, Luiz Carlos Marques
2016-07-01
Right-sided heart failure has high morbidity and mortality, and may be caused by pulmonary arterial hypertension. Fractal dimension is a differentiated and innovative method used in histological evaluations that allows the characterization of irregular and complex structures and the quantification of structural tissue changes. To assess the use of fractal dimension in cardiomyocytes of rats with monocrotaline-induced pulmonary arterial hypertension, in addition to providing histological and functional analysis. Male Wistar rats were divided into 2 groups: control (C; n = 8) and monocrotaline-induced pulmonary arterial hypertension (M; n = 8). Five weeks after pulmonary arterial hypertension induction with monocrotaline, echocardiography was performed and the animals were euthanized. The heart was dissected, the ventricles weighed to assess anatomical parameters, and histological slides were prepared and stained with hematoxylin/eosin for fractal dimension analysis, performed using box-counting method. Data normality was tested (Shapiro-Wilk test), and the groups were compared with non-paired Student t test or Mann Whitney test (p fractal dimension values were observed in group M as compared to group C (1.39 ± 0.05 vs. 1.37 ± 0.04; p fractal dimension as an effective method to evaluate cardiac morphological changes induced by ventricular dysfunction.
Estimation of soil water retention curve using fractal dimension ...
African Journals Online (AJOL)
The soil water retention curve (SWRC) is a fundamental hydraulic property majorly used to study flow transport in soils and calculate plant-available water. Since, direct measurement of SWRC is time-consuming and expensive, different models have been developed to estimate SWRC. In this study, a fractal-based model ...
Directory of Open Access Journals (Sweden)
L. Ren
2014-01-01
Full Text Available Compressive fracture is one of the most common failure patterns in geotechnical engineering. For better understanding of the local failure mechanism of compressive fractures of brittle geomaterials, three compressive fracture tests were conducted on sandstone. Edge cracked semicircular bend specimens were used and, consequently, fresh and unfilled compressive fracture surfaces were obtained. A laser profilometer was employed to measure the topography of each rough fracture surface, followed by fractal analysis of the irregularities of the obtained compression-induced fracture surfaces using the cubic cover method. To carry out a contrastive analysis with the results of compressive fracture tests, three tension mode fracture tests were also conducted and the fractal features of the obtained fracture surfaces were determined. The obtained average result of the fractal dimensions of the compression-induced surfaces was 2.070, whereas the average result was 2.067 for the tension-induced fracture surfaces. No remarkable differences between the fractal dimensions of the compression-induced and tension-induced fracture surfaces may indicate that compressive fracture may occur, at least on the investigative scale of this work, in a similar manner to tension fracture.
Feng, Yongjiu; Liu, Miaolong; Tong, Xiaohua
2007-06-01
An improved fractal measurement, the weighted radial dimension, is put forward for highway transportation networks distribution. The radial dimension (DL), originated from subway investigation in Stuttgart, is a fractal measurement for transportation systems under ideal assumption considering all the network lines to be homogeneous curves, ignoring the difference on spatial structure, quality and level, especially the highway networks. Considering these defects of radial dimension, an improved fractal measurement called weighted radial dimension (D WL) is introduced and the transportation system in Guangdong province is studied in detail using this novel method. Weighted radial dimensions are measured and calculated, and the spatial structure, intensity and connectivity of transportation networks are discussed in Guangdong province and the four sub-areas: the Pearl River Delta area, the East Costal area, the West Costal area and the Northern Guangdong area. In Guangdong province, the fractal spatial pattern characteristics of transportation system vary remarkably: it is the highest in the Pearl River Delta area, moderate in Costal area and lowest in the Northern Guangdong area. With the Pearl River Delta area as the centre, the weighted radial dimensions decrease with the distance increasing, while the decline level is smaller in the costal area and greater in the Northern Guangdong province. By analysis of the conic of highway density, it is recognized that the density decrease with the distance increasing from the calculation centre (Guangzhou), demonstrating the same trend as weighted radial dimensions shown. Evidently, the improved fractal measurement, weighted radial dimension, is an indictor describing the characteristics of highway transportation system more effectively and accurately.
Nanoparticles dynamics on a surface: fractal pattern formation and fragmentation
DEFF Research Database (Denmark)
Dick, Veronika V.; Solov'yov, Ilia; Solov'yov, Andrey V.
2010-01-01
In this paper we review our recent results on the formation and the post-growth relaxation processes of nanofractals 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 determine the final shape of the islands on surface after post-growth relaxation. We consider different scenarios of fractal relaxation and analyze the time evolution of the island's morphology....
Fractal dimensions: A new paradigm to assess spatial memory and learning using Morris water maze.
Singh, Surjeet; Kaur, Harpreet; Sandhir, Rajat
2016-02-15
Morris water maze has been widely used for analysis of cognitive functions and relies on the time taken by animal to find the platform i.e. escape latency as a parameter to quantify spatial memory and learning. However, escape latency is confounded by swimming speed which is not necessarily a cognitive factor. Rather, path length may be a more appropriate and reliable parameter to assess spatial learning. This paper presents fractal dimension as a new paradigm to assess spatial memory and learning in animals. Male wistar rats were administrated with pentylenetetrazole and scopolamine to induce chronic epilepsy and dementia respectively. Fractal dimension of the random path followed by the animals on Morris water maze was analyzed and statistically compared among different experimental groups; the results suggest that fractal dimension is more reliable and accurate parameter to assess cognitive deficits compared to escape latency. Thus, the present study suggests that fractal dimensions could be used as an independent parameter to assess spatial memory and learning in animals using Morris water maze. Copyright © 2015 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Jo, Junghyo; Periwal, Vipul; Hörnblad, Andreas; Ahlgren, Ulf; Kilimnik, German; Hara, Manami
2013-01-01
The islets of Langerhans, responsible for controlling blood glucose levels, are dispersed within the pancreas. A universal power law governing the fractal spatial distribution of islets in two-dimensional pancreatic sections has been reported. However, the fractal geometry in the actual three-dimensional pancreas volume, and the developmental process that gives rise to such a self-similar structure, has not been investigated. Here, we examined the three-dimensional spatial distribution of islets in intact mouse pancreata using optical projection tomography and found a power law with a fractal dimension of 2.1. Furthermore, based on two-dimensional pancreatic sections of human autopsies, we found that the distribution of human islets also follows a universal power law with a fractal dimension of 1.5 in adult pancreata, which agrees with the value previously reported in smaller mammalian pancreas sections. Finally, we developed a self-avoiding growth model for the development of the islet distribution and found that the fractal nature of the spatial islet distribution may be associated with the self-avoidance in the branching process of vascularization in the pancreas. (paper)
Fractal spatial distribution of pancreatic islets in three dimensions: a self-avoiding growth model
Jo, Junghyo; Hörnblad, Andreas; Kilimnik, German; Hara, Manami; Ahlgren, Ulf; Periwal, Vipul
2013-01-01
The islets of Langerhans, responsible for controlling blood glucose levels, are dispersed within the pancreas. A universal power law governing the fractal spatial distribution of islets in two-dimensional pancreatic sections has been reported. However, the fractal geometry in the actual three-dimensional pancreas volume, and the developmental process that gives rise to such a self-similar structure, have not been investigated. Here, we examined the three-dimensional spatial distribution of islets in intact mouse pancreata using optical projection tomography and found a power law with a fractal dimension, 2.1. Furthermore, based on two-dimensional pancreatic sections of human autopsies, we found that the distribution of human islets also follows a universal power law with fractal dimension 1.5 in adult pancreata, which agrees with the value previously reported in smaller mammalian pancreas sections. Finally, we developed a self-avoiding growth model for the development of the islet distribution and found that the fractal nature of the spatial islet distribution may be associated with the self-avoidance in the branching process of vascularization in the pancreas. PMID:23629025
Suer, Berkay Tolga; Yaman, Zekai; Buyuksarac, Bora
2016-01-01
Fractal analysis is a mathematical method used to describe the internal architecture of complex structures such as trabecular bone. Fractal analysis of panoramic radiographs of implant recipient sites could help to predict the quality of the bone prior to implant placement. This study investigated the correlations between the fractal dimension values obtained from panoramic radiographs and the insertion torque and resonance frequency values of mandibular implants. Thirty patients who received a total of 55 implants of the same brand, diameter, and length in the mandibular premolar and molar regions were included in the study. The same surgical procedures were applied to each patient, and the insertion torque and resonance frequency values were recorded for each implant at the time of placement. The radiographic fractal dimensions of the alveolar bone in the implant recipient area were calculated from preoperative panoramic radiographs using a box-counting algorithm. The insertion torque and resonance frequency values were compared with the fractal dimension values using the Spearman test. All implants were successful, and none were lost during the follow-up period. Linear correlations were observed between the fractal dimension and resonance frequency, between the fractal dimension and insertion torque, and between resonance frequency and insertion torque. These results suggest that the noninvasive measurement of the fractal dimension from panoramic radiographs might help to predict the bone quality, and thus the primary stability of dental implants, before implant surgery.
A simpler and elegant algorithm for computing fractal dimension in ...
Indian Academy of Sciences (India)
Conventional algorithms for computing dimension of such systems in higher dimen- sional state space face an unavoidable problem of enormous storage requirement. Here we present an algorithm, which uses a simple but very powerful technique and faces no problem in computing dimension in higher dimensional state ...
A simpler and elegant algorithm for computing fractal dimension in ...
Indian Academy of Sciences (India)
Chaotic systems are now frequently encountered in almost all branches of sciences. Dimension of such systems provides an important measure for easy characterization of dynamics of the systems. Conventional algorithms for computing dimension of such systems in higher dimensional state space face an unavoidable ...
Directory of Open Access Journals (Sweden)
Smirnov Vladimir
2004-06-01
Full Text Available An estimation and analysis of temporal and spatial variations (on the surface, and depending on depth of the parameters of the seismic regime (fractal dimension of the earthquakes distribution d and slope of the seismic recurrence curve b in Colombia are carried out, considering the fractal properties of seismicity. The variations of thedifference (b - d/a, in time are analyzed (where a is the exponent of the power law E ~ la which establishes the relation between the energy E of the earthquake and the size l of its focus. This difference describes the deviation of the geophysical medium from a "stable" state for intervals of time in which strong earthquakes occur. The possibilities to use the variations of the parameters of seismic regime to forecast earthquakes are discussed.
Are fractal dimensions of the spatial distribution of mineral deposits meaningful?
Raines, G.L.
2008-01-01
It has been proposed that the spatial distribution of mineral deposits is bifractal. An implication of this property is that the number of deposits in a permissive area is a function of the shape of the area. This is because the fractal density functions of deposits are dependent on the distance from known deposits. A long thin permissive area with most of the deposits in one end, such as the Alaskan porphyry permissive area, has a major portion of the area far from known deposits and consequently a low density of deposits associated with most of the permissive area. On the other hand, a more equi-dimensioned permissive area, such as the Arizona porphyry permissive area, has a more uniform density of deposits. Another implication of the fractal distribution is that the Poisson assumption typically used for estimating deposit numbers is invalid. Based on datasets of mineral deposits classified by type as inputs, the distributions of many different deposit types are found to have characteristically two fractal dimensions over separate non-overlapping spatial scales in the range of 5-1000 km. In particular, one typically observes a local dimension at spatial scales less than 30-60 km, and a regional dimension at larger spatial scales. The deposit type, geologic setting, and sample size influence the fractal dimensions. The consequence of the geologic setting can be diminished by using deposits classified by type. The crossover point between the two fractal domains is proportional to the median size of the deposit type. A plot of the crossover points for porphyry copper deposits from different geologic domains against median deposit sizes defines linear relationships and identifies regions that are significantly underexplored. Plots of the fractal dimension can also be used to define density functions from which the number of undiscovered deposits can be estimated. This density function is only dependent on the distribution of deposits and is independent of the
Fractal harmonic law and waterproof/dustproof
Directory of Open Access Journals (Sweden)
Kong Hai-Yan
2014-01-01
Full Text Available The fractal harmonic law admits that the friction between the pure water and the moving surface is the minimum when fractal dimensions of water in Angstrom scale are equal to fractal dimensions of the moving surface in micro scale. In the paper, the fractal harmonic law is applied to demonstrate the mechanism of waterproof/ dustproof. The waterproof phenomenon of goose feathers and lotus leaves is illustrated to verify our results and experimental results agree well with our theoretical analysis.
Directory of Open Access Journals (Sweden)
Grbić G.
2008-01-01
Full Text Available The aim of our study was to investigate the effect of camphor essential oil on rat cerebral cortex activity by fractal analysis. Fractal dimension (FD values of the parietal electrocortical activity were calculated before and after intra-peritoneal administration of camphor essential oil (450-675 μl/kg in anesthetized rats. Camphor oil induced seizure-like activity with single and multiple spiking of high amplitudes in the parietal electrocorticogram and occasional clonic limb convulsions. The FD values of cortical activity after camphor oil administration increased on the average. Only FD values of cortical ECoG sequences were lower than those before camphor oil administration.
Dimensions of Fractals Generated by Bi-Lipschitz Maps
Directory of Open Access Journals (Sweden)
Qi-Rong Deng
2014-01-01
Full Text Available On the class of iterated function systems of bi-Lipschitz mappings that are contractions with respect to some metrics, we introduce a logarithmic distortion property, which is weaker than the well-known bounded distortion property. By assuming this property, we prove the equality of the Hausdorff and box dimensions of the attractor. We also obtain a formula for the dimension of the attractor in terms of certain modified topological pressure functions, without imposing any separation condition. As an application, we prove the equality of Hausdorff and box dimensions for certain iterated function systems consisting of affine maps and nonsmooth maps.
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.
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....
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
Fractal dimension and neurotoxicity in rats intoxicated by aluminium
Directory of Open Access Journals (Sweden)
Martać Ljiljana
2015-01-01
Full Text Available We used animal model of neurotoxicity in rats, which provided the possibility of studying biological pathophysiological phenomena in vivo and afterwards in vitro conditions. The analysis of electrocortical brain activity using mathematical methods can describe the changes induced by aluminum intoxication in rat as an animal model. In physiological and pathophysiological conditions, on experimental models, mechanisms related to changes in behavior, plasticity and accumulation of aluminum in nervous tissue of the rat brain were observed. Animal models of rats used in the experiments described changes in the group of neuronal activity in the brain of rats in different modes of intoxication aluminum. This study describes ECoG activity in the brain of rats under anesthesia in both the control and aluminum treated animals. Fractal and spectral analysis was used to present qualitative and quantitative changes in the conditions of neurotoxicity. Changes in neurotransmission, as well as the structure and function of the neural network are connected to the molecular-physiological mechanisms of neurotoxicity. Aluminium toxicity was monitored through changes in glutamatergic activity and calcium channel activity. By spectrum analysis neurotoxicity was described through changes in spectral power in the corresponding frequency ranges. By comparing the FD of intoxicated and control individuals there was obtained the range of the change in correlation with the corresponding pathophysiological conditions of intoxication. The shange in FD might be an indication of neurotoxicity.
Effect of image quality, color, and format on the measurement of retinal vascular fractal dimension.
Wainwright, Alan; Liew, Gerald; Burlutsky, George; Rochtchina, Elena; Zhang, Yong Ping; Hsu, Wynne; Lee, Janice MongLi; Wong, Tien Yin; Mitchell, Paul; Wang, Jie Jin
2010-11-01
Fractal dimension of retinal vasculature is a global summary measure of retinal vascular network pattern and geometry. This study was conducted to examine the effect of variations in image color, brightness, focus, contrast, and format on the measurement of retinal vascular fractal dimension. A set of 30 retinal images from the Blue Mountains Eye Study was used for a series of experiments by varying brightness, focus (blur), contrast, and color (color versus monochrome). The original and the modified images were graded for fractal dimension (D(f)) using dedicated retinal imaging software (IRIS-Fractal). A further set of 20 grayscale images was used to compare image format (.jpg versus .tif) with regard to the resultant D(f) and processing time. The mean D(f) of original images in this sample was 1.454. Compared with the original set of images, variations in brightness, focus, contrast, and color affected the measurements to a small to moderate degree (Pearson correlation coefficient, r, ranged from 0.47 to 0.97). Very dark or blurry images resulted in a substantially lower estimate of D(f). Monochrome images were also consistently associated with lower D(f) compared with that obtained from color images. Using .jpg or .tif image formats did not affect the measurement or the time needed to process and measure D(f). Variations in image brightness, focus, and contrast can significantly affect the measurement of retinal vascular fractals. Standardization of image parameters and consistent use of either monochrome or color images would reduce measurement noise and enhance the comparability of the results.
Zone specific fractal dimension of retinal images as predictor of stroke incidence.
Aliahmad, Behzad; Kumar, Dinesh Kant; Hao, Hao; Unnikrishnan, Premith; Che Azemin, Mohd Zulfaezal; Kawasaki, Ryo; Mitchell, Paul
2014-01-01
Fractal dimensions (FDs) are frequently used for summarizing the complexity of retinal vascular. However, previous techniques on this topic were not zone specific. A new methodology to measure FD of a specific zone in retinal images has been developed and tested as a marker for stroke prediction. Higuchi's fractal dimension was measured in circumferential direction (FDC) with respect to optic disk (OD), in three concentric regions between OD boundary and 1.5 OD diameter from its margin. The significance of its association with future episode of stroke event was tested using the Blue Mountain Eye Study (BMES) database and compared against spectrum fractal dimension (SFD) and box-counting (BC) dimension. Kruskal-Wallis analysis revealed FDC as a better predictor of stroke (H = 5.80, P = 0.016, α = 0.05) compared with SFD (H = 0.51, P = 0.475, α = 0.05) and BC (H = 0.41, P = 0.520, α = 0.05) with overall lower median value for the cases compared to the control group. This work has shown that there is a significant association between zone specific FDC of eye fundus images with future episode of stroke while this difference is not significant when other FD methods are employed.
Fractal Dimension and Vessel Complexity in Patients with Cerebral Arteriovenous Malformations
Reishofer, Gernot; Koschutnig, Karl; Enzinger, Christian; Ebner, Franz; Ahammer, Helmut
2012-01-01
The fractal dimension (FD) can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM) and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs. PMID:22815946
Controlling Molecular Growth between Fractals and Crystals on Surfaces.
Zhang, Xue; Li, Na; Gu, Gao-Chen; Wang, Hao; Nieckarz, Damian; Szabelski, Paweł; He, Yang; Wang, Yu; Xie, Chao; Shen, Zi-Yong; Lü, Jing-Tao; Tang, Hao; Peng, Lian-Mao; Hou, Shi-Min; Wu, Kai; Wang, Yong-Feng
2015-12-22
Recent studies demonstrate that simple functional molecules, which usually form two-dimensional (2D) crystal structures when adsorbed on solid substrates, are also able to self-assemble into ordered openwork fractal aggregates. To direct and control the growth of such fractal supramolecules, it is necessary to explore the conditions under which both fractal and crystalline patterns develop and coexist. In this contribution, we study the coexistence of Sierpiński triangle (ST) fractals and 2D molecular crystals that were formed by 4,4″-dihydroxy-1,1':3',1″-terphenyl molecules on Au(111) in ultrahigh vacuum. Growth competition between the STs and 2D crystals was realized by tuning substrate and molecular surface coverage and changing the functional groups of the molecular building block. Density functional theory calculations and Monte Carlo simulations are used to characterize the process. Both experimental and theoretical results demonstrate the possibility of steering the surface self-assembly to generate fractal and nonfractal structures made up of the same molecular building block.
Energy Technology Data Exchange (ETDEWEB)
Timbo, Christiano dos Santos
2004-07-01
This method relies on the application of an algorithm for the quantitative and statistic differentiation of a sample of cells stricken by a certain kind of pathology and a sample of healthy cells. This differentiation is made by applying the principles of fractal dimension to digital images of the cells. The algorithm was developed using the the concepts of Object- Oriented Programming, resulting in a simple code, divided in 5 distinct procedures, and a user-friendly interface. To obtain the fractal dimension of the images of the cells, the program processes the image, extracting its border, and uses it to characterize the complexity of the form of the cell in a quantitative way. In order to validate the code, it was used a digitalized image found in an article by W. Bauer, developer of an analog method. The result showed a difference of 6% between the value obtained by Bauer and the value obtained the algorithm developed in this work. (author)
Verma, Garima; Luciani, Maria Laura; Palombo, Alessandro; Metaxa, Linda; Panzironi, Giovanna; Pediconi, Federica; Giuliani, Alessandro; Bizzarri, Mariano; Todde, Virginia
2018-02-01
Herein, we propose a Systems Biology approach aimed at identifying quantitative morphological parameters useful in discriminating benign from malignant breast microcalcifications at digital mammography. The study includes 31 patients in which microcalcifications had been detected during XR mammography and were further confirmed by stereotactic (XR-guided) biopsies. Patients were classified according to the BIRADS (Breast Imaging-Reporting and Data System), along with their parenchyma fractal dimension and biopsy size. A geometrical-topological characterization of microcalcifications was obtained as well. The 'size of biopsy' was the parameter endowed with the highest discriminant power between malignant and benign lesions thus confirming the reliability of surgeon judgment. The quantitative shape evaluation of both lesions and parenchyma allowed for a promising prediction of the BIRADS score. The area of lesions and parenchyma fractal dimension show a complex distribution for malignant breast calcifications that are consistent with their qualitative morphological pattern. Fractal dimension analysis enables the user to obtain reliable results as proved by its efficiency in the prediction of the morphology of breast cancer. By reconstructing a phase-space distribution of biophysical parameters, different patterns of aggregation are recognized corresponding to different calcium deposition patterns, while the combination of tissue and microcalcification morphological descriptors provide a statistically significant prediction of tumour grade. The development of an automated morphology evaluation system can help during clinical evaluation while also sketching mechanistic hypotheses of microcalcification generation. Copyright © 2017 Elsevier Ltd. All rights reserved.
Bikou, Olga; Delides, Alexander; Drougou, Aggeliki; Nonni, Afroditi; Patsouris, Efstratios; Pavlakis, Kitty
Fractal dimension (FD) is widely used in medicine and biology as a tool for defining features of structure. This study aimed to compare pathological endometrium (simple-complex hyperplasia and endometrial carcinoma), as well as the endometrial changes, during the phases of the menstrual cycle. The main goal was the objective measurement of fractal dimension and to refrain from subjective evaluation. Two thousand cases of endometrial tissue from patients who underwent dilatation and curettage (D&C) were reviewed. Out of these, 137 cases were eligible for the study. In each case, immunohistochemistry with cytokeratin Ae1/AE3 was performed in order to simplify the evaluation of the FD. Endometria with carcinoma, simple or complex hyperplasia showed significant differences only in the immunohistochemically stained fractal dimensions. As expected, significant differences were also found between atrophic and secretory endometrium and carcinoma. FD is an objective, rapid and simple procedure for the differential diagnosis between complex hyperplasia and endometrial adenocarcinoma. Copyright © 2016 International Institute of Anticancer Research (Dr. John G. Delinassios), All rights reserved.
International Nuclear Information System (INIS)
Ul'yanov, A S; Lyapina, A M; Ulianova, O V; Fedorova, V A; Uianov, S S
2011-01-01
Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated. (optical technologies in biophysics and medicine)
Fractal dimension of chromatin: potential molecular diagnostic applications for cancer prognosis
Metze, Konradin
2013-01-01
Fractal characteristics of chromatin, revealed by light or electron microscopy, have been reported during the last 20 years. Fractal features can easily be estimated in digitalized microscopic images and are helpful for diagnosis and prognosis of neoplasias. During carcinogenesis and tumor progression, an increase of the fractal dimension (FD) of stained nuclei has been shown in intraepithelial lesions of the uterine cervix and the anus, oral squamous cell carcinomas or adenocarcinomas of the pancreas. Furthermore, an increased FD of chromatin is an unfavorable prognostic factor in squamous cell carcinomas of the oral cavity and the larynx, melanomas and multiple myelomas. High goodness-of-fit of the regression line of the FD is a favorable prognostic factor in acute leukemias and multiple myelomas. The nucleus has fractal and power-law organization in several different levels, which might in part be interrelated. Some possible relations between modifications of the chromatin organization during carcinogenesis and tumor progression and an increase of the FD of stained chromatin are suggested. Furthermore, increased complexity of the chromatin structure, loss of heterochromatin and a less-perfect self-organization of the nucleus in aggressive neoplasias are discussed. PMID:24063399
Zhao, Leihong; Yang, Lining; Lin, Hongjun; Zhang, Meijia; Yu, Haiying; Liao, Bao-Qiang; Wang, Fangyuan; Zhou, Xiaoling; Li, Renjie
2016-12-01
While the adsorptive fouling in membrane bioreactors (MBRs) is highly dependent of the surface morphology, little progress has been made on modeling biocake layer surface morphology. In this study, a novel method, which combined static light scattering method for fractal dimension (D f ) measurement with fractal method represented by the modified two-variable Weierstrass-Mandelbrot function, was proposed to model biocake layer surface in a MBR. Characterization by atomic force microscopy showed that the biocake surface was stochastic, disorder, self-similarity, and with non-integer dimension, illustrating obvious fractal features. Fractal dimension (D f ) of sludge suspension experienced a significant change with operation of the MBR. The constructed biocake layer surface by the proposed method was quite close to the real surface, showing the feasibility of the proposed method. It was found that D f was the critical factor affecting surface morphology, while other factors exerted moderate or minor effects on the roughness of biocake layer. Copyright © 2016 Elsevier Ltd. All rights reserved.
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.
Directory of Open Access Journals (Sweden)
Javier Rodríguez
2006-12-01
Full Text Available Introduction. The fractal geometry has shownto be adapted in the mathematical description ofirregular objects; this measurement has denominatedfractal dimension. The application of thefractal analysis to measure the contours of thenormal cells as well as those that present sometype of abnormality, has shown the possibility of mathematical characterization of itsirregularity. Objectives. To measure, from thefractal geometry cells of the squamous epitheliumof uterine neck classified like normal,atypical squamous cells of undetermined significance(ASC-US and Low Grade IntraepitelialLesion (L-SIL, diagnosed by means of microscopicobservation, in search of mathematicalmeasurements that distinguish them. Methodology.This is an exploratory descriptive studyin which the fractal dimensions were calculated,with the simplified and the conventional boxcounting method, of the cellular and nuclearcontours of 13 normal and with abnormalitiescells of the scaly epithelium of uterine neck likeASC-US and L-SIL, from digital photographiesof 7 normal cells, 2 ASC-US and 4 L-SIL diagnosedwith cytomorphologic criteria by meansof microscopic conventional observation. Results.There developed a quantitative, objective and reproduciblemeasurement of the degree of irregularityin the cells of the scaly epithelium of uterineneck identified microscopically like normal, ASCUSy LEI BG. Conclusions an fractal organizationwas demonstrated in the cellular normal architecture,as well as in cells ASC-US and the injuriesintraepiteliales of low degree L-SIL. They did notfind differences between the cellular studied types.
Fractal dimension of soil aggregates as an index of soil erodibility
Ahmadi, Abbas; Neyshabouri, Mohammad-Reza; Rouhipour, Hassan; Asadi, Hossein
2011-04-01
SummaryAggregate stability is an influential factor governing soil erodibility. The fractal dimension of soil aggregates has been related to their size distributions and stabilities. Several fractal models have been proposed for estimating fractal dimension of soil aggregates. This study was conducted to investigate how closely the soil interrill erodibility factor in WEPP model can be correlated to and predicted from soil aggregate size distribution or from their fractal dimensions. Samples from 36 soil series with contrasting properties were collected from northwest of Iran. The fractal dimensions of soil aggregates were calculated from Rieu and Sposito ( D n), Tyler and Wheatcraft ( D mT), and Young and Crawford ( D mY) models using aggregate size distribution (ASD) data. A rainfall simulator with drainable tilting flume (1 × 0.5 m) at slope of 9% was employed and total interrill erosion ( TIE), total splashed soil ( TS) and interrill erodibility factor ( K i) were calculated for 20, 37, and 47 mm h -1 rainfall intensities. Results showed that both D n and D mT estimated from aggregate wet-sieving data characterized ASD of the examined soils and significantly ( p < 0.01) correlated to TS, TIE and K i. Values of D n and D mT estimated from dry-sieving data only correlated to TS but not to TIE and K i. Using air-dried aggregates of 4.75-8 mm size range, instead of aggregates <4.75 mm, in wet-sieving was better for estimating D n as an index for the predication of TIE, TS and K i. Correction of ASD for the particle fraction greater than lower sieve mesh size in each size class decreased the correlation coefficient between TIE, TS or K i and D n or D mT. The values of D mY were not correlated to TS, TIE and K i. The correlation coefficient TIE and K i with D n and D mT derived from wet-sieving data, were higher than those with wet-aggregate stability (WAS), mean weight diameter (MWD) and geometric mean diameter (GMD), implying that D n and D mT may be better
Classification of diabetic retinopathy using fractal dimension analysis of eye fundus image
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.
Synthetic Minority Oversampling Technique and Fractal Dimension for Identifying Multiple Sclerosis
Zhang, Yu-Dong; Zhang, Yin; Phillips, Preetha; Dong, Zhengchao; Wang, Shuihua
Multiple sclerosis (MS) is a severe brain disease. Early detection can provide timely treatment. Fractal dimension can provide statistical index of pattern changes with scale at a given brain image. In this study, our team used susceptibility weighted imaging technique to obtain 676 MS slices and 880 healthy slices. We used synthetic minority oversampling technique to process the unbalanced dataset. Then, we used Canny edge detector to extract distinguishing edges. The Minkowski-Bouligand dimension was a fractal dimension estimation method and used to extract features from edges. Single hidden layer neural network was used as the classifier. Finally, we proposed a three-segment representation biogeography-based optimization to train the classifier. Our method achieved a sensitivity of 97.78±1.29%, a specificity of 97.82±1.60% and an accuracy of 97.80±1.40%. The proposed method is superior to seven state-of-the-art methods in terms of sensitivity and accuracy.
Fractal Dimension of Structurally Controlled River Networks of Pinar del Río, Cuba
Directory of Open Access Journals (Sweden)
Robert Ramírez-Hernández
2017-04-01
Full Text Available River networks were studied applying the fractal systems approach and based on morphometric parameters. Procedures are applied to Cangre, Los Pozos, Paso Viejo, San Diego, Los Palacios, Santa Cruz and San Cristóbal river basins (Pinar del Río, Cuba. Drainage areas were extracted taking into account isolevel lines configurations and river lengths. For every stream the Euclidian length was also estimated, to calculate the river network fractal dimension. It seems that Takayasu approach is the most appropriate to describe basins with the geological characteristics like those included in this study. The shift of order 2 streams with respect to order 1 streams is explained by the presence of drainage zones where streams have short lengths, typically in tectonically active areas. The lithologic factor seems to have influenced the drainage characteristics of Cangre basin, although, in general, the numerous faults and fractures exert a major control on every basin, which is supported by the high fractal values of Cangre, San Diego and Los Palacios basins. The Hurst coefficients of these basins are close to one, revealing a self-similar behavior of the river network. For the remaining basins it is no possible to assume a typical behavior because of the Hurst values are greater than one.
Measuring capital market efficiency: long-term memory, fractal dimension and approximate entropy
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav; Vošvrda, Miloslav
2014-01-01
Roč. 87, č. 7 (2014), "162-1"-"162-9" ISSN 1434-6028 R&D Projects: GA ČR(CZ) GBP402/12/G097 EU Projects: European Commission(XE) FP7/2007-2013 Program:FP7 Institutional support: RVO:67985556 Keywords : Statistical and Nonlinear Physics * fractal dimension * stock market efficiency Subject RIV: AH - Economics Impact factor: 1.345, year: 2014 http://library.utia.cas.cz/separaty/2014/E/kristoufek-0431151.pdf
Cichański, Artur; Nowicki, Krzysztof; Mazurkiewicz, Adam; Topoliński, Tomasz
2010-01-01
The paper presents linear, logarithmic and exponential regression tabecular bone indices, fractal dimensions and strength. The analysis of the above parameters was supported by determining non-parametric correlation coefficients: Spearman's ρ, gamma and Kendall's τ. The principal components' analysis (PCA) was also performed in order to reduce the number of indices describing the variance in the data set. The analysis showed the most independent indices: lacunarity (λm, λmin, λmax), BMD, Conn.D., SMI, DA, ρA and age.
Fractal Dimension of Tumor Microvasculature by DCE-US: Preliminary Study in Mice.
