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.
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
Fractal dimension of the fractured surface of materials
International Nuclear Information System (INIS)
Lung, C.W.; Zhang, S.Z.
1989-05-01
Fractal dimension of the fractured surface of materials is discussed to show that the origin of the negative correlation between D F and toughness lies in the method of fractal dimension measurement with perimeter-area relation and also in the physical mechanism of crack propagation. (author). 8 refs, 4 figs, 1 tab
International Nuclear Information System (INIS)
Ren Xincheng; Guo Lixin
2008-01-01
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)
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.
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.
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.
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.
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy
2017-01-01
This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
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 ...
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....
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)
FRACTAL ANALYSIS OF PHYSICAL ADSORPTION ON SURFACES OF ACID ACTIVATED BENTONITES FROM SERBIA
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Ljiljana Rožić
2008-11-01
Full Text Available Solid surfaces are neither ideally regular, that is, morphological and energeticcally homogeneous, nor are they fully irregular or fractal. Instead, real solid surfaces exhibit a limited degree of organization quantified by the fractal dimension, D. Fractal analysis was applied to investigate the effect of concentrations of HCl solutions on the structural and textural properties of chemically activated bentonite from southern Serbia. Acid treatment of bentonites is applied in order to remove impurities and various exchangeable cations from bentonite clay. Important physical changes in acid-activated smectite are the increase of the specific surface area and of the average pore volume, depending on acid strength, time and temperature of a treatment. On the basis of the sorption-structure analysis, the fractal dimension of the bentonite surfaces was determined by Mahnke and Mögel method. The fractal dimension evaluated by this method was 2.11 for the AB3 and 1.94 for the AB4.5 sample. The estimation of the values of the fractal dimension of activated bentonites was performed in the region of small pores, 0.5 nm < rp < 2 nm.
A simple method for estimating the size of nuclei on fractal surfaces
Zeng, Qiang
2017-10-01
Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.
Effect of 3D fractal dimension on contact area and asperity interactions in elastoplastic contact
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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.
Fractal modeling of fluidic leakage through metal sealing surfaces
Zhang, Qiang; Chen, Xiaoqian; Huang, Yiyong; Chen, Yong
2018-04-01
This paper investigates the fluidic leak rate through metal sealing surfaces by developing fractal models for the contact process and leakage process. An improved model is established to describe the seal-contact interface of two metal rough surface. The contact model divides the deformed regions by classifying the asperities of different characteristic lengths into the elastic, elastic-plastic and plastic regimes. Using the improved contact model, the leakage channel under the contact surface is mathematically modeled based on the fractal theory. The leakage model obtains the leak rate using the fluid transport theory in porous media, considering that the pores-forming percolation channels can be treated as a combination of filled tortuous capillaries. The effects of fractal structure, surface material and gasket size on the contact process and leakage process are analyzed through numerical simulations for sealed ring gaskets.
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....
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Davis, Ethan, E-mail: ethan.davis4@huskers.unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States); Liu, Ying; Jiang, Lijia; Lu, Yongfeng [Laser Assisted Nano Engineering Lab, Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, 209N Scott Engineering Center, Lincoln, NE 68588-0511 (United States); Ndao, Sidy, E-mail: sndao2@unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States)
2017-01-15
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
International Nuclear Information System (INIS)
Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy
2017-01-01
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
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
Fractal Image Coding Based on a Fitting Surface
Directory of Open Access Journals (Sweden)
Sheng Bi
2014-01-01
Full Text Available A no-search fractal image coding method based on a fitting surface is proposed. In our research, an improved gray-level transform with a fitting surface is introduced. One advantage of this method is that the fitting surface is used for both the range and domain blocks and one set of parameters can be saved. Another advantage is that the fitting surface can approximate the range and domain blocks better than the previous fitting planes; this can result in smaller block matching errors and better decoded image quality. Since the no-search and quadtree techniques are adopted, smaller matching errors also imply less number of blocks matching which results in a faster encoding process. Moreover, by combining all the fitting surfaces, a fitting surface image (FSI is also proposed to speed up the fractal decoding. Experiments show that our proposed method can yield superior performance over the other three methods. Relative to range-averaged image, FSI can provide faster fractal decoding process. Finally, by combining the proposed fractal coding method with JPEG, a hybrid coding method is designed which can provide higher PSNR than JPEG while maintaining the same Bpp.
Directory of Open Access Journals (Sweden)
Painter Page R
2005-08-01
Full Text Available Abstract Background A prominent theoretical explanation for 3/4-power allometric scaling of metabolism proposes that the nutrient exchange surface of capillaries has properties of a space-filling fractal. The theory assumes that nutrient exchange surface area has a fractal dimension equal to or greater than 2 and less than or equal to 3 and that the volume filled by the exchange surface area has a fractal dimension equal to or greater than 3 and less than or equal to 4. Results It is shown that contradicting predictions can be derived from the assumptions of the model. When errors in the model are corrected, it is shown to predict that metabolic rate is proportional to body mass (proportional scaling. Conclusion The presence of space-filling fractal nutrient exchange surfaces does not provide a satisfactory explanation for 3/4-power metabolic rate scaling.
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.
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 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.
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.
International Nuclear Information System (INIS)
Altajskij, M.V.; Ivanov, V.V.; Korenev, S.A.; Orelovich, O.L.; Puzynin, I.V.; Chernik, V.V.
1997-01-01
We discuss the results of scanning electron microscopy of surfaces of the solids subjected to high intensity electron and ion beam treatment. The appearance of fractal structures on the modified surfaces is shown. The fractal dimensions of these structures were estimated by box-counting algorithm
Directory of Open Access Journals (Sweden)
Silvester Tursiloadi
2010-06-01
Full Text Available A technique to determine the surface fractal dimension of mesoporous TiO2 using a dynamic flow adsorption instrument is described. Fractal dimension is an additional technique to characterize surface morphology. Surface fractal dimension, a quantitative measurement of surface ruggedness, can be determined by adsorbing a homologous series of adsorbates onto an adsorbent sample of mesoporous TiO2. Titania wet gel prepared by hydrolysis of Ti-alkoxide was immersed in the flow of supercritical CO2 at 60 °C and the solvent was extracted. Mesoporous TiO2 consists of anatase nano-particles, about 5nm in diameter, have been obtained. After calcination at 600 °C, the average pore size of the extracted gel, about 20nm in diameter, and the pore volume, about 0.35cm3g-1, and the specific surface area, about 58 m2g-1. Using the N2 adsorption isotherm, the surface fractal dimension, DS, has been estimated according to the Frenkel-Halsey-Hill (FHH theory. The N2 adsorption isotherm for the as-extracted aerogel indicates the mesoporous structure. Two linear regions are found for the FHH plot of the as-extracted aerogel. The estimated surface fractal dimensions are about 2.49 and 2.68. Both of the DS values indicate rather complex surface morphology. The TEM observation shows that there are amorphous and crystalline particles. Two values of DS may be attributed to these two kinds of particles. The two regions are in near length scales, and the smaller DS, DS =2.49, for the smaller region. This result indicates that there are two kinds of particles, probably amorphous and anatase particles as shown by the TEM observation. Keywords: surface fractal dimensions, CO2 supercritically extraction, sol-gel, aerogel, titania
International Nuclear Information System (INIS)
Pan Wei; Ni Guoqiang; Li Hanbo
2010-01-01
Computing Methods of fractal dimension and multifractal spectrum about the remote sensing image are briefly introduced. The fractal method is used to study the characteristics of remote sensing images in Xiangshan and Yuhuashan volcanic uranium metallogenic areas in southern China. The research results indicate that the Xiangshan basin in which lots of volcanic uranium deposits occur,is of bigger fractal dimension based on remote sensing image texture than that of the Yuhuashan basin in which two uranium ore occurrences exist, and the multifractal spectrum in the Xiangshan basin obviously leans to less singularity index than in the Yuhuashan basin. The relation of the fractal dimension and multifractal singularity of remote sensing image to uranium metallogeny are discussed. The fractal dimension and multifractal singularity index of remote sensing image may be used to predict the volcanic uranium metallogenic areas. (authors)
Directory of Open Access Journals (Sweden)
Вікторія Юріївна Іващенко
2015-03-01
Full Text Available Optimization of complex modes of heat treatments, in which control the properties of processed steel occurs by varying the large number of parameters, is quite time-consuming process. The influence of thermal processes on the formation of the metal structure manifested at the level of micro- and meso-sizes, which are realized qualitatively different mechanisms of destruction. Method of multi-factual description of the fracture’s surfaces, which was got after tests of mechanical properties, was used for the choice of the optimum thermo-cyclic mode with the variable temperatures Tmax and Tmin in cycles in this work. It vas founded the number of TCT-mode’s cycles and order changing Tmax affect the processes of dislocation motion and the formation of micro-voids in the metal. This work shows the relationship between these processes and fractal indices. Fractal indices of micro levels correlate to the dislocation density of the structure, and the meso-level indices - to the percentage reduction of area at fracture. It was proved that the analysis of the topography of the fracture’s surfaces using fractal indices to determine the optimal combination of processing parameters required to obtain the best mechanical properties. The new TCT-modes with variable temperature settings can be seen as reinforcing thermal technology that promotes self-organization phase-structural state of steels because it is able to generate an effective barrier to the movement of dislocations and cracks promotion
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)
Evaluation de la Qualité de surface par la Dimension Fractale et les ...
African Journals Online (AJOL)
Evaluation of surface quality by Fractal Dimension and Volume. Parameters .... du microscope électronique à balayage la. FEG.SUPRA 40. ... telle configuration le rapport (L/Dp), est tel que : L0 ,75 ..... du contrôle par la dimension fractale ;.
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
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
Borri, Claudia; Paggi, Marco
2015-02-01
The random process theory (RPT) has been widely applied to predict the joint probability distribution functions (PDFs) of asperity heights and curvatures of rough surfaces. A check of the predictions of RPT against the actual statistics of numerically generated random fractal surfaces and of real rough surfaces has been only partially undertaken. The present experimental and numerical study provides a deep critical comparison on this matter, providing some insight into the capabilities and limitations in applying RPT and fractal modeling to antireflective and hydrophobic rough surfaces, two important types of textured surfaces. A multi-resolution experimental campaign using a confocal profilometer with different lenses is carried out and a comprehensive software for the statistical description of rough surfaces is developed. It is found that the topology of the analyzed textured surfaces cannot be fully described according to RPT and fractal modeling. The following complexities emerge: (i) the presence of cut-offs or bi-fractality in the power-law power-spectral density (PSD) functions; (ii) a more pronounced shift of the PSD by changing resolution as compared to what was expected from fractal modeling; (iii) inaccuracy of the RPT in describing the joint PDFs of asperity heights and curvatures of textured surfaces; (iv) lack of resolution-invariance of joint PDFs of textured surfaces in case of special surface treatments, not accounted for by fractal modeling.
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).
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
Fractal behaviour of flow of an inhomogeneous fluid over a smooth inclined surface
International Nuclear Information System (INIS)
Rouhani, S.; Maleki Jirsarani, N.; Ghane Motlagh, B.; Baradaran, S.; Shokrian, E.
2001-01-01
We have observed and analyzed fractal patterns made by the flow of an inhomogeneous fluid (a suspension) over an inclined smooth surface. We observed that if the angle of inclination is above a threshold (10 d eg C - 12 d eg C), the length of fractal clusters become infinity. We measured a fractal dimension of df=1.40 ± 0.05. This falls within the same general class of patterns of flow of water over an inhomogeneous surface. This observation is consistent with the results of theoretical modes for nonlinear fluid flow in random media
Lam, Nina Siu-Ngan; Qiu, Hong-Lie; Quattrochi, Dale A.; Emerson, Charles W.; Arnold, James E. (Technical Monitor)
2001-01-01
The rapid increase in digital data volumes from new and existing sensors necessitates the need for efficient analytical tools for extracting information. We developed an integrated software package called ICAMS (Image Characterization and Modeling System) to provide specialized spatial analytical functions for interpreting remote sensing data. This paper evaluates the three fractal dimension measurement methods: isarithm, variogram, and triangular prism, along with the spatial autocorrelation measurement methods Moran's I and Geary's C, that have been implemented in ICAMS. A modified triangular prism method was proposed and implemented. Results from analyzing 25 simulated surfaces having known fractal dimensions show that both the isarithm and triangular prism methods can accurately measure a range of fractal surfaces. The triangular prism method is most accurate at estimating the fractal dimension of higher spatial complexity, but it is sensitive to contrast stretching. The variogram method is a comparatively poor estimator for all of the surfaces, particularly those with higher fractal dimensions. Similar to the fractal techniques, the spatial autocorrelation techniques are found to be useful to measure complex images but not images with low dimensionality. These fractal measurement methods can be applied directly to unclassified images and could serve as a tool for change detection and data mining.
Evolution of atomic-scale surface structures during ion bombardment: A fractal simulation
International Nuclear Information System (INIS)
Shaheen, M.A.; Ruzic, D.N.
1993-01-01
Surfaces of interest in microelectronics have been shown to exhibit fractal topographies on the atomic scale. A model utilizing self-similar fractals to simulate surface roughness has been added to the ion bombardment code TRIM. The model has successfully predicted experimental sputtering yields of low energy (less then 1000 eV) Ar on Si and D on C using experimentally determined fractal dimensions. Under ion bombardment the fractal surface structures evolve as the atoms in the collision cascade are displaced or sputtered. These atoms have been tracked and the evolution of the surface in steps of one monolayer of flux has been determined. The Ar--Si system has been studied for incidence energies of 100 and 500 eV, and incidence angles of 0 degree, 30 degree, and 60 degree. As expected, normally incident ion bombardment tends to reduce the roughness of the surface, whereas large angle ion bombardment increases the degree of surface roughness. Of particular interest though, the surfaces are still locally self-similar fractals after ion bombardment and a steady state fractal dimension is reached, except at large angles of incidence
Super Water-Repellent Fractal Surfaces of a Photochromic Diarylethene Induced by UV Light
Izumi, Norikazu; Minami, Takayuki; Mayama, Hiroyuki; Takata, Atsushi; Nakamura, Shinichiro; Yokojima, Satoshi; Tsujii, Kaoru; Uchida, Kingo
2008-09-01
Photochromic diarylethene forms super water-repellent surfaces upon irradiation with UV light. Microfibril-like crystals grow on the solid diarylethene surface after UV irradiation, and the contact angle of water on the surface becomes larger with increasing surface roughness with time. The fractal analysis was made by the box-counting method for the rough surfaces. There are three regions in the roughness size having the fractal dimension of ca. 2.4 (size of roughness smaller than 5 µm), of ca. 2.2 (size of roughness between 5-40 µm), and of ca. 2.0 (size of roughness larger than 40 µm). The fractal dimension of ca. 2.4 was due to the fibril-like structures generated gradually by UV irradiation on diarylethene surfaces accompanied with an increase in the contact angle. The surface structure with larger fractal dimension mainly contributes to realizing the super water-repellency of the diarylethene surfaces. This mechanism of spontaneous formation of fractal surfaces is similar to that for triglyceride and alkylketene dimer waxes.
AFM imaging and fractal analysis of surface roughness of AlN epilayers on sapphire substrates
Energy Technology Data Exchange (ETDEWEB)
Dallaeva, Dinara, E-mail: dinara.dallaeva@yandex.ru [Brno University of Technology, Faculty of Electrical Engineering and Communication, Physics Department, Technická 8, 616 00 Brno (Czech Republic); Ţălu, Ştefan [Technical University of Cluj-Napoca, Faculty of Mechanical Engineering, Department of AET, Discipline of Descriptive Geometry and Engineering Graphics, 103-105 B-dul Muncii Street, Cluj-Napoca 400641, Cluj (Romania); Stach, Sebastian [University of Silesia, Faculty of Computer Science and Materials Science, Institute of Informatics, Department of Biomedical Computer Systems, ul. Będzińska 39, 41-205 Sosnowiec (Poland); Škarvada, Pavel; Tománek, Pavel; Grmela, Lubomír [Brno University of Technology, Faculty of Electrical Engineering and Communication, Physics Department, Technická 8, 616 00 Brno (Czech Republic)
2014-09-01
Graphical abstract: - Highlights: • We determined the complexity of 3D surface roughness of aluminum nitride layers. • We used atomic force microscopy and analyzed their fractal geometry. • We determined the fractal dimension of surface roughness of aluminum nitride layers. • We determined the dependence of layer morphology on substrate temperature. - Abstract: The paper deals with AFM imaging and characterization of 3D surface morphology of aluminum nitride (AlN) epilayers on sapphire substrates prepared by magnetron sputtering. Due to the effect of temperature changes on epilayer's surface during the fabrication, a surface morphology is studied by combination of atomic force microscopy (AFM) and fractal analysis methods. Both methods are useful tools that may assist manufacturers in developing and fabricating AlN thin films with optimal surface characteristics. Furthermore, they provide different yet complementary information to that offered by traditional surface statistical parameters. This combination is used for the first time for measurement on AlN epilayers on sapphire substrates, and provides the overall 3D morphology of the sample surfaces (by AFM imaging), and reveals fractal characteristics in the surface morphology (fractal analysis)
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.
Energy Technology Data Exchange (ETDEWEB)
Lin, Naiming, E-mail: lnmlz33@163.com [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Guo, Junwen [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Xie, Faqin [School of Aeronautics, Northwestern Polytechnical University, Xi’an 710072 (China); Zou, Jiaojuan; Tian, Wei [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China); Yao, Xiaofei [School of Materials and Chemical Engineering, Xi’an Technological University, Xi’an 710032 (China); Zhang, Hongyan; Tang, Bin [Research Institute of Surface Engineering, Taiyuan University of Technology, Taiyuan 030024 (China)
2014-08-30
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)
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
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
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.
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.
On fractal properties of equipotentials over a real rough surface faced to plasma in fusion devices
International Nuclear Information System (INIS)
Budaev, V.P.; Yakovlev, M.
2008-01-01
We consider a sheath region bounded by a corrugated surface of material conductor and a flat boundary held to a constant voltage bias. The real profile of the film deposited from plasma on a limiter in a fusion device was used in numerical solving of the Poisson's equation to find a profile of electrostatic potential. The rough surface influences the equipotential lines over the surface. We characterized a shape of equipotential lines by a fractal dimension. The long-range correlation in the potential field is imposed by the non-trivial fractal structure of the surface. Dust particles bounced in such irregular potential field can accelerate due to the Fermi acceleration. (author)
Using fractal analysis in modeling the dynamics of forest areas and economic impact assessment
DEFF Research Database (Denmark)
Pintilii, Radu Daniel; Andronache, Ion; Diaconu, Daniel Constantin
2017-01-01
This study uses fractal analysis to quantify the spatial changes of forest resources caused by an increase of deforested areas. The method introduced contributes to the evaluation of forest resources being under significant pressure from anthropogenic activities. The pressure on the forest...... resources has been analyzed for Maramures, County, one of the most deforested counties in Romania. In order to evaluate this, the deforested areas were calculated for the period of 2001-2014, by using the Global Forest Change 2000-2014 database. The Fractal Fragmentation Index (FFI) and Fixed Grid 2D...
Adib, A.; Afzal, P.; Heydarzadeh, K.
2015-01-01
The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modelling reveal that proper soil types are located around the central city. The results derived via the fractal modelling were utilized to improve the Nogoshi and Igarashi (1970, 1971) classification results in the Meybod city. The resulting categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.
Site effect classification based on microtremor data analysis using concentration-area fractal model
Adib, A.; Afzal, P.; Heydarzadeh, K.
2014-07-01
The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.
Ahmad, A L; Mustafa, N N N
2006-09-15
The alumina ceramic membrane has been modified by the addition of palladium in order to improve the H(2) permeability and selectivity. Palladium-alumina ceramic membrane was prepared via a sol-gel method and subjected to thermal treatment in the temperature range 500-1100 degrees C. Fractal analysis from nitrogen adsorption isotherm is used to study the pore surface roughness of palladium-alumina ceramic membrane with different chemical composition (nitric acid, PVA and palladium) and calcinations process in terms of surface fractal dimension, D. Frenkel-Halsey-Hill (FHH) model was used to determine the D value of palladium-alumina membrane. Following FHH model, the D value of palladium-alumina membrane increased as the calcinations temperature increased from 500 to 700 degrees C but decreased after calcined at 900 and 1100 degrees C. With increasing palladium concentration from 0.5 g Pd/100 ml H(2)O to 2 g Pd/100 ml H(2)O, D value of membrane decreased, indicating to the smoother surface. Addition of higher amount of PVA and palladium reduced the surface fractal of the membrane due to the heterogeneous distribution of pores. However, the D value increased when nitric acid concentration was increased from 1 to 15 M. The effect of calcinations temperature, PVA ratio, palladium and acid concentration on membrane surface area, pore size and pore distribution also studied.
Energy Technology Data Exchange (ETDEWEB)
Yadav, R.P. [Department of Physics, University of Allahabad, Allahabad, UP 211002 (India); Kumar, T. [Department of Physics, Central University of Haryana, Jant-Pali, Mahendergarh, Haryana 123029 (India); Mittal, A.K. [Department of Physics, University of Allahabad, Allahabad, UP 211002 (India); K Banerjee Centre of Atmospheric and Ocean Studies, University of Allahabad, Allahabad, UP 211002 (India); Dwivedi, S., E-mail: suneetdwivedi@gmail.com [K Banerjee Centre of Atmospheric and Ocean Studies, University of Allahabad, Allahabad, UP 211002 (India); Kanjilal, D. [Inter-University Accelerator Centre, Aruna Asaf Ali Marg, PO Box 10502, New Delhi 110 067 (India)
2015-08-30
Highlights: • Fractal analysis of Si(1 0 0) surface morphology at varying ion fluences. • Autocorrelation function and height–height correlation function as fractal measures. • Surface roughness and lateral correlation length increases with ion fluence. • Ripple pattern of the surfaces is found at higher ion fluences. • Wavelength of the ripple surfaces is computed for each fluence. - Abstract: Si (1 0 0) is bombarded with 200 keV Ar{sup +} ion beam at oblique incidence with fluences ranging from 3 × 10{sup 17} ions/cm{sup 2} to 3 × 10{sup 18} ions/cm{sup 2}. The surface morphology of the irradiated surfaces is captured by the atomic force microscopy (AFM) for each ion fluence. The fractal analysis is performed on the AFM images. The autocorrelation function and height–height correlation function are used as fractal measures. It is found that the average roughness, interface width, lateral correlation length as well as roughness exponent increase with ions fluence. The analysis reveals the ripple pattern of the surfaces at higher fluences. The wavelength of the ripple surfaces is computed for each ion fluence.
Surface structures of equilibrium restricted curvature model on two fractal substrates
International Nuclear Information System (INIS)
Song Li-Jian; Tang Gang; Zhang Yong-Wei; Han Kui; Xun Zhi-Peng; Xia Hui; Hao Da-Peng; Li Yan
2014-01-01
With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature (ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension d f , but possess different dynamic exponents of random walk z rw . The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension d f , but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk z rw . The ERC model growing on the two substrates follows the well-known Family—Vicsek scaling law and satisfies the scaling relations 2α + d f ≍ z ≍ 2z rw . In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins—Herring equation. (general)
Surface fractal dimensions and textural properties of mesoporous alkaline-earth hydroxyapatites
International Nuclear Information System (INIS)
Vilchis-Granados, J.; Granados-Correa, F.; Barrera-Díaz, C.E.
2013-01-01
This work examines the surface fractal dimensions (D 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 2 -physisorption measurements. Surface fractal dimensions were determined using single N 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 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.
International Nuclear Information System (INIS)
Xie Tao; Zhao Shang-Zhuo; Fang He; Yu Wen-Jin; He Yi-Jun; Perrie, William
2016-01-01
Sea surface current has a significant influence on electromagnetic (EM) backscattering signals and may constitute a dominant synthetic aperture radar (SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section (NRCS) discrepancies between the model for a coupled wave-current fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle, as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface. (paper)
International Nuclear Information System (INIS)
Ancillao, Andrea; Galli, Manuela; Rigoldi, Chiara; Albertini, Giorgio
2014-01-01
Fractal dimension was demonstrated to be able to characterize the complexity of biological signals. The EMG time series are well known to have a complex behavior and some other studies already tried to characterize these signals by their fractal dimension. This paper is aimed at studying the correlation between the fractal dimension of surface EMG signal recorded over Rectus Femoris muscles during a vertical jump and the height reached in that jump. Healthy subjects performed vertical jumps at different heights. Surface EMG from Rectus Femoris was recorded and the height of each jump was measured by an optoelectronic motion capture system. Fractal dimension of sEMG was computed and the correlation between fractal dimension and eight of the jump was studied. Linear regression analysis showed a very high correlation coefficient between the fractal dimension and the height of the jump for all the subjects. The results of this study show that the fractal dimension is able to characterize the EMG signal and it can be related to the performance of the jump. Fractal dimension is therefore an useful tool for EMG interpretation
Szyperski, Piotr D
2018-06-01
The purpose of this research was to evaluate the applicability of the fractal dimension (FD) estimators to assess lateral shearing interferometric (LSI) measurements of tear film surface quality. Retrospective recordings of tear film measured with LSI were used: 69 from healthy subjects and 41 from patients diagnosed with dry eye syndrome. Five surface quality descriptors were considered, four based on FD and a previously reported descriptor operating in a spatial frequency domain (M 2 ), presenting temporal kinetics of post-blink tear film. A set of 12 regression parameters has been extracted and analyzed for classification purposes. The classifiers are assessed in terms of receiver operating characteristics and areas under their curves (AUC). Also, the computational loads are estimated. The maximum AUC of 82.4% was achieved for M 2 , closely followed by the binary box-counting (BBC) FD estimator with AUC=78.6%. For all descriptors, statistically significant differences between the subject groups were found (pfilm kinetics. They provide a viable alternative to previously used spectral counter parameters, and at the same time allow higher computational efficiency.
Application of fractal theory in refined reservoir description for EOR pilot area
Energy Technology Data Exchange (ETDEWEB)
Yue Li; Yonggang Duan; Yun Li; Yuan Lu
1997-08-01
A reliable reservoir description is essential to investigate scenarios for successful EOR pilot test. Reservoir characterization includes formation composition, permeability, porosity, reservoir fluids and other petrophysical parameters. In this study, various new tools have been applied to characterize Kilamayi conglomerate formation. This paper examines the merits of various statistical methods for recognizing rock property correlation in vertical columns and gives out methods to determine fractal dimension including R/S analysis and power spectral analysis. The paper also demonstrates that there is obvious fractal characteristics in conglomerate reservoirs of Kilamayi oil fields. Well log data in EOR pilot area are used to get distribution profile of parameters including permeability, porosity, water saturation and shale content.
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
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...
Fractal and multifractal analysis of LiF thin film surface
International Nuclear Information System (INIS)
Yadav, R.P.; Dwivedi, S.; Mittal, A.K.; Kumar, M.; Pandey, A.C.
2012-01-01
Highlights: ► Fractal and multifractal analysis of surface morphologies of the LiF thin films. ► Complexity and roughness of the LiF thin films increases as thickness increases. ► LiF thin films are multifractal in nature. ► Strength of the multifractality increases with thickness of the film. - Abstract: Fractal and multifractal analysis is performed on the atomic force microscopy (AFM) images of the surface morphologies of the LiF thin films of thickness 10 nm, 20 nm, and 40 nm, respectively. Autocorrelation function, height–height correlation function, and two-dimensional multifractal detrended fluctuation analysis (MFDFA) are used for characterizing the surface. It is found that the interface width, average roughness, lateral correlation length, and fractal dimension of the LiF thin film increase with the thickness of the film, whereas the roughness exponent decreases with thickness. Thus, the complexity and roughness of the LiF thin films increases as thickness increases. It is also demonstrated that the LiF thin films are multifractal in nature. Strength of the multifractality increases with thickness of the film.
International Nuclear Information System (INIS)
Micic, Miodrag; Klymyshyn, Nicholas A.; Lu, H Peter
2004-01-01
Near-field optical enhancement at metal surfaces and methods such as surface plasmon resonance (SPR), surface-enhanced Raman scattering (SERS), fluorescent quenching and enhancement, and various near-field scanning microscopies (NSOM) all depend on a metals surface properties, mainly on its morphology and SPR resonant frequency. We report on simulations of the influence of different surface morphologies on electromagnetic field enhancements at the rough surfaces of noble metals and also evaluate the optimal conditions for the generation of a surface-enhanced Raman signal of absorbed species on a metallic substrate. All simulations were performed with a classical electrodynamics approach using the full set of Maxwells equations, which were solved with the three-dimensional finite element method (FEM). Two different classes of surfaces where modeled using fractals, representing diffusion limited aggregation growth dendritic structures, such as one on the surface of electrodes, and second one representing the sponge-like structure used to model surfaces of particles with high porosity, such as metal coated catalyst supports. The simulations depict the high inhomogeneity of an enhanced electromagnetic field as both a field enhancement and field attenuation near the surface. While the diffusion limited aggregation dendritical fractals enhanced the near-field electromagnetic field, the sponge fractals significantly reduced the local electromagnetic field intensity. Moreover, the fractal orders of the fractal objects did not significantly alter the total enhancement, and the distribution of a near-field enhancement was essentially invariant to the changes in the angle of an incoming laser beam
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.
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.
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti; Jiang, Qiu; Mashraei, Yousof; Salama, Khaled N.; Alshareef, Husam N.
2017-01-01
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
Fractal characteristic in the wearing of cutting tool
Mei, Anhua; Wang, Jinghui
1995-11-01
This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.
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.
International Nuclear Information System (INIS)
Stemp, W James; Morozov, Mikhail; Key, Alastair J M
2015-01-01
Working load is one factor that affects wear on stone tools. Despite the recognition of the importance of the relationship between working load and the development of microwear on stone tools, there have been few attempts to quantify differences in wear due to changes in load. In a controlled experiment, we used 30 basalt flakes knapped from raw material collected in Olduvai Gorge, Tanzania, Africa, to cut oak branches for the same number of strokes. For each flake, a different loading level was applied starting at 150 g and increasing by increments of 150 g to a maximum load of 4.5 kg. A laser scanning confocal microscope was used to mathematically document the surface texture of the flakes. The worn surface data were compared using area-scale fractal complexity (Asfc), calculated from relative areas, to determine the degree to which variation in loading significantly affected the amount of wear on the flake surfaces. Our results indicate that working load does play a role in the development of lithic microwear on these flakes and that discrimination of two worn flake surfaces, using mean square ratios of Asfc, based on variable load is consistently possible with load differences between ∼100 g and 4.5 kg. However, discrimination of microwear on flake surfaces was not consistent for all load level differences and discrimination became less consistent when working load differences were below ∼100 g. (paper)
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.
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.
Directory of Open Access Journals (Sweden)
Sari Bahagiarti Kusumayudha
2009-11-01
Full Text Available The Gunungsewu area is a karst terrain with water scarcity, located in the Yogyakarta Special Province, adjacent to the open sea of Indian Ocean in the South. Shorelines of the Gunungsewu southern parts show fractal geometry phenomenon, and there can be found some groundwater outlets discharging to the Indian Ocean. One of the coastal outlets exists at the Baron Beach.The amount of water discharge from this spring reaches 20,000 l/sec in wet season, and approximately 9000 in dry season. In order to find other potential coastal springs, shoreline of the south coast is divided into some segments. By applying fractal analysis utilizing air photo of 1 : 30,000 scale, the fractal dimension of every shore line segment is determined, and then the fractal dimension value is correlated to the existence of spring in the segment being analyzed. The results inform us that shoreline segments having fractal dimension (D > 1.300 are potential for the occurrence of coastal springs.
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
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
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.
Arjunan, Sridhar Poosapadi; Kumar, Dinesh Kant
2010-10-21
Identifying finger and wrist flexion based actions using a single channel surface electromyogram (sEMG) can lead to a number of applications such as sEMG based controllers for near elbow amputees, human computer interface (HCI) devices for elderly and for defence personnel. These are currently infeasible because classification of sEMG is unreliable when the level of muscle contraction is low and there are multiple active muscles. The presence of noise and cross-talk from closely located and simultaneously active muscles is exaggerated when muscles are weakly active such as during sustained wrist and finger flexion. This paper reports the use of fractal properties of sEMG to reliably identify individual wrist and finger flexion, overcoming the earlier shortcomings. SEMG signal was recorded when the participant maintained pre-specified wrist and finger flexion movements for a period of time. Various established sEMG signal parameters such as root mean square (RMS), Mean absolute value (MAV), Variance (VAR) and Waveform length (WL) and the proposed fractal features: fractal dimension (FD) and maximum fractal length (MFL) were computed. Multi-variant analysis of variance (MANOVA) was conducted to determine the p value, indicative of the significance of the relationships between each of these parameters with the wrist and finger flexions. Classification accuracy was also computed using the trained artificial neural network (ANN) classifier to decode the desired subtle movements. The results indicate that the p value for the proposed feature set consisting of FD and MFL of single channel sEMG was 0.0001 while that of various combinations of the five established features ranged between 0.009 - 0.0172. From the accuracy of classification by the ANN, the average accuracy in identifying the wrist and finger flexions using the proposed feature set of single channel sEMG was 90%, while the average accuracy when using a combination of other features ranged between 58% and 73
Directory of Open Access Journals (Sweden)
Kumar Dinesh
2010-10-01
Full Text Available Abstract Background Identifying finger and wrist flexion based actions using a single channel surface electromyogram (sEMG can lead to a number of applications such as sEMG based controllers for near elbow amputees, human computer interface (HCI devices for elderly and for defence personnel. These are currently infeasible because classification of sEMG is unreliable when the level of muscle contraction is low and there are multiple active muscles. The presence of noise and cross-talk from closely located and simultaneously active muscles is exaggerated when muscles are weakly active such as during sustained wrist and finger flexion. This paper reports the use of fractal properties of sEMG to reliably identify individual wrist and finger flexion, overcoming the earlier shortcomings. Methods SEMG signal was recorded when the participant maintained pre-specified wrist and finger flexion movements for a period of time. Various established sEMG signal parameters such as root mean square (RMS, Mean absolute value (MAV, Variance (VAR and Waveform length (WL and the proposed fractal features: fractal dimension (FD and maximum fractal length (MFL were computed. Multi-variant analysis of variance (MANOVA was conducted to determine the p value, indicative of the significance of the relationships between each of these parameters with the wrist and finger flexions. Classification accuracy was also computed using the trained artificial neural network (ANN classifier to decode the desired subtle movements. Results The results indicate that the p value for the proposed feature set consisting of FD and MFL of single channel sEMG was 0.0001 while that of various combinations of the five established features ranged between 0.009 - 0.0172. From the accuracy of classification by the ANN, the average accuracy in identifying the wrist and finger flexions using the proposed feature set of single channel sEMG was 90%, while the average accuracy when using a combination
Impulse exchange at the surface of the ocean and the fractal dimension of drifter trajectories
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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.
