LCAO approximation for scaling properties of the Menger sponge fractal.
Sakoda, Kazuaki
2006-11-13
The electromagnetic eigenmodes of a three-dimensional fractal called the Menger sponge were analyzed by the LCAO (linear combination of atomic orbitals) approximation and a first-principle calculation based on the FDTD (finite-difference time-domain) method. Due to the localized nature of the eigenmodes, the LCAO approximation gives a good guiding principle to find scaled eigenfunctions and to observe the approximate self-similarity in the spectrum of the localized eigenmodes.
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.
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.
Gao, Guang-Lei; Ding, Guo-Dong; Wu, Bin; Zhang, Yu-Qing; Qin, Shu-Gao; Zhao, Yuan-Yuan; Bao, Yan-Feng; Liu, Yun-Dong; Wan, Li; Deng, Ji-Feng
2014-01-01
Background Biological soil crusts are common components of desert ecosystem; they cover ground surface and interact with topsoil that contribute to desertification control and degraded land restoration in arid and semiarid regions. Methodology/Principal Findings To distinguish the changes in topsoil affected by biological soil crusts, we compared topsoil properties across three types of successional biological soil crusts (algae, lichens, and mosses crust), as well as the referenced sandland in the Mu Us Desert, Northern China. Relationships between fractal dimensions of soil particle size distribution and selected soil properties were discussed as well. The results indicated that biological soil crusts had significant positive effects on soil physical structure (Psoil organic carbon and nutrients showed an upward trend across the successional stages of biological soil crusts. Fractal dimensions ranged from 2.1477 to 2.3032, and significantly linear correlated with selected soil properties (R2 = 0.494∼0.955, Psoil crusts cause an important increase in soil fertility, and are beneficial to sand fixation, although the process is rather slow. Fractal dimension proves to be a sensitive and useful index for quantifying changes in soil properties that additionally implies desertification. This study will be essential to provide a firm basis for future policy-making on optimal solutions regarding desertification control and assessment, as well as degraded ecosystem restoration in arid and semiarid regions. PMID:24516668
Directory of Open Access Journals (Sweden)
Guang-Lei Gao
Full Text Available BACKGROUND: Biological soil crusts are common components of desert ecosystem; they cover ground surface and interact with topsoil that contribute to desertification control and degraded land restoration in arid and semiarid regions. METHODOLOGY/PRINCIPAL FINDINGS: To distinguish the changes in topsoil affected by biological soil crusts, we compared topsoil properties across three types of successional biological soil crusts (algae, lichens, and mosses crust, as well as the referenced sandland in the Mu Us Desert, Northern China. Relationships between fractal dimensions of soil particle size distribution and selected soil properties were discussed as well. The results indicated that biological soil crusts had significant positive effects on soil physical structure (P<0.05; and soil organic carbon and nutrients showed an upward trend across the successional stages of biological soil crusts. Fractal dimensions ranged from 2.1477 to 2.3032, and significantly linear correlated with selected soil properties (R(2 = 0.494∼0.955, P<0.01. CONCLUSIONS/SIGNIFICANCE: Biological soil crusts cause an important increase in soil fertility, and are beneficial to sand fixation, although the process is rather slow. Fractal dimension proves to be a sensitive and useful index for quantifying changes in soil properties that additionally implies desertification. This study will be essential to provide a firm basis for future policy-making on optimal solutions regarding desertification control and assessment, as well as degraded ecosystem restoration in arid and semiarid regions.
Definition of fractal topography to essential understanding of scale-invariance
Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan
2017-01-01
Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals. PMID:28436450
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
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.
Spanning trees in a fractal scale-free lattice
Zhang, Zhongzhi; Liu, Hongxiao; Wu, Bin; Zou, Tao
2011-01-01
Spanning trees provide crucial insight into the origin of fractality in fractal scale-free networks. In this paper, we present the number of spanning trees in a particular fractal scale-free lattice (network). We first study analytically the topological characteristics of the lattice and show that it is simultaneously scale-free, highly clustered, “large-world,” fractal, and disassortative. Any previous model does not have all the properties as the studied one. Then, by using the renormalization group technique we derive analytically the number of spanning trees in the network under consideration, based on which we also determine the entropy for the spanning trees of the network. These results shed light on understanding the structural characteristics of and dynamical processes on scale-free networks with fractality. Moreover, our method and process for employing the decimation technique to enumerate spanning trees are general and can be easily extended to other deterministic media with self-similarity.
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
Schmitt, Daniel T; Ivanov, Plamen Ch
2007-11-01
Heart beat fluctuations exhibit temporal structure with robust long-range correlations, fractal and nonlinear features, which have been found to break down with pathologic conditions, reflecting changes in the mechanism of neuroautonomic control. It has been hypothesized that these features change and even break down also with advanced age, suggesting fundamental alterations in cardiac control with aging. Here we test this hypothesis. We analyze heart beat interval recordings from the following two independent databases: 1) 19 healthy young (average age 25.7 yr) and 16 healthy elderly subjects (average age 73.8 yr) during 2 h under resting conditions from the Fantasia database; and 2) 29 healthy elderly subjects (average age 75.9 yr) during approximately 8 h of sleep from the sleep heart health study (SHHS) database, and the same subjects recorded 5 yr later. We quantify: 1) the average heart rate (); 2) the SD sigma(R-R) and sigma(DeltaR-R) of the heart beat intervals R-R and their increments DeltaR-R; 3) the long-range correlations in R-R as measured by the scaling exponent alpha(R-R) using the Detrended Fluctuation Analysis; 4) fractal linear and nonlinear properties as represented by the scaling exponents alpha(sgn) and alpha(mag) for the time series of the sign and magnitude of DeltaR-R; and 5) the nonlinear fractal dimension D(k) of R-R using the fractal dimension analysis. We find: 1) No significant difference in (P > 0.05); 2) a significant difference in sigma(R-R) and sigma(DeltaR-R) for the Fantasia groups (P 0.5); and 3) no significant change in the fractal measures alpha(R-R) (P > 0.15), alpha(sgn) (P > 0.2), alpha(mag) (P > 0.3), and D(k) with age. Our findings do not support the hypothesis that fractal linear and nonlinear characteristics of heart beat dynamics break down with advanced age in healthy subjects. Although our results indeed show a reduced SD of heart beat fluctuations with advanced age, the inherent temporal fractal and nonlinear
Interactive Estimation of the Fractal Properties of Carbonate Rocks
Amosu, Adewale; Mahmood, Hamdi; Ofoche, Paul; Imsalem, Mohamed
2018-01-01
Scale invariance of intrinsic patterns is an important concept in geology that can be observed in numerous geological objects and phenomena. These geological objects and phenomena are described as containing statistically selfsimilar patterns often modeled with fractal geometry. Fractal geometry has been used extensively to characterize pore space and fracture distribution of both carbonate and clastic rocks as well as the transport properties of porous media and fluid flow in reservoirs. The...
Fractal scale-free networks resistant to disease spread
International Nuclear Information System (INIS)
Zhang, Zhongzhi; Zhou, Shuigeng; Zou, Tao; Chen, Guisheng
2008-01-01
The conventional wisdom is that scale-free networks are prone to epidemic propagation; in the paper we demonstrate that, on the contrary, disease spreading is inhibited in fractal scale-free networks. We first propose a novel network model and show that it simultaneously has the following rich topological properties: scale-free degree distribution, tunable clustering coefficient, 'large-world' behavior, and fractal scaling. Existing network models do not display these characteristics. Then, we investigate the susceptible–infected–removed (SIR) model of the propagation of diseases in our fractal scale-free networks by mapping it to the bond percolation process. We establish the existence of non-zero tunable epidemic thresholds by making use of the renormalization group technique, which implies that power law degree distribution does not suffice to characterize the epidemic dynamics on top of scale-free networks. We argue that the epidemic dynamics are determined by the topological properties, especially the fractality and its accompanying 'large-world' behavior
Fractal approach in characterization of spatial pattern of soil properties
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Boško Miloš
2017-01-01
Full Text Available The objective of the study was to characterize spatial pattern of soil properties (CaCO3, soil organic carbon, P2O5, K2O, and clay content using fractal concept. Total of 141 top-soil samples (0-30 cm were collected on 1850 ha in karst polje (Petrovo polje, Croatia and analyzed for listed soil properties. The semi-variogram method was used to estimate fractal dimension (D value which was performed from both of isotropic and anisotropic perspective. The D value of soil properties ranged between 1.76 to 1.97, showing a domination of the short-range variations. The SOC and K2O fractal D values 1.79 and 1.76 respectively, exhibited a spatial continuity at the entire analysed range of the scale. The D value for P2O5 (1.97 showed a nearly total absence of the spatial structure at all scales. The CaCO3 and clay content indicated a multifractal behavior mainly attributed to effects of alluviation, differences in geology and its spatial changes and transitions. The results of anisotropic analysis of soil properties pattern have showed strong relations with directions and partial self-similarity over limited ranges of scales defined by scale-break. Finally, our results showed that fractal analysis can be used as a appropriate tool for the characterization of spatial pattern irregularities of soil properties and detection of soil forming factors that cause it.
Scaling of light scattered from fractal aggregates at resonance
Ortiz, Guillermo P.; Mochán, W. Luis
2003-05-01
Due to the scale invariance of fractal aggregates, light scattered from them often decays as a power of the scattering wave vector. The exponent in this power law has been usually interpreted as the geometrical fractal dimension. However, the validity of this interpretation is questionable for frequencies close to the resonances of the system, for which multiple scattering becomes important. In this work we calculate the dipole moments optically induced in fractal aggregates and the corresponding self-consistent field, as well as the electromagnetic normal modes. To this end, we develop a multiresolution hierarchical representation of the aggregate that allows the study of large systems taking fully into account the long range of the interactions. We analyze the scaling properties of the dynamically induced dipolar distribution. We find that under resonant conditions, scaling with the geometric fractal dimension is only observed for systems much larger than a length scale that is related to the linewidth of each individual resonance. The relevance to this result for the interpretation of light scattering experiments is discussed.
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.
Generating hierarchial scale-free graphs from fractals
Energy Technology Data Exchange (ETDEWEB)
Komjathy, Julia, E-mail: komyju@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary); Simon, Karoly, E-mail: simonk@math.bme.hu [Department of Stochastics, Institute of Mathematics, Technical University of Budapest, H-1529 P.O. Box 91 (Hungary)
2011-08-15
Highlights: > We generate deterministic scale-free networks using graph-directed self similar IFS. > Our model exhibits similar clustering, power law decay properties to real networks. > The average length of shortest path and the diameter of the graph are determined. > Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal {Lambda}. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal {Lambda} we generate random graph sequence sharing similar properties.
Generating hierarchial scale-free graphs from fractals
International Nuclear Information System (INIS)
Komjathy, Julia; Simon, Karoly
2011-01-01
Highlights: → We generate deterministic scale-free networks using graph-directed self similar IFS. → Our model exhibits similar clustering, power law decay properties to real networks. → The average length of shortest path and the diameter of the graph are determined. → Using this model, we generate random graphs with prescribed power law exponent. - Abstract: Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabasi, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal Λ. With rigorous mathematical results we verify that our model captures some of the most important features of many real networks: the scale-free and the high clustering properties. We also prove that the diameter is the logarithm of the size of the system. We point out a connection between the power law exponent of the degree distribution and some intrinsic geometric measure theoretical properties of the underlying fractal. Using our (deterministic) fractal Λ we generate random graph sequence sharing similar properties.
Fractal and mechanical micro- and nanorange properties of sylvite and halite crystals
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Valery N. Aptukov
2017-09-01
Full Text Available This article involves the treatment of micro- and nanorange scanning and indentation data for salt rock crystals obtained with help of the scanning microscope Dimension Icon using the mathematical models. It also describes the basic methods of fractal analysis. It shows the effectiveness of the method of minimal covering which is chosen to research the fractal properties of salt rock crystal surfaces. The article includes the algorithm of this method and the description of its generalization for the two-dimensional case. The values of fractal index and multifractal parameters have been calculated on the basis of the minimal covering method. The article also involves the anisotropy effects for fractal properties, comparison of fractal behavior on different scale levels. It gives the values of hardness for different parts of the crystals and studies the correlation between hardness and fractal index and describes the character of the influence of fractal dimension on roughness.
Fractal Modeling and Scaling in Natural Systems - Editorial
The special issue of Ecological complexity journal on Fractal Modeling and Scaling in Natural Systems contains representative examples of the status and evolution of data-driven research into fractals and scaling in complex natural systems. The editorial discusses contributions to understanding rela...
Scaling condition for multiple scattering in fractal aggregates
Ortiz, Guillermo P.; Mochán, W. Luis
2003-10-01
It is well known that under the first Born approximation, the differential cross-section dσ/ dΩ for light scattered by a fractal of dimension df scales with wave vector Q as Q- df. The use of this formula to interpret experiments performed at frequencies close to the resonances of the system for which multiple scattering is not negligible is questionable. We study the scaling properties of the light scattered by colloidal aggregates employing a novel multi-resolution hierarchical algorithm which allows the study of large systems taking fully into account the long range of the interactions in multiple scattering calculations. We obtain the conditions under which scaling may be present and find that even under resonant conditions, the scattering cross-section may scale with the fractal dimension df, but only if the aggregate is larger than a dissipation and frequency-dependent length-scale Lh, confirming within a full vectorial calculation a result previously found for scalar interactions. For smaller aggregates, dσ/ dΩ might scale with a different exponent or it might not scale at all, depending on the frequency of light employed. This could explain the discrepancies between experiments performed on similar systems within the strong scattering regime.
Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales
Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei
2017-11-01
Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.
Experimental control of scaling behavior: what is not fractal?
Likens, Aaron D; Fine, Justin M; Amazeen, Eric L; Amazeen, Polemnia G
2015-10-01
The list of psychological processes thought to exhibit fractal behavior is growing. Although some might argue that the seeming ubiquity of fractal patterns illustrates their significance, unchecked growth of that list jeopardizes their relevance. It is important to identify when a single behavior is and is not fractal in order to make meaningful conclusions about the processes underlying those patterns. The hypothesis tested in the present experiment is that fractal patterns reflect the enactment of control. Participants performed two steering tasks: steering on a straight track and steering on a circular track. Although each task could be accomplished by holding the steering wheel at a constant angle, steering around a curve may require more constant control, at least from a psychological standpoint. Results showed that evidence for fractal behavior was strongest for the circular track; straight tracks showed evidence of two scaling regions. We argue from those results that, going forward, the goal of the fractal literature should be to bring scaling behavior under experimental control.
Fractal and transfractal recursive scale-free nets
International Nuclear Information System (INIS)
Rozenfeld, Hernan D; Havlin, Shlomo; Ben-Avraham, Daniel
2007-01-01
We explore the concepts of self-similarity, dimensionality, and (multi)scaling in a new family of recursive scale-free nets that yield themselves to exact analysis through renormalization techniques. All nets in this family are self-similar and some are fractals-possessing a finite fractal dimension-while others are small-world (their diameter grows logarithmically with their size) and are infinite-dimensional. We show how a useful measure of transfinite dimension may be defined and applied to the small-world nets. Concerning multiscaling, we show how first-passage time for diffusion and resistance between hubs (the most connected nodes) scale differently than for other nodes. Despite the different scalings, the Einstein relation between diffusion and conductivity holds separately for hubs and nodes. The transfinite exponents of small-world nets obey Einstein relations analogous to those in fractal nets
[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.
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....
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.
Directory of Open Access Journals (Sweden)
Alexander J. Bies
2016-07-01
Full Text Available Two measures are commonly used to describe scale-invariant complexity in images: fractal dimension (D and power spectrum decay rate (β. Although a relationship between these measures has been derived mathematically, empirical validation across measurements is lacking. Here, we determine the relationship between D and β for 1- and 2-dimensional fractals. We find that for 1-dimensional fractals, measurements of D and β obey the derived relationship. Similarly, in 2-dimensional fractals, measurements along any straight-line path across the fractal’s surface obey the mathematically derived relationship. However, the standard approach of vision researchers is to measure β of the surface after 2-dimensional Fourier decomposition rather than along a straight-line path. This surface technique provides measurements of β that do not obey the mathematically derived relationship with D. Instead, this method produces values of β that imply that the fractal’s surface is much smoother than the measurements along the straight lines indicate. To facilitate communication across disciplines, we provide empirically derived equations for relating each measure of β to D. Finally, we discuss implications for future research on topics including stress reduction and the perception of motion in the context of a generalized equation relating β to D.
Fractal scaling and complexity matching in ergometer rowing
den Hartigh, Ruud; Marmelat, Vivien; Cox, Ralf
Researchers increasingly acknowledge that athletes’ performance patterns emerge from multiple interacting components across different time scales. Recent research has shown “fractal scaling”, a hallmark of complex systems behavior, in the temporal structure of force-peak intervals of individual
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 2. Fractals and the Large-Scale Structure in the Universe - Introduction and Basic Concepts. A K Mittal T R Seshadri. General Article Volume 7 Issue 2 February 2002 pp 6-19 ...
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 4. Fractals and the Large-Scale Structure in the Universe - Is the Cosmological Principle Valid? A K Mittal T R Seshadri. General Article Volume 7 Issue 4 April 2002 pp 39-47 ...
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-.
Zueva, Marina V
2015-01-01
The theory that ties normal functioning and pathology of the brain and visual system with the spatial-temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult's neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author's theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered.
Directory of Open Access Journals (Sweden)
Marina Vladimirovna Zueva
2015-07-01
Full Text Available The theory that ties normal functioning and pathology of the brain and visual system with the spatial-temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Nonlinear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a nonlinear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult's neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author's theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered.
Zueva, Marina V.
2015-01-01
The theory that ties normal functioning and pathology of the brain and visual system with the spatial–temporal structure of the visual and other sensory stimuli is described for the first time in the present study. The deficit of fractal complexity of environmental influences can lead to the distortion of fractal complexity in the visual pathways of the brain and abnormalities of development or aging. The use of fractal light stimuli and fractal stimuli of other modalities can help to restore the functions of the brain, particularly in the elderly and in patients with neurodegenerative disorders or amblyopia. Non-linear dynamics of these physiological processes have a strong base of evidence, which is seen in the impaired fractal regulation of rhythmic activity in aged and diseased brains. From birth to old age, we live in a non-linear world, in which objects and processes with the properties of fractality and non-linearity surround us. Against this background, the evolution of man took place and all periods of life unfolded. Works of art created by man may also have fractal properties. The positive influence of music on cognitive functions is well-known. Insufficiency of sensory experience is believed to play a crucial role in the pathogenesis of amblyopia and age-dependent diseases. The brain is very plastic in its early development, and the plasticity decreases throughout life. However, several studies showed the possibility to reactivate the adult’s neuroplasticity in a variety of ways. We propose that a non-linear structure of sensory information on many spatial and temporal scales is crucial to the brain health and fractal regulation of physiological rhythms. Theoretical substantiation of the author’s theory is presented. Possible applications and the future research that can experimentally confirm or refute the theoretical concept are considered. PMID:26236232
Fractal approach in characterization of spatial pattern of soil properties
Boško Miloš; Aleksandra Bensa
2017-01-01
The objective of the study was to characterize spatial pattern of soil properties (CaCO3, soil organic carbon, P2O5, K2O, and clay content) using fractal concept. Total of 141 top-soil samples (0-30 cm) were collected on 1850 ha in karst polje (Petrovo polje, Croatia) and analyzed for listed soil properties. The semi-variogram method was used to estimate fractal dimension (D) value which was performed from both of isotropic and anisotropic perspective. The D value of soil properties ranged be...
Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators
Müller H.
2009-01-01
Logarithmic scaling invariance is a wide distributed natural phenomenon and was proved in the distributions of physical properties of various processes — in high en- ergy physics, chemistry, seismicity, biology, geology and technology. Based on the Gantmacher-Krein continued fraction method the present paper introduces fractal scal- ing models of resonant oscillations in chain systems of harmonic oscillators. These models generate logarithmic scaling spect...
A characteristic scale in radiation fields of fractal clouds
Energy Technology Data Exchange (ETDEWEB)
Wiscombe, W.; Cahalan, R.; Davis, A.; Marshak, A. [Goddard Space Flight Center, Greenbelt, MD (United States)
1996-04-01
The wavenumber spectrum of Landsat imagery for marine stratocumulus cloud shows a scale break when plotted on a double log plot. We offer an explanation of this scale break in terms of smoothing by horizontal radiative fluxes, which is parameterized and incorporated into an improved pixel approximation. We compute the radiation fields emerging from cloud models with horizontally variable optical depth fractal models. We use comparative spectral and multifractal analysis to qualify the validity of the independent pixel approximation at the largest scales and demonstrate it`s shortcomings on the smallest scales.
Fractals and the Large-Scale Structure in the Universe -R-ES ...
Indian Academy of Sciences (India)
In Part 1 of this article, we had introduced the reader to some basic concepts of fractals and some operational algorithms to characterize them. We had also pointed out and clarified some com- mon misconceptions about fractals. In this part we apply the fractal concepts to large-scale struc- tures in the Universe. In particular ...
Fractal scaling analysis of groundwater dynamics in confined aquifers
Tu, Tongbi; Ercan, Ali; Kavvas, M. Levent
2017-10-01
Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA) was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA) and multiscale multifractal analysis (MMA) were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm), which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.
Fractal scaling analysis of groundwater dynamics in confined aquifers
Directory of Open Access Journals (Sweden)
T. Tu
2017-10-01
Full Text Available Groundwater closely interacts with surface water and even climate systems in most hydroclimatic settings. Fractal scaling analysis of groundwater dynamics is of significance in modeling hydrological processes by considering potential temporal long-range dependence and scaling crossovers in the groundwater level fluctuations. In this study, it is demonstrated that the groundwater level fluctuations in confined aquifer wells with long observations exhibit site-specific fractal scaling behavior. Detrended fluctuation analysis (DFA was utilized to quantify the monofractality, and multifractal detrended fluctuation analysis (MF-DFA and multiscale multifractal analysis (MMA were employed to examine the multifractal behavior. The DFA results indicated that fractals exist in groundwater level time series, and it was shown that the estimated Hurst exponent is closely dependent on the length and specific time interval of the time series. The MF-DFA and MMA analyses showed that different levels of multifractality exist, which may be partially due to a broad probability density distribution with infinite moments. Furthermore, it is demonstrated that the underlying distribution of groundwater level fluctuations exhibits either non-Gaussian characteristics, which may be fitted by the Lévy stable distribution, or Gaussian characteristics depending on the site characteristics. However, fractional Brownian motion (fBm, which has been identified as an appropriate model to characterize groundwater level fluctuation, is Gaussian with finite moments. Therefore, fBm may be inadequate for the description of physical processes with infinite moments, such as the groundwater level fluctuations in this study. It is concluded that there is a need for generalized governing equations of groundwater flow processes that can model both the long-memory behavior and the Brownian finite-memory behavior.
Fractal Property in the Light Curve of BL Lac Object S5 0716+714
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... In this paper, we compile the historical R-band data of S5 0716+714 from literature and obtain its fractal dimension by using a fractal method and then simulate the data with the Weierstrass–Mandelbrot (W–M) function. It is considered that the light curve has a fractal property.
Fractal Property in the Light Curve of BL Lac Object S5 0716+ 714
Indian Academy of Sciences (India)
2016-01-27
Jan 27, 2016 ... In this paper, we compile the historical R-band data of S5 0716+714 from literature and obtain its fractal dimension by using a fractal method and then simulate the data with the Weierstrass–Mandelbrot (W–M) function. It is considered that the light curve has a fractal property.
Fractal Scaling Models of Resonant Oscillations in Chain Systems of Harmonic Oscillators
Directory of Open Access Journals (Sweden)
Müller H.
2009-04-01
Full Text Available Logarithmic scaling invariance is a wide distributed natural phenomenon and was proved in the distributions of physical properties of various processes — in high en- ergy physics, chemistry, seismicity, biology, geology and technology. Based on the Gantmacher-Krein continued fraction method the present paper introduces fractal scal- ing models of resonant oscillations in chain systems of harmonic oscillators. These models generate logarithmic scaling spectra. The introduced models are not based on any statements about the nature of the link or interaction between the elements of the oscillating system. Therefore the model statements are quite generally, what opens a wide field of possible applications.
Relations between a typical scale and averages in the breaking of fractal distribution
Ishikawa, Atushi; Suzuki, Tadao
2004-11-01
We study distributions which have both fractal and non-fractal scale regions by introducing a typical scale into a scale invariant system. As one of models in which distributions follow power law in the large-scale region and deviate further from the power law in the smaller-scale region, we employ 2-dim quantum gravity modified by the R2 term. As examples of distributions in the real world which have similar property to this model, we consider those of personal income in Japan over latest twenty fiscal years. We find relations between the typical scale and several kinds of averages in this model, and observe that these relations are also valid in recent personal income distributions in Japan with sufficient accuracy. We show the existence of the fiscal years so called bubble term in which the gap has arisen in power law, by observing that the data are away from one of these relations. We confirm, therefore, that the distribution of this model has close similarity to those of personal income. In addition, we can estimate the value of Pareto index and whether a big gap exists in power law by using only these relations. As a result, we point out that the typical scale is an useful concept different from average value and that the distribution function derived in this model is an effective tool to investigate these kinds of distributions.
Temporal fractals in seabird foraging behaviour: diving through the scales of time
Macintosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan
2013-05-01
Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (216 data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.
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.
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.
Fractal properties of percolation clusters in Euclidian neural networks
International Nuclear Information System (INIS)
Franovic, Igor; Miljkovic, Vladimir
2009-01-01
The process of spike packet propagation is observed in two-dimensional recurrent networks, consisting of locally coupled neuron pools. Local population dynamics is characterized by three key parameters - probability for pool connectedness, synaptic strength and neuron refractoriness. The formation of dynamic attractors in our model, synfire chains, exhibits critical behavior, corresponding to percolation phase transition, with probability for non-zero synaptic strength values representing the critical parameter. Applying the finite-size scaling method, we infer a family of critical lines for various synaptic strengths and refractoriness values, and determine the Hausdorff-Besicovitch fractal dimension of the percolation clusters.