Saidov, Tamerlan; Heneweer, Carola; Kuenen, Maarten; von Broich-Oppert, Julian; Wijkstra, Hessel; Rosette, Jean de la; Mischi, Massimo
2016-12-01
Neoangiogenesis, which results in the formation of an irregular network of microvessels, plays a fundamental role in the growth of several types of cancer. Characterization of microvascular architecture has therefore gained increasing attention for cancer diagnosis, treatment monitoring and evaluation of new drugs. However, this characterization requires immunohistologic analysis of the resected tumors. Currently, dynamic contrast-enhanced ultrasound imaging (DCE-US) provides new options for minimally invasive investigation of the microvasculature by analysis of ultrasound contrast agent (UCA) transport kinetics. In this article, we propose a different method of analyzing UCA concentration that is based on the spatial distribution of blood flow. The well-known concept of Mandelbrot allows vascular networks to be interpreted as fractal objects related to the regional blood flow distribution and characterized by their fractal dimension (FD). To test this hypothesis, the fractal dimension of parametric maps reflecting blood flow, such as UCA wash-in rate and peak enhancement, was derived for areas representing different microvascular architectures. To this end, subcutaneous xenograft models of DU-145 and PC-3 prostate-cancer lines in mice, which show marked differences in microvessel density spatial distribution inside the tumor, were employed to test the ability of DCE-US FD analysis to differentiate between the two models. For validation purposes, the method was compared with immunohistologic results and UCA dispersion maps, which reflect the geometric properties of microvascular architecture. The results showed good agreement with the immunohistologic analysis, and the FD analysis of UCA wash-in rate and peak enhancement maps was able to differentiate between the two xenograft models (p < 0.05). Copyright © 2016 World Federation for Ultrasound in Medicine & Biology. Published by Elsevier Inc. All rights reserved.
Directory of Open Access Journals (Sweden)
Jia Zheqiang
2017-01-01
Full Text Available The water-soaking time affects the physical and mechanical properties of coals, and the temporal and spatial evolution of acoustic emissions reflects the fracture damage process of rock. This study conducted uniaxial compression acoustic emissions tests of coal samples with different water-soaking times to investigate the influence of water-soaking time on the acoustic emissions characteristics and spatial fractal dimensions during the deformation and failure process of coals. The results demonstrate that the acoustic emissions characteristics decrease with increases in the water-soaking time. The acoustic emissions spatial fractal dimension changes from a single dimensionality reduction model to a fluctuation dimensionality reduction model, and the stress level of the initial descending point of the fractal dimension increases. With increases in the water-soaking time, the destruction of coal transitions from continuous intense failure throughout the process to a lower release of energy concentrated near the peak strength.
Nonlinear random resistor diode networks and fractal dimensions of directed percolation clusters.
Stenull, O; Janssen, H K
2001-07-01
We study nonlinear random resistor diode networks at the transition from the nonpercolating to the directed percolating phase. The resistor-like bonds and the diode-like bonds under forward bias voltage obey a generalized Ohm's law V approximately I(r). Based on general grounds such as symmetries and relevance we develop a field theoretic model. We focus on the average two-port resistance, which is governed at the transition by the resistance exponent straight phi(r). By employing renormalization group methods we calculate straight phi(r) for arbitrary r to one-loop order. Then we address the fractal dimensions characterizing directed percolation clusters. Via considering distinct values of the nonlinearity r, we determine the dimension of the red bonds, the chemical path, and the backbone to two-loop order.
Estimating the level of dynamical noise in time series by using fractal dimensions
Energy Technology Data Exchange (ETDEWEB)
Sase, Takumi, E-mail: sase@sat.t.u-tokyo.ac.jp [Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 153-8505 (Japan); Ramírez, Jonatán Peña [CONACYT Research Fellow, Center for Scientific Research and Higher Education at Ensenada (CICESE), Carretera Ensenada-Tijuana No. 3918, Zona Playitas, C.P. 22860, Ensenada, Baja California (Mexico); Kitajo, Keiichi [BSI-Toyota Collaboration Center, RIKEN Brain Science Institute, Wako, Saitama 351-0198 (Japan); Aihara, Kazuyuki; Hirata, Yoshito [Graduate School of Information Science and Technology, The University of Tokyo, Tokyo 153-8505 (Japan); Institute of Industrial Science, The University of Tokyo, Tokyo 153-8505 (Japan)
2016-03-11
We present a method for estimating the dynamical noise level of a ‘short’ time series even if the dynamical system is unknown. The proposed method estimates the level of dynamical noise by calculating the fractal dimensions of the time series. Additionally, the method is applied to EEG data to demonstrate its possible effectiveness as an indicator of temporal changes in the level of dynamical noise. - Highlights: • A dynamical noise level estimator for time series is proposed. • The estimator does not need any information about the dynamics generating the time series. • The estimator is based on a novel definition of time series dimension (TSD). • It is demonstrated that there exists a monotonic relationship between the • TSD and the level of dynamical noise. • We apply the proposed method to human electroencephalographic data.
Directory of Open Access Journals (Sweden)
Julie Fernanda Benavides Arevalo
2012-03-01
. The latter was related to the water dissolution process in order to obtain two associated properties, that is, the surface fractal dimension and the reactive fractal dimension, Conclusions: these results showed that the dissolution of glycinates occurs through the pores or cracks found in their particle surfaces and that these complexes are suitable for use in nutritional formulations as sources of magnesium, manganese and zinc.
Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.
Shanhua, Xu; Songbo, Ren; Youde, Wang
2015-01-01
To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.
Fractal analysis of sulphidic mineral
Directory of Open Access Journals (Sweden)
Miklúová Viera
2002-03-01
Full Text Available In this paper, the application of fractal theory in the characterization of fragmented surfaces, as well as the mass-size distributions are discussed. The investigated mineral-chalcopyrite of Slovak provenience is characterised after particle size reduction processes-crushing and grinding. The problem how the different size reduction methods influence the surface irregularities of obtained particles is solved. Mandelbrot (1983, introducing the fractal geometry, offered a new way of characterization of surface irregularities by the fractal dimension. The determination of the surface fractal dimension DS consists in measuring the specific surface by the BET method in several fractions into which the comminuted chalcopyrite is sieved. This investigation shows that the specific surface of individual fractions were higher for the crushed sample than for the short-term (3 min ground sample. The surface fractal dimension can give an information about the adsorption sites accessible to molecules of nitrogen and according to this, the value of the fractal dimension is higher for crushed sample.The effect of comminution processes on the mass distribution of particles crushed and ground in air as well as in polar liquids is also discussed. The estimation of fractal dimensions of particles mass distribution is done on the assumption that the particle size distribution is described by the power-law (1. The value of fractal dimension for the mass distribution in the crushed sample is lower than in the sample ground in air, because it is influenced by the energy required for comminution.The sample of chalcopyrite was ground (10min in ethanol and i-butanol [which according to Ikazaki (1991] are characterized by the parameter µ /V, where µ is its dipole moment and V is the molecular volume. The values of µ /V for the used polar liquids are of the same order. That is why the expressive differences in particle size distributions as well as in the values of
Inclan, Rosa Maria
2016-04-01
Knowledge on three dimensional soil pore architecture is important to improve our understanding of the factors that control a number of critical soil processes as it controls biological, chemical and physical processes at various scales. Computed Tomography (CT) images provide increasingly reliable information about the geometry of pores and solids in soils at very small scale with the benefit that is a non-invasive technique. Fractal formalism has revealed as a useful tool in these cases where highly complex and heterogeneous meda are studied. One of these quantifications is mass dimension (Dm) and spectral dimension (d) applied to describe the water and gas diffusion coefficients in soils (Tarquis et al., 2012). In this work, intact soil samples were collected from the first three horizons of La Herreria soil. This station is located in the lowland mountain area of Sierra de Guadarrama (Santolaria et al., 2015) and it represents a highly degraded type of site as a result of the livestock keeping. The 3D images, of 45.1 micro-m resolution (256x256x256 voxels), were obtained and then binarized following the singularity-CA method (Martín-Sotoca et al. 2016). Based on these images Dm and d were estimated. The results showed an statistical difference in porosity, Dm and d for each horizon. This fact has a direct implication in diffusion parameters for a pore network modeling based on both fractal dimensions. These soil parameters will constitute a basis for site characterization for further studies regarding soil degradation; determining the interaction between soil, plant and atmosphere with respect to human induced activities as well as the basis for several nitrogen and carbon cycles modeling. References Martin Sotoca; J.J. Ana M. Tarquis, Antonio Saa Requejo, and Juan B. Grau (2016). Pore detection in Computed Tomography (CT) soil 3D images using singularity map analysis. Geophysical Research Abstracts, 18, EGU2016-829. Santolaria-Canales, Edmundo and the Gu
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.)
Poosapadi Arjunan, Sridhar; Kumar, Dinesh Kant
2014-01-01
This research study investigates the fractal properties of surface Electromyogram (sEMG) to estimate the force levels of contraction of three muscles with different cross-sectional areas (CSA): m. quadriceps--vastus lateralis, m. biceps brachii, andm. flexor digitorum superficialis. The fractal features were computed based on the fractal analysis of sEMG, signal recorded while performing sustained muscle contraction at different force levels. A comparison was performed between the fractal features and five other features reported in the literature. Linear regression analysis was carried out to determine the relationship between the force of contraction (20-100%) and features of sEMG. The results from the coefficients of regression r² show that the new fractal feature, maximum fractal length of the signal has highest correlation (range 0.88-0.90) when compared with other features which ranges from 0.34 to 0.74 for the three different muscles. This study suggests that the estimation of various levels of sustained contraction of muscles with varied CSA will provide a better insight into the biomechanics model that involves muscle properties and muscle activation.
Directory of Open Access Journals (Sweden)
Hainian Wang
2016-01-01
Full Text Available The morphological properties of coarse aggregates, such as shape, angularity, and surface texture, have a great influence on the mechanical performance of asphalt mixtures. This study aims to investigate the effect of coarse aggregate morphological properties on the high-temperature performance of asphalt mixtures. A modified Los Angeles (LA abrasion test was employed to produce aggregates with various morphological properties by applying abrasion cycles of 0, 200, 400, 600, 800, 1000, and 1200 on crushed angular aggregates. Based on a laboratory-developed Morphology Analysis System for Coarse Aggregates (MASCA, the morphological properties of the coarse aggregate particles were quantified using the index of fractal dimension. The high-temperature performances of the dense-graded asphalt mixture (AC-16, gap-graded stone asphalt mixture (SAC-16, and stone mastic asphalt (SMA-16 mixtures containing aggregates with different fractal dimensions were evaluated through the dynamic stability (DS test and the penetration shear test in laboratory. Good linear correlations between the fractal dimension and high-temperature indexes were obtained for all three types of mixtures. Moreover, the results also indicated that higher coarse aggregate angularity leads to stronger high-temperature shear resistance of asphalt mixtures.
Donadio, Carlo; Magdaleno, Fernando; Mazzarella, Adriano; Mathias Kondolf, G.
2015-07-01
By applying fractal geometry analysis to the drainage network of three large watercourses in America and Europe, we have calculated for the first time their fractal dimension. The aim is to interpret the geomorphologic characteristics to better understand the morphoevolutionary processes of these fluvial morphotypes; to identify and discriminate geomorphic phenomena responsible for any difference or convergence of a fractal dimension; to classify hydrographic patterns, and finally to compare the fractal degree with some geomorphic-quantitative indexes. The analyzed catchment of Russian (California, USA), Ebro (Spain), and Volturno (Italy) rivers are situated in Mediterranean-climate regions sensu Köppen, but with different geologic context and tectonic styles. Results show fractal dimensions ranging from 1.08 to 1.50. According to the geological setting and geomorphic indexes of these basins, the lower fractal degree indicates a prevailing tectonics, active or not, while the higher degree indicates the stronger erosion processes on inherited landscapes.
Mishra, Jibitesh
2007-01-01
The book covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Key Features: - Fractals generated from L-System including hybrid fractals - Dimension calculation for L-system fractals - Images & codes for L-system fractals - Research directions in the area of L-system fractals - Usage of various freely downloadable tools in this area - Fractals generated from L-System including hybrid fractals- Dimension calculation for L-system fractals- Images & codes for L-system fractals- Research directions in the area of L-system fractals- Usage of various freely downloadable tools in this area
Negentropy Generation and Fractality in the Dry Friction of Polished Surfaces
Directory of Open Access Journals (Sweden)
Mordecai Segall
2010-03-01
Full Text Available We consider the Robin Hood model of dry friction to study entropy transfer during sliding. For the polished surface (steady state we study the probability distribution of slips and find an exponential behavior for all the physically relevant asperity interaction-distance thresholds. In addition, we characterize the time evolution of the sample by its spatial fractal dimension and by its entropy content. Starting from an unpolished surface, the entropy decreases during the Robin Hood process, until it reaches a plateau; thereafter the system fluctuates above the critical height. This validates the notion that friction increases information in the neighborhood of the contacting surface at the expense of losing information in remote regions. We explain the practical relevance of these results for engineering surface processing such as honing.
Detecting fetal heart sounds by means of Fractal Dimension analysis in the Wavelet domain.
Koutsiana, E; Hadjileontiadis, L J; Chouvarda, I; Khandoker, A H
2017-07-01
Phonocardiography is a low-cost technique for the detection of fetal heart sounds (FHS) that can extend clinical auscultation in mobile and home care setups. The work presented here examines the transferability of a Wavelet Transform (WT)-based method that combines also Fractal Dimension (FD) analysis, previously proposed as WT-FD for the cases of lung and bowel sound analysis [4], to the extraction of FHSs. The WT-FD method has been evaluated with 12 simulated FHS signals and has shown promising results in terms of accuracy and performance (89%) in identifying the location of heartbeat, even in cases of signals with additive noise up to (6dB). This robustness paves the way for WT-FD testing in real FHSs, recorded under clinical setting, clearly contributing to better evaluation of the fetal heart functionality.
Topological Vulnerability Evaluation Model Based on Fractal Dimension of Complex Networks
Gou, Li; Wei, Bo; Sadiq, Rehan; Sadiq, Yong; Deng, Yong
2016-01-01
With an increasing emphasis on network security, much more attentions have been attracted to the vulnerability of complex networks. In this paper, the fractal dimension, which can reflect space-filling capacity of networks, is redefined as the origin moment of the edge betweenness to obtain a more reasonable evaluation of vulnerability. The proposed model combining multiple evaluation indexes not only overcomes the shortage of average edge betweenness’s failing to evaluate vulnerability of some special networks, but also characterizes the topological structure and highlights the space-filling capacity of networks. The applications to six US airline networks illustrate the practicality and effectiveness of our proposed method, and the comparisons with three other commonly used methods further validate the superiority of our proposed method. PMID:26751371
Identification of Crack Location in Beam Structures Using Wavelet Transform and Fractal Dimension
Directory of Open Access Journals (Sweden)
Yong-Ying Jiang
2015-01-01
Full Text Available Identification of structural crack location has become an intensely investigated subject due to its practical importance. In this paper, a hybrid method is presented to detect crack locations using wavelet transform and fractal dimension (FD for beam structures. Wavelet transform is employed to decompose the mode shape of the cracked beam. In many cases, small crack location cannot be identified from approximation signal and detailed signals. And FD estimation method is applied to calculate FD parameters of detailed signals. The crack locations will be detected accurately by FD singularity of the detailed signals. The effectiveness of the proposed method is validated by numerical simulations and experimental investigations for a cantilever beam. The results indicate that the proposed method is feasible and can been extended to more complex structures.
Juniati, D.; Khotimah, C.; Wardani, D. E. K.; Budayasa, K.
2018-01-01
The heart abnormalities can be detected from heart sound. A heart sound can be heard directly with a stethoscope or indirectly by a phonocardiograph, a machine of the heart sound recording. This paper presents the implementation of fractal dimension theory to make a classification of phonocardiograms into a normal heart sound, a murmur, or an extrasystole. The main algorithm used to calculate the fractal dimension was Higuchi’s Algorithm. There were two steps to make a classification of phonocardiograms, feature extraction, and classification. For feature extraction, we used Discrete Wavelet Transform to decompose the signal of heart sound into several sub-bands depending on the selected level. After the decomposition process, the signal was processed using Fast Fourier Transform (FFT) to determine the spectral frequency. The fractal dimension of the FFT output was calculated using Higuchi Algorithm. The classification of fractal dimension of all phonocardiograms was done with KNN and Fuzzy c-mean clustering methods. Based on the research results, the best accuracy obtained was 86.17%, the feature extraction by DWT decomposition level 3 with the value of kmax 50, using 5-fold cross validation and the number of neighbors was 5 at K-NN algorithm. Meanwhile, for fuzzy c-mean clustering, the accuracy was 78.56%.
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.
SU-D-BRA-04: Fractal Dimension Analysis of Edge-Detected Rectal Cancer CTs for Outcome Prediction
International Nuclear Information System (INIS)
Zhong, H; Wang, J; Hu, W; Shen, L; Wan, J; Zhou, Z; Zhang, Z
2015-01-01
Purpose: To extract the fractal dimension features from edge-detected rectal cancer CTs, and to examine the predictability of fractal dimensions to outcomes of primary rectal cancer patients. Methods: Ninety-seven rectal cancer patients treated with neo-adjuvant chemoradiation were enrolled in this study. CT images were obtained before chemoradiotherapy. The primary lesions of the rectal cancer were delineated by experienced radiation oncologists. These images were extracted and filtered by six different Laplacian of Gaussian (LoG) filters with different filter values (0.5–3.0: from fine to coarse) to achieve primary lesions in different anatomical scales. Edges of the original images were found at zero-crossings of the filtered images. Three different fractal dimensions (box-counting dimension, Minkowski dimension, mass dimension) were calculated upon the image slice with the largest cross-section of the primary lesion. The significance of these fractal dimensions in survival, recurrence and metastasis were examined by Student’s t-test. Results: For a follow-up time of two years, 18 of 97 patients had experienced recurrence, 24 had metastasis, and 18 were dead. Minkowski dimensions under large filter values (2.0, 2.5, 3.0) were significantly larger (p=0.014, 0.006, 0.015) in patients with recurrence than those without. For metastasis, only box-counting dimensions under a single filter value (2.5) showed differences (p=0.016) between patients with and without. For overall survival, box-counting dimensions (filter values = 0.5, 1.0, 1.5), Minkowski dimensions (filter values = 0.5, 1.5, 2.0, 2,5) and mass dimensions (filter values = 1.5, 2.0) were all significant (p<0.05). Conclusion: It is feasible to extract shape information by edge detection and fractal dimensions analysis in neo-adjuvant rectal cancer patients. This information can be used to prognosis prediction
Energy Technology Data Exchange (ETDEWEB)
Chen, Shu-ying; Ma, Guo-zheng, E-mail: magz0209@163.com; Wang, Hai-dou, E-mail: wanghaidou@aliyun.com.cn; He, Peng-fei; Liu, Ming; Wang, Hai-jun; Xu, Bin-shi
2017-07-01
Highlights: • The solidification mechanism of the plasma sprayed droplets deposited on substrate preheated with different temperature was discussed. • The solidified morphology of individual splat was detected by image analysis method. • The fractal dimension, solidity, area and perimeter, were employed to characterize the morphology of the splat. • The typical solidification modes of Fe-based alloy droplet could be divided into three types, namely, flower-like splat, splashed splat and disk-like splat, which may be attributed the differences of solidification rate of the droplets and adsorption on the substrates. - Abstract: The paper deals with the quantitative characterization of spreading morphologies of plasma sprayed Fe-based alloy droplets deposited on mirror polished steels with different preheated temperature. The plasma torch was utilized as heat producer. The influence of substrate temperature on the solidification mechanism of molten droplets was investigated. The image analysis method (IMA) was employed to identify single splat from the field emission scanning electron microscope (FE-SEM) morphology. The result shows that the substrate preheated temperature has a significant effect on the flattening behavior of molten droplets. With the increment of substrate temperature, the solidification mode of splat changes from flower-like and splashed splat to disk-like splat due to the modification of wettability and cooling velocity between molten droplet and substrate. Compared with area and perimeter, both fractal dimension (FD) and solidity could separately detect the solidification mode of splat to a certain extent, while the FD seems to be more excellent in characterizing irregular morphology of splat in contrast with solidity. However, the combination of FD and solidity is more efficient in classifying solidification mode of splat.
Local connected fractal dimension analysis in gill of fish experimentally exposed to toxicants
Energy Technology Data Exchange (ETDEWEB)
Manera, Maurizio, E-mail: mmanera@unite.it [Faculty of Biosciences, Food and Environmental Technologies, University of Teramo, Piano d’Accio, I-64100 Teramo (Italy); Giari, Luisa [Department of Life Sciences and Biotechnology, University of Ferrara, St. Borsari 46, I-44121 Ferrara (Italy); De Pasquale, Joseph A. [Morphogenyx Inc., PO Box 717, East Northport, NY 11731 (United States); Sayyaf Dezfuli, Bahram [Department of Life Sciences and Biotechnology, University of Ferrara, St. Borsari 46, I-44121 Ferrara (Italy)
2016-06-15
Highlights: • An objective, operator unbiased method was developed to evaluate gill pathology. • The method relies on the measure of local connected fractal dimension frequency. • Exposure classes were adequately discriminated by linear discriminant analysis. - Abstract: An operator-neutral method was implemented to objectively assess European seabass, Dicentrarchus labrax (Linnaeus, 1758) gill pathology after experimental exposure to cadmium (Cd) and terbuthylazine (TBA) for 24 and 48 h. An algorithm-derived local connected fractal dimension (LCFD) frequency measure was used in this comparative analysis. Canonical variates (CVA) and linear discriminant analysis (LDA) were used to evaluate the discrimination power of the method among exposure classes (unexposed, Cd exposed, TBA exposed). Misclassification, sensitivity and specificity, both with original and cross-validated cases, were determined. LCFDs frequencies enhanced the differences among classes which were visually selected after their means, respective variances and the differences between Cd and TBA exposed means, with respect to unexposed mean, were analyzed by scatter plots. Selected frequencies were then scanned by means of LDA, stepwise analysis, and Mahalanobis distance to detect the most discriminative frequencies out of ten originally selected. Discrimination resulted in 91.7% of cross-validated cases correctly classified (22 out of 24 total cases), with sensitivity and specificity, respectively, of 95.5% (1 false negative with respect to 21 really positive cases) and 75% (1 false positive with respect to 3 really negative cases). CVA with convex hull polygons ensured prompt, visually intuitive discrimination among exposure classes and graphically supported the false positive case. The combined use of semithin sections, which enhanced the visual evaluation of the overall lamellar structure; of LCFD analysis, which objectively detected local variation in complexity, without the possible bias
Directory of Open Access Journals (Sweden)
Pengli Zhu
Full Text Available BACKGROUND: This study aimed to investigate the correlation between quantitative retinal vascular parameters such as central retinal arteriolar equivalent (CRAE and retinal vascular fractal dimension (D(f, and cardiovascular risk factors in the Chinese Han population residing in the in islands of southeast China. METHODOLOGY/PRINCIPLE FINDINGS: In this cross-sectional study, fundus photographs were collected and semi-automated analysis software was used to analyze retinal vessel diameters and fractal dimensions. Cardiovascular risk factors such as relevant medical history, blood pressure (BP, lipids, and blood glucose data were collected. Subjects had a mean age of 51.9 ± 12.0 years and included 812 (37.4% males and 1,357 (62.6% females. Of the subjects, 726 (33.5% were overweight, 226 (10.4% were obese, 272 (12.5% had diabetes, 738 (34.0% had hypertension, and 1,156 (53.3% had metabolic syndrome. After controlling for the effects of potential confounders, multivariate analyses found that age (β = 0.06, P = 0.008, sex (β = 1.33, P = 0.015, mean arterial blood pressure (β = -0.12, P<0.001, high-sensitivity C-reactive protein (β = -0.22, P = 0.008, and CRVE (β = 0.23, P<0.001 were significantly associated with CRAE. Age (β = -0.0012, P < 0.001, BP classification (prehypertension: β = -0.0075, P = 0.014; hypertension: β = -0.0131, P = 0.002, and hypertension history (β = -0.0007, P = 0.009 were significantly associated with D(f. CONCLUSIONS/SIGNIFICANCE: D(f exhibits a stronger association with BP than CRAE. Thus, D(f may become a useful indicator of cardiovascular risk.
International Nuclear Information System (INIS)
Flueraru, C; Mao, Y; Chang, S; Popescu, D P; Sowa, M G
2010-01-01
Optical coherence tomography (OCT) images of left-descending coronary tissues harvested from three porcine specimens were acquired with a home-build swept-source OCT setup. Despite the fact that OCT is capable of acquiring high resolution circumferential images of vessels, many distinct histological features of a vessel have comparable optical properties leading to poor contrast in OCT images. Two classification methods were tested in this report for the purpose of enhancing contrast between soft-tissue components of porcine coronary vessels. One method involved analyzing the attenuation of the OCT signal as a function of light penetration into the tissue. We demonstrated that by analyzing the signal attenuation in this manner we were able to differentiate two media sub-layers with different orientations of the smooth muscle cells. The other classification method used in our study was fractal analysis. Fractal analysis was implemented in a box-counting (fractal dimension) image-processing code and was used as a tool to differentiate and quantify variations in tissue texture at various locations in the OCT images. The calculated average fractal dimensions had different values in distinct regions of interest (ROI) within the imaged coronary samples. When compared to the results obtained by using the attenuation of the OCT signal, the method of fractal analysis demonstrated better classification potential for distinguishing amongst the tissue ROI.
Avellar, J.; Duarte, L. G. S.; da Mota, L. A. C. P.; de Melo, N.; Skea, J. E. F.
2012-09-01
A set of Maple routines is presented, fully compatible with the new releases of Maple (14 and higher). The package deals with the numerical evolution of dynamical systems and provide flexible plotting of the results. The package also brings an initial conditions generator, a numerical solver manager, and a focusing set of routines that allow for better analysis of the graphical display of the results. The novelty that the package presents an optional C interface is maintained. This allows for fast numerical integration, even for the totally inexperienced Maple user, without any C expertise being required. Finally, the package provides the routines to calculate the fractal dimension of boundaries (via box counting). New version program summary Program Title: Ndynamics Catalogue identifier: %Leave blank, supplied by Elsevier. Licensing provisions: no. Programming language: Maple, C. Computer: Intel(R) Core(TM) i3 CPU M330 @ 2.13 GHz. Operating system: Windows 7. RAM: 3.0 GB Keywords: Dynamical systems, Box counting, Fractal dimension, Symbolic computation, Differential equations, Maple. Classification: 4.3. Catalogue identifier of previous version: ADKH_v1_0. Journal reference of previous version: Comput. Phys. Commun. 119 (1999) 256. Does the new version supersede the previous version?: Yes. Nature of problem Computation and plotting of numerical solutions of dynamical systems and the determination of the fractal dimension of the boundaries. Solution method The default method of integration is a fifth-order Runge-Kutta scheme, but any method of integration present on the Maple system is available via an argument when calling the routine. A box counting [1] method is used to calculate the fractal dimension [2] of the boundaries. Reasons for the new version The Ndynamics package met a demand of our research community for a flexible and friendly environment for analyzing dynamical systems. All the user has to do is create his/her own Maple session, with the system to
Ţălu, Ştefan; Bramowicz, Miroslaw; Kulesza, Slawomir; Fiorillo, Ilenia; Giovanzana, Stefano
2017-08-01
The aim of this exploratory study was to investigate the micromorphology of surfaces of rigid gas permeable (RGP) contact lenses (CLs) using atomic force microscopy (AFM) followed by fractal analysis. In order to characterize in a quantitative manner the micromorphology of surfaces of new and unworn RGP CLs made of twelve different materials, AFM was taken and then analyzed using fractal methods. Surface topography was sampled in an intermittent-contact mode in air, on square areas of 5 × 5 µm 2 (MultiMode with Nanoscope V (Bruker). Spatial characteristics of 3-D surface texture were obtained using parameters defined in ISO 25178-2: 2012 norm. The surface texture turned out to have complex 3-D nanoscale geometry. For quantitative characterization of the properties of surface geometry at nanometer level of CL on the global scale, a series of fractal parameters was used. Statistical and fractal parameters of 3-D surfaces can be used by manufacturers to assess the micromorphology of CLs in order to improve their 3-D surface texture characteristics. These parameters can also be used in an elastic-plastic finite element model with contact elements to simulate the friction, wear and micro-elastohydrodynamic lubrication at a nanometer scale between the CL with the corneal surface.
Valle, Francesco; Brucale, Marco; Chiodini, Stefano; Bystrenova, Eva; Albonetti, Cristiano
2017-09-01
While the widespread emergence of nanoscience and nanotechnology can be dated back to the early eighties, the last decade has witnessed a true coming of age of this research field, with novel nanomaterials constantly finding their way into marketed products. The performance of nanomaterials being dominated by their nanoscale morphology, their quantitative characterization with respect to a number of properties is often crucial. In this context, those imaging techniques able to resolve nanometer scale details are clearly key players. In particular, atomic force microscopy can yield a fully quantitative tridimensional (3D) topography at the nanoscale. Herein, we will review a set of morphological analysis based on the scaling approach, which give access to important quantitative parameters for describing nanomaterial samples. To generalize the use of such morphological analysis on all D-dimensions (1D, 2D and 3D), the review will focus on specific soft matter aggregates with fractal dimension ranging from just above 1 to just below 3. Copyright © 2017 Elsevier Ltd. All rights reserved.
Complexity analysis of EEG in patients with schizophrenia using fractal dimension
International Nuclear Information System (INIS)
Raghavendra, B S; Dutt, D Narayana; Halahalli, Harsha N; John, John P
2009-01-01
We computed Higuchi's fractal dimension (FD) of resting, eyes closed EEG recorded from 30 scalp locations in 18 male neuroleptic-naïve, recent-onset schizophrenia (NRS) subjects and 15 male healthy control (HC) subjects, who were group-matched for age. Schizophrenia patients showed a diffuse reduction of FD except in the bilateral temporal and occipital regions, with the reduction being most prominent bifrontally. The positive symptom (PS) schizophrenia subjects showed FD values similar to or even higher than HC in the bilateral temporo-occipital regions, along with a co-existent bifrontal FD reduction as noted in the overall sample of NRS. In contrast, this increase in FD values in the bilateral temporo-occipital region was absent in the negative symptom (NS) subgroup. The regional differences in complexity suggested by these findings may reflect the aberrant brain dynamics underlying the pathophysiology of schizophrenia and its symptom dimensions. Higuchi's method of measuring FD directly in the time domain provides an alternative for the more computationally intensive nonlinear methods of estimating EEG complexity
Fractal dimension of EEG activity senses neuronal impairment in acute stroke.
Directory of Open Access Journals (Sweden)
Filippo Zappasodi
Full Text Available The brain is a self-organizing system which displays self-similarities at different spatial and temporal scales. Thus, the complexity of its dynamics, associated to efficient processing and functional advantages, is expected to be captured by a measure of its scale-free (fractal properties. Under the hypothesis that the fractal dimension (FD of the electroencephalographic signal (EEG is optimally sensitive to the neuronal dysfunction secondary to a brain lesion, we tested the FD's ability in assessing two key processes in acute stroke: the clinical impairment and the recovery prognosis. Resting EEG was collected in 36 patients 4-10 days after a unilateral ischemic stroke in the middle cerebral artery territory and 19 healthy controls. National Health Institute Stroke Scale (NIHss was collected at T0 and 6 months later. Highuchi FD, its inter-hemispheric asymmetry (FDasy and spectral band powers were calculated for EEG signals. FD was smaller in patients than in controls (1.447±0.092 vs 1.525±0.105 and its reduction was paired to a worse acute clinical status. FD decrease was associated to alpha increase and beta decrease of oscillatory activity power. Larger FDasy in acute phase was paired to a worse clinical recovery at six months. FD in our patients captured the loss of complexity reflecting the global system dysfunction resulting from the structural damage. This decrease seems to reveal the intimate nature of structure-function unity, where the regional neural multi-scale self-similar activity is impaired by the anatomical lesion. This picture is coherent with neuronal activity complexity decrease paired to a reduced repertoire of functional abilities. FDasy result highlights the functional relevance of the balance between homologous brain structures' activities in stroke recovery.
Tree-shaped fractal meta-surface with left-handed characteristics for absorption application
Faruque, M. R. I.; Hasan, M. M.; Islam, M. T.
2018-02-01
A tri-band fractal meta-surface absorber composed of metallic branches of a tree connected with a straight metal strip has been presented in this paper for high absorption application. The proposed tree-shaped structure shows resonance in C-, X-, and Ku-bands and left-handed characteristics in 14.15 GHz. The dimension of the tree-shaped meta-surface single unit cell structure is 9 × 9 mm2 and the effective medium ratio is 5.50. In addition, the designed absorber structure shows absorption above 84%, whereas the absorber structure printed on epoxy resin fiber substrate material. The FIT-based CST-MWS has been utilized for the design, simulation, and analysis purposes. Fabrication is also done for the experimental validation.
Measuring the surface roughness of geological rock surfaces in SAR data using fractal geometry
Ghafouri, Ali; Amini, Jalal; Dehmollaian, Mojtaba; Kavoosi, Mohammad Ali
2017-05-01
Determining surface morphology using synthetic aperture radar (SAR) data requires accurate topographic and microtopographic models. To distinguish different surface geometric patterns and to differentiate the formation of geological rock surfaces, it is necessary to model the smoothness and roughness of surfaces based on radar signal backscattering. Euclidean geometry is less able than fractal geometry to describe natural phenomena; however, in application to radar backscattering models, fractal geometry has never fully replaced Euclidean geometry. Using fractal geometry only, this paper attempts to improve the backscattering simulation generated by an Integral Equation Model to improve the description of geological rock surfaces. As the application of radar signal backscattering is a rarity in the domain of geology, the paper also discusses the efficiency of the method in improving the results of conventional geological mapping methods. The proposed method is applied to the Anaran geological formation (between Dehloran and Ilam in IRAN) using TerraSAR-X SAR data and in situ roughness measurements on pure sites with rough, intermediate, and smooth morphologies. This implementation shows fractal and diffractal behavior of geological morphologies under various conditions.
