Surface areas of fractally rough particles studied by scattering
International Nuclear Information System (INIS)
Hurd, A.J.; Schaefer, D.W.; Smith, D.M.; Ross, S.B.; Le Mehaute, A.; Spooner, S.
1989-01-01
The small-angle scattering from fractally rough surfaces has the potential to give information on the surface area at a given resolution. By use of quantitative neutron and x-ray scattering, a direct comparison of surface areas of fractally rough powders was made between scattering and adsorption techniques. This study supports a recently proposed correction to the theory for scattering from fractal surfaces. In addition, the scattering data provide an independent calibration of molecular adsorbate areas
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
Construction of fractal surfaces by recurrent fractal interpolation curves
International Nuclear Information System (INIS)
Yun, Chol-hui; O, Hyong-chol; Choi, Hui-chol
2014-01-01
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system (RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible constructions of fractal surfaces
Fractal characterization of the coal surface
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Miklúová Viera
1998-09-01
Full Text Available The aim of this paper is to point up to the characterization of the brown coal using the fractal theory. On the base of BET measurements on the adsorption surface, the surface fractal dimension of crushed and milled coal samples have been determined. These values of the fractal dimension are used in the estimation of the processes by the energy input.
Fractal cartography of urban areas.
Encarnação, Sara; Gaudiano, Marcos; Santos, Francisco C; Tenedório, José A; Pacheco, Jorge M
2012-01-01
In a world in which the pace of cities is increasing, prompt access to relevant information is crucial to the understanding and regulation of land use and its evolution in time. In spite of this, characterization and regulation of urban areas remains a complex process, requiring expert human intervention, analysis and judgment. Here we carry out a spatio-temporal fractal analysis of a metropolitan area, based on which we develop a model which generates a cartographic representation and classification of built-up areas, identifying (and even predicting) those areas requiring the most proximate planning and regulation. Furthermore, we show how different types of urban areas identified by the model co-evolve with the city, requiring policy regulation to be flexible and adaptive, acting just in time. The algorithmic implementation of the model is applicable to any built-up area and simple enough to pave the way for the automatic classification of urban areas worldwide.
Surface fractals in liposome aggregation.
Roldán-Vargas, Sándalo; Barnadas-Rodríguez, Ramon; Quesada-Pérez, Manuel; Estelrich, Joan; Callejas-Fernández, José
2009-01-01
In this work, the aggregation of charged liposomes induced by magnesium is investigated. Static and dynamic light scattering, Fourier-transform infrared spectroscopy, and cryotransmission electron microscopy are used as experimental techniques. In particular, multiple intracluster scattering is reduced to a negligible amount using a cross-correlation light scattering scheme. The analysis of the cluster structure, probed by means of static light scattering, reveals an evolution from surface fractals to mass fractals with increasing magnesium concentration. Cryotransmission electron microscopy micrographs of the aggregates are consistent with this interpretation. In addition, a comparative analysis of these results with those previously reported in the presence of calcium suggests that the different hydration energy between lipid vesicles when these divalent cations are present plays a fundamental role in the cluster morphology. This suggestion is also supported by infrared spectroscopy data. The kinetics of the aggregation processes is also analyzed through the time evolution of the mean diffusion coefficient of the aggregates.
Heat diffusion in fractal geometry cooling surface
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Ramšak Matjaz
2012-01-01
Full Text Available In the paper the numerical simulation of heat diffusion in the fractal geometry of Koch snowflake is presented using multidomain mixed Boundary Element Method. The idea and motivation of work is to improve the cooling of small electronic devices using fractal geometry of surface similar to cooling ribs. The heat diffusion is assumed as the only principle of heat transfer. The results are compared to the heat flux of a flat surface. The limiting case of infinite small fractal element is computed using Richardson extrapolation.
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.
Poosapadi Arjunan, Sridhar; Kumar, Dinesh Kant
2014-01-01
This research study investigates the fractal properties of surface Electromyogram (sEMG) to estimate the force levels of contraction of three muscles with different cross-sectional areas (CSA): m. quadriceps--vastus lateralis, m. biceps brachii, andm. flexor digitorum superficialis. The fractal features were computed based on the fractal analysis of sEMG, signal recorded while performing sustained muscle contraction at different force levels. A comparison was performed between the fractal features and five other features reported in the literature. Linear regression analysis was carried out to determine the relationship between the force of contraction (20-100%) and features of sEMG. The results from the coefficients of regression r² show that the new fractal feature, maximum fractal length of the signal has highest correlation (range 0.88-0.90) when compared with other features which ranges from 0.34 to 0.74 for the three different muscles. This study suggests that the estimation of various levels of sustained contraction of muscles with varied CSA will provide a better insight into the biomechanics model that involves muscle properties and muscle activation.
Feng, Shushu; Yu, Genying; Cai, Xiang; Eulade, Mahoro; Lin, Hongjun; Chen, Jianrong; Liu, Yong; Liao, Bao-Qiang
2017-11-01
Fractal roughness is one of the most important properties of a fractal surface. In this study, it was found that, randomly rough membrane surface was a fractal surface, which could be digitally modeled by a modified two-variable Weierstrass-Mandelbrot (WM) function. Fractal roughness of membrane surfaces has a typical power function relation with the statistical roughness of the modeled surface. Assessment of interfacial interactions showed that an increase in fractal roughness of membrane surfaces will strengthen and prolong the interfacial interactions between membranes and foulants, and under conditions in this study, will significantly increase the adhesion propensity of a foulant particle on membrane surface. This interesting result can be attributed to that increase in fractal roughness simultaneously improves separation distance and interaction surface area for adhesion of a foulant particle. This study gives deep insights into interfacial interactions and membrane fouling in MBRs. Copyright © 2017 Elsevier Ltd. All rights reserved.
Effect of Fractal Geometry on the Energy Balance at the Ground Surface
Sakai, S.; Iizawa, I.; Onishi, M.; Nakamura, M.; Kobayashi, K.; Mitsunaga, M.; Furuya, K.
2008-12-01
The surfaces of the urban areas are covered by large flat surfaces such as roads and walls of buildings while those of the rural areas are covered by many plants which have fractal structures. This difference in the surface geometry has great impact on the energy balance at the ground surface. A small leaf has large thermal conductivity to the surrounding air flow comparing with a anthropogenic large flat surface in an urban area even when the transpiration effect is ignored. For a cluster of many small leaves, the conductivity can be reduced by the interference, but trees have a structure to minimize its effect. We have conducted 3-dimensional laser measurements and analyzed their fractal dimensions. The analysis revealed that the trees have a fractal dimension of 2 although they are spread in a 3-dimensional space. Mathematically speaking, it means that the trees have 2-dimensional areas but do not have volume, in the limit of infinite self similarity. This geometry is favorable to absorb the sunlight using 2-dimensional area with minimum interruption of the 3-dimensional air flow. Being motivated by the results above, we have constructed a fractal sun roof consists of Sierpinski"fs tetrahedrons which have fractal dimension of 2. The roof covers an area of 100m2. The result shows that the surface temperature of the fractal roof is lower than the large flat surface with same material by more than 10 degrees.
Intergranular area microalloyed aluminium-silicate ceramics fractal analysis
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Purenović J.
2013-01-01
Full Text Available Porous aluminium-silicate ceramics, modified by alloying with magnesium and microalloying with alluminium belongs to a group of advanced multifunctional ceramics materials. This multiphase solid-solid system has predominantly amorphous microstructure and micro morphology. Intergranular and interphase areas are very complex, because they represent areas, where numbered processes and interactions take place, making new boundaries and regions with fractal nature. Fractal analysis of intergranular microstructure has included determination of ceramic grain fractal dimension by using Richardson method. Considering the fractal nature of intergranular contacts, it is possible to establish correlation between material electrical properties and fractal analysis, as a tool for future correlation with microstructure characterization. [Projekat Ministarstva nauke Republike Srbije, br. ON 172057 i br. III 45012
Proteins in solution: Fractal surfaces in solutions
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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.
Ţălu, Ştefan; Bramowicz, Miroslaw; Kulesza, Slawomir; Fiorillo, Ilenia; Giovanzana, Stefano
2017-08-01
The aim of this exploratory study was to investigate the micromorphology of surfaces of rigid gas permeable (RGP) contact lenses (CLs) using atomic force microscopy (AFM) followed by fractal analysis. In order to characterize in a quantitative manner the micromorphology of surfaces of new and unworn RGP CLs made of twelve different materials, AFM was taken and then analyzed using fractal methods. Surface topography was sampled in an intermittent-contact mode in air, on square areas of 5 × 5 µm 2 (MultiMode with Nanoscope V (Bruker). Spatial characteristics of 3-D surface texture were obtained using parameters defined in ISO 25178-2: 2012 norm. The surface texture turned out to have complex 3-D nanoscale geometry. For quantitative characterization of the properties of surface geometry at nanometer level of CL on the global scale, a series of fractal parameters was used. Statistical and fractal parameters of 3-D surfaces can be used by manufacturers to assess the micromorphology of CLs in order to improve their 3-D surface texture characteristics. These parameters can also be used in an elastic-plastic finite element model with contact elements to simulate the friction, wear and micro-elastohydrodynamic lubrication at a nanometer scale between the CL with the corneal surface.
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 ...
Evaluation of disturbed magnetic surfaces with fractal dimensions
International Nuclear Information System (INIS)
Mishimagi, Shigehiro; Yoshii, Keiichi; Kogoshi, Sumio; Maeda, Joji
1998-01-01
For collapsed magnetic surfaces that are produced by overlapping of two magnetic islands, the fractal dimension can effectively estimate the degradation of them. The fractal dimensions of cross sections of regular magnetic surfaces and clear magnetic islands are nearly 1, while that of a collapsed magnetic surface is more than 1.2 in the present study. The Lyapunov exponents and dimensions are also calculated, which suggest the behavior of the field line of the collapsed magnetic surface is chaos. (author)
Hu, Kang-Bo; Wang, Yi-Li; Li, Jun-Qing; Gui, Ping; Jiang, Yan-Ling
2011-07-01
Surface morphology and pore surface fractal characteristics of the sediment in the desilting basin of Queshan Reservoir were studied. Six sediment samples were collected and particle size, morphology, pore structure and fractal characteristics, surface elements distribution were analyzed as well. The objectives of this study were to investigate the reason for the differences among the pore surface fractal dimensions and fractal scales on the basis of different models, and discuss the effect of surface morphology of these sediment particles on their surface elements distribution. The results showed that these sediment particles with average diameter of 18-83 microm were mainly composed of clay, silt and fine sand. Their complex surface morphology and pore size distribution were reflected by wide range of the BET surface area (8.248-31.60 m2/g), average pore diameter (3.977-7.850 nm) and pore-size distribution (1.870-60.78 nm). Although the pore surface fractal dimensions (D(s)), based on fractal FHH or thermodynamic models, were 2.67-2.89, and their fractal scales generally ranged from several nanometers to tens of nanometers, the differences were still observed in D(s) values calculated from above two models because of inhomogeneity in surface pore size distribution. Therefore, the D(s) based on pore-size distribution were 2.12-2.60, these values close to D(s) calculated from fractal FHH models revealed that pore-size distribution could contribute significantly to D(s) calculation. In addition, the heterogeneous surface adsorption sites of these sediment particles caused by much complex surface morphology had strong influence on the each element distribution on the particle surface.
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)
Effect of 3D fractal dimension on contact area and asperity interactions in elastoplastic contact
Directory of Open Access Journals (Sweden)
Abdeljalil Jourani
2016-05-01
Full Text Available Few models are devoted to investigate the effect of 3D fractal dimension Ds on contact area and asperity interactions. These models used statistical approaches or two-dimensional deterministic simulations without considering the asperity interactions and elastic–plastic transition regime. In this study, a complete 3D deterministic model is adopted to simulate the contact between fractal surfaces which are generated using a modified two-variable Weierstrass–Mandelbrot function. This model incorporates the asperity interactions and considers the different deformation modes of surface asperities which range from entirely elastic through elastic-plastic to entirely plastic contact. The simulations reveal that the elastoplastic model is more appropriate to calculate the contact area ratio and pressure field. It is also shown that the influence of the asperity interactions cannot be neglected, especially at lower fractal dimension Ds and higher load.
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Davis, Ethan, E-mail: ethan.davis4@huskers.unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States); Liu, Ying; Jiang, Lijia; Lu, Yongfeng [Laser Assisted Nano Engineering Lab, Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, 209N Scott Engineering Center, Lincoln, NE 68588-0511 (United States); Ndao, Sidy, E-mail: sndao2@unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States)
2017-01-15
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Theoretical study of fractal growth and stability on surface
DEFF Research Database (Denmark)
Dick, Veronika V.; Solov'yov, Ilia; Solov'yov, Andrey V.
2009-01-01
We perform a theoretical study of the fractal growing process on surface by using the deposition, diffusion, aggregation method. We present a detailed analysis of the post-growth processes occurring in a nanofractal on surface. For this study we developed a method which describes the internal...... dynamics of particles in a fractal and accounts for their diffusion and detachment. We demonstrate that these kinetic processes are responsible for the formation of the final shape of the islands on surface after the post-growth relaxation....
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
Controlling Molecular Growth between Fractals and Crystals on Surfaces.
Zhang, Xue; Li, Na; Gu, Gao-Chen; Wang, Hao; Nieckarz, Damian; Szabelski, Paweł; He, Yang; Wang, Yu; Xie, Chao; Shen, Zi-Yong; Lü, Jing-Tao; Tang, Hao; Peng, Lian-Mao; Hou, Shi-Min; Wu, Kai; Wang, Yong-Feng
2015-12-22
Recent studies demonstrate that simple functional molecules, which usually form two-dimensional (2D) crystal structures when adsorbed on solid substrates, are also able to self-assemble into ordered openwork fractal aggregates. To direct and control the growth of such fractal supramolecules, it is necessary to explore the conditions under which both fractal and crystalline patterns develop and coexist. In this contribution, we study the coexistence of Sierpiński triangle (ST) fractals and 2D molecular crystals that were formed by 4,4″-dihydroxy-1,1':3',1″-terphenyl molecules on Au(111) in ultrahigh vacuum. Growth competition between the STs and 2D crystals was realized by tuning substrate and molecular surface coverage and changing the functional groups of the molecular building block. Density functional theory calculations and Monte Carlo simulations are used to characterize the process. Both experimental and theoretical results demonstrate the possibility of steering the surface self-assembly to generate fractal and nonfractal structures made up of the same molecular building block.
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.
Fractal and Lacunarity Analyses: Quantitative Characterization of Hierarchical Surface Topographies.
Ling, Edwin J Y; Servio, Phillip; Kietzig, Anne-Marie
2016-02-01
Biomimetic hierarchical surface structures that exhibit features having multiple length scales have been used in many technological and engineering applications. Their surface topographies are most commonly analyzed using scanning electron microscopy (SEM), which only allows for qualitative visual assessments. Here we introduce fractal and lacunarity analyses as a method of characterizing the SEM images of hierarchical surface structures in a quantitative manner. Taking femtosecond laser-irradiated metals as an example, our results illustrate that, while the fractal dimension is a poor descriptor of surface complexity, lacunarity analysis can successfully quantify the spatial texture of an SEM image; this, in turn, provides a convenient means of reporting changes in surface topography with respect to changes in processing parameters. Furthermore, lacunarity plots are shown to be sensitive to the different length scales present within a hierarchical structure due to the reversal of lacunarity trends at specific magnifications where new features become resolvable. Finally, we have established a consistent method of detecting pattern sizes in an image from the oscillation of lacunarity plots. Therefore, we promote the adoption of lacunarity analysis as a powerful tool for quantitative characterization of, but not limited to, multi-scale hierarchical surface topographies.
Three-Dimensional Surface Parameters and Multi-Fractal Spectrum of Corroded Steel.
Shanhua, Xu; Songbo, Ren; Youde, Wang
2015-01-01
To study multi-fractal behavior of corroded steel surface, a range of fractal surfaces of corroded surfaces of Q235 steel were constructed by using the Weierstrass-Mandelbrot method under a high total accuracy. The multi-fractal spectrum of fractal surface of corroded steel was calculated to study the multi-fractal characteristics of the W-M corroded surface. Based on the shape feature of the multi-fractal spectrum of corroded steel surface, the least squares method was applied to the quadratic fitting of the multi-fractal spectrum of corroded surface. The fitting function was quantitatively analyzed to simplify the calculation of multi-fractal characteristics of corroded surface. The results showed that the multi-fractal spectrum of corroded surface was fitted well with the method using quadratic curve fitting, and the evolution rules and trends were forecasted accurately. The findings can be applied to research on the mechanisms of corroded surface formation of steel and provide a new approach for the establishment of corrosion damage constitutive models of steel.
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.
Fractal analysis of AFM images of the surface of Bowman's membrane of the human cornea.
Ţălu, Ştefan; Stach, Sebastian; Sueiras, Vivian; Ziebarth, Noël Marysa
2015-04-01
The objective of this study is to further investigate the ultrastructural details of the surface of Bowman's membrane of the human cornea, using atomic force microscopy (AFM) images. One representative image acquired of Bowman's membrane of a human cornea was investigated. The three-dimensional (3-D) surface of the sample was imaged using AFM in contact mode, while the sample was completely submerged in optisol solution. Height and deflection images were acquired at multiple scan lengths using the MFP-3D AFM system software (Asylum Research, Santa Barbara, CA), based in IGOR Pro (WaveMetrics, Lake Oswego, OR). A novel approach, based on computational algorithms for fractal analysis of surfaces applied for AFM data, was utilized to analyze the surface structure. The surfaces revealed a fractal structure at the nanometer scale. The fractal dimension, D, provided quantitative values that characterize the scale properties of surface geometry. Detailed characterization of the surface topography was obtained using statistical parameters, in accordance with ISO 25178-2: 2012. Results obtained by fractal analysis confirm the relationship between the value of the fractal dimension and the statistical surface roughness parameters. The surface structure of Bowman's membrane of the human cornea is complex. The analyzed AFM images confirm a fractal nature of the surface, which is not taken into account by classical surface statistical parameters. Surface fractal dimension could be useful in ophthalmology to quantify corneal architectural changes associated with different disease states to further our understanding of disease evolution.
METHODS OF BIOMONITORING IN URBAN ENVIRONMENT: LEAF AREA AND FRACTAL DIMENSION
Directory of Open Access Journals (Sweden)
Nicoleta IANOVICI
2015-12-01
Full Text Available In urban conditions, we investigated several leaf traits (leaf area, specific leaf area, fractal dimension and specific leaf weight on Taraxacum officinale, Tilia tomentosa, Aesculus hippocastanum and Ambrosia artemisiifolia. The analyzed organs were mature leaves, on the first indications of senescence. This study used an exact, inexpensive and efficient in terms of costs alternative methods for determining the leaf parameters. On the other hand, this paper presents an application of the leaf area and fractal dimension in the analysis of leaf shape. Our results show that leaf area and fractal dimension are sensitive parameters that can be effectively used in biomonitoring.
Capillary pressure in a porous medium with distinct pore surface and pore volume fractal dimensions.
Deinert, M R; Dathe, A; Parlange, J-Y; Cady, K B
2008-02-01
The relationship between capillary pressure and saturation in a porous medium often exhibits a power-law dependence. The physical basis for this relation has been substantiated by assuming that capillary pressure is directly related to the pore radius. When the pore space of a medium exhibits fractal structure this approach results in a power-law relation with an exponent of 3-D(v), where D(v) is the pore volume fractal dimension. However, larger values of the exponent than are realistically allowed by this result have long been known to occur. Using a thermodynamic formulation for equilibrium capillary pressure we show that the standard result is a special case of the more general exponent (3-D(v))(3-D(s)) where D(s) is the surface fractal dimension of the pores. The analysis reduces to the standard result when D(s)=2, indicating a Euclidean relationship between a pore's surface area and the volume it encloses, and allows for a larger value for the exponent than the standard result when D(s)>2 .
Measuring the surface roughness of geological rock surfaces in SAR data using fractal geometry
Ghafouri, Ali; Amini, Jalal; Dehmollaian, Mojtaba; Kavoosi, Mohammad Ali
2017-05-01
Determining surface morphology using synthetic aperture radar (SAR) data requires accurate topographic and microtopographic models. To distinguish different surface geometric patterns and to differentiate the formation of geological rock surfaces, it is necessary to model the smoothness and roughness of surfaces based on radar signal backscattering. Euclidean geometry is less able than fractal geometry to describe natural phenomena; however, in application to radar backscattering models, fractal geometry has never fully replaced Euclidean geometry. Using fractal geometry only, this paper attempts to improve the backscattering simulation generated by an Integral Equation Model to improve the description of geological rock surfaces. As the application of radar signal backscattering is a rarity in the domain of geology, the paper also discusses the efficiency of the method in improving the results of conventional geological mapping methods. The proposed method is applied to the Anaran geological formation (between Dehloran and Ilam in IRAN) using TerraSAR-X SAR data and in situ roughness measurements on pure sites with rough, intermediate, and smooth morphologies. This implementation shows fractal and diffractal behavior of geological morphologies under various conditions.
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)
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
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
Enhanced Fluorescence from Fluorophores on Fractal Silver Surfaces
Parfenov, Alexandr; Gryczynski, Ignacy; Malicka, Joanna; Geddes, Chris D.; Lakowicz, Joseph R.
2003-01-01
Recent reports have shown enhanced fluorescence for fluorophores in close proximity to chemically deposited silver islands or colloids. To expand the usefulness of metal-enhanced fluorescence we tested fractal silver structures formed on, or near, silver electrodes by passage of electric currents. The emission intensity of fluorescein-labeled human serum albumin (FITC-HSA) was enhanced over 100-fold when adsorbed to the fractal silver structures as compared to glass. The amplitude-weighted li...
Hydrophobic fractal surface from glycerol tripalmitate and the effects on C6 glioma cell growth.
Zhang, Shanshan; Chen, Xuerui; Yu, Jing; Hong, Biyuan; Lei, Qunfang; Fang, Wenjun
2016-06-01
To provide a biomimic environment for glial cell culture, glycerol tripalmitate (PPP) has been used as a raw material to prepare fractal surfaces with different degrees of hydrophobicity. The spontaneous formation of the hydrophobic fractal surfaces was monitored by differential scanning calorimetry (DSC) and X-ray diffraction (XRD). The surface morphologies were observed by a scanning electron microscope (SEM), and then the fractal dimension (FD) values of the surfaces were determined with the box-counting method. C6 glioma cells were cultured and compared on different hydrophobic PPP surfaces and poly-L-lysine (PLL)-coated surface. The cell numbers as a function of incubation time on different surfaces during the cell proliferation process were measured, and the cell morphologies were observed under a fluorescence microscope. Influences of hydrophobic fractal surfaces on the cell number and morphology were analyzed. The experimental results show that the cell proliferation rates decrease while the cell morphology complexities increase with the growth of the fractal dimensions of the PPP surfaces. Copyright © 2016 Elsevier B.V. All rights reserved.
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
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.
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.
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
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.
Surface-enhanced Raman imaging of fractal shaped periodic metal nanostructures
DEFF Research Database (Denmark)
Beermann, Jonas; Novikov, Sergey Mikhailovich; Albrektsen, Ole
2009-01-01
Surface-enhanced Raman scattering (SERS) from Rhodamine 6G (R6G) homogenously adsorbed on fractal shaped 170-nm-period square arrays formed by 50-nm-high gold nanoparticles (diameters of 80, 100, or 120 nm are constant within each array), fabricated on a smooth gold film by electron-beam lithogra......Surface-enhanced Raman scattering (SERS) from Rhodamine 6G (R6G) homogenously adsorbed on fractal shaped 170-nm-period square arrays formed by 50-nm-high gold nanoparticles (diameters of 80, 100, or 120 nm are constant within each array), fabricated on a smooth gold film by electron...
Directory of Open Access Journals (Sweden)
L. Ren
2014-01-01
Full Text Available Compressive fracture is one of the most common failure patterns in geotechnical engineering. For better understanding of the local failure mechanism of compressive fractures of brittle geomaterials, three compressive fracture tests were conducted on sandstone. Edge cracked semicircular bend specimens were used and, consequently, fresh and unfilled compressive fracture surfaces were obtained. A laser profilometer was employed to measure the topography of each rough fracture surface, followed by fractal analysis of the irregularities of the obtained compression-induced fracture surfaces using the cubic cover method. To carry out a contrastive analysis with the results of compressive fracture tests, three tension mode fracture tests were also conducted and the fractal features of the obtained fracture surfaces were determined. The obtained average result of the fractal dimensions of the compression-induced surfaces was 2.070, whereas the average result was 2.067 for the tension-induced fracture surfaces. No remarkable differences between the fractal dimensions of the compression-induced and tension-induced fracture surfaces may indicate that compressive fracture may occur, at least on the investigative scale of this work, in a similar manner to tension fracture.
Contribution to fractal Analysis of cities : A Study of metropolitan Area of Milan
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Rabino Giovanni
2004-04-01
Full Text Available La présentation de l'analyse fractale de l'aire métropolitaine de Milan part de la description historique de l'évolution du processus d'urbanisation de la ville, de manière à pouvoir mettre en évidence des zones précises, homogènes du point de vue historique, qui seront analysées dans la suite par le biais de la technique fractale. L'analyse fractale de la ville de Milan est menée selon trois approches : l'étude du périmètre de la ville, qui utilise la méthode de la dilatation pour extraire le périmètre et l'analyse de corrélation pour calculer sa dimension fractale ; l'étude de la surface urbanisée dans son ensemble, qui utilise l'analyse de corrélation, de dilatation et du quadrillage ; l'étude de certaines zones de la ville qui ont été décrites dans la première partie de la présentation ; les résultats sont présentés avec une attention particulière au rapport entre la valeur de la dimension fractale et le contexte urbain pour lequel elle est calculée, ainsi qu'à la comparaison des dimensions fractales des différentes zones urbaines prises en considération.