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.
Doke, Atul M.; Sadana, Ajit
2006-05-01
A fractal analysis is presented for the binding and dissociation of different heart-related compounds in solution to receptors immobilized on biosensor surfaces. The data analyzed include LCAT (lecithin cholesterol acyl transferase) concentrations in solution to egg-white apoA-I rHDL immobilized on a biosensor chip surface.1 Single- and dual- fractal models were employed to fit the data. Values of the binding and the dissociation rate coefficient(s), affinity values, and the fractal dimensions were obtained from the regression analysis provided by Corel Quattro Pro 8.0 (Corel Corporation Limited).2 The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. Predictive equations are developed for the binding rate coefficient as a function of the degree of heterogeneity present on the sensor chip surface and on the LCAT concentration in solution, and for the affinity as a function of the ratio of fractal dimensions present in the binding and the dissociation phases. The analysis presented provided physical insights into these analyte-receptor reactions occurring on different biosensor surfaces.
Design and rapid prototyping of DLC coated fractal surfaces for tissue engineering applications
International Nuclear Information System (INIS)
Diaz-Lantada, A; Mosquera, A; Endrino, J L; Lafont, P
2010-01-01
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.
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.
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)
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.
International Nuclear Information System (INIS)
Dickau, Jonathan J.
2009-01-01
The use of fractals and fractal-like forms to describe or model the universe has had a long and varied history, which begins long before the word fractal was actually coined. Since the introduction of mathematical rigor to the subject of fractals, by Mandelbrot and others, there have been numerous cosmological theories and analyses of astronomical observations which suggest that the universe exhibits fractality or is by nature fractal. In recent years, the term fractal cosmology has come into usage, as a description for those theories and methods of analysis whereby a fractal nature of the cosmos is shown.
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)
International Nuclear Information System (INIS)
Hong, Wang Xu; Huijie, Qin; Zhe, Zhang; Fei, Li
2014-01-01
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
International Nuclear Information System (INIS)
Wawszczak, J.
1999-01-01
This paper presents a procedure for quantitative image analysis for determination of the fractal dimension from SEM surface images of the fracture 0H14N5CuNb steel. Investigated quenched and tempered samples of the steel after impact tests (in room and -85 o C temperatures). This method can be useful for analysing local fractal dimension of any surface parts (not oriented) of the fracture with different topography of this surface. (author)
Dual Orlicz geominimal surface area
Directory of Open Access Journals (Sweden)
Tongyi Ma
2016-02-01
Full Text Available Abstract The L p $L_{p}$ -geominimal surface area was introduced by Lutwak in 1996, which extended the important concept of the geominimal surface area. Recently, Wang and Qi defined the p-dual geominimal surface area, which belongs to the dual Brunn-Minkowski theory. In this paper, based on the concept of the dual Orlicz mixed volume, we extend the dual geominimal surface area to the Orlicz version and give its properties. In addition, the isoperimetric inequality, a Blaschke-Santaló type inequality, and the monotonicity inequality for the dual Orlicz geominimal surface areas are established.
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
Energy Technology Data Exchange (ETDEWEB)
Vinogradov, A. [Laboratory for the Physics of Strength of Materials and Intelligent Diagnostic Systems, Togliatti State University, Togliatti 445667 (Russian Federation); Laboratory of Hybrid Nanostructured Materials, NITU MISiS, Moscow 119490 (Russian Federation); Yasnikov, I. S. [Laboratory for the Physics of Strength of Materials and Intelligent Diagnostic Systems, Togliatti State University, Togliatti 445667 (Russian Federation); Estrin, Y. [Laboratory of Hybrid Nanostructured Materials, NITU MISiS, Moscow 119490 (Russian Federation); Centre for Advanced Hybrid Materials, Department of Materials Engineering, Monash University, Clayton, VIC 3800 (Australia)
2014-06-21
We demonstrate that the fractal dimension (FD) of the dislocation population in a deforming material is an important quantitative characteristic of the evolution of the dislocation structure. Thus, we show that peaking of FD signifies a nearing loss of uniformity of plastic flow and the onset of strain localization. Two techniques were employed to determine FD: (i) inspection of surface morphology of the deforming crystal by white light interferometry and (ii) monitoring of acoustic emission (AE) during uniaxial tensile deformation. A connection between the AE characteristics and the fractal dimension determined from surface topography measurements was established. As a common platform for the two methods, the dislocation density evolution in the bulk was used. The relations found made it possible to identify the occurrence of a peak in the median frequency of AE as a harbinger of plastic instability leading to necking. It is suggested that access to the fractal dimension provided by AE measurements and by surface topography analysis makes these techniques important tools for monitoring the evolution of the dislocation structure during plastic deformation—both as stand-alone methods and especially when used in tandem.
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.
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
International Nuclear Information System (INIS)
Bramowicz, Miroslaw; Braic, Laurentiu; Azem, Funda Ak; Kulesza, Slawomir; Birlik, Isil; Vladescu, Alina
2016-01-01
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"−"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
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
. Instead, I outline a fractal approach to the study of space, society, and infrastructure. A fractal orientation requires a number of related conceptual reorientations. It has implications for thinking about scale and perspective, and (sociotechnical) relations, and for considering the role of the social...... and a fractal social theory....
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.
Pore Structure and Fractal Characteristics of Niutitang Shale from China
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Zhaodong Xi
2018-04-01
Full Text Available A suite of shale samples from the Lower Cambrian Niutitang Formation in northwestern Hunan Province, China, were investigated to better understand the pore structure and fractal characteristics of marine shale. Organic geochemistry, mineralogy by X-ray diffraction, porosity, permeability, mercury intrusion and nitrogen adsorption and methane adsorption experiments were conducted for each sample. Fractal dimension D was obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH model. The relationships between total organic carbon (TOC content, mineral compositions, pore structure parameters and fractal dimension are discussed, along with the contributions of fractal dimension to shale gas reservoir evaluation. Analysis of the results showed that Niutitang shale samples featured high TOC content (2.51% on average, high thermal maturity (3.0% on average, low permeability and complex pore structures, which are highly fractal. TOC content and mineral compositions are two major factors affecting pore structure but they have different impacts on the fractal dimension. Shale samples with higher TOC content had a larger specific surface area (SSA, pore volume (PV and fractal dimension, which enhanced the heterogeneity of the pore structure. Quartz content had a relatively weak influence on shale pore structure, whereas SSA, PV and fractal dimension decreased with increasing clay mineral content. Shale with a higher clay content weakened pore structure heterogeneity. The permeability and Langmuir volume of methane adsorption were affected by fractal dimension. Shale samples with higher fractal dimension had higher adsorption capacity but lower permeability, which is favorable for shale gas adsorption but adverse to shale gas seepage and diffusion.
Saw, Vee-Liem; Chew, Lock Yue
2013-01-01
We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line ...
Fractals in several electrode materials
Energy Technology Data Exchange (ETDEWEB)
Zhang, Chunyong, E-mail: zhangchy@njau.edu.cn [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); Wu, Jingyu [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Fu, Degang [Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); State Key Laboratory of Bioelectronics, Southeast University, Nanjing 210096 (China)
2014-09-15
Highlights: • Fractal geometry was employed to characterize three important electrode materials. • The surfaces of all studied electrodes were proved to be very rough. • The fractal dimensions of BDD and ACF were scale dependent. • MMO film was more uniform than BDD and ACF in terms of fractal structures. - Abstract: In the present paper, the fractal properties of boron-doped diamond (BDD), mixed metal oxide (MMO) and activated carbon fiber (ACF) electrode have been studied by SEM imaging at different scales. Three materials are self-similar with mean fractal dimension in the range of 2.6–2.8, confirming that they all exhibit very rough surfaces. Specifically, it is found that MMO film is more uniform in terms of fractal structure than BDD and ACF. As a result, the intriguing characteristics make these electrodes as ideal candidates for high-performance decontamination processes.
Peleg, M
1993-01-01
Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.
Energy Technology Data Exchange (ETDEWEB)
Rožić, L.J., E-mail: ljrozic@nanosys.ihtmbg.ac.rs [University of Belgrade, IChTM-Department of Catalysis and Chemical Engineering, Njegoševa 12, Belgrade (Serbia); Petrović, S.; Radić, N. [University of Belgrade, IChTM-Department of Catalysis and Chemical Engineering, Njegoševa 12, Belgrade (Serbia); Stojadinović, S. [University of Belgrade, Faculty of Physics, Studentski trg 12-16, Belgrade (Serbia); Vasilić, R. [Faculty of Environmental Governance and Corporate Responsibility, Educons University, Vojvode Putnika 87, Sremska Kamenica (Serbia); Stefanov, P. [Institute of General and Inorganic Chemistry, Bulgarian Academy of Sciences, Sofia 1113 (Bulgaria); Grbić, B. [University of Belgrade, IChTM-Department of Catalysis and Chemical Engineering, Njegoševa 12, Belgrade (Serbia)
2013-07-31
In this study, we have shown that atomic force microscopy is a powerful technique to study the fractal parameters of TiO{sub 2}/WO{sub 3} coatings prepared by plasma electrolytic oxidation (PEO) process. Since the surface roughness of obtained oxide coatings affects their physical properties, an accurate description of roughness parameters is highly desirable. The surface roughness, described by root mean squared and arithmetic average values, is analyzed considering the scans of a series of atomic force micrographs. The results show that the oxide coatings exhibit lower surface roughness in initial stage of PEO process. Also, the surfaces of TiO{sub 2}/WO{sub 3} coatings exhibit fractal behavior. Positive correlation between the fractal dimension and surface roughness of the surfaces of TiO{sub 2}/WO{sub 3} coatings in initial stage of PEO process was found. - Highlights: • TiO{sub 2}/WO{sub 3} coatings were obtained by plasma electrolytic oxidation. • Oxide coatings exhibit lower surface roughness in initial stage of process. • The surfaces of TiO{sub 2}/WO{sub 3} coatings exhibit fractal behavior.
Goffman, Casper
1969-01-01
For length and area, a central fact is that the value of the length of a curve or the area of a surface, as given by the Lebesgue theory, is at least as great as that given by the classical formula, whenever the latter has meaning. This is now found not to be valid in higher dimensions. We give an example of a continuous mapping of the unit cube into itself for which the value given by the formula exceeds the three-dimensional Lebesgue area of the corresponding suface. PMID:16591750
Determination of retinal surface area.
Nagra, Manbir; Gilmartin, Bernard; Thai, Ngoc Jade; Logan, Nicola S
2017-09-01
Previous attempts at determining retinal surface area and surface area of the whole eye have been based upon mathematical calculations derived from retinal photographs, schematic eyes and retinal biopsies of donor eyes. 3-dimensional (3-D) ocular magnetic resonance imaging (MRI) allows a more direct measurement, it can be used to image the eye in vivo, and there is no risk of tissue shrinkage. The primary purpose of this study is to compare, using T2-weighted 3D MRI, retinal surface areas for superior-temporal (ST), inferior-temporal (IT), superior-nasal (SN) and inferior-nasal (IN) retinal quadrants. An ancillary aim is to examine whether inter-quadrant variations in area are concordant with reported inter-quadrant patterns of susceptibility to retinal breaks associated with posterior vitreous detachment (PVD). Seventy-three adult participants presenting without retinal pathology (mean age 26.25 ± 6.06 years) were scanned using a Siemens 3-Tesla MRI scanner to provide T2-weighted MR images that demarcate fluid-filled internal structures for the whole eye and provide high-contrast delineation of the vitreous-retina interface. Integrated MRI software generated total internal ocular surface area (TSA). The second nodal point was used to demarcate the origin of the peripheral retina in order to calculate total retinal surface area (RSA) and quadrant retinal surface areas (QRSA) for ST, IT, SN, and IN quadrants. Mean spherical error (MSE) was -2.50 ± 4.03D and mean axial length (AL) 24.51 ± 1.57 mm. Mean TSA and RSA for the RE were 2058 ± 189 and 1363 ± 160 mm 2 , respectively. Repeated measures anova for QRSA data indicated a significant difference within-quadrants (P area/mm increase in AL. Although the differences between QRSAs are relatively small, there was evidence of concordance with reported inter-quadrant patterns of susceptibility to retinal breaks associated with PVD. The data allow AL to be converted to QRSAs, which will assist further
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.
Paz-Ferreiro, J.; Bertol, I.; Vidal Vázquez, E.
2008-07-01
Changes in soil surface microrelief with cumulative rainfall under different tillage systems and crop cover conditions were investigated in southern Brazil. Surface cover was none (fallow) or the crop succession maize followed by oats. Tillage treatments were: 1) conventional tillage on bare soil (BS), 2) conventional tillage (CT), 3) minimum tillage (MT) and 4) no tillage (NT) under maize and oats. Measurements were taken with a manual relief meter on small rectangular grids of 0.234 and 0.156 m2, throughout growing season of maize and oats, respectively. Each data set consisted of 200 point height readings, the size of the smallest cells being 3×5 cm during maize and 2×5 cm during oats growth periods. Random Roughness (RR), Limiting Difference (LD), Limiting Slope (LS) and two fractal parameters, fractal dimension (D) and crossover length (l) were estimated from the measured microtopographic data sets. Indices describing the vertical component of soil roughness such as RR, LD and l generally decreased with cumulative rain in the BS treatment, left fallow, and in the CT and MT treatments under maize and oats canopy. However, these indices were not substantially affected by cumulative rain in the NT treatment, whose surface was protected with previous crop residues. Roughness decay from initial values was larger in the BS treatment than in CT and MT treatments. Moreover, roughness decay generally tended to be faster under maize than under oats. The RR and LD indices decreased quadratically, while the l index decreased exponentially in the tilled, BS, CT and MT treatments. Crossover length was sensitive to differences in soil roughness conditions allowing a description of microrelief decay due to rainfall in the tilled treatments, although better correlations between cumulative rainfall and the most commonly used indices RR and LD were obtained. At the studied scale, parameters l and D have been found to be useful in interpreting the configuration properties of
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)
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
Directory of Open Access Journals (Sweden)
Xiang Niu
2015-12-01
Full Text Available Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD and soil water retention curve (WRC under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1 the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM > Pinus thunbergii Parl. (PTP > Juglans rigia Linn. (JRL > abandoned grassland (ABG; (2 the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL were significantly higher than that in ABG, and mixed forests (QRM and PPM were higher than that in pure forests (PTP and JRL; (3 the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4 the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure.
Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu
2015-01-01
Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure. PMID:26633458
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.
Mirko Ahmadfaraj; Mirsaleh Mirmohammadi; Peyman Afzal
2016-01-01
The aim of this study is determination and separation of alteration zones using Concentration-Area (C-A) fractal model based on remote sensing data which has been extracted from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) images. The studied area is on the SW part of Saveh, 1:250,000 geological map, which is located in Urumieh-Dokhtar magmatic belt, Central Iran. The pixel values were computed by Principal Component Analysis (PCA) method used to determine phyllic, a...
Wei, Wang; Binwu, He
2008-12-01
According to the notion of Lp-affine surface area by Lutwak, in this paper, we introduce the concept of Lp-dual affine surface area. Further, we establish the affine isoperimetric inequality and the Blaschke-Santaló inequality for Lp-dual affine surface area. Besides, the dual Brunn-Minkowski inequality for Lp-dual affine surface area is presented.
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
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
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.
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.
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.
Fractal theory of radon emanation from solids
International Nuclear Information System (INIS)
Semkow, T.M.
1991-01-01
The author developed a fractal theory of Rn emanation from solids, based on α recoil from the α decay of Ra. Range straggling of the recoiling Rn atoms in the solid state is included and the fractal geometry is used to describe the roughness of the emanating surface. A fractal dimension D of the surface and the median projected range become important parameters in calculating the radon emanating power E R from solids. A relation between E R and the specific surface area measured by the gas adsorption is derived for the first time, assuming a uniform distribution of the precursor Ra throughout the samples. It is suggested that the E R measurements can be used to determine D of the surfaces on the scale from tens to hundreds of nm. One obtains, for instance, D = 2.17 ± 0.06 for Lipari volcanic glass and D = 2.83 ± 0.03 for pitchblende. In addition, the author suggests a new process of penetrating recoil and modify the role of indirect recoil. The penetrating recoil may be important for rough surfaces, in which case Rn loses its kinetic energy by penetrating a large number of small surface irregularities. The indirect recoil may be important at the very last stage of energy-loss process, for kinetic energies below ∼ 5 keV
Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga
2016-04-01
The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established
Directory of Open Access Journals (Sweden)
Mirko Ahmadfaraj
2016-06-01
Full Text Available The aim of this study is determination and separation of alteration zones using Concentration-Area (C-A fractal model based on remote sensing data which has been extracted from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER images. The studied area is on the SW part of Saveh, 1:250,000 geological map, which is located in Urumieh-Dokhtar magmatic belt, Central Iran. The pixel values were computed by Principal Component Analysis (PCA method used to determine phyllic, argillic, and propylitic alteration zones. The C-A fractal model is utilized for separation of different parts of alteration zones due to their intensity. The log-log C-A plots reveal multifractal nature for phyllic, argillic, and propylitic alteration zones. The obtained results based on fractal model show that the main trend of the alteration zones is in NW-SE direction. Compared to the geological map of the study area and copper mineralizations, the alteration zones have been detected properly and correlate with the mineral occurrences, intrusive rock, and faults.
Morphometric relations of fractal-skeletal based channel network model
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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.
Wang, Weidong; Leng, Gangsong
2007-11-01
According to the three notions of mixed affine surface area, Lp-affine surface area and Lp-mixed affine surface area proposed by Lutwak, in this article, we give the concept of ith Lp-mixed affine surface area such that the first and second notions of Lutwak are its special cases. Further, some Lutwak's results are extended associated with this concept. Besides, applying this concept, we establish an inequality for the volumes and dual quermassintegrals of a class of star bodies.
Wavelet-fractal approach to surface characterization of nanocrystalline ITO thin films
International Nuclear Information System (INIS)
Raoufi, Davood; Kalali, Zahra
2012-01-01
In this study, indium tin oxide (ITO) thin films were prepared by electron beam deposition method on glass substrates at room temperature (RT). Surface morphology characterization of ITO thin films, before and after annealing at 500 °C, were investigated by analyzing the surface profile of atomic force microscopy (AFM) images using wavelet transform formalism. The wavelet coefficients related to the thin film surface profiles have been calculated, and then roughness exponent (α) of the films has been estimated using the scalegram method. The results reveal that the surface profiles of the films before and after annealing process have self-affine nature.
Bruning, Eric C.; Thomas, Ronald J.; Krehbiel, Paul R.; Rison, William; Carey, Larry D.; Koshak, William; Peterson, Harold; MacGorman, Donald R.
2013-01-01
We will use VHF Lightning Mapping Array data to estimate NOx per flash and per unit channel length, including the vertical distribution of channel length. What s the best way to find channel length from VHF sources? This paper presents the rationale for the fractal method, which is closely related to the box-covering method.
Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.
Quodbach, J.; Moussavi, A.; Tammer, R.; Frahm, J.; Kleinebudde, P.
2014-01-01
An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this c...
Ku, Bon Ki; Kulkarni, Pramod
2012-05-01
We compare different approaches to measure surface area of aerosol agglomerates. The objective was to compare field methods, such as mobility and diffusion charging based approaches, with laboratory approach, such as Brunauer, Emmett, Teller (BET) method used for bulk powder samples. To allow intercomparison of various surface area measurements, we defined 'geometric surface area' of agglomerates (assuming agglomerates are made up of ideal spheres), and compared various surface area measurements to the geometric surface area. Four different approaches for measuring surface area of agglomerate particles in the size range of 60-350 nm were compared using (i) diffusion charging-based sensors from three different manufacturers, (ii) mobility diameter of an agglomerate, (iii) mobility diameter of an agglomerate assuming a linear chain morphology with uniform primary particle size, and (iv) surface area estimation based on tandem mobility-mass measurement and microscopy. Our results indicate that the tandem mobility-mass measurement, which can be applied directly to airborne particles unlike the BET method, agrees well with the BET method. It was also shown that the three diffusion charging-based surface area measurements of silver agglomerates were similar within a factor of 2 and were lower than those obtained from the tandem mobility-mass and microscopy method by a factor of 3-10 in the size range studied. Surface area estimated using the mobility diameter depended on the structure or morphology of the agglomerate with significant underestimation at high fractal dimensions approaching 3.
Comparison of two fractal interpolation methods
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
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
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.
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
Energy Technology Data Exchange (ETDEWEB)
Aushev, A A; Barinov, S P; Vasin, M G; Drozdov, Yu M; Ignat' ev, Yu V; Izgorodin, V M; Kovshov, D K; Lakhtikov, A E; Lukovkina, D D; Markelov, V V; Morovov, A P; Shishlov, V V [Russian Federal Nuclear Center ' All-Russian Research Institute of Experimental Physics' , Sarov, Nizhnii Novgorod region (Russian Federation)
2015-06-30
We present the results of employing the alpha-spectrometry method to determine the characteristics of porous materials used in targets for laser plasma experiments. It is shown that the energy spectrum of alpha-particles, after their passage through porous samples, allows one to determine the distribution of their path length in the foam skeleton. We describe the procedure of deriving such a distribution, excluding both the distribution broadening due to statistical nature of the alpha-particle interaction with an atomic structure (straggling) and hardware effects. The fractal analysis of micro-images is applied to the same porous surface samples that have been studied by alpha-spectrometry. The fractal dimension and size distribution of the number of the foam skeleton grains are obtained. Using the data obtained, a distribution of the total foam skeleton thickness along a chosen direction is constructed. It roughly coincides with the path length distribution of alpha-particles within a range of larger path lengths. It is concluded that the combined use of the alpha-spectrometry method and fractal analysis of images will make it possible to determine the size distribution of foam skeleton grains (or pores). The results can be used as initial data in theoretical studies on propagation of the laser and X-ray radiation in specific porous samples. (laser plasma)
Directory of Open Access Journals (Sweden)
Ali Asghar Sepahi-Gerow
2017-03-01
Full Text Available In aplites of Khaku area, located in the east of the Alvand body, tourmaline noduleswith spherical and dendritic shapes are dispersed. Some of these nodules have light halothat is actually a transition zone between the core of nodules and the host aplites.Geometrically, these nodules are fractal shapes. In these nodules fractal dimension vary from 1.46 in dendritic nodules to 1.92 in spherical nodules. In three-dimensionalreconstructions of the studied nodule, the average volume for the core is 34% and 66%for its margin. Based on evidences such as lack of veins between nodules, tourmalineswith anhedral forms, presence of a leucocratic halo in the aureole of some nodules, theirspherical shape, their linear and flow dispersion in the host rock these nodules have been crystallized in magmatic condition. In the final stages of magma crystallizationand the B content increment followed by beginning of unmixing in the melt, distinctspherical bubbles have been developed which gave rise to nodules formation. Magmaticsystem acts as chaotic systems and the presence of rotational and limited closed areas inthe vicinity of areas with disturbed paths has led to the formation of rounded anddendritic nodules beside each other.
Contact area measurements on structured surfaces
DEFF Research Database (Denmark)
Kücükyildiz, Ömer Can; Jensen, Sebastian Hoppe Nesgaard; De Chiffre, Leonardo
In connection with the use of brass specimens featuring structured surfaces in a tribology test, an algorithm was developed for automatic measurement of the contact area by optical means.......In connection with the use of brass specimens featuring structured surfaces in a tribology test, an algorithm was developed for automatic measurement of the contact area by optical means....
L p -Dual geominimal surface area
Directory of Open Access Journals (Sweden)
Weidong Wang
2011-01-01
Full Text Available Abstract Lutwak proposed the notion of Lp -geominimal surface area according to the Lp -mixed volume. In this article, associated with the Lp -dual mixed volume, we introduce the Lp -dual geominimal surface area and prove some inequalities for this notion. 2000 Mathematics Subject Classification: 52A20 52A40.
Wetted surface area of recreational boats
Bakker J; van Vlaardingen PLA; ICH; VSP
2018-01-01
The wetted surface area of recreational craft is often treated with special paint that prevents growth of algae and other organisms. The active substances in this paint (antifouling) are also emitted into the water. The extent of this emission is among others determined by the treated surface area.
Using fuzzy fractal features of digital images for the material surface analisys
Privezentsev, D. G.; Zhiznyakov, A. L.; Astafiev, A. V.; Pugin, E. V.
2018-01-01
Edge detection is an important task in image processing. There are a lot of approaches in this area: Sobel, Canny operators and others. One of the perspective techniques in image processing is the use of fuzzy logic and fuzzy sets theory. They allow us to increase processing quality by representing information in its fuzzy form. Most of the existing fuzzy image processing methods switch to fuzzy sets on very late stages, so this leads to some useful information loss. In this paper, a novel method of edge detection based on fuzzy image representation and fuzzy pixels is proposed. With this approach, we convert the image to fuzzy form on the first step. Different approaches to this conversion are described. Several membership functions for fuzzy pixel description and requirements for their form and view are given. A novel approach to edge detection based on Sobel operator and fuzzy image representation is proposed. Experimental testing of developed method was performed on remote sensing images.
Conference on Fractals and Related Fields III
Seuret, Stéphane
2017-01-01
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
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 geometry mathematical foundations and applications
Falconer, Kenneth
2013-01-01
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applica
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
Directory of Open Access Journals (Sweden)
Alireza Zarasvandi
2015-10-01
such linear trends occur at a characteristic spacing. There is 37 and 42 copper point's index in the Khezr-Abad and Shar-B-Babak areas. The Fry patterns of copper index for two areas were determined with application of Dot Proc software. Fractal analysis is another technique for determination of regional distribution of faults. In this research the fractal dimension of joints and faults was determined in different locations using box-counting fractal method and drawing the logarithmic graphs. Results - The major faults show NW/SE trends in the Khezr-Abad area. They have a similar trend with Dehshir-Baft fault. Other sets of faults show NE/SW trend. These faults are younger than the Dehshir-Baft and release sinistral sense of shear. - Intrusion of two intrusive bodies leads to the accumulation of strike-slip faults in the vicinity of intrusive rocks. In this region faults and joints mainly show NW/SE and NE/SW trends. - The results of Fry analysis show that the mineralization in the Khezr-Abad occurred in the Cretaceous (and younger rocks with NE/SW and NW/SE orientations. In the other words, these areas of mineralization are mainly related to the secondary faults or (P faults in the pull basins and cross cutting points of these faults which have similar strike with the Dehshir-Baft fault. NE/SW mineralization is probably related to the tensional stress direction or faults having the general trends of central Iran structures. - The calculations of fractal dimension show that the southeastern parts of the Khezr Abad have higher amounts of fractal dimension (Db= 1.7002. Also there is a relatively higher copper index in this part, indicating a logical relation between fault structures and mineralization. -The generated maps indicate that the mineralization in the Shahr-e-Babak area occurred at the intersection of faults and volcanic system and the Fry analysis shows a NE/SW and NW/SE trend of ore concentration. - Northwestern parts of the Share-e-Babak show higher fractal
Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.
Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter
2014-11-20
An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.
International Nuclear Information System (INIS)
Jung, Kyu-Nam; Pyun, Su-Il
2007-01-01
Lithium transport through the partially inactive fractal Li 1-δ Mn 2 O 4 film electrode under the cell-impedance-controlled constraint was theoretically investigated by using the kinetic Monte Carlo method based upon random walk approach. Under the cell-impedance-controlled constraint, all the potentiostatic current transients calculated from the totally active and partially inactive fractal electrodes hardly exhibited the generalised Cottrell behaviour and they were significantly affected in shape by the interfacial charge-transfer kinetics. In the case of the linear sweep voltammogram determined from the totally active and partially inactive fractal electrodes, all the power dependence of the peak current on the scan rate above the characteristic scan rate deviated from the generalised Randles-Sevcik behaviour. From the analyses of the current transients and the linear sweep voltammograms simulated with various values of the simulation parameters, it was further recognised that the cell-impedance-controlled lithium transport through the partially inactive fractal Li 1-δ Mn 2 O 4 film electrode strongly deviates from the generalised diffusion-controlled transport behaviour of the electrode with the totally active surface, which is attributed to the impeded interfacial charge-transfer kinetics governed by the surface inhomogeneities including the fractal dimension of the surface and the surface coverage by active sites and by the kinetic parameters including the internal cell resistance
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
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
Fractals via iterated functions and multifunctions
International Nuclear Information System (INIS)
Singh, S.L.; Prasad, Bhagwati; Kumar, Ashish
2009-01-01
Fractals have wide applications in biology, computer graphics, quantum physics and several other areas of applied sciences (see, for instance [Daya Sagar BS, Rangarajan Govindan, Veneziano Daniele. Preface - fractals in geophysics. Chaos, Solitons and Fractals 2004;19:237-39; El Naschie MS. Young double-split experiment Heisenberg uncertainty principles and cantorian space-time. Chaos, Solitons and Fractals 1994;4(3):403-09; El Naschie MS. Quantum measurement, information, diffusion and cantorian geodesics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 191-205; El Naschie MS. Iterated function systems, information and the two-slit experiment of quantum mechanics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 185-9; El Naschie MS, Rossler OE, Prigogine I. Forward. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995; El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 2004;19:209-36; El Naschie MS. Fractal black holes and information. Chaos, Solitons and Fractals 2006;29:23-35; El Naschie MS. Superstring theory: what it cannot do but E-infinity could. Chaos, Solitons and Fractals 2006;29:65-8). Especially, the study of iterated functions has been found very useful in the theory of black holes, two-slit experiment in quantum mechanics (cf. El Naschie, as mentioned above). The intent of this paper is to give a brief account of recent developments of fractals arising from IFS. We also discuss iterated multifunctions.
Normalization in quantitative [18F]FDG PET imaging: the 'body surface area' may be a volume
International Nuclear Information System (INIS)
Laffon, Eric; Suarez, Kleydis; Berthoumieu, Yannick; Ducassou, Dominique; Marthan, Roger
2006-01-01
Non-invasive methods for quantifying [ 18 F]FDG uptake in tumours often require normalization to either body weight or body surface area (BSA), as a surrogate for [ 18 F]FDG distribution volume (DV). Whereas three dimensions are involved in DV and weight (assuming that weight is proportional to volume), only two dimensions are obviously involved in BSA. However, a fractal geometry interpretation, related to an allometric scaling, suggests that the so-called 'body surface area' may stand for DV. (note)
Transient effects in friction fractal asperity creep
Goedecke, Andreas
2013-01-01
Transient friction effects determine the behavior of a wide class of mechatronic systems. Classic examples are squealing brakes, stiction in robotic arms, or stick-slip in linear drives. To properly design and understand mechatronic systems of this type, good quantitative models of transient friction effects are of primary interest. The theory developed in this book approaches this problem bottom-up, by deriving the behavior of macroscopic friction surfaces from the microscopic surface physics. The model is based on two assumptions: First, rough surfaces are inherently fractal, exhibiting roughness on a wide range of scales. Second, transient friction effects are caused by creep enlargement of the real area of contact between two bodies. This work demonstrates the results of extensive Finite Element analyses of the creep behavior of surface asperities, and proposes a generalized multi-scale area iteration for calculating the time-dependent real contact between two bodies. The toolset is then demonstrated both...
A Fractal Perspective on Scale in Geography
Directory of Open Access Journals (Sweden)
Bin Jiang
2016-06-01
Full Text Available Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution and the modifiable areal unit problem (MAUP. This paper argues that the confusion and frustration arise from traditional Euclidean geometric thinking, in which locations, directions, and sizes are considered absolute, and it is now time to revise this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, most geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we present topological and scaling analyses illustrated by street-related concepts such as natural streets, street blocks, and natural cities. We further contend that one of the two spatial properties, spatial heterogeneity, is de facto the fractal nature of geographic features, and it should be considered the first effect among the two, because it is global and universal across all scales, which should receive more attention from practitioners of geography.
Surface moisture estimation in urban areas
Jiang, Yitong
Surface moisture is an important parameter because it modifies urban microclimate and surface layer meteorology. The primary objectives of this paper are: 1) to analyze the impact of surface roughness from buildings on surface moisture in urban areas; and 2) to quantify the impact of surface roughness resulting from urban trees on surface moisture. To achieve the objectives, two hypotheses were tested: 1) the distribution of surface moisture is associated with the structural complexity of buildings in urban areas; and 2) The distribution and change of surface moisture is associated with the distribution and vigor of urban trees. The study area is Indianapolis, Indiana, USA. In the part of the morphology of urban trees, Warren Township was selected due to the limitation of tree inventory data. To test the hypotheses, the research design was made to extract the aerodynamic parameters, such as frontal areas, roughness length and displacement height of buildings and trees from Terrestrial and Airborne LiDAR data, then to input the aerodynamic parameters into the urban surface energy balance model. The methodology was developed for comparing the impact of aerodynamic parameters from LiDAR data with the parameters that were derived empirically from land use and land cover data. The analytical procedures are discussed below: 1) to capture the spatial and temporal variation of surface moisture, daily and hourly Land Surface Temperature (LST) were downscaled from 4 km to 1 km, and 960 m to 30 m, respectively, by regression between LST and various components that impact LST; 2) to estimate surface moisture, namely soil moisture and evapotranspiration (ET), land surfaces were classified into soil, vegetation, and impervious surfaces, using Linear Spectral Mixture Analysis (LSMA); 3) aerodynamic parameters of buildings and trees were extracted from Airborne and Terrestrial LiDAR data; 4) the Temperature-Vegetation-Index (TVX) method, and the Two-Source-Energy-Balance (TSEB
Surface area-volume ratios in insects.