Fractal structure of lunar topography: An interpretation of topographic characteristics
Cao, Wei; Cai, Zhanchuan; Tang, Zesheng
2015-06-01
Over the years, fractal geometry has been applied extensively in many fields of geoscience. Based on the global gridded data generated from the Lunar Reconnaissance Orbiter, we carry out our fractal measure to interpret lunar fractures by using qualitative (similar ratio) and quantitative (fractal dimension) approaches of fractal geometry. We find that most of the lunar surface exhibits fractal behavior over the given scales ranging from 1 to 256 m. Lunar maria have higher fractal dimensions than other geological units, while those of volcanic areas and highlands are lower than their surroundings. Simple and flat surfaces have low values of similar ratios and these areas indicate low surface roughness and young ages. Older-aged areas, such as the Hertzsprung basin, have low fractal dimensions and high similar ratios by their complicated topography.
The fractal harmonic law and its application to swimming suit
Directory of Open Access Journals (Sweden)
Kong Hai-Yan
2012-01-01
Full Text Available Decreasing friction force between a swimming suit and water is the key factor to design swimming suits. Water continuum mechanics forbids discontinuous fluids, but in angstrom scale water is indeed discontinuous. Swimming suit is smooth on large scale, but it is discontinuous when the scale becomes smaller. If fractal dimensions of swimming suit and water are the same, a minimum of friction force is predicted, which means fractal harmonization. In the paper, fractal harmonic law is introduced to design a swimsuit whose surface fractal dimensions on a macroscopic scale should be equal to or closed to the water's fractal dimensions on an Angstrom scale. Various possible microstructures of fabric are analyzed and a method to obtain perfect fractal structure of fabric is proposed by spraying nanofibers to its surface. The fractal harmonic law can be used to design a moving surface with a minimal friction.
Directory of Open Access Journals (Sweden)
Alessandro Costa da Silva
2003-05-01
Full Text Available The determination of fractal dimension (D of humic particles was achieved by the turbidimetric technique where diluted suspensions of humic acids, in different experimental conditions, were analyzed by spectrophotometry UV-Vis. The slope of the lines (beta was taken from the graphics (logtauvs loglambda to obtain D. The results show that the values of D changed according to pH (3.0, 5.0 and 7.0, temperature (25 and 5 ºC and shaking (magnetic and horizontal. In general, the value of D decreased with the increment of pH, increase of shaking and decrease of temperature.
International Nuclear Information System (INIS)
Dokukin, M E; Sokolov, I; Guz, N V; Woodworth, C D
2015-01-01
Despite considerable advances in understanding the molecular nature of cancer, many biophysical aspects of malignant development are still unclear. Here we study physical alterations of the surface of human cervical epithelial cells during stepwise in vitro development of cancer (from normal to immortal (premalignant), to malignant). We use atomic force microscopy to demonstrate that development of cancer is associated with emergence of simple fractal geometry on the cell surface. Contrary to the previously expected correlation between cancer and fractals, we find that fractal geometry occurs only at a limited period of development when immortal cells become cancerous; further cancer progression demonstrates deviation from fractal. Because of the connection between fractal behaviour and chaos (or far from equilibrium behaviour), these results suggest that chaotic behaviour coincides with the cancer transformation of the immortalization stage of cancer development, whereas further cancer progression recovers determinism of processes responsible for cell surface formation. (paper)
Directory of Open Access Journals (Sweden)
Matteo Beretta-Piccoli
Full Text Available Over the past decade, linear and non-linear surface electromyography descriptors for central and peripheral components of fatigue have been developed. In the current study, we tested fractal dimension (FD and conduction velocity (CV as myoelectric descriptors of central and peripheral fatigue, respectively. To this aim, we analyzed FD and CV slopes during sustained fatiguing contractions of the quadriceps femoris in healthy humans.A total of 29 recreationally active women (mean age±standard deviation: 24±4 years and two female elite athletes (one power athlete, age 24 and one endurance athlete, age 30 years performed two knee extensions: (1 at 20% maximal voluntary contraction (MVC for 30 s, and (2 at 60% MVC held until exhaustion. Surface EMG signals were detected from the vastus lateralis and vastus medialis using bidimensional arrays.Central and peripheral fatigue were described as decreases in FD and CV, respectively. A positive correlation between FD and CV (R=0.51, p<0.01 was found during the sustained 60% MVC, probably as a result of simultaneous motor unit synchronization and a decrease in muscle fiber CV during the fatiguing task.Central and peripheral fatigue can be described as changes in FD and CV, at least in young, healthy women. The significant correlation between FD and CV observed at 60% MVC suggests that a mutual interaction between central and peripheral fatigue can arise during submaximal isometric contractions.
Beretta-Piccoli, Matteo; D’Antona, Giuseppe; Barbero, Marco; Fisher, Beth; Dieli-Conwright, Christina M.; Clijsen, Ron; Cescon, Corrado
2015-01-01
Purpose Over the past decade, linear and non-linear surface electromyography descriptors for central and peripheral components of fatigue have been developed. In the current study, we tested fractal dimension (FD) and conduction velocity (CV) as myoelectric descriptors of central and peripheral fatigue, respectively. To this aim, we analyzed FD and CV slopes during sustained fatiguing contractions of the quadriceps femoris in healthy humans. Methods A total of 29 recreationally active women (mean age±standard deviation: 24±4 years) and two female elite athletes (one power athlete, age 24 and one endurance athlete, age 30 years) performed two knee extensions: (1) at 20% maximal voluntary contraction (MVC) for 30 s, and (2) at 60% MVC held until exhaustion. Surface EMG signals were detected from the vastus lateralis and vastus medialis using bidimensional arrays. Results Central and peripheral fatigue were described as decreases in FD and CV, respectively. A positive correlation between FD and CV (R=0.51, pfatiguing task. Conclusions Central and peripheral fatigue can be described as changes in FD and CV, at least in young, healthy women. The significant correlation between FD and CV observed at 60% MVC suggests that a mutual interaction between central and peripheral fatigue can arise during submaximal isometric contractions. PMID:25880369
Boccia, Gennaro; Dardanello, Davide; Beretta-Piccoli, Matteo; Cescon, Corrado; Coratella, Giuseppe; Rinaldo, Nicoletta; Barbero, Marco; Lanza, Massimo; Schena, Federico; Rainoldi, Alberto
2016-01-01
Over the past decade, linear and nonlinear surface electromyography (EMG) variables highlighting different components of fatigue have been developed. In this study, we tested fractal dimension (FD) and conduction velocity (CV) rate of changes as descriptors, respectively, of motor unit synchronization and peripheral manifestations of fatigue. Sixteen elderly (69 ± 4 years) and seventeen young (23 ± 2 years) physically active men (almost 3-5 h of physical activity per week) executed one knee extensor contraction at 70% of a maximal voluntary contraction for 30 s. Muscle fiber CV and FD were calculated from the multichannel surface EMG signal recorded from the vastus lateralis and medialis muscles. The main findings were that the two groups showed a similar rate of change of CV, whereas FD rate of change was higher in the young than in the elderly group. The trends were the same for both muscles. CV findings highlighted a non-different extent of peripheral manifestations of fatigue between groups. Nevertheless, FD rate of change was found to be steeper in the elderly than in the young, suggesting a greater increase in motor unit synchronization with ageing. These findings suggest that FD analysis could be used as a complementary variable providing further information on central mechanisms with respect to CV in fatiguing contractions.
Fractal dimension of debris-avalanche deposits in the Hawaiian submarine landslide deposits
Yokose, H.; Yamato, S.
2005-12-01
17 landslide deposits on the flanks of the southern Hawaiian Ridge have been classified into two major types: SLUMPS, which moved slowly as a coherent mass, and DEBRIS AVALANCHES, which moved quickly.The debris-avalanche deposits are predominant on submarine flanks of volcanic ocean islands elsewhere in the world. Such huge landslides are considered to produce giant tsunamis and megaturbidites covering large areas of abyssal plains. Based on the small scale topographic elements, we reinvestigated the distribution areas and emplacement styles of the debris-avalanche deposits, which differ from those previously proposed from GLORIA images without benefit of detailed bathymetric data or direct seafloor observations. There are several types of small scale topographic elements in the debris-avalanche deposits previously proposed: source amphitheater, toppled blocks, marginal levee, slide-emplaced blocks, chute, mud wave, hummocky terrain. They are very similar to those appeared in subaerial volcanic debris-avalanche fields. However, no correlation between the collapse height and runout distance are observed in the submarine debris-avalanche deposits. The hummocky terrains can be classified into two types: FLAT-TYPE, which is distributed in the nearly flat abyssal plain, less than 0.5 degree, and SLOPE-TYPE, which located on the lower part of the submarine flanks, greater than 1 degree. The size of hummocks in a slope-type hummocky terrain have an unimodal distribution pattern with a broad peak in the number of hummocks versus height category diagram. On the contrary, the size of hummocks in flat-type hummocky terrains have a power law distribution pattern in the same diagram. The fractal dimensions calculated from these diagrams are 1.19 (Nuuanu landslide), 2.32 (Ka Lae landslide) and 2.96 (Alika 2 debris-avalanche), respectively. They are expected to reflect the processes and degree of fragmentation. Therefore, among the debris_]avalanche deposits proposed previously
Eigenwave spectrum of surface acoustic waves on a rough self-affine fractal surface
Palasantzas, George
1994-01-01
The propagation of a sound wave along a statistically rough solid-vacuum interface is investigated for the case of self-affine fractals. The wave-number relation ω=ω(k) is examined for the transverse polarized surface wave. The range of existence of this wave is analyzed as a function of the degree
Directory of Open Access Journals (Sweden)
Wenwan Ding
2016-01-01
Full Text Available An improved fractal sea surface model, which can describe the capillary waves very well, is introduced to simulate the one-dimension rough sea surface. In this model, the propagation of electromagnetic waves (EWs is computed by the parabolic equation (PE method using the finite-difference (FD algorithm. The numerical simulation results of the introduced model are compared with those of the Miller-Brown model and the Elfouhaily spectrum inversion model. It has been shown that the effects of the fine structure of the sea surface on the EWs propagation in the introduced model are more apparent than those in the other two models.
Directory of Open Access Journals (Sweden)
Georgia S. Araujo
2017-12-01
Full Text Available The particle morphology and surface texture play a major role in influencing mechanical and hydraulic behaviors of sandy soils. This paper presents the use of digital image analysis combined with fractal theory as a tool to quantify the particle morphology and surface texture of two types of quartz sands widely used in the region of Vitória, Espírito Santo, southeast of Brazil. The two investigated sands are sampled from different locations. The purpose of this paper is to present a simple, straightforward, reliable and reproducible methodology that can identify representative sandy soil texture parameters. The test results of the soil samples of the two sands separated by sieving into six size fractions are presented and discussed. The main advantages of the adopted methodology are its simplicity, reliability of the results, and relatively low cost. The results show that sands from the coastal spit (BS have a greater degree of roundness and a smoother surface texture than river sands (RS. The values obtained in the test are statistically analyzed, and again it is confirmed that the BS sand has a slightly greater degree of sphericity than that of the RS sand. Moreover, the RS sand with rough surface texture has larger specific surface area values than the similar BS sand, which agree with the obtained roughness fractal dimensions. The consistent experimental results demonstrate that image analysis combined with fractal theory is an accurate and efficient method to quantify the differences in particle morphology and surface texture of quartz sands.
Assessing severity of obstructive sleep apnea by fractal dimension sequence analysis of sleep EEG
Zhang, J.; Yang, X. C.; Luo, L.; Shao, J.; Zhang, C.; Ma, J.; Wang, G. F.; Liu, Y.; Peng, C.-K.; Fang, J.
2009-10-01
Different sleep stages are associated with distinct dynamical patterns in EEG signals. In this article, we explored the relationship between the sleep architecture and fractal dimension (FD) of sleep EEG. In particular, we applied the FD analysis to the sleep EEG of patients with obstructive sleep apnea-hypopnea syndrome (OSAHS), which is characterized by recurrent oxyhemoglobin desaturation and arousals from sleep, a disease which received increasing public attention due to its significant potential impact on health. We showed that the variation of FD reflects the macrostructure of sleep. Furthermore, the fast fluctuation of FD, as measured by the zero-crossing rate of detrended FD (zDFD), is a useful indicator of sleep disturbance, and therefore, correlates with apnea-hypopnea index (AHI), and hourly number of blood oxygen saturation (SpO 2) decreases greater than 4%, as obstructive apnea/hypopnea disturbs sleep architecture. For practical purpose, a modified index combining zDFD of EEG and body mass index (BMI) may be useful for evaluating the severity of OSAHS symptoms.
Directory of Open Access Journals (Sweden)
Natasa Reljin
2015-04-01
Full Text Available In this paper, we propose the use of blanket fractal dimension (BFD to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5 healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE. The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained. The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days.
Reljin, Natasa; Reyes, Bersain A; Chon, Ki H
2015-04-27
In this paper, we propose the use of blanket fractal dimension (BFD) to estimate the tidal volume from smartphone-acquired tracheal sounds. We collected tracheal sounds with a Samsung Galaxy S4 smartphone, from five (N = 5) healthy volunteers. Each volunteer performed the experiment six times; first to obtain linear and exponential fitting models, and then to fit new data onto the existing models. Thus, the total number of recordings was 30. The estimated volumes were compared to the true values, obtained with a Respitrace system, which was considered as a reference. Since Shannon entropy (SE) is frequently used as a feature in tracheal sound analyses, we estimated the tidal volume from the same sounds by using SE as well. The evaluation of the performed estimation, using BFD and SE methods, was quantified by the normalized root-mean-squared error (NRMSE). The results show that the BFD outperformed the SE (at least twice smaller NRMSE was obtained). The smallest NRMSE error of 15.877% ± 9.246% (mean ± standard deviation) was obtained with the BFD and exponential model. In addition, it was shown that the fitting curves calculated during the first day of experiments could be successfully used for at least the five following days.
Apolinário, Ana C; Sindeaux, Rafael; de Souza Figueiredo, Paulo T; Guimarães, Ana T B; Acevedo, Ana C; Castro, Luiz C; de Paula, Ana P; de Paula, Lilian M; de Melo, Nilce S; Leite, André F
2016-01-01
To verify radiomorphometric indices and fractal dimension (FD) in dental panoramic radiographs (DPRs) of children with different types of osteogenesis imperfecta (OI) and also to verify the effect of pamidronate (PAM) treatment in such panoramic analyses. In this retrospective study, 197 DPRs of 62 children with OI Types I, III and IV who were in treatment with a comparable dosage of intravenous PAM were selected. The mandibular cortical width (MCW), mandibular cortical index, visual estimation of the cortical width and FD of three standardized trabecular and cortical mandibular regions of interest were obtained from the radiographs. Factorial analysis of variance and Fisher test were used to compare FD and MCW measurements in children with different types of OI for different PAM cycles. Children with all types of OI have thinner and more porous mandibular cortices at the beginning of treatment. There were significant differences between MCW and FD of the cortical bone, regarding different types of OI and number of PAM cycles (p = 0.037 and p = 0.044, respectively). FD measurements of the trabecular bone were not statistically different among OI types nor were PAM cycles (p > 0.05). Children with OI presented cortical bone alterations after PAM treatment. Both MCW and the FD of the cortical bone were higher in children with OI after PAM treatment. It is argued that cortical bone should be considered for analyzing patients with OI, as well as to monitor the progress of PAM treatment.
Shi, Zhi-Jian; Guo, Qiong; Xu, Yi-Qun; Wu, Dan; Liao, Si-Mo; Zhang, Fu-Yue; Zhang, Zheng-Zhe; Jin, Ren-Cun
2017-11-01
In this study, the mass transfer, rheological behavior and fractal dimension of anaerobic ammonium oxidation (anammox) granules in upflow anaerobic sludge blanket reactors at various temperatures (8.5-34.5°C) and upflow velocities (0.06, 0.18mh -1 ) were investigated. The results demonstrated that a lower temperature increased the external mass transfer coefficient and apparent viscosity and impaired the performance of anammox granules. The external mass transfer coefficient was decreased, but efficient nitrogen removal of up to 96% was achieved under high upflow velocity, which also decreased the apparent viscosity. Furthermore, a fractal dimension of up to 2.93 achieved at low temperature was higher than the previously reported values for mesophilic anammox granules. A higher upflow velocity was associated with the lower fractal dimension. Because of the disturbance in granule flaking, the effectiveness factor was less suitable than the external mass transfer coefficient for characterization of mass transfer resistance. Copyright © 2017 Elsevier Ltd. All rights reserved.
Puškaš, Nela; Zaletel, Ivan; Stefanović, Bratislav D; Ristanović, Dušan
2015-03-04
Pyramidal neurons of the mammalian cerebral cortex have specific structure and pattern of organization that involves the presence of apical dendrite. Morphology of the apical dendrite is well-known, but quantification of its complexity still remains open. Fractal analysis has proved to be a valuable method for analyzing the complexity of dendrite morphology. The aim of this study was to establish the fractal dimension of apical dendrite arborization of pyramidal neurons in distinct neocortical laminae by using the modified box-counting method. A total of thirty, Golgi impregnated neurons from the rat brain were analyzed: 15 superficial (cell bodies located within lamina II-III), and 15 deep pyramidal neurons (cell bodies situated within lamina V-VI). Analysis of topological parameters of apical dendrite arborization showed no statistical differences except in total dendritic length (p=0.02), indicating considerable homogeneity between the two groups of neurons. On the other hand, average fractal dimension of apical dendrite was 1.33±0.06 for the superficial and 1.24±0.04 for the deep cortical neurons, showing statistically significant difference between these two groups (pfractal dimension values, apical dendrites of the superficial pyramidal neurons tend to show higher structural complexity compared to the deep ones. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.
Fractal Analysis on Asphalt Mixture Using a Two-Dimensional Imaging Technique
Directory of Open Access Journals (Sweden)
Yue Hou
2016-01-01
Full Text Available Fractal is a mathematical set that has a fractal dimension which usually exceeds its topological dimension and may be nonintegral. Since the asphalt pavement texture has limitations of randomness and self-similarity, fractal theory has been explored to quantify the asphalt pavement texture and employs good applicability in processing and analyzing the complex details of research object. In this paper, the 2D digital image of the pavement surface is measured in terms of area fractal dimension and contour fractal dimension, which are used to correlate with aggregate gradation and British Pendulum Number (BPN value, respectively. It turns out the area fractal dimension of aggregate provides a simple way to acquire the continuous gradation of asphalt concrete sample and the contour fractal dimension is an available parameter to characterize roughness and friction of pavement surface texture.
Directory of Open Access Journals (Sweden)
Luis García Domínguez
2005-01-01
Full Text Available ABSTRACTThe Autoregressive Dimensional Index (ARDI was measured in a subset of R-R recordings corresponding to 257 patients from the Cardiac Arrhythmia Suppression Trial (CAST-study, both before, and during treatment with the anti-arrhythmic drug Encainide (E. Encainide induced an average ARDI increase of 47% (PA similar analysis with 127 patients treated with Flecainide (F did not reveal statistical differences related to treatment. Since ARDI is negatively correlated to the Fractal Dimension (FD of HRV data (Hernandez et al, Electron J Biomed 2004;1:4-15 we conclude that E exerts a reduction in FD among these patients. Since changes suggesting FD reduction are predictive of health worsening and sudden death, our results may provide an explanation for the reported increase in mortality induced by E among CAST patients. The lack of effect from F may be in agreement with recent reports suggesting that this drug does not increase the risk of sudden death.RESUMENEl Índice Dimensional Autorregresivo (Autoregressive Dimensional Index ARDI fue evaluado sobre un subconjunto de registros de intervalos R-R correspondientes a 257 pacientes incluidos en el estudio "CAST", un conocido ensayo de supresión de arritmia en pacientes que sufrieron infarto agudo del miocardio. Los registros fueron obtenidos tanto antes como durante el tratamiento con el medicamento antiarrítmico Encainida (E. La Encainida inducía un incremento en el valor de ARDI de aproximadamente un 47% (P<0.001, prueba de la "t" pareada.Un análisis similar realizado con 127 pacientes tratados con Flecainida (F no mostró ningún cambio significativa asociada al tratamiento. Por cuanto ARDI se correlaciona negativamente con la Dimensión Fractal (FD de los datos de variabilidad de la frecuencia cardiaca (Hernández et al, Electrón J Biomed 2004;1:4-15, concluimos que E ejerce una acción reductora de la FD en ese grupo de pacientes. Por cuanto la reducción de la FD predice acerca del
Directory of Open Access Journals (Sweden)
Franz Konstantin Fuss
2013-01-01
Full Text Available Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal’s time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
Fuss, Franz Konstantin
2013-01-01
Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
Fractal Analysis of Rock Joint Profiles
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.
Surface chemistry in three dimensions
DEFF Research Database (Denmark)
Bollinger, Mikkel; Jacobsen, Karsten Wedel; Nørskov, Jens Kehlet
2000-01-01
the usual single surface ('2D') process because indirect adsorbate-adsorbate interactions in the transition state are absent in the '3D' case. The prospects for STM-induced single molecule chemistry and for '3D' catalysts are discussed. (C) 2000 Elsevier Science B.V. All rights reserved.......Based on self-consistent density functional calculations it is shown that a new dissociation process for CO adsorbed on a Ru(0001) surface is made possible when the distance to a second Ru(0001) surface placed just above it is below some critical value. This '3D' process is more facile than...
Directory of Open Access Journals (Sweden)
Camarero, Jesús Julio
2002-06-01
Full Text Available We quantified the complexity of leaf margin in a set of Quercus tree species using fractal dimension estimated by the box-counting method (FDb. Leaves were sampled from seedlings in a set of 15 Quercus species with a wide range of leaf morphology (Q. agrifolia, Q. alba, Q. cerris, Q. chrysolepis, Q. coccifera, Q.faginea, Q. frainetto, Q. ilex subsp. ballota, Q. ilex subsp. ilex, Q. petraea, Q. pyrenaica, Q. robur, Q. rubra, Q. suber, and Q. velutina. To describe leaf-edge roughness, we used simple indices: P/L - the ratio of leaf perimeter (P to maximum leaf length (L along the main nerve; P/A - the ratio of leaf perimeter to leaf-blade area (A and its dimensionless version (P/A0'; and WM/Wm -the ratio of maximum distance from the lobe tip to the main nerve (WM to minimum distance from the lobe incision to the main nerve (Wm. There was a strong positive relationship between FDb and P/A. Clustering analysis revealed the existence of three groups of leaves, namely those with: smooth or spiny margins (e.g., Q. coccifera, Q. velutina, shallow lobes (e.g., Q. petraea, and deep lobes (e.g., Q. pyrenaica. In the studied Quercus species, the ratio WM/Wm is a simple and suitable leaflobation index. It is suggested that the flux rate along the leaf edge is related to the complexity of this boundary.Se ha cuantificado la complejidad del margen de las hojas de varias especies arboreas del genero Quercus utilizando la dimension fractal estimada mediante el modo del recuento de cajas (FDb. Se tomaron hojas procedentes de plantulas pertenecientes a 15 especies de Quercus con un amplio rango de morfologfa foliar (Q. agrifolia, Q. alba, Q. cerris, Q. chrysolepis, Q. coccifera, Q. faginea, Q. frainetto, Q. ilex subsp. ballota, Q. ilex subsp. ilex, Q. petraea, Q. pyrenaica, Q. robur, Q. rubra, Q. suber y Q. velutina. Se usaron varios Indices sencillos para describir la complejidad del borde de la hoja: P/L, la relation entre el perimetro foliar (P y la longitud
Enhanced Fluorescence from Fluorophores on Fractal Silver Surfaces
Parfenov, Alexandr; Gryczynski, Ignacy; Malicka, Joanna; Geddes, Chris D.; Lakowicz, Joseph R.
2003-01-01
Recent reports have shown enhanced fluorescence for fluorophores in close proximity to chemically deposited silver islands or colloids. To expand the usefulness of metal-enhanced fluorescence we tested fractal silver structures formed on, or near, silver electrodes by passage of electric currents. The emission intensity of fluorescein-labeled human serum albumin (FITC-HSA) was enhanced over 100-fold when adsorbed to the fractal silver structures as compared to glass. The amplitude-weighted li...
2-D Fractal Carpet Antenna Design and Performance
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
Rawat, Kishan Singh; Singh, Sudhir Kumar; Jacintha, T. German Amali; Nemčić-Jurec, Jasna; Tripathi, Vinod Kumar
2017-12-01
A review has been made to understand the hydrogeochemical behaviour of groundwater through statistical analysis of long term water quality data (year 2005-2013). Water Quality Index ( WQI), descriptive statistics, Hurst exponent, fractal dimension and predictability index were estimated for each water parameter. WQI results showed that majority of samples fall in moderate category during 2005-2013, but monitoring site four falls under severe category (water unfit for domestic use). Brownian time series behaviour (a true random walk nature) exists between calcium (Ca^{2+}) and electric conductivity (EC); magnesium (Mg^{2+}) with EC; sodium (Na+) with EC; sulphate (SO4^{2-}) with EC; total dissolved solids (TDS) with chloride (Cl-) during pre- (2005-2013) and post- (2006-2013) monsoon season. These parameters have a closer value of Hurst exponent ( H) with Brownian time series behaviour condition (H=0.5). The result of times series analysis of water quality data shows a persistent behaviour (a positive autocorrelation) that has played a role between Cl- and Mg^{2+}, Cl- and Ca^{2+}, TDS and Na+, TDS and SO4^{2-}, TDS and Ca^{2+} in pre- and post-monsoon time series because of the higher value of H (>1). Whereas an anti-persistent behaviour (or negative autocorrelation) was found between Cl- and EC, TDS and EC during pre- and post-monsoon due to low value of H. The work outline shows that the groundwater of few areas needs treatment before direct consumption, and it also needs to be protected from contamination.
Rawat, Kishan Singh; Singh, Sudhir Kumar; Jacintha, T. German Amali; Nemčić-Jurec, Jasna; Tripathi, Vinod Kumar
2018-02-01
A review has been made to understand the hydrogeochemical behaviour of groundwater through statistical analysis of long term water quality data (year 2005-2013). Water Quality Index ( WQI), descriptive statistics, Hurst exponent, fractal dimension and predictability index were estimated for each water parameter. WQI results showed that majority of samples fall in moderate category during 2005-2013, but monitoring site four falls under severe category (water unfit for domestic use). Brownian time series behaviour (a true random walk nature) exists between calcium (Ca^{2+}) and electric conductivity (EC); magnesium (Mg^{2+}) with EC; sodium (Na+) with EC; sulphate (SO4^{2-}) with EC; total dissolved solids (TDS) with chloride (Cl-) during pre- (2005-2013) and post- (2006-2013) monsoon season. These parameters have a closer value of Hurst exponent ( H) with Brownian time series behaviour condition (H=0.5). The result of times series analysis of water quality data shows a persistent behaviour (a positive autocorrelation) that has played a role between Cl- and Mg^{2+}, Cl- and Ca^{2+}, TDS and Na+, TDS and SO4^{2-}, TDS and Ca^{2+} in pre- and post-monsoon time series because of the higher value of H (>1). Whereas an anti-persistent behaviour (or negative autocorrelation) was found between Cl- and EC, TDS and EC during pre- and post-monsoon due to low value of H. The work outline shows that the groundwater of few areas needs treatment before direct consumption, and it also needs to be protected from contamination.
Feng, Shushu; Yu, Genying; Cai, Xiang; Eulade, Mahoro; Lin, Hongjun; Chen, Jianrong; Liu, Yong; Liao, Bao-Qiang
2017-11-01
Fractal roughness is one of the most important properties of a fractal surface. In this study, it was found that, randomly rough membrane surface was a fractal surface, which could be digitally modeled by a modified two-variable Weierstrass-Mandelbrot (WM) function. Fractal roughness of membrane surfaces has a typical power function relation with the statistical roughness of the modeled surface. Assessment of interfacial interactions showed that an increase in fractal roughness of membrane surfaces will strengthen and prolong the interfacial interactions between membranes and foulants, and under conditions in this study, will significantly increase the adhesion propensity of a foulant particle on membrane surface. This interesting result can be attributed to that increase in fractal roughness simultaneously improves separation distance and interaction surface area for adhesion of a foulant particle. This study gives deep insights into interfacial interactions and membrane fouling in MBRs. Copyright © 2017 Elsevier Ltd. All rights reserved.
Mishin, M V; Zamotin, K Y; Protopopova, V S; Alexandrov, S E
2015-03-21
This paper covers the results from a study of the formation mechanism of fractal clusters from nanoparticles synthesised in atmospheric pressure radio frequency discharge. Two-dimensional structures with random configuration and self-similarity properties are formed by nanoparticles on a solid substrate surface. The typical linear dimensions of such structures are in the micron range. On the basis of the previously demonstrated experimental results, a physico-mathematical model of the nanoparticle self-organisation was developed. The physical model includes the electrical charge effect of the deposit surface, the spatial distribution of the surface electrical potential and the topography rearrangement phenomenon under the arising electrostatic forces. The threshold character of the agglomeration process initiation was found. The dependence of the formed structure topography on the character of the electrical potential change was demonstrated. The requisite conditions for the classical fractal formation were revealed. The results from the computational simulation, which was conducted with the use of fractal analysis, indicate a high level of coincidence with the experimental results.
Crystal, Howard A; Holman, Susan; Lui, Yvonne W; Baird, Alison E; Yu, Hua; Klein, Ronald; Rojas-Soto, Diana Marcella; Gustafson, Deborah R; Stebbins, Glenn T
2016-01-01
The fractal dimension of retinal arteries and veins is a measure of the complexity of the vascular tree. We hypothesized that retinal fractal dimension would be associated with brain volume and white matter integrity in HIV-infected women. Nested case-control within longitudinal cohort study. Women were recruited from the Brooklyn site of the Women's Interagency HIV study (WIHS); 34 HIV-infected and 21 HIV-uninfected women with analyzable MRIs and retinal photographs were included. Fractal dimension was determined using the SIVA software program on skeletonized retinal images. The relationship between predictors (retinal vascular measures) and outcomes (quantitative MRI measures) were analyzed with linear regression models. All models included age, intracranial volume, and both arterial and venous fractal dimension. Some models were adjusted for blood pressure, race/ethnicity, and HIV-infection. The women were 45.6 ± 7.3 years of age. Higher arterial dimension was associated with larger cortical volumes, but higher venous dimension was associated with smaller cortical volumes. In fully adjusted models, venous dimension was significantly associated with fractional anisotropy (standardized β = -0.41, p = 0.009) and total gray matter volume (β = -0.24, p = 0.03), and arterial dimension with mean diffusivity (β = -0.33,.p = 0.04) and fractional anisotropy (β = 0.34, p = 0.03). HIV-infection was not associated with any retinal or MRI measure. Higher venous fractal dimension was associated with smaller cortical volumes and lower fractional anisotropy, whereas higher arterial fractal dimension was associated with the opposite patterns. Longitudinal studies are needed to validate this finding.
Hong, K J; Choi, W K; Cho, J C
2003-01-01
Based on the fractal theory, this paper uses scanning electron microscopy images to investigate the roughness characteristics of nanostructured (Ba Sr)TiO sub 3 thin films by sol-gel methods. The percentage grain area, surface fractal dimensions and 3D image are evaluated using image analysis methods. The thickness of the (Ba Sr)TiO sub 3 thin films was 260-280 nm. The surface fractal dimensions were increased with strontium doping, and grain area, were decreased with it. The fractal dimension and the grain areas of the (Ba sub 0 sub . sub 7 Sr sub 0 sub . sub 3)TiO sub 3 thin films were 1.81 and 81%. Based on the image analysis, the roughness height of 3D images as 256 levels was about 3 nm and its distribution was about 35-40% for the (Ba sub 0 sub . sub 8 Sr sub 0 sub . sub 2)TiO sub 3 and (Ba sub 0 sub . sub 7 Sr sub 0 sub . sub 3)TiO sub 3 thin films. The roughness height of the BST thin films was distributed from 35% to 40% ranging from 3 nm to 4 nm. By increasing the strontium doping, the roughness hei...
Prada, D. A.; Sanabria, M. P.; Torres, A. F.; Álvarez, M. A.; Gómez, J.
2018-04-01
The study of persistence in time series in seismic events in two of the most important nets such as Hindu Kush in Afghanistan and Los Santos Santander in Colombia generate great interest due to its high presence of telluric activity. The data were taken from the global seismological network. Using the Jarque-Bera test the presence of gaussian distribution was analyzed, and because the distribution in the series was asymmetric, without presence of mesocurtisity, the Hurst coefficient was calculated using the rescaled range method, with which it was found the fractal dimension associated to these time series and under what is possible to determine the persistence, antipersistence and volatility in these phenomena.
Betancourt-Mar, J. A.; Llanos-Pérez, J. A.; Cocho, G.; Mansilla, R.; Martin, R. R.; Montero, S.; Nieto-Villar, J. M.