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...... Lacunarity (FG2DL) were used to quantify the degree of fragmentation and dispersion of the forested areas, and thereby the extent to which a forest area is affected by deforestation. The process of quantifying the pressure on forested areas included the creation of a database for the period of 2000...
Surface fractal dimensions and textural properties of mesoporous alkaline-earth hydroxyapatites
Energy Technology Data Exchange (ETDEWEB)
Vilchis-Granados, J. [Instituto Nacional de Investigaciones Nucleares, Departamento de Química, A.P. 18-1027, Col. Escandón, Delegación Miguel Hidalgo, C.P. 11801, México, DF (Mexico); Universidad Autónoma del Estado de México, Facultad de Química, Av. Paseo Colón esquina con Paseo Tollocan s/n Toluca, México (Mexico); Granados-Correa, F., E-mail: francisco.granados@inin.gob.mx [Instituto Nacional de Investigaciones Nucleares, Departamento de Química, A.P. 18-1027, Col. Escandón, Delegación Miguel Hidalgo, C.P. 11801, México, DF (Mexico); Barrera-Díaz, C.E. [Universidad Autónoma del Estado de México, Facultad de Química, Av. Paseo Colón esquina con Paseo Tollocan s/n Toluca, México (Mexico)
2013-08-15
This work examines the surface fractal dimensions (D{sub f}) and textural properties of three different alkaline-earth hydroxyapatites. Calcium, strontium and barium hydroxyapatite compounds were successfully synthesized via chemical precipitation method and characterized using X-ray diffraction, scanning electron microscopy, energy dispersive X-ray spectrometry, Fourier transform infrared spectroscopy, and N{sub 2}-physisorption measurements. Surface fractal dimensions were determined using single N{sub 2}-adsorption/desorption isotherms method to quantify the irregular surface of as-prepared compounds. The obtained materials were also characterized through their surface hydroxyl group content, determined by the mass titration method. It was found that the D{sub f} values for the three materials covered the range of 0.77 ± 0.04–2.33 ± 0.11; these results indicated that the materials tend to have smooth surfaces, except the irregular surface of barium hydroxyapatite. Moreover, regarding the synthesized calcium hydroxyapatite exhibited better textural properties compared with the synthesized strontium and barium hydroxyapatites for adsorbent purposes. However, barium hydroxyapatite shows irregular surface, indicating a high population of active sites across the surface, in comparison with the others studied hydroxyapatites. Finally, the results showed a linear correlation between the surface hydroxyl group content at the external surface of materials and their surface fractal dimensions.
Roy, Pradip Kumar; Huang, Yi-Fan; Chattopadhyay, Surojit
2014-01-01
A simple way of detecting melamine in raw milk is demonstrated via surface-enhanced Raman spectroscopy (SERS) using fractals of bare and nonfunctionalized ~30 nm gold nanoparticles (AuNP) distributed on a solid support. The technique demonstrates the formation of AuNP fractals, from a random distribution, upon exposure to melamine, that enhance the Raman scattering cross-section to enable detection by SERS. The agglomeration, which is pronounced at higher melamine concentrations, is demonstrated directly through imaging, and the red-shift of the plasmon absorption peak of the AuNP fractal away from 530 nm by finite difference time domain (FDTD) calculations. The agglomeration results in a strong plasmon field, shown by FDTD, over the interparticle sites that enhances the Raman scattering cross-section of melamine and ensures unambiguous detection. Limit of detection of 100 ppb could be achieved reproducibly.
Fractal structure of lunar topography: An interpretation of topographic characteristics
Cao, Wei; Cai, Zhanchuan; Tang, Zesheng
2015-06-01
Over the years, fractal geometry has been applied extensively in many fields of geoscience. Based on the global gridded data generated from the Lunar Reconnaissance Orbiter, we carry out our fractal measure to interpret lunar fractures by using qualitative (similar ratio) and quantitative (fractal dimension) approaches of fractal geometry. We find that most of the lunar surface exhibits fractal behavior over the given scales ranging from 1 to 256 m. Lunar maria have higher fractal dimensions than other geological units, while those of volcanic areas and highlands are lower than their surroundings. Simple and flat surfaces have low values of similar ratios and these areas indicate low surface roughness and young ages. Older-aged areas, such as the Hertzsprung basin, have low fractal dimensions and high similar ratios by their complicated topography.
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.
Directory of Open Access Journals (Sweden)
Mitić V.V.
2013-01-01
Full Text Available In this study, in order to establish grain shapes of sintered ceramics, new approach on correlation between microstructure and doped BaTiO3 -ceramics properties based, on Voronoi model and mathematical statistics calculations on fractal geometry, has been developed. BaTiO3-ceramics doped with Yb2O3 (from 0.1 to 1.0wt% of Yb were prepared by using conventional solid state procedure and were sintered from 1320°C to 1380°C for four hours. The microstructure of sintered specimens was investigated by Scanning electron microscope JEOL-SEM-5300. For better and deeper characterization and understanding of the ceramics material microstructure, the methods which include the fractal nature structure, and also Voronoi model and mathematical statistics calculations, are applied. In our research the Voronoi is one specific interface between fractal structure nature and different stochastically contact surfaces, defined by statistical mathematical methods. Also, the Voronoi model practically provided possibility to control the ceramics microstructure fractal nature. Mathematical statistic methods enabled establishing the real model for the prognosis based on correlation: synthesis-structures-properties. [Projekat Ministarstva nauke Republike Srbije, br. 172057 i br. III44006
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...
Brinkhoff, L. A.; von Savigny, C.; Randall, C. E.; Burrows, J. P.
2015-05-01
The fractal perimeter dimension is a fundamental property of clouds. It describes the cloud shape and is used to improve the understanding of atmospheric processes responsible for cloud shapes. von Savigny et al. (2011) determined the fractal perimeter dimension of noctilucent clouds (or polar mesospheric clouds) for the first time based on a limited data set of cloud images observed with the CIPS (Cloud Imaging and Particle Size) instrument on board the AIM (Aeronomy of Ice in the Mesosphere) satellite. This paper builds on von Savigny et al. (2011) by first presenting a sensitivity analysis of the determination of the fractal perimeter dimension, and secondly presenting results on the seasonal and interhemispheric differences of the perimeter dimension of noctilucent clouds (NLCs). The same method as in the earlier study is applied to an extended data set of satellite images of noctilucent cloud fields taken with the CIPS experiment. The sensitivity studies reveal that cloud holes play an important role for the area-perimeter method, since excluding clouds with holes reduces the dimension value by up to 3%. The results on the fractal perimeter dimension over six NLC seasons from 2007 to 2009 demonstrate that the dimension values of the NLCs neither show significant differences between the seasons nor between the hemispheres.
Evaluation de la Qualité de surface par la Dimension Fractale et les ...
African Journals Online (AJOL)
grand diamètre de la bille offre la possibilité de repousser plus de matière permettant le nivellement des aspérités au niveau de la surface traitée, ce qui est constaté sur la cartographie de surface (Fig.7c). En général, la dimension fractale D est comprise entre 2 < D<3, plus D tend vers 2 plus la surface est lisse et régulière ...
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 DIMENSIONING OF SAND GRAINS USING IMAGE ANALYSIS SYSTEM
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Suat AKBULUT
2002-03-01
Full Text Available Engineers and earth scientists have successfully used the concept of fractal theory to better analyze the roughness of soil and/or rock particles, and how it affects the permeability, structure and distribution of pores in sedimentary rocks and their influence on strength. Use of fractals as a way to describe irregular or rough objects has been highlighted in articles by researchers working in fields such as powder mechanics, rock and soil mechanics, sedimentary petrography and geoenvironmental applications. Fractal scaling has been found appropriate to express such scale independence for collection of soil particles and aggregates. In many aspects, soil is a fractal medium and fractal models are available for the fragmentation of aggregates with fractal pore space, and with fractal surface. Applications of fractal concepts encompass description of soil physical properties such as pore-size distribution, pore surface area, and grain-size distribution. The roughness of particulate soils is an important characteristic that affects the mass behavior of the soil. The area-perimeter technique was used to predict the fractal dimension using image analysis system. This paper presents the effects of the roughness and sorting of the sand patterns with different shapes on fractal dimension. Results confirmed the significance of the roughness effect on fractal dimension.
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.
Schultz, L. N.; Andersson, M. P.; Dalby, K. N.; Müter, D.; Okhrimenko, D. V.; Fordsmand, H.; Stipp, S. L. S.
2013-05-01
Calcite (CaCO3) is important in many fields—in nature, because it is a component of aquifers, oil reservoirs and prospective CO2 storage sites, and in industry, where it is used in products as diverse as paper, toothpaste, paint, plastic and aspirin. It is difficult to obtain high purity calcite with a high surface area but such material is necessary for industrial applications and for fundamental calcite research. Commercial powder is nearly always contaminated with growth inhibitors such as sugars, citrate or pectin and most laboratory synthesis methods deliver large precipitates, often containing vaterite or aragonite. To address this problem, we (i) adapted the method of carbonating a Ca(OH)2 slurry with CO2 gas to develop the first simple, cheap, safe and reproducible procedure using common laboratory equipment, to obtain calcite that reproducibly had a surface area of 14-17 m2/g and (ii) conducted a thorough characterization of the product. Scanning electron microscopy (SEM) revealed nanometer scale, rhombohedral crystals. X-ray diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and infrared spectroscopy (IR) confirmed highly crystalline, pure calcite that more closely resembles the dimensions of the biogenic calcite produced by algae in coccoliths than other methods for synthesizing calcite. We suggest that this calcite is useful when purity and high surface area are important.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325
Negentropy Generation and Fractality in the Dry Friction of Polished Surfaces
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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.
The effect of vertical scaling on the estimation of the fractal dimension of randomly rough surfaces
Schouwenaars, Rafael; Jacobo, Víctor H.; Ortiz, Armando
2017-12-01
Fractal analysis of randomly rough surface is an interesting tool to establish relationships between surface geometry and properties. Nonetheless, the observation that different methods to determine the fractal dimension D yield different results has raised questions about its physical meaning. This work shows that such variations are caused by the mathematical details of the methods used, particularly by the effect of vertical scaling. For the triangular prism method (TPM), applied to fractional Brownian motion, the effect of vertical scaling on the numerical estimation of D can be addressed through analytic calculations. The analytic approach was compared to simulations of surface topography obtained by the random midpoint algorithm (RMA) using TPM, box count method (BCM), differential box count (DBC) and detrended fluctuation analysis (DFA). The effect of scaling for TPM is considerable and coincides with the mathematical predictions. BCM and DBC show no effect of scaling but provide poor estimates at high D. A small effect was found for DFA. It is concluded that TPM provides a precise estimate of D which is independent of vertical scaling for infinite image resolution. At finite resolutions, the estimation error on D can be minimised by choosing an optimal vertical scaling factor.
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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.
Amato P; Cerofolini GF; Narducci D; Romano E
2008-01-01
Abstract Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.
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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.
Nogueira, Miguel
2017-01-01
The equivalency between the power law behavior of Multiscale Entropy (MSE) and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing) scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the underlying
Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind.
Directory of Open Access Journals (Sweden)
Miguel Nogueira
Full Text Available The equivalency between the power law behavior of Multiscale Entropy (MSE and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the
Mansouri, Edris; Feizi, Faranak
2016-06-01
The studied area - Chartagh - is located in the East of Azerbaijan gharbi Province, Iran. In this paper, geology map, ASTER satellite images were used and after processing these images with ENVI softwares, geochemical data analysis consisting of lithogeochemical samples, within geological field observations. On ASTER data; using a number of selected methods including band ratio, Minimum Noise Fraction (MNF) and Spectral Angle Maper (SAM) distinguished alternation zones. Geochemical anomalies were separated by number - size (N-S) fractal method. (N-S) fractal method was utilized for High intensive Au, As and Ag anomalies.
Zhao, Leihong; Yang, Lining; Lin, Hongjun; Zhang, Meijia; Yu, Haiying; Liao, Bao-Qiang; Wang, Fangyuan; Zhou, Xiaoling; Li, Renjie
2016-12-01
While the adsorptive fouling in membrane bioreactors (MBRs) is highly dependent of the surface morphology, little progress has been made on modeling biocake layer surface morphology. In this study, a novel method, which combined static light scattering method for fractal dimension (D f ) measurement with fractal method represented by the modified two-variable Weierstrass-Mandelbrot function, was proposed to model biocake layer surface in a MBR. Characterization by atomic force microscopy showed that the biocake surface was stochastic, disorder, self-similarity, and with non-integer dimension, illustrating obvious fractal features. Fractal dimension (D f ) of sludge suspension experienced a significant change with operation of the MBR. The constructed biocake layer surface by the proposed method was quite close to the real surface, showing the feasibility of the proposed method. It was found that D f was the critical factor affecting surface morphology, while other factors exerted moderate or minor effects on the roughness of biocake layer. Copyright © 2016 Elsevier Ltd. All rights reserved.
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.
Tree-shaped fractal meta-surface with left-handed characteristics for absorption application
Faruque, M. R. I.; Hasan, M. M.; Islam, M. T.
2018-02-01
A tri-band fractal meta-surface absorber composed of metallic branches of a tree connected with a straight metal strip has been presented in this paper for high absorption application. The proposed tree-shaped structure shows resonance in C-, X-, and Ku-bands and left-handed characteristics in 14.15 GHz. The dimension of the tree-shaped meta-surface single unit cell structure is 9 × 9 mm2 and the effective medium ratio is 5.50. In addition, the designed absorber structure shows absorption above 84%, whereas the absorber structure printed on epoxy resin fiber substrate material. The FIT-based CST-MWS has been utilized for the design, simulation, and analysis purposes. Fabrication is also done for the experimental validation.
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.
Design and rapid prototyping of DLC coated fractal surfaces for tissue engineering applications
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Diaz-Lantada, A; Mosquera, A; Endrino, J L; Lafont, P, E-mail: adiaz@etsii.upm.es
2010-11-01
Several medical devices (both implantable and for in vitro diagnosis) benefit greatly from having microtextured surfaces that help to improve and promote phenomena such as osteointegracion and cell / tissue growth on the surface of a device. Normally, the use of abrasives or chemical attacks are employed for obtaining such surface microtextures, however, it is sometimes difficult to precisely control the final surface characteristics (porosity, roughness, among others) and consequently the related biological aspects. In this work, we propose an alternative process based on the use of fractal surface models for designing special surfaces, which helps controlling the desired contact properties (from the design stage) in multiple applications within biomedical engineering, especially regarding tissue engineering tasks. Manufacturing can be directly accomplished by means of rapid prototyping technologies. This method supposes a focus change from a conventional 'top-down' to a more versatile 'bottom-up' approach. Finally, in order to improve the possible biological response, the surfaces of the designed devices were coated with hydrogen-free amorphous carbon (a-C) thin films, known to be highly biocompatible materials. The films were deposited at room temperature using the vacuum filter cathodic arc technique. Our first prototypes have helped verify the viability of the approach and to validate the design, manufacturing and coating processes.
Fractal Analysis on Asphalt Mixture Using a Two-Dimensional Imaging Technique
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Yue Hou
2016-01-01
Full Text Available Fractal is a mathematical set that has a fractal dimension which usually exceeds its topological dimension and may be nonintegral. Since the asphalt pavement texture has limitations of randomness and self-similarity, fractal theory has been explored to quantify the asphalt pavement texture and employs good applicability in processing and analyzing the complex details of research object. In this paper, the 2D digital image of the pavement surface is measured in terms of area fractal dimension and contour fractal dimension, which are used to correlate with aggregate gradation and British Pendulum Number (BPN value, respectively. It turns out the area fractal dimension of aggregate provides a simple way to acquire the continuous gradation of asphalt concrete sample and the contour fractal dimension is an available parameter to characterize roughness and friction of pavement surface texture.
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)
Hong, Wang Xu; Huijie, Qin; Zhe, Zhang; Fei, Li
2014-03-01
Remote sensing images are highly structured, and contiguous pixels of space domain have strong correlations that contain abundant information on land surface structure features and land surface electromagnetic radiation features. The information capacity model, which is a quality evaluation model based on a multi-dimensional histogram, includes local correlations within different pixels. Thus, the information capacity can illustrate land surface structural information more objectively and effectively than other single-pixel calculation models. Our results reveal that the information capacity value correlates well with the meaningful grey level of remote sensing imagery. This high correlation is related to the complexity of terrestrial surface landscapes. Therefore, information capacity, as applied to geoscience, is introduced in this study to demonstrate the spatial differentiation of information capacity of different landform regions. Generally, the information capacity of a mountain is large and is followed in decreasing order by those of the hills and the plains. Moreover, the correlation between information capacity and the fractal dimension is analysed. Based on the results of this study, it can be concluded that the level of correlation for information capacity and the fractal dimension is high, and the correlation coefficient for the basic landform areas and the loess landform areas is 0.874 and 0.825, respectively. Finally, this paper proposes that information capacity be used as a new reference index for geoscientific analysis in quantitative research on the characteristics of land surface complexity.
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)
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Amato P
2008-01-01
Full Text Available Abstract Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.
Fractal Patterns and Chaos Games
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
Mossotti, Victor G.; Eldeeb, A. Raouf
2000-01-01
Turcotte, 1997, and Barton and La Pointe, 1995, have identified many potential uses for the fractal dimension in physicochemical models of surface properties. The image-analysis program described in this report is an extension of the program set MORPH-I (Mossotti and others, 1998), which provided the fractal analysis of electron-microscope images of pore profiles (Mossotti and Eldeeb, 1992). MORPH-II, an integration of the modified kernel of the program MORPH-I with image calibration and editing facilities, was designed to measure the fractal dimension of the exposed surfaces of stone specimens as imaged in cross section in an electron microscope.
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
Mishin, M V; Zamotin, K Y; Protopopova, V S; Alexandrov, S E
2015-03-21
This paper covers the results from a study of the formation mechanism of fractal clusters from nanoparticles synthesised in atmospheric pressure radio frequency discharge. Two-dimensional structures with random configuration and self-similarity properties are formed by nanoparticles on a solid substrate surface. The typical linear dimensions of such structures are in the micron range. On the basis of the previously demonstrated experimental results, a physico-mathematical model of the nanoparticle self-organisation was developed. The physical model includes the electrical charge effect of the deposit surface, the spatial distribution of the surface electrical potential and the topography rearrangement phenomenon under the arising electrostatic forces. The threshold character of the agglomeration process initiation was found. The dependence of the formed structure topography on the character of the electrical potential change was demonstrated. The requisite conditions for the classical fractal formation were revealed. The results from the computational simulation, which was conducted with the use of fractal analysis, indicate a high level of coincidence with the experimental results.
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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
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.
Chen, Jingjing; He, Binghui; Wang, Xiaoyan; Ma, Yun; Xi, Weimin
2013-10-01
To evaluate if hedgerows could improve the soil physicochemical properties and enhance the soil anti-scouring and anti-shearing capabilities, the effects of Herba Andrographitis hedgerows on soil erodibility and fractal features on sloping cropland in the Three Gorges Reservoir Area were investigated. Results showed that: (1) the clay particle accumulation around the hedgerows was significantly affected by the hedgerows; (2) the fractal dimension of soil particles was positively correlated with both silt and clay contents and had a negative linear correlation with sand content; (3) fine-grained content significantly influenced fractal dimension of the soil particles; (4) soil erodibility K was significantly and positively correlated with the sand content (correlation coefficient r=0.870), but significantly and negatively correlated with the silt content (r=-0.538), clay content (r=-0.739), organic carbon content (r=-0.603), the aggregation degree (r=-0.486), and soil fractal dimension (r=-0.538); and (5) the contents of organic matter and clay particles in the soil were found to be the effective indicators for soil erodibility at the Three Gorges Reservoir Area. The hedgerows may improve soil fractal features and decrease soil erodibility. The effective distance between hedgerows on a slope of 10° was less than 6 m.
Fractal harmonic law and waterproof/dustproof
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Kong Hai-Yan
2014-01-01
Full Text Available The fractal harmonic law admits that the friction between the pure water and the moving surface is the minimum when fractal dimensions of water in Angstrom scale are equal to fractal dimensions of the moving surface in micro scale. In the paper, the fractal harmonic law is applied to demonstrate the mechanism of waterproof/ dustproof. The waterproof phenomenon of goose feathers and lotus leaves is illustrated to verify our results and experimental results agree well with our theoretical analysis.
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.
Rheological and fractal hydrodynamics of aerobic granules.
Tijani, H I; Abdullah, N; Yuzir, A; Ujang, Zaini
2015-06-01
The structural and hydrodynamic features for granules were characterized using settling experiments, predefined mathematical simulations and ImageJ-particle analyses. This study describes the rheological characterization of these biologically immobilized aggregates under non-Newtonian flows. The second order dimensional analysis defined as D2=1.795 for native clusters and D2=1.099 for dewatered clusters and a characteristic three-dimensional fractal dimension of 2.46 depicts that these relatively porous and differentially permeable fractals had a structural configuration in close proximity with that described for a compact sphere formed via cluster-cluster aggregation. The three-dimensional fractal dimension calculated via settling-fractal correlation, U∝l(D) to characterize immobilized granules validates the quantitative measurements used for describing its structural integrity and aggregate complexity. These results suggest that scaling relationships based on fractal geometry are vital for quantifying the effects of different laminar conditions on the aggregates' morphology and characteristics such as density, porosity, and projected surface area. Copyright © 2015 Elsevier Ltd. All rights reserved.
Evertsz, Carl Joseph Gabriel
1989-01-01
Laplacian Fractals are physical models for the fractal properties encountered in a selected group of natural phenomena. The basis models in this class are the Dialectric Breakdown Model and the closely related Diffusion- Limited Aggregration model and Laplacian Random Walks. A full mathematical
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)
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
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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
2015-12-03
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.
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
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.
Pond fractals in a tidal flat.
Cael, B B; Lambert, Bennett; Bisson, Kelsey
2015-11-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.
Cael, B. B.; Lambert, Bennett; Bisson, Kelsey
2015-11-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of pond sizes over three orders of magnitude with a consistent fractal area-perimeter relationship. The data are consistent with the predictions of percolation theory for unscreened perimeters and scale-free cluster size distributions and are robust to alterations of the image processing procedure. The small spatial and temporal scales of these data suggest this easily observable system may serve as a useful model for investigating the evolution of pond geometries, while emphasizing the generality of fractal behavior in geophysical surfaces.
Jurgens, Hartmut; And Others
1990-01-01
The production and application of images based on fractal geometry are described. Discussed are fractal language groups, fractal image coding, and fractal dialects. Implications for these applications of geometry to mathematics education are suggested. (CW)
Fractal 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
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.
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Jun-Ting Qiu
2015-10-01
Full Text Available The high-grade uranium deposits in the Xiemisitan area, northwestern China, are genetically associated with the faulting of felsic volcanic or sub-volcanic rocks. Ferric iron alteration indicates that oxidizing hydrothermal fluids percolated through the rocks. In this study, we measured the gamma-ray intensities of rocks in the Xiemisitan area and we propose a hybrid method for the mapping of ferric iron alteration using concentration-area fractal modeling and spectral angle mapper. The method enables ferric iron alteration to be distinguished from potash-feldspar granitic rocks. The mapping results were integrated with structural data to assist with exploration for uranium in the study area. Using this approach, six prospective areas of mineralization were proposed. Of these areas, two anomalies with high gamma-ray intensities of 104 and 650 Uγ were identified and verified by field inspection. These observations suggest that Enhanced Thematic Mapper Plus images are a valuable tool that can improve the efficiency of uranium exploration.
Dimensional analysis, scaling and fractals
International Nuclear Information System (INIS)
Timm, L.C.; Reichardt, K.; Oliveira Santos Bacchi, O.
2004-01-01
Dimensional analysis refers to the study of the dimensions that characterize physical entities, like mass, force and energy. Classical mechanics is based on three fundamental entities, with dimensions MLT, the mass M, the length L and the time T. The combination of these entities gives rise to derived entities, like volume, speed and force, of dimensions L 3 , LT -1 , MLT -2 , respectively. In other areas of physics, four other fundamental entities are defined, among them the temperature θ and the electrical current I. The parameters that characterize physical phenomena are related among themselves by laws, in general of quantitative nature, in which they appear as measures of the considered physical entities. The measure of an entity is the result of its comparison with another one, of the same type, called unit. Maps are also drawn in scale, for example, in a scale of 1:10,000, 1 cm 2 of paper can represent 10,000 m 2 in the field. Entities that differ in scale cannot be compared in a simple way. Fractal geometry, in contrast to the Euclidean geometry, admits fractional dimensions. The term fractal is defined in Mandelbrot (1982) as coming from the Latin fractus, derived from frangere which signifies to break, to form irregular fragments. The term fractal is opposite to the term algebra (from the Arabic: jabara) which means to join, to put together the parts. For Mandelbrot, fractals are non topologic objects, that is, objects which have as their dimension a real, non integer number, which exceeds the topologic dimension. For the topologic objects, or Euclidean forms, the dimension is an integer (0 for the point, 1 for a line, 2 for a surface, and 3 for a volume). The fractal dimension of Mandelbrot is a measure of the degree of irregularity of the object under consideration. It is related to the speed by which the estimate of the measure of an object increases as the measurement scale decreases. An object normally taken as uni-dimensional, like a piece of a
Fractal dimensions and porosities of Zoogloea ramigera and Saccharomyces cerevisae aggregates.