Czech Academy of Sciences Publication Activity Database
Krištoufek, Ladislav
2012-01-01
Roč. 15, č. 6 (2012), 1250065-1-1250065-13 ISSN 0219-5259 R&D Projects: GA ČR GA402/09/0965 Grant - others:GA UK(CZ) 118310; SVV(CZ) 265 504 Institutional support: RVO:67985556 Keywords : fractal markets hypothesis * scaling * fractal ity * investment horizons * efficient markets hypothesis Subject RIV: AH - Economics Impact factor: 0.647, year: 2012 http://library.utia.cas.cz/separaty/2012/E/kristoufek- fractal markets hypothesis and the global financial crisis scaling investment horizons and liquidity.pdf
Morphological Investigation and Fractal Properties of Realgar Nanoparticles
Directory of Open Access Journals (Sweden)
Amir Lashgari
2015-01-01
Full Text Available Some arsenic compounds can show extraordinary polymorphism. Realgar (As4S4 is among several minerals with various crystal forms and is one of the most important sources of arsenic for pharmaceutical use. Currently, realgar is used as an arsenic source in many industries, such as weaponry, publishing, textiles, cosmetics, and health products. In this paper, we used and reported new methods for the purification, nanonization, and structural morphological investigations of As4S4 by using planetary ball mills process for nanonization of the compound. The product was characterized using X-ray powder diffraction analysis, Fourier transform infrared spectrometry spectra, and field emission scanning electron microscope (FESEM imaging. We investigated the morphological properties of FESEM-imaged realgar nanoparticles by an image-processing technique that calculates fractal dimensions using values on a computer with MATLAB software. We applied the Statistical Package for the Social Sciences software for statistics data extracted from the FESEM image and obtained the statistics results of the fractal dimension and histogram plot for the FESEM image.
Bearing Fault Detection Using Multi-Scale Fractal Dimensions Based on Morphological Covers
Directory of Open Access Journals (Sweden)
Pei-Lin Zhang
2012-01-01
Full Text Available Vibration signals acquired from bearing have been found to demonstrate complicated nonlinear characteristics in literature. Fractal geometry theory has provided effective tools such as fractal dimension for characterizing the vibration signals in bearing faults detection. However, most of the natural signals are not critical self-similar fractals; the assumption of a constant fractal dimension at all scales may not be true. Motivated by this fact, this work explores the application of the multi-scale fractal dimensions (MFDs based on morphological cover (MC technique for bearing fault diagnosis. Vibration signals from bearing with seven different states under four operations conditions are collected to validate the presented MFDs based on MC technique. Experimental results reveal that the vibration signals acquired from bearing are not critical self-similar fractals. The MFDs can provide more discriminative information about the signals than the single global fractal dimension. Furthermore, three classifiers are employed to evaluate and compare the classification performance of the MFDs with other feature extraction methods. Experimental results demonstrate the MFDs to be a desirable approach to improve the performance of bearing fault diagnosis.
Landsat 7 Reveals Large-scale Fractal Motion of Clouds
2002-01-01
This Landsat 7 image of clouds off the Chilean coast near the Juan Fernandez Islands (also known as the Robinson Crusoe Islands) on September 15, 1999, shows a unique pattern called a 'von Karman vortex street.' This pattern has long been studied in the laboratory, where the vortices are created by oil flowing past a cylindrical obstacle, making a string of vortices only several tens of centimeters long. Study of this classic 'flow past a circular cylinder' has been very important in the understanding of laminar and turbulent fluid flow that controls a wide variety of phenomena, from the lift under an aircraft wing to Earth's weather. Here, the cylinder is replaced by Alejandro Selkirk Island (named after the true 'Robinson Crusoe,' who was stranded here for many months in the early 1700s). The island is about 1.5 km in diameter, and rises 1.6 km into a layer of marine stratocumulus clouds. This type of cloud is important for its strong cooling of the Earth's surface, partially counteracting the Greenhouse warming. An extended, steady equatorward wind creates vortices with clockwise flow off the eastern edge and counterclockwise flow off the western edge of the island. The vortices grow as they advect hundreds of kilometers downwind, making a street 10,000 times longer than those made in the laboratory. Observing the same phenomenon extended over such a wide range of sizes dramatizes the 'fractal' nature of atmospheric convection and clouds. Fractals are characteristic of fluid flow and other dynamic systems that exhibit 'chaotic' motions. Both clockwise and counter-clockwise vortices are generated by flow around the island. As the flow separates from the island's leeward (away from the source of the wind) side, the vortices 'swallow' some of the clear air over the island. (Much of the island air is cloudless due to a local 'land breeze' circulation set up by the larger heat capacity of the waters surrounding the island.) The 'swallowed' gulps of clear island air
Fractal properties of shoreline changes on a storm-exposed island.
Zhong, Xiaojing; Yu, Peng; Chen, Shenliang
2017-08-15
Extreme storm events and their consequent shoreline changes are of great importance for understanding coastal evolution and assessing storm hazards. This work investigates the fractal properties of the spatial distributions of shoreline changes caused by storms. Wavelet analysis and upper-truncated power law (UTPL) fitting are used to study the power spectra of shoreline changes and to evaluate the upper limits of the cross-shore erosion and accretion. During a period affected by storms, the alongshore shoreline change patterns are strong on the 15 km scale but are weak with lower spectral power on the 20 km scale. The areas adjacent to the eroded shoreline are usually accrete, and the cross-shore extent of erosion is larger than that of accretion when the coast is affected by storms. The fractal properties of shoreline changes due to storms are found to be temporally continuous: the effects of later storms build on the preceding shoreline conditions, including both the effects of previous storms and the subsequent shoreline recoveries. This work provides a new perspective on the various scales of the spatial variations of the morphodynamics of storm-affected shorelines.
Fractal scaling in bottlenose dolphin (Tursiops truncatus) echolocation: A case study
Perisho, Shaun T.; Kelty-Stephen, Damian G.; Hajnal, Alen; Houser, Dorian; Kuczaj, Stan A., II
2016-02-01
Fractal scaling patterns, which entail a power-law relationship between magnitude of fluctuations in a variable and the scale at which the variable is measured, have been found in many aspects of human behavior. These findings have led to advances in behavioral models (e.g. providing empirical support for cascade-driven theories of cognition) and have had practical medical applications (e.g. providing new methods for early diagnosis of medical conditions). In the present paper, fractal analysis is used to investigate whether similar fractal scaling patterns exist in inter-click interval and peak-peak amplitude measurements of bottlenose dolphin click trains. Several echolocation recordings taken from two male bottlenose dolphins were analyzed using Detrended Fluctuation Analysis and Higuchi's (1988) method for determination of fractal dimension. Both animals were found to exhibit fractal scaling patterns near what is consistent with persistent long range correlations. These findings suggest that recent advances in human cognition and medicine may have important parallel applications to echolocation as well.
Pârvu, A E; Ţălu, Ş; Crăciun, C; Alb, S F
2014-04-01
Fractal and multifractal analysis are useful additional non-invasive methods for quantitative description of complex morphological features. However, the quantitative and qualitative assessment of morphologic changes within human gingival cells and tissues are still unexplored. The aim of this work is to assess the structural gingival changes in patients with generalized chronic periodontitis (GCP), before and after scaling and root planing (SRP) by using fractal and multifractal analysis. Twelve adults with untreated chronic periodontitis were treated only by SRP. At baseline and after SRP, gingivomucosal biopsies were collected for histopathological examination. Fractal and multifractal analysis of digital images of the granular, spinous and basal and conjunctive layers structure, using the standard box-counting method was performed. The fractal dimension was determined for cell membrane, nuclear membrane of cell and nucleolus membrane of cell. In GCP a higher fractal dimension corresponds to a higher geometric complexity of cells contour, as its values increase when the contour irregularities increase. The generalized fractal dimensions were determined for the conjunctive layer structure of patients with GCP and patients with GCP and SRP. The fractal and multifractal analysis of gingival biopsies confirmed earlier findings that SRP reduces gingival injury in patients with GCP. It has been shown that fractal and multifractal analysis of tissue images as a non-invasive technique could be used to measure contrasting morphologic changes within human gingival cells and tissues and can provide detailed information for investigation of healthy and diseased gingival mucosa from patients with GCP. © 2013 John Wiley & Sons A/S. Published by John Wiley & Sons Ltd.
Temporal fractals in seabird foraging behaviour: diving through the scales of time.
Macintosh, Andrew J J; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan
2013-01-01
Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (2(16) data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.
Directory of Open Access Journals (Sweden)
Potapov A. A.
2008-10-01
Full Text Available Main results of theoretical and experimental investigations since eighties of XX that led to formation and developing of new fundamental science discipline: “Fractal Radio Physics and Fractal Radio Electronics: Fractal Radio Systems Designing” are briefly classified in the paper.
Fractal scaling behavior of heart rate variability in response to meditation techniques
International Nuclear Information System (INIS)
Alvarez-Ramirez, J.; Rodríguez, E.; Echeverría, J.C.
2017-01-01
Highlights: • The scaling properties of heart rate variability in premeditation and meditation states were studied. • Mindfulness meditation induces a decrement of the HRV long-range scaling correlations. • Mindfulness meditation can be regarded as a type of induced deep sleep-like dynamics. - Abstract: The rescaled range (R/S) analysis was used for analyzing the fractal scaling properties of heart rate variability (HRV) of subjects undergoing premeditation and meditation states. Eight novice subjects and four advanced practitioners were considered. The corresponding pre-meditation and meditation HRV data were obtained from the Physionet database. The results showed that mindfulness meditation induces a decrement of the HRV long-range scaling correlations as quantified with the time-variant Hurst exponent. The Hurst exponent for advanced meditation practitioners decreases up to values of 0.5, reflecting uncorrelated (e.g., white noise-like) HRV dynamics. Some parallelisms between mindfulness meditation and deep sleep (Stage 4) are discussed, suggesting that the former can be regarded as a type of induced deep sleep-like dynamics.
Changes in Dimensionality and Fractal Scaling Suggest Soft-Assembled Dynamics in Human EEG
DEFF Research Database (Denmark)
Wiltshire, Travis; Euler, Matthew J.; McKinney, Ty
2017-01-01
. In a repetition priming task, we assessed evidence for changes in the correlation dimension and fractal scaling exponents during stimulus-locked event-related potentials, as a function of stimulus onset and familiarity, and relative to spontaneous non-task-related activity. Consistent with predictions derived...... from soft-assembly, results indicated decreases in dimensionality and increases in fractal scaling exponents from resting to pre-stimulus states and following stimulus onset. However, contrary to predictions, familiarity tended to increase dimensionality estimates. Overall, the findings support...
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.
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
Pandey, Apoorva; Chakrabarty, Rajan K.; Liu, Li; Mishchenko, Michael I.
2015-01-01
Soot aggregates (SAs)-fractal clusters of small, spherical carbonaceous monomers-modulate the incoming visible solar radiation and contribute significantly to climate forcing. Experimentalists and climate modelers typically assume a spherical morphology for SAs when computing their optical properties, causing significant errors. Here, we calculate the optical properties of freshly-generated (fractal dimension Df = 1.8) and aged (Df = 2.6) SAs at 550 nm wavelength using the numericallyexact superposition T-Matrix method. These properties were expressed as functions of equivalent aerosol diameters as measured by contemporary aerosol instruments. This work improves upon previous efforts wherein SA optical properties were computed as a function of monomer number, rendering them unusable in practical applications. Future research will address the sensitivity of variation in refractive index, fractal prefactor, and monomer overlap of SAs on the reported empirical relationships.
Moscoso del Prado Martín, Fermín
2013-12-01
I introduce the Bayesian assessment of scaling (BAS), a simple but powerful Bayesian hypothesis contrast methodology that can be used to test hypotheses on the scaling regime exhibited by a sequence of behavioral data. Rather than comparing parametric models, as typically done in previous approaches, the BAS offers a direct, nonparametric way to test whether a time series exhibits fractal scaling. The BAS provides a simpler and faster test than do previous methods, and the code for making the required computations is provided. The method also enables testing of finely specified hypotheses on the scaling indices, something that was not possible with the previously available methods. I then present 4 simulation studies showing that the BAS methodology outperforms the other methods used in the psychological literature. I conclude with a discussion of methodological issues on fractal analyses in experimental psychology. PsycINFO Database Record (c) 2014 APA, all rights reserved.
Studying the time scale dependence of environmental variables predictability using fractal analysis.
Yuval; Broday, David M
2010-06-15
Prediction of meteorological and air quality variables motivates a lot of research in the atmospheric sciences and exposure assessment communities. An interesting related issue regards the relative predictive power that can be expected at different time scales, and whether it vanishes altogether at certain ranges. An improved understanding of our predictive powers enables better environmental management and more efficient decision making processes. Fractal analysis is commonly used to characterize the self-affinity of time series. This work introduces the Continuous Wavelet Transform (CWT) fractal analysis method as a tool for assessing environmental time series predictability. The high temporal scale resolution of the CWT enables detailed information about the Hurst parameter, a common temporal fractality measure, and thus about time scale variations in predictability. We analyzed a few years records of half-hourly air pollution and meteorological time series from which the trivial seasonal and daily cycles were removed. We encountered a general trend of decreasing Hurst values from about 1.4 (good autocorrelation and predictability), in the sub-daily time scale to 0.5 (which implies complete randomness) in the monthly to seasonal scales. The air pollutants predictability follows that of the meteorological variables in the short time scales but is better at longer scales.
A Study on the Mechanical Properties of the Representative Volume Element in Fractal Porous Media
Directory of Open Access Journals (Sweden)
Jianjun Liu
2017-01-01
Full Text Available Natural porous structure is extremely complex, and it is of great significance to study the macroscopic mechanical response of the representative volume element (RVE with the microstructure of porous media. The real porous media RVE is generated by an improved quartet structure generation set (QSGS, and the connectivity of the reconstructed porous media models is analyzed. The fractal dimension of the RVE is calculated by the box-counting method, which considers the different porosity, different fractal dimension, and different mechanical properties of the matrix. Thus, the stress-strain curves of the RVE in the elastoplastic stage under different conditions are obtained. The results show that when the matrix mechanics are consistent, the mechanical properties of the porous media RVE are negatively correlated with the porosity and fractal dimension; when the difference between the porosity and fractal dimension increases, the trend is more obvious. The mechanical properties of the RVE have a positive correlation with the modulus of elasticity of the matrix, though the correlation with Poisson’s ratio of the matrix is weak. The fractal dimension of complex porous media can better predict the RVE mechanical characteristics than the porosity.