2017-05-01
By the use of thermodynamics formalism of irreversible processes, complex systems theory and systems biology, it is derived a relationship between the production of entropy per unit time, the fractal dimension and the tumor growth rate for human tumors cells. The thermodynamics framework developed demonstrates that, the dissipation function is a Landau potential and also the Lyapunov function of the dynamical behavior of tumor growth, which indicate the directional character, stability and robustness of the phenomenon. The entropy production rate may be used as a quantitative index of the metastatic potential of tumors. The current theoretical framework will hopefully provide a better understanding of cancer and contribute to improvements in cancer treatment.
Živić, I.; Elezović-Hadžić, S.; Milošević, S.
2018-01-01
We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b ≥ 2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1 ,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b = 2 , 3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.
Energy Technology Data Exchange (ETDEWEB)
Palacios Lopez, Arturo
2002-07-01
In this thesis tree patterns of superficial breakdown in polymeric insulator of Silicon Rubber are generated. Experimental arrangement rod-rod was used on the basis of norm ASTM D 2303-85. Pollution levels on the basis of norm IEC 507 were also used. The experimental values of Fractal Dimension for each case of pollution were reported. A self similar method called Box Counting for the fractal dimension calculus and for the self affine methods an R/S and Variogram were used. According to the results, it was concluded that the tree patterns of superficial electric breakdown in Silicon Rubber is self similar and its value does not depend on the degree of pollution, that is equivalent to the concentration of salt for liter of water or to the Equivalent Salt Deposition (ESDD), in the surface of an insulator. [Spanish] En el presente trabajo se inducen descargas electricas superficiales en un aislamiento polimerico de Hule Silicon, el arreglo experimental que se utilice es punta-punta con base en la norma ASTM D 2303-85 y los niveles de contaminacion con base en la norma IEC 507. Se reportan los valores experimentales de la Dimension Fractal para cada caso de contaminacion, se utilice el metodo auto similar de conteo de cuadros, para el calculo de la Dimension Fractal y para metodos auto afines se utilice analisis R/S y variograma. Con los resultados obtenidos se concluye que la trayectoria de la descarga electrica superficial en un polimero de Hule Silicon es auto similar y su valor no depende del grado de contaminacion, el cual es equivalente a la concentracion de gramos de sal por litro de agua o a la densidad de sal depositada (DESD), en la superficie de un aislador.
Studying fractal geometry on submicron length scales by small-angle scattering
International Nuclear Information System (INIS)
Wong, P.; Lin, J.
1988-01-01
Recent studies have shown that internal surfaces of porous geological materials, such as rocks and lignite coals, can be described by fractals down to atomic length scales. In this paper, the basic properties of self-similar and self-affine fractals are reviewed and how fractal dimensions can be measured by small-angle scattering experiments are discussed
Cámara, Joaquín; Gómez-Miguel, Vicente; Martín, Miguel Ángel
2016-03-01
Geologists know that drainage networks can exhibit different drainage patterns depending on the hydrogeological properties of the underlying materials. Geographic Information System (GIS) technologies and the increasing availability and resolution of digital elevation data have greatly facilitated the delineation, quantification, and study of drainage networks. This study investigates the possibility of inferring geological information of the underlying material from fractal and linear parameters describing drainage networks automatically extracted from 5-m-resolution LiDAR digital terrain model (DTM) data. According to the lithological information (scale 1:25,000), the study area is comprised of 30 homogeneous bedrock lithologies, the lithological map units (LMUs). These are mostly igneous and metamorphic rocks, but also include some sedimentary rocks. A statistical classification model of the LMUs by rock type has been proposed based on both the fractal dimension and drainage density of the overlying drainage networks. The classification model has been built using 16 LMUs, and it has correctly classified 13 of the 14 LMUs used for its validation. Results for the study area show that LMUs, with areas ranging from 177.83 ± 0.01 to 3.16 ± 0.01 km2, can be successfully classified by rock type using the fractal dimension and the drainage density of the drainage networks derived from medium resolution LiDAR DTM data with different flow support areas. These results imply that the information included in a 5-m-resolution LiDAR DTM and the appropriate techniques employed to manage it are the only inputs required to identify the underlying geological materials.
He, Qi; Yang, Zhao; Gong, Bin; Wang, Jingjing; Xiao, Kaijun; Yang, Shang-Tian
2017-02-01
This work aimed to establish an effective approach to evaluate the quality of frozen fish, focusing on changes in fish tissue structure and chemical composition during storage. Fresh tilapia samples were treated by coating with tangerine peel (TP) extract and then stored at -4, -8 and -18 °C, respectively, for 40 days. The frozen fish tissues were analyzed for structural and chemical changes. Fractal dimension, which quantifies the porous structure formed in the tissue samples, texture properties including hardness and springiness, and moisture content and water activity all decreased during the storage, while the extents of lipid oxidation, measured as peroxide value and thiobarbituric acid concentration, and protein degradation, monitored with total volatile basic nitrogen and trichloroacetic acid soluble peptides, increased. The change rates of these parameters decreased with decreasing the storage temperature and by applying TP extract. A model was developed for predicting fractal dimension, which indicated the quality of preserved tilapia and thus can be used to predict the shelf life under different storage temperatures. The results demonstrated that TP extract could extend the shelf life of frozen tilapia by 35-45% by inhibiting changes in tissue structure, moisture loss, lipid oxidation and protein degradation during frozen storage.
Fractal dimension study of polaron effects in cylindrical GaAs/Al x Ga1- x As core-shell nanowires
Sun, Hui; Li, Hua; Tian, Qiang
2018-04-01
Polaron effects in cylindrical GaAs/Al x Ga1- x As core-shell nanowires are studied by applying the fractal dimension method. In this paper, the polaron properties of GaAs/Al x Ga1- x As core-shell nanowires with different core radii and aluminum concentrations are discussed. The polaron binding energy, polaron mass shift, and fractal dimension parameter are numerically determined as functions of shell width. The calculation results reveal that the binding energy and mass shift of the polaron first increase and then decrease as the shell width increases. A maximum value appears at a certain shell width for different aluminum concentrations and a given core radius. By using the fractal dimension method, polaron problems in cylindrical GaAs/Al x Ga1- x As core-shell nanowires are solved in a simple manner that avoids complex and lengthy calculations.
A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions
Czech Academy of Sciences Publication Activity Database
Zborovský, Imrich
2018-01-01
Roč. 33, č. 10 (2018), č. článku 1850057. ISSN 0217-751X R&D Projects: GA MŠk(CZ) LG15052 Institutional support: RVO:61389005 Keywords : Hadron interactions * self-similarity * fractality * conservation laws * quanta Subject RIV: BE - Theoretical Physics OBOR OECD: Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect) Impact factor: 1.597, year: 2016
Surface-enhanced Raman imaging of fractal shaped periodic metal nanostructures
DEFF Research Database (Denmark)
Beermann, Jonas; Novikov, Sergey Mikhailovich; Albrektsen, Ole
2009-01-01
Surface-enhanced Raman scattering (SERS) from Rhodamine 6G (R6G) homogenously adsorbed on fractal shaped 170-nm-period square arrays formed by 50-nm-high gold nanoparticles (diameters of 80, 100, or 120 nm are constant within each array), fabricated on a smooth gold film by electron-beam lithogra......Surface-enhanced Raman scattering (SERS) from Rhodamine 6G (R6G) homogenously adsorbed on fractal shaped 170-nm-period square arrays formed by 50-nm-high gold nanoparticles (diameters of 80, 100, or 120 nm are constant within each array), fabricated on a smooth gold film by electron...
Chen, Qi; Ma, Qingkai; Wu, Chaoming; Tan, Fan; Chen, Feng; Wu, Qiuyan; Zhou, Rong; Zhuang, Xiran; Lu, Fan; Qu, Jia; Shen, Meixiao
2017-07-01
To determine the ability of fractal dimension to detect early changes in the retinal microvascular network imaged by optical coherence tomography angiography (OCT-A) in type 2 diabetic patients. Sixty-seven patients with type 2 diabetic mellitus (DM) (48 with no diabetic retinopathy [DR], 19 with minimal DR) and 40 control subjects. Macular OCT-A images of the superficial and deep retinal capillary layers in a 2.5-mm diameter concentric annular zone (excluding the foveal avascular zone) were subdivided into six annular rings and four quadrants. A custom automated algorithm was developed to quantify the complexity and density of the two retinal capillary layers by fractal analysis. Compared to controls, the fractal dimensional parameter (Dbox) of the two retinal capillary layers in most regions was significantly lower in diabetic patients with minimal DR (P 0.05). Based on the receiver operating characteristic curve analysis, the Dbox values for the deep retinal capillary layer had the highest index to discriminate diabetic patients with and without minimal DR from controls. Fractal dimension based on OCT-A has the potential to quantitatively characterize retinal microvascular changes in the early stage of DM. Changes in the fractal dimension in the deep retinal capillary layer could be an early indicator of microvasculature changes associated with retinopathy in type 2 diabetic patients.
Directory of Open Access Journals (Sweden)
José G. Carriazo
2010-01-01
Full Text Available El presente trabajo muestra la modificación de una zeolita-Y y una arcilla pilarizada (tipo saponita mediante impregnación con diferentes cargas de Pt (catalizadores a base de Pt. Los sólidos se caracterizaron en cuanto a su composición química y su textura. La caracterización textural revela cambios importantes en los sólidos, mostrando que se genera microporosidad en la serie de catalizadores zeolíticos y se bloquean las estructuras microporosas en la serie de catalizadores obtenidos a partir de la arcilla pilarizada. La determinación de la dimensión fractal (mediante el método de Avnir-Jaroniec indica que la modificación con Pt afecta significativamente las características topográficas de la superficie de la arcilla pilarizada como consecuencia de la posible formación de agregados de Pt.This research shows the modification of a zeolite Y and a pillared clay (saponite by impregnation with different platinum quantities (synthesis of Pt catalysts. The solids were characterized about the chemical composition and texture. The textural characterization reveals important changes in the solids, showing that in the zeolitic catalysts microporosity is formed, whereas in the pillared clay the microporous structures are partially blocked. Fractal dimension (by Avnir-Jaroniec method indicates that the topographic features of the pillared clay surface are significantly affected due to the modification with platinum, probably as a consequence of platinum clusters formation.
Taylor, Adele M; MacGillivray, Thomas J; Henderson, Ross D; Ilzina, Lasma; Dhillon, Baljean; Starr, John M; Deary, Ian J
2015-01-01
Cerebral microvascular disease is associated with dementia. Differences in the topography of the retinal vascular network may be a marker for cerebrovascular disease. The association between cerebral microvascular state and non-pathological cognitive ageing is less clear, particularly because studies are rarely able to adjust for pre-morbid cognitive ability level. We measured retinal vascular fractal dimension (Df) as a potential marker of cerebral microvascular disease. We examined the extent to which it contributes to differences in non-pathological cognitive ability in old age, after adjusting for childhood mental ability. Participants from the Lothian Birth Cohort 1936 Study (LBC1936) had cognitive ability assessments and retinal photographs taken of both eyes aged around 73 years (n = 648). IQ scores were available from childhood. Retinal vascular Df was calculated with monofractal and multifractal analysis, performed on custom-written software. Multiple regression models were applied to determine associations between retinal vascular Df and general cognitive ability (g), processing speed, and memory. Only three out of 24 comparisons (two eyes × four Df parameters × three cognitive measures) were found to be significant. This is little more than would be expected by chance. No single association was verified by an equivalent association in the contralateral eye. The results show little evidence that fractal measures of retinal vascular differences are associated with non-pathological cognitive ageing.
DEFF Research Database (Denmark)
Pedersen, Knud B; Broe, Rebecca; Grauslund, Jakob
2016-01-01
and FD calculated with the box-counting method using SIVA-Fractal semiautomatic software. The modified Early Treatment Diabetic Retinopathy Study (ETDRS) scale was used to grade diabetic retinopathy (DR). Pitman's test of difference in variance was used to calculated inter-eye agreement in FD according......PURPOSE: To investigate inter-eye agreement in retinal vascular fractal dimension (FD) in patients with type 1 diabetes. METHODS: In a cross-sectional study, both eyes were exained in 178 patients with type 1 diabetes. All vessels in a zone 0.5-2.0 disc diameters from the optic disc were traced...... to level of DR. RESULTS: Mean age and duration of diabetes was 37.0 years and 29.5 years, respectively, and 49.4% of participants were male. Mean FD of right and left eyes was 1.4540 and 1.4472, respectively. FD did not differ between eyes in patients with no or non-proliferative DR (NPDR) in both eyes...
Roy, Pradip Kumar; Huang, Yi-Fan; Chattopadhyay, Surojit
2014-01-01
A simple way of detecting melamine in raw milk is demonstrated via surface-enhanced Raman spectroscopy (SERS) using fractals of bare and nonfunctionalized ~30 nm gold nanoparticles (AuNP) distributed on a solid support. The technique demonstrates the formation of AuNP fractals, from a random distribution, upon exposure to melamine, that enhance the Raman scattering cross-section to enable detection by SERS. The agglomeration, which is pronounced at higher melamine concentrations, is demonstrated directly through imaging, and the red-shift of the plasmon absorption peak of the AuNP fractal away from 530 nm by finite difference time domain (FDTD) calculations. The agglomeration results in a strong plasmon field, shown by FDTD, over the interparticle sites that enhances the Raman scattering cross-section of melamine and ensures unambiguous detection. Limit of detection of 100 ppb could be achieved reproducibly.
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
Raupov, Dmitry S.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Kornilin, Dmitry V.; Zakharov, Valery P.; Khramov, Alexander G.
2016-04-01
Optical coherence tomography (OCT) is usually employed for the measurement of tumor topology, which reflects structural changes of a tissue. We investigated the possibility of OCT in detecting changes using a computer texture analysis method based on Haralick texture features, fractal dimension and the complex directional field method from different tissues. These features were used to identify special spatial characteristics, which differ healthy tissue from various skin cancers in cross-section OCT images (B-scans). Speckle reduction is an important pre-processing stage for OCT image processing. In this paper, an interval type-II fuzzy anisotropic diffusion algorithm for speckle noise reduction in OCT images was used. The Haralick texture feature set includes contrast, correlation, energy, and homogeneity evaluated in different directions. A box-counting method is applied to compute fractal dimension of investigated tissues. Additionally, we used the complex directional field calculated by the local gradient methodology to increase of the assessment quality of the diagnosis method. The complex directional field (as well as the "classical" directional field) can help describe an image as set of directions. Considering to a fact that malignant tissue grows anisotropically, some principal grooves may be observed on dermoscopic images, which mean possible existence of principal directions on OCT images. Our results suggest that described texture features may provide useful information to differentiate pathological from healthy patients. The problem of recognition melanoma from nevi is decided in this work due to the big quantity of experimental data (143 OCT-images include tumors as Basal Cell Carcinoma (BCC), Malignant Melanoma (MM) and Nevi). We have sensitivity about 90% and specificity about 85%. Further research is warranted to determine how this approach may be used to select the regions of interest automatically.
Energy Technology Data Exchange (ETDEWEB)
Yadav, R. P.; Mittal, A. K. [Department of Physics, University of Allahabad, Allahabad 211002 (India); Kumar, Manvendra, E-mail: kmanav@gmail.com; Pandey, A. C. [Nanotechnology Application Centre, University of Allahabad, Allahabad 211002 (India)
2015-08-15
Fractal and multifractal characteristics of self-affine surfaces of BaF{sub 2} thin films, deposited on crystalline Si 〈1 1 1〉 substrate at room temperature, were studied. Self-affine surfaces were prepared by irradiation of 120 MeV Ag{sup 9+} ions which modified the surface morphology at nanometer scale. The surface morphology of virgin thin film and those irradiated with different ion fluences are characterized by atomic force microscopy technique. The surface roughness (interface width) shows monotonic decrease with ion fluences, while the other parameters, such as lateral correlation length, roughness exponent, and fractal dimension, did not show either monotonic decrease or increase in nature. The self-affine nature of the films is further confirmed by autocorrelation function. The power spectral density of thin films surfaces exhibits inverse power law variation with spatial frequency, suggesting the existence of fractal component in surface morphology. The multifractal detrended fluctuation analysis based on the partition function approach is also performed on virgin and irradiated thin films. It is found that the partition function exhibits the power law behavior with the segment size. Moreover, it is also seen that the scaling exponents vary nonlinearly with the moment, thereby exhibiting the multifractal nature.
A Fractal Model for the Maximum Droplet Diameter in Gas-Liquid Mist Flow
Directory of Open Access Journals (Sweden)
Xiao-Hua Tan
2013-01-01
Full Text Available Distribution characteristics of liquid droplet size are described using the fractal theory for liquid droplet size distribution in gas-liquid mist flow. Thereby, the fractal expression of the maximum droplet diameter is derived. The fractal model for maximum droplet diameter is obtained based on the internal relationship between maximum droplet diameter and the droplet fractal dimension, which is obtained by analyzing the balance between total droplet surface energy and total gas turbulent kinetic energy. Fractal model predictions of maximum droplet diameter agree with the experimental data. Maximum droplet diameter and droplet fractal dimension are both found to be related to the superficial velocity of gas and liquid. Maximum droplet diameter decreases with an increase in gas superficial velocity but increases with an increase in liquid superficial velocity. Droplet fractal dimension increases with an increase in gas superficial velocity but decreases with an increase in liquid superficial velocity. These are all consistent with the physical facts.
Butala, Harshala D; Sadana, Ajit
2004-03-15
A fractal analysis is used to analyze the influence of: (a) electrostatic interactions on binding and dissociation rate coefficients for antibodies HH8, HH10, and HH26 in solution to hen egg-white lysozyme (HEL) immobilized on a sensor chip surface [Biophys. J. 83 (2002) 2946]; and (b) the binding and dissociation of recombinant Fab in solution to random NHS-coupled Cys-HEL and oriented thiol-coupled Cys-HEL immobilized on a sensor chip surface [Methods 20 (2000) 310]. Single- and dual-fractal models were employed to fit the data. Values of the binding and the dissociation rate coefficient(s) and the fractal dimensions were obtained from a regression analysis provided by Corel Quattro Pro 8.0 (Corel Corporation Limited, Ottawa, Canada. 1997). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. It is of interest to compare the results obtained by the fractal analysis with that of the original analysis [Biophys. J. 83 (2002) 2946]. For example, as one goes from the binding of 21 nM HH10/HEL to the binding of 640 nM HH10/HEL(K97A), Sinha et al. [Biophys. J. 83 (2002) 29461 indicate that the enhancement of diffusional encounter rates may be due to 'electrostatic steering' (a long-range interaction). Our analysis indicates that there is an increase in the value of the fractal dimension, Df1 by a factor of 1.12 from a value of 2.133-2.385. This increase in the degree of heterogeneity on the surface leads to an increase in the binding rate coefficient, k1 by a factor of 1.59 from 12.92 to 20.57. The fractal analysis of binding and dissociation of recombinant Fab in solution to random NHS-coupled Cys-HEL and oriented thiol-coupled Cys-HEL immobilized on a sensor chip [Methods 20 (2000) 310] surface are consistent with the degree of heterogeneity present on the sensor chip surface for the random and the oriented case. As expected, the random case will exhibit a higher degree of heterogeneity than the oriented case
Pedersen, Knud B; Broe, Rebecca; Grauslund, Jakob
2016-01-01
To investigate inter-eye agreement in retinal vascular fractal dimension (FD) in patients with type 1 diabetes. In a cross-sectional study, both eyes were exained in 178 patients with type 1 diabetes. All vessels in a zone 0.5-2.0 disc diameters from the optic disc were traced and FD calculated with the box-counting method using SIVA-Fractal semiautomatic software. The modified Early Treatment Diabetic Retinopathy Study (ETDRS) scale was used to grade diabetic retinopathy (DR). Pitman's test of difference in variance was used to calculated inter-eye agreement in FD according to level of DR. Mean age and duration of diabetes was 37.0 years and 29.5 years, respectively, and 49.4% of participants were male. Mean FD of right and left eyes was 1.4540 and 1.4472, respectively. FD did not differ between eyes in patients with no or non-proliferative DR (NPDR) in both eyes. This was true for patients with the same level of DR in both eyes (n = 74, p = 0.73), as well as for patients in which the ETDRS level of DR between the eyes differed by 1 (n = 43, p = 0.99) or more (n = 9, p = 0.53). In patients treated for proliferative DR in one eye, FD was significantly lower in this eye compared to the other (n = 10, p = 0.03). FD did not differ significantly between the two eyes of patients with no DR or NPDR, despite differences in severity of DR.
Directory of Open Access Journals (Sweden)
Mitić V.V.
2013-01-01
Full Text Available In this study, in order to establish grain shapes of sintered ceramics, new approach on correlation between microstructure and doped BaTiO3 -ceramics properties based, on Voronoi model and mathematical statistics calculations on fractal geometry, has been developed. BaTiO3-ceramics doped with Yb2O3 (from 0.1 to 1.0wt% of Yb were prepared by using conventional solid state procedure and were sintered from 1320°C to 1380°C for four hours. The microstructure of sintered specimens was investigated by Scanning electron microscope JEOL-SEM-5300. For better and deeper characterization and understanding of the ceramics material microstructure, the methods which include the fractal nature structure, and also Voronoi model and mathematical statistics calculations, are applied. In our research the Voronoi is one specific interface between fractal structure nature and different stochastically contact surfaces, defined by statistical mathematical methods. Also, the Voronoi model practically provided possibility to control the ceramics microstructure fractal nature. Mathematical statistic methods enabled establishing the real model for the prognosis based on correlation: synthesis-structures-properties. [Projekat Ministarstva nauke Republike Srbije, br. 172057 i br. III44006
Fractal radar scattering from soil
Oleschko, Klaudia; Korvin, Gabor; Figueroa, Benjamin; Vuelvas, Marco Antonio; Balankin, Alexander S.; Flores, Lourdes; Carreón, Dora
2003-04-01
A general technique is developed to retrieve the fractal dimension of self-similar soils through microwave (radar) scattering. The technique is based on a mathematical model relating the fractal dimensions of the georadargram to that of the scattering structure. Clear and different fractal signatures have been observed over four geosystems (soils and sediments) compared in this work.
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.
Directory of Open Access Journals (Sweden)
Mathivanan Kavitha
2017-01-01
Full Text Available Objectives: To assess the alveolar bone density by fractal dimension (FD analysis in radiovisiograph of postmenopausal women of mandibular posterior region and to correlate FD values with t-scores of quantitative ultrasound of the calcaneus bone. Materials and Methods: This study, approved by the institutional review board, included 40 participants, aged 45–60 years divided into two groups. Twenty postmenopausal women with osteoporosis comprised group 1, and 20 postmenopausal women without osteoporosis comprised group 2 based on bone mineral density assessment of ultrasound of the calcaneus bone. Digital dental radiograph of mandibular first molar were obtained and used for assessing alveolar bone density by FD analysis and were correlated with t-scores of ultrasound of calcaneus bone. Results: The mean FD values were evaluated using SPSS 14 version software, and were found to be 1.738 and 1.867 for group 1 and group 2, respectively, which was statistically significant (P 0.05. Conclusion: FD analysis using direct digital periapical radiographs is a novel method, which can be used for early diagnosis of osteoporosis in the alveolar bone.
Han, H. H.; Wang, Y. L.; Ren, G. L.; LI, J. Q.; Gao, T.; Yang, M.; Yang, J. L.
2016-11-01
Remote sensing plays an important role in mineral exploration of “One Belt One Road” plan. One of its applications is extracting and locating hydrothermal alteration zones that are related to mines. At present, the extracting method for alteration anomalies from principal component image mainly relies on the data's normal distribution, without considering the nonlinear characteristics of geological anomaly. In this study, a Fractal Dimension Change Point Model (FDCPM), calculated by the self-similarity and mutability of alteration anomalies, is employed to quantitatively acquire the critical threshold of alteration anomalies. The realization theory and access mechanism of the model are elaborated by an experiment with ASTER data in Beishan mineralization belt, also the results are compared with traditional method (De-Interfered Anomalous Principal Component Thresholding Technique, DIAPCTT). The results show that the findings produced by FDCPM are agree with well with a mounting body of evidence from different perspectives, with the extracting accuracy over 80%, indicating that FDCPM is an effective extracting method for remote sensing alteration anomalies, and could be used as an useful tool for mineral exploration in similar areas in Silk Road Economic Belt.
Small-angle and surface scattering from porous and fractal materials.
Energy Technology Data Exchange (ETDEWEB)
Sinha, S. K.
1998-09-18
We review the basic theoretical methods used to treat small-angle scattering from porous materials, treated as general two-phase systems, and also the basic experimental techniques for carrying out such experiments. We discuss the special forms of the scattering when the materials exhibit mass or surface fractal behavior, and review the results of recent experiments on several types of porous media and also SANS experiments probing the phase behavior of binary fluid mixtures or polymer solutions confined in porous materials. Finally, we discuss the analogous technique of off-specular scattering from surfaces and interfaces which is used to study surface roughness of various kinds.
Modelo fractal de substâncias húmicas Fractal model of humic substances
Directory of Open Access Journals (Sweden)
Alessandro Costa da Silva
2001-10-01
Full Text Available A teoria fractal, por meio da determinação da dimensão fractal (D, tem sido considerada como uma alternativa para explicar a conforma��ão de agregados moleculares. Sua utilização no estudo de substâncias húmicas (SH reside na tentativa de descrever (representar a estrutura ramificada ou a superfície rugosa e distorcida destas substâncias. A presença de um modelo fractal por sistemas naturais implica que este pode ser decomposto em partes, em que cada uma, subseqüentemente, é cópia do todo. Do ponto de vista experimental, a dimensão fractal de sistemas húmicos pode ser determinada a partir de técnicas como turbidimetria, raios x, espalhamento de neutrons, dentre outras. Este trabalho pretende facilitar o entendimento sobre a aplicação de fractais ao estudo conformacional de SH, introduzindo conceitos e informações sobre o fundamento dos modelos fractais, bem como sobre o uso da técnica turbidimétrica na determinação do valor D.Fractal theoria application by determination of fractal dimension has been considered an alternative tool to explain the conformation of molecular aggregates. Its utilization in the study of humic substances (HS aims the attempt to describe the limbed structure or the rugous and distorced surface of these substances. The presence of fractal models indicates that the system may be decomposed in parts, each part being a copy of the whole. In the experimental point of view the fractals models of natural systems may be measured through techniques as turbidimetry, x- ray and neutrons scattering. This paper seeks to facilitate the understanding on the application of the fractals in the conformational study of HS, supply information about fractal models foundation and use of the turbidimetry in the determination of fractal dimension.
Synthesis of gold nanostars with fractal structure: application in surface-enhanced Raman scattering
Zhu, Jian; Liu, Mei-Jin; Li, Jian-Jun; Zhao, Jun-Wu
2017-11-01
Multi-branched gold nanostars with fractal feature were synthesized using the Triton X-100 participant seed-growth method. By increasing the amount of ascorbic acid, the branch length of gold nanostars could be greatly increased. It has been interesting to find that the secondary growth of new branches takes place from the elementary structure when the aspect ratio of the branches is greater than 8.0 and the corresponding plasmon absorption wavelength is greater than 900 nm. Raman activity of the gold nanostar films has been investigated by using the 4-mercaptobenzoic acid (4-MBA) as Raman active probe. Experimental results show that the surface-enhanced Raman scattering (SERS) ability of the gold nanostars could be efficiently improved when the fractal structure appears. The physical mechanism has been attributed to the intense increased secondary branch number and the increased "hot spots". These unique multi-branched gold nanostars with fractal feature and great SERS activity should have great potential in sensing applications.
Study of the grazing-incidence X-ray scattering of strongly disturbed fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Roshchin, B. S., E-mail: ross@crys.ras.ru; Chukhovsky, F. N.; Pavlyuk, M. D.; Opolchentsev, A. M.; Asadchikov, V. E. [Russian Academy of Sciences, Shubnikov Institute of Crystallography, Federal Research Centre “Crystallography and Photonics” (Russian Federation)
2017-03-15
The applicability of different approaches to the description of hard X-ray scattering from rough surfaces is generally limited by a maximum surface roughness height of no more than 1 nm. Meanwhile, this value is several times larger for the surfaces of different materials subjected to treatment, especially in the initial treatment stages. To control the roughness parameters in all stages of surface treatment, a new approach has been developed, which is based on a series expansion of wavefield over the plane eigenstate-function waves describing the small-angle scattering of incident X-rays in terms of plane q-waves propagating through the interface between two media with a random function of relief heights. To determine the amplitudes of reflected and transmitted plane q-waves, a system of two linked integral equations was derived. The solutions to these equations correspond (in zero order) to the well-known Fresnel expressions for a smooth plane interface. Based on these solutions, a statistical fractal model of an isotropic rough interface is built in terms of root-mean-square roughness σ, two-point correlation length l, and fractal surface index h. The model is used to interpret X-ray scattering data for polished surfaces of single-crystal cadmium telluride samples.
Önem, Erinç; Baksı, B Güniz; Sogur, Elif
2012-01-01
To evaluate the combination of fractal dimension (FD), lacunarity, and Feret diameter (FeD) to quantitatively characterize structural changes of mandibular alveolar bone around dental implants during initial healing. Three standard-sized regions of interest (ROIs) (mesial and distal crest and apical area) around implants and three ROIs of the same size in the alveolar bone on the contralateral side were analyzed on digital panoramic images. FD was calculated using the box-counting method, and lacunarity was calculated using the FracLac plugin of Image J software. FeD was measured in the same ROIs. Comparisons of the groups were done with the Dunnett test. Forty-two implants in the posterior mandibles of 21 patients were used for FD measurements. A total of 189 ROIs was segmented into binary images. Mean FD values for mesial, distal, and apical ROIs around implants were 1.26, 1.36, and 1.4, respectively. The mean FD of alveolar bone around premolars/molars was 1.39 for all ROIs. The mean FeD for mesial, distal, and apical ROIs around implants was 7.63, 7.86, and 8.02, respectively, whereas it ranged between 7.88 and 8.13 for premolar teeth. Mean lacunarity values for mesial, distal, and apical ROIs around implants were 0.53, 0.51, and 0.48, respectively. Lacunarity values for ROIs around premolars ranged between 0.45 and 0.50. No significant differences were observed in FD, FeD, or lacunarity measurements between ROIs around implants and around teeth. The satisfactory healing of bone following implant placement may be monitored by calculating FD, lacunarity, and FeD using digital panoramic images. Although preliminary, these values may alert the practitioner to any implants with loss of stability.
Cellulose with a High Fractal Dimension Is Easily Hydrolysable under Acid Catalysis
Directory of Open Access Journals (Sweden)
Mariana Díaz
2017-05-01
Full Text Available The adsorption of three diverse amino acids couples onto the surface of microcrystalline cellulose was studied. Characterisation of modified celluloses included changes in the polarity and in roughness. The amino acids partially break down the hydrogen bonding network of the cellulose structure, leading to more reactive cellulose residues that were easily hydrolysed to glucose in the presence of hydrochloric acid or tungstophosphoric acid catalysts. The conversion of cellulose and selectivity for glucose was highly dependent on the self-assembled amino acids adsorbed onto the cellulose and the catalyst.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325
Bilipschitz embedding of homogeneous fractals
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.
Amato P; Cerofolini GF; Narducci D; Romano E
2008-01-01
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.
Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind.
Nogueira, Miguel
2017-01-01
The equivalency between the power law behavior of Multiscale Entropy (MSE) and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing) scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the underlying
Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind.
Directory of Open Access Journals (Sweden)
Miguel Nogueira
Full Text Available The equivalency between the power law behavior of Multiscale Entropy (MSE and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the
Karemore, Gopal; Nielsen, Mads
2009-02-01
Structural texture measures are used to address the aspect of breast cancer risk assessment in screening mammograms. The current study investigates whether texture properties characterized by local Fractal Dimension (FD) and Lacunarity contribute to asses breast cancer risk. FD represents the complexity while the Lacunarity characterize the gappiness of a fractal. Our cross-sectional case-control study includes mammograms of 50 patients diagnosed with breast cancer in the subsequent 2-4 years and 50 matched controls. The longitudinal double blind placebo controlled HRT study includes 39 placebo and 36 HRT treated volunteers for two years. ROIs with same dimension (250*150 pixels) were created behind the nipple region on these radiographs. Box counting method was used to calculate the fractal dimension (FD) and the Lacunarity. Paired t-test and Pearson correlation coefficient were calculated. It was found that there were no differences between cancer and control group for FD (P=0.8) and Lacunarity (P=0.8) in crosssectional study whereas earlier published heterogeneity examination of radiographs (BC-HER) breast cancer risk score separated groups (p=0.002). In the longitudinal study, FD decreased significantly (PBIRADS (-0.34, P<0.001) and Percentage Density (-0.41, P<0.001). FD is invariant to the mammographic texture change from control to cancer population but marginally varying in HRT treated population. This study yields no evidence that lacunarity or FD are suitable surrogate markers of mammographic heterogeneity as they neither pick up breast cancer risk, nor show good sensitivity to HRT.
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.