Logan, B E; Wilkinson, D B
1991-08-05
The fractal nature microbial aggregates is a function of the type of microorganism and mixing conditions used to develop aggregates. We determined fractal dimensions from length-projected area (D(2)) and length-number scaling (D(3)) relationships. Aggregates of Zoogloea ramigera developed in rotating test tubes were both surface and mass fractals, with fractal dimensions of D(2) = 1.69 +/- 0.11 and D(3)= 1.79 +/- 0.28 (+/-standard deviation), respectively. When we grew this bacteria in a bench-top fermentor, aggregates maintained their surface fractal characteristics (D(2) = 1.78 +/- 0.11) but lost their mass fractal characteristics (D(3) = 2.99 +/- 0.36). Yeast aggregates (Saccharomyces cerevisae) grown in rotating tests tubes had higher average fractal dimensions than bacterial aggregates grown under physically identical conditions, and were also considered fractal (D(2) = 1.92 +/- 0.08 and D(3) = 2.66 +/- 0.34). Aggregates porosity can be expressed in term of a fractal dimensions, but average porosities are higher than expected. The porosities of yeast aggregates (0.9250-0.9966) were similar to porosities of bacterial aggregates (0.9250-0.9966) cultured under the same physical conditions, although bacterial aggregates developed in the reactor had higher average porosities (0.9857-0.9980). These results suggest that that scaling relationships based on fractal geometry may be more useful than equations derived from Euclidean geometry for quantifying the effects of different fluid mechanical environments on aggregates morphology and characteristics such as density, porosity, and projected surface area.
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.
Turbulent shear-flow over fractal arrays of surface-mounted cubes
Wise, Daniel J.; Brevis, Wernher; Sheffield Fluid Mechanics Group Team
2015-11-01
The turbulent shear-flow over a bottom-wall fully covered by periodic multi-scale arrangements of obstacles is examined via Particle Image Velocimetry (PIV), Volumetric 3D Velocimetry (V3V) and Acoustic Doppler Velocimetry (ADV) measurements. Three obstacle patterns are utilised, all based on different numbers of iterations of the Sierpinski carpet fractal. In each case 2D/3D velocity fields of the flow formed within the porous channels, namely the flow beneath the mean obstacle height, are presented and analysed with respect to standard statistics such as the mean, rms velocity profiles, and the Reynolds stresses. Point-wise measurements within the obstacle arrays reveal that the presence of the obstacles, and in particular their injection of energy at the associated wavelengths, has unexpected effects on the slope of the energy spectra within the turbulent porous flow. The region dominated by these spectral characteristics is defined. It is also shown that this behaviour is not observed in the outer flow.
Fractal Characteristics of Rock Fracture Surface under Triaxial Compression after High Temperature
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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.
Butala, Harshala D; Sadana, Ajit
2004-03-15
A fractal analysis is used to analyze the influence of: (a) electrostatic interactions on binding and dissociation rate coefficients for antibodies HH8, HH10, and HH26 in solution to hen egg-white lysozyme (HEL) immobilized on a sensor chip surface [Biophys. J. 83 (2002) 2946]; and (b) the binding and dissociation of recombinant Fab in solution to random NHS-coupled Cys-HEL and oriented thiol-coupled Cys-HEL immobilized on a sensor chip surface [Methods 20 (2000) 310]. Single- and dual-fractal models were employed to fit the data. Values of the binding and the dissociation rate coefficient(s) and the fractal dimensions were obtained from a regression analysis provided by Corel Quattro Pro 8.0 (Corel Corporation Limited, Ottawa, Canada. 1997). The binding rate coefficients are quite sensitive to the degree of heterogeneity on the sensor chip surface. It is of interest to compare the results obtained by the fractal analysis with that of the original analysis [Biophys. J. 83 (2002) 2946]. For example, as one goes from the binding of 21 nM HH10/HEL to the binding of 640 nM HH10/HEL(K97A), Sinha et al. [Biophys. J. 83 (2002) 29461 indicate that the enhancement of diffusional encounter rates may be due to 'electrostatic steering' (a long-range interaction). Our analysis indicates that there is an increase in the value of the fractal dimension, Df1 by a factor of 1.12 from a value of 2.133-2.385. This increase in the degree of heterogeneity on the surface leads to an increase in the binding rate coefficient, k1 by a factor of 1.59 from 12.92 to 20.57. The fractal analysis of binding and dissociation of recombinant Fab in solution to random NHS-coupled Cys-HEL and oriented thiol-coupled Cys-HEL immobilized on a sensor chip [Methods 20 (2000) 310] surface are consistent with the degree of heterogeneity present on the sensor chip surface for the random and the oriented case. As expected, the random case will exhibit a higher degree of heterogeneity than the oriented case
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
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.
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.
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.
Fractal patterns of fractures in granites
Velde, B.; Dubois, J.; Moore, D.; Touchard, G.
1991-01-01
Fractal measurements using the Cantor's dust method in a linear one-dimensional analysis mode were made on the fracture patterns revealed on two-dimensional, planar surfaces in four granites. This method allows one to conclude that: 1. (1)|The fracture systems seen on two-dimensional surfaces in granites are consistent with the part of fractal theory that predicts a repetition of patterns on different scales of observation, self similarity. Fractal analysis gives essentially the same values of D on the scale of kilometres, metres and centimetres (five orders of magnitude) using mapped, surface fracture patterns in a Sierra Nevada granite batholith (Mt. Abbot quadrangle, Calif.). 2. (2)|Fractures show the same fractal values at different depths in a given batholith. Mapped fractures (main stage ore veins) at three mining levels (over a 700 m depth interval) of the Boulder batholith, Butte, Mont. show the same fractal values although the fracture disposition appears to be different at different levels. 3. (3)|Different sets of fracture planes in a granite batholith, Central France, and in experimental deformation can have different fractal values. In these examples shear and tension modes have the same fractal values while compressional fractures follow a different fractal mode of failure. The composite fracture patterns are also fractal but with a different, median, fractal value compared to the individual values for the fracture plane sets. These observations indicate that the fractal method can possibly be used to distinguish fractures of different origins in a complex system. It is concluded that granites fracture in a fractal manner which can be followed at many scales. It appears that fracture planes of different origins can be characterized using linear fractal analysis. ?? 1991.
Nishimura, Ryo; Hyodo, Kengo; Sawaguchi, Haruna; Yamamoto, Yoshiaki; Nonomura, Yoshimune; Mayama, Hiroyuki; Yokojima, Satoshi; Nakamura, Shinichiro; Uchida, Kingo
2016-08-17
Double roughness structure, the origin of the lotus effect of natural lotus leaf, was successfully reproduced on a diarylethene microcrystalline surface. Static superwater-repellency and dynamic water-drop-bouncing were observed on the surface, in the manner of natural lotus leaves. Double roughness structure was essential for water-drop-bouncing. This ability was not observed on a single roughness microcrystalline surface showing the lotus effect of the same diarylethene derivative. The double roughness structure was reversibly controlled by alternating irradiation with UV and visible light.
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....
The Role of Resolution in the Estimation of Fractal Dimension Maps From SAR Data
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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.
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 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
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.
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
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.
A Fractal Model for the Capacitance of Lunar Dust and Lunar Dust Aggregates
Collier, Michael R.; Stubbs, Timothy J.; Keller, John W.; Farrell, William M.; Marshall, John; Richard, Denis Thomas
2011-01-01
Lunar dust grains and dust aggregates exhibit clumping, with an uneven mass distribution, as well as features that span many spatial scales. It has been observed that these aggregates display an almost fractal repetition of geometry with scale. Furthermore, lunar dust grains typically have sharp protrusions and jagged features that result from the lack of aeolian weathering (as opposed to space weathering) on the Moon. A perfectly spherical geometry, frequently used as a model for lunar dust grains, has none of these characteristics (although a sphere may be a reasonable proxy for the very smallest grains and some glasses). We present a fractal model for a lunar dust grain or aggregate of grains that reproduces (1) the irregular clumpy nature of lunar dust, (2) the presence of sharp points, and (3) dust features that span multiple scale lengths. We calculate the capacitance of the fractal lunar dust analytically assuming fixed dust mass (i.e. volume) for an arbitrary number of fractal levels and compare the capacitance to that of a non-fractal object with the same volume, surface area, and characteristic width. The fractal capacitance is larger than that of the equivalent non-fractal object suggesting that for a given potential, electrostatic forces on lunar dust grains and aggregates are greater than one might infer from assuming dust grains are sphericaL Consequently, electrostatic transport of lunar dust grains, for example lofting, appears more plausible than might be inferred by calculations based on less realistic assumptions about dust shape and associated capacitance.
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
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.
Harper, David William (Inventor)
2017-01-01
A structural support having fractal-stiffening and method of fabricating the support is presented where an optimized location of at least three nodes is predetermined prior to fabricating the structural support where a first set of webs is formed on one side of the support and joined to the nodes to form a first pocket region. A second set of webs is formed within the first pocket region forming a second pocket region where the height of the first set of webs extending orthogonally from the side of the support is greater than the second set of webs extending orthogonally from the support.
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
theorist in analyzing such relations. I find empirical illustration in the case of the development of electronic patient records in Danish health care. The role of the social theorist is explored through a comparison of the political and normative stance enabled, respectively, by a critical social theory......The relationship between the supposedly small-the micro-and the supposedly large-the macro-has been a long-standing concern in social theory. However, although many attempts have been made to link these two seemingly disjoint dimensions, in the present paper I argue against such an endeavour...... and a fractal social theory....
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
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
Berenschot, Johan W.; Jansen, Henricus V.; Tas, Niels Roelof
When it comes to high-performance filtration, separation, sunlight collection, surface charge storage or catalysis, the effective surface area is what counts. Highly regular fractal structures seem to be the perfect candidates, but manufacturing can be quite cumbersome. Here it is shown-–for the
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
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...
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.
International Nuclear Information System (INIS)
Guo Bin; Han Gaoyi; Li Miaoyu; Zhao Shizhen
2010-01-01
The ultrafine polymethylmethacrylate fibers containing gold nanoparticles have been prepared by using the electrospinning technique. Then the continuously coarse gold films formed by fractal-like thorny gold particles were deposited on the organic eletrospun fiber surface by an electroless process. The morphology of coarse gold films was characterized by scanning electron and transmission electron microscopy. The results revealed that the morphology of the gold particles was affected not only by the amount of gold seeds embedded in the organic fibers but also by the amount of gold deposited on the fiber's surfaces. The surface-enhanced Raman scattering (SERS) effect of the fibrous mats coated with gold films was evaluated by using Rhodamine B as an adsorbate. The results indicated that this kind of fibrous mat exhibited high and reproducible SERS activity and could be developed as highly sensitive SERS substrate.
A Fractal Perspective on Scale in Geography
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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.
The fractal harmonic law and its application to swimming suit
Directory of Open Access Journals (Sweden)
Kong Hai-Yan
2012-01-01
Full Text Available Decreasing friction force between a swimming suit and water is the key factor to design swimming suits. Water continuum mechanics forbids discontinuous fluids, but in angstrom scale water is indeed discontinuous. Swimming suit is smooth on large scale, but it is discontinuous when the scale becomes smaller. If fractal dimensions of swimming suit and water are the same, a minimum of friction force is predicted, which means fractal harmonization. In the paper, fractal harmonic law is introduced to design a swimsuit whose surface fractal dimensions on a macroscopic scale should be equal to or closed to the water's fractal dimensions on an Angstrom scale. Various possible microstructures of fabric are analyzed and a method to obtain perfect fractal structure of fabric is proposed by spraying nanofibers to its surface. The fractal harmonic law can be used to design a moving surface with a minimal friction.
International Nuclear Information System (INIS)
First, the cumulative deposition of the 137 Cs fallout in Austria resulting from the passage of the Chernobyl cloud has been investigated by applying correlation dimension and hyperbolic frequency distribution methods. For the analysis, a total of 1881 deposition values were used, which were collected by the Federal Environmental Agency of Austria and the Federal Ministry of Health, representing all available measurements of 137 Cs in soil made in Austria after the Chernobyl accident. From these data a hyperbolic exponent for the frequency distribution of 4.0 and a set of fractal correlation dimensions, which decreases from 1.426 ± 0.022 (for the whole network) to 0.706 ± 0.047 (for 137 Cs values ≥ 100 kBq/m 2 ), were derived, thus confirming that the fallout pattern can be described as a multifractal. Second, 222 Rn indoor, 218 Po and 222 Rn equilibrium equivalent concentrations (EEC) outdoor time series in Austria and Slovenia were determined using different chaos theory based measurements like Hurst's rescaled range analysis, capacity (fractal) dimension and the Lyapunov exponent. In addition, we tried to do short-term forecasting with a nonlinear prediction method. As one property of chaos is its determinism the forecasting algorithms applied here is based on this characteristic feature to detect deterministic chaos. For all our indoor air time series, only positive Lyapunov exponents were calculated, which is a hint to chaos. The Hurst exponents were well below 0.5 which indicates antipersistent behavior (past trends tend to reverse in the future). On the basis of our nonlinear prediction data, an estimation of the embedding dimensions could be estimated for the indoor air time series with some restrictions. For the outdoor 222 Rn EEC-time series, no proper embedding dimension could be found, which suggests non-chaotic dynamics; this allows a clear distinction between indoor and outdoor measurements. (author)
Volumes and surface areas of pendular rings
Rose, W.
1958-01-01
A packing of spheres is taken as a suitable model of porous media. The packing may be regular and the sphere size may be uniform, but in general, both should be random. Approximations are developed to give the volumes and surface areas of pendular rings that exist at points of sphere contact. From these, the total free volume and interfacial specific surface area are derived as expressive of the textural character of the packing. It was found that the log-log plot of volumes and surface areas of pendular rings vary linearly with the angle made by the line joining the sphere centers and the line from the center of the largest sphere to the closest edge of the pendular ring. The relationship, moreover, was found not to be very sensitive to variation in the size ratio of the spheres in contact. It also was found that the addition of pendular ring material to various sphere packings results in an unexpected decrease in the surface area of the boundaries that confine the resulting pore space. ?? 1958 The American Institute of Physics.
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.
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)
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
On semiautomatic estimation of surface area
DEFF Research Database (Denmark)
Dvorak, J.; Jensen, Eva B. Vedel
2013-01-01
. 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......In this paper, we propose a semiautomatic procedure for estimation of particle surface area. It uses automatic segmentation of the boundaries of the particle sections and applies different estimators depending on whether the segmentation was judged by a supervising expert to be satisfactory....... 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...
Controlled growth of polyaniline fractals on HOPG through potentiodynamic electropolymerization.
Bhattacharjya, Dhrubajyoti; Mukhopadhyay, Indrajit
2012-04-10
Polyaniline (PANI) in fractal dimension has been electrodeposited reproducibly on highly oriented pyrolytic graphite (HOPG) from 0.2 M aniline in 1 M aqueous HCl solution by potentiodynamic sweeping in the range of -0.2 to 0.76 V vs Ag/AgCl at room temperature. Fractal growth of PANI dendrimers is affected by diffusion limited polymerization (DLP) at a sweep rate of 15 mV s(-1) for 43 min. This type of PANI dendrimer is prepared for the first time on such large area HOPG substrate by electrochemical technique using rather simple cell setup. The fractal dimension has been determined by chronoamperometry (CA) and box counting technique and is found to vary from 1.4 to 1.9 with the duration of electropolymerization. The sweep rate, terminal oxidation potential, and the diverse surface anisotropy of the HOPG surface are found to be crucial factors in controlling the growth of such PANI fractals. © 2012 American Chemical Society
Characterization of high surface area silicon oxynitrides
International Nuclear Information System (INIS)
Lednor, P.W.; DeRuiter, R.; Emeis, K.A.
1992-01-01
In heterogenous catalysis, liquid or gaseous feedstocks are converted over a solid catalyst into more desirable products. Such processes form an essential part of the oil and petrochemical industries. The solid catalyst usually consists of an inorganic phase, with or without metal particles on the surface. Examples include platinum particles on gamma alumina (a reforming catalyst used in oil processing), chromium particles on silica (an ethylene polymerization catalyst) and zeolites or amorphous silica-aluminas (used as solid acids).Oxides have been widely investigated in catalysis, and silica, alumina, and aluminosilicates find application commercially on a large scale. On the other hand, non-oxide materials such as nitrides, carbides and borides have been relatively little investigated. The main reason for this has been the lack of routes to the high surface area forms usually required in catalysis. However, this situation has changed significantly in recent years, due to the interest in high surface area non-oxides as precursors to fully dense ceramics; in this paper, the authors have reviewed synthetic routes to high surface area non-oxides
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.
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.
Estimation of surface area and surface area measure of three-dimensional sets from digitizations
DEFF Research Database (Denmark)
Ziegel, Johanna; Kiderlen, Markus
2010-01-01
A local method for estimating surface area and surface area measure of three-dimensional objects from discrete binary images is presented. A weight is assigned to each 2 × 2 × 2 configuration of voxels and the total surface area of an object is given by summation of the local area contributions....... The method is based on an exact asymptotic result that holds for increasing resolution of the digitization. It states that the number of occurrences of a 2 × 2 × 2 configuration is asymptotically proportional to an integral of its “h-function” with respect to the surface area measure of the object. We find...
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.
Barton, Ray
1990-01-01
Presented is an educational game called "The Chaos Game" which produces complicated fractal images. Two basic computer programs are included. The production of fractal images by the Sierpinski gasket and the Chaos Game programs is discussed. (CW)
Chaos, Fractals, and Polynomials.
Tylee, J. Louis; Tylee, Thomas B.
1996-01-01
Discusses chaos theory; linear algebraic equations and the numerical solution of polynomials, including the use of the Newton-Raphson technique to find polynomial roots; fractals; search region and coordinate systems; convergence; and generating color fractals on a computer. (LRW)
Neutron scattering from fractals
DEFF Research Database (Denmark)
Kjems, Jørgen; Freltoft, T.; Richter, D.
1986-01-01
The scattering formalism for fractal structures is presented. Volume fractals are exemplified by silica particle clusters formed either from colloidal suspensions or by flame hydrolysis. The determination of the fractional dimensionality through scattering experiments is reviewed, and recent small...
Thamrin, Cindy; Stern, Georgette; Frey, Urs
2010-06-01
There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment. Copyright 2010 Elsevier Ltd. All rights reserved.
Fraboni, Michael; Moller, Trisha
2008-01-01
Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…
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
Risović, Dubravko; Pavlović, Zivko
2013-01-01
Processing of gray scale images in order to determine the corresponding fractal dimension is very important due to widespread use of imaging technologies and application of fractal analysis in many areas of science, technology, and medicine. To this end, many methods for estimation of fractal dimension from gray scale images have been developed and routinely used. Unfortunately different methods (dimension estimators) often yield significantly different results in a manner that makes interpretation difficult. Here, we report results of comparative assessment of performance of several most frequently used algorithms/methods for estimation of fractal dimension. To that purpose, we have used scanning electron microscope images of aluminum oxide surfaces with different fractal dimensions. The performance of algorithms/methods was evaluated using the statistical Z-score approach. The differences between performances of six various methods are discussed and further compared with results obtained by electrochemical impedance spectroscopy on the same samples. The analysis of results shows that the performance of investigated algorithms varies considerably and that systematically erroneous fractal dimensions could be estimated using certain methods. The differential cube counting, triangulation, and box counting algorithms showed satisfactory performance in the whole investigated range of fractal dimensions. Difference statistic is proved to be less reliable generating 4% of unsatisfactory results. The performances of the Power spectrum, Partitioning and EIS were unsatisfactory in 29%, 38%, and 75% of estimations, respectively. The results of this study should be useful and provide guidelines to researchers using/attempting fractal analysis of images obtained by scanning microscopy or atomic force microscopy. © Wiley Periodicals, Inc.
Turbulent premixed flames on fractal-grid-generated turbulence
Soulopoulos, N.; Kerl, J.; Sponfeldner, T.; Beyrau, F.; Hardalupas, Y.; Taylor, A. M. K. P.; Vassilicos, J. C.
2013-12-01
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.
Cael, B. B.; Bisson, Kelsey; Lambert, Bennett Spencer
2015-01-01
Studies over the past decade have reported power-law distributions for the areas of terrestrial lakes and Arctic melt ponds, as well as fractal relationships between their areas and coastlines. Here we report similar fractal structure of ponds in a tidal flat, thereby extending the spatial and temporal scales on which such phenomena have been observed in geophysical systems. Images taken during low tide of a tidal flat in Damariscotta, Maine, reveal a well-resolved power-law distribution of p...
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.
Modelo fractal de substâncias húmicas Fractal model of humic substances
Directory of Open Access Journals (Sweden)
Alessandro Costa da Silva
2001-10-01
Full Text Available A teoria fractal, por meio da determinação da dimensão fractal (D, tem sido considerada como uma alternativa para explicar a conforma��ão de agregados moleculares. Sua utilização no estudo de substâncias húmicas (SH reside na tentativa de descrever (representar a estrutura ramificada ou a superfície rugosa e distorcida destas substâncias. A presença de um modelo fractal por sistemas naturais implica que este pode ser decomposto em partes, em que cada uma, subseqüentemente, é cópia do todo. Do ponto de vista experimental, a dimensão fractal de sistemas húmicos pode ser determinada a partir de técnicas como turbidimetria, raios x, espalhamento de neutrons, dentre outras. Este trabalho pretende facilitar o entendimento sobre a aplicação de fractais ao estudo conformacional de SH, introduzindo conceitos e informações sobre o fundamento dos modelos fractais, bem como sobre o uso da técnica turbidimétrica na determinação do valor D.Fractal theoria application by determination of fractal dimension has been considered an alternative tool to explain the conformation of molecular aggregates. Its utilization in the study of humic substances (HS aims the attempt to describe the limbed structure or the rugous and distorced surface of these substances. The presence of fractal models indicates that the system may be decomposed in parts, each part being a copy of the whole. In the experimental point of view the fractals models of natural systems may be measured through techniques as turbidimetry, x- ray and neutrons scattering. This paper seeks to facilitate the understanding on the application of the fractals in the conformational study of HS, supply information about fractal models foundation and use of the turbidimetry in the determination of fractal dimension.
Facile fabrication of dendritic silver structures and their surface ...
Indian Academy of Sciences (India)
The dendritic or fractal Ag nanostructures have attracted the attention of scientists recently due to their attractive supramolecular structures, large surface area and excellent connectivity between the different parts of the structures. Significantly, it has been established that dendritic or fractal Ag nanostructures are an excel-.
Pulse regime in formation of fractal fibers
Energy Technology Data Exchange (ETDEWEB)
Smirnov, B. M., E-mail: bmsmirnov@gmail.com [Joint Institute for High Temperatures (Russian Federation)
2016-11-15
The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gas flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.
Fractal Image Informatics: from SEM to DEM
Oleschko, K.; Parrot, J.-F.; Korvin, G.; Esteves, M.; Vauclin, M.; Torres-Argüelles, V.; Salado, C. Gaona; Cherkasov, S.
2008-05-01
In this paper, we introduce a new branch of Fractal Geometry: Fractal Image Informatics, devoted to the systematic and standardized fractal analysis of images of natural systems. The methods of this discipline are based on the properties of multiscale images of selfaffine fractal surfaces. As proved in the paper, the image inherits the scaling and lacunarity of the surface and of its reflectance distribution [Korvin, 2005]. We claim that the fractal analysis of these images must be done without any smoothing, thresholding or binarization. Two new tools of Fractal Image Informatics, firmagram analysis (FA) and generalized lacunarity (GL), are presented and discussed in details. These techniques are applicable to any kind of image or to any observed positive-valued physical field, and can be used to correlate between images. It will be shown, by a modified Grassberger-Hentschel-Procaccia approach [Phys. Lett. 97A, 227 (1983); Physica 8D, 435 (1983)] that GL obeys the same scaling law as the Allain-Cloitre lacunarity [Phys. Rev. A 44, 3552 (1991)] but is free of the problems associated with gliding boxes. Several applications are shown from Soil Physics, Surface Science, and other fields.
Fractal dimension for fractal structures: A Hausdorff approach
Fernández-Martínez, M.; Sánchez-Granero, M.A.
2012-01-01
This paper provides a new model to compute the fractal dimension of a subset on a generalized-fractal space. Recall that fractal structures are a perfect place where a new definition of fractal dimension can be given, so we perform a suitable discretization of the Hausdorff theory of fractal dimension. We also find some connections between our definition and the classical ones and also with fractal dimensions I & II (see http://arxiv.org/submit/0080421/pdf). Therefore, we generalize them and ...
Formation of fractals by the self-assembly of interpolymer adducts of ...
Indian Academy of Sciences (India)
vinylpyrrolidone) in presence of sodium chloride or potassium chloride form highly ordered fractal patterns in films on glass surface on drying at ambient temperature. The structure, morphology and the conditions under which the formation of fractal patterns ...
Exploring Fractals in the Classroom.
Naylor, Michael
1999-01-01
Describes an activity involving six investigations. Introduces students to fractals, allows them to study the properties of some famous fractals, and encourages them to create their own fractal artwork. Contains 14 references. (ASK)
Fractals: To Know, to Do, to Simulate.