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".
International Trade Network: Fractal Properties and Globalization Puzzle
Karpiarz, Mariusz; Fronczak, Piotr; Fronczak, Agata
2014-12-01
Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.
Analyzing fractal property of species abundance distribution and diversity indexes.
Su, Qiang
2016-03-07
Community diversity is usually characterized by numerical indexes; however it indeed depends on the species abundance distribution (SAD). Diversity indexes and SAD are based on the same information but treating as separate themes. Ranking species abundance from largest to smallest, the decreasing pattern can give the information about the SAD. Frontier proposed such SAD might be a fractal structure, and first applied the Zipf-Mandelbrot model to the SAD study. However, this model fails to include the Zipf model, and also fails to ensure an integer rank. In this study, a fractal model of SAD was reconstructed, and tested with 104 community samples from 8 taxonomic groups. The results show that there was a good fit of the presented model. Fractal parameter (p) determines the SAD of a community. The ecological significance of p relates to the "dominance" of a community. The correlation between p and classical diversity indexes show that Shannon index decreases and Simpson index increases as p increases. The main purpose of this paper is not to compare with other SADs models; it simply provides a new interpretation of SAD model construction, and preliminarily integrates diversity indexes and SAD model into a broader perspective of community diversity. Copyright © 2015 Elsevier Ltd. All rights reserved.
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)
Scaling law of diffusivity generated by a noisy telegraph signal with fractal intermittency
International Nuclear Information System (INIS)
Paradisi, Paolo; Allegrini, Paolo
2015-01-01
In many complex systems the non-linear cooperative dynamics determine the emergence of self-organized, metastable, structures that are associated with a birth–death process of cooperation. This is found to be described by a renewal point process, i.e., a sequence of crucial birth–death events corresponding to transitions among states that are faster than the typical long-life time of the metastable states. Metastable states are highly correlated, but the occurrence of crucial events is typically associated with a fast memory drop, which is the reason for the renewal condition. Consequently, these complex systems display a power-law decay and, thus, a long-range or scale-free behavior, in both time correlations and distribution of inter-event times, i.e., fractal intermittency. The emergence of fractal intermittency is then a signature of complexity. However, the scaling features of complex systems are, in general, affected by the presence of added white or short-term noise. This has been found also for fractal intermittency. In this work, after a brief review on metastability and noise in complex systems, we discuss the emerging paradigm of Temporal Complexity. Then, we propose a model of noisy fractal intermittency, where noise is interpreted as a renewal Poisson process with event rate r p . We show that the presence of Poisson noise causes the emergence of a normal diffusion scaling in the long-time range of diffusion generated by a telegraph signal driven by noisy fractal intermittency. We analytically derive the scaling law of the long-time normal diffusivity coefficient. We find the surprising result that this long-time normal diffusivity depends not only on the Poisson event rate, but also on the parameters of the complex component of the signal: the power exponent μ of the inter-event time distribution, denoted as complexity index, and the time scale T needed to reach the asymptotic power-law behavior marking the emergence of complexity. In particular
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
Lung cancer—a fractal viewpoint
Lennon, Frances E.; Cianci, Gianguido C.; Cipriani, Nicole A.; Hensing, Thomas A.; Zhang, Hannah J.; Chen, Chin-Tu; Murgu, Septimiu D.; Vokes, Everett E.; W. Vannier, Michael; Salgia, Ravi
2016-01-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed. PMID:26169924
Lung cancer-a fractal viewpoint.
Lennon, Frances E; Cianci, Gianguido C; Cipriani, Nicole A; Hensing, Thomas A; Zhang, Hannah J; Chen, Chin-Tu; Murgu, Septimiu D; Vokes, Everett E; Vannier, Michael W; Salgia, Ravi
2015-11-01
Fractals are mathematical constructs that show self-similarity over a range of scales and non-integer (fractal) dimensions. Owing to these properties, fractal geometry can be used to efficiently estimate the geometrical complexity, and the irregularity of shapes and patterns observed in lung tumour growth (over space or time), whereas the use of traditional Euclidean geometry in such calculations is more challenging. The application of fractal analysis in biomedical imaging and time series has shown considerable promise for measuring processes as varied as heart and respiratory rates, neuronal cell characterization, and vascular development. Despite the advantages of fractal mathematics and numerous studies demonstrating its applicability to lung cancer research, many researchers and clinicians remain unaware of its potential. Therefore, this Review aims to introduce the fundamental basis of fractals and to illustrate how analysis of fractal dimension (FD) and associated measurements, such as lacunarity (texture) can be performed. We describe the fractal nature of the lung and explain why this organ is particularly suited to fractal analysis. Studies that have used fractal analyses to quantify changes in nuclear and chromatin FD in primary and metastatic tumour cells, and clinical imaging studies that correlated changes in the FD of tumours on CT and/or PET images with tumour growth and treatment responses are reviewed. Moreover, the potential use of these techniques in the diagnosis and therapeutic management of lung cancer are discussed.
Non-linear variability in geophysics scaling and fractals
Lovejoy, S
1991-01-01
consequences of broken symmetry -here parity-is studied. In this model, turbulence is dominated by a hierarchy of helical (corkscrew) structures. The authors stress the unique features of such pseudo-scalar cascades as well as the extreme nature of the resulting (intermittent) fluctuations. Intermittent turbulent cascades was also the theme of a paper by us in which we show that universality classes exist for continuous cascades (in which an infinite number of cascade steps occur over a finite range of scales). This result is the multiplicative analogue of the familiar central limit theorem for the addition of random variables. Finally, an interesting paper by Pasmanter investigates the scaling associated with anomolous diffusion in a chaotic tidal basin model involving a small number of degrees of freedom. Although the statistical literature is replete with techniques for dealing with those random processes characterized by both exponentially decaying (non-scaling) autocorrelations and exponentially decaying...
Energy Technology Data Exchange (ETDEWEB)
Souza, Jeferson de; Figueira, Isabela Francoso Rebutini; Santos, Thais Borba [Universidade Federal do Rio Grande do Norte (PPGG/DG/UFRN), Natal (Brazil). Dept. de Geologia. Programa de Pos-Graducao em Geologia; Rostirolla, Sidnei Pires [Universidade Federal do Rio Grande do Norte (DG/UFRN), Natal (Brazil). Dept. de Geologia; Pierin, Andre Ramiro; Spisila, Andre Luis [Universidade Federal do Rio Grande do Norte (DG/UFRN), Natal (Brazil). Dept. de Geologia. Programa de Iniciacao Cientifica
2008-03-15
The statistical and geometrical properties of fracture systems were obtained by analyzing remote sense images and outcrop data, in the Region of Guartela Canyon, in the central-eastern of Parana State. The probability distributions of fractures, with their parameters and attributes, were obtained through extensive statistical exploration of data. These parameters were used as input data for generating 3-D stochastic fractures models through the 'discrete fracture network - DFN' method. The modeling is performed by using the code FRED. To study the persistence of statistical parameters in multiple scales were used remote sensing images (SRTM, Landsat TM7 and aerial photos), covering a scale range from outcrops (few meters) to basin scales (hundreds of kilometers). The results indicated the presence of power-law (fractal) statistics for the spatial and size distributions. Fractals distributions were found for all sets studied, in some cases with different fractal exponents. The implications of fractal behavior for the generation of discrete fracture network, and consequently for the hydraulic properties, are briefly discussed. (author)
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
lieved to have been formed due to a number of physical processes in addition to gravity. Structures of galactic ... So we now repeat this exercise using a scale of smaller length. Naive logic would suggest that as we .... dimensional smooth curve and do this exercise, the ex- ponent D will turn out to be 1. Similarly if we do this ...
Afsar, Ozgur; Tirnakli, Ugur
2014-04-01
We numerically introduce the relationships among correlation, fractality, Lyapunov divergence and q-Gaussian distributions. The scaling arguments between the range of the q-Gaussian and correlation, fractality, Lyapunov divergence are obtained for periodic windows (i.e., periods 2, 3 and 5) of the logistic map as chaos threshold is approached. Firstly, we show that the range of the q-Gaussian (g) tends to infinity as the measure of the deviation from the correlation dimension (D=0.5) at the chaos threshold, (this deviation will be denoted by l), approaches to zero. Moreover, we verify that a scaling law of type 1/g∝lτ is evident with the critical exponent τ=0.23±0.01. Similarly, as chaos threshold is approached, the quantity l scales as l∝(, where the exponent is γ=0.84±0.01. Secondly, we also show that the range of the q-Gaussian exhibits a scaling law with the correlation length (1/g∝ξ), Lyapunov divergence (1/g∝λμ) and the distance to the critical box counting fractal dimension (1/g∝() with the same exponent μ≅0.43. Finally, we numerically verify that these three quantities (ξ, λ, D-Dc) scale with the distance to the critical control parameter of the map (i.e., a-ac) in accordance with the universal Huberman-Rudnick scaling law with the same exponent ν=0.448±0.003. All these findings can be considered as a new evidence supporting that the central limit behaviour at the chaos threshold is given by a q-Gaussian.
A study of radiative properties of fractal soot aggregates using the superposition T-matrix method
International Nuclear Information System (INIS)
Li Liu; Mishchenko, Michael I.; Patrick Arnott, W.
2008-01-01
We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D f , is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N S , and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D f f >2. However, a systematic reduction in light absorption with D f is observed for clusters with sufficiently large N S , m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed
Directory of Open Access Journals (Sweden)
Lanfa Liu
2016-12-01
Full Text Available Visible and near-infrared diffuse reflectance spectroscopy has been demonstrated to be a fast and cheap tool for estimating a large number of chemical and physical soil properties, and effective features extracted from spectra are crucial to correlating with these properties. We adopt a novel methodology for feature extraction of soil spectroscopy based on fractal geometry. The spectrum can be divided into multiple segments with different step–window pairs. For each segmented spectral curve, the fractal dimension value was calculated using variation estimators with power indices 0.5, 1.0 and 2.0. Thus, the fractal feature can be generated by multiplying the fractal dimension value with spectral energy. To assess and compare the performance of new generated features, we took advantage of organic soil samples from the large-scale European Land Use/Land Cover Area Frame Survey (LUCAS. Gradient-boosting regression models built using XGBoost library with soil spectral library were developed to estimate N, pH and soil organic carbon (SOC contents. Features generated by a variogram estimator performed better than two other estimators and the principal component analysis (PCA. The estimation results for SOC were coefficient of determination (R2 = 0.85, root mean square error (RMSE = 56.7 g/kg, the ratio of percent deviation (RPD = 2.59; for pH: R2 = 0.82, RMSE = 0.49 g/kg, RPD = 2.31; and for N: R2 = 0.77, RMSE = 3.01 g/kg, RPD = 2.09. Even better results could be achieved when fractal features were combined with PCA components. Fractal features generated by the proposed method can improve estimation accuracies of soil properties and simultaneously maintain the original spectral curve shape.
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
Energy Technology Data Exchange (ETDEWEB)
Ho, Clifford K. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Ortega, Jesus D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Christian, Joshua Mark [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Yellowhair, Julius E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Ray, Daniel A. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Kelton, John W. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Peacock, Gregory [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Andraka, Charles E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.; Shinde, Subhash [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Concentrating Solar Technologies Dept.
2016-09-01
Novel designs to increase light trapping and thermal efficiency of concentrating solar receivers at multiple length scales have been conceived, designed, and tested. The fractal-like geometries and features are introduced at both macro (meters) and meso (millimeters to centimeters) scales. Advantages include increased solar absorptance, reduced thermal emittance, and increased thermal efficiency. Radial and linear structures at the meso (tube shape and geometry) and macro (total receiver geometry and configuration) scales redirect reflected solar radiation toward the interior of the receiver for increased absorptance. Hotter regions within the interior of the receiver can reduce thermal emittance due to reduced local view factors to the environment, and higher concentration ratios can be employed with similar surface irradiances to reduce the effective optical aperture, footprint, and thermal losses. Coupled optical/fluid/thermal models have been developed to evaluate the performance of these designs relative to conventional designs. Modeling results showed that fractal-like structures and geometries can increase the effective solar absorptance by 5 – 20% and the thermal efficiency by several percentage points at both the meso and macro scales, depending on factors such as intrinsic absorptance. Meso-scale prototypes were fabricated using additive manufacturing techniques, and a macro-scale bladed receiver design was fabricated using Inconel 625 tubes. On-sun tests were performed using the solar furnace and solar tower at the National Solar Thermal Test facility. The test results demonstrated enhanced solar absorptance and thermal efficiency of the fractal-like designs.
Empirical analysis of scaling and fractal characteristics of outpatients
International Nuclear Information System (INIS)
Zhang, Li-Jiang; Liu, Zi-Xian; Guo, Jin-Li
2014-01-01
The paper uses power-law frequency distribution, power spectrum analysis, detrended fluctuation analysis, and surrogate data testing to evaluate outpatient registration data of two hospitals in China and to investigate the human dynamics of systems that use the “first come, first served” protocols. The research results reveal that outpatient behavior follow scaling laws. The results also suggest that the time series of inter-arrival time exhibit 1/f noise and have positive long-range correlation. Our research may contribute to operational optimization and resource allocation in hospital based on FCFS admission protocols.
Non-local Integrals and Derivatives on Fractal Sets with Applications
Directory of Open Access Journals (Sweden)
Golmankhaneh Alireza K.
2016-01-01
Full Text Available In this paper, we discuss non-local derivatives on fractal Cantor sets. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and compared. Related physical models are also suggested.