Insights on the fractal-fracture behaviour relationship
Directory of Open Access Journals (Sweden)
Rodrigues José de Anchieta
1998-01-01
Full Text Available The fractals theory has been increasingly applied in the field of materials science and engineering. Models of fractal lines and surfaces have been generated to describe the microstructural features of materials. Special interest is placed upon a description of the fracture surface based on a fractal geometry in order to understand the crack path in materials. Several papers have demonstrated the relationship between the fractal dimension of a fracture surface and the values of roughness and fracture toughness. In this work an extension of the theory of fractals for ceramic materials is proposed, to which the crack deflection toughening mechanism is thought to be related. In order to accomplish this objective, a review describing the concept of fractals and its relationship with the fracture toughness is presented. In the following part, a correlation between fractal dimension, total energy of fracture and the average resistance to crack propagation is proposed; all these parameters being dependent on the history and on the complexity of crack propagation path.
Anca Larisa Sandu
2008-01-01
The changes that appear in the human brain asa result of aging or diseases can be described using theconcept of fractality. The steps required to pass from rawdata to interpretable results are briefly presented. Themethod has been applied to patients with schizophrenia,children with dyslexia and to compare children with adults.
Directory of Open Access Journals (Sweden)
Anca Larisa Sandu
2008-01-01
Full Text Available The changes that appear in the human brain asa result of aging or diseases can be described using theconcept of fractality. The steps required to pass from rawdata to interpretable results are briefly presented. Themethod has been applied to patients with schizophrenia,children with dyslexia and to compare children with adults.
Fractal analysis of the fractal ultra-wideband signals
International Nuclear Information System (INIS)
Chernogor, L.F.; Lazorenko, O.V.; Onishchenko, A.A.
2015-01-01
The results of fractal analysis of the fractal ultra-wideband (FUWB) signals were proposed. With usage of the continuous wavelet transform the time-frequency structure of that signals was investigated. Calculating the box and the regularization dimensions for each model signal with various its parameters values, three different estimators were applied. The optimal estimations of the fractal dimension value for each FUWB signal model were defined
Directory of Open Access Journals (Sweden)
Kyril Tintarev
2007-05-01
Full Text Available The paper studies energy functionals on quasimetric spaces, defined by quadratic measure-valued Lagrangeans. This general model of medium, known as metric fractals, includes nested fractals and sub-Riemannian manifolds. In particular, the quadratic form of the Lagrangean satisfies Sobolev inequalities with the critical exponent determined by the (quasimetric homogeneous dimension, which is also involved in the asymptotic distribution of the form's eigenvalues. This paper verifies that the axioms of the metric fractal are preserved by space products, leading thus to examples of non-differentiable media of arbitrary intrinsic dimension.
Design and rapid prototyping of DLC coated fractal surfaces for tissue engineering applications
Energy Technology Data Exchange (ETDEWEB)
Diaz-Lantada, A; Mosquera, A; Endrino, J L; Lafont, P, E-mail: adiaz@etsii.upm.es
2010-11-01
Several medical devices (both implantable and for in vitro diagnosis) benefit greatly from having microtextured surfaces that help to improve and promote phenomena such as osteointegracion and cell / tissue growth on the surface of a device. Normally, the use of abrasives or chemical attacks are employed for obtaining such surface microtextures, however, it is sometimes difficult to precisely control the final surface characteristics (porosity, roughness, among others) and consequently the related biological aspects. In this work, we propose an alternative process based on the use of fractal surface models for designing special surfaces, which helps controlling the desired contact properties (from the design stage) in multiple applications within biomedical engineering, especially regarding tissue engineering tasks. Manufacturing can be directly accomplished by means of rapid prototyping technologies. This method supposes a focus change from a conventional 'top-down' to a more versatile 'bottom-up' approach. Finally, in order to improve the possible biological response, the surfaces of the designed devices were coated with hydrogen-free amorphous carbon (a-C) thin films, known to be highly biocompatible materials. The films were deposited at room temperature using the vacuum filter cathodic arc technique. Our first prototypes have helped verify the viability of the approach and to validate the design, manufacturing and coating processes.
Fractal analysis of time varying data
Vo-Dinh, Tuan; Sadana, Ajit
2002-01-01
Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.
Fractal Geometry of Architecture
Lorenz, Wolfgang E.
In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.
Prediction on Droplet Sauter Mean Diameter in Gas-Liquid Mist Flow Based on Droplet Fractal Theory
Directory of Open Access Journals (Sweden)
Jian-Yi Liu
2015-01-01
Full Text Available We present a fractal model for droplet Sauter mean diameter in gas-liquid mist flow, based on the droplet fractal theory and the balance relationship between total droplet surface energy and total gas turbulent kinetic energy. The present model is expressed as functions of the droplet fractal dimension, gas superficial velocity, liquid superficial velocity, and other fluid characteristics. Agreement between the present model predictions and experimental measurements is obtained. Results verify the reliability of the present model.
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
theorist in analyzing such relations. I find empirical illustration in the case of the development of electronic patient records in Danish health care. The role of the social theorist is explored through a comparison of the political and normative stance enabled, respectively, by a critical social theory......The relationship between the supposedly small-the micro-and the supposedly large-the macro-has been a long-standing concern in social theory. However, although many attempts have been made to link these two seemingly disjoint dimensions, in the present paper I argue against such an endeavour...... and a fractal social theory....
International Nuclear Information System (INIS)
Fong, R.W.L.; McRae, G.A.; Coleman, C.E.; Nitheanandan, T.; Sanderson, D.B.
1999-10-01
In CANDU fuel channels, Zircaloy calandria tubes isolate the hot pressure tubes from the cool heavy water moderator. The heavy-water moderator provides a backup heat sink during some postulated loss-of-coolant accidents. The decay heat from the fuel is transferred to the moderator to ensure fuel channel integrity during emergencies. Moderator temperature requirements are specified to ensure that the transfer of decay heat does not exceed the critical heat flux (CHF) on the outside surface of the calandria tube. An enhanced CHF provides increases in safety margin. Pool boiling experiments indicate the CHF is enhanced with glass-peening of the outside surface of the calandria tubes. The objective of this study was to evaluate the surface characteristics of glass-peened tubes and relate these characteristics to CHF. The micro-topologies of the tube surfaces were analysed using stereo-pair micrographs obtained from scanning electron microscopy (SEM) and photogrammetry techniques. A linear relationship correlated the CHF as a function of the 'fractal' surface roughness of the tubes. (author)
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
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.
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
Fractal Characteristics of Rock Fracture Surface under Triaxial Compression after High Temperature
Directory of Open Access Journals (Sweden)
X. L. Xu
2016-01-01
Full Text Available Scanning Electron Microscopy (SEM test on 30 pieces of fractured granite has been researched by using S250MK III SEM under triaxial compression of different temperature (25~1000°C and confining pressure (0~40 MPa. Research results show that (1 the change of fractal dimension (FD of rock fracture with temperature is closely related to confining pressure, which can be divided into two categories. In the first category, when confining pressure is in 0~30 MPa, FD fits cubic polynomial fitting curve with temperature, reaching the maximum at 600°C. In the second category, when confining pressure is in 30~40 MPa, FD has volatility with temperature. (2 The FD of rock fracture varies with confining pressure and is also closely related to the temperature, which can be divided into three categories. In the first category, FD has volatility with confining pressure at 25°C, 400°C, and 800°C. In the second category, it increases exponentially at 200°C and 1000°C. In the third category, it decreases exponentially at 600°C. (3 It is found that 600°C is the critical temperature and 30 MPa is the critical confining pressure of granite. The rock transfers from brittle to plastic phase transition when temperature exceeds 600°C and confining pressure exceeds 30 MPa.
Fractal Analysis of Mobile Social Networks
International Nuclear Information System (INIS)
Zheng Wei; Pan Qian; Sun Chen; Deng Yu-Fan; Zhao Xiao-Kang; Kang Zhao
2016-01-01
Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks (MSNs) are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs. (paper)
Rheological and fractal hydrodynamics of aerobic granules.
Tijani, H I; Abdullah, N; Yuzir, A; Ujang, Zaini
2015-06-01
The structural and hydrodynamic features for granules were characterized using settling experiments, predefined mathematical simulations and ImageJ-particle analyses. This study describes the rheological characterization of these biologically immobilized aggregates under non-Newtonian flows. The second order dimensional analysis defined as D2=1.795 for native clusters and D2=1.099 for dewatered clusters and a characteristic three-dimensional fractal dimension of 2.46 depicts that these relatively porous and differentially permeable fractals had a structural configuration in close proximity with that described for a compact sphere formed via cluster-cluster aggregation. The three-dimensional fractal dimension calculated via settling-fractal correlation, U∝l(D) to characterize immobilized granules validates the quantitative measurements used for describing its structural integrity and aggregate complexity. These results suggest that scaling relationships based on fractal geometry are vital for quantifying the effects of different laminar conditions on the aggregates' morphology and characteristics such as density, porosity, and projected surface area. Copyright © 2015 Elsevier Ltd. All rights reserved.
Theoretical aspects of the Semkow fractal model in the radon emanation in solids
International Nuclear Information System (INIS)
Cruz G, H.S.
1997-01-01
The basic elements of the Fractals theory are developed. The physical basis of radon emission in solids are described briefly. It is obtained that the emanation power E R of mineral grains is scaled as r 0 D-3 (r 0 : grain radius). From a logarithmic graph E R versus grain size is deduced the fractal dimension of the emanation surface. The experimental data of different materials give an interval in the fractal dimension D between 2.1 and 2.8 (Author)
Fractal Electromagnetic Showers
Anchordoqui, L. A.; Kirasirova, M.; McCauley, T. P.; Paul, T.; Reucroft, S.; Swain, J. D.
2000-01-01
We study the self-similar structure of electromagnetic showers and introduce the notion of the fractal dimension of a shower. Studies underway of showers in various materials and at various energies are presented, and the range over which the fractal scaling behaviour is observed is discussed. Applications to fast shower simulations and identification, particularly in the context of extensive air showers, are also discussed.
International Nuclear Information System (INIS)
Fan Yue-Nong; Cheng Yong-Zhi; Nie Yan; Wang Xian; Gong Rong-Zhou
2013-01-01
We propose an ultrathin wide-band metamaterial absorber (MA) based on a Minkowski (MIK) fractal frequency selective surface and resistive film. This absorber consists of a periodic arrangement of dielectric substrates sandwiched with an MIK fractal loop structure electric resonator and a resistive film. The finite element method is used to simulate and analyze the absorption of the MA. Compared with the MA-backed copper film, the designed MA-backed resistive film exhibits an absorption of 90% at a frequency region of 2 GHz–20 GHz. The power loss density distribution of the MA is further illustrated to explain the mechanism of the proposed MA. Simulated absorptions at different incidence cases indicate that this absorber is polarization-insensitive and wide-angled. Finally, further simulated results indicate that the surface resistance of the resistive film and the dielectric constant of the substrate can affect the absorbing property of the MA. This absorber may be used in many military fields
Encounters with chaos and fractals
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.
Energy Technology Data Exchange (ETDEWEB)
Bramowicz, Miroslaw [University of Warmia and Mazury in Olsztyn, Faculty of Technical Sciences, Oczapowskiego 11, 10-719 Olsztyn (Poland); Braic, Laurentiu [National Institute for Optoelectronics, 409 Atomistilor, 077125, Magurele (Romania); Azem, Funda Ak [Dokuz Eylul University, Engineering Faculty, Metallurgical and Materials Engineering Department, Tinaztepe Campus, 35397, Izmir (Turkey); Kulesza, Slawomir [University of Warmia and Mazury in Olsztyn, Faculty of Mathematics and Computer Science, Sloneczna 54, 10-710 Olsztyn (Poland); Birlik, Isil [Dokuz Eylul University, Engineering Faculty, Metallurgical and Materials Engineering Department, Tinaztepe Campus, 35397, Izmir (Turkey); Vladescu, Alina, E-mail: alinava@inoe.ro [National Institute for Optoelectronics, 409 Atomistilor, 077125, Magurele (Romania)
2016-08-30
Highlights: • Hydroxyapatite were prepared at temperatures in the range from 400 to 800 °C. • The coatings prepared at 800 °C is closer to the stoichiometric hydroxyapatite. • Hardness and elastic modulus decreased with increasing deposition temperature. • The surface morphology strongly depends on the deposition temperature. • Mesokurtic height distribution pulled towards larger heights were formed at high temperature. - Abstract: This aim of this work is to establish a relationship between the surface morphology and mechanical properties of hydroxyapatite coatings prepared using RF magnetron sputtering at temperatures in the range from 400 to 800 °C. The topography of the samples was scanned using atomic force microscopy, and the obtained 3D maps were analyzed using fractal methods to derive the spatial characteristics of the surfaces. X-ray photoelectron spectroscopy revealed the strong influence of the deposition temperature on the Ca/P ratio in the growing films. The coatings deposited at 600–800 °C exhibited a Ca/P ratio between 1.63 and 1.69, close to the stoichiometric hydroxyapatite (Ca/P = 1.67), which is crucial for proper osseointegration. Fourier-transform infrared spectroscopy showed that the intensity of phosphate absorption bands increased with increasing substrate temperature. Each sample exhibited well defined and sharp hydroxyapatite band at 566 cm{sup −1}, although more pronounced for the coatings deposited above 500 °C. Both the hardness and elastic modulus of the coated samples decrease with increasing deposition temperature. The surface morphology strongly depends on the deposition temperature. The sample deposited at 400 °C exhibits circular cavities dug in an otherwise flat surface. At higher deposition temperatures, these cavities increase in size and start to overlap each other so that at 500 °C the surface is composed of closely packed peaks and ridges. At that point, the characteristics of the surface turns from the
Amezquita-Sanchez, Juan P.; Valtierra-Rodriguez, Martin; Perez-Ramirez, Carlos A.; Camarena-Martinez, David; Garcia-Perez, Arturo; Romero-Troncoso, Rene J.
2017-07-01
Squirrel-cage induction motors (SCIMs) are key machines in many industrial applications. In this regard, the monitoring of their operating condition aiming at avoiding damage and reducing economical losses has become a demanding task for industry. In the literature, several techniques and methodologies to detect faults that affect the integrity and performance of SCIMs have been proposed. However, they have only been focused on analyzing either the start-up transient or the steady-state operation regimes, two common operating scenarios in real practice. In this work, a novel methodology for broken rotor bar (BRB) detection in SCIMs during both start-up and steady-state operation regimes is proposed. It consists of two main steps. In the first one, the analysis of three-axis vibration signals using fractal dimension (FD) theory is carried out. Since different FD-based algorithms can give different results, three algorithms named Katz’ FD, Higuchi’s FD, and box dimension, are tested. In the second step, a fuzzy logic system for each regime is presented for automatic diagnosis. To validate the proposal, a motor with different damage levels has been tested: one with a partially BRB, a second with one fully BRB, and the third with two BRBs. The obtained results demonstrate the proposed effectiveness.
International Nuclear Information System (INIS)
Amezquita-Sanchez, Juan P; Valtierra-Rodriguez, Martin; Perez-Ramirez, Carlos A; Camarena-Martinez, David; Garcia-Perez, Arturo; Romero-Troncoso, Rene J
2017-01-01
Squirrel-cage induction motors (SCIMs) are key machines in many industrial applications. In this regard, the monitoring of their operating condition aiming at avoiding damage and reducing economical losses has become a demanding task for industry. In the literature, several techniques and methodologies to detect faults that affect the integrity and performance of SCIMs have been proposed. However, they have only been focused on analyzing either the start-up transient or the steady-state operation regimes, two common operating scenarios in real practice. In this work, a novel methodology for broken rotor bar (BRB) detection in SCIMs during both start-up and steady-state operation regimes is proposed. It consists of two main steps. In the first one, the analysis of three-axis vibration signals using fractal dimension (FD) theory is carried out. Since different FD-based algorithms can give different results, three algorithms named Katz’ FD, Higuchi’s FD, and box dimension, are tested. In the second step, a fuzzy logic system for each regime is presented for automatic diagnosis. To validate the proposal, a motor with different damage levels has been tested: one with a partially BRB, a second with one fully BRB, and the third with two BRBs. The obtained results demonstrate the proposed effectiveness. (paper)
Multiple wave scattering from fractal aggregates
Energy Technology Data Exchange (ETDEWEB)
Korvin, Gabor E-mail: gabor@kfupm.edu.sa; Oleschko, Klavdia
2004-01-01
Multiple scattered waves from fractal aggregates create spurious resonances in the high-frequency part of the wave-field's Fourier spectrum. It is shown by a probabilistic convolutional model that for extended fractal media with strong scattering cross-section, multiple scattering can affect the value of the fractal dimension estimated from the wave-field's Fourier power spectrum.
Fractales en Arqueología: aplicación en la pintura rupestre de sitios del México prehispánico.
Directory of Open Access Journals (Sweden)
Aline Lara Galicia
2013-05-01
The structure fractal describes the dimension of the represented objects, not only according to its space where the figure is placed, but the possibility of being a fraction in which all the surfaces can be observed (rock, paint.
Directory of Open Access Journals (Sweden)
T.-W. Wang
1996-09-01
Full Text Available Fractal theory is applied in a quantitative analysis of geomagnetic storms. Fractal dimensions (D of the attractor for storm data from the Beijing observatory (40.0°N, 116.2°E using several time intervals are calculated. A maximum value of 1.4 has been obtained for a geomagnetic storm; on quite days the dimension is only slightly larger than 0.5. Data from two storms are analyzed here. Results show that a combination of both D and the magnetic index, k, can perhaps describe the degree of solar disturbance better than the single parameter k.
International Nuclear Information System (INIS)
Wu, Z.L.; Chen, Y.T.; Kim, S.G.
1995-09-01
Using the Wigner-distribution estimation, the high-frequency fall-off of source spectra was estimated. The technique was applied to the analysis of the source spectra of the July 22, 1994, Vladivostok M6.4 deep-focus earthquake and that of the July 22, 1994, Northern Japan Sea M5.7 deep-focus earthquake. It is shown that the high-frequency fall-off of the source spectra of these two earthquakes may be characterized by two parts. Between the first corner frequency f 1 and the second corner frequency f 2 , the high-frequency fall-off of the source spectra can be represented by f 5.0 : above f 2 , the high-frequency fall-off can be represented by f 1.4 . In the perspective of the fractal geometry of earthquake source, it seems that the deep-focus earthquakes under consideration may be characterized as being composed of some 'sub events'. On the other hand, each sub event has its complex structure. (author). 12 refs, 3 figs, 1 tab
He, Lili; Kim, Nam-Jung; Li, Hao; Hu, Zhiqiang; Lin, Mengshi
2008-11-12
The safety of imported seafood products because of the contamination of prohibited substances, including crystal violet (CV) and malachite green (MG), raised a great deal of concern in the United States. In this study, a fractal-like gold nanostructure was developed through a self-assembly process and the feasibility of using surface-enhanced Raman spectroscopy (SERS) coupled with this nanostructure for detection of CV, MG, and their mixture (1:1) was explored. SERS was capable of characterizing and differentiating CV, MG, and their mixture on fractal-like gold nanostructures quickly and accurately. The enhancement factor of the gold nanostructures could reach an impressive level of approximately 4 x 10(7), and the lowest detectable concentration for the dye molecules was at approximately 0.2 ppb level. These results indicate that SERS coupled with fractal-like gold nanostructures holds a great potential as a rapid and ultra-sensitive method for detecting trace amounts of prohibited substances in contaminated food samples.
Random fractal characters and length uncertainty of the continental ...
Indian Academy of Sciences (India)
2Collaborative Innovation Center on Yellow River Civilization of Henan Province, Kaifeng 475 001, China. ∗. Corresponding author. e-mail: mjh@henu.edu.cn. A coastline is a random fractal ... research showed that the fractal dimension (D) of. Keywords. Continental coastline of China; scaling region; random fractal; fractal ...
International Nuclear Information System (INIS)
Sun, Haitao; Li, Ning; Guo, Lijun; Gao, Fei; Liu, Cheng
2011-01-01
The aim of this study was to use fractal dimension (FD) analysis on multidetector CT (MDCT) images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension (PH). Fourteen patients with PH and 17 patients without PH as controls were studied. All of the patients underwent contrast-enhanced helical CT and transthoracic echocardiography. The pulmonary artery trees were generated using post-processing software, and the FD and projected image area of the pulmonary artery trees were determined with Image J software in a personal computer. The FD, the projected image area and the pulmonary artery pressure (PAP) were statistically evaluated in the two groups. The FD, the projected image area and the PAP of the patients with PH were higher than those values of the patients without PH (p < 0.05, t-test). There was a high correlation of FD with the PAP (r = 0.82, p < 0.05, partial correlation analysis). There was a moderate correlation of FD with the projected image area (r = 0.49, p < 0.05, partial correlation analysis). There was a correlation of the PAP with the projected image area (r = 0.65, p < 0.05, Pearson correlation analysis). The FD of the pulmonary arteries in the PH patients was significantly higher than that of the controls. There is a high correlation of FD with the PAP.
Energy Technology Data Exchange (ETDEWEB)
Sun, Haitao; Li, Ning; Guo, Lijun; Gao, Fei; Liu, Cheng [Shandong University, Shandong Medical Imaging Research Institute, Shandong (Korea, Republic of)
2011-06-15
The aim of this study was to use fractal dimension (FD) analysis on multidetector CT (MDCT) images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension (PH). Fourteen patients with PH and 17 patients without PH as controls were studied. All of the patients underwent contrast-enhanced helical CT and transthoracic echocardiography. The pulmonary artery trees were generated using post-processing software, and the FD and projected image area of the pulmonary artery trees were determined with Image J software in a personal computer. The FD, the projected image area and the pulmonary artery pressure (PAP) were statistically evaluated in the two groups. The FD, the projected image area and the PAP of the patients with PH were higher than those values of the patients without PH (p < 0.05, t-test). There was a high correlation of FD with the PAP (r = 0.82, p < 0.05, partial correlation analysis). There was a moderate correlation of FD with the projected image area (r = 0.49, p < 0.05, partial correlation analysis). There was a correlation of the PAP with the projected image area (r = 0.65, p < 0.05, Pearson correlation analysis). The FD of the pulmonary arteries in the PH patients was significantly higher than that of the controls. There is a high correlation of FD with the PAP.
Directory of Open Access Journals (Sweden)
Evy Kamilah Ratnasari
2014-07-01
Full Text Available Penyakit yang menyerang tebu dapat disebabkan oleh bakteri, jamur maupun virus. Penyakit noda merupakan penyakit pada tanaman tebu yang disebabkan oleh jamur dengan menampakkan lesi atau bercak pada permukaan daun. Penyakit noda tersebut dapat menghambat proses fotosintesis yang akan berakibat menurunkan produksi gula karena mempengaruhi pertumbuhan tebu. Upaya pengendalian dini dapat dilakukan dengan mengenali jenis penyakit melalui lesinya yang bermanfaat dalam menentukan tindakan penanganan yang tepat. Lesi yang disebabkan oleh penyakit noda masing-masing dapat dikenali secara visual karena memiliki ciri warna dan tekstur yang unik. Tetapi pengamatan secara visual memiliki beberapa kekurangan seperti subjektifitas dan kurang akurat. Penelitian ini mengusulkan pengenalan penyakit noda tanaman tebu yang terdiri dari noda cincin, noda karat, dan noda kuning berdasarkan fitur tekstur yang merupakan kombinasi dari konsep Gray Level Co-Occurrence Matrix (GLCM dan dimensi fraktal yang dinamakan Fractal Dimension Co-Occurrence Matrix (FDCM. Sedangkan fitur warna didapatkan dari perhitungan statistik col or moments pada citra L*a*b*. Kombinasi fitur tersebut menghasilkan 12 fitur warna dan 6 fitur tekstur yang kemudian digunakan sebagai masukan klasifikasi k-Nearest Neighbor (KNN. Pengenalan penyakit noda pada tanaman tebu menggunakan metode tersebut dapat menghasilkan akurasi tertinggi 90%.
Fractal physiology and the fractional calculus: a perspective.
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
[Molecular structure and fractal analysis of oligosaccharide].
Liu, Wen-long; Wang, Lu-man; He, Dong-qi; Zhang, Tian-lan; Gou, Bao-di; Li, Qing
2014-10-18
To propose a calculation method of oligosaccharides' fractal dimension, and to provide a new approach to studying the drug molecular design and activity. By using the principle of energy optimization and computer simulation technology, the steady structures of oligosaccharides were found, and an effective way of oligosaccharides fractal dimension's calculation was further established by applying the theory of box dimension to the chemical compounds. By using the proposed method, 22 oligosaccharides' fractal dimensions were calculated, with the mean 1.518 8 ± 0.107 2; in addition, the fractal dimensions of the two activity multivalent oligosaccharides which were confirmed by experiments, An-2 and Gu-4, were about 1.478 8 and 1.516 0 respectively, while C-type lectin-like receptor Dectin-1's fractal dimension was about 1.541 2. The experimental and computational results were expected to help to find a class of glycoside drugs whose target receptor was Dectin-1. Fractal dimension, differing from other known macro parameters, is a useful tool to characterize the compound molecules' microscopic structure and function, which may play an important role in the molecular design and biological activity study. In the process of oligosaccharides drug screening, the fractal dimension of receptor and designed oligosaccharides or glycoclusters can be calculated respectively. The oligosaccharides with fractal dimension close to that of target receptor should then take priority compared with others, to get the drug molecules with latent activity.
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.
Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study
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
Fractal Scattering of Microwaves from Soils
Oleschko, K.; Korvin, G.; Balankin, A. S.; Khachaturov, R. V.; Flores, L.; Figueroa, B.; Urrutia, J.; Brambila, F.
2002-10-01
Using a combination of laboratory experiments and computer simulation we show that microwaves reflected from and transmitted through soil have a fractal dimension correlated to that of the soil's hierarchic permittivity network. The mathematical model relating the ground-penetrating radar record to the mass fractal dimension of soil structure is also developed. The fractal signature of the scattered microwaves correlates well with some physical and mechanical properties of soils.
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.
Doherty, Cailbhe; Bleakley, Chris; Hertel, Jay; Caulfield, Brian; Ryan, John; Delahunt, Eamonn
2014-01-01
Instrumented postural control analysis plays an important role in evaluating the effects of injury on dynamic stability during balance tasks, and is often conveyed with measures based on the displacement of the center-of-pressure (COP) assessed with a force platform. However, the desired outcome of the task is frequently characterized by a loss of dynamic stability, secondary to injury. Typically, these failed trials are discarded during research investigations, with the potential loss of informative data pertaining to task success. The novelty of the present study is that COP characteristics of failed trials in injured participants are compared to successful trial data in another injured group, and a control group of participants, using the fractal dimension (FD) method. Three groups of participants attempted a task of eyes closed single limb stance (SLS): twenty-nine participants with acute ankle sprain successfully completed the task on their non-injured limb (successful injury group); twenty eight participants with acute ankle sprain failed their attempt on their injured limb (failed injury group); sixteen participants with no current injury successfully completed the task on their non-dominant limb (successful non-injured group). Between trial analyses of these groups revealed significant differences in COP trajectory FD (successful injury group: 1.58±0.06; failed injury group: 1.54±0.07; successful non-injured group: 1.64±0.06) with a large effect size (0.27). These findings demonstrate that successful eyes-closed SLS is characterized by a larger FD of the COP path when compared to failed trials, and that injury causes a decrease in COP path FD. Copyright © 2014 Elsevier B.V. All rights reserved.
López, Carmen; Martí, Joan; Abella, Rafael; Tarraga, Marta
2014-07-01
The impossibility of observing magma migration inside the crust obliges us to rely on geophysical data and mathematical modelling to interpret precursors and to forecast volcanic eruptions. Of the geophysical signals that may be recorded before and during an eruption, deformation and seismicity are two of the most relevant as they are directly related to its dynamic. The final phase of the unrest episode that preceded the 2011-2012 eruption on El Hierro (Canary Islands) was characterized by local and accelerated deformation and seismic energy release indicating an increasing fracturing and a migration of the magma. Application of time varying fractal analysis to the seismic data and the characterization of the seismicity pattern and the strain and the stress rates allow us to identify different stages in the source mechanism and to infer the geometry of the path used by the magma and associated fluids to reach the Earth's surface. The results obtained illustrate the relevance of such studies to understanding volcanic unrest and the causes that govern the initiation of volcanic eruptions.
Evertsz, Carl Joseph Gabriel
1989-01-01
Laplacian Fractals are physical models for the fractal properties encountered in a selected group of natural phenomena. The basis models in this class are the Dialectric Breakdown Model and the closely related Diffusion- Limited Aggregration model and Laplacian Random Walks. A full mathematical
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Results are presented of a preliminary investigation of the fractal nature of the plan-view shapes of lava flows in Hawaii (based on field measurements and aerial photographs), as well as in Idaho and the Galapagos Islands (using aerial photographs only). The shapes of the lava flow margins are found to be fractals: lava flow shape is scale-invariant. This observation suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. A'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14-1.23). The analysis is extended to other planetary bodies by measuring flows from orbital images of Venus, Mars, and the moon. All are fractal and have D consistent with the range of terrestrial a'a and have D consistent with the range of terrestrial a'a and pahoehoe values.
International Nuclear Information System (INIS)
Fong, R.W.L.; Nitheanandan, T.; Bullock, C.D.; Slater, L.F.; McRae, G.A.
2003-05-01
Glass-bead peening the outside surfaces of zirconium alloy tubes has been shown to increase the Critical Heat Flux (CHF) in pool boiling of water. The CHF is found to correlate with the fractal roughness of the metal tube surfaces. In this study on the effect of oxidation on glass-peened surfaces, test measurements for CHF, surface wettability and roughness have been evaluated using various glass-peened and oxidized zirconium alloy tubes. The results show that oxidation changes the solid-liquid contact angle (i.e., decreases wettability of the metal-oxide surface), but does not change the fractal surface roughness, appreciably. Thus, oxidation of the glass-peened surfaces of zirconium alloy tubes is not expected to degrade the CHF enhancement obtained by glass-bead peening. (author)
Fractal model of anomalous diffusion
Gmachowski, Lech
2015-01-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An...
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 study of Ni-Cr-Mo alloy for dental applications: effect of beryllium
Energy Technology Data Exchange (ETDEWEB)
Eftekhari, Ali
2003-12-30
Different Ni-based alloys with various compositions were prepared by varying the amounts of beryllium. Effect of the amount of beryllium added to the alloy on its corrosion in an electrolyte solution of artificial saliva was investigated. Fractal dimension was used as a quantitative factor for surface analysis of the alloys before and after storage in the artificial salvia. The fractal dimensions of the electrode surfaces were determined by means of the most reliable method in this context viz. time dependency of the diffusion-limited current for a system involving 'diffusion towards electrode surface'. The results showed that increase of the beryllium amount in the alloy composition significantly increases the alloy corrosion. It is accompanied by increase of the fractal dimension and roughness of the electrode surface, whereas a smooth and shiny surface is required for dentures. From the methodology point of view, the approach utilized for fractal analysis of the alloy surfaces (Au-masking of metallic surfaces) is a novel and efficient method for study of denture surfaces. Generally, this approach is of interest for corrosion studies of different metals and alloys, particularly where changes in surface structure have a significant importance.
Fractal study of Ni Cr Mo alloy for dental applications: effect of beryllium
Eftekhari, Ali
2003-12-01
Different Ni-based alloys with various compositions were prepared by varying the amounts of beryllium. Effect of the amount of beryllium added to the alloy on its corrosion in an electrolyte solution of artificial saliva was investigated. Fractal dimension was used as a quantitative factor for surface analysis of the alloys before and after storage in the artificial salvia. The fractal dimensions of the electrode surfaces were determined by means of the most reliable method in this context viz. time dependency of the diffusion-limited current for a system involving "diffusion towards electrode surface". The results showed that increase of the beryllium amount in the alloy composition significantly increases the alloy corrosion. It is accompanied by increase of the fractal dimension and roughness of the electrode surface, whereas a smooth and shiny surface is required for dentures. From the methodology point of view, the approach utilized for fractal analysis of the alloy surfaces (Au-masking of metallic surfaces) is a novel and efficient method for study of denture surfaces. Generally, this approach is of interest for corrosion studies of different metals and alloys, particularly where changes in surface structure have a significant importance.
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
Definition of fractal topography to essential understanding of scale-invariance
Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan
2017-01-01
Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals. PMID:28436450
Fractal Property in the Light Curve of BL Lac Object S5 0716+714 ...
Indian Academy of Sciences (India)
- tion and fractal dimension. ... tional data, here, we obtain the long-term light curve of S5 0716 +714 and fractal dimension and then ... Science Foundation of Yunnan Educational Department under grant 2012Z016. References. Cristiano, S.
Nasehnejad, Maryam; Nabiyouni, G.; Gholipour Shahraki, Mehran
2018-03-01
In this study a 3D multi-particle diffusion limited aggregation method is employed to simulate growth of rough surfaces with fractal behavior in electrodeposition process. A deposition model is used in which the radial motion of the particles with probability P, competes with random motions with probability 1 - P. Thin films growth is simulated for different values of probability P (related to the electric field) and thickness of the layer(related to the number of deposited particles). The influence of these parameters on morphology, kinetic of roughening and the fractal dimension of the simulated surfaces has been investigated. The results show that the surface roughness increases with increasing the deposition time and scaling exponents exhibit a complex behavior which is called as anomalous scaling. It seems that in electrodeposition process, radial motion of the particles toward the growing seeds may be an important mechanism leading to anomalous scaling. The results also indicate that the larger values of probability P, results in smoother topography with more densely packed structure. We have suggested a dynamic scaling ansatz for interface width has a function of deposition time, scan length and probability. Two different methods are employed to evaluate the fractal dimension of the simulated surfaces which are "cube counting" and "roughness" methods. The results of both methods show that by increasing the probability P or decreasing the deposition time, the fractal dimension of the simulated surfaces is increased. All gained values for fractal dimensions are close to 2.5 in the diffusion limited aggregation model.