Talanquer, Vicente; Irazoque, Glinda
1993-01-01
Discusses the development of fractal theory and suggests fractal aggregates as an attractive alternative for introducing fractal concepts. Describes methods for producing metallic fractals and a computer simulation for drawing fractals. (MVL)
Representing fractals by superoscillations
International Nuclear Information System (INIS)
Berry, M V; Morley-Short, S
2017-01-01
Fractals provide an extreme test of representing fine detail in terms of band-limited functions, i.e. by superoscillations. We show that this is possible, using the example of the Weierstrass nondifferentiable fractal. If this is truncated at an arbitrarily fine scale, it can be expressed to any desired accuracy with a simple superoscillatory function. In illustrative simulations, fractals truncated with fastest frequency 2 16 are easily represented by superoscillations with fastest Fourier frequency 1. (letter)
Usefulness of fractal analysis for the diagnosis of periodontitis
International Nuclear Information System (INIS)
Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung
2001-01-01
To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979±0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006±0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis
Usefulness of fractal analysis for the diagnosis of periodontitis
Energy Technology Data Exchange (ETDEWEB)
Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung [Dankook Univ. School of Dentistry, Seoul (Korea, Republic of)
2001-03-15
To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979{+-}0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006{+-}0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.
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
Fractal Geometry of Architecture
Lorenz, Wolfgang E.
In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.
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.
Method for treatment of a surface area of steel
Bhowmik, S.; Aaldert, P.J.
2009-01-01
The invention relates to a method for treatment of a surface area of steel by polishing said surface area and performing a plasma treatment of said surface area wherein the plasma treatment is performed at at least atmospheric conditions and wherein the plasma treatment is carried out at a power of
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Categorization of fractal plants
International Nuclear Information System (INIS)
Chandra, Munesh; Rani, Mamta
2009-01-01
Fractals in nature are always a result of some growth process. The language of fractals which has been created specifically for the description of natural growth process is called L-systems. Recently, superior iterations (essentially, investigated by Mann [Mann WR. Mean value methods in iteration. Proc Am Math Soc 1953;4:506-10 [MR0054846 (14,988f)
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed. Copyright © 2014 Elsevier B.V. All rights reserved.
Studying fractal geometry on submicron length scales by small-angle scattering
International Nuclear Information System (INIS)
Wong, P.; Lin, J.
1988-01-01
Recent studies have shown that internal surfaces of porous geological materials, such as rocks and lignite coals, can be described by fractals down to atomic length scales. In this paper, the basic properties of self-similar and self-affine fractals are reviewed and how fractal dimensions can be measured by small-angle scattering experiments are discussed
Electromagnetic fields in fractal continua
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Mena, Baltasar [Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F. (Mexico); Patiño, Julián [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Morales, Daniel [Instituto Mexicano del Petróleo, México D.F., 07730 Mexico (Mexico)
2013-04-01
Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum Φ{sub D}{sup 3}⊂E{sup 3} with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space F{sup α} accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.
Directory of Open Access Journals (Sweden)
Jie Fan
2015-01-01
Full Text Available The relationship between the unique internal structure of biomimic woven fabric and its moisture management property is investigated using fractal derivative method. The biomimic fabric exhibits a fractal hierarchic inner structure, and its fractal hierarchy can be further extended by fleece finishing treatment on both surfaces of the fabric. Fractal derivative analysis indicates that the fuzzy biomimic fabric with a higher hierarchic construction after fleece finishing performs better in moisture permeability, and the result was proved by experimental tests.
Nondestructive, stereological estimation of canopy surface area
DEFF Research Database (Denmark)
Wulfsohn, Dvora-Laio; Sciortino, Marco; Aaslyng, Jesper M.
2010-01-01
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...
Surface texturing of crystalline silicon and effective area measurement
Sun, Tietun; Chen, Dong; Chui, Rongqiang
2000-11-01
In this paper, the surface area of solar cell is determined by the capacitance measurements of MOS structure. The texture etching technology can be controlled according to the change of silicon surface area, furthermore, the textured silicon surface and interface characteristic of solar cell can be studied by measuring the relationship of capacitance and voltage for MOS structure.
Hand surface area as a percentage of body surface area in Asian children: a pilot study.
Choi, Hyuk; Park, Man Sik; Lee, Heung-Man
2011-09-01
The hand surface area (HSA) of one hand has been estimated as 1% of the body surface area (BSA). This does change with the patient's age, gender, and body mass index (BMI). There are many HSA studies done on adult populations, but fewer done on children. Our hypothesis in this study is that the general HSA equation for Caucasian adults cannot be applied as accurately to children and Asian people. HSA was defined as the area of the palm without fingers in this study. Children are in a stage of growth. If a child's hand growth ratio is not the same as that of an adult, the result of HSA/BSA calculation could be different. We undertook this study to determine whether or not there were any differences in HSA/BSA among Korean children (7-18 years) and adults (20-60 years), and compared our results with western data. A total of 186 boys aged between 7 and 18 years, were recruited for this study; their HSA was measured, directly. A total of 186 adults aged between 20 and 60 years were selected as well. BSA was calculated only for volunteers in subjects who HSA had been measured. From these results, HSA/BSA was calculated. HSA/BSA ratio of Korean boys was 0.69±0.05%, which was less than 1%. It is suggested that the ratio of the western data may not be applicable to Asian children, particularly, Korean children. HSA/BSA ratio can be applied in administration of drug doses and estimation of the area of burns. Copyright © 2011 Elsevier Ltd and ISBI. All rights reserved.
Directory of Open Access Journals (Sweden)
Kyril Tintarev
2007-05-01
Full Text Available The paper studies energy functionals on quasimetric spaces, defined by quadratic measure-valued Lagrangeans. This general model of medium, known as metric fractals, includes nested fractals and sub-Riemannian manifolds. In particular, the quadratic form of the Lagrangean satisfies Sobolev inequalities with the critical exponent determined by the (quasimetric homogeneous dimension, which is also involved in the asymptotic distribution of the form's eigenvalues. This paper verifies that the axioms of the metric fractal are preserved by space products, leading thus to examples of non-differentiable media of arbitrary intrinsic dimension.
SurfaceWater Source Protection Areas (SPAs)
Vermont Center for Geographic Information — Source Protection Area (SPA) boundaries have been located on RF 24000 & RF 25000 scale USGS topographic maps by Water Supply Division (DEC) and VT Dept of Health...
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.
The Surface Chemical Properties of Novel High Surface Area Solids ...
African Journals Online (AJOL)
during zeolite synthesis.22 Because raw fly ash has large quanti- ties of a host of elements, many of these will act as nucleation sites, which results in many small crystals rather than a few large ones. Acid etching removed the needle-like structures on the particle surfaces, revealing a porous underlying structure. (Fig. 1c).
[Recent progress of research and applications of fractal and its theories in medicine].
Cai, Congbo; Wang, Ping
2014-10-01
Fractal, a mathematics concept, is used to describe an image of self-similarity and scale invariance. Some organisms have been discovered with the fractal characteristics, such as cerebral cortex surface, retinal vessel structure, cardiovascular network, and trabecular bone, etc. It has been preliminarily confirmed that the three-dimensional structure of cells cultured in vitro could be significantly enhanced by bionic fractal surface. Moreover, fractal theory in clinical research will help early diagnosis and treatment of diseases, reducing the patient's pain and suffering. The development process of diseases in the human body can be expressed by the fractal theories parameter. It is of considerable significance to retrospectively review the preparation and application of fractal surface and its diagnostic value in medicine. This paper gives an application of fractal and its theories in the medical science, based on the research achievements in our laboratory.
Fractal generalized Pascal matrices
Burlachenko, E.
2016-01-01
Set of generalized Pascal matrices whose elements are generalized binomial coefficients is considered as an integral object. The special system of generalized Pascal matrices, based on which we are building fractal generalized Pascal matrices, is introduced. Pascal matrix (Pascal triangle) is the Hadamard product of the fractal generalized Pascal matrices. The concept of zero generalized Pascal matrices, an example of which is the Pascal triangle modulo 2, arise in connection with the system ...
Fractal Electromagnetic Showers
Anchordoqui, L. A.; Kirasirova, M.; McCauley, T. P.; Paul, T.; Reucroft, S.; Swain, J. D.
2000-01-01
We study the self-similar structure of electromagnetic showers and introduce the notion of the fractal dimension of a shower. Studies underway of showers in various materials and at various energies are presented, and the range over which the fractal scaling behaviour is observed is discussed. Applications to fast shower simulations and identification, particularly in the context of extensive air showers, are also discussed.
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
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
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.
Sánchez, Iván; Uzcátegui, Gladys
2011-04-01
To systematically review applications of fractal geometry in different aspects of dental practice. In this review, we present a short introduction to fractals and specifically address the following topics: treatment and healing monitoring, dental materials, dental tissue, caries, osteoporosis, periodontitis, cancer, Sjögren's syndrome, diagnosis of several other conditions and a discussion on the reliability of FD determinations from dental radiographs. Google Scholar, Ovid MEDLINE, ScienceDirect, etc. (up to August 2010). The review considered original studies, reviews and conference proceedings, published in English or Spanish. Abstracts and posters were not taken into account. Fractal geometry has found plenty of applications in several branches of dental practice. It provides a way to quantify the complexity of structures. Whereas one desires to study a radiograph, an histological section or the signal from a transducer, there are several methods available to determine the degree of complexity using fractal analysis. Several pathological conditions can alter the complexity of anatomical structures, and this change can be detectable with the help of fractal parameters. Although during the last two decades there have been plenty of works on the field, reported cases having enough reproducibility, with different groups showing similar results are not very common. Further replications are needed before we can establish statistically significant correlations amongst fractal parameters and pathological conditions. Copyright © 2011 Elsevier Ltd. All rights reserved.
Wideband Monopole Fractal Heptagonal Antenna Implementation in X-Band Frequency Range
Iqbal, Muhammad Naeem; Ur-Rahman, Hamood; Tauqeer, T.; Ramer, Rodica
2017-10-01
A wideband heptagonal fractal monopole antenna with coplanar waveguide feed is designed and fabricated in X-band frequency range. Comparison of heptagonal fractal monopole antennas with two different substrates to achieve optimum efficiency for UWB applications is presented. FR4 and RT/Duroid 5880 substrates are used for antenna design and fabrication. Four iterations of base shape are used. Fractal antenna has omni-directional radiation pattern. Simulated and measured results showed that monopole fractal antenna with RT/Duroid 5880 substrate has better performance than fractal antenna with FR4 substrate in terms of bandwidth and return loss. Major application area of proposed antenna is wireless body area networks.
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.
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…
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.
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...
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
Fractals, Their importance in geology. Simulation of fractal natural patterns
Gumiel Martínez, Pablo
1996-01-01
An introduction to the Symposium 16 on Fractals and Geology is presented in this contribution. A summary on fractal concepts and natural geometrical fractal patterns are showed. Finally, computational simulations of natural geological structures are performed, using techniques of Iterated Function Systems (IFS of Barnsley, 1988)
The fractal forest: fractal geometry and applications in forest science.
Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary
1994-01-01
Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.
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.
Chaos, fractals, and our concept of disease.
Varela, Manuel; Ruiz-Esteban, Raul; Mestre de Juan, Maria Jose
2010-01-01
The classic anatomo-clinic paradigm based on clinical syndromes is fraught with problems. Nevertheless, for multiple reasons, clinicians are reluctant to embrace a more pathophysiological approach, even though this is the prevalent paradigm under "which basic sciences work. In recent decades, nonlinear dynamics ("chaos theory") and fractal geometry have provided powerful new tools to analyze physiological systems. However, these tools are embedded in the pathophysiological perspective and are not easily translated to our classic syndromes. This article comments on the problems raised by the conventional anatomo-clinic paradigm and reviews three areas in which the influence of nonlinear dynamics and fractal geometry can be especially prominent: disease as a loss of complexity, the idea of homeostasis, and fractals in pathology.
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...
Insights on the fractal-fracture behaviour relationship
Directory of Open Access Journals (Sweden)
Rodrigues José de Anchieta
1998-01-01
Full Text Available The fractals theory has been increasingly applied in the field of materials science and engineering. Models of fractal lines and surfaces have been generated to describe the microstructural features of materials. Special interest is placed upon a description of the fracture surface based on a fractal geometry in order to understand the crack path in materials. Several papers have demonstrated the relationship between the fractal dimension of a fracture surface and the values of roughness and fracture toughness. In this work an extension of the theory of fractals for ceramic materials is proposed, to which the crack deflection toughening mechanism is thought to be related. In order to accomplish this objective, a review describing the concept of fractals and its relationship with the fracture toughness is presented. In the following part, a correlation between fractal dimension, total energy of fracture and the average resistance to crack propagation is proposed; all these parameters being dependent on the history and on the complexity of crack propagation path.
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Results are presented of a preliminary investigation of the fractal nature of the plan-view shapes of lava flows in Hawaii (based on field measurements and aerial photographs), as well as in Idaho and the Galapagos Islands (using aerial photographs only). The shapes of the lava flow margins are found to be fractals: lava flow shape is scale-invariant. This observation suggests that nonlinear forces are operating in them because nonlinear systems frequently produce fractals. A'a and pahoehoe flows can be distinguished by their fractal dimensions (D). The majority of the a'a flows measured have D between 1.05 and 1.09, whereas the pahoehoe flows generally have higher D (1.14-1.23). The analysis is extended to other planetary bodies by measuring flows from orbital images of Venus, Mars, and the moon. All are fractal and have D consistent with the range of terrestrial a'a and have D consistent with the range of terrestrial a'a and pahoehoe values.
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....
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...
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
... in Nigeria) showed good correlation with the geological maps of the areas. The results also indicated that basement rocks can generally be represented by scaling exponents with values ranging between -3.0 and -2.0. Keywords: Fractal, dimension, susceptibility, spectra, scaling exponent. Nigerian Journal of Physics Vol.
Fractal radar scattering from soil
Oleschko, Klaudia; Korvin, Gabor; Figueroa, Benjamin; Vuelvas, Marco Antonio; Balankin, Alexander S.; Flores, Lourdes; Carreón, Dora
2003-04-01
A general technique is developed to retrieve the fractal dimension of self-similar soils through microwave (radar) scattering. The technique is based on a mathematical model relating the fractal dimensions of the georadargram to that of the scattering structure. Clear and different fractal signatures have been observed over four geosystems (soils and sediments) compared in this work.
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.
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...
Directory of Open Access Journals (Sweden)
T.-W. Wang
1996-09-01
Full Text Available Fractal theory is applied in a quantitative analysis of geomagnetic storms. Fractal dimensions (D of the attractor for storm data from the Beijing observatory (40.0°N, 116.2°E using several time intervals are calculated. A maximum value of 1.4 has been obtained for a geomagnetic storm; on quite days the dimension is only slightly larger than 0.5. Data from two storms are analyzed here. Results show that a combination of both D and the magnetic index, k, can perhaps describe the degree of solar disturbance better than the single parameter k.
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....
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.
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.
A Fractal Model for the Maximum Droplet Diameter in Gas-Liquid Mist Flow
Directory of Open Access Journals (Sweden)
Xiao-Hua Tan
2013-01-01
Full Text Available Distribution characteristics of liquid droplet size are described using the fractal theory for liquid droplet size distribution in gas-liquid mist flow. Thereby, the fractal expression of the maximum droplet diameter is derived. The fractal model for maximum droplet diameter is obtained based on the internal relationship between maximum droplet diameter and the droplet fractal dimension, which is obtained by analyzing the balance between total droplet surface energy and total gas turbulent kinetic energy. Fractal model predictions of maximum droplet diameter agree with the experimental data. Maximum droplet diameter and droplet fractal dimension are both found to be related to the superficial velocity of gas and liquid. Maximum droplet diameter decreases with an increase in gas superficial velocity but increases with an increase in liquid superficial velocity. Droplet fractal dimension increases with an increase in gas superficial velocity but decreases with an increase in liquid superficial velocity. These are all consistent with the physical facts.
Fractal elements and their applications
Gil’mutdinov, Anis Kharisovich; El-Khazali, Reyad
2017-01-01
This book describes a new type of passive electronic components, called fractal elements, from a theoretical and practical point of view. The authors discuss in detail the physical implementation and design of fractal devices for application in fractional-order signal processing and systems. The concepts of fractals and fractal signals are explained, as well as the fundamentals of fractional calculus. Several implementations of fractional impedances are discussed, along with comparison of their performance characteristics. Details of design, schematics, fundamental techniques and implementation of RC-based fractal elements are provided. .
Assessment of textural differentiations in forest resources in Romania using fractal analysis
DEFF Research Database (Denmark)
Andronache, Ion; Fensholt, Rasmus; Ahammer, Helmut
2017-01-01
Deforestation and forest degradation have several negative effects on the environment including a loss of species habitats, disturbance of the water cycle and reduced ability to retain CO2, with consequences for global warming. We investigated the evolution of forest resources from development...... regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis.We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas......, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested...
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.
Moisture diffusivity in structure of random fractal fiber bed
International Nuclear Information System (INIS)
Zhu, Fanglong; Zhou, Yu; Feng, Qianqian; Xia, Dehong
2013-01-01
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.
Effect of impervious surface area and vegetation changes on mean ...
African Journals Online (AJOL)
This land use or land cover changes are also thought to affect the climate of the Tshwane metropolis as is evidenced by heat waves in 2013 and 2014. This paper describes how vegetation and impervious surface area (ISA) or built up areas were classified from Landsat 8 LCDM, 2013, and Landsat 7 ETM+, 2003 images ...
Hsü, K J; Hsü, A J
1990-01-01
Music critics have compared Bach's music to the precision of mathematics. What "mathematics" and what "precision" are the questions for a curious scientist. The purpose of this short note is to suggest that the mathematics is, at least in part, Mandelbrot's fractal geometry and the precision is the deviation from a log-log linear plot.
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...
Bottorff, Mark; Ferland, Gary
2001-03-01
This paper examines whether a fractal cloud geometry can reproduce the emission-line spectra of active galactic nuclei (AGNs). The nature of the emitting clouds is unknown, but many current models invoke various types of magnetohydrodynamic confinement. Recent studies have argued that a fractal distribution of clouds, in which subsets of clouds occur in self-similar hierarchies, is a consequence of such confinement. Whatever the confinement mechanism, fractal cloud geometries are found in nature and may be present in AGNs too. We first outline how a fractal geometry can apply at the center of a luminous quasar. Scaling laws are derived that establish the number of hierarchies, typical sizes, column densities, and densities. Photoionization simulations are used to predict the integrated spectrum from the ensemble. Direct comparison with observations establishes all model parameters so that the final predictions are fully constrained. Theory suggests that denser clouds might form in regions of higher turbulence and that larger turbulence results in a wider dispersion of physical gas densities. An increase in turbulence is expected deeper within the gravitational potential of the black hole, resulting in a density gradient. We mimic this density gradient by employing two sets of clouds with identical fractal structuring but different densities. The low-density clouds have a lower column density and large covering factor similar to the warm absorber. The high-density clouds have high column density and smaller covering factor similar to the broad-line region (BLR). A fractal geometry can simultaneously reproduce the covering factor, density, column density, BLR emission-line strengths, and BLR line ratios as inferred from observation. Absorption properties of the model are consistent with the integrated line-of-sight column density as determined from observations of X-ray absorption, and when scaled to a Seyfert galaxy, the model is consistent with the number of
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 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
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.
Directory of Open Access Journals (Sweden)
Alexander J. Bies
2016-07-01
Full Text Available Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D and power spectrum decay rate (β. Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. Here, we determine the relationship between D and β for 1- and 2-dimensional fractals. We find that for 1-dimensional fractals, measurements of D and β obey the derived relationship. Similarly, in 2-dimensional fractals, measurements along any straight-line path across the fractal’s surface obey the mathematically derived relationship. However, the standard approach of vision researchers is to measure β of the surface after 2-dimensional Fourier decomposition rather than along a straight-line path. This surface technique provides measurements of β that do not obey the mathematically derived relationship with D. Instead, this method produces values of β that imply that the fractal’s surface is much smoother than the measurements along the straight lines indicate. To facilitate communication across disciplines, we provide empirically derived equations for relating each measure of β to D. Finally, we discuss implications for future research on topics including stress reduction and the perception of motion in the context of a generalized equation relating β to D.
Students' and Teachers' Application of Surface Area to Volume Relationships
Taylor, Amy R.; Jones, M. Gail
2013-02-01
The National Science Education Standards emphasize teaching unifying concepts and processes such as basic functions of living organisms, the living environment, and scale (NRC 2011). Scale includes understanding that different characteristics, properties, or relationships within a system might change as its dimensions are increased or decreased (NRC 2011). One such relationship involves surface area to volume which is a pervasive concept that can be found throughout different sciences. This concept is important for students to not only understand the association of the two, but to also be able to apply this relationship in science contexts. The purpose of this study is to investigate the factors that influence the understanding surface area to volume relationships. This study examined middle school students', high school students', and science teachers' logical thinking skills (including proportional reasoning), visual-spatial skills, and understandings of surface area to volume relationships. Regression results indicated that participants' reasoning abilities and components of visual-spatial skills could be possible predictors for one's ability to understand surface area to volume relationships. Implications for teaching scale concepts such as surface area to volume relationships in the science classroom are discussed.
Surface deformation of the secondary former mining areas
Directory of Open Access Journals (Sweden)
Tadeusz Głowacki
2013-09-01
Full Text Available The paper discuss the problem of secondary deformation observed on the surface of the land in the area of the old, non-existent copper and coal mines. The authors discuss the formation of the deformation in the final period of the mine, and after his arrest, after the close of any work of protecting the surface area of influence of mining activities. Discusses the reduction of the surface of the example of two disused mines: mining copper “Konrad” in Iwiny and “Thorez” in Walbrzych, an old coal mine. In the first part of the paper discusses a brief history of the creation of old copper basin and the Lower Silesian coal basin. It then discusses the formation of deformation processes in mining areas. Conducting continuous surveying allows you to monitor changes in the formation of land, in the paper indicate the source of the vertical displacements after ending of operation, the closure of the mine and stopped all work safety. In the area of Lower Silesia there are many remnants of disused mines, surface geodetic measurements show a constant activity in post-mining areas and the need to control the formation of the surface.
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.
Fractal analysis of the fractal ultra-wideband signals
International Nuclear Information System (INIS)
Chernogor, L.F.; Lazorenko, O.V.; Onishchenko, A.A.
2015-01-01
The results of fractal analysis of the fractal ultra-wideband (FUWB) signals were proposed. With usage of the continuous wavelet transform the time-frequency structure of that signals was investigated. Calculating the box and the regularization dimensions for each model signal with various its parameters values, three different estimators were applied. The optimal estimations of the fractal dimension value for each FUWB signal model were defined
High surface area electrode for high efficient microbial electrosynthesis
Nie, Huarong; Cui, Mengmeng; Lu, Haiyun; Zhang, Tian; Russell, Thomas; Lovley, Derek
2012-02-01
Microbial electrosynthesis, a process in which microorganisms directly accept electrons from an electrode to convert carbon dioxide and water into multi carbon organic compounds, affords a novel route for the generation of valuable products from electricity or even wastewater. The surface area of the electrode is critical for high production. A biocompatible, highly conductive, three-dimensional cathode was fabricated from a carbon nanotube textile composite to support the microorganism to produce acetate from carbon dioxide. The high surface area and macroscale porous structure of the intertwined CNT coated textile ?bers provides easy microbe access. The production of acetate using this cathode is 5 fold larger than that using a planar graphite electrode with the same volume. Nickel-nanowire-modified carbon electrodes, fabricated by microwave welding, increased the surface area greatly, were able to absorb more bacteria and showed a 1.5 fold increase in performance
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, cultur...... for determining bacterial activity might provide a means for future monitoring and assessment of microbial water quality in aquaculture farming systems......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......-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...
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.
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.
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.
Surface barrier silicon detectors with a large active area
International Nuclear Information System (INIS)
Kim, Y.; Husimi, K.; Ikeda, Y.; Kim, C.; Ohkawa, S.; Sakai, T.
1985-01-01
Surface barrier silicon detectors with a large active area have been produced by using high resistive n-type silicon crystals, diameters of which are 3 to 5 inches. High quality detectors with a low leakage current and a low noise were achieved by developing the improved surface treatment. Characteristics of detectors obtained are good in energy resolution compared with conventional large area Si(Li) detectors. It has also been confirmed that local dead region is not found from measuring results of photo-pulse injection
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...
Determining Surface Roughness in Urban Areas Using Lidar Data
Holland, Donald
2009-01-01
An automated procedure has been developed to derive relevant factors, which can increase the ability to produce objective, repeatable methods for determining aerodynamic surface roughness. Aerodynamic surface roughness is used for many applications, like atmospheric dispersive models and wind-damage models. For this technique, existing lidar data was used that was originally collected for terrain analysis, and demonstrated that surface roughness values can be automatically derived, and then subsequently utilized in disaster-management and homeland security models. The developed lidar-processing algorithm effectively distinguishes buildings from trees and characterizes their size, density, orientation, and spacing (see figure); all of these variables are parameters that are required to calculate the estimated surface roughness for a specified area. By using this algorithm, aerodynamic surface roughness values in urban areas can then be extracted automatically. The user can also adjust the algorithm for local conditions and lidar characteristics, like summer/winter vegetation and dense/sparse lidar point spacing. Additionally, the user can also survey variations in surface roughness that occurs due to wind direction; for example, during a hurricane, when wind direction can change dramatically, this variable can be extremely significant. In its current state, the algorithm calculates an estimated surface roughness for a square kilometer area; techniques using the lidar data to calculate the surface roughness for a point, whereby only roughness elements that are upstream from the point of interest are used and the wind direction is a vital concern, are being investigated. This technological advancement will improve the reliability and accuracy of models that use and incorporate surface roughness.