Non-local Integrals and Derivatives on Fractal Sets with Applications
Golmankhaneh, Alireza K.; Baleanu, Dumitru
2017-01-01
In this paper, we discussed the non-local derivative on the fractal Cantor set. The scaling properties are given for both local and non-local fractal derivatives. The local and non-local fractal differential equations are solved and compared and related physical models are suggested.
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
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.
Analyzing Self-Similar and Fractal Properties of the C. elegans Neural Network
Reese, Tyler M.; Brzoska, Antoni; Yott, Dylan T.; Kelleher, Daniel J.
2012-01-01
The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons). A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron “giant component” of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been “rewired” to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs. PMID:23071485
Detecting abrupt dynamic change based on changes in the fractal properties of spatial images
Liu, Qunqun; He, Wenping; Gu, Bin; Jiang, Yundi
2017-10-01
Many abrupt climate change events often cannot be detected timely by conventional abrupt detection methods until a few years after these events have occurred. The reason for this lag in detection is that abundant and long-term observational data are required for accurate abrupt change detection by these methods, especially for the detection of a regime shift. So, these methods cannot help us understand and forecast the evolution of the climate system in a timely manner. Obviously, spatial images, generated by a coupled spatiotemporal dynamical model, contain more information about a dynamic system than a single time series, and we find that spatial images show the fractal properties. The fractal properties of spatial images can be quantitatively characterized by the Hurst exponent, which can be estimated by two-dimensional detrended fluctuation analysis (TD-DFA). Based on this, TD-DFA is used to detect an abrupt dynamic change of a coupled spatiotemporal model. The results show that the TD-DFA method can effectively detect abrupt parameter changes in the coupled model by monitoring the changing in the fractal properties of spatial images. The present method provides a new way for abrupt dynamic change detection, which can achieve timely and efficient abrupt change detection results.
FRACTAL DIMENSIONING OF SAND GRAINS USING IMAGE ANALYSIS SYSTEM
Directory of Open Access Journals (Sweden)
Suat AKBULUT
2002-03-01
Full Text Available Engineers and earth scientists have successfully used the concept of fractal theory to better analyze the roughness of soil and/or rock particles, and how it affects the permeability, structure and distribution of pores in sedimentary rocks and their influence on strength. Use of fractals as a way to describe irregular or rough objects has been highlighted in articles by researchers working in fields such as powder mechanics, rock and soil mechanics, sedimentary petrography and geoenvironmental applications. Fractal scaling has been found appropriate to express such scale independence for collection of soil particles and aggregates. In many aspects, soil is a fractal medium and fractal models are available for the fragmentation of aggregates with fractal pore space, and with fractal surface. Applications of fractal concepts encompass description of soil physical properties such as pore-size distribution, pore surface area, and grain-size distribution. The roughness of particulate soils is an important characteristic that affects the mass behavior of the soil. The area-perimeter technique was used to predict the fractal dimension using image analysis system. This paper presents the effects of the roughness and sorting of the sand patterns with different shapes on fractal dimension. Results confirmed the significance of the roughness effect on fractal dimension.
Directory of Open Access Journals (Sweden)
Liang Xue
2017-01-01
Full Text Available The traditional geostatistics to describe the spatial variation of hydrogeological properties is based on the assumption of stationarity or statistical homogeneity. However, growing evidences show and it has been widely recognized that the spatial distribution of many hydrogeological properties can be characterized as random fractals with multiscale feature, and spatial variation can be described by power variogram model. It is difficult to generate a multiscale random fractal field by directly using nonstationary power variogram model due to the lack of explicit covariance function. Here we adopt the stationary truncated power variogram model to avoid this difficulty and generate the multiscale random fractal field using Karhunen–Loève (KL expansion. The results show that either the unconditional or conditional (on measurements multiscale random fractal field can be generated by using truncated power variogram model and KL expansion when the upper limit of the integral scale is sufficiently large, and the main structure of the spatial variation can be described by using only the first few dominant KL expansion terms associated with large eigenvalues. The latter provides a foundation to perform dimensionality reduction and saves computational effort when analyzing the stochastic flow and transport problems.
The frictional properties of a simulated gouge having a fractal particle distribution
Biegel, R.L.; Sammis, C.G.; Dieterich, J.H.
1989-01-01
The frictional properties of a layer of simulated Westerly granite fault gouge sandwiched between sliding blocks of Westerly granite have been measured in a high-speed servo-controlled double-direct shear apparatus. Most gouge layers were prepared to have a self-similar particle distribution with a fractal dimension of 2.6. The upper fractal limit was varied between 45 and 710 ??m. Some gouges were prepared with all particles in the range between 360 and 710 ??m. In each experiment the sliding velocity was cyclically alternated between 1 and 10 ??ms-1 and the coefficient of friction ??m and its transient parameters a, b and Dc were measured as functions of displacement. In addition to the particle size distribution, the following experimental variables were also investigated: the layer thickness (1 and 3 mm), the roughness of the sliding surfaces (Nos 60 and 600 grit) and the normal stress (10 and 25 MPa). Some of the sample assemblies were epoxy impregnated following a run so the gouge structure could be microscopically examined in thin section. We observed that gouges which were initially non-fractal evolved to a fractal distribution with dimension 2.6. Gouges which had an initial fractal distribution remained fractal. When the sliding blocks had smooth surfaces, the coefficient of friction was relatively low and was independent of the particle distribution. In these cases, strong velocity weakening was observed throughout the experiment and the transient parameters a, b and Dc, remained almost constant. When the sliding blocks had rough surfaces, the coefficient of friction was larger and more dependent on the particle distribution. Velocity strengthening was observed initially but evolved to velocity weakening with increased sliding displacement. All three transient parameters changed with increasing displacement. The a and b values were about three times as large for rough surfaces as for smooth. The characteristic displacement Dc was not sensitive to surface
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.
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.
Impact of morphology on the radiative properties of fractal soot aggregates
International Nuclear Information System (INIS)
Doner, Nimeti; Liu, Fengshan
2017-01-01
The impact of morphology on the radiative properties of fractal soot aggregates was investigated using the discrete dipole approximation (DDA). The optical properties of four different types of aggregates of freshly emitted soot with a fractal dimension D f =1.65 and a fractal pre-factor k f =1.76 were calculated. The four types of aggregates investigated are formed by uniform primary particles in point-touch, by uniform but overlapping primary particles, by uniform but enlarged primary particles in point-touch, and formed by point-touch and polydisperse primary particles. The radiative properties of aggregates consisting of N=20, 56 and 103 primary particles were numerically evaluated for a given refractive index at 0.532 and 1.064 μm. The radiative properties of soot aggregates vary strongly with the volume equivalent radius a eff and wavelength. The accuracy of DDA was evaluated in the first and fourth cases against the generalized multi-sphere Mie (GMM) solution in terms of the vertical–vertical differential scattering cross section (C vv ). The model predicted the average relative deviations from the base case to be within 15–25% for C vv , depending on the number of particles for the aggregate. The scattering cross sections are only slightly affected by the overlapping but more significantly influenced by primary particle polydispersity. It was also found that the enlargement of primary particles by 20% has a strong effect on soot aggregate radiative properties. - Highlights: • The radiative properties of aggregates of N=20, 56 and 103 primary particles were investigated. • Four different cases, formed by point-touch, overlapping, aggregate expansion and polydispersion, were studied. • The effects of overlapping and aggregate expansion on morphology are found to be the same.
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.
2-D Fractal Wire Antenna Design and Performance
Tebbens, S. F.; Barton, C. C.; Peterman, D. J.; Ewing, J. J.; Abbott, C. S.; Rizki, M. M.
2017-12-01
A 2-D fractal wire antenna uses a fractal (self-similar) pattern to increase its length by iteration and can receive or transmit electromagnetic radiation. 2-D fractals are shapes that, at their mathematical limit (of infinite iterations) have an infinite length. The fractal dimension describes the degree of space filling. A fundamental property of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that can be very compact, wideband and multiband. As the number of iterations increases, the antenna tends to have additional frequencies that minimize far field return loss. This differs from traditional antenna designs in that a single fractal antenna can operate well at multiple frequencies. We have created a MATLAB code to generate deterministic and stochastic modes of fractal wire antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, and number of iterations have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance.
Zhang, Qian; Harman, Ciaran J.; Kirchner, James W.
2018-02-01
River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1) fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2) the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling - in the form of spectral slope (β) or other equivalent scaling parameters (e.g., Hurst exponent) - are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1) they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0) to Brown noise (β = 2) and (2) their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths) in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb-Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among all methods for a wide range of
Directory of Open Access Journals (Sweden)
Q. Zhang
2018-02-01
Full Text Available River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1 fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2 the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β or other equivalent scaling parameters (e.g., Hurst exponent – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1 they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β = 0 to Brown noise (β = 2 and (2 their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among
Verifying the Dependence of Fractal Coefficients on Different Spatial Distributions
International Nuclear Information System (INIS)
Gospodinov, Dragomir; Marekova, Elisaveta; Marinov, Alexander
2010-01-01
A fractal distribution requires that the number of objects larger than a specific size r has a power-law dependence on the size N(r) = C/r D ∝r -D where D is the fractal dimension. Usually the correlation integral is calculated to estimate the correlation fractal dimension of epicentres. A 'box-counting' procedure could also be applied giving the 'capacity' fractal dimension. The fractal dimension can be an integer and then it is equivalent to a Euclidean dimension (it is zero of a point, one of a segment, of a square is two and of a cube is three). In general the fractal dimension is not an integer but a fractional dimension and there comes the origin of the term 'fractal'. The use of a power-law to statistically describe a set of events or phenomena reveals the lack of a characteristic length scale, that is fractal objects are scale invariant. Scaling invariance and chaotic behavior constitute the base of a lot of natural hazards phenomena. Many studies of earthquakes reveal that their occurrence exhibits scale-invariant properties, so the fractal dimension can characterize them. It has first been confirmed that both aftershock rate decay in time and earthquake size distribution follow a power law. Recently many other earthquake distributions have been found to be scale-invariant. The spatial distribution of both regional seismicity and aftershocks show some fractal features. Earthquake spatial distributions are considered fractal, but indirectly. There are two possible models, which result in fractal earthquake distributions. The first model considers that a fractal distribution of faults leads to a fractal distribution of earthquakes, because each earthquake is characteristic of the fault on which it occurs. The second assumes that each fault has a fractal distribution of earthquakes. Observations strongly favour the first hypothesis.The fractal coefficients analysis provides some important advantages in examining earthquake spatial distribution, which are
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
Directory of Open Access Journals (Sweden)
Amato P
2008-01-01
Full Text Available Abstract Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.
Fractal Property in the Light Curve of BL Lac Object S5 0716+714 ...
Indian Academy of Sciences (India)
- tion and fractal dimension. ... tional data, here, we obtain the long-term light curve of S5 0716 +714 and fractal dimension and then ... Science Foundation of Yunnan Educational Department under grant 2012Z016. References. Cristiano, S.
Fractal assembly of micrometre-scale DNA origami arrays with arbitrary patterns
Tikhomirov, Grigory; Petersen, Philip; Qian, Lulu
2017-12-01
Self-assembled DNA nanostructures enable nanometre-precise patterning that can be used to create programmable molecular machines and arrays of functional materials. DNA origami is particularly versatile in this context because each DNA strand in the origami nanostructure occupies a unique position and can serve as a uniquely addressable pixel. However, the scale of such structures has been limited to about 0.05 square micrometres, hindering applications that demand a larger layout and integration with more conventional patterning methods. Hierarchical multistage assembly of simple sets of tiles can in principle overcome this limitation, but so far has not been sufficiently robust to enable successful implementation of larger structures using DNA origami tiles. Here we show that by using simple local assembly rules that are modified and applied recursively throughout a hierarchical, multistage assembly process, a small and constant set of unique DNA strands can be used to create DNA origami arrays of increasing size and with arbitrary patterns. We illustrate this method, which we term ‘fractal assembly’, by producing DNA origami arrays with sizes of up to 0.5 square micrometres and with up to 8,704 pixels, allowing us to render images such as the Mona Lisa and a rooster. We find that self-assembly of the tiles into arrays is unaffected by changes in surface patterns on the tiles, and that the yield of the fractal assembly process corresponds to about 0.95m - 1 for arrays containing m tiles. When used in conjunction with a software tool that we developed that converts an arbitrary pattern into DNA sequences and experimental protocols, our assembly method is readily accessible and will facilitate the construction of sophisticated materials and devices with sizes similar to that of a bacterium using DNA nanostructures.
Topology of the Italian airport network: A scale-free small-world network with a fractal structure?
International Nuclear Information System (INIS)
Guida, Michele; Maria, Funaro
2007-01-01
In this paper, for the first time we analyze the structure of the Italian Airport Network (IAN) looking at it as a mathematical graph and investigate its topological properties. We find that it has very remarkable features, being like a scale-free network, since both the degree and the 'betweenness centrality' distributions follow a typical power-law known in literature as a Double Pareto Law. From a careful analysis of the data, the Italian Airport Network turns out to have a self-similar structure. In short, it is characterized by a fractal nature, whose typical dimensions can be easily determined from the values of the power-law scaling exponents. Moreover, we show that, according to the period examined, these distributions exhibit a number of interesting features, such as the existence of some 'hubs', i.e. in the graph theory's jargon, nodes with a very large number of links, and others most probably associated with geographical constraints. Also, we find that the IAN can be classified as a small-world network because the average distance between reachable pairs of airports grows at most as the logarithm of the number of airports. The IAN does not show evidence of 'communities' and this result could be the underlying reason behind the smallness of the value of the clustering coefficient, which is related to the probability that two nearest neighbors of a randomly chosen airport are connected
Link between truncated fractals and coupled oscillators in biological systems.