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
Zivić, Ivan; Elezović-Hadzić, Suncica; Milosević, Sava
2009-12-01
We present an exact and Monte Carlo renormalization group (MCRG) study of semiflexible polymer chains on an infinite family of the plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension df is equal to 2 for all members of the fractal family enumerated by the odd integer b(3fractals (for 3fractals to the same problem on the regular Euclidean lattices.
Lung cancer—a fractal viewpoint
Lennon, Frances E.; Cianci, Gianguido C.; Cipriani, Nicole A.; Hensing, Thomas A.; Zhang, Hannah J.; Chen, Chin-Tu; Murgu, Septimiu D.; Vokes, Everett E.; W. Vannier, Michael; Salgia, Ravi
2016-01-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed. PMID:26169924
Lung cancer-a fractal viewpoint.
Lennon, Frances E; Cianci, Gianguido C; Cipriani, Nicole A; Hensing, Thomas A; Zhang, Hannah J; Chen, Chin-Tu; Murgu, Septimiu D; Vokes, Everett E; Vannier, Michael W; Salgia, Ravi
2015-11-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.
Controlled growth of polyaniline fractals on HOPG through potentiodynamic electropolymerization.
Bhattacharjya, Dhrubajyoti; Mukhopadhyay, Indrajit
2012-04-10
Polyaniline (PANI) in fractal dimension has been electrodeposited reproducibly on highly oriented pyrolytic graphite (HOPG) from 0.2 M aniline in 1 M aqueous HCl solution by potentiodynamic sweeping in the range of -0.2 to 0.76 V vs Ag/AgCl at room temperature. Fractal growth of PANI dendrimers is affected by diffusion limited polymerization (DLP) at a sweep rate of 15 mV s(-1) for 43 min. This type of PANI dendrimer is prepared for the first time on such large area HOPG substrate by electrochemical technique using rather simple cell setup. The fractal dimension has been determined by chronoamperometry (CA) and box counting technique and is found to vary from 1.4 to 1.9 with the duration of electropolymerization. The sweep rate, terminal oxidation potential, and the diverse surface anisotropy of the HOPG surface are found to be crucial factors in controlling the growth of such PANI fractals. © 2012 American Chemical Society
Jurgens, Hartmut; And Others
1990-01-01
The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)
Fractal Electrochemical Microsupercapacitors
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.
Monitoring of dry sliding wear using fractal analysis
Zhang, Jindang; Regtien, Paulus P.L.; Korsten, Maarten J.
2005-01-01
Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
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
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
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
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.
Chaos and fractals an elementary introduction
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.
Turbulent shear-flow over fractal arrays of surface-mounted cubes
Wise, Daniel J.; Brevis, Wernher; Sheffield Fluid Mechanics Group Team
2015-11-01
The turbulent shear-flow over a bottom-wall fully covered by periodic multi-scale arrangements of obstacles is examined via Particle Image Velocimetry (PIV), Volumetric 3D Velocimetry (V3V) and Acoustic Doppler Velocimetry (ADV) measurements. Three obstacle patterns are utilised, all based on different numbers of iterations of the Sierpinski carpet fractal. In each case 2D/3D velocity fields of the flow formed within the porous channels, namely the flow beneath the mean obstacle height, are presented and analysed with respect to standard statistics such as the mean, rms velocity profiles, and the Reynolds stresses. Point-wise measurements within the obstacle arrays reveal that the presence of the obstacles, and in particular their injection of energy at the associated wavelengths, has unexpected effects on the slope of the energy spectra within the turbulent porous flow. The region dominated by these spectral characteristics is defined. It is also shown that this behaviour is not observed in the outer flow.
Statistical analysis of the Martian surface
Landais, F.; Schmidt, F.; Lovejoy, S.
2015-10-01
We investigate the scaling properties of the topography of Mars [10]. Planetary topographic fields are well known to exhibit (mono)fractal behavior. Indeed, fractal formalism is efficient to reproduce the variability observed in topography. Still, a single fractal dimension is not enough to explain the huge variability and intermittency. Previous study have shown that fractal dimensions might be different from a region to another, excluding a general description at the planetary scale. In this project, we are analyzing the Martian topographic data with a multifractal formalism to study the scaling intermittency. In the multifractal paradigm, the local variation of the fractal dimension is interpreted as a statistical property of multifractal fields. The results suggest a multifractal behaviour from planetary scale down to 10 km. From 10 km to 600 m, the topography seems to be simple monofractal. This transition indicates a significant in the geological processes governing the Red Planet's surface.
Chen, X.; Yao, G.; Cai, J.
2017-12-01
Pore structure characteristics are important factors in influencing the fluid transport behavior of porous media, such as pore-throat ratio, pore connectivity and size distribution, moreover, wettability. To accurately characterize the diversity of pore structure among HFUs, five samples selected from different HFUs (porosities are approximately equal, however permeability varies widely) were chosen to conduct micro-computerized tomography test to acquire direct 3D images of pore geometries and to perform mercury injection experiments to obtain the pore volume-radii distribution. To characterize complex and high nonlinear pore structure of all samples, three classic fractal geometry models were applied. Results showed that each HFU has similar box-counting fractal dimension and generalized fractal dimension in the number-area model, but there are significant differences in multifractal spectrums. In the radius-volume model, there are three obvious linear segments, corresponding to three fractal dimension values, and the middle one is proved as the actual fractal dimension according to the maximum radius. In the number-radius model, the spherical-pore size distribution extracted by maximum ball algorithm exist a decrease in the number of small pores compared with the fractal power rate rather than the traditional linear law. Among the three models, only multifractal analysis can classify the HFUs accurately. Additionally, due to the tightness and low-permeability in reservoir rocks, connate water film existing in the inner surface of pore channels commonly forms bound water. The conventional model which is known as Yu-Cheng's model has been proved to be typically not applicable. Considering the effect of irreducible water saturation, an improved fractal permeability model was also deduced theoretically. The comparison results showed that the improved model can be applied to calculate permeability directly and accurately in such unconventional rocks.
Losa, Gabriele A
2009-01-01
The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".
Identifying surfaces of low dimensions in high dimensional data
DEFF Research Database (Denmark)
Høskuldsson, Agnar
1996-01-01
Methods are presented that find a nonlinear subspace in low dimensions that describe data given by many variables. The methods include nonlinear extensions of Principal Component Analysis and extensions of linear regression analysis. It is shown by examples that these methods give more reliable...
3-D surface anthropometry ; accurate determination of body dimensions
Daanen, H.A.M.
1998-01-01
Body dimensions of the user population have to be the starting point of design and evaluation of many workplaces and products. Insufficient attention to these aspects may lead to uncomfortable, unhealthy, or dangerous situations. Few up-to-date anthropometric databases are available. The shortage of
Fractal analysis of Xylella fastidiosa biofilm formation
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.
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
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
Fractal organization of feline oocyte cytoplasm
Directory of Open Access Journals (Sweden)
G De Vico
2009-06-01
Full Text Available The present study aimed at verifying whether immature cat oocytes with morphologic irregular cytoplasm display selfsimilar features which can be analytically described by fractal analysis. Original images of oocytes collected by ovariectomy were acquired at a final magnification of 400 X with a CCD video camera connected to an optic microscope. After greyscale thresholding segmentation of cytoplasm, image profiles were submitted to fractal analysis using FANAL++, a program which provided an analytical standard procedure for determining the fractal dimension (FD. The presentation of the oocyte influenced the magnitude of the fractal dimension with the highest FD of 1.91 measured on grey-dark cytoplasm characterized by a highly connected network of lipid droplets and intracellular membranes. Fractal analysis provides an effective quantitative descriptor of the real cytoplasm morphology, which can influence the acquirement of in vitro developmental competence, without introducing any bias or shape approximation and thus contributes to an objective and reliable classification of feline oocytes.
Fractals and cosmological large-scale structure
Luo, Xiaochun; Schramm, David N.
1992-01-01
Observations of galaxy-galaxy and cluster-cluster correlations as well as other large-scale structure can be fit with a 'limited' fractal with dimension D of about 1.2. This is not a 'pure' fractal out to the horizon: the distribution shifts from power law to random behavior at some large scale. If the observed patterns and structures are formed through an aggregation growth process, the fractal dimension D can serve as an interesting constraint on the properties of the stochastic motion responsible for limiting the fractal structure. In particular, it is found that the observed fractal should have grown from two-dimensional sheetlike objects such as pancakes, domain walls, or string wakes. This result is generic and does not depend on the details of the growth process.
Measurement Based Quantum Computation on Fractal Lattices
Directory of Open Access Journals (Sweden)
Michal Hajdušek
2010-06-01
Full Text Available In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
Fractal pattern of canine trichoblastoma.
De Vico, Gionata; Cataldi, Marielda; Maiolino, Paola; Carella, Francesca; Beltraminelli, Stefano; Losa, Gabriele A
2011-06-01
To assess by fractal analysis the specific architecture, growth pattern, and tissue distribution that characterize subtypes of canine trichoblastoma, a benign tumor derived from or reduplicating the primitive hair germ of embryonic follicular development. Tumor masks and outlines obtained from immunohistologic images by gray threshold segmentation of epithelial components were analyzed by fractal and conventional morphometry. The fractal dimension [FD] of each investigated case was determined from the slope of the regression line describing the fractal region within a bi-asymptotic curve experimentally established. All tumor masks and outlines obtained by gray threshold segmentation of epithelial components showed fractal self-similar properties that were evaluated by peculiar FDs. However, only masks revealed significantly different FD values, ranging from 1.75 to 1.85, enabling the discrimination of canine trichoblastoma subtypes. The FD data suggest that an iterative morphogenetic process, involving both the air germ and associated dermal papilla, may be responsible of the peculiar tissue architecture of trichoblastoma. The present study emphasized the reliability of fractal analysis in achieving the objective characterization of canine trichoblastoma.
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......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 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 patterns of fractures in granites
Velde, B.; Dubois, J.; Moore, D.; Touchard, G.
1991-01-01
Fractal measurements using the Cantor's dust method in a linear one-dimensional analysis mode were made on the fracture patterns revealed on two-dimensional, planar surfaces in four granites. This method allows one to conclude that: 1. (1)|The fracture systems seen on two-dimensional surfaces in granites are consistent with the part of fractal theory that predicts a repetition of patterns on different scales of observation, self similarity. Fractal analysis gives essentially the same values of D on the scale of kilometres, metres and centimetres (five orders of magnitude) using mapped, surface fracture patterns in a Sierra Nevada granite batholith (Mt. Abbot quadrangle, Calif.). 2. (2)|Fractures show the same fractal values at different depths in a given batholith. Mapped fractures (main stage ore veins) at three mining levels (over a 700 m depth interval) of the Boulder batholith, Butte, Mont. show the same fractal values although the fracture disposition appears to be different at different levels. 3. (3)|Different sets of fracture planes in a granite batholith, Central France, and in experimental deformation can have different fractal values. In these examples shear and tension modes have the same fractal values while compressional fractures follow a different fractal mode of failure. The composite fracture patterns are also fractal but with a different, median, fractal value compared to the individual values for the fracture plane sets. These observations indicate that the fractal method can possibly be used to distinguish fractures of different origins in a complex system. It is concluded that granites fracture in a fractal manner which can be followed at many scales. It appears that fracture planes of different origins can be characterized using linear fractal analysis. ?? 1991.
Nishimura, Ryo; Hyodo, Kengo; Sawaguchi, Haruna; Yamamoto, Yoshiaki; Nonomura, Yoshimune; Mayama, Hiroyuki; Yokojima, Satoshi; Nakamura, Shinichiro; Uchida, Kingo
2016-08-17
Double roughness structure, the origin of the lotus effect of natural lotus leaf, was successfully reproduced on a diarylethene microcrystalline surface. Static superwater-repellency and dynamic water-drop-bouncing were observed on the surface, in the manner of natural lotus leaves. Double roughness structure was essential for water-drop-bouncing. This ability was not observed on a single roughness microcrystalline surface showing the lotus effect of the same diarylethene derivative. The double roughness structure was reversibly controlled by alternating irradiation with UV and visible light.
Consistency of Lower-Body Dimensions Using Surface Landmarks and Simple Measurement Tools.
Caia, Johnpaul; Weiss, Lawrence W; Chiu, Loren Z F; Schilling, Brian K; Paquette, Max R
2016-09-01
Caia, J, Weiss, LW, Chiu, LZF, Schilling, BK, and Paquette, MR. Consistency of lower-body dimensions using surface landmarks and simple measurement tools. J Strength Cond Res 30(9): 2600-2608, 2016-Body dimensions may influence various types of physical performance. This study was designed to establish the reliability and precision of bilateral lower-body dimensions using surface anatomic landmarks and either sliding calipers or goniometry. Fifty university students (25 men and 25 women) were measured on 2 separate occasions separated by 48 or 72 hours. A small digital caliper was used to acquire longitudinal dimensions of the feet, whereas a larger broad-blade caliper was used to measure lower-limb, hip, and pelvic dimensions. Quadriceps angle (Q-angle) was determined through surface goniometry. Data for all foot and lower-limb dimensions were both reliable and precise (intraclass correlation coefficient (ICC) ≥0.72, SEM 0.1-0.5 cm). Measures of Q-angle were also reliable and precise (ICC ≥0.85, SEM 0.2-0.4°). Findings from this investigation demonstrate that lower-body dimensions may be reliably and precisely measured through simple practical tests, when surface anatomic landmarks and standardized procedures are used. Although intertester reliability remains to be established, meticulous adherence to specific measurement protocols is likely to yield viable output for lower-body dimensions when more sophisticated methods are unavailable or inappropriate.
Textural characterization of coals using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Mahamud, Manuel; Lopez, Oscar [Faculty of Chemistry, Department of Chemical and Environmental Engineering, University of Oviedo, Campus de El Cristo, 33071 Oviedo (Spain); Pis, Jose Juan; Pajares, Jesus Alberto [Instituto Nacional del Carbon (C.S.I.C.), Apartado 73, 33080 Oviedo (Spain)
2003-05-15
The aim of this study is to show how fractal analysis can be effectively used to characterize the texture of porous solids. The materials under study were series of coals oxidized in air at various temperatures for different time intervals. Data from mercury porosimetry determinations of samples was analyzed using fractal models. The methods employed were those proposed by Neimark, Friesen and Mikula and that developed by Zhang and Li. Some methods are able to supply a fractal profile or 'fractal fingerprint' of materials, i.e. ranges of pore sizes with different fractal dimensions are detected. These fractal profiles are very sensitive to the oxidation treatment. The average fractal dimension can also be used as a valid parameter to monitor the textural evolution of the coals as the treatment progresses, as this behaves in a similar way to other textural parameters. The use of fractal analysis in conjunction with the results of classical characterization methods leads to a better understanding of textural modifications in the processing of materials.
Using Fractal And Morphological Criteria For Automatic Classification Of Lung Diseases
Vehel, Jacques Levy
1989-11-01
Medical Images are difficult to analyze by means of classical image processing tools because they are very complex and irregular. Such shapes are obtained for instance in Nuclear Medecine with the spatial distribution of activity for organs such as lungs, liver, and heart. We have tried to apply two different theories to these signals: - Fractal Geometry deals with the analysis of complex irregular shapes which cannot well be described by the classical Euclidean geometry. - Integral Geometry treats sets globally and allows to introduce robust measures. We have computed three parameters on three kinds of Lung's SPECT images: normal, pulmonary embolism and chronic desease: - The commonly used fractal dimension (FD), that gives a measurement of the irregularity of the 3D shape. - The generalized lacunarity dimension (GLD), defined as the variance of the ratio of the local activity by the mean activity, which is only sensitive to the distribution and the size of gaps in the surface. - The Favard length that gives an approximation of the surface of a 3-D shape. The results show that each slice of the lung, considered as a 3D surface, is fractal and that the fractal dimension is the same for each slice and for the three kind of lungs; as for the lacunarity and Favard length, they are clearly different for normal lungs, pulmonary embolisms and chronic diseases. These results indicate that automatic classification of Lung's SPECT can be achieved, and that a quantitative measurement of the evolution of the disease could be made.
Fractal patterns on the onset of coherent structures in a coupled map ...
Indian Academy of Sciences (India)
We report the formation of Cantor set-like fractals during the development of coherent structures in a coupled map lattice (CML). The dependence of these structures on the size of the lattice as well as the first three dimensions of the associated fractal patterns are analyzed numerically. Keywords. Fractal dimensions ...
Fractal Property in the Light Curve of BL Lac Object S5 0716+714 ...
Indian Academy of Sciences (India)
Introduction. A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers, so it is typically self- similar patterns (Mandelbrot 1982). In recent years, fractal theory is also used to solve the astrophysical problems, e.g., Cristiano (2007) confirmed that ...
2-D Fractal Wire Antenna Design and Performance
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.
International Nuclear Information System (INIS)
Jha, Shailendra K.; Kant, Rama
2010-01-01
We developed a mathematical model for the first order homogeneous catalytic chemical reaction coupled with an electron transfer (EC') on a rough working electrode. Results are obtained for the various roughness models of electrode corrugations, viz., (i) roughness as an exact periodic function, (ii) roughness as a random function with known statistical properties, and (iii) roughness as a random function with statistical self-affine fractality over a finite range of length scales. Method of Green's function is used in the formulation to obtain second-order perturbation (in roughness profile) expressions for the concentration, the local current density and the current transients. A general operator structure between these quantities and arbitrary roughness profile is emphasized. The statistically averaged (randomly rough) electrode response is obtained by an ensemble averaging over all possible surface configurations. An elegant mathematical formula between the average electrochemical current transient and surface structure factor or power-spectrum of roughness is obtained. This formula is used to obtain an explicit equation for the current on an approximately self-affine (or realistic) fractal electrode with a limited range of length scales of irregularities. This description of realistic fractal is obtained by cutoff power law power-spectrum of roughness. The realistic fractal power-spectrum consists of four physical characteristics, viz., the fractal dimension (D H ), lower (l) and upper (L) cutoff length scales of fractality and a proportionality factor (μ), which is related to the topothesy or strength of fractality. Numerical calculations are performed on final results to understand the effect of catalytic reaction and fractal morphological characteristics on potentiostatic current transients.
Normal Contacts of Lubricated Fractal Rough Surfaces at the Atomic Scale
Solhjoo, Soheil; Vakis, Antonis I.
The friction of contacting interfaces is a function of surface roughness and applied normal load. Under boundary lubrication, this frictional behavior changes as a function of lubricant wettability, viscosity, and density, by practically decreasing the possibility of dry contact. Many studies on
FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY
Directory of Open Access Journals (Sweden)
Ian Parkinson
2011-05-01
Full Text Available A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge. The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals, with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.
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.
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 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.
On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: a review.
Pippa, Natassa; Dokoumetzidis, Aristides; Demetzos, Costas; Macheras, Panos
2013-11-18
Fractals have been very successful in quantifying nature's geometrical complexity, and have captured the imagination of scientific community. The development of fractal dimension and its applications have produced significant results across a wide variety of biomedical applications. This review deals with the application of fractals in pharmaceutical sciences and attempts to account the most important developments in the fields of pharmaceutical technology, especially of advanced Drug Delivery nano Systems and of biopharmaceutics and pharmacokinetics. Additionally, fractal kinetics, which has been applied to enzyme kinetics, drug metabolism and absorption, pharmacokinetics and pharmacodynamics are presented. This review also considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain information and more realistic description on different parts of pharmaceutical sciences. As a conclusion, the purpose of the present work is to highlight the presence of fractal geometry in almost all fields of pharmaceutical research. Copyright © 2013 Elsevier B.V. All rights reserved.
After notes on self-similarity exponent for fractal structures
Directory of Open Access Journals (Sweden)
Fernández-Martínez Manuel
2017-06-01
Full Text Available Previous works have highlighted the suitability of the concept of fractal structure, which derives from asymmetric topology, to propound generalized definitions of fractal dimension. The aim of the present article is to collect some results and approaches allowing to connect the self-similarity index and the fractal dimension of a broad spectrum of random processes. To tackle with, we shall use the concept of induced fractal structure on the image set of a sample curve. The main result in this paper states that given a sample function of a random process endowed with the induced fractal structure on its image, it holds that the self-similarity index of that function equals the inverse of its fractal dimension.
Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions
International Nuclear Information System (INIS)
Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander
2010-01-01
A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/r D ∝r -D where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A 'box-counting' procedure could also be applied giving the 'capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term 'fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis.The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are
Fractal Model for Acoustic Absorbing of Porous Fibrous Metal Materials
Directory of Open Access Journals (Sweden)
Weihua Chen
2016-01-01
Full Text Available To investigate the changing rules between sound absorbing performance and geometrical parameters of porous fibrous metal materials (PFMMs, this paper presents a fractal acoustic model by incorporating the static flow resistivity based on Biot-Allard model. Static flow resistivity is essential for an accurate assessment of the acoustic performance of the PFMM. However, it is quite difficult to evaluate the static flow resistivity from the microstructure of the PFMM because of a large number of disordered pores. In order to overcome this difficulty, we firstly established a static flow resistivity formula for the PFMM based on fractal theory. Secondly, a fractal acoustic model was derived on the basis of the static flow resistivity formula. The sound absorption coefficients calculated by the presented acoustic model were validated by the values of Biot-Allard model and experimental data. Finally, the variation of the surface acoustic impedance, the complex wave number, and the sound absorption coefficient with the fractal dimensions were discussed. The research results can reveal the relationship between sound absorption and geometrical parameters and provide a basis for improving the sound absorption capability of the PFMMs.
FRACTAL ANALYSIS OF FRACTURE SYSTEMS IN UPPER TRIASSIC DOLOMITES IN ŽUMBERAK MOUNTAIN, CROATIA
Ivica Pavičić; Ivan Dragičević; Tatjana Vlahović; Tonći Grgasović
2017-01-01
This paper presents results of fractal analysis of fracture systems in upper Triassic dolomites in Žumberak Mountain, Croatia. Mechanical rock characteristics together with structural and diagenetic processes results with fracture systems that can be considered as fractals. They are scale-invariant in specific range of scales. Distribution of fractures can be than described with power law distribution and fractal dimension. Fractal dimension is a measure of how fractures fill the space. Fract...
Fractal analysis of granular activated carbons using isotherm data
Energy Technology Data Exchange (ETDEWEB)
Khalili, N.R.; Pan, M. [Illinois Institute of Technology, Chicago, IL (United States). Dept. of Chemical and Environmental Engineering; Sandi, G. [Argonne National Lab., IL (United States)
1997-08-01
Utilization of adsorption on solid surfaces was exercised for the first time in 1785. Practical application of unactivated carbon filters, and powdered carbon were first demonstrated in the American water treatment plant, and a municipal treatment plant in New Jersey, in 1883 and 1930, respectively. The use of activated carbon became widespread in the next few decades. At present, adsorption on carbons has a wide spread application in water treatment and removal of taste, odor, removal of synthetic organic chemicals, color-forming organics, and desinfection by-products and their naturally occurring precursors. This paper presents an analysis of the surface fractal dimension and adsorption capacity of a group of carbons.
Directory of Open Access Journals (Sweden)
Alessandro Chiaudani
2017-11-01
Full Text Available In this research, univariate and bivariate statistical methods were applied to rainfall, river and piezometric level datasets belonging to 24-year time series (1986–2009. These methods, which often are used to understand the effects of precipitation on rivers and karstic springs discharge, have been used to assess piezometric level response to rainfall and river level fluctuations in a porous aquifer. A rain gauge, a river level gauge and three wells, located in Central Italy along the lower Pescara River valley in correspondence of its important alluvial aquifer, provided the data. Statistical analysis has been used within a known hydrogeological framework, which has been refined by mean of a photo-interpretation and a GPS survey. Water–groundwater relationships were identified following the autocorrelation and cross-correlation analyses. Spectral analysis and mono-fractal features of time series were assessed to provide information on multi-year variability, data distributions, their fractal dimension and the distribution return time within the historical time series. The statistical–mathematical results were interpreted through fieldwork that identified distinct groundwater flowpaths within the aquifer and enabled the implementation of a conceptual model, improving the knowledge on water resources management tools.
Aesthetic Responses to Exact Fractals Driven by Physical Complexity.
Bies, Alexander J; Blanc-Goldhammer, Daryn R; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E
2016-01-01
Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a
Random sequential adsorption on fractals.
Ciesla, Michal; Barbasz, Jakub
2012-07-28
Irreversible adsorption of spheres on flat collectors having dimension d fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.
Harper, David William (Inventor)
2017-01-01
A structural support having fractal-stiffening and method of fabricating the support is presented where an optimized location of at least three nodes is predetermined prior to fabricating the structural support where a first set of webs is formed on one side of the support and joined to the nodes to form a first pocket region. A second set of webs is formed within the first pocket region forming a second pocket region where the height of the first set of webs extending orthogonally from the side of the support is greater than the second set of webs extending orthogonally from the support.
Usefulness of fractal analysis for the diagnosis of periodontitis
International Nuclear Information System (INIS)
Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung
2001-01-01
To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979±0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006±0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis
Usefulness of fractal analysis for the diagnosis of periodontitis
Energy Technology Data Exchange (ETDEWEB)
Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung [Dankook Univ. School of Dentistry, Seoul (Korea, Republic of)
2001-03-15
To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979{+-}0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006{+-}0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.
Fractal nature of humic materials
Rice, J. A.; Lin, J. S.
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 fractions 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.
Directory of Open Access Journals (Sweden)
Roberto Douglas Moreira
2011-06-01
Full Text Available INTRODUÇÃO: O termo "fractal" é derivado do latim fractus, que significa "irregular" ou "quebrado", considerando a estrutura observada como tendo uma dimensão não-inteira. Há muitos estudos que empregaram a Dimensão Fractal (DF como uma ferramenta de diagnóstico. Um dos métodos mais comuns para o seu estudo é a "Box-plot counting" (Método de contagem de caixas. OBJETIVO: O objetivo do estudo foi tentar estabelecer a contribuição da DF na quantificação da rejeição celular miocárdica após o transplante cardíaco. MÉTODOS: Imagens microscópicas digitalizadas foram capturadas na resolução 800x600 (aumento de 100x. A DF foi calculada com auxílio do "software ImageJ", com adaptações. A classificação dos graus de rejeição foi de acordo com a "Sociedade Internacional de Transplante Cardíaco e Pulmonar" (ISHLT 2004. O relatório final do grau de rejeição foi confirmado e redefinido após exaustiva revisão das lâminas por um patologista experiente externo. No total, 658 lâminas foram avaliadas, com a seguinte distribuição entre os graus de rejeição (R: 335 (0R, 214 (1R, 70 (2R, 39 (3R. Os dados foram analisados estatisticamente com os testes Kruskal-Wallis e curvas ROC sendo considerados significantes valores de P INTRODUCTION: The term "Fractal" is derived from the Latin fractus meaning "irregular" or "broken" considering the observed structure with a non-integer dimension. There are many studies which employed the Fractal Dimension (FD as a diagnostic tool. One of the most common methods for its study is the "Box Counting Method". OBJECTIVE: The aim of the present study was to try to establish the contribution of FD in the quantification of myocardial cellular rejection after cardiac transplantation. METHODS: Microscopic digital images were captured at 800x600 resolution (magnification 100x. FD was calculated with the aid of "ImageJ software" with adaptations. The classification of the degrees of rejection was in
Contribution to fractal Analysis of cities : A Study of metropolitan Area of Milan
Directory of Open Access Journals (Sweden)
Rabino Giovanni
2004-04-01
Full Text Available La présentation de l'analyse fractale de l'aire métropolitaine de Milan part de la description historique de l'évolution du processus d'urbanisation de la ville, de manière à pouvoir mettre en évidence des zones précises, homogènes du point de vue historique, qui seront analysées dans la suite par le biais de la technique fractale. L'analyse fractale de la ville de Milan est menée selon trois approches : l'étude du périmètre de la ville, qui utilise la méthode de la dilatation pour extraire le périmètre et l'analyse de corrélation pour calculer sa dimension fractale ; l'étude de la surface urbanisée dans son ensemble, qui utilise l'analyse de corrélation, de dilatation et du quadrillage ; l'étude de certaines zones de la ville qui ont été décrites dans la première partie de la présentation ; les résultats sont présentés avec une attention particulière au rapport entre la valeur de la dimension fractale et le contexte urbain pour lequel elle est calculée, ainsi qu'à la comparaison des dimensions fractales des différentes zones urbaines prises en considération.
[Chaos and fractals and their applications in electrocardial signal research].
Jiao, Qing; Guo, Yongxin; Zhang, Zhengguo
2009-06-01
Chaos and fractals are ubiquitous phenomena of nature. A system with fractal structure usually behaves chaos. As a complicated nonlinear dynamics system, heart has fractals structure and behaves as chaos. The deeper inherent mechanism of heart can be opened out when the chaos and fractals theory is utilized in the research of the electrical activity of heart. Generally a time series of a system was used for describing the status of the strange attractor of the system. The indices include Poincare plot, fractals dimension, Lyapunov exponent, entropy, scaling exponent, Hurst index and so on. In this article, the basic concepts and the methods of chaos and fractals were introduced firstly. Then the applications of chaos and fractals theories in the study of electrocardial signal were expounded with example of how they are used for ventricular fibrillation.
Cheng, Jun; Sun, Jing; Huang, Yun; Zhou, Junhu; Cen, Kefa
2014-10-01
The effects of ultrasonic treatment on fractal microstructures of wet microalgal cells were investigated for lipid extraction. Fractal dimension of cells with distorted surfaces increased with power and ultrasonication time. Microalgal cells shrank owing to dehydration and cytomembranes were reduced to debris, but cell walls were not fragmented. When ultrasonication power increased from 0 to 500W for 30min, the fractal dimension of cells increased from 1.21 to 1.51, cell sizes decreased from 2.78 to 1.68μm and cell wall thickness decreased from 0.08 to 0.05μm. When ultrasonication time increased from 5 to 30min with a power of 150W, the fractal dimension of cells increased from 1.24 to 1.37, cell sizes decreased from 2.72 to 2.38μm and cell wall thickness first increased to a peak of 0.22μm and then decreased. Long-chain and unsaturated lipids were degraded into short-chain and saturated lipids with ultrasonic cavitation. Copyright © 2014 Elsevier Ltd. All rights reserved.
Evaluation of 3D Printer Accuracy in Producing Fractal Structure.
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.
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
Fractal analysis of fractures and microstructures in rocks
International Nuclear Information System (INIS)
Merceron, T.; Nakashima, S.; Velde, B.; Badri, A.
1991-01-01
Fractal geometry was used to characterize the distribution of fracture fields in rocks, which represent main pathways for material migration such as groundwater flow. Fractal investigations of fracture distribution were performed on granite along Auriat and Shikoku boreholes. Fractal dimensions range between 0.3 and 0.5 according to the different sets of fracture planes selected for the analyses. Shear, tension and compressional modes exhibit different fractal values while the composite fracture patterns are also fractal but with a different, median, fractal value. These observations indicate that the fractal method can be used to distinguish fracture types of different origins in a complex system. Fractal results for Shikoku borehole also correlate with geophysical parameters recorded along, drill-holes such as resistivity and possibly permeability. These results represent the first steps of the fractal investigation along drill-holes. Future studies will be conducted to verify relationships between fractal dimensions and permeability by using available geophysical data. Microstructures and microcracks were analysed in the Inada granite. Microcrack patterns are fractal but fractal dimensions values vary according to both mineral type and orientations of measurement within the mineral. Microcracks in quartz are characterized by more irregular distribution (average D = 0.40) than those in feldspars (D = 0.50) suggesting a different mode of rupture. Highest values of D are reported along main cleavage planes for feldspars or C axis for quartz. Further fractal investigations of microstructure in granite will be used to characterize the potential pathways for fluid migration and diffusion in the rock matrix. (author)
Ion-mixing-induced fractal growth in thin alloy films
Energy Technology Data Exchange (ETDEWEB)
Liu Baixin (Dept. of Materials Science and Engineering, Tsinghua Univ., Beijing (China) Center of Condensed Matter and Radiation Physics, CCAST (World Lab.), Beijing (China))
1991-07-01
Fractal patterns were observed in Ni-Mo and Ag-Co multilayers after ion mixing to a critical dose. The formation of these fractals was through a multinucleation growth process similar to the cluster-diffusion-limited aggregation (CDLA). The Ni-Mo fractals had a fractal dimension of 1.72, being the same as predicted by the CDLA model, while the Co fractals on Ag-Co films had a smaller dimension, because of the magnetic interaction among the aggregating particles. Another study was performed on four magnetic metals, i.e. Fe, Co, Cr and Ni, under similar conditions and a linear correlation between the fractal dimension and the magneton number was discovered. A new fractal structure, i.e. the discontinuously branching tree morphology (DBTM), was formed by interfacial mixing of AgCo/NaCl layered samples. The DBTM patterns emerging in AgCo films consisted of many NaCl single crystals and shared some common features with the Lattice Animals, e.g. the dimension was around 1.59. A semiquantitative analysis was completed to interpret that the fractal dimension increased with increasing ion dose. (orig.).