Fractals in geology and geophysics
Turcotte, Donald L.
1989-01-01
The definition of a fractal distribution is that the number of objects N with a characteristic size greater than r scales with the relation N of about r exp -D. The frequency-size distributions for islands, earthquakes, fragments, ore deposits, and oil fields often satisfy this relation. This application illustrates a fundamental aspect of fractal distributions, scale invariance. The requirement of an object to define a scale in photograhs of many geological features is one indication of the wide applicability of scale invariance to geological problems; scale invariance can lead to fractal clustering. Geophysical spectra can also be related to fractals; these are self-affine fractals rather than self-similar fractals. Examples include the earth's topography and geoid.
Phase Transitions on Fractals and Networks
Stauffer, D.
2007-01-01
For Encyclopedia of Complexist and System Science No abstract given I. Definition and Introduction II. Ising Model III. Fractals IV. Diffusion on Fractals V. Ising Model on Fractals VI. Other Subjects ? VII. Networks VIII. Future Directions
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.
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
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.
Robust Sierpiński triangle fractals on symmetry-mismatched Ag(100).
Zhang, Xue; Li, Na; Liu, Liwei; Gu, Gaochen; Li, Chao; Tang, Hao; Peng, Lianmao; Hou, Shimin; Wang, Yongfeng
2016-08-18
Sierpiński triangle fractals were constructed on both Ag(111) and symmetry-mismatched fourfold Ag(100) surfaces through chemical reaction between H3PH molecules and Fe atoms under vacuum. Density functional theory calculations revealed that the fractals were stabilized by the strong coordination interaction between Fe and O atoms. In comparison, pure H3PH molecules formed fractals via moderately strong hydrogen bonds only on Ag(111), not on Ag(100).
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...
Prediction of osteoporosis using fractal analysis on periapical radiographs
Energy Technology Data Exchange (ETDEWEB)
Park, Gum Mi; Jung, Yun Hoa; Nah, Kyung Soo [Pusan National University College of Medicine, Busan (Korea, Republic of)
2005-03-15
To purpose of this study was to investigate whether the fractal dimension and radiographic image brightness of periapical radiograph were useful in predicting osteoporosis. Ninety-two postmenopausal women were classified as normal, osteopenia and osteoporosis group according to the bone mineral density of lumbar vertebrae and periapical radiographs of both mandibular molar areas were taken. The ROIs of 358 areas were selected at periapical and interdental areas and fractal dimension and radiographic image brightness were measured. The fractal dimension in normal group was significantly higher than that in osteoporosis group at periapical ROI (p<0.05). The radiographic image brightness in normal group was higher than that in osteopenia and osteoporosis group. There was significant difference not only between normal and osteopenia group (p<0.05) but also within osteopenia and osteoporosis group (p<0.01) at periapical ROI. Significant difference was observed not only between normal and osteopenia group but also between normal and osteoporosis group at interdental ROI (p<0.01). Positive linear relationship was weakly shown at Pearson correlation analysis between fractal dimension and radiographic image brightness. BMD significantly correlated with fractal dimension at periapical ROI (p<0.01), and BMD and radiographic image brightness significantly correlated at both periapical and interdental ROIs (p<0.01). This study suggests that the fractal dimension and radiographic image brightness of periapical ROI may predict BMD.
Darwinian Evolution and Fractals
Carr, Paul H.
2009-05-01
Did nature's beauty emerge by chance or was it intelligently designed? Richard Dawkins asserts that evolution is blind aimless chance. Michael Behe believes, on the contrary, that the first cell was intelligently designed. The scientific evidence is that nature's creativity arises from the interplay between chance AND design (laws). Darwin's ``Origin of the Species,'' published 150 years ago in 1859, characterized evolution as the interplay between variations (symbolized by dice) and the natural selection law (design). This is evident in recent discoveries in DNA, Madelbrot's Fractal Geometry of Nature, and the success of the genetic design algorithm. Algorithms for generating fractals have the same interplay between randomness and law as evolution. Fractal statistics, which are not completely random, characterize such phenomena such as fluctuations in the stock market, the Nile River, rainfall, and tree rings. As chaos theorist Joseph Ford put it: God plays dice, but the dice are loaded. Thus Darwin, in discovering the evolutionary interplay between variations and natural selection, was throwing God's dice!
Fractals in biology and medicine
Havlin, S.; Buldyrev, S. V.; Goldberger, A. L.; Mantegna, R. N.; Ossadnik, S. M.; Peng, C. K.; Simons, M.; Stanley, H. E.
1995-01-01
Our purpose is to describe some recent progress in applying fractal concepts to systems of relevance to biology and medicine. We review several biological systems characterized by fractal geometry, with a particular focus on the long-range power-law correlations found recently in DNA sequences containing noncoding material. Furthermore, we discuss the finding that the exponent alpha quantifying these long-range correlations ("fractal complexity") is smaller for coding than for noncoding sequences. We also discuss the application of fractal scaling analysis to the dynamics of heartbeat regulation, and report the recent finding that the normal heart is characterized by long-range "anticorrelations" which are absent in the diseased heart.
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...
Plasma Creatinine, Age and Body Surface Area in Nigerian Children ...
African Journals Online (AJOL)
In a bid to establish reference values for plasma creatinine in children and adolescents using age, and body surface area (BSA), 462 apparently healthy Nigerian children/adolescents aged one day to 15 years were studied. They were recruited from well baby clinics, as well as primary and secondary schools. Plasma ...
Evaluation of five formulae for estimating body surface area of ...
African Journals Online (AJOL)
Background: Physiological functions are often assessed by standardizing for body surface area (BSA) to avoid excessive variation in calculations in pediatric practice. Aim: To explore the suitability of existing formulae for estimating the BSA of Nigerian children. Subjects and Methods: This cross‑sectional study involved ...
(Impervious) Surfaces on the Microclimate of Urban Area
African Journals Online (AJOL)
The present paper shows the considerable impacts of both vegetated and synthetic surfaces on the microclimate of urban area. Vegetation of a particular place affects the microclimate through reduced solar radiation and lower air temperature due to shading and evapotranspiration. Lower air temperatures are essential ...
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)
Low correlation (r = 0.12) was observed between body weight and ear width. There were no correlations between ear width, respiratory rates and pulse rate. However, a residual correlation (r = -0.03) was obtained between ear width and body temperature. Large ear surface area in composite rabbits enhances better ...
Assessment of large aperture scintillometry for large-area surface ...
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 126; Issue 5. Assessment of large aperture scintillometry for large-area surface energy ﬂuxes over an irrigated cropland in north India. Abhishek Danodia V K Sehgal N R Patel R Dhakar J Mukherjee S K Saha A Senthil Kumar. Volume 126 Issue 5 July 2017 Article ...
Application of fractal-wavelet analysis for separation of geochemical anomalies
Afzal, Peyman; Ahmadi, Kamyar; Rahbar, Kambiz
2017-04-01
The purpose of this paper is separation and detection of different geochemical populations and anomalies from background utilizing fractal-wavelet analysis. Daubechies2 and Morlet wavelets were used for transformation of the Cu estimated data to spatial frequency based on lithogeochemical data in Bardaskan area (SE Iran) by a MATLAB code. Wavelet is a significant tool for transformation of exploratory data because the noise data are removed from results and also, accuracy for determination of thresholds can be higher than other conventional methods. The Cu threshold values for extremely, highly and moderately anomalies are 1.4%, 0.66% and 0.4%, respectively, according to the fractal-wavelet analysis based on the Daubichies2 transformation. Moreover, the fractal-wavelet analysis by the Morlet wavelet shows that the Cu threshold values are 2%, 0.75% and 0.46% for extremely, highly and moderately anomalies and populations, respectively. The results obtained by the both WT methods indicate that the main Cu enriched anomalies and populations were situated in the central parts of the Bardaskan district which are associated with surface mineralization and ancient mining digs. Furthermore, results derived via the Morlet WT is better than Daubichies2 WT according to the correlation with geological characteristics by logratio matrix. The results obtained by the fractal-wavelet method have a good correlation with geological particulars including alteration zones and surface Cu mineralization which reveals the proposed technique is an applicable approach for identification of various geochemical anomalies and zones from background. However, the main targets for detailed exploration is located in the central part of the studied area.
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)
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 differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems. ... for the treatment of diffusion, heat conduction, waves, etc., on self-similar fractals [25–28]. Harmonic ... differential equations offer possibilities of modeling dynamical behaviours naturally for which ordinary differential ...
Fractal Fragmentation triggered by meteor impact: The Ries Crater (Germany)
Paredes Marino, Joali; Perugini, Diego; Rossi, Stefano; Kueppers, Ulrich
2015-04-01
FRACTAL FRAGMENTATION TRIGGERED BY METEOR IMPACT: THE RIES CRATER (GERMANY) Joali Paredes (1), Stefano Rossi (1), Diego Perugini (1), Ulrich Kueppers (2) 1. Department of Physics and Geology, University of Perugia, Italy 2. Department of Earth and Environmental Sciences, University of Munich, Germany The Nördlinger Ries is a large circular depression in western Bavaria, Germany. The depression was caused by a meteor impact, which occurred about 14.3 million-14.5 million years ago. The original crater rim had an estimated diameter of 24 kilometers. Computer modeling of the impact event indicates that the impact or probably had diameters of about 1.5 kilometers and impacted the target area at an angle around 30 to 50 degrees from the surface in a west- southwest to east-northeast direction. The impact velocity is thought to have been about 20 km/s. The meteor impact generated extensive fragmentation of preexisting rocks. In addition, melting of these rocks also occurred. The impact melt was ejected at high speed provoking its extensive fragmentation. Quenched melt fragments are ubiquitous in the outcrops. Here we study melt fragment size distributions with the aim of understanding the style of melt fragmentation during ejection and to constrain the rheological properties of such melts. Digital images of suevite (i.e. the rock generated after deposition and diagenesis of ash and fragments produced by the meteor impact) were obtained using a high-resolution optical scanner. Successively, melt fragments were traced by image analysis and the images segmented in order to obtain binary images on which impact melt fragments are in black color, embedded on a white background. Hence, the size of fragments was determined by image analysis. Fractal fragmentation theory has been applied to fragment size distributions of melt fragments in the Ries crater. Results indicate that melt fragments follow fractal distributions indicating that fragmentation of melt generated by the
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.
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.
Fractals and the Kepler equation
Kasten, Volker
1992-09-01
The application of fractal mathematics to Kepler's equation is addressed. Complex solutions to Kepler's equation are considered along with methods to determine them. The roles of regions of attraction and their boundaries, Julia quantities, Fatou quantities, and fractal quantities in these methods are discussed.
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.)
Tropical cyclone rainfall area controlled by relative sea surface temperature.
Lin, Yanluan; Zhao, Ming; Zhang, Minghua
2015-03-12
Tropical cyclone rainfall rates have been projected to increase in a warmer climate. The area coverage of tropical cyclones influences their impact on human lives, yet little is known about how tropical cyclone rainfall area will change in the future. Here, using satellite data and global atmospheric model simulations, we show that tropical cyclone rainfall area is controlled primarily by its environmental sea surface temperature (SST) relative to the tropical mean SST (that is, the relative SST), while rainfall rate increases with increasing absolute SST. Our result is consistent with previous numerical simulations that indicated tight relationships between tropical cyclone size and mid-tropospheric relative humidity. Global statistics of tropical cyclone rainfall area are not expected to change markedly under a warmer climate provided that SST change is relatively uniform, implying that increases in total rainfall will be confined to similar size domains with higher rainfall rates.
Enhanced Fluorescent Immunoassays on Silver Fractal-like Structures
Shtoyko, Tanya; Matveeva, Evgenia G.; Chang, I-Fen; Gryczynski, Zygmunt; Goldys, Ewa; Gryczynski, Ignacy
2009-01-01
Using the effect of the fluorescence enhancement in close proximity to metal nanostructures, we have been able to demonstrate ultrasensitive immunoassays suitable for the detection of biomarkers. Silver fractal-like structures have been grown by electrochemical reduction of silver on the surface of glass slides. A model immunoassay was performed on the slide surface with rabbit IgG (antigen) non-covalently immobilized on the slide, and Rhodamine Red-X labeled anti-rabbit IgG conjugate subsequently bound to the immobilized antigen. The fluorescence signal was measured from the glass-fractals surface using a confocal microscope, and the images were compared to the images from the same surface not coated with fractals. Our results showed significant enhancement (more than 100-fold) of the signal detected on fractals compared to bare glass. We thus demonstrate that such fractal-like structures can assist in improving the signals from assays used in medical diagnostics, especially those for analytes with molecular weight under 100 kD. PMID:18288816
Terahertz spectroscopy of plasmonic fractals.
Agrawal, A; Matsui, T; Zhu, W; Nahata, A; Vardeny, Z V
2009-03-20
We use terahertz time-domain spectroscopy to study the transmission properties of metallic films perforated with aperture arrays having deterministic or stochastic fractal morphologies ("plasmonic fractals"), and compare them with random aperture arrays. All of the measured plasmonic fractals show transmission resonances and antiresonances at frequencies that correspond to prominent features in their structure factors in k space. However, in sharp contrast to periodic aperture arrays, the resonant transmission enhancement decreases with increasing array size. This property is explained using a density-density correlation function, and is utilized for determining the underlying fractal dimensionality, D(fractals relative to the transmission of the corresponding random aperture arrays is obtained, and is shown to be universal.
Fractals analysis of cardiac arrhythmias.
Saeed, Mohammed
2005-09-06
Heart rhythms are generated by complex self-regulating systems governed by the laws of chaos. Consequently, heart rhythms have fractal organization, characterized by self-similar dynamics with long-range order operating over multiple time scales. This allows for the self-organization and adaptability of heart rhythms under stress. Breakdown of this fractal organization into excessive order or uncorrelated randomness leads to a less-adaptable system, characteristic of aging and disease. With the tools of nonlinear dynamics, this fractal breakdown can be quantified with potential applications to diagnostic and prognostic clinical assessment. In this paper, I review the methodologies for fractal analysis of cardiac rhythms and the current literature on their applications in the clinical context. A brief overview of the basic mathematics of fractals is also included. Furthermore, I illustrate the usefulness of these powerful tools to clinical medicine by describing a novel noninvasive technique to monitor drug therapy in atrial fibrillation.
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.
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...
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.
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)
Multispectral image fusion based on fractal features
Tian, Jie; Chen, Jie; Zhang, Chunhua
2004-01-01
Imagery sensors have been one indispensable part of the detection and recognition systems. They are widely used to the field of surveillance, navigation, control and guide, et. However, different imagery sensors depend on diverse imaging mechanisms, and work within diverse range of spectrum. They also perform diverse functions and have diverse circumstance requires. So it is unpractical to accomplish the task of detection or recognition with a single imagery sensor under the conditions of different circumstances, different backgrounds and different targets. Fortunately, the multi-sensor image fusion technique emerged as important route to solve this problem. So image fusion has been one of the main technical routines used to detect and recognize objects from images. While, loss of information is unavoidable during fusion process, so it is always a very important content of image fusion how to preserve the useful information to the utmost. That is to say, it should be taken into account before designing the fusion schemes how to avoid the loss of useful information or how to preserve the features helpful to the detection. In consideration of these issues and the fact that most detection problems are actually to distinguish man-made objects from natural background, a fractal-based multi-spectral fusion algorithm has been proposed in this paper aiming at the recognition of battlefield targets in the complicated backgrounds. According to this algorithm, source images are firstly orthogonally decomposed according to wavelet transform theories, and then fractal-based detection is held to each decomposed image. At this step, natural background and man-made targets are distinguished by use of fractal models that can well imitate natural objects. Special fusion operators are employed during the fusion of area that contains man-made targets so that useful information could be preserved and features of targets could be extruded. The final fused image is reconstructed from the
How surface roughness affects the angular dependence of the sputtering yield
International Nuclear Information System (INIS)
Hu, A.; Hassanein, A.
2012-01-01
Comprehensive model is developed to study the impact of surface roughness on the angular dependence of sputtering yield. Instead of assuming surfaces to be flat or composed of exact self-similar fractals, we developed a new method to describe the surfaces. Random fractal surfaces generated by midpoint displacement algorithm in computer graphics area and Support vector machine algorithm in pattern recognition area are combined with the Monte Carlo ion bombardment simulation code, i.e., Ion Transport in Materials and Compounds (ITMC) code . With this new fractal version of ITMC-F, we successfully simulated the angular dependence of sputtering yield for various ion-target combinations. Examples are given for 5 keV Ar ions bombarding iron, graphite, and silicon surfaces, with the input surface roughness exponent directly depicted from experimental data. Comparison is made with previous models to account for surface roughness and recent experimental data. The ITMC-F code showed good agreement with the experimental data.
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...
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)
Wicks, Keith R
1991-01-01
Addressed to all readers with an interest in fractals, hyperspaces, fixed-point theory, tilings and nonstandard analysis, this book presents its subject in an original and accessible way complete with many figures. The first part of the book develops certain hyperspace theory concerning the Hausdorff metric and the Vietoris topology, as a foundation for what follows on self-similarity and fractality. A major feature is that nonstandard analysis is used to obtain new proofs of some known results much more slickly than before. The theory of J.E. Hutchinson's invariant sets (sets composed of smaller images of themselves) is developed, with a study of when such a set is tiled by its images and a classification of many invariant sets as either regular or residual. The last and most original part of the book introduces the notion of a "view" as part of a framework for studying the structure of sets within a given space. This leads to new, elegant concepts (defined purely topologically) of self-similarity and fracta...
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.
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.
Losa, Gabriele A
2009-01-01
The extension of the concepts of Fractal Geometry (Mandelbrot [1983]) toward the life sciences has led to significant progress in understanding complex functional properties and architectural / morphological / structural features characterising cells and tissues during ontogenesis and both normal and pathological development processes. It has even been argued that fractal geometry could provide a coherent description of the design principles underlying living organisms (Weibel [1991]). Fractals fulfil a certain number of theoretical and methodological criteria including a high level of organization, shape irregularity, functional and morphological self-similarity, scale invariance, iterative pathways and a peculiar non-integer fractal dimension [FD]. Whereas mathematical objects are deterministic invariant or self-similar over an unlimited range of scales, biological components are statistically self-similar only within a fractal domain defined by upper and lower limits, called scaling window, in which the relationship between the scale of observation and the measured size or length of the object can be established (Losa and Nonnenmacher [1996]). Selected examples will contribute to depict complex biological shapes and structures as fractal entities, and also to show why the application of the fractal principle is valuable for measuring dimensional, geometrical and functional parameters of cells, tissues and organs occurring within the vegetal and animal realms. If the criteria for a strict description of natural fractals are met, then it follows that a Fractal Geometry of Life may be envisaged and all natural objects and biological systems exhibiting self-similar patterns and scaling properties may be considered as belonging to the new subdiscipline of "fractalomics".
Tahavvor, Ali Reza
2017-03-01
In the present study artificial neural network and fractal geometry are used to predict frost thickness and density on a cold flat plate having constant surface temperature under forced convection for different ambient conditions. These methods are very applicable in this area because phase changes such as melting and solidification are simulated by conventional methods but frost formation is a most complicated phase change phenomenon consists of coupled heat and mass transfer. Therefore conventional mathematical techniques cannot capture the effects of all parameters on its growth and development because this process influenced by many factors and it is a time dependent process. Therefore, in this work soft computing method such as artificial neural network and fractal geometry are used to do this manner. The databases for modeling are generated from the experimental measurements. First, multilayer perceptron network is used and it is found that the back-propagation algorithm with Levenberg-Marquardt learning rule is the best choice to estimate frost growth properties due to accurate and faster training procedure. Second, fractal geometry based on the Von-Koch curve is used to model frost growth procedure especially in frost thickness and density. Comparison is performed between experimental measurements and soft computing methods. Results show that soft computing methods can be used more efficiently to determine frost properties over a flat plate. Based on the developed models, wide range of frost formation over flat plates can be determined for various conditions.
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.
The transience of virtual fractals.
Taylor, R P
2012-01-01
Artists have a long and fruitful tradition of exploiting electronic media to convert static images into dynamic images that evolve with time. Fractal patterns serve as an example: computers allow the observer to zoom in on virtual images and so experience the endless repetition of patterns in a matter that cannot be matched using static images. This year's featured cover artist, Susan Lowedermilk, instead plans to employ persistence of human vision to bring virtual fractals to life. This will be done by incorporating her prints of fractal patterns into zoetropes and phenakistoscopes.
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
Metal-organic framework materials with ultrahigh surface areas
Farha, Omar K.; Hupp, Joseph T.; Wilmer, Christopher E.; Eryazici, Ibrahim; Snurr, Randall Q.; Gomez-Gualdron, Diego A.; Borah, Bhaskarjyoti
2015-12-22
A metal organic framework (MOF) material including a Brunauer-Emmett-Teller (BET) surface area greater than 7,010 m.sup.2/g. Also a metal organic framework (MOF) material including hexa-carboxylated linkers including alkyne bond. Also a metal organic framework (MOF) material including three types of cuboctahedron cages fused to provide continuous channels. Also a method of making a metal organic framework (MOF) material including saponifying hexaester precursors having alkyne bonds to form a plurality of hexa-carboxylated linkers including alkyne bonds and performing a solvothermal reaction with the plurality of hexa-carboxylated linkers and one or more metal containing compounds to form the MOF material.
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....
Analysis of fractal electrodes for efficient neural stimulation
Golestanirad, Laleh; Elahi, Behzad; Molina, Alberto; Mosig, Juan R.; Pollo, Claudio; Chen, Robert; Graham, Simon J.
2013-01-01
Planar electrodes are increasingly used in therapeutic neural stimulation techniques such as functional electrical stimulation, epidural spinal cord stimulation (ESCS), and cortical stimulation. Recently, optimized electrode geometries have been shown to increase the efficiency of neural stimulation by increasing the variation of current density on the electrode surface. In the present work, a new family of modified fractal electrode geometries is developed to enhance the efficiency of neural stimulation. It is shown that a promising approach in increasing the neural activation function is to increase the “edginess” of the electrode surface, a concept that is explained and quantified by fractal mathematics. Rigorous finite element simulations were performed to compute electric potential produced by proposed modified fractal geometries. The activation of 256 model axons positioned around the electrodes was then quantified, showing that modified fractal geometries required a 22% less input power while maintaining the same level of neural activation. Preliminary in vivo experiments investigating muscle evoked potentials due to median nerve stimulation showed encouraging results, supporting the feasibility of increasing neural stimulation efficiency using modified fractal geometries. PMID:23874290
Overcoming the reference large-area sources non-uniformity in surface area monitor calibration
Energy Technology Data Exchange (ETDEWEB)
Junior, Iremar Alves S.; Siqueira, Paulo de T.D.; Xavier, Marcs; Nascimento, Eduardo do; Potiens, Maria da Penha A., E-mail: iremarjr@usp.br, E-mail: ptsiquei@ipen.br, E-mail: mxavier@ipen.br, E-mail: eduardon@ufba.br, E-mail: mppalbu@ipen.br [Instituto de Pesquisas Energeticas e Nucleares (IPEN/CNEN-SP), Sao Paulo, SP (Brazil)
2015-07-01
This paper describes a study using MCNP5 simulations, a Monte Carlo based radiation transport code, in order to evaluate the possibility of using reference large-area sources that do not meet the uniformity recommendations of the ISO 8769:2010 in surface contamination monitors calibration. {sup 14}C, {sup 36}Cl, {sup 99}Tc, {sup 137}Cs and {sup 90}Sr + {sup 90}Y large area reference sources were simulated as well as the setup and the detector probe. Simulations were carried out for both uniform and non-uniform surface distributions. In the case of uniform distribution, specific weights for each region were considered, as obtained in the uniformity evaluation measurements. To each simulation, it was considered the average number of signals generated in each detector probe, i.e., it was determined the fraction of stories depositing energy in the corresponding gas filled region of the detector. Simulations results show differences in detection efficiency values up to 15%. (author)
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...
Error bounds for surface area estimators based on Crofton's formula
DEFF Research Database (Denmark)
Kiderlen, Markus; Meschenmoser, Daniel
2009-01-01
According to Crofton’s formula, the surface area S(A) of a sufficiently regular compact set A in R^d is proportional to the mean of all total projections pA (u) on a linear hyperplane with normal u, uniformly averaged over all unit vectors u. In applications, pA (u) is only measured in k directio...... in the sense that the relative error of the surface area estimator is very close to the minimal error....... and the mean is approximated by a finite weighted sum S(A) of the total projections in these directions. The choice of the weights depends on the selected quadrature rule. We define an associated zonotope Z (depending only on the projection directions and the quadrature rule), and show that the relative error...... S (A)/S (A) is bounded from below by the inradius of Z and from above by the circumradius of Z. Applying a strengthened isoperimetric inequality due to Bonnesen, we show that the rectangular quadrature rule does not give the best possible error bounds for d = 2. In addition, we derive asymptotic...
Fractal model of anomalous diffusion
Gmachowski, Lech
2015-01-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An...
Fractals in Power Reactor Noise
International Nuclear Information System (INIS)
Aguilar Martinez, O.