Kühsel, Sara; Brückner, Adrian; Schmelzle, Sebastian; Heethoff, Michael; Blüthgen, Nico
2017-10-01
Body mass, volume and surface area are important for many aspects of the physiology and performance of species. Whereas body mass scaling received a lot of attention in the literature, surface areas of animals have not been measured explicitly in this context. We quantified surface area-volume (SA/V) ratios for the first time using 3D surface models based on a structured light scanning method for 126 species of pollinating insects from 4 orders (Diptera, Hymenoptera, Lepidoptera, and Coleoptera). Water loss of 67 species was measured gravimetrically at very dry conditions for 2 h at 15 and 30 °C to demonstrate the applicability of the new 3D surface measurements and relevance for predicting the performance of insects. Quantified SA/V ratios significantly explained the variation in water loss across species, both directly or after accounting for isometric scaling (residuals of the SA/V ∼ mass 2/3 relationship). Small insects with a proportionally larger surface area had the highest water loss rates. Surface scans of insects to quantify allometric SA/V ratios thus provide a promising method to predict physiological responses, improving the potential of body mass isometry alone that assume geometric similarity. © 2016 Institute of Zoology, Chinese Academy of Sciences.
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
Fractal corrections of BaTiO3-ceramic sintering parameters
Directory of Open Access Journals (Sweden)
Mitić V.V.
2014-01-01
Full Text Available Morphology of ceramics grains and pores as well as Brownian character of particle dynamics inside ceramics specimen contributes to better understanding of the sintering process. BaTiO3-ceramics, studied in this paper, has light fractal form and it is emanated in three aspects. First, the surface of grains, even in starting green body as well as distribution of grains shows fractal behavior. Second, existence of pores and their distribution follow the rules of fractal geometry. Third, movement of particles inside viscous flow underlies the rule of Brownian motion, which is essentially a fractal category. These three elements, each in its domain influence sintering dynamics, and can be described by dimensionless quantitative factors, αs αp and αm, being normalized to the interval [0,1]. Following sintering process, the associate formulae of Frenkel, Scherer and Mackenzie-Shuttleworth are shown from the angle of view of ceramics fractal dimension changing that approaches to 3. Also, it is shown that the energy balance is not violated after applying fractal correction to quasi equilibrium of the energy emanating from surface area reduction ES and energy adopted by viscous flow Ef .[Projekat Ministarstva nauke Republike Srbije, br. 172057: Directed synthesis, structure and properties of multifunctional materials
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.
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.
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...
FELICIA RAMONA BIRAU
2012-01-01
In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and...
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
Monitoring System for ALICE Surface Areas
Demirbasci, Oguz
2016-01-01
I have been at CERN for 12 weeks within the scope of Summer Student Programme working on a monitoring system project for surface areas of the ALICE experiment during this period of time. The development and implementation of a monitoring system for environmental parameters in the accessible areas where a cheap hardware setup can be deployed were aim of this project. This report explains how it was developed by using Arduino, Raspberry PI, WinCC OA and DIM protocol.
Osmosis and Surface Area to Volume Ratio.
Barrett, D. R. B.
1984-01-01
Describes an experiment designed to help students understand the concepts of osmosis and surface area to volume ratio (SA:VOL). The task for students is to compare water uptake in different sizes of potato cubes and relate differences to their SA:VOL ratios. (JN)
Estimating surface area in early hominins.
Directory of Open Access Journals (Sweden)
Alan Cross
Full Text Available Height and weight-based methods of estimating surface area have played an important role in the development of the current consensus regarding the role of thermoregulation in human evolution. However, such methods may not be reliable when applied to early hominins because their limb proportions differ markedly from those of humans. Here, we report a study in which this possibility was evaluated by comparing surface area estimates generated with the best-known height and weight-based method to estimates generated with a method that is sensitive to proportional differences. We found that the two methods yield indistinguishable estimates when applied to taxa whose limb proportions are similar to those of humans, but significantly different results when applied to taxa whose proportions differ from those of humans. We also found that the discrepancy between the estimates generated by the two methods is almost entirely attributable to inter-taxa differences in limb proportions. One corollary of these findings is that we need to reassess hypotheses about the role of thermoregulation in human evolution that have been developed with the aid of height and weight-based methods of estimating body surface area. Another is that we need to use other methods in future work on fossil hominin body surface areas.
Nondestructive, stereological estimation of canopy surface area
DEFF Research Database (Denmark)
Wulfsohn, Dvora-Laio; Sciortino, Marco; Aaslyng, Jesper M.
2010-01-01
We describe a stereological procedure to estimate the total leaf surface area of a plant canopy in vivo, and address the problem of how to predict the variance of the corresponding estimator. The procedure involves three nested systematic uniform random sampling stages: (i) selection of plants from...... a canopy using the smooth fractionator, (ii) sampling of leaves from the selected plants using the fractionator, and (iii) area estimation of the sampled leaves using point counting. We apply this procedure to estimate the total area of a chrysanthemum (Chrysanthemum morifolium L.) canopy and evaluate both...... the time required and the precision of the estimator. Furthermore, we compare the precision of point counting for three different grid intensities with that of several standard leaf area measurement techniques. Results showed that the precision of the plant leaf area estimator based on point counting...
Directory of Open Access Journals (Sweden)
FELICIA RAMONA BIRAU
2012-05-01
Full Text Available In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and of course, the manner in which they interpret that information may be different. Also, Fractal Market Hypothesis refers to the way that liquidity and investment horizons influence the behaviour of financial investors.
Turbulent premixed flames on fractal-grid-generated turbulence
Energy Technology Data Exchange (ETDEWEB)
Soulopoulos, N; Kerl, J; Sponfeldner, T; Beyrau, F; Hardalupas, Y; Taylor, A M K P [Mechanical Engineering Department, Imperial College London, London SW7 2AZ (United Kingdom); Vassilicos, J C, E-mail: ns6@ic.ac.uk [Department of Aeronautics, Imperial College London, London SW7 2AZ (United Kingdom)
2013-12-15
A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area. (paper)
High Surface Area Tunnels in Hexagonal WO₃.
Sun, Wanmei; Yeung, Michael T; Lech, Andrew T; Lin, Cheng-Wei; Lee, Chain; Li, Tianqi; Duan, Xiangfeng; Zhou, Jun; Kaner, Richard B
2015-07-08
High surface area in h-WO3 has been verified from the intracrystalline tunnels. This bottom-up approach differs from conventional templating-type methods. The 3.67 Å diameter tunnels are characterized by low-pressure CO2 adsorption isotherms with nonlocal density functional theory fitting, transmission electron microscopy, and thermal gravimetric analysis. These open and rigid tunnels absorb H(+) and Li(+), but not Na(+) in aqueous electrolytes without inducing a phase transformation, accessing both internal and external active sites. Moreover, these tunnel structures demonstrate high specific pseudocapacitance and good stability in an H2SO4 aqueous electrolyte. Thus, the high surface area created from 3.67 Å diameter tunnels in h-WO3 shows potential applications in electrochemical energy storage, selective ion transfer, and selective gas adsorption.
High surface area fibrous silica nanoparticles
Polshettiwar, Vivek; Basset, Jean-Marie
2014-01-01
Disclosed are high surface area nanoparticles that have a fibrous morphology. The nanoparticles have a plurality of fibers, wherein each fiber is in contact with one other fiber and each fiber has a length of between about 1 nm and about 5000 nm. Also disclosed are applications of the nanoparticles of the present invention, and methods of fabrication of the nanoparticles of the present invention.
High surface area fibrous silica nanoparticles
Polshettiwar, Vivek
2014-11-11
Disclosed are high surface area nanoparticles that have a fibrous morphology. The nanoparticles have a plurality of fibers, wherein each fiber is in contact with one other fiber and each fiber has a length of between about 1 nm and about 5000 nm. Also disclosed are applications of the nanoparticles of the present invention, and methods of fabrication of the nanoparticles of the present invention.
International Nuclear Information System (INIS)
Pyun, Su-Il; Rhee, Chang-Kyu
2004-01-01
Fractal characteristics of mesoporous carbon electrodes were investigated with various pore structures using the N 2 gas adsorption method and the transmission electron microscopy (TEM) image analysis method. The mesoporous carbons with various pore structures were prepared by imprinting mesophase pitch used as a carbonaceous precursor with different colloidal silica particles. All imprinted mesoporous carbons were composed of two groups of pores produced from the carbonisation of mesophase pitch and from the silica imprinting. The overall surface fractal dimensions of the carbon specimens were determined from the analyses of the N 2 gas adsorption isotherms. In order to distinguish the surface fractal dimension of the carbonisation-induced pore surface from that fractal dimension of the silica-imprinted pore surface, the individual surface fractal dimensions were determined from the image analyses of the TEM images. From the comparison of the overall surface fractal dimension with the individual surface fractal dimensions, it was recognised that the overall surface fractal dimension is crucially influenced by the individual surface fractal dimension of the silica-imprinted pore surface. Moreover, from the fact that the silica-imprinted pore surface with broad relative pore size distribution (PSD) gave lower value of the individual surface fractal dimension than that pore surface with narrow relative PSD, it is concluded that as the silica-imprinted pores comprising the carbon specimen agglomerate, the individual surface fractal dimension of that pore surface decreases
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.
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
On semiautomatic estimation of surface area
DEFF Research Database (Denmark)
Dvorak, J.; Jensen, Eva B. Vedel
2013-01-01
and the surfactor. For ellipsoidal particles, it is shown that the flower estimator is equal to the pivotal estimator based on support function measurements along four perpendicular rays. This result makes the pivotal estimator a powerful approximation to the flower estimator. In a simulation study of prolate....... If the segmentation is correct the estimate is computed automatically, otherwise the expert performs the necessary measurements manually. In case of convex particles we suggest to base the semiautomatic estimation on the so-called flower estimator, a new local stereological estimator of particle surface area....... For convex particles, the estimator is equal to four times the area of the support set (flower set) of the particle transect. We study the statistical properties of the flower estimator and compare its performance to that of two discretizations of the flower estimator, namely the pivotal estimator...
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.
Characteristics of Pore Structure and Fractal Dimension of Isometamorphic Anthracite
Directory of Open Access Journals (Sweden)
Di Gao
2017-11-01
Full Text Available The geologic conditions of No. 3 coal seams are similar to Sihe and Zhaozhuang Collieries, however, the gas production is significantly different. To better understand the effect of pores, by means of experimental measurements and quantitative analysis, the pore properties of high-rank isometamorphic anthracite were thoroughly studied. Our study showed that the pore structures were predominantly adsorptive, accounting for more than 88% of the specific surface area. The coal pores showed typical three-stage fractal characteristics at boundary points of 1 nm and 9 nm (7 nm of coal samples from Zhaozhuang Colliery, and the fractal dimension with 1–9 nm (or 1–7 nm, as being significantly larger than those measured outside the given ranges. Pores in samples from Sihe Colliery were mainly open spherical or ellipsoidal pores in shape; conversely, those from Zhaozhuang Colliery were mainly Y-shaped, V-shaped, or ‘ink-bottle’ type.
International Conference on Advances of Fractals and Related Topics
Lau, Ka-Sing
2014-01-01
This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
A Simple Proof of Cauchy's Surface Area Formula
Tsukerman, Emmanuel; Veomett, Ellen
2016-01-01
We give a short and simple proof of Cauchy's surface area formula, which states that the average area of a projection of a convex body is equal to its surface area up to a multiplicative constant in the dimension.
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.
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)
Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L.
1997-01-01
We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.
Thermodynamics for Fractal Statistics
da Cruz, Wellington
1998-01-01
We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.
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
Accessible surface area from NMR chemical shifts
Energy Technology Data Exchange (ETDEWEB)
Hafsa, Noor E.; Arndt, David; Wishart, David S., E-mail: david.wishart@ualberta.ca [University of Alberta, Department of Computing Science (Canada)
2015-07-15
Accessible surface area (ASA) is the surface area of an atom, amino acid or biomolecule that is exposed to solvent. The calculation of a molecule’s ASA requires three-dimensional coordinate data and the use of a “rolling ball” algorithm to both define and calculate the ASA. For polymers such as proteins, the ASA for individual amino acids is closely related to the hydrophobicity of the amino acid as well as its local secondary and tertiary structure. For proteins, ASA is a structural descriptor that can often be as informative as secondary structure. Consequently there has been considerable effort over the past two decades to try to predict ASA from protein sequence data and to use ASA information (derived from chemical modification studies) as a structure constraint. Recently it has become evident that protein chemical shifts are also sensitive to ASA. Given the potential utility of ASA estimates as structural constraints for NMR we decided to explore this relationship further. Using machine learning techniques (specifically a boosted tree regression model) we developed an algorithm called “ShiftASA” that combines chemical-shift and sequence derived features to accurately estimate per-residue fractional ASA values of water-soluble proteins. This method showed a correlation coefficient between predicted and experimental values of 0.79 when evaluated on a set of 65 independent test proteins, which was an 8.2 % improvement over the next best performing (sequence-only) method. On a separate test set of 92 proteins, ShiftASA reported a mean correlation coefficient of 0.82, which was 12.3 % better than the next best performing method. ShiftASA is available as a web server ( http://shiftasa.wishartlab.com http://shiftasa.wishartlab.com ) for submitting input queries for fractional ASA calculation.
Electro-chemical manifestation of nanoplasmonics in fractal media
Baskin, Emmanuel; Iomin, Alexander
2013-06-01
Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.
Fractal-Based Image Analysis In Radiological Applications
Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.
1987-10-01
We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.
High-surface-area active carbon
International Nuclear Information System (INIS)
O'Grady, T.M.; Wennerberg, A.N.
1986-01-01
This paper describes the preparation and properties of a unique active carbon having exceptionally high surface areas, over 2500 m 2 /gm, and extraordinary adsorptive capacities. The carbon is made by a direct chemical activation route in which petroleum coke or other carbonaceous sources are reacted with excess potassium hydroxide at 400 0 to 500 0 C to an intermediate product that is subsequently pyrolyzed at 800 0 to 900 0 C to active carbon containing potassium salts. These are removed by water washing and the carbon is dried to produce a powdered product. A granular carbon can also be made by further processing the powdered carbon by using specialized granulation techniques. Typical properties of the carbon include Iodine Numbers of 3000 to 3600, methylene blue adsorption of 650 to 750 mg/gm, pore volumes of 2.0 to 2.6 cc/gm and less than 3.0% ash. This carbon's high adsorption capacities make it uniquely suited for numerous demanding applications in the medical area, purifications, removal of toxic substances, as catalyst carriers, etc
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.
Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.
2012-04-01
In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Bouguer correction density determination from fractal analysis using ...
African Journals Online (AJOL)
In this work, Bouguer density is determined using the fractal approach. This technique was applied to the gravity data of the Kwello area of the Basement Complex, north-western Nigeria. The density obtained using the fractal approach is 2500 kgm which is lower than the conventional value of 2670 kgm used for average ...
Fractal analysis of rainfall occurrence observed in the synoptic ...
African Journals Online (AJOL)
Fractal analysis is important for characterizing and modeling rainfall's space-time variations in hydrology. The purpose of this study consists on determining, in a mono-fractal framework, the scale invariance of rainfall series in Benin synopticstations located in two main geographical area: Cotonou, Bohicon , Savè in a sub ...
International Conference and Workshop on Fractals and Wavelets
Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod
2014-01-01
Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
Willson, Stephen J.
1991-01-01
Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)
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
regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis.We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas......, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested...... and compact organization) in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters). Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby...
Energy Technology Data Exchange (ETDEWEB)
Clausse, A; Delmastro, D F
1991-12-31
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author). [Espanol] En este trabajo se presenta una descripcion de las lineas de investigacion que los autores estan llevando a cabo en teoria de caos y fractales orientadas al campo nuclear. Es de especial importancia las posibilidades que se abren en el area de la seguridad nuclear, en donde la informacion proveniente de las tecnicas de caos y fractales pueden ayudar al desarrollo de mejores criterios y disenos mas confiables. (Autor).
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
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.
Computer Security: The dilemma of fractal defence
Stefan Lueders, Computer Security Team
2015-01-01
Aren’t mathematical fractals just beautiful? The Mandelbrot set and the Julia set, the Sierpinski gasket, the Menger sponge, the Koch curve (see here)… Based on very simple mathematical rules, they quickly develop into a mosaic of facets slightly different from each other. More and more features appear the closer you zoom into a fractal and expose similar but not identical features of the overall picture. Computer security is like these fractals, only much less pretty: simple at first glance, but increasingly complex and complicated when you look more closely at the details. The deeper you dig, the more and more possibilities open up for malicious people as the attack surface grows, just like that of “Koch’s snowflakes”, where the border length grows exponentially. Consequently, the defensive perimeter also increases when we follow the bits and bytes layer by layer from their processing in the CPU, trickling up the software stack thro...
Fractal design concepts for stretchable electronics.
Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A
2014-01-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal design concepts for stretchable electronics
Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.
2014-02-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Fractal studies on the positron annihilation in metals
International Nuclear Information System (INIS)
Lung, C.W.
1994-06-01
Traditionally, the Euclidean lines, circles and spheres have served as the basis of the intuitive understanding of the geometry of nature. Recently, the concept of fractals has caught the imagination of scientists in many fields. This paper is to continue our previous work on position annihilation near fractal surfaces to demonstrate that the concept of fractals provides a powerful tool for understanding the structure and properties of defects and rough surfaces in relation to positron annihilation studies. Some problems on Berry geometrical phase have also been discussed. (author). 15 refs, fig., 1 tab
FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY
Directory of Open Access Journals (Sweden)
Hynek Lauschmann
2011-05-01
Full Text Available The morphology of fatigue fracture surface (caused by constant cycle loading is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness. Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.
Palatal Surface Area of Maxillary Plaster Casts
DEFF Research Database (Denmark)
Darvann, Tron Andre; Hermann, Nuno V.; Ersbøll, Bjarne Kjær
2007-01-01
Objective: To investigate the relationship between corresponding two-dimensional and three-dimensional measurements on maxillary plaster casts taken from photographs and three-dimensional surface scans, respectively. Materials and Methods: Corresponding two-dimensional and three-dimensional measu...
Effect of impervious surface area and vegetation changes on mean ...
African Journals Online (AJOL)
adeniyi adeyemi
Land surface temperature (LST) is measured by the surface energy balance, .... climatic and environmental conditions (Cheng et al., 2006). ..... urban areas have generally resulted in a high reflection and emission of solar radiation and greater.
Random walk through fractal environments
Isliker, H.; Vlahos, L.
2002-01-01
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...
Lectures on fractal geometry and dynamical systems
Pesin, Yakov
2009-01-01
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular "chaotic" motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples o...
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...
Fractal analytical approach of urban form based on spatial correlation function
International Nuclear Information System (INIS)
Chen, Yanguang
2013-01-01
Highlights: ► Many fractal parameter relations of cities can be derived by scaling analysis. ► The area-radius scaling of cities suggests a spatial correlation function. ► Spectral analysis can be used to estimate fractal dimension values of urban form. ► The valid range of fractal dimension of urban form comes between 1.5 and 2. ► The traditional scale concept will be replaced by scaling concept in geography. -- Abstract: Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning
Directory of Open Access Journals (Sweden)
Nicholas A. Famoso
2016-07-01
Full Text Available Enamel patterns on the occlusal surfaces of equid teeth are asserted to have tribal-level differences. The most notable example compares the Equini and Hipparionini, where Equini have higher crowned teeth with less enamel-band complexity and less total occlusal enamel than Hipparionini. Whereas previous work has successfully quantified differences in enamel band shape by dividing the length of enamel band by the square root of the occlusal surface area (Occlusal Enamel Index, OEI, it was clear that OEI only partially removes the effect of body size. Because enamel band length scales allometrically, body size still has an influence on OEI, with larger individuals having relatively longer enamel bands than smaller individuals. Fractal dimensionality (D can be scaled to any level, so we have used it to quantify occlusal enamel complexity in a way that allows us to get at an accurate representation of the relationship between complexity and body size. To test the hypothesis of tribal-level complexity differences between Equini and Hipparionini, we digitally traced a sample of 98 teeth, one tooth per individual; 31 Hipparionini and 67 Equini. We restricted our sampling to the P3-M2 to reduce the effect of tooth position. After calculating the D of these teeth with the fractal box method which uses the number of boxes of various sizes to calculate the D of a line, we performed a t-test on the individual values of D for each specimen, comparing the means between the two tribes, and a phylogenetically informed generalized least squares regression (PGLS for each tribe with occlusal surface area as the independent variable and D as the dependent variable. The slopes of both PGLS analyses were compared using a t-test to determine if the same linear relationship existed between the two tribes. The t-test between tribes was significant (p < 0.0001, suggesting different D populations for each lineage. The PGLS for Hipparionini was a positive but not
Stemp, W James; Chung, Steven
2011-01-01
This pilot study tests the reliability of laser scanning confocal microscopy (LSCM) to quantitatively measure wear on experimental obsidian tools. To our knowledge, this is the first use of confocal microscopy to study wear on stone flakes made from an amorphous silicate like obsidian. Three-dimensional surface roughness or texture area scans on three obsidian flakes used on different contact materials (hide, shell, wood) were documented using the LSCM to determine whether the worn surfaces could be discriminated using area-scale analysis, specifically relative area (RelA). When coupled with the F-test, this scale-sensitive fractal analysis could not only discriminate the used from unused surfaces on individual tools, but was also capable of discriminating the wear histories of tools used on different contact materials. Results indicate that such discriminations occur at different scales. Confidence levels for the discriminations at different scales were established using the F-test (mean square ratios or MSRs). In instances where discrimination of surface roughness or texture was not possible above the established confidence level based on MSRs, photomicrographs and RelA assisted in hypothesizing why this was so. Copyright © 2011 Wiley Periodicals, Inc.
Electrochemical Properties of High Surface Area Vanadium Oxide Aerogels
National Research Council Canada - National Science Library
Dong, Winny
2001-01-01
.... Traditional composite electrode structures have prevented truly quantitative analysis of surface area effects in nanoscale battery materials, as well as a study of their innate electrochemical behavior...
DEFF Research Database (Denmark)
Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.
2010-01-01
applications. THz radiation can be employed for various purposes, among them the study of vibrations in biological molecules, motion of electrons in semiconductors and propagation of acoustic shock waves in crystals. We propose here a new THz fractal MTM design that shows very high transmission in the desired...... frequency range as well as a clear differentiation between one polarisation and another. Based on theoretical predictions we fabricated and measured a fractal based THz metamaterial that shows more than 60% field transmission at around 1THz for TE polarized light while the TM waves have almost 80% field...... transmission peak at 0.6THz. One of the main characteristics of this design is its tunability by design: by simply changing the length of the fractal elements one can choose the operating frequency window. The modelling, fabrication and characterisation results will be presented in this paper. Due to the long...
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.
Transmission and reflection properties of terahertz fractal metamaterials
DEFF Research Database (Denmark)
Malureanu, Radu; Lavrinenko, Andrei; Cooke, David
2010-01-01
We use THz time-domain spectroscopy to investigate transmission and reflection properties of metallic fractal metamaterial structures. We observe loss of free-space energy at certain resonance frequencies, indicating excitation of surface modes of the metamaterial.......We use THz time-domain spectroscopy to investigate transmission and reflection properties of metallic fractal metamaterial structures. We observe loss of free-space energy at certain resonance frequencies, indicating excitation of surface modes of the metamaterial....
Surface Area Distribution Descriptor for object matching
Directory of Open Access Journals (Sweden)
Mohamed F. Gafar
2010-07-01
Full Text Available Matching 3D objects by their similarity is a fundamental problem in computer vision, computer graphics and many other fields. The main challenge in object matching is to find a suitable shape representation that can be used to accurately and quickly discriminate between similar and dissimilar shapes. In this paper we present a new volumetric descriptor to represent 3D objects. The proposed descriptor is used to match objects under rigid transformations including uniform scaling. The descriptor represents the object by dividing it into shells, acquiring the area distribution of the object through those shells. The computed areas are normalised to make the descriptor scale-invariant in addition to rotation and translation invariant. The effectiveness and stability of the proposed descriptor to noise and variant sampling density as well as the effectiveness of the similarity measures are analysed and demonstrated through experimental results.
International Nuclear Information System (INIS)
Li, W.; Bak, P.
1986-01-01
At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D = 1 to the cantorus is governed by an exponent ν = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent
Fractal actors and infrastructures
DEFF Research Database (Denmark)
Bøge, Ask Risom
2011-01-01
-network-theory (ANT) into surveillance studies (Ball 2002, Adey 2004, Gad & Lauritsen 2009). In this paper, I further explore the potential of this connection by experimenting with Marilyn Strathern’s concept of the fractal (1991), which has been discussed in newer ANT literature (Law 2002; Law 2004; Jensen 2007). I...... under surveillance. Based on fieldwork conducted in 2008 and 2011 in relation to my Master’s thesis and PhD respectively, I illustrate fractal concepts by describing the acts, actors and infrastructure that make up the ‘DNA surveillance’ conducted by the Danish police....
Bioinspired fractal electrodes for solar energy storages.
Thekkekara, Litty V; Gu, Min
2017-03-31
Solar energy storage is an emerging technology which can promote the solar energy as the primary source of electricity. Recent development of laser scribed graphene electrodes exhibiting a high electrical conductivity have enabled a green technology platform for supercapacitor-based energy storage, resulting in cost-effective, environment-friendly features, and consequent readiness for on-chip integration. Due to the limitation of the ion-accessible active porous surface area, the energy densities of these supercapacitors are restricted below ~3 × 10 -3 Whcm -3 . In this paper, we demonstrate a new design of biomimetic laser scribed graphene electrodes for solar energy storage, which embraces the structure of Fern leaves characterized by the geometric family of space filling curves of fractals. This new conceptual design removes the limit of the conventional planar supercapacitors by significantly increasing the ratio of active surface area to volume of the new electrodes and reducing the electrolyte ionic path. The attained energy density is thus significantly increased to ~10 -1 Whcm -3 - more than 30 times higher than that achievable by the planar electrodes with ~95% coulombic efficiency of the solar energy storage. The energy storages with these novel electrodes open the prospects of efficient self-powered and solar-powered wearable, flexible and portable applications.
Bioinspired fractal electrodes for solar energy storages
Thekkekara, Litty V.; Gu, Min
2017-03-01
Solar energy storage is an emerging technology which can promote the solar energy as the primary source of electricity. Recent development of laser scribed graphene electrodes exhibiting a high electrical conductivity have enabled a green technology platform for supercapacitor-based energy storage, resulting in cost-effective, environment-friendly features, and consequent readiness for on-chip integration. Due to the limitation of the ion-accessible active porous surface area, the energy densities of these supercapacitors are restricted below ~3 × 10-3 Whcm-3. In this paper, we demonstrate a new design of biomimetic laser scribed graphene electrodes for solar energy storage, which embraces the structure of Fern leaves characterized by the geometric family of space filling curves of fractals. This new conceptual design removes the limit of the conventional planar supercapacitors by significantly increasing the ratio of active surface area to volume of the new electrodes and reducing the electrolyte ionic path. The attained energy density is thus significantly increased to ~10-1 Whcm-3- more than 30 times higher than that achievable by the planar electrodes with ~95% coulombic efficiency of the solar energy storage. The energy storages with these novel electrodes open the prospects of efficient self-powered and solar-powered wearable, flexible and portable applications.
Why Do We Need the Derivative for the Surface Area?
Hristova, Yulia; Zeytuncu, Yunus E.
2016-01-01
Surface area and volume computations are the most common applications of integration in calculus books. When computing the surface area of a solid of revolution, students are usually told to use the frustum method instead of the disc method; however, a rigorous explanation is rarely provided. In this note, we provide one by using geometric…
On the specific surface area of nanoporous materials
Detsi, E.; De Jong, E.; Zinchenko, A.; Vukovic, Z.; Vukovic, I.; Punzhin, S.; Loos, K.; ten Brinke, G.; De Raedt, H. A.; Onck, P. R.; De Hosson, J. T. M.
2011-01-01
A proper quantification of the specific surface area of nanoporous materials is necessary for a better understanding of the properties that are affected by the high surface-area-to-volume ratio of nanoporous metals, nanoporous polymers and nanoporous ceramics. In this paper we derive an analytical
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.
Earnshow, R; Jones, H
1991-01-01
This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...
Fractal characteristics of fracture morphology of steels irradiated with high-energy ions
Energy Technology Data Exchange (ETDEWEB)
Xian, Yongqiang; Liu, Juan [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); University of Chinese Academy of Science, Beijing 100049 (China); Zhang, Chonghong, E-mail: c.h.zhang@impcas.ac.cn [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); Chen, Jiachao [Paul Scherrer Institute, Villigen PSI (Switzerland); Yang, Yitao; Zhang, Liqing; Song, Yin [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China)
2015-06-15
Highlights: • Fractal dimensions of fracture surfaces of steels before and after irradiation were calculated. • Fractal dimension can effectively describe change of fracture surfaces induced by irradiation. • Correlation of change of fractal dimension with embrittlement of irradiated steels is discussed. - Abstract: A fractal analysis of fracture surfaces of steels (a ferritic/martensitic steel and an oxide-dispersion-strengthened ferritic steel) before and after the irradiation with high-energy ions is presented. Fracture surfaces were acquired from a tensile test and a small-ball punch test (SP). Digital images of the fracture surfaces obtained from scanning electron microscopy (SEM) were used to calculate the fractal dimension (FD) by using the pixel covering method. Boundary of binary image and fractal dimension were determined with a MATLAB program. The results indicate that fractal dimension can be an effective parameter to describe the characteristics of fracture surfaces before and after irradiation. The rougher the fracture surface, the larger the fractal dimension. Correlation of the change of fractal dimension with the embrittlement of the irradiated steels is discussed.
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.
Moisture diffusivity in structure of random fractal fiber bed
Energy Technology Data Exchange (ETDEWEB)
Zhu, Fanglong, E-mail: zhufanglong_168@163.com [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); The Chinese People' s Armed Police Forces Academy, Langfan City (China); Zhou, Yu; Feng, Qianqian [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); Xia, Dehong [School of Mechanical Engineering, University of Science and Technology, Beijing (China)
2013-11-08
A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.
Neustupa, J
2016-02-01
The surface area-to-volume ratio of cells is one of the key factors affecting fundamental biological processes and, thus, fitness of unicellular organisms. One of the general models for allometric increase in surface-to-volume scaling involves fractal-like elaboration of cellular surfaces. However, specific data illustrating this pattern in natural populations of the unicellular organisms have not previously been available. This study shows that unicellular green algae of the genus Micrasterias (Desmidiales) have positive allometric surface-to-volume scaling caused by changes in morphology of individual species, especially in the degree of cell lobulation. This allometric pattern was also detected within most of the cultured and natural populations analysed. Values of the allometric S:V scaling within individual populations were closely correlated to the phylogenetic structure of the clade. In addition, they were related to species-specific cellular morphology. Individual populations differed in their allometric patterns, and their position in the allometric space was strongly correlated with the degree of allometric S:V scaling. This result illustrates that allometric shape patterns are an important correlate of the capacity of individual populations to compensate for increases in their cell volumes by increasing the surface area. However, variation in allometric patterns was not associated with phylogenetic structure. This indicates that the position of the populations in the allometric space was not evolutionarily conserved and might be influenced by environmental factors. © 2015 European Society For Evolutionary Biology. Journal of Evolutionary Biology © 2015 European Society For Evolutionary Biology.
Lage-area planar RF plasma productions by surface waves
International Nuclear Information System (INIS)
Nonaka, S.
1994-01-01
Large-area rf plasmas are confirmed to be produced by means of RF discharges inside a large-area dielectric tube. The plasma space is 73 cm x 176 cm and 2.5 cm. The plasma is thought to be produced by an odd plasma-surface wave (PSW ο ) in case of using large-area electrodes and by an even plasma-surface wave (PSW ο ) in case of without the electrodes. (author). 7 refs, 4 figs
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
Indexing aortic valve area by body surface area increases the prevalence of severe aortic stenosis
DEFF Research Database (Denmark)
Jander, Nikolaus; Gohlke-Bärwolf, Christa; Bahlmann, Edda
2014-01-01
To account for differences in body size in patients with aortic stenosis, aortic valve area (AVA) is divided by body surface area (BSA) to calculate indexed AVA (AVAindex). Cut-off values for severe stenosis are......To account for differences in body size in patients with aortic stenosis, aortic valve area (AVA) is divided by body surface area (BSA) to calculate indexed AVA (AVAindex). Cut-off values for severe stenosis are...
Hand burns surface area: A rule of thumb.
Dargan, Dallan; Mandal, Anirban; Shokrollahi, Kayvan
2018-03-11
Rapid estimation of acute hand burns is important for communication, standardisation of assessment, rehabilitation and research. Use of an individual's own thumbprint area as a fraction of their total hand surface area was evaluated to assess potential utility in hand burn evaluation. Ten health professionals used an ink-covered dominant thumb pulp to cover the surfaces of their own non-dominant hand using the contralateral thumb. Thumbprints were assessed on the web spaces, sides of digits and dorsum and palm beyond the distal wrist crease. Hand surface area was estimated using the Banerjee and Sen method, and thumbprint ellipse area calculated to assess correlation. Mean estimated total hand surface area was 390.0cm 2 ±SD 51.5 (328.3-469.0), mean thumbprint ellipse area was 5.5cm 2 ±SD 1.3 (3.7-8.4), and mean estimated print number was 73.5±SD 11.0 (range 53.1-87.8, 95% CI 6.8). The mean observed number of thumbprints on one hand was 80.1±SD 5.9 (range 70.0-88.0, 95% CI 3.7), χ 2 =0.009. The combined mean of digital prints was 42, comprising a mean of two prints each on volar, dorsal, radial and ulnar digit surfaces, except volar middle and ring (3 prints each). Palmar prints were 15 (11-19), dorsal 15 (11-19), ulnar palm border 3, first web space 2, and second, third and fourth web spaces one each. Using the surface of the palm alone, excluding digits, as 0.5% of total body surface area, the area of one thumbprint was approximated as 1/30th of 1%. We have demonstrated how thumbprint area serves as a simple method for evaluating hand burn surface area. Copyright © 2018 Elsevier Ltd and ISBI. All rights reserved.