Comprehensive Fractal Description of Porosity of Coal of Different Ranks
Ren, Jiangang; Zhang, Guocheng; Song, Zhimin; Liu, Gaofeng; Li, Bing
2014-01-01
We selected, as the objects of our research, lignite from the Beizao Mine, gas coal from the Caiyuan Mine, coking coal from the Xiqu Mine, and anthracite from the Guhanshan Mine. We used the mercury intrusion method and the low-temperature liquid nitrogen adsorption method to analyze the structure and shape of the coal pores and calculated the fractal dimensions of different aperture segments in the coal. The experimental results show that the fractal dimension of the aperture segment of lignite, gas coal, and coking coal with an aperture of greater than or equal to 10 nm, as well as the fractal dimension of the aperture segment of anthracite with an aperture of greater than or equal to 100 nm, can be calculated using the mercury intrusion method; the fractal dimension of the coal pore, with an aperture range between 2.03 nm and 361.14 nm, can be calculated using the liquid nitrogen adsorption method, of which the fractal dimensions bounded by apertures of 10 nm and 100 nm are different. Based on these findings, we defined and calculated the comprehensive fractal dimensions of the coal pores and achieved the unity of fractal dimensions for full apertures of coal pores, thereby facilitating, overall characterization for the heterogeneity of the coal pore structure. PMID:24955407
Fractal structures and fractal functions as disease indicators
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.
International Nuclear Information System (INIS)
Guo Bin; Han Gaoyi; Li Miaoyu; Zhao Shizhen
2010-01-01
The ultrafine polymethylmethacrylate fibers containing gold nanoparticles have been prepared by using the electrospinning technique. Then the continuously coarse gold films formed by fractal-like thorny gold particles were deposited on the organic eletrospun fiber surface by an electroless process. The morphology of coarse gold films was characterized by scanning electron and transmission electron microscopy. The results revealed that the morphology of the gold particles was affected not only by the amount of gold seeds embedded in the organic fibers but also by the amount of gold deposited on the fiber's surfaces. The surface-enhanced Raman scattering (SERS) effect of the fibrous mats coated with gold films was evaluated by using Rhodamine B as an adsorbate. The results indicated that this kind of fibrous mat exhibited high and reproducible SERS activity and could be developed as highly sensitive SERS substrate.
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...... vasculature may affect the retinal response to potential vascular disease in later life....
Fractal analysis of scatter imaging signatures to distinguish breast pathologies
Eguizabal, Alma; Laughney, Ashley M.; Krishnaswamy, Venkataramanan; Wells, Wendy A.; Paulsen, Keith D.; Pogue, Brian W.; López-Higuera, José M.; Conde, Olga M.
2013-02-01
Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object's complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons.
Retinal fractals and acute lacunar stroke.
Cheung, Ning; Liew, Gerald; Lindley, Richard I; Liu, Erica Y; Wang, Jie Jin; Hand, Peter; Baker, Michelle; Mitchell, Paul; Wong, Tien Y
2010-07-01
This study aimed to determine whether retinal fractal dimension, a quantitative measure of microvascular branching complexity and density, is associated with lacunar stroke. A total of 392 patients presenting with acute ischemic stroke had retinal fractal dimension measured from digital photographs, and lacunar infarct ascertained from brain imaging. After adjusting for age, gender, and vascular risk factors, higher retinal fractal dimension (highest vs lowest quartile and per standard deviation increase) was independently and positively associated with lacunar stroke (odds ratio [OR], 4.27; 95% confidence interval [CI], 1.49-12.17 and OR, 1.85; 95% CI, 1.20-2.84, respectively). Increased retinal microvascular complexity and density is associated with lacunar stroke.
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.
The application of fractals to Xiazhuang uranium ore field
International Nuclear Information System (INIS)
Li She; Guan Taiyang; Chinese Academy of Sciences, Guiyang; Pan Jiayong; Cao Shuanglin; Nanjing Univ., Nanjing
2006-01-01
Fractal theory is utilized to study spatial distribution features of uranium deposits in Xiazhuang region. The results show that the spatial distribution of uranium deposits has self-similarity statistically and the distribution regularity of uranium deposits can be quantitatively described with fractal dimension. The fractal dimension value of spatial distribution of uranium deposits are calculated with counting box method. The dimension value of different metallogenic regions are compared. The results show that the number of box correlates well to the scale with a correlation coefficient of more than 0.98. (authors)
Is the co-seismic slip distribution fractal?
Milliner, Christopher; Sammis, Charles; Allam, Amir; Dolan, James
2015-04-01
Co-seismic along-strike slip heterogeneity is widely observed for many surface-rupturing earthquakes as revealed by field and high-resolution geodetic methods. However, this co-seismic slip variability is currently a poorly understood phenomenon. Key unanswered questions include: What are the characteristics and underlying causes of along-strike slip variability? Do the properties of slip variability change from fault-to-fault, along-strike or at different scales? We cross-correlate optical, pre- and post-event air photos using the program COSI-Corr to measure the near-field, surface deformation pattern of the 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes in high-resolution. We produce the co-seismic slip profiles of both events from over 1,000 displacement measurements and observe consistent along-strike slip variability. Although the observed slip heterogeneity seems apparently complex and disordered, a spectral analysis reveals that the slip distributions are indeed self-affine fractal i.e., slip exhibits a consistent degree of irregularity at all observable length scales, with a 'short-memory' and is not random. We find a fractal dimension of 1.58 and 1.75 for the Landers and Hector Mine earthquakes, respectively, indicating that slip is more heterogeneous for the Hector Mine event. Fractal slip is consistent with both dynamic and quasi-static numerical simulations that use non-planar faults, which in turn causes heterogeneous along-strike stress, and we attribute the observed fractal slip to fault surfaces of fractal roughness. As fault surfaces are known to smooth over geologic time due to abrasional wear and fracturing, we also test whether the fractal properties of slip distributions alters between earthquakes from immature to mature fault systems. We will present results that test this hypothesis by using the optical image correlation technique to measure historic, co-seismic slip distributions of earthquakes from structurally mature, large
Assessment of the dimensions and surface characteristics of orthodontic wires and bracket slots
Directory of Open Access Journals (Sweden)
Gabriel Schmidt Dolci
2013-04-01
Full Text Available OBJECTIVE: The purpose of this study was to evaluate the dimensions and surface characteristics of orthodontic wires and bracket slots of different commercial brands. METHODS: Thirty metallic brackets (0.022 x 0.028-in and 0.022 x 0.030-in were divided in three groups: DYN/3M group = Dyna-Lock, 3M/Unitek (stainless steel, or SS; STD/MO group = Slim Morelli (SS; and Ni-Free/MO group = Slim Morelli (Ni-Free. The stainless steel wires (0.019 x 0.025in were divided into two groups: MO group = Morelli; and 3M group = 3M/Unitek. The bracket and wire measurements were done by two methods: (a Surface Electron Microscopy (SEM, and (b Profile projection. The surface analysis was done qualitatively, based on SEM images and/or by a rugosimeter. The quantitative results were analyzed by ANOVA with Tukey's test (p < 0.05 and Student's t test. RESULTS: A significant difference in the dimensions of slots was observed, and the NiFree/MO group showed the greatest changes when compared to the other groups. The analysis of surface topography of the brackets indicated greater homogeneity of the metallic matrix for DYN/3M and STD/MO groups. As for the dimensions of the wires, groups showed statistically different mean heights. CONCLUSIONS: It was concluded that wires and brackets slots can present altered dimensions, which might directly and unintentionally affect the planned tooth movement.
Dimension of surface microstructure as an osteogenic factor in calcium phosphate ceramics
Zhang, Jingwei; Luo, Xiaoman; Barbieri, D.; Barradas, A.M.C.; de Bruijn, Joost Dick; van Blitterswijk, Clemens; Yuan, Huipin
2014-01-01
Microporosity of calcium phosphate (CaP) ceramics has shown its essential role in osteoinduction by CaP ceramics after ectopic implantation. Here we show that not the microporosity but the dimension of surface microstructural features is likely the osteogenic factor. Two tricalcium phosphate
Explicit Spectral Decimation for a Class of Self-Similar Fractals
Directory of Open Access Journals (Sweden)
Sergio A. Hernández
2013-01-01
Full Text Available The method of spectral decimation is applied to an infinite collection of self-similar fractals. The sets considered are a generalization of the Sierpinski Gasket to higher dimensions; they belong to the class of nested fractals and are thus very symmetric. An explicit construction is given to obtain formulas for the eigenvalues of the Laplace operator acting on these fractals.
Fractal Property in the Light Curve of BL Lac Object S5 0716+714
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... In this paper, we compile the historical R-band data of S5 0716+714 from literature and obtain its fractal dimension by using a fractal method and then simulate the data with the Weierstrass–Mandelbrot (W–M) function. It is considered that the light curve has a fractal property.
Fractal Property in the Light Curve of BL Lac Object S5 0716+ 714
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... In this paper, we compile the historical R-band data of S5 0716+714 from literature and obtain its fractal dimension by using a fractal method and then simulate the data with the Weierstrass–Mandelbrot (W–M) function. It is considered that the light curve has a fractal property.
Separation in Data Mining Based on Fractal Nature of Data
Czech Academy of Sciences Publication Activity Database
Jiřina, Marcel; Jiřina jr., M.
2013-01-01
Roč. 3, č. 1 (2013), s. 44-60 ISSN 2225-658X Institutional support: RVO:67985807 Keywords : nearest neighbor * fractal set * multifractal * IINC method * correlation dimension Subject RIV: JC - Computer Hardware ; Software http://sdiwc.net/digital-library/separation-in-data-mining-based-on- fractal -nature-of-data.html
Separation in Data Mining Based on Fractal Nature of Data
Czech Academy of Sciences Publication Activity Database
Jiřina, Marcel; Jiřina jr., M.
2013-01-01
Roč. 3, č. 1 (2013), s. 44-60 ISSN 2225-658X Institutional support: RVO:67985807 Keywords : nearest neighbor * fractal set * multifractal * IINC method * correlation dimension Subject RIV: JC - Computer Hardware ; Software http://sdiwc.net/digital-library/separation-in-data-mining-based-on-fractal-nature-of-data.html
An event driven algorithm for fractal cluster formation
González, S.; Thornton, Anthony Richard; Luding, Stefan
2010-01-01
A new cluster based event-driven algorithm is developed to simulate the formation of clusters in a two dimensional gas: particles move freely until they collide and "stick" together irreversibly. These clusters aggregate into bigger structures in an isotompic way, forming fractal structures whose fractal dimension depends on the initial density of the system.
Random fractal characters and length uncertainty of the continental ...
Indian Academy of Sciences (India)
A coastline is a random fractal object in a geographical system whose length is uncertain. To determine the coastline length of a country or a region, the scaling region and fractal dimension of the coastline is first calculated, and then, the length of the coastline is measured using the scale at the lower limit or near the limit of ...
Synergetics and fractals in tribology
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.
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.
Directory of Open Access Journals (Sweden)
W. Y. Xu
2016-09-01
Full Text Available Landslides are one of the major natural disasters that are frequently occurring in southwestern China. The main objective of this study is to investigate the relationship between failure of landslide and fractal dimension using displacement time-series. Taking two slopes in southwestern China as examples, we estimate the fractal parameters of displacement time-series and analyze the relationship between fractal dimension and the stability of the slope during the evolution of landslides. The result shows that the fractal dimension increases when a landslide undergoes a transition from stability to failure, but decreases during the evolution from active to stable. Fractal dimension has a critical value of 1.10 in the transition between active and stable, which indicates that fractal dimension is an important nonlinear parameter in the evaluation of the stability of landslides, although more studies and in situ data are required for validation.
Assessment of textural differentiations in forest resources in Romania using fractal analysis
DEFF Research Database (Denmark)
Andronache, Ion; Fensholt, Rasmus; Ahammer, Helmut
2017-01-01
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...
Mapping physical problems on fractals onto boundary value problems within continuum framework
Balankin, Alexander S.
2018-01-01
In this Letter, we emphasize that methods of fractal homogenization should take into account a loop structure of the fractal, as well as its connectivity and geodesic metric. The fractal attributes can be quantified by a set of dimension numbers. Accordingly, physical problems on fractals can be mapped onto the boundary values problems in the fractional-dimensional space with metric induced by the fractal topology. The solutions of these problems represent analytical envelopes of non-analytical functions defined on the fractal. Some examples are briefly discussed. The interplay between effects of fractal connectivity, loop structure, and mass distributions on electromagnetic fields in fractal media is highlighted. The effects of fractal connectivity, geodesic metric, and loop structure are outlined.
Barton, Ray
1990-01-01
Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)
Chaos, Fractals, and Polynomials.
Tylee, J. Louis; Tylee, Thomas B.
1996-01-01
Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)
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...
Thamrin, Cindy; Stern, Georgette; Frey, Urs
2010-06-01
There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment. Copyright 2010 Elsevier Ltd. All rights reserved.
Fractal analysis for osteoporosis: a likelihood ratio approach
Directory of Open Access Journals (Sweden)
Jessica B. Lepschy
2010-01-01
Full Text Available Based on the traditional fractal theory and on the paper of Stehlík, (2009 the range of fractal dimension of osteoporosis vertebras is analysed. First we give an insight into the field of fractals and the usage of fractals in medicine. After this we show how the analytical tool of Stehlík, (2009 may be applied to the osteoporosis vertebras. It turns out that the used method can be applied very well and that it could help with medical diagnosis. Real data example illustrates the methods discussed.
Directory of Open Access Journals (Sweden)
Adewale Amosu
2018-02-01
Full Text Available Reservoir modeling of carbonate rocks requires a proper understanding of the pore space distribution and its relationship to permeability. Using a pigeonhole fractal model we characterize the fractal geometry of moldic pore spaces and extract the fractal dimension. We apply the Kozeny-Carman equation and equations relating the tortuosity and the porosity to the fractal dimension to derive an empirical relationship between permeability and porosity.
Passenger flow analysis of Beijing urban rail transit network using fractal approach
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.
Goñi, Joaquín; Sporns, Olaf; Cheng, Hu; Aznárez-Sanado, Maite; Wang, Yang; Josa, Santiago; Arrondo, Gonzalo; Mathews, Vincent P; Hummer, Tom A; Kronenberger, William G; Avena-Koenigsberger, Andrea; Saykin, Andrew J; Pastor, María A
2013-12-01
High-resolution isotropic three-dimensional reconstructions of human brain gray and white matter structures can be characterized to quantify aspects of their shape, volume and topological complexity. In particular, methods based on fractal analysis have been applied in neuroimaging studies to quantify the structural complexity of the brain in both healthy and impaired conditions. The usefulness of such measures for characterizing individual differences in brain structure critically depends on their within-subject reproducibility in order to allow the robust detection of between-subject differences. This study analyzes key analytic parameters of three fractal-based methods that rely on the box-counting algorithm with the aim to maximize within-subject reproducibility of the fractal characterizations of different brain objects, including the pial surface, the cortical ribbon volume, the white matter volume and the gray matter/white matter boundary. Two separate datasets originating from different imaging centers were analyzed, comprising 50 subjects with three and 24 subjects with four successive scanning sessions per subject, respectively. The reproducibility of fractal measures was statistically assessed by computing their intra-class correlations. Results reveal differences between different fractal estimators and allow the identification of several parameters that are critical for high reproducibility. Highest reproducibility with intra-class correlations in the range of 0.9-0.95 is achieved with the correlation dimension. Further analyses of the fractal dimensions of parcellated cortical and subcortical gray matter regions suggest robustly estimated and region-specific patterns of individual variability. These results are valuable for defining appropriate parameter configurations when studying changes in fractal descriptors of human brain structure, for instance in studies of neurological diseases that do not allow repeated measurements or for disease
Fraboni, Michael; Moller, Trisha
2008-01-01
Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…
Heritability of retinal vascular fractals: a twin study
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
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-degree, disc-centred fundus photographs from 59 monozygotic and 55 dizygotic, same-sex twin pairs aged 20-46 years....... 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...... vascular fractal dimensions were measurable for both twins in 50 monozygotic and 49 dizygotic twin pairs. 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...
Coskun, Aycan; Sonmez, Harun; Ercin Kasapoglu, K.; Ozge Dinc, S.; Celal Tunusluoglu, M.
2010-05-01
dimensions. To determine fractal dimensions of more than hundred andesite blocks in cores, a computer program namely FRACRUN were developed. Fractal geometry has been used as practical and popular tool to define particularly irregular shaped bodies in literature since the theory of fractal was developed by Mandelbrot (1967) (Hyslip and Vallejo, 1997; Kruhl and Nega, 1996; Bagde etal., 2002; Gulbin and Evangulova, 2003; Pardini, 2003; Kolay and Kayabali, 2006; Hamdi, 2008; Zorlu, 2009 and Sezer, 2009). Although there are some methods to determine fractal dimensions, square grid-cell count method for 2D and segment count method for 1D were followed in the algorithm of FRACRUN. FRACRUN has capable of determine fractal dimensions of many closed polygons on a single surface. In the study, a database composed of uniaxial compressive strength, volumetric block proportion, fractal dimensions and number of blocks for each core was established. Finally, prediction models were developed by regression analyses and compared with the empirical equations proposed by Sonmez et al. (2006). Acknowledgement This study is a product of ongoing project supported by TUBITAK (The Scientific and Technological Research Council of Turkey - Project No: 108Y002). References Bagde, M.N., Raina, A.K., Chakraborty, A.K., Jethwa, J.L., 2002. Rock mass characterization by fractal dimension. Engineering Geology 63, 141-155. Gokceoglu, C., 2002. A fuzzy triangular chart to predict the uniaxial compressive strength of the Ankara agglomerates from their petrographic composition. Engineering Geology, 66 (1-2), 39-51. Gulbin, Y.L., Evangulova, E.B., 2003. Morphometry of quartz aggregates in granites: fractal images referring to nucleation and growth processes. Mathematical Geology 35 (7), 819-833 Hamdi, E., 2008. A fractal description of simulated 3D discontinuity networks. Rock Mechanics and Rock Engineering 41, 587-599. Hyslip, J.P., Vallejo, L.E., 1997. Fractals analysis of the roughness and size distribution
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
Fractal analysis of polyferric chloride-humic acid (PFC-HA) flocs in different topological spaces.
Wang, Yili; Lu, Jia; Baiyu, Du; Shi, Baoyou; Wang, Dongsheng
2009-01-01
The fractal dimensions in different topological spaces of polyferric chloride-humic acid (PFC-HA) flocs, formed in flocculating different kinds of humic acids (HA) water at different initial pH (9.0, 7.0, 5.0) and PFC dosages, were calculated by effective density-maximum diameter, image analysis, and N2 absorption-desorption methods, respectively. The mass fractal dimensions (Df) of PFC-HA flocs were calculated by bi-logarithm relation of effective density with maximum diameter and Logan empirical equation. The Df value was more than 2.0 at initial pH of 7.0, which was 11% and 13% higher than those at pH 9.0 and 5.0, respectively, indicating the most compact flocs formed in flocculated HA water at initial pH of 7.0. The image analysis for those flocs indicates that after flocculating the HA water at initial pH greater than 7.0 with PFC flocculant, the fractal dimensions of D2 (logA vs. logdL) and D3 (logVsphere VS. logdL) of PFC-HA flocs decreased with the increase of PFC dosages, and PFC-HA flocs showed a gradually looser structure. At the optimum dosage of PFC, the D2 (logA vs. logdL) values of the flocs show 14%-43% difference with their corresponding Df, and they even had different tendency with the change of initial pH values. However, the D2 values of the flocs formed at three different initial pH in HA solution had a same tendency with the corresponding Dr. Based on fractal Frenkel-Halsey-Hill (FHH) adsorption and desorption equations, the pore surface fractal dimensions (Ds) for dried powders of PFC-HA flocs formed in HA water with initial pH 9.0 and 7.0 were all close to 2.9421, and the Ds values of flocs formed at initial pH 5.0 were less than 2.3746. It indicated that the pore surface fractal dimensions of PFC-HA flocs dried powder mainly show the irregularity from the mesopore-size distribution and marcopore-size distribution.
Dynamic structure factor of vibrating fractals.
Reuveni, Shlomi; Klafter, Joseph; Granek, Rony
2012-02-10
Motivated by novel experimental work and the lack of an adequate theory, we study the dynamic structure factor S(k,t) of large vibrating fractal networks at large wave numbers k. We show that the decay of S(k,t) is dominated by the spatially averaged mean square displacement of a network node, which evolves subdiffusively in time, ((u[over →](i)(t)-u[over →](i)(0))(2))∼t(ν), where ν depends on the spectral dimension d(s) and fractal dimension d(f). As a result, S(k,t) decays as a stretched exponential S(k,t)≈S(k)e(-(Γ(k)t)(ν)) with Γ(k)∼k(2/ν). Applications to a variety of fractal-like systems are elucidated.
NEW METHOD FOR ACTIVE SURFACES QUALITY INSPECTION FOR HIGH DIMENSIONS BEARINGS
Directory of Open Access Journals (Sweden)
BRAUN Barbu
2016-07-01
Full Text Available The paper presents a stage of an ample research on high quality control for different type of large dimension bearings, with application in wind turbines for electrical energy production. There is presented a new and efficient method for bearing’s active surfaces quality control, in terms of roughness, to ensure a good and safety functioning and a long life of these. The research involved the use of a powerful digital microscope for surface analysis followed by an assisted by PC algorithm for results obtaining in terms of roughness values. It has been observed that the proposed analyzing method could in the future to be successfully applied for a very large range of bearings, different dimensions and applications.
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...
Fractals properties of EEG during event-related desynchronization of motor imagery.
Nguyen, Ngoc Quang; Truong, Quang Dang Khoa; Kondo, Toshiyuki
2015-01-01
Chaos and fractal dimension are emerging modalities for the research of electroencephalogram (EEG) signal processing. The capability of measuring non-linear characteristics of the fractal dimension enables new methodologies to identify distinct brain activities. Recent studies on the topic focus on utilizing various types of fractals as features in order to design better brain state classification system. However, we have little insight about the EEG signals projected in fractal dimension. In this paper, we investigate the relationship between the non-linear characteristics of ongoing EEG signals and event-related desynchronization (ERD) during motor imagery. We observed a considerable synchronization between ERD and fractal dimension. This finding suggests further usage of chaos and fractal theory in investigating brain activities.
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
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......: 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...... by a certified grader, and fractal dimensions were calculated using the box-counting method. At follow-up (in 2011), diabetic neuropathy, nephropathy and proliferative retinopathy were assessed and related to baseline fractal dimensions in multiple regressions adjusted for sex and baseline age, diabetes duration...
Prediction of osteoporosis using fractal analysis on periapical radiographs
Energy Technology Data Exchange (ETDEWEB)
Park, Gum Mi; Jung, Yun Hoa; Nah, Kyung Soo [Pusan National University College of Medicine, Busan (Korea, Republic of)
2005-03-15
To purpose of this study was to investigate whether the fractal dimension and radiographic image brightness of periapical radiograph were useful in predicting osteoporosis. Ninety-two postmenopausal women were classified as normal, osteopenia and osteoporosis group according to the bone mineral density of lumbar vertebrae and periapical radiographs of both mandibular molar areas were taken. The ROIs of 358 areas were selected at periapical and interdental areas and fractal dimension and radiographic image brightness were measured. The fractal dimension in normal group was significantly higher than that in osteoporosis group at periapical ROI (p<0.05). The radiographic image brightness in normal group was higher than that in osteopenia and osteoporosis group. There was significant difference not only between normal and osteopenia group (p<0.05) but also within osteopenia and osteoporosis group (p<0.01) at periapical ROI. Significant difference was observed not only between normal and osteopenia group but also between normal and osteoporosis group at interdental ROI (p<0.01). Positive linear relationship was weakly shown at Pearson correlation analysis between fractal dimension and radiographic image brightness. BMD significantly correlated with fractal dimension at periapical ROI (p<0.01), and BMD and radiographic image brightness significantly correlated at both periapical and interdental ROIs (p<0.01). This study suggests that the fractal dimension and radiographic image brightness of periapical ROI may predict BMD.
Textural characterization of chars using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Mahamud, Manuel; Lopez, Oscar [Department of Chemical and Environmental Engineering, Faculty of Chemistry, University of Oviedo, Campus de El Cristo, 33071 Oviedo (Spain); Pis, Jose Juan; Pajares, Jesus Alberto [Instituto Nacional del Carbon C.S.I.C., Apartado 73, 33080 Oviedo (Spain)
2004-11-25
The aim of this study is to explore the potential of fractal analysis in helping to understand the textural changes of materials during the manufacture of active carbons. Textural characterization of the chars is carried out in order to obtain a better understanding of the phenomena underlying char formation. The materials selected for study were a series of chars obtained from coals oxidized in air at various temperatures for different periods of time. The data from mercury porosimetry were analyzed using fractal models. The average fractal dimensions for the chars were calculated by using the methods proposed by Friesen and Mikula and that of Zhang and Li. Fractal profiles of the chars obtained by the method of Neimark were compared with the corresponding fractal profiles of the precursor coals. Pore development during carbonization depends-among other factors that are kept constant in this study-on the textural properties of the precursor coal, the devolatilization process and the plastic properties of coals. The evolution of the fractal characteristics of the chars is also studied. At the same time pore volume development is analyzed. These analyses help to clarify the role that various phenomena occurring during carbonization have on the textural properties of the chars.
Solar Cycle Phase Dependence of Supergranular Fractal ...
Indian Academy of Sciences (India)
Solar Cycle Phase Dependence of Supergranular Fractal Dimension. U. Paniveni1,2,∗. , V. Krishan2, J. Singh2 & R. Srikanth3,4. 1NIE Institute of Technology, Mysore, India. 2Indian Institute of Astrophysics, Bangalore, India. 3Poornaprajna Institute of Research, 4 Sadashivnagar, Bangalore, India. 4Optics Group, Raman ...
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
... in Nigeria) showed good correlation with the geological maps of the areas. The results also indicated that basement rocks can generally be represented by scaling exponents with values ranging between -3.0 and -2.0. Keywords: Fractal, dimension, susceptibility, spectra, scaling exponent. Nigerian Journal of Physics Vol.
Fractal structures and intermittency in QCD
International Nuclear Information System (INIS)
Gustafson, Goesta.
1990-04-01
New results are presented for fractal structures and intermittency in QCD parton showers. A geometrical interpretation of the anomalous dimension in QCD is given. It is shown that model predications for factorial moments in the PEP-PETRA energy range are increased. if the properties of directly produced pions are more carefully taken into account
DEFF Research Database (Denmark)
Teisbæk, Henrik Bjørn; Jakobsen, Kaj Bjarne
2009-01-01
A Yagi-Uda antenna constructed of three Koch fractal elements is presented. Simulated and measured characteristics of the antenna shows a half-power beam-width of 64◦ achieved with dimensions below a third of a wavelength. Furthermore, the Koch dipole and its size miniaturization capabilities are...
An Explanation for the Arctic Sea Ice Melt Pond Fractal Transition
Popovic, P.; Abbot, D. S.
2016-12-01
As Arctic sea ice melts during the summer, pools of melt water form on its surface. This decreases the ice's albedo, which signifcantly impacts its subsequent evolution. Understanding this process is essential for buiding accurate sea ice models in GCMs and using them to forecast future changes in sea ice. A feature of melt ponds that helps determine their impact on ice albedo is that they often form complex geometric shapes. One characteristic of their shape, the fractal dimension of the pond boundaries, D, 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 taken during the SHEBA mission, 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. While ice is impermeable, the maximum fractal dimension is less than 2, whereas after it becomes permeable, the maximum fractal dimension becomes very close to 2. We then show how the fractal dimension of the boundary 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. Previously, this length scale has been associated with the typical size of snow dunes created on the ice surface during winter. We provide an alternative explanation 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. Finally, we provide some remarks on how to observationally distinguish between the two ideas for what
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 Image Informatics: from SEM to DEM
Oleschko, K.; Parrot, J.-F.; Korvin, G.; Esteves, M.; Vauclin, M.; Torres-Argüelles, V.; Salado, C. Gaona; Cherkasov, S.
2008-05-01
In this paper, we introduce a new branch of Fractal Geometry: Fractal Image Informatics, devoted to the systematic and standardized fractal analysis of images of natural systems. The methods of this discipline are based on the properties of multiscale images of selfaffine fractal surfaces. As proved in the paper, the image inherits the scaling and lacunarity of the surface and of its reflectance distribution [Korvin, 2005]. We claim that the fractal analysis of these images must be done without any smoothing, thresholding or binarization. Two new tools of Fractal Image Informatics, firmagram analysis (FA) and generalized lacunarity (GL), are presented and discussed in details. These techniques are applicable to any kind of image or to any observed positive-valued physical field, and can be used to correlate between images. It will be shown, by a modified Grassberger-Hentschel-Procaccia approach [Phys. Lett. 97A, 227 (1983); Physica 8D, 435 (1983)] that GL obeys the same scaling law as the Allain-Cloitre lacunarity [Phys. Rev. A 44, 3552 (1991)] but is free of the problems associated with gliding boxes. Several applications are shown from Soil Physics, Surface Science, and other fields.
FRACTAL ANALYSIS OF FRACTURE SYSTEMS IN UPPER TRIASSIC DOLOMITES IN ŽUMBERAK MOUNTAIN, CROATIA
Directory of Open Access Journals (Sweden)
Ivica Pavičić
2017-01-01
Full Text Available This paper presents results of fractal analysis of fracture systems in upper Triassic dolomites in Žumberak Mountain, Croatia. Mechanical rock characteristics together with structural and diagenetic processes results with fracture systems that can be considered as fractals. They are scale-invariant in specific range of scales. Distribution of fractures can be than described with power law distribution and fractal dimension. Fractal dimension is a measure of how fractures fill the space. Fractal dimension can be estimated form photographs of outcrops by converting photographs to binary photographs. In binary photo there is only black (rock or fractures and white (fractures or rock. Fractal dimension is then estimated based on box-counting method. In this paper we present results of fractal analysis from three outcrops. Results are very similar to previous published results from outcrops of dolomites in Slovenia. Obtained fractal dimensions are in range 2,69-2,78 and it depends on how fracture systems are distributed in the outcrop. Lower values indicate smaller number of fractures and higher significance of larger fractures. Higher values indicate distribution of more similar sized fractures throughout whole outcrop. Fractal dimension is very significant parameter in rock fracture system characterisation sense it describes how fractures are distributed in the outcrop. It can be used in discrete fracture network modelling if spatial distribution of fractures is represented with power law distribution.
Gao, Guang-Lei; Ding, Guo-Dong; Wu, Bin; Zhang, Yu-Qing; Qin, Shu-Gao; Zhao, Yuan-Yuan; Bao, Yan-Feng; Liu, Yun-Dong; Wan, Li; Deng, Ji-Feng
2014-01-01
Background Biological soil crusts are common components of desert ecosystem; they cover ground surface and interact with topsoil that contribute to desertification control and degraded land restoration in arid and semiarid regions. Methodology/Principal Findings To distinguish the changes in topsoil affected by biological soil crusts, we compared topsoil properties across three types of successional biological soil crusts (algae, lichens, and mosses crust), as well as the referenced sandland in the Mu Us Desert, Northern China. Relationships between fractal dimensions of soil particle size distribution and selected soil properties were discussed as well. The results indicated that biological soil crusts had significant positive effects on soil physical structure (Psoil organic carbon and nutrients showed an upward trend across the successional stages of biological soil crusts. Fractal dimensions ranged from 2.1477 to 2.3032, and significantly linear correlated with selected soil properties (R2 = 0.494∼0.955, Psoil crusts cause an important increase in soil fertility, and are beneficial to sand fixation, although the process is rather slow. Fractal dimension proves to be a sensitive and useful index for quantifying changes in soil properties that additionally implies desertification. This study will be essential to provide a firm basis for future policy-making on optimal solutions regarding desertification control and assessment, as well as degraded ecosystem restoration in arid and semiarid regions. PMID:24516668
Directory of Open Access Journals (Sweden)
Guang-Lei Gao
Full Text Available BACKGROUND: Biological soil crusts are common components of desert ecosystem; they cover ground surface and interact with topsoil that contribute to desertification control and degraded land restoration in arid and semiarid regions. METHODOLOGY/PRINCIPAL FINDINGS: To distinguish the changes in topsoil affected by biological soil crusts, we compared topsoil properties across three types of successional biological soil crusts (algae, lichens, and mosses crust, as well as the referenced sandland in the Mu Us Desert, Northern China. Relationships between fractal dimensions of soil particle size distribution and selected soil properties were discussed as well. The results indicated that biological soil crusts had significant positive effects on soil physical structure (P<0.05; and soil organic carbon and nutrients showed an upward trend across the successional stages of biological soil crusts. Fractal dimensions ranged from 2.1477 to 2.3032, and significantly linear correlated with selected soil properties (R(2 = 0.494∼0.955, P<0.01. CONCLUSIONS/SIGNIFICANCE: Biological soil crusts cause an important increase in soil fertility, and are beneficial to sand fixation, although the process is rather slow. Fractal dimension proves to be a sensitive and useful index for quantifying changes in soil properties that additionally implies desertification. This study will be essential to provide a firm basis for future policy-making on optimal solutions regarding desertification control and assessment, as well as degraded ecosystem restoration in arid and semiarid regions.