1994-01-01
In this work the non- lineal dynamic problem of power reactor is analyzed using classic concepts of fractal analysis as: attractors, Hausdorff-Besikovics dimension, phase space, etc. A new non-linear problem is also analyzed: the discrimination of chaotic signals from random neutron noise signals and processing for diagnosis purposes. The advantages of a fractal analysis approach in the power reactor noise are commented in details
Fractal pattern of canine trichoblastoma.
De Vico, Gionata; Cataldi, Marielda; Maiolino, Paola; Carella, Francesca; Beltraminelli, Stefano; Losa, Gabriele A
2011-06-01
To assess by fractal analysis the specific architecture, growth pattern, and tissue distribution that characterize subtypes of canine trichoblastoma, a benign tumor derived from or reduplicating the primitive hair germ of embryonic follicular development. Tumor masks and outlines obtained from immunohistologic images by gray threshold segmentation of epithelial components were analyzed by fractal and conventional morphometry. The fractal dimension [FD] of each investigated case was determined from the slope of the regression line describing the fractal region within a bi-asymptotic curve experimentally established. All tumor masks and outlines obtained by gray threshold segmentation of epithelial components showed fractal self-similar properties that were evaluated by peculiar FDs. However, only masks revealed significantly different FD values, ranging from 1.75 to 1.85, enabling the discrimination of canine trichoblastoma subtypes. The FD data suggest that an iterative morphogenetic process, involving both the air germ and associated dermal papilla, may be responsible of the peculiar tissue architecture of trichoblastoma. The present study emphasized the reliability of fractal analysis in achieving the objective characterization of canine trichoblastoma.
Prediction on Droplet Sauter Mean Diameter in Gas-Liquid Mist Flow Based on Droplet Fractal Theory
Directory of Open Access Journals (Sweden)
Jian-Yi Liu
2015-01-01
Full Text Available We present a fractal model for droplet Sauter mean diameter in gas-liquid mist flow, based on the droplet fractal theory and the balance relationship between total droplet surface energy and total gas turbulent kinetic energy. The present model is expressed as functions of the droplet fractal dimension, gas superficial velocity, liquid superficial velocity, and other fluid characteristics. Agreement between the present model predictions and experimental measurements is obtained. Results verify the reliability of the present model.
Directory of Open Access Journals (Sweden)
Marta Lafuente
2018-01-01
Full Text Available One of the main limitations of the technique surface-enhanced Raman scattering (SERS for chemical detection relies on the homogeneity, reproducibility and reusability of the substrates. In this work, SERS active platforms based on 3D-fractal microstructures is developed by combining corner lithography and anisotropic wet etching of silicon, to extend the SERS-active area into 3D, with electrostatically driven Au@citrate nanoparticles (NPs assembly, to ensure homogeneous coating of SERS active NPs over the entire microstructured platforms. Strong SERS intensities are achieved using 3D-fractal structures compared to 2D-planar structures; leading to SERS enhancement factors for R6G superior than those merely predicted by the enlarged area effect. The SERS performance of Au monolayer-over-mirror configuration is demonstrated for the label-free real-time gas phase detection of 1.2 ppmV of dimethyl methylphosphonate (DMMP, a common surrogate of G-nerve agents. Thanks to the hot spot accumulation on the corners and tips of the 3D-fractal microstructures, the main vibrational modes of DMMP are clearly identified underlying the spectral selectivity of the SERS technique. The Raman acquisition conditions for SERS detection in gas phase have to be carefully chosen to avoid photo-thermal effects on the irradiated area.
Method for producing high surface area chromia materials for catalysis
Gash, Alexander E [Brentwood, CA; Satcher, Joe [Patterson, CA; Tillotson, Thomas [Tracy, CA; Hrubesh, Lawrence [Pleasanton, CA; Simpson, Randall [Livermore, CA
2007-05-01
Nanostructured chromium(III)-oxide-based materials using sol-gel processing and a synthetic route for producing such materials are disclosed herein. Monolithic aerogels and xerogels having surface areas between 150 m.sup.2/g and 520 m.sup.2/g have been produced. The synthetic method employs the use of stable and inexpensive hydrated-chromium(III) inorganic salts and common solvents such as water, ethanol, methanol, 1-propanol, t-butanol, 2-ethoxy ethanol, and ethylene glycol, DMSO, and dimethyl formamide. The synthesis involves the dissolution of the metal salt in a solvent followed by an addition of a proton scavenger, such as an epoxide, which induces gel formation in a timely manner. Both critical point (supercritical extraction) and atmospheric (low temperature evaporation) drying may be employed to produce monolithic aerogels and xerogels, respectively.
Fully automated algorithm for wound surface area assessment.
Deana, Alessandro Melo; de Jesus, Sérgio Henrique Costa; Sampaio, Brunna Pileggi Azevedo; Oliveira, Marcelo Tavares; Silva, Daniela Fátima Teixeira; França, Cristiane Miranda
2013-01-01
Worldwide, clinicians, dentists, nurses, researchers, and other health professionals need to monitor the wound healing progress and to quantify the rate of wound closure. The aim of this study is to demonstrate, step by step, a fully automated numerical method to estimate the size of the wound and the percentage damaged relative to the body surface area (BSA) in images, without the requirement for human intervention. We included the formula for BSA in rats in the algorithm. The methodology was validated in experimental wounds and human ulcers and was compared with the analysis of an experienced pathologist, with good agreement. Therefore, this algorithm is suitable for experimental wounds and burns and human ulcers, as they have a high contrast with adjacent normal skin. © 2013 by the Wound Healing Society.
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.
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.
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.
Surface ozone in the urban area of Manaus, Amazonas, Brazil
Souza, R. A. F. D.; Costa, P. S.; Silva, C.; Godoi, R. M.; Martin, S. T.; Tota, J.; Barbosa, H. M.; Pauliquevis, T.; Ferreira De Brito, J.; Artaxo, P.; Manzi, A. O.; Wolf, S. A.; Cirino, G. G.
2014-12-01
When nitrogen oxides from vehicle and industrial emissions mix with volatile organic compounds from trees and plants with exposure to sunlight, a chemical reaction occurs contributing to ground-level ozone pollution. The preliminary results of the surface ozone study in urban area of Manaus, Amazonas State, Brazil, are presented for the first intensive operating period (IOP1) of the GoAmazon experiment (February/March 2014). Photochemical ozone production was found to be a regular process, with an afternoon maximum of the ozone mixing ratio of lower than 20 ppbv for cloudy days or clear sky weather. Typical ozone concentrations at mid-day were low (about 10 ppb). On the other hand, several high-value ozone episodes with surface ozone mixing ratios up to three times larger were registered during the dry season of 2013 (September/October). At the beginning of the wet season, the ozone concentration in Manaus decreased significantly, but diurnal variations can be found during the days with rainfall and other fast changes of meteorological conditions. Possible explanations of the nature of pulsations are discussed. Photochemical ozone production by local urban plumes of Manaus is named as a first possible source of the ozone concentration and biomass burning or power plant emissions are suggested as an alternative or an additional source.
Sandwich type plasmonic platform for MEF using silver fractals
DEFF Research Database (Denmark)
Raut, Sangram L.; Rich, Ryan; Shtoyko, Tanya
2015-01-01
In this report, we describe a plasmonic platform with silver fractals for metal enhanced fluorescence (MEF) measurements. When a dye containing surface was brought into contact with silver fractals, a significantly enhanced fluorescence signal from the dye was observed. Fluorescence enhancement...... was studied with the N-methyl-azadioxatriangulenium chloride salt (Me-ADOTA·Cl) in PVA films made from 0.2% PVA (w/v) solution spin-coated on a clean glass coverslip. The Plasmonic Platforms (PP) were assembled by pressing together silver fractals on one glass slide and a separate glass coverslip spin...... of PP can be a convenient approach for constructing assays utilizing metal enhanced fluorescence (MEF) without the need for depositing the material directly on metal structures platforms....
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
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.
Relationship between the anomalous diffusion and the fractal dimension of the environment
Zhokh, Alexey; Trypolskyi, Andrey; Strizhak, Peter
2018-03-01
In this letter, we provide an experimental study highlighting a relation between the anomalous diffusion and the fractal dimension of the environment using the methanol anomalous transport through the porous solid pellets with various pores geometries and different chemical compositions. The anomalous diffusion exponent was derived from the non-integer order of the time-fractional diffusion equation that describes the methanol anomalous transport through the solid media. The surface fractal dimension was estimated from the nitrogen adsorption isotherms using the Frenkel-Halsey-Hill method. Our study shows that decreasing the fractal dimension leads to increasing the anomalous diffusion exponent, whereas the anomalous diffusion constant is independent on the fractal dimension. We show that the obtained results are in a good agreement with the anomalous diffusion model on a fractal mesh.
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...
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.
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...
Moving to 3D: relationships between coral planar area, surface area and volume.
House, Jenny E; Brambilla, Viviana; Bidaut, Luc M; Christie, Alec P; Pizarro, Oscar; Madin, Joshua S; Dornelas, Maria
2018-01-01
Coral reefs are a valuable and vulnerable marine ecosystem. The structure of coral reefs influences their health and ability to fulfill ecosystem functions and services. However, monitoring reef corals largely relies on 1D or 2D estimates of coral cover and abundance that overlook change in ecologically significant aspects of the reefs because they do not incorporate vertical or volumetric information. This study explores the relationship between 2D and 3D metrics of coral size. We show that surface area and volume scale consistently with planar area, albeit with morphotype specific conversion parameters. We use a photogrammetric approach using open-source software to estimate the ability of photogrammetry to provide measurement estimates of corals in 3D. Technological developments have made photogrammetry a valid and practical technique for studying coral reefs. We anticipate that these techniques for moving coral research from 2D into 3D will facilitate answering ecological questions by incorporating the 3rd dimension into monitoring.
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.
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.
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 symmetry of protein interior: what have we learned?
Banerji, Anirban; Ghosh, Indira
2011-08-01
environments. The fold 'conotoxins' (peptides) could be unambiguously identified as one type with the least stability. The same analyses revealed that peptide-dipoles in the α/β class of proteins, in general, are more correlated to each other than are the peptide-dipoles in proteins belonging to the all-α class. Highly favorable electrostatic milieu in the interiors of TIM-barrel, α/β-hydrolase structures could explain their remarkably conserved (evolutionary) stability from a new light. Finally, we point out certain inherent limitations of fractal constructs before attempting to identify the areas and problems where the implementation of fractal dimension-based constructs can be of paramount help to unearth latent information on protein structural properties.
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.
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.
Sound absorption by Menger sponge fractal.
Kawabe, Tetsuji; Miyazaki, Takatsuna; Oka, Daisuke; Koyanagi, Sin'ichiro; Hinokidani, Atsushi
2009-05-01
For the purpose of investigation on acoustic properties of fractals, the sound absorption coefficients are experimentally measured by using the Menger sponge which is one of typical three-dimensional fractals. From the two-microphone measurement, the frequency range of effectively absorbing sound waves is shown to broaden with degree of fractality, which comes from the fractal property of the homothetic character. It is shown that experimental features are qualitatively explained by an electrical equivalent circuit model for the Menger sponge.
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
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
lien from Harish-Chandra. Research Institute,. Allahabad. Areas of his interest include cosmic microwave background radiation, large scale structures in the Universe and application of fractals in these. A K Mittal and T R Seshadri. During the last decade it has been argued by some investigators that the distribution of galax-.
Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...
African Journals Online (AJOL)
In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...
Fractal 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.
Fractal Dimension and the Cantor Set
Indian Academy of Sciences (India)
IAS Admin
1000. RESONANCE ⎜ November 2014. GENERAL ⎜ ARTICLE. Fractal Dimension and the Cantor Set. Shailesh A Shirali. Keywords. Dimension, topological dimen- sion, Hausdorff–Besicovitch di- mension, fractal dimension, fractal, Cantor set, Sierpinski triangle, Koch curve. Shailesh Shirali is. Director of Sahyadri School.
Multiple wave scattering from fractal aggregates
Energy Technology Data Exchange (ETDEWEB)
Korvin, Gabor E-mail: gabor@kfupm.edu.sa; Oleschko, Klavdia
2004-01-01
Multiple scattered waves from fractal aggregates create spurious resonances in the high-frequency part of the wave-field's Fourier spectrum. It is shown by a probabilistic convolutional model that for extended fractal media with strong scattering cross-section, multiple scattering can affect the value of the fractal dimension estimated from the wave-field's Fourier power spectrum.
Fractal analysis of time varying data
Vo-Dinh, Tuan; Sadana, Ajit
2002-01-01
Characteristics of time varying data, such as an electrical signal, are analyzed by converting the data from a temporal domain into a spatial domain pattern. Fractal analysis is performed on the spatial domain pattern, thereby producing a fractal dimension D.sub.F. The fractal dimension indicates the regularity of the time varying data.
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.
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
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.
Climatologies at high resolution for the earth's land surface areas
Karger, Dirk Nikolaus; Conrad, Olaf; Böhner, Jürgen; Kawohl, Tobias; Kreft, Holger; Soria-Auza, Rodrigo Wilber; Zimmermann, Niklaus E.; Linder, H. Peter; Kessler, Michael
2017-09-01
High-resolution information on climatic conditions is essential to many applications in environmental and ecological sciences. Here we present the CHELSA (Climatologies at high resolution for the earth's land surface areas) data of downscaled model output temperature and precipitation estimates of the ERA-Interim climatic reanalysis to a high resolution of 30 arc sec. The temperature algorithm is based on statistical downscaling of atmospheric temperatures. The precipitation algorithm incorporates orographic predictors including wind fields, valley exposition, and boundary layer height, with a subsequent bias correction. The resulting data consist of a monthly temperature and precipitation climatology for the years 1979-2013. We compare the data derived from the CHELSA algorithm with other standard gridded products and station data from the Global Historical Climate Network. We compare the performance of the new climatologies in species distribution modelling and show that we can increase the accuracy of species range predictions. We further show that CHELSA climatological data has a similar accuracy as other products for temperature, but that its predictions of precipitation patterns are better.
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.
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.
30 CFR 912.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 912.764 Section 912.764 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE IDAHO § 912.764 Process for designating areas unsuitable for surface coal mining... coal mining and reclamation operations. ...
Fractal analysis of sound signals in SAMPO 3065 combine harvester
Directory of Open Access Journals (Sweden)
F Mahdiyeh Broujeni
2017-05-01
Full Text Available Introduction Nowadays, many studies were performed about noise source and its type and effects related to duration of sound emission. Most of these researches just report sound pressure level in frequency or time domain. These researches should be continued in order to find better absorber material in noise pollution. Use of fractal geometry is a new method in this filed. Wave fractal dimension value is a strong tool for diagnosis of signal instability and fractal analysis is a good method to finding sound signal characteristics. Therefore the aim of this study is on the fractal geometry of SAMPO 3065 combine harvester signals and determine the fractal dimension value of these signals in different operational conditions by Katz, Sevcik, Higuchi and MRBC methods. Materials and Methods In this research, sound signals of SAMPO 3065 harvester combine that were recorded by Maleki and Lashgari (2014, were analyzed. Engine speed (high and low, gear ratio (neutral, 1st, 2nd, 3rd gear, type of operation (traveling and harvesting and microphone position (in and out of the cabin were the main factors of this research. For determining signal fractal dimension value in time domain, wave shape supposed as a geometrical shape and for calculation of fractal dimension value of these signals, total area of wave shape was divided into boxes in 50, 100, 200 milliseconds with an interval 25 millisecond box. Then Fractal dimension value of these boxes was calculated by Katz, Sevcik, Higuchi and MRBC methods using MATLAB (2010a software. SPSS (Ver.20 software was used for further analysis. Results and Discussion Results showed mean effects of engine speed, microphone position, gear ratio, type of operation, box length, calculation method and all of two way interaction effects were significant. Means of Fractal Dimension in the road and field position were 1.4 and 1.28 respectively. The Maximum growth ratio of fractal dimension value during engine speed levels was
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
30 CFR 941.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... WITHIN EACH STATE SOUTH DAKOTA § 941.761 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... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 937.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... 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 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 905.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... WITHIN EACH STATE CALIFORNIA § 905.761 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... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 910.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... WITHIN EACH STATE GEORGIA § 910.761 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... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 903.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... WITHIN EACH STATE ARIZONA § 903.761 Areas designated unsuitable for surface coal mining by act of Congress. Part 761 of this chapter, Areas Designated by Act of Congress, applies to surface coal mining... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 939.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... WITHIN EACH STATE RHODE ISLAND § 939.761 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... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 922.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... WITHIN EACH STATE MICHIGAN § 922.761 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... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 921.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... WITHIN EACH STATE MASSACHUSETTS § 921.761 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... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 912.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... 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 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 947.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... WITHIN EACH STATE WASHINGTON § 947.761 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... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 942.761 - Areas designated unsuitable for surface coal mining by act of Congress.
2010-07-01
... WITHIN EACH STATE TENNESSEE § 942.761 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... 30 Mineral Resources 3 2010-07-01 2010-07-01 false Areas designated unsuitable for surface coal...
30 CFR 903.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 903.762 Section 903.762 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE ARIZONA § 903.762 Criteria for designating areas as unsuitable for surface coal mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining...
30 CFR 922.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 922.762 Section 922.762 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE MICHIGAN § 922.762 Criteria for designating areas as unsuitable for surface coal mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining...
30 CFR 937.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 937.762 Section 937.762 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE OREGON § 937.762 Criteria for designating areas as unsuitable for surface coal mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining...
30 CFR 912.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 912.762 Section 912.762 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE IDAHO § 912.762 Criteria for designating areas as unsuitable for surface coal mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining...
30 CFR 910.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 910.762 Section 910.762 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE GEORGIA § 910.762 Criteria for designating areas as unsuitable for surface coal mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining...
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
Pressure Transient Analysis of Dual Fractal Reservoir
Directory of Open Access Journals (Sweden)
Xiao-Hua Tan
2013-01-01
Full Text Available A dual fractal reservoir transient flow model was created by embedding a fracture system simulated by a tree-shaped fractal network into a matrix system simulated by fractal porous media. The dimensionless bottom hole pressure model was created using the Laplace transform and Stehfest numerical inversion methods. According to the model's solution, the bilogarithmic type curves of the dual fractal reservoirs are illustrated, and the influence of different fractal factors on pressure transient responses is discussed. This semianalytical model provides a practical and reliable method for empirical applications.
Assembling molecular Sierpiński triangle fractals.
Shang, Jian; Wang, Yongfeng; Chen, Min; Dai, Jingxin; Zhou, Xiong; Kuttner, Julian; Hilt, Gerhard; Shao, Xiang; Gottfried, J Michael; Wu, Kai
2015-05-01
Fractals, being "exactly the same at every scale or nearly the same at different scales" as defined by Benoit B. Mandelbrot, are complicated yet fascinating patterns that are important in aesthetics, mathematics, science and engineering. Extended molecular fractals formed by the self-assembly of small-molecule components have long been pursued but, to the best of our knowledge, not achieved. To tackle this challenge we designed and made two aromatic bromo compounds (4,4″-dibromo-1,1':3',1″-terphenyl and 4,4‴-dibromo-1,1':3',1″:4″,1‴-quaterphenyl) to serve as building blocks. The formation of synergistic halogen and hydrogen bonds between these molecules is the driving force to assemble successfully a whole series of defect-free molecular fractals, specifically Sierpiński triangles, on a Ag(111) surface below 80 K. Several critical points that govern the preparation of the molecular Sierpiński triangles were scrutinized experimentally and revealed explicitly. This new strategy may be applied to prepare and explore various planar molecular fractals at surfaces.
Scaling relations in the diffusive infiltration in fractals.
Aarão Reis, F D A
2016-11-01
In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F∼t^{n}, with nfractals, but the exponent n is very different from the anomalous exponent ν=1/D_{W} of single-particle diffusion in the same fractals (D_{W} is the random-walk dimension). Here we use a scaling approach to show that those exponents are related as n=ν(D_{F}-D_{B}), where D_{F} and D_{B} are the fractal dimensions of the bulk and the border from which diffusing particles come, respectively. This relation is supported by accurate numerical estimates in two SCs and in two generalized Menger sponges (MSs), in which we performed simulations of single-particle random walks (RWs) with a rigid impermeable border and of a diffusive infiltration model in which that border is permanently filled with diffusing particles. This study includes one MS whose external border is also fractal. The exponent relation is also consistent with the recent simulational and experimental results on fluid infiltration in SCs, and explains the approximate quadratic dependence of n on D_{F} in these fractals. We also show that the mean-square displacement of single-particle RWs has log-periodic oscillations, whose periods are similar for fractals with the same scaling factor in the generator (even with different embedding dimensions), which is consistent with the discrete scale invariance scenario. The roughness of a diffusion front defined in the infiltration problem also shows this type of oscillation, which is enhanced in fractals with narrow channels between large lacunas.
Effect of exposure time and image resolution on fractal dimension
Energy Technology Data Exchange (ETDEWEB)
An, Byung Mo; Heo, Min Suk; Lee, Seung Pyo; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won [College of Dentistry, Seoul National University, Seoul (Korea, Republic of); Kim, Jong Dae [Division of Information and Communication Engineering, Hallym University, Chuncheon (Korea, Republic of)
2002-06-15
To evaluate the effect of exposure time and image resolution on fractal dimension calculations for determining the optimal range of these two variances. Thirty-one radiographs of the mandibular angle area of sixteen human dry mandibles were taken at different exposure times (0.01, 0.08, 0.16, 0.25, 0.40, 0.64, and 0.80 s). Each radiograph was digitized at 1200 dpi, 8 bit, 256 gray level using a film scanner. We selected an Region of Interest (ROI) that corresponded to the same region as in each radiograph, but the resolution of ROI was degraded to 1000, 800, 600, 500, 400, 300, 200, and 100 dpi. The fractal dimension was calculated by using the tile-counting method for each image, and the calculated values were then compared statistically. As the exposure time and the image resolution increased, the mean value of the fractal dimension decreased, except the case where exposure time was set at 0.01 seconds (alpha = 0.05). The exposure time and image resolution affected the fractal dimension by interaction (p<0.001). When the exposure time was set to either 0.64 seconds or 0.80 seconds, the resulting fractal dimensions were lower, irrespective of image resolution, than at shorter exposure times (alpha = 0.05). The optimal range for exposure time and resolution was determined to be 0.08-0.40 seconds and from 400-1000 dpi, respectively. Adequate exposure time and image resolution is essential for acquiring the fractal dimension using tile-counting method for evaluation of the mandible.
Effect of exposure time and image resolution on fractal dimension
International Nuclear Information System (INIS)
An, Byung Mo; Heo, Min Suk; Lee, Seung Pyo; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won; Kim, Jong Dae
2002-01-01
To evaluate the effect of exposure time and image resolution on fractal dimension calculations for determining the optimal range of these two variances. Thirty-one radiographs of the mandibular angle area of sixteen human dry mandibles were taken at different exposure times (0.01, 0.08, 0.16, 0.25, 0.40, 0.64, and 0.80 s). Each radiograph was digitized at 1200 dpi, 8 bit, 256 gray level using a film scanner. We selected an Region of Interest (ROI) that corresponded to the same region as in each radiograph, but the resolution of ROI was degraded to 1000, 800, 600, 500, 400, 300, 200, and 100 dpi. The fractal dimension was calculated by using the tile-counting method for each image, and the calculated values were then compared statistically. As the exposure time and the image resolution increased, the mean value of the fractal dimension decreased, except the case where exposure time was set at 0.01 seconds (alpha = 0.05). The exposure time and image resolution affected the fractal dimension by interaction (p<0.001). When the exposure time was set to either 0.64 seconds or 0.80 seconds, the resulting fractal dimensions were lower, irrespective of image resolution, than at shorter exposure times (alpha = 0.05). The optimal range for exposure time and resolution was determined to be 0.08-0.40 seconds and from 400-1000 dpi, respectively. Adequate exposure time and image resolution is essential for acquiring the fractal dimension using tile-counting method for evaluation of the mandible.
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.
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)
Self-affine fractals and the limit H→0
Palasantzas, George
1994-01-01
A modified form for the surface-height-fluctuation correlation function of rough surfaces, gγ(R) ∝ ∫ a0/ξ R/ξ x^2H (e^–x/x)dx, is investigated which depicts behavior related to self-affine fractals for 0 < H < 1, and for H →0 with a0 « R « ξ reveals logarithmic behavior gγ(R) ∝ ln(R/a0).
Marks-Tarlow, Terry
2010-01-01
In this article, the author draws on contemporary science to illuminate the relationship between early play experiences, processes of self-development, and the later emergence of the fractal self. She argues that orientation within social space is a primary function of early play and developmentally a two-step process. With other people and with…
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti......Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs......, the retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficients. Falconer's formula and quantitative genetic models were used to determine the genetic component of variation. Results: The mean...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0...
Fractal transforms and Feature invariance
Paul M. de Zeeuw; B.A.M. Ben Schouten
2000-01-01
In this paper, fractal transforms are employed with the aim of image recognition. It is known that such transforms are highly sensitive to distortions like a small shift of an image. However, by using features based on statistics kept during the actual decomposition we can derive features from
Mossotti, Victor G.; Eldeeb, A. Raouf; Oscarson, Robert
1998-01-01
MORPH-I is a set of C-language computer programs for the IBM PC and compatible minicomputers. The programs in MORPH-I are used for the fractal analysis of scanning electron microscope and electron microprobe images of pore profiles exposed in cross-section. The program isolates and traces the cross-sectional profiles of exposed pores and computes the Richardson fractal dimension for each pore. Other programs in the set provide for image calibration, display, and statistical analysis of the computed dimensions for highly complex porous materials. Requirements: IBM PC or compatible; minimum 640 K RAM; mathcoprocessor; SVGA graphics board providing mode 103 display.