Flames in fractal grid generated turbulence
Energy Technology Data Exchange (ETDEWEB)
Goh, K H H; Hampp, F; Lindstedt, R P [Department of Mechanical Engineering, Imperial College, London SW7 2AZ (United Kingdom); Geipel, P, E-mail: p.lindstedt@imperial.ac.uk [Siemens Industrial Turbomachinery AB, SE-612 83 Finspong (Sweden)
2013-12-15
Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values {approx}0.1 and {approx}0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration. (paper)
Fractality and the law of the wall
Xu, Haosen H. A.; Yang, X. I. A.
2018-05-01
Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.
Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.
Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A
2017-11-28
We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.
Particle surface area and bacterial activity in recirculating aquaculture systems
DEFF Research Database (Denmark)
Pedersen, Per Bovbjerg; von Ahnen, Mathis; Fernandes, Paulo
2017-01-01
Suspended particles in recirculating aquaculture systems (RAS) provide surface area that can be colonized by bacteria. More particles accumulate as the intensity of recirculation increases thus potentially increasing the bacterial carrying capacity of the systems. Applying a recent, rapid, culture...... but may provide significant surface area. Hence, the study substantiates that particles in RAS provide surface area supporting bacterial activity, and that particles play a key role in controlling the bacterial carrying capacity at least in less intensive RAS. Applying fast, culture-independent techniques......-independent fluorometric detection method (Bactiquant®) for measuring bacterial activity, the current study explored the relationship between total particle surface area (TSA, derived from the size distribution of particles >5 μm) and bacterial activity in freshwater RAS operated at increasing intensity of recirculation...
On $L_p$ Affine Surface Area and Curvature Measures
Zhao, Yiming
2015-01-01
The relationship between $L_p$ affine surface area and curvature measures is investigated. As a result, a new representation of the existing notion of $L_p$ affine surface area depending only on curvature measures is derived. Direct proofs of the equivalence between this new representation and those previously known are provided. The proofs show that the new representation is, in a sense, "polar" to that of Lutwak's and "dual" to that of Sch\\"utt & Werner's.
Fractal statistics of brittle fragmentation
Directory of Open Access Journals (Sweden)
M. Davydova
2013-04-01
Full Text Available The study of fragmentation statistics of brittle materials that includes four types of experiments is presented. Data processing of the fragmentation of glass plates under quasi-static loading and the fragmentation of quartz cylindrical rods under dynamic loading shows that the size distribution of fragments (spatial quantity is fractal and can be described by a power law. The original experimental technique allows us to measure, apart from the spatial quantity, the temporal quantity - the size of time interval between the impulses of the light reflected from the newly created surfaces. The analysis of distributions of spatial (fragment size and temporal (time interval quantities provides evidence of obeying scaling laws, which suggests the possibility of self-organized criticality in fragmentation.
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
Categorization of new fractal carpets
International Nuclear Information System (INIS)
Rani, Mamta; Goel, Saurabh
2009-01-01
Sierpinski carpet is one of the very beautiful fractals from the historic gallery of classical fractals. Carpet designing is not only a fascinating activity in computer graphics, but it has real applications in carpet industry as well. One may find illusionary delighted carpets designed here, which are useful in real designing of carpets. In this paper, we attempt to systematize their generation and put them into categories. Each next category leads to a more generalized form of the fractal carpet.
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.
FONT DISCRIMINATIO USING FRACTAL DIMENSIONS
Directory of Open Access Journals (Sweden)
S. Mozaffari
2014-09-01
Full Text Available One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dimension was introduced in this paper for the first time. Our feature extraction methods which consider font recognition as texture identification are independent of document content. Experimental results on different pages written by several font types show that fractal geometry can overcome the complexities of font recognition problem.
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.
Quantifying object and material surface areas in residences
Energy Technology Data Exchange (ETDEWEB)
Hodgson, Alfred T.; Ming, Katherine Y.; Singer, Brett C.
2005-01-05
The dynamic behavior of volatile organic compounds (VOCs) in indoor environments depends, in part, on sorptive interactions between VOCs in the gas phase and material surfaces. Since information on the types and quantities of interior material surfaces is not generally available, this pilot-scale study was conducted in occupied residences to develop and demonstrate a method for quantifying surface areas of objects and materials in rooms. Access to 33 rooms in nine residences consisting of bathrooms, bedroom/offices and common areas was solicited from among research group members living in the East San Francisco Bay Area. A systematic approach was implemented for measuring rooms and objects from 300 cm{sup 2} and larger. The ventilated air volumes of the rooms were estimated and surface area-to-volume ratios were calculated for objects and materials, each segregated into 20 or more categories. Total surface area-to-volume ratios also were determined for each room. The bathrooms had the highest total surface area-to-volume ratios. Bedrooms generally had higher ratios than common areas consisting of kitchens, living/dining rooms and transitional rooms. Total surface area-to-volume ratios for the 12 bedrooms ranged between 2.3 and 4.7 m{sup 2} m{sup -3}. The importance of individual objects and materials with respect to sorption will depend upon the sorption coefficients for the various VOC/materials combinations. When combined, the highly permeable material categories, which may contribute to significant interactions, had a median ratio of about 0.5 m{sup 2} m{sup -3} for all three types of rooms.
Quantification of lung surface area using computed tomography
Directory of Open Access Journals (Sweden)
Xing Li
2010-10-01
Full Text Available Abstract Objective To refine the CT prediction of emphysema by comparing histology and CT for specific regions of lung. To incorporate both regional lung density measured by CT and cluster analysis of low attenuation areas for comparison with histological measurement of surface area per unit lung volume. Methods The histological surface area per unit lung volume was estimated for 140 samples taken from resected lung specimens of fourteen subjects. The region of the lung sampled for histology was located on the pre-operative CT scan; the regional CT median lung density and emphysematous lesion size were calculated using the X-ray attenuation values and a low attenuation cluster analysis. Linear mixed models were used to examine the relationships between histological surface area per unit lung volume and CT measures. Results The median CT lung density, low attenuation cluster analysis, and the combination of both were important predictors of surface area per unit lung volume measured by histology (p Conclusion Combining CT measures of lung density and emphysematous lesion size provides a more accurate estimate of lung surface area per unit lung volume than either measure alone.
Surface area considerations for corroding N reactor fuel
International Nuclear Information System (INIS)
Johnson, A.B. Jr.; Pitner, A.L.
1996-06-01
The N Reactor fuel is corroding at sites where the Zircaloy cladding was damaged when the fuel was discharged from the reactor. Corroding areas are clearly visible on the fuel stored in open cans in the K East Basin. There is a need to estimate the area of the corroding uranium to analyze aspects of fuel behavior as it is transitioned. from current wet storage to dry storage. In this report, the factors that contribute to open-quotes trueclose quotes surface area are analyzed in terms of what is currently known about the N Reactor fuel. Using observations from a visual examinations of the fuel in the K East wet storage facility, a value for the corroding geometric area is estimated. Based on observations of corroding uranium and surface roughness values for other metals, a surface roughness factor is also estimated and applied to the corroding K East fuel to provide an estimated open-quotes trueclose quotes surface area. While the estimated area may be modified as additional data become available from fuel characterization studies, the estimate provides a basis to assess effects of exposed uranium metal surfaces on fuel behavior in operations involved in transitioning from wet to dry storage, during shipment and staging, conditioning, and dry interim storage
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation ... involving scaling and memory effects. But most of ..... begin by recalling the definition of the Riemann integral in ordinary calculus [33]. Let g: [a ...
Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.
2010-01-01
The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103
Directory of Open Access Journals (Sweden)
Francisco Maduell
2015-05-01
Conclusion: The increase in 40% and 80% of dialyzer surface area entails an increase in convective volume of 6 and 16% respectively, showing minimal differences both in convective volume and clearance capacity when UFC was greater than 45 mL/h/mmHg. It is advisable to optimise dialyser efficiency to the smallest surface area possible, adjusting treatment prescription.
Specific surface area evaluation method by using scanning electron microscopy
International Nuclear Information System (INIS)
Petrescu, Camelia; Petrescu, Cristian; Axinte, Adrian
2000-01-01
Ceramics are among the most interesting materials for a large category of applications, including both industry and health. Among the characteristic of the ceramic materials, the specific surface area is often difficult to evaluate.The paper presents a method of evaluation for the specific surface area of two ceramic powders by means of scanning electron microscopy measurements and an original method of computing the specific surface area.Cumulative curves are used to calculate the specific surface area under assumption that the values of particles diameters follow a normal logarithmic distribution. For two powder types, X7R and NPO the results are the following: - for the density ρ (g/cm 2 ), 5.5 and 6.0, respectively; - for the average diameter D bar (μm), 0.51 and 0.53, respectively; - for σ, 1.465 and 1.385, respectively; - for specific surface area (m 2 /g), 1.248 and 1.330, respectively. The obtained results are in good agreement with the values measured by conventional methods. (authors)
Electromagnetism on anisotropic fractal media
Ostoja-Starzewski, Martin
2013-04-01
Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.
Fractals and multifractals in physics
International Nuclear Information System (INIS)
Arcangelis, L. de.
1987-01-01
We present a general introduction to the world of fractals. The attention is mainly devoted to stress how fractals do indeed appear in the real world and to find quantitative methods for characterizing their properties. The idea of multifractality is also introduced and it is presented in more details within the framework of the percolation problem
Simoson, Andrew J.
2009-01-01
This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)
Turbulent wakes of fractal objects
Staicu, A.D.; Mazzi, B.; Vassilicos, J.C.; Water, van de W.
2003-01-01
Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density.
Can foot anthropometric measurements predict dynamic plantar surface contact area?
Directory of Open Access Journals (Sweden)
Collins Natalie
2009-10-01
Full Text Available Abstract Background Previous studies have suggested that increased plantar surface area, associated with pes planus, is a risk factor for the development of lower extremity overuse injuries. The intent of this study was to determine if a single or combination of foot anthropometric measures could be used to predict plantar surface area. Methods Six foot measurements were collected on 155 subjects (97 females, 58 males, mean age 24.5 ± 3.5 years. The measurements as well as one ratio were entered into a stepwise regression analysis to determine the optimal set of measurements associated with total plantar contact area either including or excluding the toe region. The predicted values were used to calculate plantar surface area and were compared to the actual values obtained dynamically using a pressure sensor platform. Results A three variable model was found to describe the relationship between the foot measures/ratio and total plantar contact area (R2 = 0.77, p R2 = 0.76, p Conclusion The results of this study indicate that the clinician can use a combination of simple, reliable, and time efficient foot anthropometric measurements to explain over 75% of the plantar surface contact area, either including or excluding the toe region.
de Bartolo, S.; Fallico, C.; Straface, S.; Troisi, S.; Veltri, M.
2009-04-01
The complexity characterization of the porous media structure, in terms of the "pore" phase and the "solid" phase, can be carried out by means of the fractal geometry which is able to put in relationship the soil structural properties and the water content. It is particularly complicated to describe analytically the hydraulic conductivity for the irregularity of the porous media structure. However these can be described by many fractal models considering the soil structure as the distribution of particles dimensions, the distribution of the solid aggregates, the surface of the pore-solid interface and the fractal mass of the "pore" and "solid" phases. In this paper the fractal model of Yu and Cheng (2002) and Yu and Liu (2004), for a saturated bidispersed porous media, was considered. This model, using the Sierpinsky-type gasket scheme, doesn't contain empiric constants and furnishes a well accord with the experimental data. For this study an unconfined aquifer was reproduced by means of a tank with a volume of 10 Ã- 7 Ã- 3 m3, filled with a homogeneous sand (95% of SiO2), with a high percentage (86.4%) of grains between 0.063mm and 0.125mm and a medium-high permeability. From the hydraulic point of view, 17 boreholes, a pumping well and a drainage ring around its edge were placed. The permeability was measured utilizing three different methods, consisting respectively in pumping test, slug test and laboratory analysis of an undisturbed soil cores, each of that involving in the measurement a different support volume. The temporal series of the drawdown obtained by the pumping test were analyzed by the Neuman-type Curve method (1972), because the saturated part above the bottom of the facility represents an unconfined aquifer. The data analysis of the slug test were performed by the Bouwer & Rice (1976) method and the laboratory analysis were performed on undisturbed saturated soil samples utilizing a falling head permeameter. The obtained values either of the
Contour fractal analysis of grains
Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB
2017-06-01
Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.
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.
STEREOLOGICAL ESTIMATION OF SURFACE AREA FROM DIGITAL IMAGES
Directory of Open Access Journals (Sweden)
Johanna Ziegel
2011-05-01
Full Text Available A sampling design of local stereology is combined with a method from digital stereology to yield a novel estimator of surface area based on counts of configurations observed in a digitization of an isotropic 2- dimensional slice with thickness s. As a tool, a result of the second author and J. Rataj on infinitesimal increase of volumes of morphological transforms is refined and used. The proposed surface area estimator is asymptotically unbiased in the case of sets contained in the ball centred at the origin with radius s and in the case of balls centred at the origin with unknown radius. For general shapes bounds for the asymptotic expected relative worst case error are given. A simulation example is discussed for surface area estimation based on 2×2×2-configurations.
MCO gas composition for low reactive surface areas
International Nuclear Information System (INIS)
Packer, M.J.
1998-01-01
This calculation adjusts modeled output (HNF-SD-SNF-TI-040, Rev. 2) by considering lower reactive fuel surface areas and by increasing the input helium backfill overpressure from 0.5 to 1.5 atm (2.5 atm abs) to verify that MCO gas-phase oxygen concentrations can remain below 4 mole % over a 40 year interim period under a worst case condition of zero reactive surface area. Added backfill gas will dilute any gases generated during interim storage and is a strategy within the current design capability. The zero reactive surface area represents a hypothetical worst case example where there is no fuel scrap and/or damaged spent fuel rods in an MCO. Also included is a hypothetical case where only K East fuel exists in an MCO with an added backfill overpressure of 0.5 atm (1.5 atm abs)
OBSERVED ASTEROID SURFACE AREA IN THE THERMAL INFRARED
Energy Technology Data Exchange (ETDEWEB)
Nugent, C. R. [Infrared Processing and Analysis Center, California Institute of Technology, Pasadena, CA 91125 (United States); Mainzer, A.; Masiero, J.; Bauer, J.; Kramer, E.; Sonnett, S. [Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109 (United States); Wright, E. L. [Department of Physics and Astronomy, University of California, Los Angeles, CA 90095 (United States); Grav, T. [Planetary Science Institute, Tucson, AZ (United States)
2017-02-01
The rapid accumulation of thermal infrared observations and shape models of asteroids has led to increased interest in thermophysical modeling. Most of these infrared observations are unresolved. We consider what fraction of an asteroid’s surface area contributes the bulk of the emitted thermal flux for two model asteroids of different shapes over a range of thermal parameters. The resulting observed surface in the infrared is generally more fragmented than the area observed in visible wavelengths, indicating high sensitivity to shape. For objects with low values of the thermal parameter, small fractions of the surface contribute the majority of thermally emitted flux. Calculating observed areas could enable the production of spatially resolved thermal inertia maps from non-resolved observations of asteroids.
Fractal analysis for studying the evolution of forests
International Nuclear Information System (INIS)
Andronache, Ion C.; Ahammer, Helmut; Jelinek, Herbert F.; Peptenatu, Daniel; Ciobotaru, Ana-M.; Draghici, Cristian C.; Pintilii, Radu D.; Simion, Adrian G.
2016-01-01
Highlights: • Legal and illegal deforestation is investigated by fractal analysis. • A new fractal fragmentation index FFI is proposed. • Differences in shapes of forest areas indicate the type of deforestation. • Support of ecological management. - Abstract: Deforestation is an important phenomenon that may create major imbalances in ecosystems. In this study we propose a new mathematical analysis of the forest area dynamic, enabling qualitative as well as quantitative statements and results. Fractal dimensions of the area and the perimeter of a forest were determined using digital images. The difference between fractal dimensions of the area and the perimeter images turned out to be a crucial quantitative parameter. Accordingly, we propose a new fractal fragmentation index, FFI, which is based on this difference and which highlights the degree of compaction or non-compaction of the forest area in order to interpret geographic features. Particularly, this method was applied to forests, where large areas have been legally or illegally deforested. However, these methods can easily be used for other ecological or geographical investigations based on digital images, including deforestation of rainforests.
Application Of Fractal Dimension On Atmospheric Corrosion Of Galvanized Iron Roofing Material
Directory of Open Access Journals (Sweden)
Issa A.K
2015-08-01
Full Text Available Abstract Corrosion rates of galvanized iron roofing sheet In yola north eastern part of Nigeria were assessed and determined by weight loss method and scanner fractal analysis method. Scanning electronic machine SEM was used to transform corrosion coupons to electronic form for image j processing and analysing software The result of corrosion rates for these two methods after six months of the samples exposure in industrial. Coastal market and urban areas in the region are 1.51 1.079 1.051 0.779 and 1.9941 1.9585 1.9565 1.9059 for weight loss and scanner fractal dimension methods respectively. and the results from the two methods were in agreement This establish the reliability of fractal dimension in measuring atmospheric corrosion this research also provides alternative method of measuring atmospheric corrosion and overcome the limitation of conventional weight loss technique in its inability to measure corrosion rate which is not significantly change over a long period of time moreover weight loss cannot demonstrate the area of concentration of corrosion on the surface of the coupon it rather gives the weight loss value and this will aid in determining the real level or extent of corrosion damage in the material and this can be obtained when measuring the material through fractal analysis these results clearly indicate that corrosion is heavier on locations close to the industrial areas. This also shows the negative impact of industrial activities on the corrodible materials and consequently on the plants and environment.
Bony change of apical lesion healing process using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo [Yonsei University College of Medicine, Seoul (Korea, Republic of)
2005-06-15
To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L{sub 0}) is 0.940 {+-} 0.361 and that of normal area (N{sub 0}) is 1.186 {+-} 0.727 (p<0.05). Fractal dimension at apical lesion of 6 months after endodontic treatment (L{sub 1}) is 1.076 {+-} 0.069 and that of normal area (N{sub 1}) is 1.192 {+-} 0.055 (p<0.05). Fractal dimension at apical lesion of 1 year after endodontic treatment (L{sub 2}) is 1.163 {+-} 0.074 and that of normal area (N{sub 2}) is 1.225 {+-} 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.
Stereological estimation of surface area from digital images
DEFF Research Database (Denmark)
Ziegel, Johanna; Kiderlen, Markus
2010-01-01
A sampling design of local stereology is combined with a method from digital stereology to yield a novel estimator of surface area based on counts of configurations observed in a digitization of an isotropic 2- dimensional slice with thickness s. As a tool, a result of the second author and J....... Rataj on infinitesimal increase of volumes of morphological transforms is refined and used. The proposed surface area estimator is asymptotically unbiased in the case of sets contained in the ball centred at the origin with radius s and in the case of balls centred at the origin with unknown radius...
Large area, surface discharge pumped, vacuum ultraviolet light source
Sze, R.C.; Quigley, G.P.
1996-12-17
Large area, surface discharge pumped, vacuum ultraviolet (VUV) light source is disclosed. A contamination-free VUV light source having a 225 cm{sup 2} emission area in the 240-340 nm region of the electromagnetic spectrum with an average output power in this band of about 2 J/cm{sup 2} at a wall-plug efficiency of approximately 5% is described. Only ceramics and metal parts are employed in this surface discharge source. Because of the contamination-free, high photon energy and flux, and short pulse characteristics of the source, it is suitable for semiconductor and flat panel display material processing. 3 figs.
High surface area carbon and process for its production
Energy Technology Data Exchange (ETDEWEB)
Romanos, Jimmy; Burress, Jacob; Pfeifer, Peter; Rash, Tyler; Shah, Parag; Suppes, Galen
2016-12-13
Activated carbon materials and methods of producing and using activated carbon materials are provided. In particular, biomass-derived activated carbon materials and processes of producing the activated carbon materials with prespecified surface areas and pore size distributions are provided. Activated carbon materials with preselected high specific surface areas, porosities, sub-nm (<1 nm) pore volumes, and supra-nm (1-5 nm) pore volumes may be achieved by controlling the degree of carbon consumption and metallic potassium intercalation into the carbon lattice during the activation process.
Fractals: Giant impurity nonlinearities in optics of fractal clusters
International Nuclear Information System (INIS)
Butenko, A.V.; Shalaev, V.M.; Stockman, M.I.
1988-01-01
A theory of nonlinear optical properties of fractals is developed. Giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal. This enhancement occurs if the exciting radiation frequency lies within the absorption band of the fractal. The giant optical nonlinearities are due to existence of high local electric fields in the sites of impurity locations. Such fields are due to the inhomogeneously broadened character of a fractal spectrum, i.e. partial conservation of individuality of fractal-forming particles (monomers). The field enhancement is proportional to the Q-factor of the resonance of a monomer. The effects of coherent anti-Stokes Raman scattering (CARS) and phase conjugation (PC) of light waves are enhanced to a much greater degree than generation of higher harmonics. In a general case the susceptibility of a higher-order is enhanced in the maximum way if the process includes ''subtraction'' of photons (at least one of the strong field frequencies enters the susceptibility with the minus sign). Alternatively, enhancement for the highest-order harmonic generation (when all the photons are ''accumulated'') is minimal. The predicted phenomena bear information on spectral properties of both impurity molecules and a fractal. In particular, in the CARS spectra a narrow (with the natural width) resonant structure, which is proper to an isolated monomer of a fractal, is predicted to be observed. (orig.)
Clay mineralogy in different geomorphic surfaces in sugarcane areas
Camargo, L.; Marques, J., Jr.
2012-04-01
The crystallization of the oxides and hydroxides of iron and aluminum and kaolinite of clay fraction is the result of pedogenetic processes controlled by the relief. These minerals have influence on the physical and chemical attributes of soil and exhibit spatial dependence. The pattern of spatial distribution is influenced by forms of relief as the geomorphic surfaces. In this sense, the studies aimed at understanding the relationship between relief and the distribution pattern of the clay fraction attributes contribute to the delineation of specific areas of management in the field. The objective of this study was to evaluate the spatial distribution of oxides and hydroxides of iron and aluminum and kaolinite of clay fraction and its relationship with the physical and chemical attributes in different geomorphic surfaces. Soil samples were collected in a transect each 25 m (100 samples) and in the sides of the same (200 samples) as well as an area of 500 ha (1 sample each six hectare). Geomorphic surfaces (GS) in the transect were mapped in detail to support mapping the entire area. The soil samples were taken to the laboratory for chemical, physical, and mineralogical analysis, and the pattern of spatial distribution of soil attributes was obtained by statistics and geostatistics. The GS I is considered the oldest surface of the study area, with depositional character, and a slope ranging from 0 to 4%. GS II and III are considered to be eroded, and the surface II plan a gentle slope that extends from the edge of the surface until the beginning of I and III. The crystallographic characteristics of the oxides and hydroxides of iron and aluminum and kaolinite showed spatial dependence and the distribution pattern corresponding to the limits present of the GS in the field. Surfaces I and II showed the best environments to the degree of crystallinity of hematite and the surface III to the greatest degree of crystallinity of goethite agreeing to the pedoenvironment
Exploring the relationship between fractal features and bacterial essential genes
International Nuclear Information System (INIS)
Yu Yong-Ming; Yang Li-Cai; Zhao Lu-Lu; Liu Zhi-Ping; Zhou Qian
2016-01-01
Essential genes are indispensable for the survival of an organism in optimal conditions. Rapid and accurate identifications of new essential genes are of great theoretical and practical significance. Exploring features with predictive power is fundamental for this. Here, we calculate six fractal features from primary gene and protein sequences and then explore their relationship with gene essentiality by statistical analysis and machine learning-based methods. The models are applied to all the currently available identified genes in 27 bacteria from the database of essential genes (DEG). It is found that the fractal features of essential genes generally differ from those of non-essential genes. The fractal features are used to ascertain the parameters of two machine learning classifiers: Naïve Bayes and Random Forest. The area under the curve (AUC) of both classifiers show that each fractal feature is satisfactorily discriminative between essential genes and non-essential genes individually. And, although significant correlations exist among fractal features, gene essentiality can also be reliably predicted by various combinations of them. Thus, the fractal features analyzed in our study can be used not only to construct a good essentiality classifier alone, but also to be significant contributors for computational tools identifying essential genes. (paper)
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)
Installation and performance evaluation of an indigenous surface area analyser
International Nuclear Information System (INIS)
Pillai, S.N.; Solapurkar, M.N.; Venkatesan, V.; Prakash, A.; Khan, K.B.; Kumar, Arun; Prasad, R.S.
2014-01-01
An indigenously available surface area analyser was installed inside glove box and checked for its performance by analyzing uranium oxide and thorium oxide powders at RMD. The unit has been made ready for analysis of Plutonium oxide powders after incorporating several important features. (author)
Influence of Ear Surface Area on Heat Tolerance of Composite ...
African Journals Online (AJOL)
Relative importance of ear surface area on heat tolerance of composite rabbit population was evaluated. The study was conducted during the dry and rainy seasons, climatic data were recorded to obtain categorical heat stress index. Physiological parameters, growth performance, ear length and ear width of the rabbits ...
Surface water and groundwater interaction in Marala - Khanki area, Punjab
International Nuclear Information System (INIS)
Akram, W.; Ahmad, M.; Latif, Z.; Tariq, J.A.; Malik, M.R.
2011-07-01
Isotope hydrological investigations were carried out in two selected areas of Indus Basin viz. Haripur Area and Chashma- Taunsa Area for elucidating various aspects of surface water and groundwater interaction. Groundwater samples were collected on seasonal basis (low and high river discharge periods) while surface water samples were collected more frequently (weekly or monthly basis). Isotopic data suggested that there is no contribution of surface water to groundwater recharge in Haripur Area and rain is the prevailing source of groundwater recharge. The data further revealed that isotopic values of the Haripur pocket of Tarbela Lake are higher than those of Main Lake / Indus River meaning that there is a significant contribution of base flow in this pocket. Indus River appeared to be the dominant source of groundwater recharge at most of the locations in Chashma- Taunsa Area. Isotopic data of Indus River showed an increase at Taunsa as compared to Chashma in low flow period indicating the high contribution of base flow at this point in time. Stable isotopes were successfully used to quantify the base flow contribution. (author)
Usov, V. V.; Gopkalo, E. E.; Shkatulyak, N. M.; Gopkalo, A. P.; Cherneva, T. S.
2015-09-01
Crystallographic texture and fracture features are studied after low-cycle fatigue tests of laboratory specimens cut from the base metal and the characteristic zones of a welded joint in a pipeline after its longterm operation. The fractal dimensions of fracture surfaces are determined. The fractal dimension is shown to increase during the transition from ductile to quasi-brittle fracture, and a relation between the fractal dimension of a fracture surface and the fatigue life of the specimen is found.
Growth of contact area between rough surfaces under normal stress
Stesky, R. M.; Hannan, S. S.
1987-05-01
The contact area between deforming rough surfaces in marble, alabaster, and quartz was measured from thin sections of surfaces bonded under load with low viscosity resin epoxy. The marble and alabaster samples had contact areas that increased with stress at an accelerating rate. This result suggests that the strength of the asperity contacts decreased progressively during the deformation, following some form of strain weakening relationship. This conclusion is supported by petrographic observation of the thin sections that indicate that much of the deformation was cataclastic, with minor twinning of calcite and kinking of gypsum. In the case of the quartz, the observed contact area was small and increased approximately linearly with normal stress. Only the irreversible cataclastic deformation was observed; however strain-induced birefringence and cracking of the epoxy, not observed with the other rocks, suggests that significant elastic deformation occurred, but recovered during unloading.
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.
Moghilevsky, Débora Estela
2011-01-01
A lo largo de los últimos años del siglo veinte se ha desarrollado la teoría de la complejidad. Este modelo relaciona las ciencias duras tales como la matemática, la teoría del caos, la física cuántica y la geometría fractal con las llamadas seudo ciencias. Dentro de este contexto podemos definir la Psicología Fractal como la ciencia que estudia los aspectos psíquicos como dinámicamente fractales.
Francisco Maduell; Raquel Ojeda; Marta Arias-Guillén; Giannina Bazan; Manel Vera; Néstor Fontseré; Elisabeth Massó; Miquel Gómez; Lida Rodas; Mario Jiménez-Hernández; Gastón Piñeiro; Nayra Rico
2015-01-01
Introduction: Online haemodiafiltration (OL-HDF) is most effective technique; several randomised studies and meta-analyses have shown a reduction in mortality, with a directly related association with convective volume. At present, it is not properly established whether the increasing in dialyser surface area may suppose better outcomes in terms of convective and clearance efficacy. The purpose of the study was to assess the effect of increase in dialyser surface area on the convective volume...
The fractal nature materials microstructure influence on electrochemical energy sources
Directory of Open Access Journals (Sweden)
Mitić V.V.
2015-01-01
Full Text Available With increasing of the world energy crisis, research for new, renewable and alternative energy sources are in growth. The focus is on research areas, sometimes of minor importance and applications, where the different synthesis methods and microstructure properties optimization, performed significant improvement of output materials’ and components’ electro-physical properties, which is important for higher energy efficiency and in the electricity production (batteries and battery systems, fuel cells and hydrogen energy contribution. Also, the storage tanks capacity improvement, for the energy produced on such way, which is one of the most important development issues in the energy sphere, represents a very promising research and application area. Having in mind, the results achieved in the electrochemical energy sources field, especially electrolyte development, these energy sources, materials fractal nature optimization analysis contribution, have been investigated. Based on materials fractal structure research field, particularly electronic materials, we have performed microstructure influence parameters research in electrochemistry area. We have investigated the Ho2O3 concentration influence (from 0.01wt% to 1wt% and sintering temperature (from 1320°C to 1380°C, as consolidation parameters, and thus, also open the electrochemical function fractalization door and in the basic thermodynamic parameters the fractal correction introduced. The fractal dimension dependence on additive concentration is also investigated. [Projekat Ministarstva nauke Republike Srbije, br. 172057: Directed synthesis, structure and properties of multifunctional materials
Fractal analysis of fracture increasing spontaneous imbibition in porous media with gas-saturated
Cai, Jianchao; Sun, Shuyu
2013-01-01
Spontaneous imbibition (SI) of wetting liquid into matrix blocks due to capillary pressure is regarded as an important recovery mechanism in low permeability fractured reservoir. In this paper, an analytical model is proposed for characterizing SI horizontally from a single plane fracture into gas-saturated matrix blocks. The presented model is based on the fractal character of pores in porous matrix, with gravity force included in the entire imbibition process. The accumulated mass of wetting liquid imbibed into matrix blocks is related to a number of factors such as contact area, pore fractal dimension, tortuosity, maximum pore size, porosity, liquid density and viscosity, surface tension, contact angle, as well as height and tilt angle of the fracture. The mechanism of fracture-enhanced SI is analyzed accordingly. Because of the effect of fracture, the gravity force is positive to imbibition process. Additionally, the farther away from the fracture top of the pore, the more influential the hydrostatic pressure is upon the imbibition action. The presented fractal analysis of horizontal spontaneous imbibition from a single fracture could also shed light on the scaling study of the mass transfer function between matrix and fracture system of fractured reservoirs. © 2013 World Scientific Publishing Company.
Fractal analysis of fracture increasing spontaneous imbibition in porous media with gas-saturated
Cai, Jianchao
2013-08-01
Spontaneous imbibition (SI) of wetting liquid into matrix blocks due to capillary pressure is regarded as an important recovery mechanism in low permeability fractured reservoir. In this paper, an analytical model is proposed for characterizing SI horizontally from a single plane fracture into gas-saturated matrix blocks. The presented model is based on the fractal character of pores in porous matrix, with gravity force included in the entire imbibition process. The accumulated mass of wetting liquid imbibed into matrix blocks is related to a number of factors such as contact area, pore fractal dimension, tortuosity, maximum pore size, porosity, liquid density and viscosity, surface tension, contact angle, as well as height and tilt angle of the fracture. The mechanism of fracture-enhanced SI is analyzed accordingly. Because of the effect of fracture, the gravity force is positive to imbibition process. Additionally, the farther away from the fracture top of the pore, the more influential the hydrostatic pressure is upon the imbibition action. The presented fractal analysis of horizontal spontaneous imbibition from a single fracture could also shed light on the scaling study of the mass transfer function between matrix and fracture system of fractured reservoirs. © 2013 World Scientific Publishing Company.
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.
Small carpal bone surface area, a characteristic of Turner's syndrome
International Nuclear Information System (INIS)
Cleveland, R.H.; Done, S.; Correia, J.A.; Crawford, J.D.; Kushner, D.C.; Herman, T.E.
1985-01-01
An abnormality which has received little attention but may be easily recognized on radiographs of the hand of patients with Turner's syndrome is described. Eleven of thirty-one patients (35.5%) with Turner's syndrome were shown on radiographs of the hand to have a visually detectable smallness of the bone surface area of the carpus when compared to the area of the second through fifth metacarpals. Values for the ''C/M'' ratio (the area of the carpals divided by the area of the second through fifth metacarpals) were calculated for films of 31 individuals with gonadal dysgenesis and compared with those from bone age-matched films of seventy-six individuals with normal development of the hand and wrist. A consistent difference with minimal overlap was documented. (orig./WL)
Map of fluid flow in fractal porous medium into fractal continuum flow.