Formation of fractals by the self-assembly of interpolymer adducts of ...
Indian Academy of Sciences (India)
vinylpyrrolidone) in presence of sodium chloride or potassium chloride form highly ordered fractal patterns in films on glass surface on drying at ambient temperature. The structure, morphology and the conditions under which the formation of fractal patterns ...
Two-dimensional free-surface flow under gravity: A new benchmark case for SPH method
Wu, J. Z.; Fang, L.
2018-02-01
Currently there are few free-surface benchmark cases with analytical results for the Smoothed Particle Hydrodynamics (SPH) simulation. In the present contribution we introduce a two-dimensional free-surface flow under gravity, and obtain an analytical expression on the surface height difference and a theoretical estimation on the surface fractal dimension. They are preliminarily validated and supported by SPH calculations.
The frictional properties of a simulated gouge having a fractal particle distribution
Biegel, R.L.; Sammis, C.G.; Dieterich, J.H.
1989-01-01
The frictional properties of a layer of simulated Westerly granite fault gouge sandwiched between sliding blocks of Westerly granite have been measured in a high-speed servo-controlled double-direct shear apparatus. Most gouge layers were prepared to have a self-similar particle distribution with a fractal dimension of 2.6. The upper fractal limit was varied between 45 and 710 ??m. Some gouges were prepared with all particles in the range between 360 and 710 ??m. In each experiment the sliding velocity was cyclically alternated between 1 and 10 ??ms-1 and the coefficient of friction ??m and its transient parameters a, b and Dc were measured as functions of displacement. In addition to the particle size distribution, the following experimental variables were also investigated: the layer thickness (1 and 3 mm), the roughness of the sliding surfaces (Nos 60 and 600 grit) and the normal stress (10 and 25 MPa). Some of the sample assemblies were epoxy impregnated following a run so the gouge structure could be microscopically examined in thin section. We observed that gouges which were initially non-fractal evolved to a fractal distribution with dimension 2.6. Gouges which had an initial fractal distribution remained fractal. When the sliding blocks had smooth surfaces, the coefficient of friction was relatively low and was independent of the particle distribution. In these cases, strong velocity weakening was observed throughout the experiment and the transient parameters a, b and Dc, remained almost constant. When the sliding blocks had rough surfaces, the coefficient of friction was larger and more dependent on the particle distribution. Velocity strengthening was observed initially but evolved to velocity weakening with increased sliding displacement. All three transient parameters changed with increasing displacement. The a and b values were about three times as large for rough surfaces as for smooth. The characteristic displacement Dc was not sensitive to surface
Exploring Fractals in the Classroom.
Naylor, Michael
1999-01-01
Describes an activity involving six investigations. Introduces students to fractals, allows them to study the properties of some famous fractals, and encourages them to create their own fractal artwork. Contains 14 references. (ASK)
Fractals: To Know, to Do, to Simulate.
Talanquer, Vicente; Irazoque, Glinda
1993-01-01
Discusses the development of fractal theory and suggests fractal aggregates as an attractive alternative for introducing fractal concepts. Describes methods for producing metallic fractals and a computer simulation for drawing fractals. (MVL)
The virtual education fractality: nature and organization
Directory of Open Access Journals (Sweden)
Osbaldo Turpo Gebera
2013-04-01
Full Text Available The potential generated by ICT in education raises reflect on the underlying frameworks. In this sense, the fractal is an opportunity to explain how it organizes and manages virtual education.This approach recognizes that educational dynamics are recursive and iterative processes instituted as progressive sequences, by way of fractals. This understanding enables becoming as mediated and articulated successive levels. In each dimension are embodied own activities and in turn, involves the recurrence of subsequent levels as possible solving of problem situations. Thus, the knowledge built in response to a collaborative action, participation in networks, ranging from autonomous to the cultural level or conversely.
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
Assessment of the dimensions and surface characteristics of orthodontic wires and bracket slots.
Dolci, Gabriel Schmidt; Spohr, Ana Maria; Zimmer, Eduardo Rigon; Marchioro, Ernani Menezes
2013-01-01
The purpose of this study was to evaluate the dimensions and surface characteristics of orthodontic wires and bracket slots of different commercial brands. Thirty metallic brackets (0.022 x 0.028-in and 0.022 x 0.030-in) were divided into three groups: DYN/3M group = Dyna-Lock, 3M/Unitek (stainless steel, or SS); STD/MO group = Slim Morelli (SS); and Ni-Free/MO group = Slim Morelli (Ni-Free). The stainless steel wires (0.019 x 0.025-in) were divided into two groups: MO group = Morelli; and 3M group = 3M/Unitek. The bracket and wire measurements were done by two methods: (a) Surface Electron Microscopy (SEM), and (b) Profile Projection. The surface analysis was done qualitatively, based on SEM images and/or by a rugosimeter. The quantitative results were analyzed by ANOVA with Tukey's test (p wires, groups showed statistically different mean heights. It was concluded that wires and brackets slots can present altered dimensions, which might directly and unintentionally affect the planned tooth movement.
Representing fractals by superoscillations
International Nuclear Information System (INIS)
Berry, M V; Morley-Short, S
2017-01-01
Fractals provide an extreme test of representing fine detail in terms of band-limited functions, i.e. by superoscillations. We show that this is possible, using the example of the Weierstrass nondifferentiable fractal. If this is truncated at an arbitrarily fine scale, it can be expressed to any desired accuracy with a simple superoscillatory function. In illustrative simulations, fractals truncated with fastest frequency 2 16 are easily represented by superoscillations with fastest Fourier frequency 1. (letter)
Temporal fractals in movies and mind.
Cutting, James E; DeLong, Jordan E; Brunick, Kaitlin L
2018-01-01
Fractal patterns are seemingly everywhere. They can be analyzed through Fourier and power analyses, and other methods. Cutting, DeLong, and Nothelfer (2010) analyzed as time-series data the fluctuations of shot durations in 150 popular movies released over 70 years. They found that these patterns had become increasingly fractal-like and concluded that they might be linked to those found in the results of psychological tasks involving attention. To explore this possibility further, we began by analyzing the shot patterns of almost twice as many movies released over a century. The increasing fractal-like nature of shot patterns is affirmed, as determined by both a slope measure and a long-range dependence measure, neither of which is sensitive to the vector lengths of their inputs within the ranges explored here. But the main reason for increased long-range dependence is related to, but not caused by, the increasing vector length of the shot-series samples. It appears that, in generating increasingly fractal-like patterns, filmmakers have systematically explored dimensions that are important for holding our attention-shot durations, scene durations, motion, and sound amplitude-and have crafted fluctuations in them like those of our endogenous attention patterns. Other dimensions-luminance, clutter, and shot scale-are important to film style but their variations seem not to be important to holding viewers' moment-to-moment attention and have not changed in their fractional dimension over time.
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
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...
Rheological and fractal characteristics of unconditioned and conditioned water treatment residuals.
Dong, Y J; Wang, Y L; Feng, J
2011-07-01
The rheological and fractal characteristics of raw (unconditioned) and conditioned water treatment residuals (WTRs) were investigated in this study. Variations in morphology, size, and image fractal dimensions of the flocs/aggregates in these WTR systems with increasing polymer doses were analyzed. The results showed that when the raw WTRs were conditioned with the polymer CZ8688, the optimum polymer dosage was observed at 24 kg/ton dry sludge. The average diameter of irregularly shaped flocs/aggregates in the WTR suspensions increased from 42.54 μm to several hundred micrometers with increasing polymer doses. Furthermore, the aggregates in the conditioned WTR system displayed boundary/surface and mass fractals. At the optimum polymer dosage, the aggregates formed had a volumetric average diameter of about 820.7 μm, with a one-dimensional fractal dimension of 1.01 and a mass fractal dimension of 2.74 on the basis of the image analysis. Rheological tests indicated that the conditioned WTRs at the optimum polymer dosage showed higher levels of shear-thinning behavior than the raw WTRs. Variations in the limiting viscosity (η(∞)) of conditioned WTRs with sludge content could be described by a linear equation, which were different from the often-observed empirical exponential relationship for most municipal sludge. With increasing temperature, the η(∞) of the raw WTRs decreased more rapidly than that of the raw WTRs. Good fitting results for the relationships between lgη(∞)∼T using the Arrhenius equation indicate that the WTRs had a much higher activation energy for viscosity of about 17.86-26.91 J/mol compared with that of anaerobic granular sludge (2.51 J/mol) (Mu and Yu, 2006). In addition, the Bingham plastic model adequately described the rheological behavior of the conditioned WTRs, whereas the rheology of the raw WTRs fit the Herschel-Bulkley model well at only certain sludge contents. Considering the good power-law relationships between the
Effects of contact cap dimension on dry adhesion of bioinspired mushroom-shaped surfaces
Wang, Yue; Shao, Jinyou; Ding, Yucheng; Li, Xiangming; Tian, Hongmiao; Hu, Hong
2015-03-01
Dry adhesion observed in small creatures, such as spiders, insects, and geckos, has many great advantages such as repeatability and strong adhesiveness. In order to mimic these unique performances, fibrillar surface with a mushroom shaped end has drawn lots of attentions because of its advantage in efficiently enhancing adhesion compared with other sphere or simple flat ends. Here, in order to study the effects of contact cap dimension on adhesion strength, patterned surfaces of mushroom-shaped micropillars with differing cap diameters are fabricated based on the conventional photolithography and molding. The normal adhesion strength of these dry adhesives with varying cap diameters is measured with home-built equipment. The strength increases with the rise of cap diameter, and interestingly it becomes strongest when the mushroom caps join together.
Intergranular area microalloyed aluminium-silicate ceramics fractal analysis
Directory of Open Access Journals (Sweden)
Purenović J.
2013-01-01
Full Text Available Porous aluminium-silicate ceramics, modified by alloying with magnesium and microalloying with alluminium belongs to a group of advanced multifunctional ceramics materials. This multiphase solid-solid system has predominantly amorphous microstructure and micro morphology. Intergranular and interphase areas are very complex, because they represent areas, where numbered processes and interactions take place, making new boundaries and regions with fractal nature. Fractal analysis of intergranular microstructure has included determination of ceramic grain fractal dimension by using Richardson method. Considering the fractal nature of intergranular contacts, it is possible to establish correlation between material electrical properties and fractal analysis, as a tool for future correlation with microstructure characterization. [Projekat Ministarstva nauke Republike Srbije, br. ON 172057 i br. III 45012
Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method
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.
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
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)
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.
Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua
2016-12-01
Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.
Quantifying inhomogeneity in fractal sets
Fraser, Jonathan M.; Todd, Mike
2018-04-01
An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the ‘most difficult location and scale’ at which to cover the set and its difference from box dimension can be thought of as a first-level overall measure of how inhomogeneous the set is. For the next level of analysis, we develop a quantitative theory of inhomogeneity by considering the measure of the set of points around which the set exhibits a given level of inhomogeneity at a certain scale. For a set of examples, a family of -invariant subsets of the 2-torus, we show that this quantity satisfies a large deviations principle. We compare members of this family, demonstrating how the rate function gives us a deeper understanding of their inhomogeneity.
Black carbon fractal morphology and short-wave radiative impact: a modelling study
Directory of Open Access Journals (Sweden)
M. Kahnert
2011-11-01
Full Text Available We investigate the impact of the morphological properties of freshly emitted black carbon aerosols on optical properties and on radiative forcing. To this end, we model the optical properties of fractal black carbon aggregates by use of numerically exact solutions to Maxwell's equations within a spectral range from the UVC to the mid-IR. The results are coupled to radiative transfer computations, in which we consider six realistic case studies representing different atmospheric pollution conditions and surface albedos. The spectrally integrated radiative impacts of black carbon are compared for two different fractal morphologies, which brace the range of recently reported experimental observations of black carbon fractal structures. We also gauge our results by performing corresponding calculations based on the homogeneous sphere approximation, which is commonly employed in climate models. We find that at top of atmosphere the aggregate models yield radiative impacts that can be as much as 2 times higher than those based on the homogeneous sphere approximation. An aggregate model with a low fractal dimension can predict a radiative impact that is higher than that obtained with a high fractal dimension by a factor ranging between 1.1–1.6. Although the lower end of this scale seems like a rather small effect, a closer analysis reveals that the single scattering optical properties of more compact and more lacy aggregates differ considerably. In radiative flux computations there can be a partial cancellation due to the opposing effects of different error sources. However, this cancellation effect can strongly depend on atmospheric conditions and is therefore quite unpredictable. We conclude that the fractal morphology of black carbon aerosols and their fractal parameters can have a profound impact on their radiative forcing effect, and that the use of the homogeneous sphere model introduces unacceptably high biases in radiative impact studies. We
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed. Copyright © 2014 Elsevier B.V. All rights reserved.
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)
Small-Angle Scattering from Nanoscale Fat Fractals.
Anitas, E M; Slyamov, A; Todoran, R; Szakacs, Z
2017-12-01
Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and scaling factors at each structural level. This is in agreement with general results deduced in the context of small-angle scattering analysis of a system of randomly oriented, non-interacting, nano-/micro-fractals. We apply our results to a two-dimensional fat Cantor-like fractal, calculating analytic expressions for the scattering intensities and structure factors. We explain how the structural properties can be computed from experimental data and show their correlation to the variation of the scaling factor with the iteration number. The model can be used to interpret recorded experimental SAS data in the framework of fat fractals and can reveal structural properties of materials characterized by a regular law of changing of the fractal dimensions. It can describe successions of power-law decays, with arbitrary decreasing values of the scattering exponents, and interleaved by regions of constant intensity.
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.
The study of a novel ultrasonic A-scan signal processing method based on fractal theory
Zhu, Ye; Wei, Shi-Cheng; Dong, Yu-Cai; Liang, Yi; Wang, Yu-Jiang
2017-07-01
Concerning ultrasonic non-destructive testing of ceramic-lined composite steel pipes, a novel bonding flaw locating method based on fractal dimension is proposed. Ultrasonic A-scan method is used on different positions of the composite steel pipe test piece. The fractal dimension of each curve of ultrasonic vibration signal is calculated. The transformation of each fractal dimension is compared and abnormal positions where bonding defects potentially exist are detected. The result indicates that ultrasonic A-scan signal has an excellent fractal conduct characteristic. It is feasible to compare fractal dimension of signal with the normal range and find out abnormal positions, which can provide basis for follow-up inspections.
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.
The Fractal Nature of Wood Revealed by Drying
2000-01-01
The materials for this investigation came from two species, one was a 37-year- old plantation-grown Ginkgo ( Ginkgo biloba ) and the other was a 48-year...bacterial colonies, tumor cells, axon termi- nals, tree crown properties , and so on. Wood is a typical porous material that exhibits interconnected...a set of fractal dimensions. But there was no explanation leading to the characterization of wood properties . A typical property of fractals relates
Hou, Haihai; Shao, Longyi; Li, Yonghong; Li, Zhen; Zhang, Wenlong; Wen, Huaijun
2018-03-01
The continental shales from the Middle Jurassic Shimengou Formation of the northern Qaidam Basin, northwestern China, have been investigated in recent years because of their shale gas potential. In this study, a total of twenty-two shale samples were collected from the YQ-1 borehole in the Yuqia Coalfield, northern Qaidam Basin. The total organic carbon (TOC) contents, pore structure parameters, and fractal characteristics of the samples were investigated using TOC analysis, low-temperature nitrogen adsorption experiments, and fractal analysis. The results show that the average pore size of the Shimengou shales varied from 8.149 nm to 20.635 nm with a mean value of 10.74 nm, which is considered mesopore-sized. The pores of the shales are mainly inkbottle- and slit-shaped. The sedimentary environment plays an essential role in controlling the TOC contents of the low maturity shales, with the TOC values of shales from deep to semi-deep lake facies (mean: 5.23%) being notably higher than those of the shore-shallow lake facies (mean: 0.65%). The fractal dimensions range from 2.4639 to 2.6857 with a mean of 2.6122, higher than those of marine shales, which indicates that the pore surface was rougher and the pore structure more complex in these continental shales. The fractal dimensions increase with increasing total pore volume and total specific surface area, and with decreasing average pore size. With increasing TOC contents in shales, the fractal dimensions increase first and then decrease, with the highest value occurring at 2% of TOC content, which is in accordance with the trends between the TOC and both total specific surface area and total pore volume. The pore structure complexity and pore surface roughness of these low-maturity shales would be controlled by the combined effects of both sedimentary environments and the TOC contents.
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.
Directory of Open Access Journals (Sweden)
Jie Fan
2015-01-01
Full Text Available The relationship between the unique internal structure of biomimic woven fabric and its moisture management property is investigated using fractal derivative method. The biomimic fabric exhibits a fractal hierarchic inner structure, and its fractal hierarchy can be further extended by fleece finishing treatment on both surfaces of the fabric. Fractal derivative analysis indicates that the fuzzy biomimic fabric with a higher hierarchic construction after fleece finishing performs better in moisture permeability, and the result was proved by experimental tests.
Bloch surface waves confined in one dimension with a single polymeric nanofibre
Wang, Ruxue; Xia, Hongyan; Zhang, Douguo; Chen, Junxue; Zhu, Liangfu; Wang, Yong; Yang, Erchan; Zang, Tianyang; Wen, Xiaolei; Zou, Gang; Wang, Pei; Ming, Hai; Badugu, Ramachandram; Lakowicz, Joseph R.
2017-02-01
Polymeric fibres with small radii (such as ≤125 nm) are delicate to handle and should be laid down on a solid substrate to obtain practical devices. However, placing these nanofibres on commonly used glass substrates prevents them from guiding light. In this study, we numerically and experimentally demonstrate that when the nanofibre is placed on a suitable dielectric multilayer, it supports a guided mode, a Bloch surface wave (BSW) confined in one dimension. The physical origin of this new mode is discussed in comparison with the typical two-dimensional BSW mode. Polymeric nanofibres are easily fabricated to contain fluorophores, which make the dielectric nanofibre and multilayer configuration suitable for developing a large range of new nanometric scale devices, such as processor-memory interconnections, devices with sensitivity to target analytes, incident polarization and multi-colour BSW modes.
Surface modification of the MoSiON phase shift mask to reduce critical dimension variation
Choo, Hyeokseong; Seo, Dongwan; Lim, Sangwoo
2013-10-01
Phase shift masks (PSMs) were introduced to extend the limits of optical lithography. However, cleaning a MoSiON-based PSM pattern with an ammonium hydroxide/hydrogen peroxide mixture (APM), although efficient at cleaning the PSM pattern, etches the PSM layer, inducing changes in the phase angle and transmittance due to the introduction of variation of the critical dimension (CD). In this study, we investigated the effects of plasma treatment and furnace annealing on the etching of the MoSiON PSM in APM. In particular, we found that the etch behavior and surface chemical state after each treatment were correlated. We also compared variations in the CD between patterned PSM layers and blank masks. After O2 or N2 plasma treatment, the top surface of MoSiON had a thicker transition layer with an extreme increase in O, and a huge variation in CD was also observed after APM treatment. However, CD variation of the patterned MoSiON layer was minimal when the sample was first annealed in NH3 ambient gas and then subjected to APM treatment. This phenomenon may be related to an increase in the portion of the SiO2-like state at the top surface of the MoSiON PSM layer and its optimization without a change in the transition layer thickness.
Heritability of Retinal Vascular Fractals: A Twin Study.
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line; Hougaard, Jesper Leth; Möller, Sören; Kyvik, Kirsten Ohm; Larsen, Michael; Munch, Inger Christine; Grauslund, Jakob
2017-08-01
To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. 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 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. 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 = 0.0002) 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. In young adult twins, the branching pattern of the retinal vessels demonstrated a higher structural similarity in monozygotic than in dizygotic twin pairs. The retinal vascular fractal dimension was mainly determined by genetic factors, which accounted for 54% of the variation. The genetically predetermination of the retinal vasculature may affect the retinal response to potential vascular disease in later life.
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 Segmentation and Clustering Analysis for Seismic Time Slices
Ronquillo, G.; Oleschko, K.; Korvin, G.; Arizabalo, R. D.
2002-05-01
Fractal analysis has become part of the standard approach for quantifying texture on gray-tone or colored images. In this research we introduce a multi-stage fractal procedure to segment, classify and measure the clustering patterns on seismic time slices from a 3-D seismic survey. Five fractal classifiers (c1)-(c5) were designed to yield standardized, unbiased and precise measures of the clustering of seismic signals. The classifiers were tested on seismic time slices from the AKAL field, Cantarell Oil Complex, Mexico. The generalized lacunarity (c1), fractal signature (c2), heterogeneity (c3), rugosity of boundaries (c4) and continuity resp. tortuosity (c5) of the clusters are shown to be efficient measures of the time-space variability of seismic signals. The Local Fractal Analysis (LFA) of time slices has proved to be a powerful edge detection filter to detect and enhance linear features, like faults or buried meandering rivers. The local fractal dimensions of the time slices were also compared with the self-affinity dimensions of the corresponding parts of porosity-logs. It is speculated that the spectral dimension of the negative-amplitude parts of the time-slice yields a measure of connectivity between the formation's high-porosity zones, and correlates with overall permeability.
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
Observation of two different fractal structures in nanoparticle, protein and surfactant complexes
International Nuclear Information System (INIS)
Mehan, Sumit; Kumar, Sugam; Aswal, V. K.
2014-01-01
Small angle neutron scattering has been carried out from a complex of nanoparticle, protein and surfactant. Although all the components are similarly (anionic) charged, we have observed strong interactions in their complex formation. It is characterized by the coexistence of two different mass fractal structures. The first fractal structure is originated from the protein and surfactant interaction and second from the depletion effect of first fractal structure leading the nanoparticle aggregation. The fractal structure of protein-surfactant complex represents to bead necklace structure of micelle-like clusters of surfactant formed along the unfolded protein chain. Its fractal dimension depends on the surfactant to protein ratio (r) and decreases with the increase in r. However, fractal dimension of nanoparticle aggregates in nanoparticle-protein complex is found to be independent of protein concentration and governed by the diffusion limited aggregation like morphology
Fracture Surface Morphology and Impact Strength of Cellulose/PLA Composites.
Gao, Honghong; Qiang, Tao
2017-06-07
Polylactide (PLA)-based composite materials reinforced with ball-milled celluloses were manufactured by extrusion blending followed by injection molding. Their surface morphology from impact fracture were imaged with scanning electron microscopy (SEM) and investigated by calculating their fractal dimensions. Then, linear regression was used to explore the relationship between fractal dimension and impact strength of the resultant cellulose/PLA composite materials. The results show that filling the ball-milled celluloses into PLA can improve the impact toughness of PLA by a minimum of 38%. It was demonstrated that the fracture pattern of the cellulose/PLA composite materials is different from that of pristine PLA. For the resultant composite materials, the fractal dimension of the impact fractured surfaces increased with increasing filling content and decreasing particle size of the ball-milled cellulose particles. There were highly positive correlations between fractal dimension of the fractured surfaces and impact strength of the cellulose/PLA composites. However, the linearity between fractal dimension and impact strength were different for the different methods, due to their different R-squared values. The approach presented in this work will help to understand the structure-property relationships of composite materials from a new perspective.
Zuingli Santo Bandaso; Johannes Leonard
2017-01-01
Turning process is the removal of metal from the outer diameter of a rotating cylindrical workpiece. Turning is used to reduce the diameter of the workpiece, usually to a specified dimension, and to produce a smooth finish on the metal. This research investigates the effect of feed rate, spindle speed, tool overhang and tool dimensions toward vibration amplitude and surface roughness on turning process. This study uses both statistical and graphical analysis of the data collected. The experim...
Ge, Xinmin; Fan, Yiren; Deng, Shaogui; Han, Yujiao; Liu, Jiaxiong
2016-09-01
We present an improved fractal model for pore structure evaluation and permeability estimation based on the high pressure mercury porosimetry data. An accumulative fractal equation is introduced to characterize the piecewise nature of the capillary pressure and the mercury saturation. The iterative truncated singular value decomposition algorithm is developed to solve the accumulative fractal equation and obtain the fractal dimension distributions. Furthermore, the fractal dimension distributions and relevant parameters are used to characterize the pore structure and permeability. The results demonstrate that the proposed model provides better characterization of the mercury injection capillary pressure than conventional monofractal theory. In addition, there is a direct relationship between the pore structure types and the fractal dimension spectrums. What is more, the permeability is strongly correlated with the geometric and the arithmetic mean values of fractal dimensions, and the permeability estimated using these new fractal dimension parameters achieve excellent result. The improved model and solution give a fresh perspective of the conventional monofractal theory, which may be applied in many geological and geophysical fields.
Small-angle scattering from generalized self-similar Vicsek fractals
International Nuclear Information System (INIS)
Cherny, Alexander Yu; Anitas, Eugen M; Osipov, Vladimir A; Kuklin, Alexander I
2012-01-01
An analytical approach for calculating the small-angle X-ray or neutron scattering (SAXS/SANS) from generalized self-similar Vicsek fractals (GSSVF) is presented; each fractal consists of spherical subunits. The system considered is a mass-fractal, generated iteratively from a regular 3D Vicsek fractal structure. Its fractal dimension is controllable and increases with increasing the value of the scaling factor. Small-angle scattering (SAS) intensity is determined from a set of non-interacting, randomly oriented and uniformly distributed GSSVF fractals. It is shown that in the fractal region, the curve I(q)q D is approximately log-periodic with the period equal to the scaling factor of fractal; here D and I(q) are the fractal dimension and the SAS intensity, respectively. In particular, the positions of deepest minima and highest maxima are log-periodic, and their number coincides with the number of fractal iterations. The log-periodicity of the scattering curves is a consequence of the self-similarity of GSSVF.
[Recent progress of research and applications of fractal and its theories in medicine].
Cai, Congbo; Wang, Ping
2014-10-01
Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.
Fractal generalized Pascal matrices
Burlachenko, E.
2016-01-01
Set of generalized Pascal matrices whose elements are generalized binomial coefficients is considered as an integral object. The special system of generalized Pascal matrices, based on which we are building fractal generalized Pascal matrices, is introduced. Pascal matrix (Pascal triangle) is the Hadamard product of the fractal generalized Pascal matrices. The concept of zero generalized Pascal matrices, an example of which is the Pascal triangle modulo 2, arise in connection with the system ...
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
Retinal vascular fractals and cognitive impairment.
Ong, Yi-Ting; Hilal, Saima; Cheung, Carol Yim-Lui; Xu, Xin; Chen, Christopher; Venketasubramanian, Narayanaswamy; Wong, Tien Yin; Ikram, Mohammad Kamran
2014-05-01
Retinal microvascular network changes have been found in patients with age-related brain diseases such as stroke and dementia including Alzheimer's disease. We examine whether retinal microvascular network changes are also present in preclinical stages of dementia. This is a cross-sectional study of 300 Chinese participants (age: ≥60 years) from the ongoing Epidemiology of Dementia in Singapore study who underwent detailed clinical examinations including retinal photography, brain imaging and neuropsychological testing. Retinal vascular parameters were assessed from optic disc-centered photographs using a semiautomated program. A comprehensive neuropsychological battery was administered, and cognitive function was summarized as composite and domain-specific Z-scores. Cognitive impairment no dementia (CIND) and dementia were diagnosed according to standard diagnostic criteria. Among 268 eligible nondemented participants, 78 subjects were categorized as CIND-mild and 69 as CIND-moderate. In multivariable adjusted models, reduced retinal arteriolar and venular fractal dimensions were associated with an increased risk of CIND-mild and CIND-moderate. Reduced fractal dimensions were associated with poorer cognitive performance globally and in the specific domains of verbal memory, visuoconstruction and visuomotor speed. A sparser retinal microvascular network, represented by reduced arteriolar and venular fractal dimensions, was associated with cognitive impairment, suggesting that early microvascular damage may be present in preclinical stages of dementia.
Retinal Vascular Fractals and Cognitive Impairment
Directory of Open Access Journals (Sweden)
Yi-Ting Ong
2014-08-01
Full Text Available Background: Retinal microvascular network changes have been found in patients with age-related brain diseases such as stroke and dementia including Alzheimer's disease. We examine whether retinal microvascular network changes are also present in preclinical stages of dementia. Methods: This is a cross-sectional study of 300 Chinese participants (age: ≥60 years from the ongoing Epidemiology of Dementia in Singapore study who underwent detailed clinical examinations including retinal photography, brain imaging and neuropsychological testing. Retinal vascular parameters were assessed from optic disc-centered photographs using a semiautomated program. A comprehensive neuropsychological battery was administered, and cognitive function was summarized as composite and domain-specific Z-scores. Cognitive impairment no dementia (CIND and dementia were diagnosed according to standard diagnostic criteria. Results: Among 268 eligible nondemented participants, 78 subjects were categorized as CIND-mild and 69 as CIND-moderate. In multivariable adjusted models, reduced retinal arteriolar and venular fractal dimensions were associated with an increased risk of CIND-mild and CIND-moderate. Reduced fractal dimensions were associated with poorer cognitive performance globally and in the specific domains of verbal memory, visuoconstruction and visuomotor speed. Conclusion: A sparser retinal microvascular network, represented by reduced arteriolar and venular fractal dimensions, was associated with cognitive impairment, suggesting that early microvascular damage may be present in preclinical stages of dementia.
Comparison of Planar Fractal Filters on Defected Ground Substrate
Directory of Open Access Journals (Sweden)
M. Kufa
2012-12-01
Full Text Available The paper discusses approaches to the reduction of dimensions of planar filters (microstrip ones and coplanar ones. Filter dimensions are reduced by applying the fractal theory to the geometry of a filter, and by the defecting of the ground plane of a filter. An optimum combination of both approaches enables us to reach smaller dimensions of planar filters and protect other parameters. In order to demonstrate advantages of the fractal defected ground approach, we review the designs of existing low-pass filters with defected ground structures (DGS. Results produced by simulations of these filters are compared with results of simulations of a novel fractal DGS filter. The investigated filters are manufactured and measured.
Sánchez, Iván; Uzcátegui, Gladys
2011-04-01
To systematically review applications of fractal geometry in different aspects of dental practice. In this review, we present a short introduction to fractals and specifically address the following topics: treatment and healing monitoring, dental materials, dental tissue, caries, osteoporosis, periodontitis, cancer, Sjögren's syndrome, diagnosis of several other conditions and a discussion on the reliability of FD determinations from dental radiographs. Google Scholar, Ovid MEDLINE, ScienceDirect, etc. (up to August 2010). The review considered original studies, reviews and conference proceedings, published in English or Spanish. Abstracts and posters were not taken into account. Fractal geometry has found plenty of applications in several branches of dental practice. It provides a way to quantify the complexity of structures. Whereas one desires to study a radiograph, an histological section or the signal from a transducer, there are several methods available to determine the degree of complexity using fractal analysis. Several pathological conditions can alter the complexity of anatomical structures, and this change can be detectable with the help of fractal parameters. Although during the last two decades there have been plenty of works on the field, reported cases having enough reproducibility, with different groups showing similar results are not very common. Further replications are needed before we can establish statistically significant correlations amongst fractal parameters and pathological conditions. Copyright © 2011 Elsevier Ltd. All rights reserved.
International Nuclear Information System (INIS)
Das, Bipul; Bag, Swarup; Pal, Sukhomay
2017-01-01
Providing solutions towards the improvisation of welding technologies is the recent trend in the Friction stir welding (FSW) process. We present a monitoring approach for ultimate tensile strength of the friction stir welded joints based on information extracted from process signals through implementing fractal theory. Higuchi and Katz algorithms were executed on current and tool rotational speed signals acquired during friction stir welding to estimate fractal dimensions. Estimated fractal dimensions when correlated with the ultimate tensile strength of the joints deliver an increasing trend with the increase in joint strength. It is observed that dynamicity of the system strengthens the weld joint, i.e., the greater the fractal dimension, the better will be the quality of the weld. Characterization of signals by fractal theory indicates that the single-valued indicator can be an alternative for effective monitoring of the friction stir welding process.
Energy Technology Data Exchange (ETDEWEB)
Das, Bipul; Bag, Swarup; Pal, Sukhomay [Indian Institute of Technology Guwahati, Assam (India)
2017-05-15
Providing solutions towards the improvisation of welding technologies is the recent trend in the Friction stir welding (FSW) process. We present a monitoring approach for ultimate tensile strength of the friction stir welded joints based on information extracted from process signals through implementing fractal theory. Higuchi and Katz algorithms were executed on current and tool rotational speed signals acquired during friction stir welding to estimate fractal dimensions. Estimated fractal dimensions when correlated with the ultimate tensile strength of the joints deliver an increasing trend with the increase in joint strength. It is observed that dynamicity of the system strengthens the weld joint, i.e., the greater the fractal dimension, the better will be the quality of the weld. Characterization of signals by fractal theory indicates that the single-valued indicator can be an alternative for effective monitoring of the friction stir welding process.
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.