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.
Effect of impervious surface area and vegetation changes on mean ...
African Journals Online (AJOL)
adeniyi adeyemi
sprawl and this has contributed to increase in surface temperature. Keyword: Thematic indices, surface temperature, Landsat, vegetation, ISA, Tshwane Metropolis. 1. Introduction. Globally, rapid increase in population in major cities has led to urban sprawl at an unprecedented rate which is, according to the analysis and ...
Fractal nature of humic materials
Rice, J. A.; Lin, J. S.
Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this 'disorder within disorder.' Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fractions has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis.
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.
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.
APPLICATION IN BUILDING A NEW TYPE CATALYST WITH FRACTALS V. ECO CATALYST
Directory of Open Access Journals (Sweden)
RADU Ionuţ Valentin
2012-09-01
Full Text Available This paper presents a study on the existence of fractal and pollution prevention methods. One way to reduce emissions of greenhouse gases from motor vehicles is to systematically collect and dispose of any waste (high emissions. This paper treats a new type of catalyst, the catalytic oxidation process improvement. This new type of catalyst can be produced at sizes much smaller than those on the market because the surface of monolithic spiral have introduced a series of fractals.
[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.
Sandwich type plasmonic platform for MEF using silver fractals.
Raut, Sangram L; Rich, Ryan; Shtoyko, Tanya; Bora, Ilkay; Laursen, Bo W; Sørensen, Thomas Just; Borejdo, Julian; Gryczynski, Zygmunt; Gryczynski, Ignacy
2015-11-14
In this report, we describe a plasmonic platform with silver fractals for metal enhanced fluorescence (MEF) measurements. When a dye containing surface was brought into contact with silver fractals, a significantly enhanced fluorescence signal from the dye was observed. Fluorescence enhancement was studied with the N-methyl-azadioxatriangulenium chloride salt (Me-ADOTA·Cl) in PVA films made from 0.2% PVA (w/v) solution spin-coated on a clean glass coverslip. The Plasmonic Platforms (PP) were assembled by pressing together silver fractals on one glass slide and a separate glass coverslip spin-coated with a uniform Me-ADOTA·Cl in PVA film. In addition, we also tested ADOTA labeled human serum albumin (HSA) deposited on a glass slide for potential PP bioassay applications. Using the new PP, we could achieve more than a 20-fold fluorescence enhancement (bright spots) accompanied by a decrease in the fluorescence lifetime. The experimental results were used to calculate the extinction (excitation) enhancement factor (GA) and fluorescence radiative rate enhancements factor (GF). No change in emission spectrum was observed for a dye with or without contact with fractals. Our studies indicate that this type of PP can be a convenient approach for constructing assays utilizing metal enhanced fluorescence (MEF) without the need for depositing the material directly on metal structures platforms.
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.
SMAPVEX12 Surface Roughness Data for Agricultural Area V001
National Aeronautics and Space Administration — This data set contains surface roughness data collected at several agricultural sites as a part of the Soil Moisture Active Passive Validation Experiment 2012...
Lung cancer—a fractal viewpoint
Lennon, Frances E.; Cianci, Gianguido C.; Cipriani, Nicole A.; Hensing, Thomas A.; Zhang, Hannah J.; Chen, Chin-Tu; Murgu, Septimiu D.; Vokes, Everett E.; W. Vannier, Michael; Salgia, Ravi
2016-01-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed. PMID:26169924
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.
Lung cancer-a fractal viewpoint.
Lennon, Frances E; Cianci, Gianguido C; Cipriani, Nicole A; Hensing, Thomas A; Zhang, Hannah J; Chen, Chin-Tu; Murgu, Septimiu D; Vokes, Everett E; Vannier, Michael W; Salgia, Ravi
2015-11-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.
Properties that influence the specific surface areas of carbon nanotubes and nanofibers.
Birch, M Eileen; Ruda-Eberenz, Toni A; Chai, Ming; Andrews, Ronnee; Hatfield, Randal L
2013-11-01
Commercially available carbon nanotubes and nanofibers were analyzed to examine possible relationships between their Brunauer-Emmett-Teller specific surface areas (SSAs) and their physical and chemical properties. Properties found to influence surface area were number of walls/diameter, impurities, and surface functionalization with hydroxyl and carboxyl groups. Characterization by electron microscopy, energy-dispersive X-ray spectrometry, thermogravimetric analysis, and elemental analysis indicates that SSA can provide insight on carbon nanomaterials properties, which can differ vastly depending on synthesis parameters and post-production treatments. In this study, how different properties may influence surface area is discussed. The materials examined have a wide range of surface areas. The measured surface areas differed from product specifications, to varying degrees, and between similar products. Findings emphasize the multiple factors that influence surface area and mark its utility in carbon nanomaterial characterization, a prerequisite to understanding their potential applications and toxicities. Implications for occupational monitoring are discussed.
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.
Lung deposited surface area concentrations in a street canyon
Kuuluvainen, Heino; Hietikko, Riina; Järvinen, Anssi; Saukko, Erkka; Irjala, Matti; Niemi, Jarkko V.; Timonen, Hilkka; Keskinen, Jorma; Rönkkö, Topi
2017-04-01
Street canyons are interesting environments with respect to the dispersion of traffic emissions and human exposure. Pedestrians may be exposed to relatively high concentrations of fine particles and the vertical dispersion affects the human exposure above the ground level in buildings. Previously, particle concentrations have been measured in street canyons at a few different heights (Marini et al., 2015). The information on the lung deposited surface area (LDSA) concentration, which is a relevant metric for the negative health effects, is very limited even at the ground level of street canyons (Kuuluvainen et al., 2016). More information especially on the vertical dispersion and the ground level concentrations is needed, for instance, for the use of urban planning and the design of ventilation systems in buildings. Measurements were carried out in a busy street canyon in Helsinki, Finland, at an urban super-site measurement station (Mäkelänkatu 50). The data included vertical concentration profiles measured in an intensive measurement campaign with a Partector (Naneos GmbH) installed into a drone, long-term measurements with an AQ Urban particle sensor (Pegasor Ltd.), and an extensive comparison measurement in the field with different devices measuring the LDSA. These devices were an AQ Urban, Partector, DiSCmini (Testo AG), NSAM (TSI Inc.), and an ELPI+ (Dekati Ltd.). In addition, continuous measurements of gas phase components, particle size distributions, and meteorology were run at the supersite. The vertical profile measurements were con-ducted in November 2016 during two days. In the measurements, the drone was flown from the ground level to an altitude of 50 or 100 m, which is clearly above the roof level of the buildings. Altogether, 48 up-and-down flights were conducted during the two days. The vertical profiles were supported by continuous measurements at the ground level on both sides of the street canyon. The long-term measurements were conducted
Prediction of osteoporosis using fractal analysis on periapical and panoramic radiographs
Energy Technology Data Exchange (ETDEWEB)
Kim, Joo Yeon; Jung, Yun Hoa; Nah, Kyung Soo [Department of Oral and Maxillofacial Radiology, College of Dentistry, Pusan National University, Pusan (Korea, Republic of)
2008-09-15
The purpose of this study was to investigate whether fractal analysis of periapical and panoramic radiographs was useful in predicting osteoporosis risk. 37 postmenoposal women between the age of 42 and 79 were classified as normal and osteoporosis group according to the bone mineral density of lumbar vertebrae and periapical and panoramic radiographs were taken. Fractal dimensions at periapical areas of mandibular first molars were calculated to differentiate the two groups. The mean fractal dimensions of normal group on periapical and panoramic radiographs were 1.413 {+-} 0.079, 1.517 {+-} 0.071 each. The mean fractal dimensions of osteoporotic group on periapical and panoramic radiographs were 1.498 {+-} 0.086, 1.388 {+-} 0.083 each. The mean fractal dimension from peripaical radiographs of osteoporotic group was statistically significantly higher than that of normal group. The mean fractal dimension from panoramic radiographs of osteoporotic group was statistically significantly lower than that of normal group. Fractal analysis using periapical and panoramic radiographs was useful in predicting osteoporosis.
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.
Military Surface Grid Areas: Atlantic / Gulf of Mexico
National Oceanic and Atmospheric Administration, Department of Commerce — A regular pattern of polygons that represent arbitrary delineations of an Operating Area (OPAREA). The MarineCadastre.gov team worked with the Navy to provide this...
30 CFR 910.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 910.764 Section 910.764 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION AND ENFORCEMENT, DEPARTMENT OF THE INTERIOR PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE GEORGIA § 910.764 Process for designating areas unsuitable for surface coal mining...
30 CFR 937.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 937.764 Section 937.764 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION AND ENFORCEMENT, DEPARTMENT OF THE INTERIOR PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE OREGON § 937.764 Process for designating areas unsuitable for surface coal mining...
30 CFR 947.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 947.762 Section 947.762 Mineral Resources OFFICE OF SURFACE MINING... mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining Operations, shall apply to surface coal mining and reclamation operations. ...
30 CFR 921.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 921.762 Section 921.762 Mineral Resources OFFICE OF SURFACE MINING... mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining Operations, shall apply to surface coal mine operations. ...
30 CFR 922.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 922.764 Section 922.764 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION AND ENFORCEMENT, DEPARTMENT OF THE INTERIOR PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE MICHIGAN § 922.764 Process for designating areas unsuitable for surface coal mining...
30 CFR 942.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 942.764 Section 942.764 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE TENNESSEE § 942.764 Process for designating areas unsuitable for surface coal mining... Mining Operations, shall apply to surface coal mining and reclamation operations. (b) The Secretary shall...
30 CFR 941.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 941.764 Section 941.764 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION AND ENFORCEMENT, DEPARTMENT OF THE INTERIOR PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE SOUTH DAKOTA § 941.764 Process for designating areas unsuitable for surface coal mining...
30 CFR 941.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 941.762 Section 941.762 Mineral Resources OFFICE OF SURFACE MINING... mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining Operations, shall apply to surface coal mine operations. ...
30 CFR 939.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 939.764 Section 939.764 Mineral Resources OFFICE OF SURFACE MINING RECLAMATION AND ENFORCEMENT, DEPARTMENT OF THE INTERIOR PROGRAMS FOR THE CONDUCT OF SURFACE MINING OPERATIONS WITHIN EACH STATE RHODE ISLAND § 939.764 Process for designating areas unsuitable for surface coal mining...
30 CFR 933.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 933.762 Section 933.762 Mineral Resources OFFICE OF SURFACE MINING... mining operations. Part 762 of this chapter, Criteria for Designation Areas Unsuitable for Surface Coal Mining Operations, shall apply to surface coal mining and reclamation operations. ...
30 CFR 939.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 939.762 Section 939.762 Mineral Resources OFFICE OF SURFACE MINING... mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining Operations, shall apply to surface coal mining and reclamation operations. ...
30 CFR 905.762 - Criteria for designating areas as unsuitable for surface coal mining operations.
2010-07-01
... for surface coal mining operations. 905.762 Section 905.762 Mineral Resources OFFICE OF SURFACE MINING... mining operations. Part 762 of this chapter, Criteria for Designating Areas Unsuitable for Surface Coal Mining Operations, shall apply to surface coal mining operations. ...
Is the co-seismic slip distribution fractal?
Milliner, Christopher; Sammis, Charles; Allam, Amir; Dolan, James
2015-04-01
Co-seismic along-strike slip heterogeneity is widely observed for many surface-rupturing earthquakes as revealed by field and high-resolution geodetic methods. However, this co-seismic slip variability is currently a poorly understood phenomenon. Key unanswered questions include: What are the characteristics and underlying causes of along-strike slip variability? Do the properties of slip variability change from fault-to-fault, along-strike or at different scales? We cross-correlate optical, pre- and post-event air photos using the program COSI-Corr to measure the near-field, surface deformation pattern of the 1992 Mw 7.3 Landers and 1999 Mw 7.1 Hector Mine earthquakes in high-resolution. We produce the co-seismic slip profiles of both events from over 1,000 displacement measurements and observe consistent along-strike slip variability. Although the observed slip heterogeneity seems apparently complex and disordered, a spectral analysis reveals that the slip distributions are indeed self-affine fractal i.e., slip exhibits a consistent degree of irregularity at all observable length scales, with a 'short-memory' and is not random. We find a fractal dimension of 1.58 and 1.75 for the Landers and Hector Mine earthquakes, respectively, indicating that slip is more heterogeneous for the Hector Mine event. Fractal slip is consistent with both dynamic and quasi-static numerical simulations that use non-planar faults, which in turn causes heterogeneous along-strike stress, and we attribute the observed fractal slip to fault surfaces of fractal roughness. As fault surfaces are known to smooth over geologic time due to abrasional wear and fracturing, we also test whether the fractal properties of slip distributions alters between earthquakes from immature to mature fault systems. We will present results that test this hypothesis by using the optical image correlation technique to measure historic, co-seismic slip distributions of earthquakes from structurally mature, large
Fractal Dimension of Structurally Controlled River Networks of Pinar del Río, Cuba
Robert Ramírez-Hernández; Alina Rodríguez-Infante; Alexis Ordaz-Hernández
2017-01-01
River networks were studied applying the fractal systems approach and based on morphometric parameters. Procedures are applied to Cangre, Los Pozos, Paso Viejo, San Diego, Los Palacios, Santa Cruz and San Cristóbal river basins (Pinar del Río, Cuba). Drainage areas were extracted taking into account isolevel lines configurations and river lengths. For every stream the Euclidian length was also estimated, to calculate the river network fractal dimension. It seems that Takayasu approach is the ...
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.
Aggregate surface areas quantified through laser measurements for South African asphalt mixtures
CSIR Research Space (South Africa)
Anochie-Boateng, Joseph
2012-02-01
Full Text Available on the geometrical similarity among the same type of aggregate particles with different sizes, has been used (The Asphalt Institute 1993; Kandhal et al. 1998). The geometrical similarity concept used in fractal analysis defines an object as composed of sub... the funding for the 3D laser scanning device and the thematic project. References Feder J. (1988). Fractals. Plenum Press, New York. Field, F. (1978). ?Voids in the mineral aggregate: Test methods and specification criteria.? Proc., Canadian...
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...
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
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...
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.
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
Fractal properties of financial markets
Budinski-Petković, Lj.; Lončarević, I.; Jakšić, Z. M.; Vrhovac, S. B.
2014-09-01
We present an analysis of the USA stock market using a simple fractal function. Financial bubbles preceding the 1987, 2000 and 2007 crashes are investigated using the Besicovitch-Ursell fractal function. Fits show a good agreement with the S&P 500 data when a complete financial growth is considered, starting at the threshold of the abrupt growth and ending at the peak. Moving the final time of the fitting interval towards earlier dates causes growing discrepancy between two curves. On the basis of a detailed analysis of the financial index behavior we propose a method for identifying the stage of the current financial growth and estimating the time in which the index value is going to reach the maximum.
Fractal Scattering of Microwaves from Soils
Oleschko, K.; Korvin, G.; Balankin, A. S.; Khachaturov, R. V.; Flores, L.; Figueroa, B.; Urrutia, J.; Brambila, F.
2002-10-01
Using a combination of laboratory experiments and computer simulation we show that microwaves reflected from and transmitted through soil have a fractal dimension correlated to that of the soil's hierarchic permittivity network. The mathematical model relating the ground-penetrating radar record to the mass fractal dimension of soil structure is also developed. The fractal signature of the scattered microwaves correlates well with some physical and mechanical properties of soils.
Fractal properties of nanostructured semiconductors
Energy Technology Data Exchange (ETDEWEB)
Zhanabaev, Z.Zh. [Al-Farabi Khazakh National University, Tole bi Street, 96, Almaty 050012 (Kazakhstan); Grevtseva, T.Yu. [Al-Farabi Khazakh National University, Tole bi Street, 96, Almaty 050012 (Kazakhstan)]. E-mail: kenwp@mail.ru
2007-03-15
A theory for the temperature and time dependence of current carrier concentration in semiconductors with different non-equilibrium nanocluster structure has been developed. It was shown that the scale-invariant fractal self-similar and self-affine laws can exist near by the transition point to the equilibrium state. Results of the theory have been compared to the experimental data from electrical properties of semiconductor films with nanoclusters.
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti...... vasculature may affect the retinal response to potential vascular disease in later life....
Fractal-like kinetics of the solid-state anaerobic digestion.
Wang, Zhi-Wu; Xu, Fuqing; Manchala, Karthik R; Sun, Yewei; Li, Yebo
2016-07-01
Total solid content (TS) negatively impacts the methane production efficiency (MPE) of solid-state anaerobic digestion (SS-AD), to which the classic mass action-based kinetics failed to provide a unified explanation. This study revealed that SS-AD reactions actually follow the fractal-like kinetics in light of the surface reactions in crowded SS-AD environment packed with heterogeneous media. The fractal characteristics of the SS-AD kinetics were found increasingly pronounced as TS increased. This study represents the first attempt to resolve the dilemma in SS-AD kinetics with the application of fractal theory. Employing this new concept allows explaining the reduced MPE at high TS and offers an easy assessment of the fractal characteristics of the SS-AD media. Copyright © 2016. Published by Elsevier Ltd.
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.
Agus Nur, Andi; Syafri, Ildrem; Muslim, Dicky; Hirnawan, Febri; Raditya, Pradnya P.; Sulastri, Murni; Abdulah, Fikri
2016-01-01
Bumiayu in Central Java, Indonesia, has a typical landform characteristics. Differences of topography on each geomorphological unit indicated by the value of fractal dimension. This research provides important information on the influence of geomorphology conditions and subsurface geological phenomenon of research area based on fractal application. This research methodology relies on laboratory analysis and field observation. Landform is a characteristics of Bouguer anomaly contour manifestation. It is indicated by occurences of significant correlation between the Bouguer anomaly countour and geological cross section as well topography contour slope and Bouguer anomaly contour slope. Based on spatial analysis, morphology of research area is dominated by very high steep hills (more than 60%). Result of Bouguer anomaly countour analysis also shows that research area dominated by very high steep hills (more than 55%). Statistical analysis between the fractal value of lineament in Digital Elevation Model and fractal value of lineament in Bouguer anomaly countour as well the fractal value of topography countour and fractal value of Bouguer anomaly countour shows that the relationship was not significant. Further, the entire result of this verified research shows clearly that geomorphology conditions represents subsurface geological phenomenon.
Fractal Metrology for biogeosystems analysis
Torres-Argüelles, V.; Oleschko, K.; Tarquis, A. M.; Korvin, G.; Gaona, C.; Parrot, J.-F.; Ventura-Ramos, E.
2010-11-01
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 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.
The Effect of 200 MPa Pressure on Specific Surface Area of Clay
Directory of Open Access Journals (Sweden)
Koszela-Marek Ewa
2015-02-01
Full Text Available The paper presents the results of laboratory studies of the 200 MPa pressure effect on specific surface area of clay. The original high-pressure investigation stand was used for the pressure tests. Determination of the specific surface area was performed by the methylene blue adsorption method. The results of the specific surface area test were compared for non-pressurized clays and for clays pressured in a high-pressure chamber. It was found that the specific surface area of pressurized soil clearly increased. This shows that some microstructural changes take place in the soil skeleton of clays.
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.
Assessment of large aperture scintillometry for large-area surface ...
Indian Academy of Sciences (India)
29
This study defines that large aperture scintillometer is robust instrument which can evaluate energy flux over a large area with a long term series time domain. Moreover, further studied should be conducted to use in crop simulation modelling, developing of new model with calibration and validation of remote sensing energy ...
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.
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)...
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.
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)
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.
From Newton to Mandelbrot a primer in theoretical physics with fractals for the Macintosh
Stauffer, Dietrich
1996-01-01
From Newton to Mandelbrot A Primer in Theoretical Physics with Fractals for the Macintosh ( ) takes the student on a tour of the most important landmarks of theoretical physics classical, quantum, and statistical mechanics, relativity, electrodynamics, and, the most modern and exciting of all, the physics of fractals The treatment is confined to the essentials of each area, and short computer programs, numerous problems, and beautiful color illustrations round off this unusual textbook Ideally suited for a one-year course in theoretical physics it will also prove useful in preparing and revising for exams This edition is corrected and includes a new appendix on elementary particle physics, answers to all short questions, and a Macintosh diskette where a selection of executable programs exploring the fractal concept can be found The Diskette The program FRACTAL DIMENSION can be used on any 68030-, 68040,- or PowerPC-based Macintosh with 4 Mb RAM and 256 color display running System 67 - 75 - Sierpinski gasket ...
FRACTAL ANALYSIS OF MONTHLY EVAPORATION AND PRECIPITATION TIME SERIES AT CENTRAL MEXICO
Directory of Open Access Journals (Sweden)
Rafael Magallanes Quintanar
2015-07-01
Full Text Available Advances on climate change research, as well as the assessment of the potential impacts of climate change on water resources, would allow the understanding of the spatial and temporal variability of land-surface precipitation and evaporation time series at local and regional levels. In the present study, the spectral analysis approach was applied on monthly evaporation and precipitation anomaly time series with the aim of estimating their self-affinity statistics. The behavior of estimated fractal dimension values of evaporation time series throughout Zacatecas State territory is irregular, and noise in all the evaporation anomaly time series tends to have a persistent behavior. On the other hand, the behavior of estimated fractal dimension values of most of the precipitation time series throughout Zacatecas State territory tends to be like the Brownian motion. Self-affinity statistics of monthly evaporation or precipitation anomaly time series and geographic coordinates of 32 stations were used to estimate correlation coefficients; the results are compelling evidence concerning monthly precipitation anomaly behavior tends to be more regular toward North of Zacatecas State territory, that is, toward driest areas.
Cylindrically-Symmetric Equilibria in Ideal MHD with Fractal Pressure Profiles
Kraus, Brian; Hudson, Stuart
2016-10-01
In ideal magnetohydrodynamics, unphysical, pressure-driven currents exist where flux surfaces with rational rotational transform coincide with pressure gradients, a situation Grad termed ``pathological''. As an alternative, we construct a non-trivial, continuous pressure profile that is flat on sufficiently wide intervals near each rational surface. Such a profile must be self-similar and thus fractal, because intervals of flat pressure exist around high-order rational surfaces at all scales. This infinite-resolution fractal pressure is analyzed as a homeomorphism of the Cantor set. Additionally, an algorithm has been written to numerically produce an approximation of the pressure profile, where only a finite number of rational surfaces are considered. Using this algorithm, we investigate the magnetic field and current profiles associated with the fractal pressure and a given rotational transform in cylindrical geometry. This work was supported by DOE contract DE-AC02-09CH11466.
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.
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...
Cyclic Brunn-Minkowski Inequalities for p -affine surface area | Zhao ...
African Journals Online (AJOL)
In 2010, Werner and Ye extended the denition for mixed p-affine surface area to all real numbers p. Following this, we establish some isoperimetric inequalities for the general mixed p-affine surface area. The results in special cases yield some of the recent results on inequalities of this type. Mathematics Subject ...
30 CFR 933.761 - Areas designated unsuitable for surface coal mining by Act of Congress.
2010-07-01
... WITHIN EACH STATE NORTH CAROLINA § 933.761 Areas designated unsuitable for surface coal mining by Act of Congress. Part 761 of this chapter, Areas Designated Unsuitable for Coal Mining by Act of Congress, with the exception of §§ 761.11(c) and 761.12(f)(1), shall apply to surface coal mining and reclamation...
Suer, Berkay Tolga; Yaman, Zekai; Buyuksarac, Bora
2016-01-01
Fractal analysis is a mathematical method used to describe the internal architecture of complex structures such as trabecular bone. Fractal analysis of panoramic radiographs of implant recipient sites could help to predict the quality of the bone prior to implant placement. This study investigated the correlations between the fractal dimension values obtained from panoramic radiographs and the insertion torque and resonance frequency values of mandibular implants. Thirty patients who received a total of 55 implants of the same brand, diameter, and length in the mandibular premolar and molar regions were included in the study. The same surgical procedures were applied to each patient, and the insertion torque and resonance frequency values were recorded for each implant at the time of placement. The radiographic fractal dimensions of the alveolar bone in the implant recipient area were calculated from preoperative panoramic radiographs using a box-counting algorithm. The insertion torque and resonance frequency values were compared with the fractal dimension values using the Spearman test. All implants were successful, and none were lost during the follow-up period. Linear correlations were observed between the fractal dimension and resonance frequency, between the fractal dimension and insertion torque, and between resonance frequency and insertion torque. These results suggest that the noninvasive measurement of the fractal dimension from panoramic radiographs might help to predict the bone quality, and thus the primary stability of dental implants, before implant surgery.
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
Target surface area effects on hot electron dynamics from high intensity laser-plasma interactions
Zulick, C.; Raymond, A.; McKelvey, A.; Chvykov, V.; Maksimchuk, A.; Thomas, A. G. R.; Willingale, L.; Yanovsky, V.; Krushelnick, K.
2016-06-01
Reduced surface area targets were studied using an ultra-high intensity femtosecond laser in order to determine the effect of electron sheath field confinement on electron dynamics. X-ray emission due to energetic electrons was imaged using a {K}α imaging crystal. Electrons were observed to travel along the surface of wire targets, and were slowed mainly by the induced fields. Targets with reduced surface areas were correlated with increased hot electron densities and proton energies. Hybrid Vlasov-Fokker-Planck simulations demonstrated increased electric sheath field strength in reduced surface area targets.