Balankin, Alexander S; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Thermal transport in fractal systems
DEFF Research Database (Denmark)
Kjems, Jørgen
1992-01-01
Recent experiments on the thermal transport in systems with partial fractal geometry, silica aerogels, are reviewed. The individual contributions from phonons, fractons and particle modes, respectively, have been identified and can be described by quantitative models consistent with heat capacity...
Fractal analysis in oral leukoplakia
Directory of Open Access Journals (Sweden)
Prashant Bhai Pandey
2015-01-01
Full Text Available Introduction: Fractal analysis (FA quantifies complex geometric structures by generating a fractal dimension (FD, which can measure the complexity of mucosa. FA is a quantitative tool used to measure the complexity of self-similar or semi-self-similar structures. Aim and Objective: The study was done to perform the FA of oral mucosa with keratotic changes, as it is also made up of self-similar tissues, and thus, its FD can be calculated. Results: In oral leukoplakia, keratinization increases the complexity of mucosa, which denotes fractal geometry. We evaluated and compared pretreated and post-treated oral leukoplakia in 50 patients with clinically proven oral leukoplakia and analyzed the normal oral mucosa and lesional or keratinized mucosa in oral leukoplakia patients through FA using box counting method. Conclusion: FA using the fractal geometry is an efficient, noninvasive prediction tool for early detection of oral leukoplakia and other premalignant conditions in patients.
Sintering of uranium oxide of high specific surface area
International Nuclear Information System (INIS)
Bel, Alain; Francois, Bernard; Delmas, Roger; Caillat, Roger
1959-01-01
The extent to which a uranium oxide powder deriving from ammonium uranate or uranium peroxide lends itself to the sintering process depends largely on its specific surface area. When this is greater than 5 m 2 / g there is an optimum temperature for sintering in hydrogen. This temperature becomes less as the specific area of the powder is greater. Reprint of a paper published in Comptes rendus des seances de l'Academie des Sciences, t. 249, p. 1045-1047, sitting of 21 September 1959 [fr
Model to estimate fractal dimension for ion-bombarded materials
Energy Technology Data Exchange (ETDEWEB)
Hu, A., E-mail: hu77@purdue.edu; Hassanein, A.
2014-03-15
Comprehensive fractal Monte Carlo model ITMC-F (Hu and Hassanein, 2012 [1]) is developed based on the Monte Carlo ion bombardment simulation code, i.e., Ion Transport in Materials and Compounds (ITMC) code (Hassanein, 1985 [2]). The ITMC-F studies the impact of surface roughness on the angular dependence of sputtering yield. Instead of assuming material surfaces to be flat or composed of exact self-similar fractals in simulation, we developed a new method to describe the surface shapes. Random fractal surfaces which are generated by midpoint displacement algorithm and support vector machine algorithm are combined with ITMC. With this new fractal version of ITMC-F, we successfully simulated the angular dependence of sputtering yield for various ion-target combinations, with the input surface roughness exponent directly depicted from experimental data (Hu and Hassanein, 2012 [1]). The ITMC-F code showed good agreement with the experimental data. In advanced, we compare other experimental sputtering yield with the results from ITMC-F to estimate the surface roughness exponent for ion-bombarded material in this research.
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
Spectral theory of infinite-area hyperbolic surfaces
Borthwick, David
2016-01-01
This text introduces geometric spectral theory in the context of infinite-area Riemann surfaces, providing a comprehensive account of the most recent developments in the field. For the second edition the context has been extended to general surfaces with hyperbolic ends, which provides a natural setting for development of the spectral theory while still keeping technical difficulties to a minimum. All of the material from the first edition is included and updated, and new sections have been added. Topics covered include an introduction to the geometry of hyperbolic surfaces, analysis of the resolvent of the Laplacian, scattering theory, resonances and scattering poles, the Selberg zeta function, the Poisson formula, distribution of resonances, the inverse scattering problem, Patterson-Sullivan theory, and the dynamical approach to the zeta function. The new sections cover the latest developments in the field, including the spectral gap, resonance asymptotics near the critical line, and sharp geometric constan...
Random walk through fractal environments
International Nuclear Information System (INIS)
Isliker, H.; Vlahos, L.
2003-01-01
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D F of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D F ≤2 can thus be considered as defective Levy walks. The distribution of jump increments for D F >2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D F F >2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations
Thermal Desorption Analysis of Effective Specific Soil Surface Area
Smagin, A. V.; Bashina, A. S.; Klyueva, V. V.; Kubareva, A. V.
2017-12-01
A new method of assessing the effective specific surface area based on the successive thermal desorption of water vapor at different temperature stages of sample drying is analyzed in comparison with the conventional static adsorption method using a representative set of soil samples of different genesis and degree of dispersion. The theory of the method uses the fundamental relationship between the thermodynamic water potential (Ψ) and the absolute temperature of drying ( T): Ψ = Q - aT, where Q is the specific heat of vaporization, and a is the physically based parameter related to the initial temperature and relative humidity of the air in the external thermodynamic reservoir (laboratory). From gravimetric data on the mass fraction of water ( W) and the Ψ value, Polyanyi potential curves ( W(Ψ)) for the studied samples are plotted. Water sorption isotherms are then calculated, from which the capacity of monolayer and the target effective specific surface area are determined using the BET theory. Comparative analysis shows that the new method well agrees with the conventional estimation of the degree of dispersion by the BET and Kutilek methods in a wide range of specific surface area values between 10 and 250 m2/g.
Hand surface area estimation formula using 3D anthropometry.
Hsu, Yao-Wen; Yu, Chi-Yuang
2010-11-01
Hand surface area is an important reference in occupational hygiene and many other applications. This study derives a formula for the palm surface area (PSA) and hand surface area (HSA) based on three-dimensional (3D) scan data. Two-hundred and seventy subjects, 135 males and 135 females, were recruited for this study. The hand was measured using a high-resolution 3D hand scanner. Precision and accuracy of the scanner is within 0.67%. Both the PSA and HSA were computed using the triangular mesh summation method. A comparison between this study and previous textbook values (such as in the U.K. teaching text and Lund and Browder chart discussed in the article) was performed first to show that previous textbooks overestimated the PSA by 12.0% and HSA by 8.7% (for the male, PSA 8.5% and HSA 4.7%, and for the female, PSA 16.2% and HSA 13.4%). Six 1D measurements were then extracted semiautomatically for use as candidate estimators for the PSA and HSA estimation formula. Stepwise regressions on these six 1D measurements and variable dependency test were performed. Results show that a pair of measurements (hand length and hand breadth) were able to account for 96% of the HSA variance and up to 98% of the PSA variance. A test of the gender-specific formula indicated that gender is not a significant factor in either the PSA or HSA estimation.
The fourth dimension of life: fractal geometry and allometric scaling of organisms.
West, G B; Brown, J H; Enquist, B J
1999-06-04
Fractal-like networks effectively endow life with an additional fourth spatial dimension. This is the origin of quarter-power scaling that is so pervasive in biology. Organisms have evolved hierarchical branching networks that terminate in size-invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules. Natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms.
Solvent accessible surface area (ASA) of simulated phospholipid membranes
DEFF Research Database (Denmark)
Tuchsen, E.; Jensen, Morten Østergaard; Westh, P.
2003-01-01
The membrane-solvent interface has been investigated through calculations of the solvent accessible surface area (ASA) for simulated membranes of DPPC and POPE. For DPPC at 52 degreesC we found an ASA of 126 +/- 8 Angstrom(2) per lipid molecule, equivalent to twice the projected lateral area......, even the most exposed parts of the PC head-group show average ASAs of less than half of its maximal or 'fully hydrated' value. The average ASA of a simulated POPE membrane was 96 +/- 7 Angstrom(2) per lipid. The smaller value than for DPPC reflects much lower ASA of the ammonium ion, which is partially...... compensated by increased exposure of the ethylene and phosphate moieties. The ASA of the polar moieties Of (PO4, NH3 and COO) constitutes 65% of the total accessible area for POPE, making this interface more polar than that of DPPC. It is suggested that ASA information can be valuable in attempts...
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
of fractals. Measuring the Length of a Curve. Consider the problem of measuring the length of a ..... a two dimensional smooth surface embedded in 3 dimen- ... interesting measure of a I-dimensional object is its length and not the volume.
Spatial Behaviour of Singularities in Fractal- and Gaussian Speckle Fields
DEFF Research Database (Denmark)
Angelsky, Oleg V.; Maksimyak, Alexander P.; Maksimyak, Peter P.
2009-01-01
Peculiarities of the spatial behaviour of the dislocation lines resulting from scattering of coherent radiation from random and fractal rough surfaces are studied. The technique of optical correlation is proposed for diagnostics of phase singularities in a complex speckle field by comparing...
Fractal analysis of electrolytically-deposited palladium hydride dendrites
International Nuclear Information System (INIS)
Bursill, L.A.; Julin, Peng; Xudong, Fan.
1990-01-01
The fractal scaling characteristics of the surface profile of electrolytically-deposited palladium hydride dendritic structures have been obtained using conventional and high resolution transmission electron microscopy. The results are in remarkable agreement with the modified diffusion-limited aggregation model. 19 refs., 3 tabs., 13 figs
Field and electric potential of conductors with fractal geometry
Energy Technology Data Exchange (ETDEWEB)
Assis, Thiago A de; Mota, Fernando de B; Miranda, Jose G V; Andrade, Roberto F S; Castilho, Caio M C de [Instituto de Fisica, Universidade Federal da Bahia, Campus Universitario da Federacao, 40210-340, Salvador (Brazil)
2007-11-28
In this study, the behavior of the electric field and its potential are investigated in a region bounded by a rough fractal surface and a distant plane. Both boundaries, maintained at distinct potential values, are assumed to be conductors and, as such, the electric potential is obtained by numerically solving Laplace's equation subject to the appropriate Dirichlet's condition. The rough boundaries, generated by the ballistic deposition and fractal Brownian motion methods, are characterized by the values of the surface roughness W and the local fractal dimension df = 3-{alpha}, where {alpha} is the usual roughness exponent. The equipotential surfaces, obtained from Laplace's equation, are characterized by these same parameters. Results presented show how df depends on the potential value, on the method used to generate the boundary and on W. The behavior of the electric field with respect to the equipotential surface is also considered. Its average intensity was found to increase as a function of the average distance from the equipotential to the fractal boundary; however, its intensity reaches a maximum before decreasing towards an asymptotic constant value, an effect that increases as the value of W increases.
Field and electric potential of conductors with fractal geometry
International Nuclear Information System (INIS)
Assis, Thiago A de; Mota, Fernando de B; Miranda, Jose G V; Andrade, Roberto F S; Castilho, Caio M C de
2007-01-01
In this study, the behavior of the electric field and its potential are investigated in a region bounded by a rough fractal surface and a distant plane. Both boundaries, maintained at distinct potential values, are assumed to be conductors and, as such, the electric potential is obtained by numerically solving Laplace's equation subject to the appropriate Dirichlet's condition. The rough boundaries, generated by the ballistic deposition and fractal Brownian motion methods, are characterized by the values of the surface roughness W and the local fractal dimension df = 3-α, where α is the usual roughness exponent. The equipotential surfaces, obtained from Laplace's equation, are characterized by these same parameters. Results presented show how df depends on the potential value, on the method used to generate the boundary and on W. The behavior of the electric field with respect to the equipotential surface is also considered. Its average intensity was found to increase as a function of the average distance from the equipotential to the fractal boundary; however, its intensity reaches a maximum before decreasing towards an asymptotic constant value, an effect that increases as the value of W increases
Body surface area prediction in normal, hypermuscular, and obese mice.
Cheung, Michael C; Spalding, Paul B; Gutierrez, Juan C; Balkan, Wayne; Namias, Nicholas; Koniaris, Leonidas G; Zimmers, Teresa A
2009-05-15
Accurate determination of body surface area (BSA) in experimental animals is essential for modeling effects of burn injury or drug metabolism. Two-dimensional surface area is related to three-dimensional body volume, which in turn can be estimated from body mass. The Meeh equation relates body surface area to the two-thirds power of body mass, through a constant, k, which must be determined empirically by species and size. We found older values of k overestimated BSA in certain mice; thus we determined empirically k for various strains of normal, obese, and hypermuscular mice. BSA was computed from digitally scanned pelts and nonlinear regression analysis was used to determine the best-fit k. The empirically determined k for C57BL/6J mice of 9.82 was not significantly different from other inbred and outbred mouse strains of normal body composition. However, mean k of the nearly spheroid, obese lepr(db/db) mice (k = 8.29) was significantly lower than for normals, as were values for dumbbell-shaped, hypermuscular mice with either targeted deletion of the myostatin gene (Mstn) (k = 8.48) or with skeletal muscle specific expression of a dominant negative myostatin receptor (Acvr2b) (k = 8.80). Hypermuscular and obese mice differ substantially from normals in shape and density, resulting in considerably altered k values. This suggests Meeh constants should be determined empirically for animals of altered body composition. Use of these new, improved Meeh constants will allow greater accuracy in experimental models of burn injury and pharmacokinetics.
Fractal apertures in waveguides, conducting screens and cavities analysis and design
Ghosh, Basudeb; Kartikeyan, M V
2014-01-01
This book deals with the design and analysis of fractal apertures in waveguides, conducting screens and cavities using numerical electromagnetics and field-solvers. The aim is to obtain design solutions with improved accuracy for a wide range of applications. To achieve this goal, a few diverse problems are considered. The book is organized with adequate space dedicated for the design and analysis of fractal apertures in waveguides, conducting screens, and cavities, microwave/millimeter wave applications followed by detailed case-study problems to infuse better insight and understanding of the subject. Finally, summaries and suggestions are given for future work. Fractal geometries were widely used in electromagnetics, specifically for antennas and frequency selective surfaces (FSS). The self-similarity of fractal geometry gives rise to a multiband response, whereas the space-filling nature of the fractal geometries makes it an efficient element in antenna and FSS unit cell miniaturization. Until now, no e...
Indexing Glomerular Filtration Rate to Body Surface Area
DEFF Research Database (Denmark)
Redal-Baigorri, Belén; Rasmussen, Knud; Heaf, James Goya
2014-01-01
BACKGROUND: Kidney function is mostly expressed in terms of glomerular filtration rate (GFR). A common feature is the expression as ml/min per 1.73 m(2) , which represents the adjustment of the individual kidney function to a standard body surface area (BSA) to allow comparison between individuals....... We investigated the impact of indexing GFR to BSA in cancer patients, as this BSA indexation might affect the reported individual kidney function. METHODS: Cross-sectional study of 895 adults who had their kidney function measured with (51) chrome ethylene diamine tetraacetic acid. Mean values of BSA...
Asymptotic variance of grey-scale surface area estimators
DEFF Research Database (Denmark)
Svane, Anne Marie
Grey-scale local algorithms have been suggested as a fast way of estimating surface area from grey-scale digital images. Their asymptotic mean has already been described. In this paper, the asymptotic behaviour of the variance is studied in isotropic and sufficiently smooth settings, resulting...... in a general asymptotic bound. For compact convex sets with nowhere vanishing Gaussian curvature, the asymptotics can be described more explicitly. As in the case of volume estimators, the variance is decomposed into a lattice sum and an oscillating term of at most the same magnitude....
EFFECT OF RATIO OF SURFACE AREA ON THE CORROSION RATE
Dody Prayitno; M. Irsyad
2018-01-01
Aluminum and steel are used to be a construction for a building outdoor panel. Aluminum and steel are connected by bolt and nut. An atmosphere due to a corrosion of the aluminum. The corrosion possibly to cause the hole diameter of bolt and nut to become larger. Thus the bolt and nut can not enough strong to hold the panel. The panel may collapse. The aim of the research is first to answer a question where does the corrosion starts. The second is to know the effect of ratio surface area of st...
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-01-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape
A fractal-based image encryption system
Abd-El-Hafiz, S. K.; Radwan, Ahmed Gomaa; Abdel Haleem, Sherif H.; Barakat, Mohamed L.
2014-01-01
single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved
Assessment of Textural Differentiations in Forest Resources in Romania Using Fractal Analysis
Directory of Open Access Journals (Sweden)
Ion Andronache
2017-02-01
Full Text Available Deforestation and forest degradation have several negative effects on the environment including a loss of species habitats, disturbance of the water cycle and reduced ability to retain CO2, with consequences for global warming. We investigated the evolution of forest resources from development regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis. We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested and compact organization in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters. Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby enabling quantification of the uniformity, fragmentation, heterogeneity and homogeneity of forests.
Integration of Fractal Biosensor in a Digital Microfluidic Platform
Mashraei, Yousof
2016-06-08
The digital microfluidic (DMF) platform introduces many applications in biomedical assays. If it is to be commercially available to the public, it needs to have the essential features of smart sensing and a compact size. In this work, we report on a fractal electrode biosensor that is used for both droplet actuation and sensing C-reactive protein (CRP) concentration levels to assess cardiac disease risk. Our proposed electrode is the first two-terminal electrode design to be integrated into DMF platforms. A simulation of the electrical field distribution shows reduced peak intensities and uniform distribution of the field. When compared to a V-notch square electrode, the fractal electrode shows a superior performance in both aspects, i.e. field uniformity and intensity. These improvements are translated into a successful and responsive actuation of a water droplet with 100V. Likewise, the effective dielectric strength is improved by a 33% increase in the fractal electrode breakdown voltage. Additionally, the capability of the fractal electrode to work as a capacitive biosensor is evaluated with CRP quantification test. Selected fractal electrodes undergo a surface treatment to immobilize anti-CRP antibodies on their surface. The measurement shows a response to the added CRP in capacitance within three minutes. When the untreated electrodes were used for quantification, there was no significant change in capacitance, and this suggested that immobilization was necessary. The electrodes configuration in the fabricated DMF platform allows the fractal electrodes to be selectively used as biosensors, which means the device could be integrated into point-of-care applications.
Directory of Open Access Journals (Sweden)
Liliana Violeta Constantin
2012-01-01
Full Text Available Starting from the experimental data referring to the main parameters of the fracture surfaces of some 300-grade maraging steel reported by the classical work published in Nature 308, 721–722(1984, this work studied (a the multifractal scaling by the main parameters of the slit islands of fracture surfaces produced by a uniaxial tensile loading and (b the dependence of the impact energy to fracture and of the fractal dimensional increment on the temperature of the studied steels heat treatment, for the fracture surfaces produced by Charpy impact. The obtained results were analyzed, pointing out the spectral (size distribution of the found slit islands in the frame of some specific clusters (fractal components of the multifractal scaling of representative points of the logarithms of the slit islands areas and perimeters, respectively.
Optimized Ultrawideband and Uniplanar Minkowski Fractal Branch Line Coupler
Directory of Open Access Journals (Sweden)
Mohammad Jahanbakht
2012-01-01
Full Text Available The non-Euclidean Minkowski fractal geometry is used in design, optimization, and fabrication of an ultrawideband (UWB branch line coupler. Self-similarities of the fractal geometries make them act like an infinite length in a finite area. This property creates a smaller design with broader bandwidth. The designed 3 dB microstrip coupler has a single layer and uniplanar platform with quite easy fabrication process. This optimized 180° coupler also shows a perfect isolation and insertion loss over the UWB frequency range of 3.1–10.6 GHz.
Effects of fractal pore on coal devolatilization
Energy Technology Data Exchange (ETDEWEB)
Chen, Yongli; He, Rong [Tsinghua Univ., Beijing (China). Dept. of Thermal Engineering; Wang, Xiaoliang; Cao, Liyong [Dongfang Electric Corporation, Chengdu (China). Centre New Energy Inst.
2013-07-01
Coal devolatilization is numerically investigated by drop tube furnace and a coal pyrolysis model (Fragmentation and Diffusion Model). The fractal characteristics of coal and char pores are investigated. Gas diffusion and secondary reactions in fractal pores are considered in the numerical simulations of coal devolatilization, and the results show that the fractal dimension is increased firstly and then decreased later with increased coal conversions during devolatilization. The mechanisms of effects of fractal pores on coal devolatilization are analyzed.
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.
2014-08-28
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fan, Jieran; Wang, Di; DeVault, Clayton
2016-01-01
We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure.......We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure....
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
Feng, Guixiang; Ming, Dongping; Wang, Min; Yang, Jianyu
2017-06-01
Scale problems are a major source of concern in the field of remote sensing. Since the remote sensing is a complex technology system, there is a lack of enough cognition on the connotation of scale and scale effect in remote sensing. Thus, this paper first introduces the connotations of pixel-based scale and summarizes the general understanding of pixel-based scale effect. Pixel-based scale effect analysis is essentially important for choosing the appropriate remote sensing data and the proper processing parameters. Fractal dimension is a useful measurement to analysis pixel-based scale. However in traditional fractal dimension calculation, the impact of spatial resolution is not considered, which leads that the scale effect change with spatial resolution can't be clearly reflected. Therefore, this paper proposes to use spatial resolution as the modified scale parameter of two fractal methods to further analyze the pixel-based scale effect. To verify the results of two modified methods (MFBM (Modified Windowed Fractal Brownian Motion Based on the Surface Area) and MDBM (Modified Windowed Double Blanket Method)); the existing scale effect analysis method (information entropy method) is used to evaluate. And six sub-regions of building areas and farmland areas were cut out from QuickBird images to be used as the experimental data. The results of the experiment show that both the fractal dimension and information entropy present the same trend with the decrease of spatial resolution, and some inflection points appear at the same feature scales. Further analysis shows that these feature scales (corresponding to the inflection points) are related to the actual sizes of the geo-object, which results in fewer mixed pixels in the image, and these inflection points are significantly indicative of the observed features. Therefore, the experiment results indicate that the modified fractal methods are effective to reflect the pixel-based scale effect existing in remote sensing
Surface States and Effective Surface Area on Photoluminescent P-Type Porous Silicon
Weisz, S. Z.; Porras, A. Ramirez; Resto, O.; Goldstein, Y.; Many, A.; Savir, E.
1997-01-01
The present study is motivated by the possibility of utilizing porous silicon for spectral sensors. Pulse measurements on the porous-Si/electrolyte system are employed to determine the surface effective area and the surface-state density at various stages of the anodization process used to produce the porous material. Such measurements were combined with studies of the photoluminescence spectra. These spectra were found to shift progressively to the blue as a function of anodization time. The luminescence intensity increases initially with anodization time, reaches a maximum and then decreases with further anodization. The surface state density, on the other hand, increases with anodization time from an initial value of about 2 x 10(exp 12)/sq cm surface to about 1013 sq cm for the anodized surface. This value is attained already after -2 min anodization and upon further anodization remains fairly constant. In parallel, the effective surface area increases by a factor of 10-30. This behavior is markedly different from the one observed previously for n-type porous Si.
A fractal derivative constitutive model for three stages in granite creep
Directory of Open Access Journals (Sweden)
R. Wang
Full Text Available In this paper, by replacing the Newtonian dashpot with the fractal dashpot and considering damage effect, a new constitutive model is proposed in terms of time fractal derivative to describe the full creep regions of granite. The analytic solutions of the fractal derivative creep constitutive equation are derived via scaling transform. The conventional triaxial compression creep tests are performed on MTS 815 rock mechanics test system to verify the efficiency of the new model. The granite specimen is taken from Beishan site, the most potential area for the China’s high-level radioactive waste repository. It is shown that the proposed fractal model can characterize the creep behavior of granite especially in accelerating stage which the classical models cannot predict. The parametric sensitivity analysis is also conducted to investigate the effects of model parameters on the creep strain of granite. Keywords: Beishan granite, Fractal derivative, Damage evolution, Scaling transformation
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.
2014-08-28
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape separated by a vertical distance from a lower first metal plate with a complementary fractal shape; and a substrate above which the capacitor body is suspended.
An enhanced fractal image denoising algorithm
International Nuclear Information System (INIS)
Lu Jian; Ye Zhongxing; Zou Yuru; Ye Ruisong
2008-01-01
In recent years, there has been a significant development in image denoising using fractal-based method. This paper presents an enhanced fractal predictive denoising algorithm for denoising the images corrupted by an additive white Gaussian noise (AWGN) by using quadratic gray-level function. Meanwhile, a quantization method for the fractal gray-level coefficients of the quadratic function is proposed to strictly guarantee the contractivity requirement of the enhanced fractal coding, and in terms of the quality of the fractal representation measured by PSNR, the enhanced fractal image coding using quadratic gray-level function generally performs better than the standard fractal coding using linear gray-level function. Based on this enhanced fractal coding, the enhanced fractal image denoising is implemented by estimating the fractal gray-level coefficients of the quadratic function of the noiseless image from its noisy observation. Experimental results show that, compared with other standard fractal-based image denoising schemes using linear gray-level function, the enhanced fractal denoising algorithm can improve the quality of the restored image efficiently
Steady laminar flow of fractal fluids
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)
2017-02-12
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.
Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...
African Journals Online (AJOL)
In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0.......0002) in monozygotic twins than in dizygotic twins (0.108, P = 0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, dominant genetic effects explained 54% of the variation and 46% was individually environmentally determined. Conclusions: In young adult twins...
Towards thermomechanics of fractal media
Ostoja-Starzewski, Martin
2007-11-01
Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.
Dielectric dispersion of porous media as a fractal phenomenon
Thevanayagam, S.
1997-09-01
It is postulated that porous media is made up of fractal solid skeleton structure and fractal pore surface. The model thus developed satisfies measured anomalous dielectric behavior of three distinctly different porous media: kaolin, montmorillonite, and shaly sand rock. It is shown that the underlying mechanism behind dielectric dispersion in the kHz range to high MHz range is indeed Maxwell-Wagner mechanism but modified to take into account the multiphase nature of the porous media as opposed to the traditional two-phase Maxwell-Wagner charge accumulation effect. The conductivity of the surface water associated with the solid surface and charge accumulation across the surface irregularities, asperity, and bridging between particles at the micro-scale-level pores are shown to contribute to this modified Maxwell-Wagner mechanism. The latter is dominant at low frequencies. The surface water thickness is calculated to be about 2-6 nm for a variety of porous media.
Fractal universe and quantum gravity.
Calcagni, Gianluca
2010-06-25
We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
Fractals control in particle's velocity
International Nuclear Information System (INIS)
Zhang Yongping; Liu Shutang; Shen Shulan
2009-01-01
Julia set, a fractal set of the literature of nonlinear physics, has significance for the engineering applications. For example, the fractal structure characteristics of the generalized M-J set could visually reflect the change rule of particle's velocity. According to the real world requirement, the system need show various particle's velocity in some cases. Thus, the control of the nonlinear behavior, i.e., Julia set, has attracted broad attention. In this work, an auxiliary feedback control is introduced to effectively control the Julia set that visually reflects the change rule of particle's velocity. It satisfies the performance requirement of the real world problems.
Taylor dispersion on a fractal
International Nuclear Information System (INIS)
Mazo, R.M.
1998-01-01
Taylor dispersion is the greatly enhanced diffusion in the direction of a fluid flow caused by ordinary diffusion in directions orthogonal to the flow. It is essential that the system be bounded in space in the directions orthogonal to the flow. We investigate the situation where the medium through which the flow occurs has fractal properties so that diffusion in the orthogonal directions is anomalous and non-Fickian. The effective diffusion in the flow direction remains normal; its width grows proportionally with the time. However, the proportionality constant depends on the fractal dimension of the medium as well as its walk dimension. (author)
Applications of fractals in ecology.
Sugihara, G; M May, R
1990-03-01
Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
, the retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficients. Falconer's formula and quantitative genetic models were used to determine the genetic component of variation. Results: The mean...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0...
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.
2010-07-01
... alluvial valley floor exists if it finds that— (i) Unconsolidated streamlaid deposits holding streams are... on areas or adjacent to areas including alluvial valley floors in the arid and semiarid areas west of....19 Surface coal mining and reclamation operations on areas or adjacent to areas including alluvial...
International Nuclear Information System (INIS)
Nonaka, S.
1992-01-01
Recently, large-area plasma production has been tested by means of a 13.56 MHz radio-frequency (RF) discharge between a pair of large-area planar electrodes, approximately 0.5 m x 1.4 m, as one of the semiconductor technologies for fabrication of large-area amorphous silicon solar cells in the ''Sunshine Project'' of the Agency of Industrial Science and Technology in Japan. We also confirmed long plasma production between a pair of long electrodes. In this paper, normal electromagnetic (EM) waves propagating in a region between a planar waveguide with one plasma and two dielectric layers are analyzed in order to study the feasibility of large-area plasma productions by EM wave-discharges between a pair of large-area RF electrodes larger than the half-wavelength of RF wave. In conclusion, plasmas higher than an electron plasma frequency will be produced by an odd TMoo surface mode. (author) 4 refs., 3 figs
Human cortical areas involved in perception of surface glossiness.
Wada, Atsushi; Sakano, Yuichi; Ando, Hiroshi
2014-09-01
Glossiness is the visual appearance of an object's surface as defined by its surface reflectance properties. Despite its ecological importance, little is known about the neural substrates underlying its perception. In this study, we performed the first human neuroimaging experiments that directly investigated where the processing of glossiness resides in the visual cortex. First, we investigated the cortical regions that were more activated by observing high glossiness compared with low glossiness, where the effects of simple luminance and luminance contrast were dissociated by controlling the illumination conditions (Experiment 1). As cortical regions that may be related to the processing of glossiness, V2, V3, hV4, VO-1, VO-2, collateral sulcus (CoS), LO-1, and V3A/B were identified, which also showed significant correlation with the perceived level of glossiness. This result is consistent with the recent monkey studies that identified selective neural response to glossiness in the ventral visual pathway, except for V3A/B in the dorsal visual pathway, whose involvement in the processing of glossiness could be specific to the human visual system. Second, we investigated the cortical regions that were modulated by selective attention to glossiness (Experiment 2). The visual areas that showed higher activation to attention to glossiness than that to either form or orientation were identified as right hV4, right VO-2, and right V3A/B, which were commonly identified in Experiment 1. The results indicate that these commonly identified visual areas in the human visual cortex may play important roles in glossiness perception. Copyright © 2014. Published by Elsevier Inc.
Bony change of apical lesion healing process using fractal analysis
International Nuclear Information System (INIS)
Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo
2005-01-01
To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L 0 ) is 0.940 ± 0.361 and that of normal area (N 0 ) is 1.186 ± 0.727 (p 1 ) is 1.076 ± 0.069 and that of normal area (N 1 ) is 1.192 ± 0.055 (p 2 ) is 1.163 ± 0.074 and that of normal area (N 2 ) is 1.225 ± 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.
Czan, Andrej; Babík, Ondrej; Miklos, Matej; Záušková, Lucia; Mezencevová, Viktória
2017-10-01
Since most of the implant surface is in direct contact with bone tissue, shape and integrity of said surface has great influence on successful osseointegration. Among other characteristics that predetermine titanium of different grades of pureness as ideal biomaterial, titanium shows high mechanical strength making precise miniature machining increasingly difficult. Current titanium-based implants are often anodized due to colour coding. This anodized layer has important functional properties for right usage and also bio-compatibility of dental implants. Physical method of anodizing and usage of anodizing mediums has a significant influence on the surface quality and itself functionality. However, basic requirement of the dental implant with satisfactory properties is quality of machined surface before anodizing. Roughness, for example, is factor affecting of time length of anodizing operation and so whole productivity. The paper is focused on monitoring of surface and area characteristics, such as roughness or surface integrity after different cutting conditions of miniature machining of dental implants and their impact on suitability for creation of satisfactory anodized layer with the correct biocompatible functional properties.
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
Robot Towed Shortwave Infrared Camera for Specific Surface Area Retrieval of Surface Snow
Elliott, J.; Lines, A.; Ray, L.; Albert, M. R.
2017-12-01
Optical grain size and specific surface area are key parameters for measuring the atmospheric interactions of snow, as well as tracking metamorphosis and allowing for the ground truthing of remote sensing data. We describe a device using a shortwave infrared camera with changeable optical bandpass filters (centered at 1300 nm and 1550 nm) that can be used to quickly measure the average SSA over an area of 0.25 m^2. The device and method are compared with calculations made from measurements taken with a field spectral radiometer. The instrument is designed to be towed by a small autonomous ground vehicle, and therefore rides above the snow surface on ultra high molecular weight polyethylene (UHMW) skis.
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.
Estimating the surface area of birds: using the homing pigeon (Columba livia as a model
Directory of Open Access Journals (Sweden)
Cristina R. Perez
2014-05-01
Full Text Available Estimation of the surface area of the avian body is valuable for thermoregulation and metabolism studies as well as for assessing exposure to oil and other surface-active organic pollutants from a spill. The use of frozen carcasses for surface area estimations prevents the ability to modify the posture of the bird. The surface area of six live homing pigeons in the fully extended flight position was estimated using a noninvasive method. An equation was derived to estimate the total surface area of a pigeon based on its body weight. A pigeon's surface area in the fully extended flight position is approximately 4 times larger than the surface area of a pigeon in the perching position. The surface area of a bird is dependent on its physical position, and, therefore, the fully extended flight position exhibits the maximum area of a bird and should be considered the true surface area of a bird.