Paar, V; Pavin, N; Rosandić, M
2001-09-07
This article aims at providing a new theoretical insight into the fundamental question of the origin of truncated fractals in biological systems. It is well known that fractal geometry is one of the characteristics of living organisms. However, contrary to mathematical fractals which are self-similar at all scales, the biological fractals are truncated, i.e. their self-similarity extends at most over a few orders of magnitude of separation. We show that nonlinear coupled oscillators, modeling one of the basic features of biological systems, may generate truncated fractals: a truncated fractal pattern for basin boundaries appears in a simple mathematical model of two coupled nonlinear oscillators with weak dissipation. This fractal pattern can be considered as a particular hidden fractal property. At the level of sufficiently fine precision technique the truncated fractality acts as a simple structure, leading to predictability, but at a lower level of precision it is effectively fractal, limiting the predictability of the long-term behavior of biological systems. We point out to the generic nature of our result. Copyright 2001 Academic Press.
Fractal Property in the Light Curve of BL Lac Object S5 0716+714 ...
Indian Academy of Sciences (India)
Introduction. A fractal is a mathematical set that has a fractal dimension that usually exceeds its topological dimension and may fall between the integers, so it is typically self- similar patterns (Mandelbrot 1982). In recent years, fractal theory is also used to solve the astrophysical problems, e.g., Cristiano (2007) confirmed that ...
Implications of chaos, scale-invariance, and fractal statistics in geology
Turcotte, D. L.
1990-01-01
A set of three nonlinear total differential equations (Lorenz equations) exhibiting deterministic chaos is considered, and it is shown that these equations demonstrate that deterministic equations with deterministic initial conditions can yield stocastic solutions with fractal statistics. The logistic map, fractal distributions, and fragmentation are discussed. It is pointed out that well-defined fractal distributions of earthquakes are found both regionally and globally, and that the general applicability of the fractal relation for seismicity can provide the basis for a quantitative seismic hazard assessment. It is suggested that the governing physics of erosional topography is nonlinear and may be related to a fractal distribution of storms and floods that generate and renew erosional feature such as gullies and drainage systems.
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)
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)
Structural and fractal properties of particles emitted from spark ignition engines.
Chakrabarty, Rajan K; Moosmüller, Hans; Arnott, W Patrick; Garro, Mark A; Walker, John
2006-11-01
Size, morphology, and microstructure of particles emitted from one light-duty passenger vehicle (Buick Century; model year 1990; PM (particulate matter) mass emission rate 3.1 mg/km) and two light-duty trucks (Chevrolet C2; model year 1973; PM mass emission rate 282 mg/km, and Chevrolet El Camino; model year 1976; PM mass emission rate 31 mg/km), running California's unified driving cycles (UDC) on a chassis dynamometer, were studied using scanning electron microscopy (SEM). SEM images yielded particle properties including three-dimensional density fractal dimensions, monomer and agglomerate number size distributions, and three different shape descriptors, namely aspect ratio, root form factor, and roundness. The density fractal dimension of the particles was between 1.7 and 1.78, while the number size distribution of the particles placed the majority of the particles in the accumulation mode (0.1-0.3 microm). The shape descriptors were found to decrease with increasing particle size. Partial melting of particles, a rare and previously unreported phenomenon, was observed upon exposure of particles emitted during phase 2 of the UDC to the low accelerating voltage electron beam of the SEM. The rate of melting was quantified for individual particles, establishing a near linear relationship between the melting rate and the organic carbon 1 to elemental carbon ratio.
COMPARISON OF CHAOTIC AND FRACTAL PROPERTIES OF POLAR FACULAE WITH SUNSPOT ACTIVITY
Energy Technology Data Exchange (ETDEWEB)
Deng, L. H.; Xiang, Y. Y.; Dun, G. T. [Yunnan Observatories, Chinese Academy of Sciences, Kunming 650216 (China); Li, B., E-mail: wooden@escience.cn [Shandong Provincial Key Laboratory of Optical Astronomy and Solar-Terrestrial Environment, School of Space Science and Physics, Shandong University at Weihai, Weihai 264209 (China)
2016-01-15
The solar magnetic activity is governed by a complex dynamo mechanism and exhibits a nonlinear dissipation behavior in nature. The chaotic and fractal properties of solar time series are of great importance to understanding the solar dynamo actions, especially with regard to the nonlinear dynamo theories. In the present work, several nonlinear analysis approaches are proposed to investigate the nonlinear dynamical behavior of the polar faculae and sunspot activity for the time interval from 1951 August to 1998 December. The following prominent results are found: (1) both the high- and the low-latitude solar activity are governed by a three-dimensional chaotic attractor, and the chaotic behavior of polar faculae is the most complex, followed by that of the sunspot areas, and then the sunspot numbers; (2) both the high- and low-latitude solar activity exhibit a high degree of persistent behavior, and their fractal nature is due to such long-range correlation; (3) the solar magnetic activity cycle is predictable in nature, but the high-accuracy prediction should only be done for short- to mid-term due to its intrinsically dynamical complexity. With the help of the Babcock–Leighton dynamo model, we suggest that the nonlinear coupling of the polar magnetic fields with strong active-region fields exhibits a complex manner, causing the statistical similarities and differences between the polar faculae and the sunspot-related indicators.
The role of the circadian system in fractal neurophysiological control.
Pittman-Polletta, Benjamin R; Scheer, Frank A J L; Butler, Matthew P; Shea, Steven A; Hu, Kun
2013-11-01
Many neurophysiological variables such as heart rate, motor activity, and neural activity are known to exhibit intrinsic fractal fluctuations - similar temporal fluctuation patterns at different time scales. These fractal patterns contain information about health, as many pathological conditions are accompanied by their alteration or absence. In physical systems, such fluctuations are characteristic of critical states on the border between randomness and order, frequently arising from nonlinear feedback interactions between mechanisms operating on multiple scales. Thus, the existence of fractal fluctuations in physiology challenges traditional conceptions of health and disease, suggesting that high levels of integrity and adaptability are marked by complex variability, not constancy, and are properties of a neurophysiological network, not individual components. Despite the subject's theoretical and clinical interest, the neurophysiological mechanisms underlying fractal regulation remain largely unknown. The recent discovery that the circadian pacemaker (suprachiasmatic nucleus) plays a crucial role in generating fractal patterns in motor activity and heart rate sheds an entirely new light on both fractal control networks and the function of this master circadian clock, and builds a bridge between the fields of circadian biology and fractal physiology. In this review, we sketch the emerging picture of the developing interdisciplinary field of fractal neurophysiology by examining the circadian system's role in fractal regulation. © 2013 The Authors. Biological Reviews © 2013 Cambridge Philosophical Society.
Hagerhall, C M; Laike, T; Küller, M; Marcheschi, E; Boydston, C; Taylor, R P
2015-01-01
Psychological and physiological benefits of viewing nature have been extensively studied for some time. More recently it has been suggested that some of these positive effects can be explained by nature's fractal properties. Virtually all studies on human responses to fractals have used stimuli that represent the specific form of fractal geometry found in nature, i.e. statistical fractals, as opposed to fractal patterns which repeat exactly at different scales. This raises the question of whether human responses like preference and relaxation are being driven by fractal geometry in general or by the specific form of fractal geometry found in nature. In this study we consider both types of fractals (statistical and exact) and morph one type into the other. Based on the Koch curve, nine visual stimuli were produced in which curves of three different fractal dimensions evolve gradually from an exact to a statistical fractal. The patterns were shown for one minute each to thirty-five subjects while qEEG was continuously recorded. The results showed that the responses to statistical and exact fractals differ, and that the natural form of the fractal is important for inducing alpha responses, an indicator of a wakefully relaxed state and internalized attention.
Fractals properties of EEG during event-related desynchronization of motor imagery.
Nguyen, Ngoc Quang; Truong, Quang Dang Khoa; Kondo, Toshiyuki
2015-01-01
Chaos and fractal dimension are emerging modalities for the research of electroencephalogram (EEG) signal processing. The capability of measuring non-linear characteristics of the fractal dimension enables new methodologies to identify distinct brain activities. Recent studies on the topic focus on utilizing various types of fractals as features in order to design better brain state classification system. However, we have little insight about the EEG signals projected in fractal dimension. In this paper, we investigate the relationship between the non-linear characteristics of ongoing EEG signals and event-related desynchronization (ERD) during motor imagery. We observed a considerable synchronization between ERD and fractal dimension. This finding suggests further usage of chaos and fractal theory in investigating brain activities.
Fractal properties of SYM-H during quiet and active times
Wanliss, James
2005-03-01
Detrended fluctuation analysis was applied to the magnetic storm index SYM-H for the epoch 1981-2002. The objective was to determine the characteristic fractal statistical differences, if any, between a quiet and active magnetosphere. The entire data set comprises over 11 million points that include numerous intervals that can be classified as quiet or active. For quiet intervals we required Kp ≤ 1 for 10,000 consecutive minutes. Similarly, to qualify as an active interval required Kp ≥ 4 for 10,000 consecutive minutes. All active intervals included magnetic storms. Detrended fluctuation analysis was applied to each of these intervals to obtain local scaling exponents. A clear difference in statistical behavior during quiet and active intervals is implied through analysis of the scaling exponents for the quiet and active intervals; active intervals generally have larger values of scaling exponents. This implies that although SYM-H appears monofractal on shorter timescales, it is more properly described as a multifractional Brownian motion. An overall trend toward higher scaling exponents was also discovered for increasing magnetospheric activity, possibly implying an increase in organization with magnetospheric activity. The overall distribution of the scaling exponents for active intervals was Gaussian. For quiet intervals, however, it was bi-Gaussian, perhaps indicative of different internal (magnetospheric) and external (solar wind) nonlinear forcings.
Directory of Open Access Journals (Sweden)
Catherine K. Denny
2017-04-01
Full Text Available Spatial heterogeneity of vegetation is an important landscape characteristic, but is difficult to assess due to scale-dependence. Here we examine how spatial patterns in the forest canopy affect those of understory plants, using the shrub Canada buffaloberry (Shepherdia canadensis (L. Nutt. as a focal species. Evergreen and deciduous forest canopy and buffaloberry shrub presence were measured with line-intercept sampling along ten 2-km transects in the Rocky Mountain foothills of west-central Alberta, Canada. Relationships between overstory canopy and understory buffaloberry presence were assessed for scales ranging from 2 m to 502 m. Fractal dimensions of both canopy and buffaloberry were estimated and then related using box-counting methods to evaluate spatial heterogeneity based on patch distribution and abundance. Effects of canopy presence on buffaloberry were scale-dependent, with shrub presence negatively related to evergreen canopy cover and positively related to deciduous cover. The effect of evergreen canopy was significant at a local scale between 2 m and 42 m, while that of deciduous canopy was significant at a meso-scale between 150 m and 358 m. Fractal analysis indicated that buffaloberry heterogeneity positively scaled with evergreen canopy heterogeneity, but was unrelated to that of deciduous canopy. This study demonstrates that evergreen canopy cover is a determinant of buffaloberry heterogeneity, highlighting the importance of spatial scale and canopy composition in understanding canopy-understory relationships.
Fractal Image Informatics: from SEM to DEM
Oleschko, K.; Parrot, J.-F.; Korvin, G.; Esteves, M.; Vauclin, M.; Torres-Argüelles, V.; Salado, C. Gaona; Cherkasov, S.
2008-05-01
In this paper, we introduce a new branch of Fractal Geometry: Fractal Image Informatics, devoted to the systematic and standardized fractal analysis of images of natural systems. The methods of this discipline are based on the properties of multiscale images of selfaffine fractal surfaces. As proved in the paper, the image inherits the scaling and lacunarity of the surface and of its reflectance distribution [Korvin, 2005]. We claim that the fractal analysis of these images must be done without any smoothing, thresholding or binarization. Two new tools of Fractal Image Informatics, firmagram analysis (FA) and generalized lacunarity (GL), are presented and discussed in details. These techniques are applicable to any kind of image or to any observed positive-valued physical field, and can be used to correlate between images. It will be shown, by a modified Grassberger-Hentschel-Procaccia approach [Phys. Lett. 97A, 227 (1983); Physica 8D, 435 (1983)] that GL obeys the same scaling law as the Allain-Cloitre lacunarity [Phys. Rev. A 44, 3552 (1991)] but is free of the problems associated with gliding boxes. Several applications are shown from Soil Physics, Surface Science, and other fields.
Fractal Analysis of 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)
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.
Small-Angle Scattering from Nanoscale Fat Fractals.
Anitas, E M; Slyamov, A; Todoran, R; Szakacs, Z
2017-12-01
Small-angle scattering (of neutrons, x-ray, or light; SAS) is considered to describe the structural characteristics of deterministic nanoscale fat fractals. We show that in the case of a polydisperse fractal system, with equal probability for any orientation, one obtains the fractal dimensions and scaling factors at each structural level. This is in agreement with general results deduced in the context of small-angle scattering analysis of a system of randomly oriented, non-interacting, nano-/micro-fractals. We apply our results to a two-dimensional fat Cantor-like fractal, calculating analytic expressions for the scattering intensities and structure factors. We explain how the structural properties can be computed from experimental data and show their correlation to the variation of the scaling factor with the iteration number. The model can be used to interpret recorded experimental SAS data in the framework of fat fractals and can reveal structural properties of materials characterized by a regular law of changing of the fractal dimensions. It can describe successions of power-law decays, with arbitrary decreasing values of the scattering exponents, and interleaved by regions of constant intensity.