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.
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.
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
30 CFR 905.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 905.764 Section 905.764 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE CALIFORNIA § 905.764 Process for designating areas unsuitable for surface coal mining... coal mining operations beginning one year after the effective date of this program. ...
30 CFR 947.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 947.764 Section 947.764 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE WASHINGTON § 947.764 Process for designating areas unsuitable for surface coal mining... coal mining and reclamation operations. (b) The Secretary shall notify the Washington Department of...
30 CFR 903.764 - Process for designating areas unsuitable for surface coal mining operations.
2010-07-01
... surface coal mining operations. 903.764 Section 903.764 Mineral Resources OFFICE OF SURFACE MINING... WITHIN EACH STATE ARIZONA § 903.764 Process for designating areas unsuitable for surface coal mining... coal mining operations beginning June 24, 1996, one year after the effective date of this program. ...
Fractals in petroleum geology and earth processes
Barton, Christopher C.; La Pointe, Paul R.
1995-01-01
In this unique volume, renowned experts discuss the applications of fractals in petroleum research-offering an excellent introduction to the subject. Contributions cover a broad spectrum of applications from petroleum exploration to production. Papers also illustrate how fractal geometry can quantify the spatial heterogeneity of different aspects of geology and how this information can be used to improve exploration and production results.
Fractal basins in an ecological model
Directory of Open Access Journals (Sweden)
I. Djellit
2013-09-01
Full Text Available Complex dynamics is detected in an ecological model of host-parasitoid interaction. It illustrates fractalization of basins with self-similarity and chaotic attractors. This paper describes these dynamic behaviors, bifurcations, and chaos. Fractals basins are displayed by numerical simulations.
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…
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. 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
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.
Textural characterization of coals using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Mahamud, Manuel; Lopez, Oscar [Faculty of Chemistry, Department of Chemical and Environmental Engineering, University of Oviedo, Campus de El Cristo, 33071 Oviedo (Spain); Pis, Jose Juan; Pajares, Jesus Alberto [Instituto Nacional del Carbon (C.S.I.C.), Apartado 73, 33080 Oviedo (Spain)
2003-05-15
The aim of this study is to show how fractal analysis can be effectively used to characterize the texture of porous solids. The materials under study were series of coals oxidized in air at various temperatures for different time intervals. Data from mercury porosimetry determinations of samples was analyzed using fractal models. The methods employed were those proposed by Neimark, Friesen and Mikula and that developed by Zhang and Li. Some methods are able to supply a fractal profile or 'fractal fingerprint' of materials, i.e. ranges of pore sizes with different fractal dimensions are detected. These fractal profiles are very sensitive to the oxidation treatment. The average fractal dimension can also be used as a valid parameter to monitor the textural evolution of the coals as the treatment progresses, as this behaves in a similar way to other textural parameters. The use of fractal analysis in conjunction with the results of classical characterization methods leads to a better understanding of textural modifications in the processing of materials.
Fractal Music: The Mathematics Behind "Techno" Music
Padula, Janice
2005-01-01
This article describes sound waves, their basis in the sine curve, Fourier's theorem of infinite series, the fractal equation and its application to the composition of music, together with algorithms (such as those employed by meteorologist Edward Lorenz in his discovery of chaos theory) that are now being used to compose fractal music on…
[Molecular structure and fractal analysis of oligosaccharide].
Liu, Wen-long; Wang, Lu-man; He, Dong-qi; Zhang, Tian-lan; Gou, Bao-di; Li, Qing
2014-10-18
To propose a calculation method of oligosaccharides' fractal dimension, and to provide a new approach to studying the drug molecular design and activity. By using the principle of energy optimization and computer simulation technology, the steady structures of oligosaccharides were found, and an effective way of oligosaccharides fractal dimension's calculation was further established by applying the theory of box dimension to the chemical compounds. By using the proposed method, 22 oligosaccharides' fractal dimensions were calculated, with the mean 1.518 8 ± 0.107 2; in addition, the fractal dimensions of the two activity multivalent oligosaccharides which were confirmed by experiments, An-2 and Gu-4, were about 1.478 8 and 1.516 0 respectively, while C-type lectin-like receptor Dectin-1's fractal dimension was about 1.541 2. The experimental and computational results were expected to help to find a class of glycoside drugs whose target receptor was Dectin-1. Fractal dimension, differing from other known macro parameters, is a useful tool to characterize the compound molecules' microscopic structure and function, which may play an important role in the molecular design and biological activity study. In the process of oligosaccharides drug screening, the fractal dimension of receptor and designed oligosaccharides or glycoclusters can be calculated respectively. The oligosaccharides with fractal dimension close to that of target receptor should then take priority compared with others, to get the drug molecules with latent activity.
Fractal analysis of polar bear hairs
Directory of Open Access Journals (Sweden)
Wang Qing-Li
2015-01-01
Full Text Available Hairs of a polar bear (Ursus maritimus are of superior properties such as the excellent thermal protection. Why do polar bears can resist such cold environment? The paper concludes that its fractal porosity plays an important role, and its fractal dimensions are very close to the golden mean, 1.618, revealing the possible optimal structure of polar bear hair.
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
Fractal organization of feline oocyte cytoplasm
Directory of Open Access Journals (Sweden)
G De Vico
2009-06-01
Full Text Available The present study aimed at verifying whether immature cat oocytes with morphologic irregular cytoplasm display selfsimilar features which can be analytically described by fractal analysis. Original images of oocytes collected by ovariectomy were acquired at a final magnification of 400 X with a CCD video camera connected to an optic microscope. After greyscale thresholding segmentation of cytoplasm, image profiles were submitted to fractal analysis using FANAL++, a program which provided an analytical standard procedure for determining the fractal dimension (FD. The presentation of the oocyte influenced the magnitude of the fractal dimension with the highest FD of 1.91 measured on grey-dark cytoplasm characterized by a highly connected network of lipid droplets and intracellular membranes. Fractal analysis provides an effective quantitative descriptor of the real cytoplasm morphology, which can influence the acquirement of in vitro developmental competence, without introducing any bias or shape approximation and thus contributes to an objective and reliable classification of feline oocytes.
Fractals and cosmological large-scale structure
Luo, Xiaochun; Schramm, David N.
1992-01-01
Observations of galaxy-galaxy and cluster-cluster correlations as well as other large-scale structure can be fit with a 'limited' fractal with dimension D of about 1.2. This is not a 'pure' fractal out to the horizon: the distribution shifts from power law to random behavior at some large scale. If the observed patterns and structures are formed through an aggregation growth process, the fractal dimension D can serve as an interesting constraint on the properties of the stochastic motion responsible for limiting the fractal structure. In particular, it is found that the observed fractal should have grown from two-dimensional sheetlike objects such as pancakes, domain walls, or string wakes. This result is generic and does not depend on the details of the growth process.
Designing fractal nanostructured biointerfaces for biomedical applications.
Zhang, Pengchao; Wang, Shutao
2014-06-06
Fractal structures in nature offer a unique "fractal contact mode" that guarantees the efficient working of an organism with an optimized style. Fractal nanostructured biointerfaces have shown great potential for the ultrasensitive detection of disease-relevant biomarkers from small biomolecules on the nanoscale to cancer cells on the microscale. This review will present the advantages of fractal nanostructures, the basic concept of designing fractal nanostructured biointerfaces, and their biomedical applications for the ultrasensitive detection of various disease-relevant biomarkers, such microRNA, cancer antigen 125, and breast cancer cells, from unpurified cell lysates and the blood of patients. © 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.
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
Fractal study of Ni-Cr-Mo alloy for dental applications: effect of beryllium
Energy Technology Data Exchange (ETDEWEB)
Eftekhari, Ali
2003-12-30
Different Ni-based alloys with various compositions were prepared by varying the amounts of beryllium. Effect of the amount of beryllium added to the alloy on its corrosion in an electrolyte solution of artificial saliva was investigated. Fractal dimension was used as a quantitative factor for surface analysis of the alloys before and after storage in the artificial salvia. The fractal dimensions of the electrode surfaces were determined by means of the most reliable method in this context viz. time dependency of the diffusion-limited current for a system involving 'diffusion towards electrode surface'. The results showed that increase of the beryllium amount in the alloy composition significantly increases the alloy corrosion. It is accompanied by increase of the fractal dimension and roughness of the electrode surface, whereas a smooth and shiny surface is required for dentures. From the methodology point of view, the approach utilized for fractal analysis of the alloy surfaces (Au-masking of metallic surfaces) is a novel and efficient method for study of denture surfaces. Generally, this approach is of interest for corrosion studies of different metals and alloys, particularly where changes in surface structure have a significant importance.
Fractal study of Ni Cr Mo alloy for dental applications: effect of beryllium
Eftekhari, Ali
2003-12-01
Different Ni-based alloys with various compositions were prepared by varying the amounts of beryllium. Effect of the amount of beryllium added to the alloy on its corrosion in an electrolyte solution of artificial saliva was investigated. Fractal dimension was used as a quantitative factor for surface analysis of the alloys before and after storage in the artificial salvia. The fractal dimensions of the electrode surfaces were determined by means of the most reliable method in this context viz. time dependency of the diffusion-limited current for a system involving "diffusion towards electrode surface". The results showed that increase of the beryllium amount in the alloy composition significantly increases the alloy corrosion. It is accompanied by increase of the fractal dimension and roughness of the electrode surface, whereas a smooth and shiny surface is required for dentures. From the methodology point of view, the approach utilized for fractal analysis of the alloy surfaces (Au-masking of metallic surfaces) is a novel and efficient method for study of denture surfaces. Generally, this approach is of interest for corrosion studies of different metals and alloys, particularly where changes in surface structure have a significant importance.
Random sequential adsorption on fractals.
Ciesla, Michal; Barbasz, Jakub
2012-07-28
Irreversible adsorption of spheres on flat collectors having dimension d fractals (1 < d < 2), and on general Cantor set (d < 1). Adsorption process is modeled numerically using random sequential adsorption (RSA) algorithm. The paper concentrates on measurement of fundamental properties of coverages, i.e., maximal random coverage ratio and density autocorrelation function, as well as RSA kinetics. Obtained results allow to improve phenomenological relation between maximal random coverage ratio and collector dimension. Moreover, simulations show that, in general, most of known dimensional properties of adsorbed monolayers are valid for non-integer dimensions.
Fractal dimension of bioconvection patterns
Noever, David A.
1990-01-01
Shallow cultures of the motile algal strain, Euglena gracilis, were concentrated to 2 x 10 to the 6th organisms per ml and placed in constant temperature water baths at 24 and 38 C. Bioconvective patterns formed an open two-dimensional structure with random branches, similar to clusters encountered in the diffusion-limited aggregation (DLA) model. When averaged over several example cultures, the pattern was found to have no natural length scale, self-similar branching, and a fractal dimension (d about 1.7). These agree well with the two-dimensional DLA.
Fractal dimension of wind speed time series
International Nuclear Information System (INIS)
Chang, Tian-Pau; Ko, Hong-Hsi; Liu, Feng-Jiao; Chen, Pai-Hsun; Chang, Ying-Pin; Liang, Ying-Hsin; Jang, Horng-Yuan; Lin, Tsung-Chi; Chen, Yi-Hwa
2012-01-01
Highlights: ► Fractal dimension of wind speeds in Taiwan is studied considering climate factors. ► Relevant algorithms for the calculation of fractal dimension are presented graphically. ► Fractal dimension reveals negative correlation with mean wind speed. ► Fractal dimension is not lower even wind distribution is well described by Weibull pdf. - Abstract: The fluctuation of wind speed within a specific time period affects a lot the energy conversion rate of wind turbine. In this paper, the concept of fractal dimension in chaos theory is applied to investigate wind speed characterizations; numerical algorithms for the calculation of the fractal dimension are presented graphically. Wind data selected is observed at three wind farms experiencing different climatic conditions from 2006 to 2008 in Taiwan, where wind speed distribution can be properly classified to high wind season from October to March and low wind season from April to September. The variations of fractal dimensions among different wind farms are analyzed from the viewpoint of climatic conditions. The results show that the wind speeds studied are characterized by medium to high values of fractal dimension; the annual dimension values lie between 1.61 and 1.66. Because of monsoon factor, the fluctuation of wind speed during high wind months is not as significant as that during low wind months; the value of fractal dimension reveals negative correlation with that of mean wind speed, irrespective of wind farm considered. For a location where the wind distribution is well described by Weibull function, its fractal dimension is not necessarily lower. These findings are useful to wind analysis.
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
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.
Development of cortical thickness and surface area in autism spectrum disorder
Directory of Open Access Journals (Sweden)
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.
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…
Random fractal characters and length uncertainty of the continental ...
Indian Academy of Sciences (India)
2Collaborative Innovation Center on Yellow River Civilization of Henan Province, Kaifeng 475 001, China. ∗. Corresponding author. e-mail: mjh@henu.edu.cn. A coastline is a random fractal ... research showed that the fractal dimension (D) of. Keywords. Continental coastline of China; scaling region; random fractal; fractal ...
Fractal gait patterns are retained after entrainment to a fractal stimulus.
Rhea, Christopher K; Kiefer, Adam W; Wittstein, Matthew W; Leonard, Kelsey B; MacPherson, Ryan P; Wright, W Geoffrey; Haran, F Jay
2014-01-01
Previous work has shown that fractal patterns in gait can be altered by entraining to a fractal stimulus. However, little is understood about how long those patterns are retained or which factors may influence stronger entrainment or retention. In experiment one, participants walked on a treadmill for 45 continuous minutes, which was separated into three phases. The first 15 minutes (pre-synchronization phase) consisted of walking without a fractal stimulus, the second 15 minutes consisted of walking while entraining to a fractal visual stimulus (synchronization phase), and the last 15 minutes (post-synchronization phase) consisted of walking without the stimulus to determine if the patterns adopted from the stimulus were retained. Fractal gait patterns were strengthened during the synchronization phase and were retained in the post-synchronization phase. In experiment two, similar methods were used to compare a continuous fractal stimulus to a discrete fractal stimulus to determine which stimulus type led to more persistent fractal gait patterns in the synchronization and post-synchronization (i.e., retention) phases. Both stimulus types led to equally persistent patterns in the synchronization phase, but only the discrete fractal stimulus led to retention of the patterns. The results add to the growing body of literature showing that fractal gait patterns can be manipulated in a predictable manner. Further, our results add to the literature by showing that the newly adopted gait patterns are retained for up to 15 minutes after entrainment and showed that a discrete visual stimulus is a better method to influence retention.
Specific surface area of a crushed welded tuff before and after aqueous dissolution
Reddy, M.M.; Claassen, H.C.
1994-01-01
Specific surface areas were measured for several reference minerals (anorthoclase, labradorite and augite), welded tuff and stream sediments from Snowshoe Mountain, near Creede, Colorado. Crushed and sieved tuff had an unexpectedly small variation in specific surface area over a range of size fractions. Replicate surface area measurements of the largest and smallest tuff particle size fractions examined (1-0.3 mm and <0.212 mm) were 2.3 ?? 0.2 m2/g for each size fraction. Reference minerals prepared in the same way as the tuff had smaller specific surface areas than that of the tuff of the same size fraction. Higher than expected tuff specific surface areas appear to be due to porous matrix. Tuff, reacted in solutions with pH values from 2 to 6, had little change in specific surface area in comparison with unreacted tuff. Tuff, reacted with solutions having high acid concentrations (0.1 M hydrochloric acid or sulfuric-hydrofluoric acid), exhibited a marked increase in specific surface area compared to unreacted tuff. ?? 1994.
H-fractal seismic metamaterial with broadband low-frequency bandgaps
Du, Qiujiao; Zeng, Yi; Xu, Yang; Yang, Hongwu; Zeng, Zuoxun
2018-03-01
The application of metamaterial in civil engineering to achieve isolation of a building by controlling the propagation of seismic waves is a substantial challenge because seismic waves, a superposition of longitudinal and shear waves, are more complex than electromagnetic and acoustic waves. In this paper, we design a broadband seismic metamaterial based on H-shaped fractal pillars and report numerical simulation of band structures for seismic surface waves propagating. Comparative study on the band structures of H-fractal seismic metamaterials with different levels shows that a new level of fractal structure creates new band gap, widens the total band gaps and shifts the same band gap towards lower frequencies. Moreover, the vibration modes for H-fractal seismic metamaterials are computed and analyzed to clarify the mechanism of widening band gaps. A numerical investigation of seismic surface waves propagation on a 2D array of fractal unit cells on the surface of semi-infinite substrate is proposed to show the efficiency of earthquake shielding in multiple complete band gaps.
Ponnuvel, S.; Ananth, M. Prem
2018-03-01
In this study the effect of specific surface area of the MWCNTs on the drilled hole qualities was investigated. Epoxy araldite LY556 with hardener HY951 and E-glass coarse plain weave fabric are used for the fabrication of reference material (specimen A). Multi-WalledCarbon Nanotubes (MWCNTs) with diameters fabrication of study materials, namely specimen B and specimen C respectively. In specimen B the epoxy resin was filled with MWCNTs having a specific surface area >500 m2 g‑1. MWCNTs in specimen C had a specific surface area >110 m2 g‑1. Drilling experiments were conducted on all the three specimens. Two dimensional delamination factor and the surface roughness of the inner wall of the drilled holes were investigated using Grey Relational Analysis (GRA) and Analysis of variance (ANOVA). Two dimensional delamination factor showed better performance from specimen B and specimen C in comparison with specimen A suggesting improvement in the bonding between epoxy and the glass fiber in the presence of MWCNTs. Similar observations were made for surface roughness of the inner wall of the drilled holes at 1250 rpm. Whereas the presence of MWCNTs (Specimen B and specimen C) produced poor surface finish at 500 rpm in comparison with specimen A. Variations in the hole quality characteristics between specimen B and specimen C was marginal with better observations in specimen C.
Zhang, Xin; Liu, Haitao; Zhong, Ying
2013-10-07
We theoretically investigate the electromagnetic enhancement on a metallic surface patterned with periodic subwavelength structures. Fully-vectorial calculations show a large-area electromagnetic enhancement (LAEE) on the surface, which strongly contrasts with the previously reported "hot spots" that occur in specific tiny regions and which relieves the rigorous requirement of the nano-scale location of sample molecules. The LAEE allows for designing more practicable substrates for many enhanced-spectra applications. By building up microscopic models, the LAEE is shown due to a resonant excitation of surface waves that include both the surface plasmon polariton (SPP) and a quasi-cylindrical wave (QCW). The surface waves propagate on the substrate over a long distance and thus greatly enlarge the area of electromagnetic enhancement compared to the nano-sized hot spots caused by localized modes. Gain medium is introduced to further strengthen the large-area surface-wave resonance, with which an enhancement factor (EF) of electric-field intensity up to a few thousands is achieved.
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.
THE “SPORT” OF ROUGH CONTACTS AND THE FRACTAL PARADOX IN WEAR LAWS
Directory of Open Access Journals (Sweden)
Michele Ciavarella
2018-02-01
Full Text Available In a recent paper in Science, namely, “The Contact Sport of Rough Surfaces”, Carpick summarizes recent efforts in a “contact challenge” to predict in detail an elastic contact between the mathematically defined fractal rough surfaces under (very little adhesion. He also suggests the next steps that are needed to “fulfill da Vinci’s dream of understanding what causes friction”. However, this is disappointing as friction has been studied since the times of Leonardo and in 500 years, no predictive model has emerged, nor any significant improvement from rough contact models. Similarly, a very large effort we have spent on the “sport” of studying rough surfaces has not made us any closer to being able to predict the coefficient of proportionality between wear loss and friction dissipation which was already observed by Reye in 1860. Recent nice simulations by Aghababaei, Warner and Molinari have confirmed the criterion for the formation of debris of a single particle, proposed in 1958 by Rabinowicz, as well as Reye’s assumption for the proportionality with frictional loss, which is very close to Archard anyway. More recent investigations under variable loads suggest that Reye’s assumption is probably much more general than Archard’s law. The attempts to obtain exact coefficients with rough surfaces models are very far from predictive, essentially because for fractals most authors fail to recognize that resolution-dependence of the contact area makes the models very ill-defined. We also suggest that in the models of wear, rough contacts should be considered “plastic” and “adhesive” and introduce a new length scale in the problem.
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.
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.
Directory of Open Access Journals (Sweden)
Dongqi Wen
2015-12-01
Full Text Available Geochemical and biological processes that operate in the soil matrix and on the soil surface are important to the degradation of biosolids in soil. Due to the large surface area of soils it is assumed that the microbial ecology is associated with mineral soil surface area. The total mineral surface areas were determined for soils from eight different fields selected from a long term study (1972–2006 of annual biosolids application to 41 fields in central Illinois varying in size from 3.6 to 66 ha. The surface areas for the soils varied from 1 to 9 m2/g of soil. The biological degradation rates for the eight soils were determined using a biological degradation rate model (DRM and varied from 0.02 to 0.20/year−1. Regression analysis revealed that the degradation rate was positively associated with mineral soil surface area (1 m2/g produces 0.018 year−1 increase in the degradation rate. The annual soil sequestration rate was calculated to increase from 1% to 6% when the soil total surface area increased from 1 to 9 m2/g of soil. Therefore, land application of biosolids is an effective way to enhance carbon sequestration in soils and reduce greenhouse gas emissions.
On the ubiquitous presence of fractals and fractal concepts in pharmaceutical sciences: a review.
Pippa, Natassa; Dokoumetzidis, Aristides; Demetzos, Costas; Macheras, Panos
2013-11-18
Fractals have been very successful in quantifying nature's geometrical complexity, and have captured the imagination of scientific community. The development of fractal dimension and its applications have produced significant results across a wide variety of biomedical applications. This review deals with the application of fractals in pharmaceutical sciences and attempts to account the most important developments in the fields of pharmaceutical technology, especially of advanced Drug Delivery nano Systems and of biopharmaceutics and pharmacokinetics. Additionally, fractal kinetics, which has been applied to enzyme kinetics, drug metabolism and absorption, pharmacokinetics and pharmacodynamics are presented. This review also considers the potential benefits of using fractal analysis along with considerations of nonlinearity, scaling, and chaos as calibration tools to obtain information and more realistic description on different parts of pharmaceutical sciences. As a conclusion, the purpose of the present work is to highlight the presence of fractal geometry in almost all fields of pharmaceutical research. Copyright © 2013 Elsevier B.V. All rights reserved.
Comparative analysis of surface soil moisture retrieval using VSWI and TVDI in karst areas
Yan, Hongbo; Zhou, Guoqing; Lu, Xianjian
2015-12-01
Vegetation Supply Water Index (VSWI) and Temperature Vegetation dryness Index (TVDI) are two most commonly used methods for surface soil moisture (SSM) retrieval using electromagnetic spectrum of visible, near infrared and thermal infrared band. Both of them take into account the effect of vegetation index (VI) and surface temperature (Ts) on SSM. A comparative analysis of the ability and effect of the two methods for SSM retrieval in karst areas was carried out, using the remote sensing data of Landsat 8 OLI_TIRS. The study area is located in Guilin, which is a typical karst area. The experimental results show that TVDI is more suitable for SSM retrieval in karst areas.
Influence of Ecological Factors on Estimation of Impervious Surface Area Using Landsat 8 Imagery
Directory of Open Access Journals (Sweden)
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
Measurement Based Quantum Computation on Fractal Lattices
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Michal Hajdušek
2010-06-01
Full Text Available In this article we extend on work which establishes an analology between one-way quantum computation and thermodynamics to see how the former can be performed on fractal lattices. We find fractals lattices of arbitrary dimension greater than one which do all act as good resources for one-way quantum computation, and sets of fractal lattices with dimension greater than one all of which do not. The difference is put down to other topological factors such as ramification and connectivity. This work adds confidence to the analogy and highlights new features to what we require for universal resources for one-way quantum computation.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fang, Jieran; Wang, Di; DeVault, Clayton T
2017-01-01
optical absorption, which hinders its incorporation with modern photodetecting systems. In this work, we propose a gold snowflake-like fractal metasurface design to realize broadband and polarization-insensitive plasmonic enhancement in graphene photodetector. We experimentally obtain an enhanced...... photovoltage from the fractal metasurface that is an order of magnitude greater than that generated at a plain gold-graphene edge and such an enhancement in the photovoltage sustains over the entire visible spectrum. We also observed a relatively constant photoresponse with respect to polarization angles...... of incident light, as a result of the combination of two orthogonally oriented concentric hexagonal fractal geometries in one metasurface....
Fractal boundaries in chaotic hamiltonian systems
Viana, R. L.; Mathias, A. C.; Marcus, F. A.; Kroetz, T.; Caldas, I. L.
2017-10-01
Fractal structures are typically present in the dynamics of chaotic orbits in non-integrable open Hamiltonian systems and result from the extremely complicated nature of the invariant manifolds of unstable periodic orbits. Exit basins, the set of initial conditions leading to orbits escaping through a given exit, have very frequently fractal boundaries. In this work we analyze exit basin boundaries in a dynamical system of physical interest, namely the motion of charged particles in a magnetized plasma subjected to electrostatic drift waves, and characterize in a quantitative way the fractality of these structures and their observable consequences, as the final-state uncertainty.
CLPX-Satellite: EO-1 Hyperion Surface Reflectance, Snow-Covered Area, and Grain Size
National Aeronautics and Space Administration — This data set consists of apparent surface reflectance, subpixel snow-covered area and grain size collected from the Hyperion hyperspectral imager. The Hyperion...
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