Evolution of Fractal Parameters through Development Stage of Soil Crust
Ospina, Abelardo; Florentino, Adriana; Tarquis, Ana Maria
2016-04-01
Soil surface characteristics are subjected to changes driven by several interactions between water, air, biotic and abiotic components. One of the examples of such interactions is provided through biological soil crusts (BSC) in arid and semi-arid environments. BSC are communities composed of cyanobacteria, fungi, mosses, lichens, algae and liverworts covering the soil surface and play an important role in ecosystem functioning. The characteristics and formation of these BSC influence the soil hydrological balance, control the mass of eroded sediment, increase stability of soil surface, and influence plant productivity through the modification of nitrogen and carbon cycle. The site of this work is located at Quibor and Ojo de Agua (Lara state, Venezuela). The Quibor Depression in Venezuela is a major agricultural area being at semi-arid conditions and limited drainage favor the natural process of salinization. Additionally, the extension and intensification of agriculture has led to over-exploitation of groundwater in the past 30 years (Méndoza et al., 2013). The soil microbial crust develops initially on physical crusts which are mainly generated since wetting and drying, being a recurrent feature in the Quíbor arid zone. The microbiotic crust is organic, composed of macro organisms (bryophytes and lichens) and microorganisms (cyanobacteria, fungi algae, etc.); growing on the ground, forming a thickness no greater than 3 mm. For further details see Toledo and Florentino (2009). This study focus on characterize the development stage of the BSC based on image analysis. To this end, grayscale images of different types of biological soil crust at different stages where taken, each image corresponding to an area of 12.96 cm2 with a resolution of 1024x1024 pixels (Ospina et al., 2015). For each image lacunarity and fractal dimension through the differential box counting method were calculated. These were made with the software ImageJ/Fraclac (Karperien, 2013
Hong Shen
2011-01-01
The concepts of curve profile, curve intercept, curve intercept density, curve profile area density, intersection density in containing intersection (or intersection density relied on intersection reference), curve profile intersection density in surface (or curve intercept intersection density relied on intersection of containing curve), and curve profile area density in surface (AS) were defined. AS expressed the amount of curve profile area of Y phase in the unit containing surface area, S...
Correlation of optical properties with the fractal microstructure of black molybdenum coatings
Energy Technology Data Exchange (ETDEWEB)
Barrera, Enrique; Gonzalez, Federico [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Rodriguez, Eduardo [Area de Computacion y Sistemas, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Alvarez-Ramirez, Jose, E-mail: jjar@xanum.uam.mx [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico)
2010-01-01
Coating is commonly used for improving the optical properties of surfaces for solar collector applications. The coating morphology depends on the deposition conditions, and this determines the final optical characteristics. Coating morphologies are irregular and of fractal nature, so a suitable approach for its characterization should use methods borrowed from fractal analysis. The aim of this work is to study the fractal characteristics of black molybdenum coatings on copper and to relate the fractal parameters to the optical properties. To this end, coating surfaces were prepared via immersion in a solution of ammonium paramolybdate for different deposition periods. The fractal analysis was carried out for SEM and AFM images of the coating surface and the fractal properties were obtained with a recently developed high-dimensional extension of the well-known detrended fluctuation analysis (DFA). The most salient parameter drawn from the application of the DFA is the Hurst index, a parameter related to the roughness of the coating surface, and the multifractality index, which is related to the non-linearity features of the coating morphology. The results showed that optical properties, including absorptance and emittance, are decreasing functions of the Hurst and multifractality indices. This suggests that coating surfaces with high absorptance and emittance values are related to complex coating morphologies conformed within a non-linear structure.
Directory of Open Access Journals (Sweden)
Li Ma
2018-05-01
Full Text Available Pore structure has a significant influence on coal-bed methane (CBM enhancement. Injecting liquid CO2 into coal seams is an effective way to increase CBM recovery. However, there has been insufficient research regarding the damage effects and fractal characteristics of pore structure at low temperature induced by injecting liquid CO2 into coal samples. Therefore, the methods of low-pressure nitrogen adsorption-desorption (LP-N2-Ad and mercury intrusion porosimetry (MIP were used to investigate the damage effects and fractal characteristics of pore structure with full aperture as the specimens were frozen by liquid CO2. The adsorption isotherms revealed that the tested coal samples belonged to type B, indicating that they contained many bottle and narrow-slit shaped pores. The average pore diameter (APD; average growth rate of 18.20%, specific surface area (SSA; average growth rate of 7.38%, and total pore volume (TPV; average growth rate of 18.26% increased after the specimens were infiltrated by liquid CO2, which indicated the generation of new pores and the transformation of original pores. Fractal dimensions D1 (average of 2.58 and D2 (average of 2.90 of treated coal samples were both larger the raw coal (D1, average of 2.55 and D2, average of 2.87, which indicated that the treated specimens had more rough pore surfaces and complex internal pore structures than the raw coal samples. The seepage capacity was increased because D4 (average of 2.91 of the treated specimens was also higher than the raw specimens (D4, average of 2.86. The grey relational coefficient between the fractal dimension and pore structure parameters demonstrated that the SSA, APD, and porosity positively influenced the fractal features of the coal samples, whereas the TPV and permeability exerted negative influences.
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost ... Here a(t) is the cosmic scale factor and it measures the expansion of the Universe. ..... effectively appear as self-conserved dark energy, with a non-trivial ...
Fractals in DNA sequence analysis
Institute of Scientific and Technical Information of China (English)
Yu Zu-Guo(喻祖国); Vo Anh; Gong Zhi-Min(龚志民); Long Shun-Chao(龙顺潮)
2002-01-01
Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance,and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view)to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.
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 nature of humic materials
International Nuclear Information System (INIS)
Rice, J.A.
1992-01-01
Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this ''disorder within disorder.'' Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fraction has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis
Fractal character of structural control on uranium mineralization in south china
International Nuclear Information System (INIS)
Zhou Quanyu; Tan Kaixuan; Xie Yanshi
2009-01-01
South China is the most important uranium producer in the country. Most uranium ore deposits in south China are strictly controlled by NE-NNE trending regional fracture structure. Fractal analyses on spatial distribution of uranium ore deposits and regional fracture structure in south China have been done in this paper. It indicates that the spatial distribution of both uranium ore deposits and regional fracture structure in south China show fractal character. The fractal dimension D=1.414 2 for the spatial distribution of regional fracture structure in the whole area indicate a higher ripening degree in the fracture structure evolution and an advantages to fluid flow and uranium mineralization. The fractal dimension D=1.052 7 for the spatial distribution of uranium ore deposits in south China show a lower complexity than regional fracture structure. The fractal dimensions in three sub-areas in south China on spatial distribution of uranium ore deposits show a positive correlation to which of regional fracture structure. The fractal spatial distribution of uranium ore deposits in south China is the result of the evolution of the fractal fracture structure system. (authors)
Dynamic characterisation of the specific surface area for fracture networks
Cvetkovic, V.
2017-12-01
One important application of chemical transport is geological disposal of high-level nuclear waste for which crystalline rock is a prime candidate for instance in Scandinavia. Interconnected heterogeneous fractures of sparsely fractured rock such as granite, act as conduits for transport of dissolved tracers. Fluid flow is known to be highly channelized in such rocks. Channels imply narrow flow paths, adjacent to essentially stagnant water in the fracture and/or the rock matrix. Tracers are transported along channelised flow paths and retained by minerals and/or stagnant water, depending on their sorption properties; this mechanism is critical for rocks to act as a barrier and ultimately provide safety for a geological repository. The sorbing tracers are retained by diffusion and sorption on mineral surfaces, whereas non-sorbing tracers can be retained only by diffusion into stagnant water of fractures. The retention and transport properties of a sparsely fractured rock will primarily depend on the specific surface area (SSA) of the fracture network which is determined by the heterogeneous structure and flow. The main challenge when characterising SSA on the field-scale is its dependence on the flow dynamics. We first define SSA as a physical quantity and clarify its importance for chemical transport. A methodology for dynamic characterisation of SSA in fracture networks is proposed that relies on three sets of data: i) Flow rate data as obtained by a flow logging procedure; ii) transmissivity data as obtained by pumping tests; iii) fracture network data as obtained from outcrop and geophysical observations. The proposed methodology utilises these data directly as well as indirectly through flow and particle tracking simulations in three-dimensional discrete fracture networks. The methodology is exemplified using specific data from the Swedish site Laxemar. The potential impact of uncertainties is of particular significance and is illustrated for radionuclide
The winds regime of surface in the Colombian coffee area
International Nuclear Information System (INIS)
Orlando Guzman Martinez; Lucia Gomez Gomez
1994-01-01
The characteristics of the address and gust of wind of the surface winds have been studied in 15 stations of the Colombian coffee area. It was found that the relief plays an important paper in the wind circulation so that during the day (7 a.m. - 7 p.m.) these they blow of the low sector toward the mountain and at night (7 p.m. - 7 a.m.) this situation is invested, that which is consistent with the characteristic pattern of circulation valley-mountain of the mountainous regions. For this fact, in most of the analyzed places a single day and night dominant address that it takes the orientation in that it is the respective hydrographic basin. It was not observed that the Alisios winds of the northeast and southeast modify the address settled down by the local circulation (valley-mountain) on the other hand a remarkable increase of the gust of wind was appreciated in July and August in the Florida and Ospina, stations located to the south of the country, as direct consequence of the Alisios of the southeast. The daily gust of wind in most of the studied places is low and it doesn't exceed of the 10 km/h, reason why it can consider that the Colombian coffee area is free of important damages for the action of the wind. Nevertheless, in some stations as Alban, Maracay and Paraguaicito the daily maximum gust of wind can surpass the 30 km/h and in occasions to cause damage mechanic to cultivations of high behavior and not well anchored facilities
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.
Determination of effective thermal conductivity for polyurethane foam by use of fractal method
Institute of Scientific and Technical Information of China (English)
SHI Mingheng; LI Xiaochuan; CHEN Yongping
2006-01-01
The microstructure of polyurethane foam is disordered, which influences the foam heat conduction process significantly. In this paper foam structure is described by using the local area fractal dimension in a certain small range of length scales. An equivalent element cell is constructed based on the local fractal dimensions along the directions parallel and transverse to the heat flux. By use of fractal void fraction a simplified heat conduction model is proposed to calculate the effective thermal conductivity of polyurethane foam. The predicted effective thermal conductivity agrees well with the experimental data.
Extent of Stream Burial and Relationships to Watershed Area, Topography, and Impervious Surface Area
Directory of Open Access Journals (Sweden)
Roy E. Weitzell
2016-11-01
Full Text Available Stream burial—the routing of streams through culverts, pipes, and concrete lined channels, or simply paving them over—is common during urbanization, and disproportionately affects small, headwater streams. Burial undermines the physical and chemical processes governing life in streams, with consequences for water quality and quantity that may amplify from headwaters to downstream receiving waters. Knowledge of the extent of stream burial is critical for understanding cumulative impacts to stream networks, and for future decision-making allowing for urban development while protecting ecosystem function. We predicted stream burial across the urbanizing Potomac River Basin (USA for each 10-m stream segment in the basin from medium-resolution impervious cover data and training observations obtained from high-resolution aerial photography in a GIS. Results were analyzed across a range in spatial aggregation, including counties and independent cities, small watersheds, and regular spatial grids. Stream burial was generally correlated with total impervious surface area (ISA, with areas exhibiting ISA above 30% often subject to elevated ratios of stream burial. Recurring patterns in burial predictions related to catchment area and topographic slope were also detected. We discuss these results in the context of physiographic constraints on stream location and urban development, including implications for environmental management of aquatic resources.
Invited Article: Plasmonic growth of patterned metamaterials with fractal geometry
Directory of Open Access Journals (Sweden)
Nobuyuki Takeyasu
2016-08-01
Full Text Available Large-scale metallic three-dimensional (3D structures composed of sub-wavelength fine details, called metamaterials, have attracted optical scientists and materials scientists because of their unconventional and extraordinary optical properties that are not seen in nature. However, existing nano-fabrication technologies including two-photon fabrication, e-beam, focused ion-beam, and probe microscopy are not necessarily suitable for fabricating such large-scale 3D metallic nanostructures. In this article, we propose a different method of fabricating metamaterials, which is based on a bottom-up approach. We mimicked the generation of wood forest under the sunlight and rain in nature. In our method, a silver nano-forest is grown from the silver seeds (nanoparticles placed on the glass substrate in silver-ion solution. The metallic nano-forest is formed only in the area where ultraviolet light is illuminated. The local temperature increases at nano-seeds and tips of nano-trees and their branches due to the plasmonic heating as a result of UV light excitation of localized mode of surface plasmon polaritons. We have made experiments of growth of metallic nano-forest patterned by the light distribution. The experimental results show a beautiful nano-forest made of silver with self-similarity. Fractal dimension and spectral response of the grown structure are discussed. The structures exhibit a broad spectral response from ultraviolet to infrared, which was used for surface-enhanced Raman detection of molecules.
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.
Discrepancy between body surface area and body composition in cancer.
Stobäus, Nicole; Küpferling, Susanne; Lorenz, Marie-Luise; Norman, Kristina
2013-01-01
Calculation of cytostatic dose is typically based on body surface area (BSA) regardless of body composition. The aim of this study was to assess the discrepancy between BSA and low fat-free mass (FFM) by investigating the prevalence of low FFM with regard to BSA in 630 cancer patients. First, BSA was calculated according to DuBois and DuBois. Patients were divided into 6 categories with respect to their BSA. Each BSA category was further divided into 3 groups according to FFM: low (FFM), normal (-0.99 and 0.99 SD of mean FFM) or high (>1 SD of mean FFM), which was derived through bioelectric impedance analysis. FFM was reduced in 15.7% of patients, 69% had normal and 15.2% had high FFM. In patients with low FFM (i.e., more than-1 SD lower than the mean FFM within their BSA group), body mass index and fatigue were higher whereas functional status was reduced. Moreover, in the subcohort of patients receiving chemotherapy, absolute FFM [Hazard ratio (HR) = 0.970, P = 0.026] as well as the allocation to the low FFM group (HR = 1.644, P = 0.025) emerged as predictors of increased 1-yr mortality. In conclusion, there was a large discrepancy between FFM and BSA. Particularly women were affected by low FFM.
Modeling surface area to volume effects on borosilicate glass dissolution
International Nuclear Information System (INIS)
Bourcier, W.L.; Ebert, W.L.; Feng, X.
1992-11-01
We simulated the reaction of SRL-131 glass with equilibrated J-13 water in order to investigate the effects of surface area to volume ratio (SA/V) on glass dissolution. We show that glass-fluid ion exchange causes solution pH to rise to progressively higher values as SA/V increases. Because the ion exchange is rapid relative to the duration of the glass dissolution experiment, the pH effect does not scale with (SA/V)*time. Experiments compared at the same (SA/V)*time value therefore have different pHs, with higher pHs at higher SA/V ratios. Both experimental data and our simulation results show similar trends of increasing reaction rate as a function of SA/V ratio when scaled to (SA/V)*time. Glasses which react in systems of differing SA/V ratio therefore follow different reaction paths and high SA/V ratios cannot be used to generate data which accurately scales to long time periods unless the ion exchange effect is taken into account. We suggest some simple test designs which enable more reliable high. SA/V accelerated tests
Surface Rupture Effects on Earthquake Moment-Area Scaling Relations
Luo, Yingdi; Ampuero, Jean-Paul; Miyakoshi, Ken; Irikura, Kojiro
2017-09-01
Empirical earthquake scaling relations play a central role in fundamental studies of earthquake physics and in current practice of earthquake hazard assessment, and are being refined by advances in earthquake source analysis. A scaling relation between seismic moment ( M 0) and rupture area ( A) currently in use for ground motion prediction in Japan features a transition regime of the form M 0- A 2, between the well-recognized small (self-similar) and very large (W-model) earthquake regimes, which has counter-intuitive attributes and uncertain theoretical underpinnings. Here, we investigate the mechanical origin of this transition regime via earthquake cycle simulations, analytical dislocation models and numerical crack models on strike-slip faults. We find that, even if stress drop is assumed constant, the properties of the transition regime are controlled by surface rupture effects, comprising an effective rupture elongation along-dip due to a mirror effect and systematic changes of the shape factor relating slip to stress drop. Based on this physical insight, we propose a simplified formula to account for these effects in M 0- A scaling relations for strike-slip earthquakes.
Tracheobronchial and Alveolar Particle Surface Area Doses in Smokers
Directory of Open Access Journals (Sweden)
Fernanda Carmen Fuoco
2017-01-01
Full Text Available Cigarette smoke is the main cause of lung cancer events. Mainstream cigarette smoke (MSS is a direct concern for smokers, but also the secondhand smoke (SHS contributes to the smoker exposure. In addition, smoker exposure is affected by the “free-smoke” particle exposure (B, related to the micro-environments where smokers spend time. The aim of this paper is to evaluate the daily alveolar and tracheobronchial deposited fractions of airborne particles for smokers as the sum of these three contributions: MSS, SHS, and B. Measurements of particle surface area distributions in the MSS were performed through a Scanning Mobility Particle Sizer, an Aerodynamic Particle Sizer, and a Thermo-dilution system on five types of conventional cigarettes. A Monte Carlo method was then applied to evaluate the most probable value of dose received during the inhalation of MSS by smokers. Measurements of particle concentrations in SHS and at the “free-smoke” particle background (B were performed through 24-h monitoring at a personal scale of adult smoker through hand-held devices. This paper found that the total daily deposited dose for typical smokers was 1.03 × 105 mm2·day−1. The main contribution of such a huge daily dose was addressable to the MSS (98% while SHS contributed 1.1%, increasing up to 2% for people smoking only while traveling in a car.
Terahertz response of fractal meta-atoms based on concentric rectangular square resonators
Energy Technology Data Exchange (ETDEWEB)
Song, Zhiqiang; Zhao, Zhenyu, E-mail: zyzhao@shnu.edu.cn; Shi, Wangzhou [Department of Physics, Shanghai Normal University, Shanghai 200234 (China); Peng, Wei [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050 (China)
2015-11-21
We investigate the terahertz electromagnetic responses of fractal meta-atoms (MAs) induced by different mode coupling mechanisms. Two types of MAs based on concentric rectangular square (CRS) resonators are presented: independent CRS (I-CRS) and junctional-CRS (J-CRS). In I-CRS, each resonator works as an independent dipole so as to result in the multiple resonance modes when the fractal level is above 1. In J-CRS, however, the generated layer is rotated by π/2 radius to the adjacent CRS in one MA. The multiple resonance modes are coupled into a single mode resonance. The fractal level increasing induces resonance modes redshift in I-CRS while blueshift in J-CRS. When the fractal level is below 4, the mode Q factor of J-CRS is in between the two modes of I-CRS; when the fractal level is 4 or above, the mode Q factor of J-CRS exceeds the two modes of I-CRS. Furthermore, the modulation depth (MD) decreases in I-CRS while it increases in J-CRS with the increase in fractal levels. The surface currents analysis reveals that the capacitive coupling of modes in I-CRS results in the modes redshift, while the conductive coupling of modes in J-CRS induces the mode blueshift. A high Q mode with large MD can be achieved via conductive coupling between the resonators of different scales in a fractal MA.
Energy Technology Data Exchange (ETDEWEB)
Chamousis, RL; Chang, LL; Watterson, WJ; Montgomery, RD; Taylor, RP; Moule, AJ; Shaheen, SE; Ilan, B; van de Lagemaat, J; Osterloh, FE
2014-08-21
Living organisms use fractal structures to optimize material and energy transport across regions of differing size scales. Here we test the effect of fractal silver electrodes on light distribution and charge collection in organic semiconducting polymer films made of P3HT and PCBM. The semiconducting polymers were deposited onto electrochemically grown fractal silver structures (5000 nm x 500 nm; fractal dimension of 1.71) with PEDOT:PSS as hole-selective interlayer. The fractal silver electrodes appear black due to increased horizontal light scattering, which is shown to improve light absorption in the polymer. According to surface photovoltage spectroscopy, fractal silver electrodes outperform the flat electrodes when the BHJ film thickness is large (>400 nm, 0.4 V photovoltage). Photocurrents of up to 200 microamperes cm(-2) are generated from the bulk heterojunction (BHJ) photoelectrodes under 435 nm LED (10-20 mW cm(-2)) illumination in acetonitrile solution containing 0.005 M ferrocenium hexafluorophosphate as the electron acceptor. The low IPCE values (0.3-0.7%) are due to slow electron transfer to ferrocenium ion and due to shunting along the large metal-polymer interface. Overall, this work provides an initial assessment of the potential of fractal electrodes for organic photovoltaic cells.
[Modeling continuous scaling of NDVI based on fractal theory].
Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng
2013-07-01
Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.
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.
Electromagnetic Scattering Characteristics of Fractal Rough Coated Objects in the Terahertz Range
Directory of Open Access Journals (Sweden)
Zhao Hua
2018-02-01
Full Text Available Based on the physical optics method, the scattering characteristics of fractal rough surface coated objects are studied in the terahertz (THz range herein. A blunt model based on fractal rough surfaces is built. The surface current is calculated according to the Fresnel reflection coefficient, and the Radar Cross Section (RCS of the rough coated target is obtained. The RCS of rough and smooth surface targets are compared. Numerical results for a rough coated blunt cone model are provided, and discussed from the perspective of different frequencies and coating thickness values. The results show that the surface roughness of the target has a significant effect on scattering in the terahertz range.
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.
Chaos, Fractals and Their Applications
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
Fractals, malware, and data models
Jaenisch, Holger M.; Potter, Andrew N.; Williams, Deborah; Handley, James W.
2012-06-01
We examine the hypothesis that the decision boundary between malware and non-malware is fractal. We introduce a novel encoding method derived from text mining for converting disassembled programs first into opstrings and then filter these into a reduced opcode alphabet. These opcodes are enumerated and encoded into real floating point number format and used for characterizing frequency of occurrence and distribution properties of malware functions to compare with non-malware functions. We use the concept of invariant moments to characterize the highly non-Gaussian structure of the opcode distributions. We then derive Data Model based classifiers from identified features and interpolate and extrapolate the parameter sample space for the derived Data Models. This is done to examine the nature of the parameter space classification boundary between families of malware and the general non-malware category. Preliminary results strongly support the fractal boundary hypothesis, and a summary of our methods and results are presented here.
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...
Fuzzy fractals, chaos, and noise
Energy Technology Data Exchange (ETDEWEB)
Zardecki, A.
1997-05-01
To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-01-01
reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics
Node insertion in Coalescence Fractal Interpolation Function
International Nuclear Information System (INIS)
Prasad, Srijanani Anurag
2013-01-01
The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed
Fractional hydrodynamic equations for fractal media
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2005-01-01
We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered
Power Load Prediction Based on Fractal Theory
Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song
2015-01-01
The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...
Fractal Metrology for biogeosystems analysis
Directory of Open Access Journals (Sweden)
V. Torres-Argüelles
2010-11-01
Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal Characteristics of Pores in Taiyuan Formation Shale from Hedong Coal Field, China
Li, Kunjie; Zeng, Fangui; Cai, Jianchao; Sheng, Guanglong; Xia, Peng; Zhang, Kun
For the purpose of investigating the fractal characteristics of pores in Taiyuan formation shale, a series of qualitative and quantitative experiments were conducted on 17 shale samples from well HD-1 in Hedong coal field of North China. The results of geochemical experiments show that Total organic carbon (TOC) varies from 0.67% to 5.32% and the organic matters are in the high mature or over mature stage. The shale samples consist mainly of clay minerals and quartz with minor pyrite and carbonates. The FE-SEM images indicate that three types of pores, organic-related pores, inorganic-related pores and micro-fractures related pores, are developed well, and a certain number of intragranular pores are found inside quartz and carbonates formed by acid liquid corrosion. The pore size distributions (PSDs) broadly range from several to hundreds nanometers, but most pores are smaller than 10nm. As the result of different adsorption features at relative pressure (0-0.5) and (0.5-1) on the N2 adsorption isotherm, two fractal dimensions D1 and D2 were obtained with the Frenkel-Halsey-Hill (FHH) model. D1 and D2 vary from 2.4227 to 2.6219 and from 2.6049 to 2.7877, respectively. Both TOC and brittle minerals have positive effect on D1 and D2, whereas clay minerals, have a negative influence on them. The fractal dimensions are also influenced by the pore structure parameters, such as the specific surface area, BJH pore volume, etc. Shale samples with higher D1 could provide more adsorption sites leading to a greater methane adsorption capacity, whereas shale samples with higher D2 have little influence on methane adsorption capacity.
Measurement of DEM roughness using the local fractal dimension
Taud, Hind; Parrot, Jean-François
2008-01-01
Les relations entre les traits géomorphologiques et la rugosité de surface des Modèles Numériques de Terrain (MNT) ont été étudiées par l’intermédiaire de la géométrie fractale. La dimension fractale dans l’espace à trois dimensions est estimée localement sur la surface du MNT. Cette mesure se fait à l’aide d’une procédure dérivée de la technique du « comptage de boîtes ». Ce traitement a été appliqué sur deux zones tests choisies pour leurs différences lithologiques et tectoniques. La premiè...
Shirazinodeh, Alireza; Noubari, Hossein Ahmadi; Rabbani, Hossein; Dehnavi, Alireza Mehri
2015-01-01
Recent studies on wavelet transform and fractal modeling applied on mammograms for the detection of cancerous tissues indicate that microcalcifications and masses can be utilized for the study of the morphology and diagnosis of cancerous cases. It is shown that the use of fractal modeling, as applied to a given image, can clearly discern cancerous zones from noncancerous areas. In this paper, for fractal modeling, the original image is first segmented into appropriate fractal boxes followed by identifying the fractal dimension of each windowed section using a computationally efficient two-dimensional box-counting algorithm. Furthermore, using appropriate wavelet sub-bands and image Reconstruction based on modified wavelet coefficients, it is shown that it is possible to arrive at enhanced features for detection of cancerous zones. In this paper, we have attempted to benefit from the advantages of both fractals and wavelets by introducing a new algorithm. By using a new algorithm named F1W2, the original image is first segmented into appropriate fractal boxes, and the fractal dimension of each windowed section is extracted. Following from that, by applying a maximum level threshold on fractal dimensions matrix, the best-segmented boxes are selected. In the next step, the segmented Cancerous zones which are candidates are then decomposed by utilizing standard orthogonal wavelet transform and db2 wavelet in three different resolution levels, and after nullifying wavelet coefficients of the image at the first scale and low frequency band of the third scale, the modified reconstructed image is successfully utilized for detection of breast cancer regions by applying an appropriate threshold. For detection of cancerous zones, our simulations indicate the accuracy of 90.9% for masses and 88.99% for microcalcifications detection results using the F1W2 method. For classification of detected mictocalcification into benign and malignant cases, eight features are identified and
Estimation of Specific Surface Area using Langmuir Isotherm ...
African Journals Online (AJOL)
Michael Horsfall
Y= KCe/(1+KCe) (1) where Y is the fraction of fish carbon surface covered ..... transmigration of adsorbate in the plane surface. (Hameed et al., 2006). ... and to the Technologists of Agric Soil Science. Laboratory of ... Biosorption of Heavy Metals by Activated. Sludge and their Desorption Characteristics. J. Environ Mgt. 84: ...
Fractal model for estimating fracture toughness of carbon nanotube reinforced aluminum oxide
International Nuclear Information System (INIS)
Rishabh, Abhishek; Joshi, Milind R.; Balani, Kantesh
2010-01-01
The current work focuses on predicting the fracture toughness of Al 2 O 3 ceramic matrix composites using a modified Mandelbrot's fractal approach. The first step confirms that the experimental fracture toughness values fluctuate within the fracture toughness range predicted as per the modified fractal approach. Additionally, the secondary reinforcements [such as carbon nanotubes (CNTs)] have shown to enhance the fracture toughness of Al 2 O 3 . Conventional fractural toughness evaluation via fractal approach underestimates the fracture toughness by considering the shortest crack path. Hence, the modified Mandelbrot's fractal approach considers the crack propagation along the CNT semicircumferential surface (three-dimensional crack path propagation) for achieving an improved fracture toughness estimation of Al 2 O 3 -CNT composite. The estimations obtained in the current approach range within 4% error regime of the experimentally measured fracture toughness values of the Al 2 O 3 -CNT composite.
Fractal based modelling and analysis of electromyography (EMG) to identify subtle actions.
Arjunan, Sridhar P; Kumar, Dinesh K
2007-01-01
The paper reports the use of fractal theory and fractal dimension to study the non-linear properties of surface electromyogram (sEMG) and to use these properties to classify subtle hand actions. The paper reports identifying a new feature of the fractal dimension, the bias that has been found to be useful in modelling the muscle activity and of sEMG. Experimental results demonstrate that the feature set consisting of bias values and fractal dimension of the recordings is suitable for classification of sEMG against the different hand gestures. The scatter plots demonstrate the presence of simple relationships of these features against the four hand gestures. The results indicate that there is small inter-experimental variation but large inter-subject variation. This may be due to differences in the size and shape of muscles for different subjects. The possible applications of this research include use in developing prosthetic hands, controlling machines and computers.
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)...
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-05-01
In this work, Paper-based inkjet-printed Ultra-wide band (UWB) fractal antennas are presented. Three new designs, a combined UWB fractal monopole based on the fourth order Koch Snowflake fractal which utilizes a Sierpinski Gasket fractal for ink reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics. It is shown that fractals prove to be a successful method of reducing fabrication cost in inkjet printed antennas while retaining or enhancing printed antenna performance.
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.
Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.
2015-07-01
Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful
Transition in the fractal geometry of Arctic melt ponds
Directory of Open Access Journals (Sweden)
C. Hohenegger
2012-10-01
Full Text Available During the Arctic melt season, the sea ice surface undergoes a remarkable transformation from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is determined by the complex evolution of melt pond configurations. In fact, ice–albedo feedback has played a major role in the recent declines of the summer Arctic sea ice pack. However, understanding melt pond evolution remains a significant challenge to improving climate projections. By analyzing area–perimeter data from hundreds of thousands of melt ponds, we find here an unexpected separation of scales, where pond fractal dimension D transitions from 1 to 2 around a critical length scale of 100 m^{2} in area. Pond complexity increases rapidly through the transition as smaller ponds coalesce to form large connected regions, and reaches a maximum for ponds larger than 1000 m^{2}, whose boundaries resemble space-filling curves, with D ≈ 2. These universal features of Arctic melt pond evolution are similar to phase transitions in statistical physics. The results impact sea ice albedo, the transmitted radiation fields under melting sea ice, the heat balance of sea ice and the upper ocean, and biological productivity such as under ice phytoplankton blooms.
International Nuclear Information System (INIS)
Nagao, Michinobu; Murase, Kenya
2002-01-01
This review article describes a method for quantifying heterogeneous distribution on Technegas ( 99m Tc-carbon particle radioaerosol) SPECT images by three-dimensional fractal analysis (3D-FA). Technegas SPECT was performed to quantify the severity of pulmonary emphysema. We delineated the SPECT images by using five cut-offs (15, 20, 25, 30 and 35% of the maximal voxel radioactivity), and measured the total number of voxels in the areas surrounded by the contours obtained with each cut-off level. We calculated fractal dimensions from the relationship between the total number of voxels and the cut-off levels transformed into natural logarithms. The fractal dimension derived from 3D-FA is the relative and objective measurement, which can assess the heterogeneous distribution on Technegas SPECT images. The fractal dimension strongly correlate pulmonary function in patients with emphysema and well documented the overall and regional severity of emphysema. (author)
High-surface-area silica nanospheres (KCC-1) with a fibrous morphology
Polshettiwar, Vivek; Cha, Dong Kyu; Zhang, Xixiang; Basset, Jean-Marie
2010-01-01
Fibrous nanosilica: A new family of high-surface-area silica nanospheres (KCC-1) have been prepared (see picture). KCC-1 features excellent physical properties, including high surface area, unprecedented fibrous surface morphology, high thermal (up to 950 °C) and hydrothermal stabilities, and high mechanical stability. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
Determining eyeball surface area directly exposed to the effects of external factors.
Juliszewski, Tadeusz; Kadłuczka, Filip; Kiełbasa, Paweł
2016-01-01
This article discusses determining the surface area of eyeballs of men and women exposed to the direct effects of external factors in the working environment. For one eye, the mean surface is 172-182 mm(2). The determined surface area can be used in formulas for calculating the exposure of eyeballs to harmful chemical substances in workplace air.
30 CFR 942.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by act of Congress. 942.761 Section 942.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining...
30 CFR 903.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by act of Congress. 903.761 Section 903.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, applies to surface coal mining...
30 CFR 910.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by Act of Congress. 910.761 Section 910.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining...
30 CFR 937.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... mining by Act of Congress. 937.761 Section 937.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... WITHIN EACH STATE OREGON § 937.761 Areas designated unsuitable for surface coal mining by Act of Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining and...
30 CFR 921.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by Act of Congress. 921.761 Section 921.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining...
30 CFR 912.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... mining by act of Congress. 912.761 Section 912.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... WITHIN EACH STATE IDAHO § 912.761 Areas designated unsuitable for surface coal mining by act of Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining and...
30 CFR 947.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by act of Congress. 947.761 Section 947.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining...
30 CFR 939.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by Act of Congress. 939.761 Section 939.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining...
30 CFR 941.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by act of Congress. 941.761 Section 941.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining...
30 CFR 922.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by act of Congress. 922.761 Section 922.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining...
30 CFR 905.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by act of Congress. 905.761 Section 905.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated by Act of Congress, shall apply to surface coal mining...
High-surface-area silica nanospheres (KCC-1) with a fibrous morphology
Polshettiwar, Vivek
2010-08-02
Fibrous nanosilica: A new family of high-surface-area silica nanospheres (KCC-1) have been prepared (see picture). KCC-1 features excellent physical properties, including high surface area, unprecedented fibrous surface morphology, high thermal (up to 950 °C) and hydrothermal stabilities, and high mechanical stability. Copyright © 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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.
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-09-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.
Fractal Image Coding with Digital Watermarks
Directory of Open Access Journals (Sweden)
Z. Klenovicova
2000-12-01
Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.
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.
Undergraduate Experiment with Fractal Diffraction Gratings
Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.
2011-01-01
We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
Clausse, A.; Delmastro, D.F.
1990-01-01
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es
Restoration of eroded surfaces in Serbian ski-areas
Directory of Open Access Journals (Sweden)
Ristić Ratko
2009-01-01
Full Text Available The environmental impacts in Serbian ski areas are very strong, leading to landscape degradation and functionality losses. Construction or improvement works cause serious destruction of topsoil and native vegetation. Some activities enhance erosion production and sediment yield: clear cuttings; trunk transport down the slope; road construction and large excavations. Also, lack of erosion control works in ski areas, especially between April and October, result in various forms of land degradation such as furrows, gullies, landslides, or debris from rock weathering. The consequences of mismanagement in ski areas are noticeable in downstream sections of river beds, causing floods and bed-load deposition. Planning and designing activities, with the application of technical and biotechnical erosion control structures, through the concept of restoration, are necessary measures in the protection of ski areas.