Directory of Open Access Journals (Sweden)
Franz Konstantin Fuss
2013-01-01
Full Text Available Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal’s time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
Fuss, Franz Konstantin
2013-01-01
Standard methods for computing the fractal dimensions of time series are usually tested with continuous nowhere differentiable functions, but not benchmarked with actual signals. Therefore they can produce opposite results in extreme signals. These methods also use different scaling methods, that is, different amplitude multipliers, which makes it difficult to compare fractal dimensions obtained from different methods. The purpose of this research was to develop an optimisation method that computes the fractal dimension of a normalised (dimensionless) and modified time series signal with a robust algorithm and a running average method, and that maximises the difference between two fractal dimensions, for example, a minimum and a maximum one. The signal is modified by transforming its amplitude by a multiplier, which has a non-linear effect on the signal's time derivative. The optimisation method identifies the optimal multiplier of the normalised amplitude for targeted decision making based on fractal dimensions. The optimisation method provides an additional filter effect and makes the fractal dimensions less noisy. The method is exemplified by, and explained with, different signals, such as human movement, EEG, and acoustic signals.
Tumor growth in the space-time with temporal fractal dimension
International Nuclear Information System (INIS)
Molski, Marcin; Konarski, Jerzy
2008-01-01
An improvement of the Waliszewski and Konarski approach [Waliszewski P, Konarski J. The Gompertzian curve reveals fractal properties of tumor growth. Chaos, Solitons and Fractals 2003;16:665-74] to determination of the time-dependent temporal fractal dimension b t (t) and the scaling factor a t (t) for the tumor formation in the fractal space-time is presented. The analytical formulae describing the time-dependence of b t (t) and a t (t), which take into account appropriate boundary conditions for t → 0 and t → ∞, are derived. Their validity is tested on the experimental growth curve obtained by Laird for the Flexner-Jobling rat's tumor. A hypothesis is formulated that tumorigenesis has a lot in common with the neuronal differentiation and synapse formation. These processes are qualitatively described by the same Gompertz function of growth and take place in the fractal space-time whose mean temporal fractal dimension is lost during progression
Slim Fractals: The Geometry of Doubly Transient Chaos
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Xiaowen Chen
2017-06-01
Full Text Available Traditional studies of chaos in conservative and driven dissipative systems have established a correspondence between sensitive dependence on initial conditions and fractal basin boundaries, but much less is known about the relation between geometry and dynamics in undriven dissipative systems. These systems can exhibit a prevalent form of complex dynamics, dubbed doubly transient chaos because not only typical trajectories but also the (otherwise invariant chaotic saddles are transient. This property, along with a manifest lack of scale invariance, has hindered the study of the geometric properties of basin boundaries in these systems—most remarkably, the very question of whether they are fractal across all scales has yet to be answered. Here, we derive a general dynamical condition that answers this question, which we use to demonstrate that the basin boundaries can indeed form a true fractal; in fact, they do so generically in a broad class of transiently chaotic undriven dissipative systems. Using physical examples, we demonstrate that the boundaries typically form a slim fractal, which we define as a set whose dimension at a given resolution decreases when the resolution is increased. To properly characterize such sets, we introduce the notion of equivalent dimension for quantifying their relation with sensitive dependence on initial conditions at all scales. We show that slim fractal boundaries can exhibit complex geometry even when they do not form a true fractal and fractal scaling is observed only above a certain length scale at each boundary point. Thus, our results reveal slim fractals as a geometrical hallmark of transient chaos in undriven dissipative systems.
ABC of multi-fractal spacetimes and fractional sea turtles
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2016-04-15
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)
ABC of multi-fractal spacetimes and fractional sea turtles
Calcagni, Gianluca
2016-04-01
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.
ABC of multi-fractal spacetimes and fractional sea turtles
International Nuclear Information System (INIS)
Calcagni, Gianluca
2016-01-01
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)
Biometric feature extraction using local fractal auto-correlation
International Nuclear Information System (INIS)
Chen Xi; Zhang Jia-Shu
2014-01-01
Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme: (i) using two-dimensional Gabor filter to extract the texture features of biometric images; (ii) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and (iii) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach. (condensed matter: structural, mechanical, and thermal properties)
Fractal 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.
Aerodynamic properties of fractal grains: implications for the primordial solar nebula
International Nuclear Information System (INIS)
Meakin, P.; Donn, B.
1988-01-01
Under conditions in the primordial solar nebula and dense interstellar clouds, small grains have low relative velocities. This is the condition for efficient sticking and formation of fractal aggregates. A calculation of the ratio of cross section, sigma, to number of primary particles, N, for fractal clusters yielded 1n sigma/N = 0.2635 + 0.5189N sup (-0.1748). This ratio decreases slowly with N and approaches a constant for large N. Under the usual assumption of collisions producing spherical compact, uniform density aggregates, sigma/N varies as N sup -1/3 and decreases rapidly. Fractal grains are therefore much more closely coupled to the gas than are compact aggregates. This has a significant effect on the aerodynamic behavior of aggregates and consequently on their evolution and that of the nebula
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.
The generalized 20/80 law using probabilistic fractals applied to petroleum field size
Crovelli, R.A.
1995-01-01
Fractal properties of the Pareto probability distribution are used to generalize "the 20/80 law." The 20/80 law is a heuristic law that has evolved over the years into the following rule of thumb for many populations: 20 percent of the population accounts for 80 percent of the total value. The general p100/q100 law in probabilistic form is defined with q as a function of p, where p is the population proportion and q is the proportion of total value. Using the Pareto distribution, the p100/q100 law in fractal form is derived with the parameter q being a fractal, where q unexpectedly possesses the scale invariance property. The 20/80 law is a special case of the p100/q100 law in fractal form. The p100/q100 law in fractal form is applied to petroleum fieldsize data to obtain p and q such that p100% of the oil fields greater than any specified scale or size in a geologic play account for q100% of the total oil of the fields. The theoretical percentages of total resources of oil using the fractal q are extremely close to the empirical percentages from the data using the statistic q. Also, the empirical scale invariance property of the statistic q for the petroleum fieldsize data is in excellent agreement with the theoretical scale invariance property of the fractal q. ?? 1995 Oxford University Press.
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.
Discrimination of Earthquakes and Explosions using Multi-fractal Singularity Spectrums Properties
Czech Academy of Sciences Publication Activity Database
Lyubushin, A. A.; Kaláb, Zdeněk; Lednická, Markéta; Haggag, H. M.
2013-01-01
Roč. 17, č. 3 (2013), s. 975-983 ISSN 1383-4649 Institutional support: RVO:68145535 Keywords : multi- fractal parameters * singularity spectrum * seismic event discrimination Subject RIV: DC - Siesmology, Volcanology, Earth Structure Impact factor: 1.386, year: 2013 http://link.springer.com/content/pdf/10.1007%2Fs10950-013-9366-3.pdf
Directory of Open Access Journals (Sweden)
Tao Sun
2017-12-01
Full Text Available The Southern Jiangxi Province (SJP hosts one of the best known districts of tungsten deposits in the world. Delineating spatial complexities of geological features and their controls on regional-scale tungsten mineralization by using an integrated fractal and weights-of-evidence (WofE method can provide insights into the understanding of ore genesis and facilitate further prospecting in this area. The box-counting fractal analysis shows that most of the tungsten occurrences are distributed in regions with high fractal dimensions of faults and fault intersections, suggesting ore-forming favorability of areas with highly complex structural patterns. The WofE-derived indices are employed to quantitatively measure the controls of analyzed features on mineralization, which illustrate that tungsten anomalies, faults, Yanshanian granites, and manganese anomalies have high contrast values, implying a spatially strong correlation of these features with tungsten occurrences. In particular, high manganese anomalies in host rock may provide a novel indication for mineral prospecting in this area. A predictive map is extracted based on the combination of fractal and WofE results, providing intuitive guides for future prospectivity in this area. Regions identified by high posterior probability in conjunction with high fractal dimensions of both faults and fault intersections are evaluated as the most favorable targets.
Zhang, Zhenwei; VanSwearingen, Jessie; Brach, Jennifer S; Perera, Subashan; Sejdić, Ervin
2017-01-01
Human gait is a complex interaction of many nonlinear systems and stride intervals exhibiting self-similarity over long time scales that can be modeled as a fractal process. The scaling exponent represents the fractal degree and can be interpreted as a "biomarker" of relative diseases. The previous study showed that the average wavelet method provides the most accurate results to estimate this scaling exponent when applied to stride interval time series. The purpose of this paper is to determine the most suitable mother wavelet for the average wavelet method. This paper presents a comparative numerical analysis of 16 mother wavelets using simulated and real fractal signals. Simulated fractal signals were generated under varying signal lengths and scaling exponents that indicate a range of physiologically conceivable fractal signals. The five candidates were chosen due to their good performance on the mean square error test for both short and long signals. Next, we comparatively analyzed these five mother wavelets for physiologically relevant stride time series lengths. Our analysis showed that the symlet 2 mother wavelet provides a low mean square error and low variance for long time intervals and relatively low errors for short signal lengths. It can be considered as the most suitable mother function without the burden of considering the signal length. Copyright © 2016 Elsevier Ltd. All rights reserved.
Fractal frontiers in cardiovascular magnetic resonance: towards clinical implementation.
Captur, Gabriella; Karperien, Audrey L; Li, Chunming; Zemrak, Filip; Tobon-Gomez, Catalina; Gao, Xuexin; Bluemke, David A; Elliott, Perry M; Petersen, Steffen E; Moon, James C
2015-09-07
Many of the structures and parameters that are detected, measured and reported in cardiovascular magnetic resonance (CMR) have at least some properties that are fractal, meaning complex and self-similar at different scales. To date however, there has been little use of fractal geometry in CMR; by comparison, many more applications of fractal analysis have been published in MR imaging of the brain.This review explains the fundamental principles of fractal geometry, places the fractal dimension into a meaningful context within the realms of Euclidean and topological space, and defines its role in digital image processing. It summarises the basic mathematics, highlights strengths and potential limitations of its application to biomedical imaging, shows key current examples and suggests a simple route for its successful clinical implementation by the CMR community.By simplifying some of the more abstract concepts of deterministic fractals, this review invites CMR scientists (clinicians, technologists, physicists) to experiment with fractal analysis as a means of developing the next generation of intelligent quantitative cardiac imaging tools.
Fractal dimensions of rampart impact craters on Mars
Ching, Delwyn; Taylor, G. Jeffrey; Mouginis-Mark, Peter; Bruno, Barbara C.
1993-01-01
Ejecta blanket morphologies of Martian rampart craters may yield important clues to the atmospheric densities during impact, and the nature of target materials (e.g., hard rock, fine-grained sediments, presence of volatiles). In general, the morphologies of such craters suggest emplacement by a fluidized, ground hugging flow instead of ballistic emplacement by dry ejecta. We have quantitatively characterized the shape of the margins of the ejecta blankets of 15 rampart craters using fractal geometry. Our preliminary results suggest that the craters are fractals and are self-similar over scales of approximately 0.1 km to 30 km. Fractal dimensions (a measure of the extent to which a line fills a plane) range from 1.06 to 1.31. No correlations of fractal dimension with target type, elevation, or crater size were observed, though the data base is small. The range in fractal dimension and lack of correlation may be due to a complex interplay of target properties (grain size, volatile content), atmospheric pressure, and crater size. The mere fact that the ejecta margins are fractals, however, indicates that viscosity and yield strength of the ejecta were at least as low as those of basalts, because silicic lava flows are not generally fractals.
Intrinsic half-metallicity in fractal carbon nitride honeycomb lattices.
Wang, Aizhu; Zhao, Mingwen
2015-09-14
Fractals are natural phenomena that exhibit a repeating pattern "exactly the same at every scale or nearly the same at different scales". Defect-free molecular fractals were assembled successfully in a recent work [Shang et al., Nature Chem., 2015, 7, 389-393]. Here, we adopted the feature of a repeating pattern in searching two-dimensional (2D) materials with intrinsic half-metallicity and high stability that are desirable for spintronics applications. Using first-principles calculations, we demonstrate that the electronic properties of fractal frameworks of carbon nitrides have stable ferromagnetism accompanied by half-metallicity, which are highly dependent on the fractal structure. The ferromagnetism increases gradually with the increase of fractal order. The Curie temperature of these metal-free systems estimated from Monte Carlo simulations is considerably higher than room temperature. The stable ferromagnetism, intrinsic half-metallicity, and fractal characteristics of spin distribution in the carbon nitride frameworks open an avenue for the design of metal-free magnetic materials with exotic properties.
Directory of Open Access Journals (Sweden)
Tiago Barbosa
2016-10-01
Full Text Available The aim of this study was to compare the nonlinear properties of the four competitive swim strokes. Sixty-eight swimmers performed a set of maximal 4x25m using the four competitive swim strokes. The hip’s speed-data as a function of time was collected with a speedo-meter. The speed fluctuation (dv, approximate entropy (ApEn and the fractal dimension by Higuchi’s method (D were computed. Swimming data exhibited nonlinear properties that were different among the four strokes (14.048≤dv≤39.722; 0.682≤ApEn≤1.025; 1.823≤D≤1.919. The ApEn showed the lowest value for front-crawl, followed by breaststroke, butterfly and backstroke (P<0.001. Fractal dimension and dv had the lowest values for front-crawl and backstroke, followed by butterfly and breaststroke (P<0.001. It can be concluded that swimming data exhibits nonlinear properties, which are different among the four competitive swimming strokes.