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
Assessment of large aperture scintillometry for large-area surface ...
Indian Academy of Sciences (India)
29
1995), flat pastoral surfaces. (McAneny ... heat flux using net radiometer and soil heat flux plate, respectively and synchronized with ..... order to facilitates development of satellite based application for ET and drought monitoring, the .... daytime sensible heat flux and momentum fluxes;Boundary- Layer Meteorol.,68 357-373.
Surface albedo measurements in Mexico City metropolitan area
Energy Technology Data Exchange (ETDEWEB)
Castro, T; Mar, B; Longoria, R; Ruiz Suarez, L. G [Centro de Ciencias de la Atmosfera, UNAM, Mexico, D.F. (Mexico); Morales, L [Instituto de Geografia, UNAM, Mexico, D.F. (Mexico)
2001-04-01
Optical and thermal properties of soils are important input data for the meteorological and photochemical modules of air quality models. As development of these models increase on spatial resolution good albedo data become more important. In this paper measurements of surface albedo of UV (295-385 nm) and visible (450-550 nm) radiation are reported for different urban and rural surfaces in the vicinity of Mexico City. It was found for the downtown zone and average albedo value of 0.05 which is in very good agreement with reported values for urban surfaces. Our albedo values measured in UV region for grey cement and green grass are of 0.10 and 0.009, respectively, and quite similar to those found at the literature of 0.11 and 0.008 for those type of surfaces. [Spanish] Las propiedades opticas y termicas de suelos son datos importantes para los modulos meteorologicos y fotoquimicos de los modelos de calidad del aire. Conforme aumenta la resolucion espacial del modelo se vuelve mas importante contar con buenos datos de albedo. En este articulo se presentan mediciones de albedo superficial de radiacion Ultravioleta (295-385 nm) y visible (450-550 nm) para diferentes superficies urbanas. Los valores medidos de albedo en la region UV para cemento gris y pasto verde son de 0.10 y 0.009, respectivamente, y son muy similares a los reportados en la literatura, 0.11 y 0.008 para este tipo de superficies.
Large Area Diamond Tribological Surfaces with Negligible Wear in Extreme Environments, Phase I
National Aeronautics and Space Administration — In Phase I we propose to demonstrate the processing of very large area diamond sliding bearings and tribological surfaces. The bearings and surfaces will experience...
An extended fractal growth regime in the diffusion limited aggregation including edge diffusion
Directory of Open Access Journals (Sweden)
Aritra Ghosh
2016-01-01
Full Text Available We have investigated on-lattice diffusion limited aggregation (DLA involving edge diffusion and compared the results with the standard DLA model. For both cases, we observe the existence of a crossover from the fractal to the compact regime as a function of sticking coefficient. However, our modified DLA model including edge diffusion shows an extended fractal growth regime like an earlier theoretical result using realistic growth models and physical parameters [Zhang et al., Phys. Rev. Lett. 73 (1994 1829]. While the results of Zhang et al. showed the existence of the extended fractal growth regime only on triangular but not on square lattices, we find its existence on the square lattice. There is experimental evidence of this growth regime on a square lattice. The standard DLA model cannot characterize fractal morphology as the fractal dimension (Hausdorff dimension, DH is insensitive to morphology. It also predicts DH = DP (the perimeter dimension. For the usual fractal structures, observed in growth experiments on surfaces, the perimeter dimension can differ significantly (DH ≠ DP depending on the morphology. Our modified DLA model shows minor sensitivity to this difference.
Possibilities of surface waters monitoring at mining areas using UAV
Lisiecka, Ewa; Motyka, Barbara; Motyka, Zbigniew; Pierzchała, Łukasz; Szade, Adam
2018-04-01
The selected, remote measurement methods are discussed, useful for determining surface water properties using mobile unmanned aerial platforms (UAV). The possibilities of using this type of solutions in the scope of measuring spatial, physicochemical and biological parameters of both natural and anthropogenic water reservoirs, including flood polders, water-filled pits, settling tanks and mining sinks were analyzed. Methods of remote identification of the process of overgrowing this type of ecosystems with water and coastal plant formations have also been proposed.
Estimating the surface area of birds: using the homing pigeon (Columba livia) as a model.
Perez, Cristina R; Moye, John K; Pritsos, Chris A
2014-05-08
Estimation of the surface area of the avian body is valuable for thermoregulation and metabolism studies as well as for assessing exposure to oil and other surface-active organic pollutants from a spill. The use of frozen carcasses for surface area estimations prevents the ability to modify the posture of the bird. The surface area of six live homing pigeons in the fully extended flight position was estimated using a noninvasive method. An equation was derived to estimate the total surface area of a pigeon based on its body weight. A pigeon's surface area in the fully extended flight position is approximately 4 times larger than the surface area of a pigeon in the perching position. The surface area of a bird is dependent on its physical position, and, therefore, the fully extended flight position exhibits the maximum area of a bird and should be considered the true surface area of a bird. © 2014. Published by The Company of Biologists Ltd | Biology Open.
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.
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…
Orlando, José Ignacio; van Keer, Karel; Barbosa Breda, João; Manterola, Hugo Luis; Blaschko, Matthew B; Clausse, Alejandro
2017-12-01
Diabetic retinopathy (DR) is one of the most widespread causes of preventable blindness in the world. The most dangerous stage of this condition is proliferative DR (PDR), in which the risk of vision loss is high and treatments are less effective. Fractal features of the retinal vasculature have been previously explored as potential biomarkers of DR, yet the current literature is inconclusive with respect to their correlation with PDR. In this study, we experimentally assess their discrimination ability to recognize PDR cases. A statistical analysis of the viability of using three reference fractal characterization schemes - namely box, information, and correlation dimensions - to identify patients with PDR is presented. These descriptors are also evaluated as input features for training ℓ1 and ℓ2 regularized logistic regression classifiers, to estimate their performance. Our results on MESSIDOR, a public dataset of 1200 fundus photographs, indicate that patients with PDR are more likely to exhibit a higher fractal dimension than healthy subjects or patients with mild levels of DR (P≤1.3×10-2). Moreover, a supervised classifier trained with both fractal measurements and red lesion-based features reports an area under the ROC curve of 0.93 for PDR screening and 0.96 for detecting patients with optic disc neovascularizations. The fractal dimension of the vasculature increases with the level of DR. Furthermore, PDR screening using multiscale fractal measurements is more feasible than using their derived fractal dimensions. Code and further resources are provided at https://github.com/ignaciorlando/fundus-fractal-analysis. © 2017 American Association of Physicists in Medicine.
Tritium in Precipitation, Surface and Groundwaters in the Zagreb Area
International Nuclear Information System (INIS)
Horvatincic, N.; Baresic, J.; Sironic, A.; Krajcar Bronic, I.; Obelic, B.
2011-01-01
Radioactive isotope tritium (3H) and stable isotopes of hydrogen (2H/1H) and oxygen (18O/16O) were measured in Sava River, precipitation and groundwater at 3 monitoring wells (piezometers) and 1 production well of the Petrusevec aquifer, close to the Sava River. Samples were collected monthly during 2010. The investigation is included in the Regional IAEA Project RER/8/016 Using Environmental Isotopes for Evaluation of Streamwater/Groundwater Interactions in Selected Aquifers in the Danube Basin. Sava River is a tributary of Danube River and the aim of the investigation is to determine the influence of surface stream of Sava River to the groundwater of aquifer used for water exploitation. In this work only 3H results were presented. 3H was measured by liquid scintillation counter Quantulus 1220, using electrolytic enrichment for all samples. 3H activity in precipitation showed slight seasonal fluctuation between 4 TU and 14 TU, with higher values in summer. 3H activity of Sava River and groundwater of the Petrusevec aquifer followed 3H of precipitation till May 2010. Significant increase of 3H in Sava River was observed in June, (199 @ 20) TU, and in the next month it fell down at 6 TU. Increase of 3H was also observed in groundwater but with damped response (maximum 60 TU) and with delay of 2 - 3 months related to Sava River. Different response of different piezometers and the well indicated the different infiltration times of surface water of Sava River to groundwater of the Petrusevec aquifer. The increased 3H activity in surface and groundwaters was caused by release of tritiated water from the Krsko Nuclear Power Plant, 30 km upstream from Zagreb. The results of 3H, 2H/1H and 18O/16O measurements will be used to determine the infiltration time of groundwater of the Petrusevec aquifer using conceptual and mathematical models. (author)
Possibilities of surface waters monitoring at mining areas using UAV
Directory of Open Access Journals (Sweden)
Lisiecka Ewa
2018-01-01
Full Text Available The selected, remote measurement methods are discussed, useful for determining surface water properties using mobile unmanned aerial platforms (UAV. The possibilities of using this type of solutions in the scope of measuring spatial, physicochemical and biological parameters of both natural and anthropogenic water reservoirs, including flood polders, water-filled pits, settling tanks and mining sinks were analyzed. Methods of remote identification of the process of overgrowing this type of ecosystems with water and coastal plant formations have also been proposed.
Effect of solution and leaf surface polarity on droplet spread area and contact angle.
Nairn, Justin J; Forster, W Alison; van Leeuwen, Rebecca M
2016-03-01
How much an agrochemical spray droplet spreads on a leaf surface can significantly influence efficacy. This study investigates the effect solution polarity has on droplet spreading on leaf surfaces and whether the relative leaf surface polarity, as quantified using the wetting tension dielectric (WTD) technique, influences the final spread area. Contact angles and spread areas were measured using four probe solutions on 17 species. Probe solution polarity was found to affect the measured spread area and the contact angle of the droplets on non-hairy leaves. Leaf hairs skewed the spread area measurement, preventing investigation of the influence of surface polarity on hairy leaves. WTD-measured leaf surface polarity of non-hairy leaves was found to correlate strongly with the effect of solution polarity on spread area. For non-polar leaf surfaces the spread area decreases with increasing solution polarity, for neutral surfaces polarity has no effect on spread area and for polar leaf surfaces the spread area increases with increasing solution polarity. These results attest to the use of the WTD technique as a means to quantify leaf surface polarity. © 2015 Society of Chemical Industry. © 2015 Society of Chemical Industry.
International Nuclear Information System (INIS)
Lu Yong; Song, Paul Y.; Li Shidong; Spelbring, Danny R.; Vijayakumar, Srinivasan; Haraf, Daniel J.; Chen, George T.Y.
1995-01-01
Purpose: To develop a method of analyzing rectal surface area irradiated and rectal complications in prostate conformal radiotherapy. Methods and Materials: Dose-surface histograms of the rectum, which state the rectal surface area irradiated to any given dose, were calculated for a group of 27 patients treated with a four-field box technique to a total (tumor minimum) dose ranging from 68 to 70 Gy. Occurrences of rectal toxicities as defined by the Radiation Therapy Oncology Group (RTOG) were recorded and examined in terms of dose and rectal surface area irradiated. For a specified end point of rectal complication, the complication probability was analyzed as a function of dose irradiated to a fixed rectal area, and as a function of area receiving a fixed dose. Lyman's model of normal tissue complication probability (NTCP) was used to fit the data. Results: The observed occurrences of rectal complications appear to depend on the rectal surface area irradiated to a given dose level. The patient distribution of each toxicity grade exhibits a maximum as a function of percentage surface area irradiated, and the maximum moves to higher values of percentage surface area as the toxicity grade increases. The dependence of the NTCP for the specified end point on dose and percentage surface area irradiated was fitted to Lyman's NTCP model with a set of parameters. The curvature of the NTCP as a function of the surface area suggests that the rectum is a parallel structured organ. Conclusions: The described method of analyzing rectal surface area irradiated yields interesting insight into understanding rectal complications in prostate conformal radiotherapy. Application of the method to a larger patient data set has the potential to facilitate the construction of a full dose-surface-complication relationship, which would be most useful in guiding clinical practice
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.
Classification of radar echoes using fractal geometry
International Nuclear Information System (INIS)
Azzaz, Nafissa; Haddad, Boualem
2017-01-01
Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.
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.
Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael
2016-02-01
One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.
Large area optical mapping of surface contact angle.
Dutra, Guilherme; Canning, John; Padden, Whayne; Martelli, Cicero; Dligatch, Svetlana
2017-09-04
Top-down contact angle measurements have been validated and confirmed to be as good if not more reliable than side-based measurements. A range of samples, including industrially relevant materials for roofing and printing, has been compared. Using the top-down approach, mapping in both 1-D and 2-D has been demonstrated. The method was applied to study the change in contact angle as a function of change in silver (Ag) nanoparticle size controlled by thermal evaporation. Large area mapping reveals good uniformity for commercial Aspen paper coated with black laser printer ink. A demonstration of the forensic and chemical analysis potential in 2-D is shown by uncovering the hidden CsF initials made with mineral oil on the coated Aspen paper. The method promises to revolutionize nanoscale characterization and industrial monitoring as well as chemical analyses by allowing rapid contact angle measurements over large areas or large numbers of samples in ways and times that have not been possible before.
Fractality and growth of He bubbles in metals
Kajita, Shin; Ito, Atsushi M.; Ohno, Noriyasu
2017-08-01
Pinholes are formed on surfaces of metals by the exposure to helium plasmas, and they are regarded as the initial process of the growth of fuzzy nanostructures. In this study, number density of the pinholes is investigated in detail from the scanning electron microscope (SEM) micrographs of tungsten and tantalum exposed to the helium plasmas. A power law relation was identified between the number density and the size of pinholes. From the slope and the region where the power law was satisfied, the fractal dimension D and smin, which characterize the SEM images, are deduced. Parametric dependences and material dependence of D and smin are revealed. To explain the fractality, simple Monte-Carlo simulations including random walks of He atoms and absorption on bubble was introduced. It is shown that the initial position of the random walk is one of the key factors to deduce the fractality. The results indicated that new nucleations of bubbles are necessary to reproduce the number-density distribution of bubbles.
Federal Geographic Data Committee — The SMA implementation is comprised of one feature dataset, with several polygon feature classes, rather than a single feature class. SurfaceManagementAgency: The...
Undergraduate experiment with fractal diffraction gratings
International Nuclear Information System (INIS)
Monsoriu, Juan A; Furlan, Walter D; Pons, Amparo; Barreiro, Juan C; Gimenez, Marcos H
2011-01-01
We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics laboratories and compared with those obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. Good agreement is obtained between experimental and numerical results.
Surface and subsurface conditions in permafrost areas - a literature review
International Nuclear Information System (INIS)
Vidstrand, Patrik
2003-02-01
This report contains a summary of some of the information within existing technical and scientific literature on permafrost. Permafrost is viewed as one of the future climate driven process domains that may exist in Scandinavia, and that may give rise to significantly different surface and subsurface conditions than the present. Except for changes in the biosphere, permafrost may impact hydraulic, mechanical, and chemical subsurface processes and conditions. Permafrost and its influences on the subsurface conditions are thus of interest for the performance and safety assessments of deep geological waste repositories. The definition of permafrost is 'ground that stays at or below 0 deg C for at least two consecutive years'. Permafrost will effect the geological subsurface to some depth. How deep the permafrost may grow is a function of the heat balance, thermal conditions at the surface and within the ground, and the geothermal heat flux from the Earth's inner parts. The main chapters of the report summaries the knowledge on permafrost evolution, occurrence and distribution, and extracts information concerning hydrology and mechanical and chemical impacts due to permafrost related conditions. The results of a literature review are always dependent on the available literature. Concerning permafrost there is some literature available from investigations in the field of long-term repositories and some from mining industries. However, reports of these investigations are few and the bulk of permafrost literature comes from the science departments concerned with surficial processes (e.g. geomorphology, hydrology, agriculture, etc) and from engineering concerns, such as foundation of constructions and pipeline design. This focus within the permafrost research inevitably yields a biased but also an abundant amount of information on localised surficial processes and a limited amount on regional and deep permafrost characteristics. Possible conclusions are that there is
Surface and subsurface conditions in permafrost areas - a literature review
Energy Technology Data Exchange (ETDEWEB)
Vidstrand, Patrik [Bergab, Goeteborg (Sweden)
2003-02-01
This report contains a summary of some of the information within existing technical and scientific literature on permafrost. Permafrost is viewed as one of the future climate driven process domains that may exist in Scandinavia, and that may give rise to significantly different surface and subsurface conditions than the present. Except for changes in the biosphere, permafrost may impact hydraulic, mechanical, and chemical subsurface processes and conditions. Permafrost and its influences on the subsurface conditions are thus of interest for the performance and safety assessments of deep geological waste repositories. The definition of permafrost is 'ground that stays at or below 0 deg C for at least two consecutive years'. Permafrost will effect the geological subsurface to some depth. How deep the permafrost may grow is a function of the heat balance, thermal conditions at the surface and within the ground, and the geothermal heat flux from the Earth's inner parts. The main chapters of the report summaries the knowledge on permafrost evolution, occurrence and distribution, and extracts information concerning hydrology and mechanical and chemical impacts due to permafrost related conditions. The results of a literature review are always dependent on the available literature. Concerning permafrost there is some literature available from investigations in the field of long-term repositories and some from mining industries. However, reports of these investigations are few and the bulk of permafrost literature comes from the science departments concerned with surficial processes (e.g. geomorphology, hydrology, agriculture, etc) and from engineering concerns, such as foundation of constructions and pipeline design. This focus within the permafrost research inevitably yields a biased but also an abundant amount of information on localised surficial processes and a limited amount on regional and deep permafrost characteristics. Possible conclusions are that
30 CFR 933.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal mining by Act of Congress. 933.761 Section 933.761 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION... Congress. Part 761 of this chapter, Areas Designated Unsuitable for Coal Mining by Act of Congress, with...
Surface area of antimony oxide by isotope exchange and other methods
Energy Technology Data Exchange (ETDEWEB)
Rao, Y.K.; Acharya, B.V.; Rangamannar, B.
1985-06-17
Specific surface areas of antimony oxide samples, one commercial, the other prepared from antimony trichloride were measured by heterogeneous isotope exchange, gas adsorption, air permeability and microscopic methods. Specific surface areas obtained by these four methods for the two samples were compared and the observed differences are explained.
Fractal morphology in lignite coal: a small angle x-ray scattering investigation
International Nuclear Information System (INIS)
Chitra, R.; Sen, D.; Mazumder, S.; Chandrasekaran, K.S.
1999-01-01
Small angle x-ray scattering technique has been used to study the pore morphology in lignite coal from Neyveli lignite mine (Tamilnadu, India). The sample were collected from three different locations of the same mine. SAXS profiles from all the three samples show almost identical functionality, irrespective of the locations from where the samples were collected. SAXS experiment using two different wavelengths also exhibit same functionality indicating the absence of multiple scattering. The analysis indicates the surface fractal nature of the pore morphology. The surface fractal dimension is calculated to be 2.58. (author)
The protection of urban areas from surface wastewater pollutions
Directory of Open Access Journals (Sweden)
Vialkova Elena
2017-01-01
Full Text Available In this paper it considered the problem of collection, treatment and discharge into waters of rain and melted wastewater. To reduce the load on the combined sewer system, there are engineering solutions collect rain and melt water for use in the irrigation of lawns and green spaces. Research carried out at the department “Water supply and sanitation”, (Russia, confirm the high pollution concentrations of meltwater and rainfall in urban arias. Series of measurements of heavy metal in rainwater runoff carried out in Hungary demonstrates clearly the differences in concentrations in the function of distance from the edge of the road. Also differences are introduced between pollution concentrations in runoff water from within and outside urban traffic roads. The quality of snow cover, forming meltwater is observed to be changing in dependence on roadway location. Quality characteristics of surface runoff and its sediments can be effectively improved with super-high frequency radiation (SHF treatment which is presented in this paper.
High surface area silicon materials: fundamentals and new technology.
Buriak, Jillian M
2006-01-15
Crystalline silicon forms the basis of just about all computing technologies on the planet, in the form of microelectronics. An enormous amount of research infrastructure and knowledge has been developed over the past half-century to construct complex functional microelectronic structures in silicon. As a result, it is highly probable that silicon will remain central to computing and related technologies as a platform for integration of, for instance, molecular electronics, sensing elements and micro- and nanoelectromechanical systems. Porous nanocrystalline silicon is a fascinating variant of the same single crystal silicon wafers used to make computer chips. Its synthesis, a straightforward electrochemical, chemical or photochemical etch, is compatible with existing silicon-based fabrication techniques. Porous silicon literally adds an entirely new dimension to the realm of silicon-based technologies as it has a complex, three-dimensional architecture made up of silicon nanoparticles, nanowires, and channel structures. The intrinsic material is photoluminescent at room temperature in the visible region due to quantum confinement effects, and thus provides an optical element to electronic applications. Our group has been developing new organic surface reactions on porous and nanocrystalline silicon to tailor it for a myriad of applications, including molecular electronics and sensing. Integration of organic and biological molecules with porous silicon is critical to harness the properties of this material. The construction and use of complex, hierarchical molecular synthetic strategies on porous silicon will be described.
Directory of Open Access Journals (Sweden)
María Eugenia Torres
2007-01-01
Full Text Available En este trabajo comparamos tres métodos diferentes utilizados para estimar el exponente de Hurst, y analizamos su eficiencia cuando son aplicados a series de datos de diferentes longitudes. Se analizan series temporales de fBm sintetizada pura y con tendencias sinusoidales superpuestas. Mostraremos que los tres métodos aquí discutidos, DFA, basado en wavelets y de variaciones discretas, no sólo son altamente dependientes de la longitud de la señal, sino también del orden o número de los momentos (polinómico, regularidad wavelet o variaciones discretas. Para longitudes de datos suficientemente grandes (superiores a 212, los métodos basados en wavelets y de variaciones discretas mostraron ser menos sesgados y más estables para señales fBm simuladas. Mostraremos que el método de DFA, más utilizado en el ambiente biomédico, es el que proporciona peores estimaciones, arrojando resultados ambiguos cuando son aplicados a señales biológicas de diferentes longitudes o con diferentes parámetros de estimación, sin que pueda considerarse a ninguno de los otros dos como métodos confiables en el momento de desear obtener resultados de relevancia física o fisiológica. Los resultados obtenidos indican que debería procederse con más cautela cuando se trata de obtener conclusiones fisiológicas a partir de estimaciones realizadas a partir de señales reales.
Measurement of the specific surface area of loose copper deposit by electrochemical methods
Directory of Open Access Journals (Sweden)
E. A. Dolmatova
2016-07-01
Full Text Available In the work the surface area of the electrode with dispersed copper deposit obtained within 30 seconds was evaluated by techniques of chronopotentiometry (CPM and impedance spectroscopy. In method CPM the electrode surface available for measurement depends on the value of the polarizing current. At high currents during the transition time there is a change of surface relief that can not determine the full surface of loose deposit. The electrochemical impedance method is devoid of this shortcoming since the measurements are carried out in indifferent electrolyte in the absence of current. The area measured by the impedance is tens of times higher than the value obtained by chronopotentiometry. It is found that from a solution containing sulfuric acid the deposits form with a high specific surface area. Based on these data it was concluded that the method of impedance spectroscopy can be used to measure in situ the surface area of the dispersed copper deposits.
A fractal analysis of protein to DNA binding kinetics using biosensors.
Sadana, Ajit
2003-08-01
A fractal analysis of a confirmative nature only is presented for the binding of estrogen receptor (ER) in solution to its corresponding DNA (estrogen response element, ERE) immobilized on a sensor chip surface [J. Biol. Chem. 272 (1997) 11384], and for the cooperative binding of human 1,25-dihydroxyvitamin D(3) receptor (VDR) to DNA with the 9-cis-retinoic acid receptor (RXR) [Biochemistry 35 (1996) 3309]. Ligands were also used to modulate the first reaction. Data taken from the literature may be modeled by using a single- or a dual-fractal analysis. Relationships are presented for the binding rate coefficient as a function of either the analyte concentration in solution or the fractal dimension that exists on the biosensor surface. The binding rate expressions developed exhibit a wide range of dependence on the degree of heterogeneity that exists on the surface, ranging from sensitive (order of dependence equal to 1.202) to very sensitive (order of dependence equal to 12.239). In general, the binding rate coefficient increases as the degree of heterogeneity or the fractal dimension of the surface increases. The predictive relationships presented provide further physical insights into the reactions occurring on the biosensor surface. Even though these reactions are occurring on the biosensor surface, the relationships presented should assist in understanding and in possibly manipulating the reactions occurring on cellular surfaces.
Size and surface AREA analysis of some metallic and intermetallic powders
International Nuclear Information System (INIS)
Elmasry, M.A.A.; Elsayed, A.A.; Abadir, M.F.
1988-01-01
The powder characterization of three intermetallic compounds ( Cr B, B 4 c and S ib 4 ) and three metallic powders (Fe, Co, and Ni) has been performed. This included the determination of powder density, chemical analysis, impurity analysis, shape factor, particle size analysis and specific surface area. The particle size analysis for the six powders was carried out using three techniques, namely; the 0-23, the microtrac and the fisher sub sieve and size. It was found that the analysis of the two powders and deviates from the log-normal probability distribution and the deviation was corrected. The specific surface area of the powders was measured using the high speed surface area analysis (BET method), and it was also calculated from surface area analysis findings, the BET technique was found to give the highest specific surface area values, and was attributed to the inclusion of internal porosity in the measurement. 8 fig., 10 tab
Surface and groundwater Nitrate distribution in the area of Vicenza
International Nuclear Information System (INIS)
Altissimo, L.; Dal Pra, A.
1999-01-01
Public aqueducts in the Province of Vicenza (Italy) are supplied entirely by various kinds of water sources: the sub river bed strata of the mountain valleys, water-bearing aquifers of the high plan, pressurized water-bearing aquifers of the middle plain, karstic reservoirs of the mountain massifs and local springs. Progressive increase in nitrate concentration has long been detected in the underground water of many parts of the Vicenza region. The nitrates originate from various sources: human waste, industrial dumping (e.g. the tanning industry) and the use of animal and chemical fertilizers. Nitrate distribution was studied in all wells used for extracting underground water including source waters which replenishing underground aquifers. During the study period ('91-'95), water courses in the recharge areas were found to have nitrate concentrations ranging between 2.0 and 42.0 mg/l. These values remained substantially stable in time. Underground aquifers showed stable nitrate concentration between 5.0 mg/l (mountain karstic aquifers; sub-river bed strata of valley bottom) and 44.0 mg/l (water bearing strata of the high plain of Astico and Brenta rivers). The pressurized flooding aquifers of the middle plain have lower concentrations (6.0-21.0 mg/l) but tend to increase by about 0.5 mg/l per year [it
Fractal behaviour of the seismicity in the Southern Iberian Peninsula
Directory of Open Access Journals (Sweden)
X. Lana
2005-01-01
Full Text Available The fractal behaviour of the seismicity in the Southern Iberian Peninsula is analysed by considering two different series of data: the distance and the elapsed time between consecutive seismic events recorded by the seismic network of the Andalusian Institute of Geophysics (AIG. The fractal analyses have been repeated by considering four threshold magnitudes of 2.5, 3.0, 3.5 and 4.0. The re-scaled analysis lets to determine if the seismicity shows strong randomness or if it is characterised by time-persistence and the cluster dimension indicates the degree of time and spatial clustering of the seismicity. Another analysis, based on the reconstruction theorem, permits to evaluate the minimum number of nonlinear equations describing the dynamical mechanism of the seismicity, its 'loss of memory', its chaotic character and the instability of a possible predicting algorithm. The results obtained depict some differences depending on distances or elapsed times and the different threshold levels of magnitude also lead to slightly different results. Additionally, only a part of the fractal tools, the re-scaled analysis, have been applied to five seismic crises in the same area.
Feature extraction algorithm for space targets based on fractal theory
Tian, Balin; Yuan, Jianping; Yue, Xiaokui; Ning, Xin
2007-11-01
In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.
Fractal analysis of urban environment: land use and sewer system
Gires, A.; Ochoa Rodriguez, S.; Van Assel, J.; Bruni, G.; Murla Tulys, D.; Wang, L.; Pina, R.; Richard, J.; Ichiba, A.; Willems, P.; Tchiguirinskaia, I.; ten Veldhuis, M. C.; Schertzer, D. J. M.
2014-12-01
Land use distribution are usually obtained by automatic processing of satellite and airborne pictures. The complexity of the obtained patterns which are furthermore scale dependent is enhanced in urban environment. This scale dependency is even more visible in a rasterized representation where only a unique class is affected to each pixel. A parameter commonly analysed in urban hydrology is the coefficient of imperviousness, which reflects the proportion of rainfall that will be immediately active in the catchment response. This coefficient is strongly scale dependent with a rasterized representation. This complex behaviour is well grasped with the help of the scale invariant notion of fractal dimension which enables to quantify the space occupied by a geometrical set (here the impervious areas) not only at a single scale but across all scales. This fractal dimension is also compared to the ones computed on the representation of the catchments with the help of operational semi-distributed models. Fractal dimensions of the corresponding sewer systems are also computed and compared with values found in the literature for natural river networks. This methodology is tested on 7 pilot sites of the European NWE Interreg IV RainGain project located in France, Belgium, Netherlands, United-Kingdom and Portugal. Results are compared between all the case study which exhibit different physical features (slope, level of urbanisation, population density...).
Long-term studies on the effects of nonvolatile organic compounds on porous media surface areas.
Khachikian, Crist S; Harmon, Thomas C
2002-01-01
This paper investigates the long-term behavior of porous media contaminated by nonvolatile organic compounds (NVOC) in terms of specific interfacial surface area. Specifically, a natural sand, Moffett sand (MS), was contaminated with naphthalene and the surface area was measured repeatedly over time using nitrogen adsorption-desorption techniques. A field-contaminated sand affected by lamp-black material (LB) from former manufactured gas plant operations was also studied. Lampblack is a carbonaceous skeleton containing polycyclic aromatic hydrocarbons (PAHs) and other hydrocarbons. It is hypothesized that soils contaminated by these types of chemicals will exhibit significantly less surface area than their clean counterparts. The surface areas for the contaminated MS samples increased toward their clean-MS values during the 700-h aging period, but achieved the clean values only after pentane extraction or heating at 60 degrees C. Heating at 50 degrees C failed to achieve a similar recovery of the clean-MS surface area value. Nonspecific mass loss tracked the increase in surface area as indirect evidence that naphthalene loss was the cause of the surface area increase. For the LB samples, aging at 100 degrees C produced a slight decrease in surface area and mass while aging at 250 degrees C caused the surface area to increase roughly threefold while the mass decreased by approximately 1%. These results suggest that, under moderate heating and over the time scale of this investigation, there is a redistribution of the complex contaminant mixture on the solid matrix. Greater temperatures remove mass more efficiently and therefore exhibited the surface area increase expected in this experiment.
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
Surface Area, and Oxidation Effects on Nitridation Kinetics of Silicon Powder Compacts
Bhatt, R. T.; Palczer, A. R.
1998-01-01
Commercially available silicon powders were wet-attrition-milled from 2 to 48 hr to achieve surface areas (SA's) ranging from 1.3 to 70 sq m/g. The surface area effects on the nitridation kinetics of silicon powder compacts were determined at 1250 or 1350 C for 4 hr. In addition, the influence of nitridation environment, and preoxidation on nitridation kinetics of a silicon powder of high surface area (approximately equals 63 sq m/g) was investigated. As the surface area increased, so did the percentage nitridation after 4 hr in N2 at 1250 or 1350 C. Silicon powders of high surface area (greater than 40 sq m/g) can be nitrided to greater than 70% at 1250 C in 4 hr. The nitridation kinetics of the high-surface-area powder compacts were significantly delayed by preoxidation treatment. Conversely, the nitridation environment had no significant influence on the nitridation kinetics of the same powder. Impurities present in the starting powder, and those accumulated during attrition milling, appeared to react with the silica layer on the surface of silicon particles to form a molten silicate layer, which provided a path for rapid diffusion of nitrogen and enhanced the nitridation kinetics of high surface area silicon powder.
Environmental and geochemical assessment of surface sediments on irshansk ilmenite deposit area
Directory of Open Access Journals (Sweden)
Наталия Олеговна Крюченко
2015-03-01
Full Text Available It is revealed the problem of pollution of surface sediments of Irshansk ilmenite deposit area of various chemical elements hazard class (Mn, V, Ba, Ni, Co, Cr, Mo, Cu, Pb, Zn. It is determined its average content in surface sediments of various functional areas (forest and agricultural land, flood deposits, reclaimed land, calculated geochemical criteria, so given ecological and geochemical assessment of area
Matias,Sammy S. R.; Marques Júnior,José; Siqueira,Diego S.; Pereira,Gener T.
2014-01-01
There is an increasing demand for detailed maps that represent in a simplified way the knowledge of the variability of a particular area or region maps. The objective was to outline precision boundaries among areas with different accuracy variability standards using magnetic susceptibility and geomorphic surfaces. The study was conducted in an area of 110 ha, which identified three compartment landscapes based on the geomorphic surfaces model. To determinate pH, organic matter, phosphorus, po...
Inspecting plastic deformation of Pd by means of fractal geometry
International Nuclear Information System (INIS)
Eftekhari, Ali
2007-01-01
The influence of phase transformation-induced plastic deformation in Pd|H system on the electrode surface was investigated. Since the Pd surface is subject of severe plastic deformation during this process, the structure and roughness of the electrode surface significantly change. Quantitative analysis of the electrode surfaces for comparative study of such changes is a valuable tool to inspect the plastic deformation induced. Fractal dimension can be used as a quantitative measure for this purpose. Since inappropriate methods may lead to significant errors, an appropriate approach was proposed for the determination of fractal dimensions in such systems. It was demonstrated that the surface roughness generated is mainly due to the plastic deformation induced, not the other side processes, as the electrodes were coated with a uniform layer of gold with thickness smaller than 10 nm. Since plastic deformation is due to hydrogen insertion/extraction and occurs in atomic-scale, it is necessary to divide structural changes appeared in nano- and micro-scale
Model of fractal aggregates induced by shear
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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.
A Parallel Approach to Fractal Image Compression
Lubomir Dedera
2004-01-01
The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
Random walks of oriented particles on fractals
International Nuclear Information System (INIS)
Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko
2014-01-01
Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features. (paper)
Changes in the Surface Area of Glaciers in Northern Eurasia
Khromova, T.; Nosenko, G.
2012-12-01
Glaciers are widely recognized as key indicators of climate change. Recent evidence suggests an acceleration of glacier mass loss in several key mountain regions. Glacier recession implies the landscape changes in the glacial zone, origin of new lakes and activation of natural disaster processes, catastrophic mudflows, ice avalanches, outburst floods, and etc. The presence of glaciers in itself threats to human life, economic activity and growing infrastructure. Economical and recreational human activity in mountain regions requires relevant information on snow and ice objects. Absence or inadequacy of such information results in financial and human losses. A more comprehensive evaluation of glacier changes is imperative to assess ice contributions to global sea level rise and the future of water resources from glacial basins. One of the urgent steps is a full inventory of all ice bodies, their volume and changes The first estimation of glaciers state and glaciers distribution in the big part of Northern Eurasia has been done in the USSR Glacier Inventory published in 1966 -1980 as a part of IHD activity. The Inventory is based on topographic maps and air photos and reflects the status of the glaciers in 1957-1970y. There is information about 23796 glaciers with area of 78222.3 km2 in the Inventory. It covers 23 glacier systems on Northern Eurasia. In the 80th the USSR Glacier Inventory has been transformed in the digital form as a part of the World Glacier Inventory. Recent satellite data provide a unique opportunity to look again at these glaciers and to evaluate changes in glacier extent for the second part of XX century. In the paper we report about 15 000 glaciers outlines for Caucasus, Pamir, Tien-Shan, Altai, Syntar-Khayata, Cherskogo Range, Kamchatka and Russian Arctic which have been derived from ASTER and Landsat imagery and could be used for glacier changes evaluation. The results show that glaciers are retreating in all these regions. There is, however
Designing a fractal antenna of 2400 MHz
International Nuclear Information System (INIS)
Miranda Hamburger, Fabio
2012-01-01
The design of a fractal antenna with 2400 MHz of frequency has been studied. The fractal used is described by Waclaw Spierpi.ski. The initial figure, also known as seed, is divided using equilateral triangles with the aim of obtaining a perimeter similar to a meaningful portion of wave length. The use of λ to establish an ideal perimeter has reduced the radiation resistance. The adequate number of iterations needed to design the antenna is calculated based on λ. (author) [es
Fractal effects on excitations in diluted ferromagnets
International Nuclear Information System (INIS)
Kumar, D.
1981-08-01
The low energy spin-wave like excitations in diluted ferromagnets near percolation threshold are studied. For this purpose an explicit use of the fractal model for the backbone of the infinite percolating cluster due to Kirkpatrick is made. Three physical effects are identified, which cause the softening of spin-waves as the percolation point is approached. The importance of fractal effects in the calculation of density of states and the low temperature thermodynamics is pointed out. (author)
A fractal-like resistive network
International Nuclear Information System (INIS)
Saggese, A; De Luca, R
2014-01-01
The equivalent resistance of a fractal-like network is calculated by means of approaches similar to those employed in defining the equivalent resistance of an infinite ladder. Starting from an elementary triangular circuit, a fractal-like network, named after Saggese, is developed. The equivalent resistance of finite approximations of this network is measured, and the didactical implications of the model are highlighted. (paper)
Heat kernels and zeta functions on fractals
International Nuclear Information System (INIS)
Dunne, Gerald V
2012-01-01
On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
Development of cortical thickness and surface area in autism spectrum disorder
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Vincent T. Mensen
2017-01-01
Full Text Available Autism spectrum disorder (ASD is a neurodevelopmental disorder often associated with changes in cortical volume. The constituents of cortical volume – cortical thickness and surface area – have separable developmental trajectories and are related to different neurobiological processes. However, little is known about the developmental trajectories of cortical thickness and surface area in ASD. In this magnetic resonance imaging (MRI study, we used an accelerated longitudinal design to investigate the cortical development in 90 individuals with ASD and 90 typically developing controls, aged 9 to 20 years. We quantified cortical measures using the FreeSurfer software package, and then used linear mixed model analyses to estimate the developmental trajectories for each cortical measure. Our primary finding was that the development of surface area follows a linear trajectory in ASD that differs from typically developing controls. In typical development, we found a decline in cortical surface area between the ages of 9 and 20 that was absent in ASD. We found this pattern in all regions where developmental trajectories for surface area differed between groups. When we applied a more stringent correction that takes the interdependency of measures into account, this effect on cortical surface area retained significance for left banks of superior temporal sulcus, postcentral area, and right supramarginal area. These areas have previously been implicated in ASD and are involved in the interpretation and processing of audiovisual social stimuli and distinction between self and others. Although some differences in cortical volume and thickness were found, none survived the more stringent correction for multiple testing. This study underscores the importance of distinguishing between cortical surface area and thickness in investigating cortical development, and suggests the development of cortical surface area is of importance to ASD.
Root surface area measurement of permanent dentition in Indian population – CBCT analysis
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Kanika Lakhani
2017-01-01
Full Text Available The area of the root surface of human teeth has been investigated extensively in the dental literature. All previous attempts mainly rely on the use of physical methods to calculate surface area on extracted teeth or use virtual 3D Models for the same. The aim is to develop an algorithm using MATLAB software that estimates the dimensions of 3-D image produced with the help of CBCT so that the same can be utilized to calculate the root surface area of teeth among Indian population. Present research utilizes CBCT images of samples of extracted teeth mounted on a customized jpg. A descriptive chart for statistical analysis has been prepared to obtain average root surface area of each tooth type. The currently developed algorithm has been successfully applied to the CBCT images of complete sample of teeth to obtain their root surface area. The algorithm developed to calculate root surface area of the teeth holds wide spread application in the field of dentistry pursuing its high expediency in even various specializations of dentistry including orthodontics, prosthodontics, periodontology and implantalogy. It is concluded that it has now become a reality to accurately determine the surface area of the root of human teeth without extracting them using the CBCT radiographs of the patients.
International Nuclear Information System (INIS)
Xiao, Boqi; Fan, Jintu; Ding, Feng
2014-01-01
The study of water and gas transport through fibrous gas diffusion layer (GDL) is important to the optimization of proton exchange membrane fuel cells (PEMFCs). In this work, analytical models of dimensionless permeability, and water and gas relative permeabilities of fibrous GDL in PEMFCs are derived using fractal theory. In our models, the structure of fibrous GDL is characterized in terms of porosity, tortuosity fractal dimension (D T ), pore area fractal dimensions (d f ), water phase (d f,w ) and gas phase (d f,g ) fractal dimensions. The predicted dimensionless permeability, water and gas relative permeabilities based on the proposed models are in good agreement with experimental data and predictions of numerical simulations reported in the literature. The model reveals that, although water phase and gas phase fractal dimensions strongly depend on porosity, the water and gas relative permeabilities are independent of porosity and are a function of water saturation only. It is also shown that the dimensionless permeability decreases significantly with the increase of tortuosity fractal dimension. On the other hand, there is only a small decrease in the water and gas relative permeabilities when tortuosity fractal dimension increases. One advantage of the proposed analytical model is that it contains no empirical constant, which is normally required in past models
Self-stabilized Fractality of Sea-coasts Through Damped Erosion
Sapoval, B.; Baldassari, A.; Gabrielli, A.
2004-05-01
Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).
On the Lipschitz condition in the fractal calculus
International Nuclear Information System (INIS)
Golmankhaneh, Alireza K.; Tunc, Cemil
2017-01-01
In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.
Band structures in fractal grading porous phononic crystals
Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin
2018-05-01
In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.
Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions
Lapidus, Michael L
1999-01-01
A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...
The fractal character of radiation defects aggregation in crystals
International Nuclear Information System (INIS)
Akylbekov, A.; Akimbekov, E.; Baktybekov, K.; Vasil'eva, I.
2002-01-01
In processes of self-organization, which characterize open systems, the source of ordering is a non-equilibrium. One of the samples of ordering system is radiation-stimulated aggregation of defects in solids. In real work the analysis of criterions of ordering defects structures in solid, which is continuously irradiate at low temperature is presented. The method of cellular automata used in simulation of irradiation. It allowed us to imitate processes of defects formation and recombination. The simulation realized on the surfaces up to 1000x1000 units with initial concentration of defects C n (the power of dose) 0.1-1 %. The number of iterations N (duration of irradiation) mounted to 10 6 cycles. The single centers, which are the sources of formation aggregates, survive in the result of probabilistic nature of formation and recombination genetic pairs of defects and with strictly fixed radius of recombination (the minimum inter anionic distance). For determination the character of same type defects distribution the potential of their interaction depending of defects type and reciprocal distance is calculated. For more detailed study of processes, proceeding in cells with certain sizes of aggregates, the time dependence of potential interaction is constructed. It is shown, that on primary stage the potential is negative, then it increase and approach the saturation in positive area. The minimum of interaction potential corresponds to state of physical chaos in system. Its increasing occurs with formation of same type defects aggregates. Further transition to saturation and 'undulating' character of curves explains by formation and destruction aggregates. The data indicated that - these processes occur simultaneously in cells with different sizes. It allows us to assume that the radiation defects aggregation have a fractal nature
Directory of Open Access Journals (Sweden)
Cai Lin
2017-01-01
Full Text Available This paper describes a numerical analysis of a heat transfer enhancement technique that introduces fractal-shaped design for impingement cooling. Based on the gas turbine combustion chamber cooling, a fractal-shaped nozzle is designed for the constant flow area in a single impingement cooling model. The incompressible Reynolds-averaged Navier-Stokes equations are applied to the system using CFD software. The numerical results are compared with the experiment results for array impingement cooling.
Rapid fabrication of large-area, corrosion-resistant superhydrophobic Mg alloy surfaces.
Xu, Wenji; Song, Jinlong; Sun, Jing; Lu, Yao; Yu, Ziyuan
2011-11-01
A superhydrophobic magnesium (Mg) alloy surface was successfully fabricated via a facile electrochemical machining process, and subsequently covered with a fluoroalkylsilane (FAS) film. The surface morphologies and chemical compositions were investigated using a scanning electron microscope (SEM) equipped with an energy-dispersive spectroscopy (EDS) and a Fourier-transform infrared spectrophotometer (FTIR). The results show hierarchal rough structures and an FAS film with a low surface energy on the Mg alloy surfaces, which confers good superhydrophobicity with a water contact angle of 165.2° and a water tilting angle of approximately 2°. The processing conditions, such as the processing time and removal rate per unit area at a constant removal mass per unit area, were investigated to determine their effects on the superhydrophobicity. Interestingly, when the removal mass per unit area is constant at approximately 11.10 mg/cm(2), the superhydrophobicity does not change with the removal rate per unit area. Therefore, a superhydrophobic Mg alloy surface can be rapidly fabricated based on this property. A large-area superhydrophobic Mg alloy surface was also fabricated for the first time using a small-area moving cathode. The corrosion resistance and durability of the superhydrophobic surfaces were also examined.
Water redistribution at the soil surface : ponding and surface runoff in flat areas
Appels, W.M.
2013-01-01
In The Netherlands, one of the most important targets for the improvement of surface water quality as aimed for in the European Water Framework Directive, is the reduction of nutrient concentrations (both nitrogen and phosphorus). To identify the most suitable and effective measures for reducing the
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.
Influence of Ecological Factors on Estimation of Impervious Surface Area Using Landsat 8 Imagery
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Yuqiu Jia
2017-07-01
Full Text Available Estimation of impervious surface area is important to the study of urban environments and social development, but surface characteristics, as well as the temporal, spectral, and spatial resolutions of remote sensing images, influence the estimation accuracy. To investigate the effects of regional environmental characteristics on the estimation of impervious surface area, we divided China into seven sub-regions based on climate, soil type, feature complexity, and vegetation phenology: arid and semi-arid areas, Huang-Huai-Hai winter wheat production areas, typical temperate regions, the Pearl River Delta, the middle and lower reaches of the Yangtze River, typical tropical and subtropical regions, and the Qinghai Tibet Plateau. Impervious surface area was estimated from Landsat 8 images of five typical cities, including Yinchuan, Shijiazhuang, Shenyang, Ningbo, and Kunming. Using the linear spectral unmixing method, impervious and permeable surface areas were determined at the pixel-scale based on end-member proportions. We calculated the producer’s accuracy, user’s accuracy, and overall accuracy to assess the estimation accuracy, and compared the accuracies among images acquired from different seasons and locations. In tropical and subtropical regions, vegetation canopies can confound the identification of impervious surfaces and, thus, images acquired in winter, early spring, and autumn are most suitable; estimations in the Pearl River Delta, the middle and lower reaches of the Yangtze River are influenced by soil, vegetation phenology, vegetation canopy, and water, and images acquired in spring, summer, and autumn provide the best results; in typical temperate areas, images acquired from spring to autumn are most effective for estimations; in winter wheat-growing areas, images acquired throughout the year are suitable; and in arid and semi-arid areas, summer and early autumn, during which vegetation is abundant, are the optimal seasons for
Laser-induced dendritic microstructures on the surface of Ag+-doped glass
International Nuclear Information System (INIS)
Nahal, A.; Mostafavi-Amjad, J.; Ghods, A.; Khajehpour, M. R. H.; Reihani, S. N. S.; Kolahchi, M. R.
2006-01-01
Fractal dendritic silver microstructures are observed on the surface of the Ag + -doped glasses as a result of a photothermal interaction with a focused multiline cw high-power (P max =8 W) Ag + laser beam. It is found that evolution of the structures depends on the exposure time and also on the concentration of the silver ions in the sample. The fractal dimension of the generated dendritic microstructures increases with the exposure time. Instability of the contact line of the molten silver flow toward the periphery of the interaction area is discussed as a result of the temperature gradient, due to the Gaussian intensity distribution across the laser beam
Porous silicon structures with high surface area/specific pore size
Northrup, M.A.; Yu, C.M.; Raley, N.F.
1999-03-16
Fabrication and use of porous silicon structures to increase surface area of heated reaction chambers, electrophoresis devices, and thermopneumatic sensor-actuators, chemical preconcentrates, and filtering or control flow devices. In particular, such high surface area or specific pore size porous silicon structures will be useful in significantly augmenting the adsorption, vaporization, desorption, condensation and flow of liquids and gases in applications that use such processes on a miniature scale. Examples that will benefit from a high surface area, porous silicon structure include sample preconcentrators that are designed to adsorb and subsequently desorb specific chemical species from a sample background; chemical reaction chambers with enhanced surface reaction rates; and sensor-actuator chamber devices with increased pressure for thermopneumatic actuation of integrated membranes. Examples that benefit from specific pore sized porous silicon are chemical/biological filters and thermally-activated flow devices with active or adjacent surfaces such as electrodes or heaters. 9 figs.
Structural dynamics of fore-crisis area on a heat emission surface of a fuel element's
International Nuclear Information System (INIS)
Sharaevskij, I.G.; Fialko, N.M.; Sharaevskaya, E.I.
2011-01-01
The known theoretical and experimental data regarding the nature of dry spots evolution are reviewed and the idea regarding the mechanism of heat emission from the heated surface in fore-crisis area are defined more precisely.
Lp-dual affine surface area forms of Busemann–Petty type problems
Indian Academy of Sciences (India)
Associated with the notion of Lp-intersection body which was defined ... Lp-dual affine surface area; Lp-intersection body; Busemann–Petty ..... [11] Schneider R, Convex Bodies: The Brunn–Minkowski Theory (1993) (Cambridge: Cam-.
Fractals as objects with nontrivial structures at all scales
International Nuclear Information System (INIS)
Lacan, Francis; Tresser, Charles
2015-01-01
Toward the middle of 2001, the authors started arguing that fractals are important when discussing the operational resilience of information systems and related computer sciences issues such as artificial intelligence. But in order to argue along these lines it turned out to be indispensable to define fractals so as to let one recognize as fractals some sets that are very far from being self similar in the (usual) metric sense. This paper is devoted to define (in a loose sense at least) fractals in ways that allow for instance all the Cantor sets to be fractals and that permit to recognize fractality (the property of being fractal) in the context of the information technology issues that we had tried to comprehend. Starting from the meta-definition of a fractal as an “object with non-trivial structure at all scales” that we had used for long, we ended up taking these words seriously. Accordingly we define fractals in manners that depend both on the structures that the fractals are endowed with and the chosen sets of structure compatible maps, i.e., we approach fractals in a category-dependent manner. We expect that this new approach to fractals will contribute to the understanding of more of the fractals that appear in exact and other sciences than what can be handled presently
Park, J. Y.; Ramachandran, G.; Raynor, P. C.; Kim, S. W.
2011-10-01
Surface area was estimated by three different methods using number and/or mass concentrations obtained from either two or three instruments that are commonly used in the field. The estimated surface area concentrations were compared with reference surface area concentrations (SAREF) calculated from the particle size distributions obtained from a scanning mobility particle sizer and an optical particle counter (OPC). The first estimation method (SAPSD) used particle size distribution measured by a condensation particle counter (CPC) and an OPC. The second method (SAINV1) used an inversion routine based on PM1.0, PM2.5, and number concentrations to reconstruct assumed lognormal size distributions by minimizing the difference between measurements and calculated values. The third method (SAINV2) utilized a simpler inversion method that used PM1.0 and number concentrations to construct a lognormal size distribution with an assumed value of geometric standard deviation. All estimated surface area concentrations were calculated from the reconstructed size distributions. These methods were evaluated using particle measurements obtained in a restaurant, an aluminum die-casting factory, and a diesel engine laboratory. SAPSD was 0.7-1.8 times higher and SAINV1 and SAINV2 were 2.2-8 times higher than SAREF in the restaurant and diesel engine laboratory. In the die casting facility, all estimated surface area concentrations were lower than SAREF. However, the estimated surface area concentration using all three methods had qualitatively similar exposure trends and rankings to those using SAREF within a workplace. This study suggests that surface area concentration estimation based on particle size distribution (SAPSD) is a more accurate and convenient method to estimate surface area concentrations than estimation methods using inversion routines and may be feasible to use for classifying exposure groups and identifying exposure trends.
International Nuclear Information System (INIS)
Park, J. Y.; Ramachandran, G.; Raynor, P. C.; Kim, S. W.
2011-01-01
Surface area was estimated by three different methods using number and/or mass concentrations obtained from either two or three instruments that are commonly used in the field. The estimated surface area concentrations were compared with reference surface area concentrations (SA REF ) calculated from the particle size distributions obtained from a scanning mobility particle sizer and an optical particle counter (OPC). The first estimation method (SA PSD ) used particle size distribution measured by a condensation particle counter (CPC) and an OPC. The second method (SA INV1 ) used an inversion routine based on PM1.0, PM2.5, and number concentrations to reconstruct assumed lognormal size distributions by minimizing the difference between measurements and calculated values. The third method (SA INV2 ) utilized a simpler inversion method that used PM1.0 and number concentrations to construct a lognormal size distribution with an assumed value of geometric standard deviation. All estimated surface area concentrations were calculated from the reconstructed size distributions. These methods were evaluated using particle measurements obtained in a restaurant, an aluminum die-casting factory, and a diesel engine laboratory. SA PSD was 0.7–1.8 times higher and SA INV1 and SA INV2 were 2.2–8 times higher than SA REF in the restaurant and diesel engine laboratory. In the die casting facility, all estimated surface area concentrations were lower than SA REF . However, the estimated surface area concentration using all three methods had qualitatively similar exposure trends and rankings to those using SA REF within a workplace. This study suggests that surface area concentration estimation based on particle size distribution (SA PSD ) is a more accurate and convenient method to estimate surface area concentrations than estimation methods using inversion routines and may be feasible to use for classifying exposure groups and identifying exposure trends.
Interdependence between body surface area and ultraviolet B dose in vitamin D production
DEFF Research Database (Denmark)
Bogh, M K B; Schmedes, Anne; Philipsen, P A
2011-01-01
Ultraviolet (UV) B radiation increases serum vitamin D level expressed as 25-hydroxyvitamin-D(3) [25(OH)D], but the relationship to body surface area and UVB dose needs investigation.......Ultraviolet (UV) B radiation increases serum vitamin D level expressed as 25-hydroxyvitamin-D(3) [25(OH)D], but the relationship to body surface area and UVB dose needs investigation....
Directory of Open Access Journals (Sweden)
Frederick Policelli
2018-02-01
Full Text Available Lake Chad, located in the middle of the African Sahel belt, underwent dramatic decreases in the 1970s and 1980s leaving less than ten percent of its 1960s surface water extent as open water. In this paper, we present an extended record (dry seasons 1988–2016 of the total surface water area of the lake (including both open water and flooded vegetation derived using Land Surface Temperature (LST data (dry seasons 2000–2016 from the NASA Terra MODIS sensor and EUMETSAT Meteosat-based LST measurements (dry seasons 1988–2001 from an earlier study. We also examine the total surface water area for Lake Chad using radar data (dry seasons 2015–2016 from the ESA Sentinel-1a mission. For the limited number of radar data sets available to us (18 data sets, we find on average a close match between the estimates from these data and the corresponding estimates from LST, though we find spatial differences in the estimates using the two types of data. We use these spatial differences to adjust the record (dry seasons 2000–2016 from MODIS LST. Then we use the adjusted record to remove the bias of the existing LST record (dry seasons 1988–2001 derived from Meteosat measurements and combine the two records. From this composite, extended record, we plot the total surface water area of the lake for the dry seasons of 1988–1989 through 2016–2017. We find for the dry seasons of 1988–1989 to 2016–2017 that the maximum total surface water area of the lake was approximately 16,800 sq. km (February and May, 2000, the minimum total surface water area of the lake was approximately 6400 sq. km (November, 1990, and the average was approximately 12,700 sq. km. Further, we find the total surface water area of the lake to be highly variable during this period, with an average rate of increase of approximately 143 km2 per year.
Assessment of nanoparticle surface area by measuring unattached fraction of radon progeny
Energy Technology Data Exchange (ETDEWEB)
Ruzer, Lev S. [Ernest Orlando Lawrence Berkeley National Laboratory, Indoor Environment Department (United States)], E-mail: LSRuzer@lbl.gov
2008-05-15
A number of studies on the exposure of nanometer aerosols have indicated that health effects associated with low-solubility inhaled particles in the range of 1-100 nm may be more appropriately associated with particulate surface area than mass concentration. Such data on correlation between number, surface area and mass concentration are needed for exposure investigations, but the means for measuring aerosol surface area are not readily available. In this paper we propose a method for particle surface area assessment based on a new approach, deposition of the 'unattached fraction of radon progeny' onto nanometer aerosols.The proposed approach represents a synthesis of:(1) Derived direct analytical correlation between the 'unattached fraction' of radon progeny and surface area particle concentration in the range of 1-100 nm particle diameter;(2) Experimental data on correlation between the unattached fraction of radon progeny and particle surface area for particles with diameter in the range of 44 nm-2.1 {mu}m.
Adsorption of water vapour and the specific surface area of arctic zone soils (Spitsbergen)
Cieśla, Jolanta; Sokołowska, Zofia; Witkowska-Walczak, Barbara; Skic, Kamil
2018-01-01
Water vapour/nitrogen adsorption were investigated and calculated the specific surface areas of arctic-zone soil samples (Turbic Cryosols) originating from different micro-relief forms (mud boils, cell forms and sorted circles) and from different depths. For the characterisation of the isotherms obtained for arctic soils, the Brunauer-Emmet-Teller model was then compared with the two other models (Aranovich-Donohue and Guggenheim-Anderson-de Boer) which were developed from Brunauer-Emmet-Teller. Specific surface area was calculated using the Brunauer-Emmet-Teller model at p p0-1 range of 0.05-0.35 for the water vapour desorption and nitrogen adsorption isotherms. The values of total specific surface area were the highest in Cryosols on mud boils, lower on cell forms, and the lowest on sorted circles. Such tendency was observed for the results obtained by both the water vapour and nitrogen adsorption. The differences in the values of specific surface area at two investigated layers were small. High determination coefficients were obtained for relationships between the specific surface areas and contents of clay and silt fraction in Cryosols. No statistically significant correlation between the total carbon amount and the values of specific surface area in Cryosols has been found.
Greenland surface mass-balance observations from the ice-sheet ablation area and local glaciers
DEFF Research Database (Denmark)
Machguth, Horst; Thomsen, Henrik H.; Weidick, Anker
2016-01-01
Glacier surface mass-balance measurements on Greenland started more than a century ago, but no compilation exists of the observations from the ablation area of the ice sheet and local glaciers. Such data could be used in the evaluation of modelled surface mass balance, or to document changes in g...
Determining surface areas of marine alga cells by acid-base titration method.
Wang, X; Ma, Y; Su, Y
1997-09-01
A new method for determining the surface area of living marine alga cells was described. The method uses acid-base titration to measure the surface acid/base amount on the surface of alga cells and uses the BET (Brunauer, Emmett, and Teller) equation to estimate the maximum surface acid/base amount, assuming that hydrous cell walls have carbohydrates or other structural compounds which can behave like surface Brönsted acid-base sites due to coordination of environmental H2O molecules. The method was applied to 18 diverse alga species (including 7 diatoms, 2 flagellates, 8 green algae and 1 red alga) maintained in seawater cultures. For the species examined, the surface areas of individual cells ranged from 2.8 x 10(-8) m2 for Nannochloropsis oculata to 690 x 10(-8) m2 for Dunaliella viridis, specific surface areas from 1,030 m2.g-1 for Dunaliella salina to 28,900 m2.g-1 for Pyramidomonas sp. Measurement accuracy was 15.2%. Preliminary studies show that the method may be more promising and accurate than light/electron microscopic measurements for coarse estimation of the surface area of living algae.
30 CFR 717.15 - Disposal of excess rock and earth materials on surface areas.
2010-07-01
... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Disposal of excess rock and earth materials on surface areas. 717.15 Section 717.15 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION AND ENFORCEMENT, DEPARTMENT OF THE INTERIOR INITIAL PROGRAM REGULATIONS UNDERGROUND MINING GENERAL PERFORMANCE STANDARDS § 717.15 Disposal of excess rock and...
Greenland surface mass-balance observations from the ice-sheet ablation area and local glaciers
Machguth, Horst; Thomsen, Henrik H.; Weidick, Anker; Ahlstrøm, Andreas P.; Abermann, Jakob; Andersen, Morten L.; Andersen, Signe B.; Bjørk, Anders A.; Box, Jason E.; Braithwaite, Roger J.; Bøggild, Carl E.; Citterio, Michele; Clement, Poul; Colgan, William; Fausto, Robert S.; Gleie, Karin; Gubler, Stefanie; Hasholt, Bent; Hynek, Bernhard; Knudsen, Niels T.; Larsen, Signe H.; Mernild, Sebastian H.; Oerlemans, Johannes; Oerter, Hans; Olesen, Ole B.; Smeets, C. J P Paul; Steffen, Konrad; Stober, Manfred; Sugiyama, Shin; Van As, Dirk; Van Den Broeke, Michiel R.; Van De Wal, Roderik S W
2016-01-01
Glacier surface mass-balance measurements on Greenland started more than a century ago, but no compilation exists of the observations from the ablation area of the ice sheet and local glaciers. Such data could be used in the evaluation of modelled surface mass balance, or to document changes in
Changes in Thickness and Surface Area of the Human Cortex and Their Relationship with Intelligence
Schnack, H.G.; van Haren, N.E.M.; Brouwer, R.M.; Evans, A.; Durston, S.; Boomsma, D.I.; Kahn, R.S.; Hulshoff Pol, H.E.
2015-01-01
Changes in cortical thickness over time have been related to intelligence, but whether changes in cortical surface area are related to general cognitive functioning is unknown. We therefore examined the relationship between intelligence quotient (IQ) and changes in cortical thickness and surface
a Predictive Model of Permeability for Fractal-Based Rough Rock Fractures during Shear
Huang, Na; Jiang, Yujing; Liu, Richeng; Li, Bo; Zhang, Zhenyu
This study investigates the roles of fracture roughness, normal stress and shear displacement on the fluid flow characteristics through three-dimensional (3D) self-affine fractal rock fractures, whose surfaces are generated using the modified successive random additions (SRA) algorithm. A series of numerical shear-flow tests under different normal stresses were conducted on rough rock fractures to calculate the evolutions of fracture aperture and permeability. The results show that the rough surfaces of fractal-based fractures can be described using the scaling parameter Hurst exponent (H), in which H = 3 - Df, where Df is the fractal dimension of 3D single fractures. The joint roughness coefficient (JRC) distribution of fracture profiles follows a Gauss function with a negative linear relationship between H and average JRC. The frequency curves of aperture distributions change from sharp to flat with increasing shear displacement, indicating a more anisotropic and heterogeneous flow pattern. Both the mean aperture and permeability of fracture increase with the increment of surface roughness and decrement of normal stress. At the beginning of shear, the permeability increases remarkably and then gradually becomes steady. A predictive model of permeability using the mean mechanical aperture is proposed and the validity is verified by comparisons with the experimental results reported in literature. The proposed model provides a simple method to approximate permeability of fractal-based rough rock fractures during shear using fracture aperture distribution that can be easily obtained from digitized fracture surface information.
Surface-Casting Synthesis of Mesoporous Zirconia with a CMK-5-Like Structure and High Surface Area.
Gu, Dong; Schmidt, Wolfgang; Pichler, Christian M; Bongard, Hans-Josef; Spliethoff, Bernd; Asahina, Shunsuke; Cao, Zhengwen; Terasaki, Osamu; Schüth, Ferdi
2017-09-04
About 15 years ago, the Ryoo group described the synthesis of CMK-5, a material consisting of a hexagonal arrangement of carbon nanotubes. Extension of the surface casting synthesis to oxide compositions, however, was not possible so far, in spite of many attempts. Here it is demonstrated, that crystalline mesoporous hollow zirconia materials with very high surface areas up to 400 m 2 g -1 , and in selected cases in the form of CMK-5-like, are indeed accessible via such a surface casting process. The key for the successful synthesis is an increased interaction between the silica hard template surface and the zirconia precursor species by using silanol group-rich mesoporous silica as a hard template. The surface areas of the obtained zirconias exceed those of conventionally hard-templated ones by a factor of two to three. The surface casting process seems to be applicable also to other oxide materials. © 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim.
Models of bedrock surface and overburden thickness over Olkiluoto island and nearby sea area
International Nuclear Information System (INIS)
Moenkkoenen, H.
2012-04-01
In this report, a model of bedrock surface and a model of overburden thickness over the Olkiluoto Island and the nearby sea area are presented. Also in purpose to produce material for biosphere and radionuclide transport modelling, stratigraphy models of different sediment layers were created at two priority areas north and south of the Olkiluoto Island. The work concentrated on the collection and description of available data of bedrock surface and overburden thickness. Because the information on the bedrock surface and overburden is collected from different sources and is based on a number of types of data the quality and applicability of data sets varies. Consequently also the reliability in different parts of the models varies. Input data for the bedrock surface and overburden thickness models include 2928 single points and additional outcrops observations (611 polygons) in the modelled area. In addition, the input data include 173 seismic refraction lines (6534 points) and acousticseismic sounding lines (26655 points from which 13721 points are located in model area) in the Olkiluoto offshore area. The average elevation of bedrock surface in area is 2.1 metres above the sea level. The average thickness of overburden is 2.5 metres varying typically between 2 - 4 metres. Thickest overburden covers (approximately 16 metres) of terrestrial area are located at the western end of the Olkiluoto Island and in sea basin south of the island. (orig.)
Models of bedrock surface and overburden thickness over Olkiluoto island and nearby sea area
Energy Technology Data Exchange (ETDEWEB)
Moenkkoenen, H. [WSP Finland Oy, Helsinki (Finland)
2012-04-15
In this report, a model of bedrock surface and a model of overburden thickness over the Olkiluoto Island and the nearby sea area are presented. Also in purpose to produce material for biosphere and radionuclide transport modelling, stratigraphy models of different sediment layers were created at two priority areas north and south of the Olkiluoto Island. The work concentrated on the collection and description of available data of bedrock surface and overburden thickness. Because the information on the bedrock surface and overburden is collected from different sources and is based on a number of types of data the quality and applicability of data sets varies. Consequently also the reliability in different parts of the models varies. Input data for the bedrock surface and overburden thickness models include 2928 single points and additional outcrops observations (611 polygons) in the modelled area. In addition, the input data include 173 seismic refraction lines (6534 points) and acousticseismic sounding lines (26655 points from which 13721 points are located in model area) in the Olkiluoto offshore area. The average elevation of bedrock surface in area is 2.1 metres above the sea level. The average thickness of overburden is 2.5 metres varying typically between 2 - 4 metres. Thickest overburden covers (approximately 16 metres) of terrestrial area are located at the western end of the Olkiluoto Island and in sea basin south of the island. (orig.)
The relationship of fractals in geophysics to 'the new science'
International Nuclear Information System (INIS)
Turcotte, Donald L.
2004-01-01
Many phenomena in geophysics satisfy fractal statistics, examples range from the frequency-area statistics of earthquakes to the time series of the earth's magnetic field. Solutions to classical differential equations cannot give this type of behavior. Several 'cellular automata' models have successfully reproduced the observed statistics. For example, the slider-block model for earthquakes. Stephen Wolfram's recent book A New Kind of Science sets forth a 'new science' based on cellular automata. This paper discusses the role of cellular automata in geophysics
Fractal and multifractal analyses of bipartite networks
Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua
2017-03-01
Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.
Fractal analysis of cervical intraepithelial neoplasia.
Directory of Open Access Journals (Sweden)
Markus Fabrizii
Full Text Available INTRODUCTION: Cervical intraepithelial neoplasias (CIN represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. METHODS: Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods. RESULTS: Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. CONCLUSION: Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.