International Nuclear Information System (INIS)
Popescu, E.; Ardeleanu, L.; Bazacliu, O.; Popa, M.; Radulian, M.; Rizescu, M.
2002-01-01
now (first two stages) refer to the determination of the fractal properties of the time and space distributions for the Vrancea subcrustal earthquakes. The application of the variation coefficient method in time domain outlines the existence of different types of generation models in the two segments delimited on depth in the Vrancea subcrustal region: crack-like events (M D ≤ 3.6) which are more clustered in the upper segment of the subducted lithosphere; asperity-like events (M D > 3.6) which on the contrary are more clustered in the lower segment of the subducted lithosphere. Application of fractal statistics leads us to the following conclusions: Time fractal dimension, D t , of the Vrancea subcrustal earthquakes varies in a relative small interval, D t with in the range [0.81 - 0.92]; these values indicate a clustering tendency in all analyzed cases; Data set is well approximated by a fractal model for a time domain τ with in the range [2 to 2 7 days]; in the same time interval, deviations from the linearity are also noticed, indicating a superposition of the scale invariance behavior (fractal properties) with a Poisson distribution (random). As concerns the space clustering properties of the Vrancea subcrustal events, our purpose is to test the hypothesis of segmentation on depth of the subducted lithosphere. Our work emphasized consequently the existence of two maxima in the depth-earthquake distribution: a) 60 ≤ h ≤110 km; b)110 < h ≤ 220 km. The space clustering analysis showed also that: 1. In the case of the upper segment, the fractal dimension of the epicenter distribution decreases in time from 1.83 to 1.71; 2. In the case of the lower segment, the fractal dimension of the epicenter distribution has a tendency of increase in time from 1.65 to 1.91; 3. In the case of the whole subducted slab, there is a trend of increase in time from 1.65 to 1.91. In conclusion, the analysis of the clustering properties in time and space in the case of Vrancea
Fractal characterization of acupuncture-induced spike trains of rat WDR neurons
International Nuclear Information System (INIS)
Chen, Yingyuan; Guo, Yi; Wang, Jiang; Hong, Shouhai; Wei, Xile; Yu, Haitao; Deng, Bin
2015-01-01
Highlights: •Fractal analysis is a valuable tool for measuring MA-induced neural activities. •In course of the experiments, the spike trains display different fractal properties. •The fractal properties reflect the long-term modulation of MA on WDR neurons. •The results may explain the long-lasting effects induced by acupuncture. -- Abstract: The experimental and the clinical studies have showed manual acupuncture (MA) could evoke multiple responses in various neural regions. Characterising the neuronal activities in these regions may provide more deep insights into acupuncture mechanisms. This paper used fractal analysis to investigate MA-induced spike trains of Wide Dynamic Range (WDR) neurons in rat spinal dorsal horn, an important relay station and integral component in processing acupuncture information. Allan factor and Fano factor were utilized to test whether the spike trains were fractal, and Allan factor were used to evaluate the scaling exponents and Hurst exponents. It was found that these two fractal exponents before and during MA were different significantly. During MA, the scaling exponents of WDR neurons were regulated in a small range, indicating a special fractal pattern. The neuronal activities were long-range correlated over multiple time scales. The scaling exponents during and after MA were similar, suggesting that the long-range correlations not only displayed during MA, but also extended to after withdrawing the needle. Our results showed that fractal analysis is a useful tool for measuring acupuncture effects. MA could modulate neuronal activities of which the fractal properties change as time proceeding. This evolution of fractal dynamics in course of MA experiments may explain at the level of neuron why the effect of MA observed in experiment and in clinic are complex, time-evolutionary, long-range even lasting for some time after stimulation
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.
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
Directory of Open Access Journals (Sweden)
Adewale Amosu
2018-02-01
Full Text Available Reservoir modeling of carbonate rocks requires a proper understanding of the pore space distribution and its relationship to permeability. Using a pigeonhole fractal model we characterize the fractal geometry of moldic pore spaces and extract the fractal dimension. We apply the Kozeny-Carman equation and equations relating the tortuosity and the porosity to the fractal dimension to derive an empirical relationship between permeability and porosity.
Optical properties of fractal aggregates of nanoparticles: Effects of particle size polydispersity
Naeimi, Zahra; Miri, Mirfaez
2009-12-01
We study the effects of particle size dispersion on the absorption spectrum of nonfractal random gas of particles and fractal cluster-cluster aggregates. We use the coupled-dipole equations to describe the interaction of particles with the external electromagnetic wave. We express the absorption in terms of the spectral variable introduced by Bergman [Phys. Rev. B 19, 2359 (1979)]. In the case of nonfractal clusters, the particle size dispersion has no influence on the overall shape of the spectrum. In the case of fractal clusters, the bandwidth of the spectrum decreases as the particle size dispersion increases. Moreover, the maxima and minima of the spectrum vary, shift, and even disappear, as the particle size dispersion increases.
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.)
Le Chatelier's Principle in Sensation and Perception: Fractal-Like Enfolding at Different Scales
Norwich, Kenneth H.
2010-01-01
Le Chatelier's principle asserts that a disturbance, when applied to a resting system may drive the system away from its equilibrium state, but will invoke a countervailing influence that will counteract the effect of the disturbance. When applied to the field of sensation and perception, a generalized stimulus will displace the system from equilibrium, and a generalized adaptation process will serve as the countervailing influence tending to reduce the impact of the stimulus. The principle applies at all levels, from the behavioral to the neural, the larger enfolding the smaller in fractal-like form. Le Chatelier's principle, so applied, leads to the unification of many concepts in sensory science. Ideas as diverse as sensory adaptation, reflex arcs, and simple deductive logic can be brought under the umbrella of a single orienting principle. Beyond unification, this principle allows us to approach many questions in pathophysiology from a different perspective. For example, we find new direction toward the reduction of phantom-limb pain and possibly of vertigo. PMID:21423359
Le Chatelier's principle in sensation and perception: fractal-like enfolding at different scales
Directory of Open Access Journals (Sweden)
Ken Norwich
2010-06-01
Full Text Available Le Chatelier’s principle asserts that a disturbance, when applied to a resting system may drive the system away from its equilibrium state, but will invoke a countervailing influence that will counteract the effect of the disturbance. When applied to the field of sensation and perception, a generalized stimulus will displace the system from equilibrium, and a generalized adaptation process will serve as the countervailing influence tending to reduce the impact of the stimulus. The principle applies at all levels, from the behavioral to the neural, the larger enfolding the smaller in fractal-like form. Le Chatelier’s principle, so applied, leads to the unification of many concepts in sensory science. Ideas as diverse as sensory adaptation, reflex arcs, and simple deductive logic can be brought under the umbrella of a single orienting principle. Beyond unification, this principle allows us to approach many questions in pathophysiology from a different perspective. For example, we find new direction toward the reduction of phantom limb pain and possibly of vertigo.
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
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.
The effect of ventricular assist devices on cerebral blood flow and blood pressure fractality
International Nuclear Information System (INIS)
Bellapart, Judith; Fraser, John F; Chan, Gregory S H; Tzeng, Yu-Chieh; Ainslie, Philip N; Dunster, Kimble R; Barnett, Adrian G; Boots, Rob
2011-01-01
Biological signals often exhibit self-similar or fractal scaling characteristics which may reflect intrinsic adaptability to their underlying physiological system. This study analysed fractal dynamics of cerebral blood flow in patients supported with ventricular assist devices (VAD) to ascertain if sustained modifications of blood pressure waveform affect cerebral blood flow fractality. Simultaneous recordings of arterial blood pressure and cerebral blood flow velocity using transcranial Doppler were obtained from five cardiogenic shock patients supported by VAD, five matched control patients and five healthy subjects. Computation of a fractal scaling exponent (α) at the low-frequency time scale by detrended fluctuation analysis showed that cerebral blood flow velocity exhibited 1/f fractal scaling in both patient groups (α = 0.95 ± 0.09 and 0.97 ± 0.12, respectively) as well as in the healthy subjects (α = 0.86 ± 0.07). In contrast, fluctuation in blood pressure was similar to non-fractal white noise in both patient groups (α = 0.53 ± 0.11 and 0.52 ± 0.09, respectively) but exhibited 1/f scaling in the healthy subjects (α = 0.87 ± 0.04, P < 0.05 compared with the patient groups). The preservation of fractality in cerebral blood flow of VAD patients suggests that normal cardiac pulsation and central perfusion pressure changes are not the integral sources of cerebral blood flow fractality and that intrinsic vascular properties such as cerebral autoregulation may be involved. However, there is a clear difference in the fractal scaling properties of arterial blood pressure between the cardiogenic shock patients and the healthy subjects
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 ...
Cichański, Artur; Nowicki, Krzysztof; Mazurkiewicz, Adam; Topoliński, Tomasz
2010-01-01
The paper presents linear, logarithmic and exponential regression tabecular bone indices, fractal dimensions and strength. The analysis of the above parameters was supported by determining non-parametric correlation coefficients: Spearman's ρ, gamma and Kendall's τ. The principal components' analysis (PCA) was also performed in order to reduce the number of indices describing the variance in the data set. The analysis showed the most independent indices: lacunarity (λm, λmin, λmax), BMD, Conn.D., SMI, DA, ρA and age.
A multiple fractal model for estimating permeability of dual-porosity media
Li, Bo; Liu, Richeng; Jiang, Yujing
2016-09-01
A multiple fractal model that considers the fractal properties of both porous matrices and fracture networks is proposed for the permeability of dual-porosity media embedded with randomly distributed fractures. In this model, the aperture distribution is verified to follow the fractal scaling law, and the porous matrix is assumed to comprise a bundle of tortuous capillaries that also follow the fractal scaling law. Analytical expressions for fractal aperture distribution, total flow rate, total equivalent permeability, and dimensionless permeability are established, where the dimensionless permeability is defined as the ratio of permeability of the porous matrices to that of the fracture networks. The dimensionless permeability is closely correlated to the structural parameters (i.e., α, θ, Dtf, Dtp, De, Dp, emax, λmax) of the dual-porosity media, and it is more sensitive to the fractal dimension for the size distribution of fracture aperture than to that for the size distribution of pore/capillary diameter. The maximum pore/capillary diameter has a greater impact on the dimensionless permeability than that of the maximum fracture aperture. The dimensionless permeability of fracture networks constructed by the fractal aperture distribution has close values with those of models with lognormal aperture distribution. The proposed multiple fractal model does not involve any empirical constants that do not have clear physical meanings, which could serve as a quick estimation method for assessing permeability of dual-porosity media.
de Rezende Barbosa, Marianne P da C; Vanderlei, Luiz C M; Neves, Lucas M; Takahashi, Carolina; Torquato, Paula R Dos S; Fortaleza, Ana Claúdia de S; Freitas Júnior, Ismael F; Sorpreso, Isabel C E; Abreu, Luiz C; Pérez Riera, Andrés R
2018-01-01
To evaluate the influence of functional training on the geometric indices of heart rate variability (HRV) and fractal correlation properties of the dynamics of heart rate in menopausal women. Of 39 women who were in the period of menopause for more than a year and who did not practice any regular physical activity were divided into: Functional training group (FTG = 50 ± 4.5 years; 67.64 ± 11.64 kg; 1.5 ± 0.05 m) that executed the functional training (FT) and all proposals by reviews and the Control group (58.45 ± 4.8 years; 66.91 ± 13.24 kg; 1.55 ± 0.05 m) who performed all assessments but not FT. The training consisted of 18 weeks (three times a week) and the volunteers performed three sets of 11 functional exercises followed by a walk in each of the sessions. The autonomic nervous system modulation was evaluated by analysis of HRV and the indices obtained were: RR intervals, RRTRI, TINN, SD1, SD2, SD1/SD2, qualitative analysis of Poincaré plot and DFA (alfa-1, alfa-2 and alfa-1/alfa-2). The Student's t-test for unpaired samples (normal data) or Mann-Whitney test nonnormal data) were used to compare the differences obtained between the final moment and the initial moment of the studied groups (p < .05). Were observed in the FTG: increased SD1 (CG 0.13 ± 4.00 vs. 3.60 ± 8.43), beat-to-beat global dispersion much greater as an increased in the dispersion of long-term RR intervals and increased fractal properties of short-term (α1) (CG -0.04 ± 0.13 vs. 0.07 ± 0.21). FT promoted a beneficial impact on cardiac autonomic modulation, characterized by increased parasympathetic activity and short-term fractal properties of the dynamics of the heart rate. © 2017 Wiley Periodicals, Inc.
Fractals and the Large-Scale Structure in the Universe -R-ES ...
Indian Academy of Sciences (India)
in the Universe. The latter structures are broadly re- ferred to as large-scale structures and understanding the physics operating at these scales is an important chal- lenge to present day cosmology. The standard model of cosmology rests on the assump- tion that although there are structures at various scales,. A K Mittal is ...
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
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)
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.
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.
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.
Structural characterization of chaos game fractals using small-angle scattering analysis.
Anitas, Eugen Mircea; Slyamov, Azat
2017-01-01
Small-angle scattering (SAS) technique is applied to study the nano and microstructural properties of spatial patterns generated from chaos game representation (CGR). Using a simplified version of Debye formula, we calculate and analyze in momentum space, the monodisperse scattering structure factor from a system of randomly oriented and non-interacting 2D Sierpinski gaskets (SG). We show that within CGR approach, the main geometrical and fractal properties, such as the overall size, scaling factor, minimal distance between scattering units, fractal dimension and the number of units composing the SG, can be recovered. We confirm the numerical results, by developing a theoretical model which describes analytically the structure factor of SG. We apply our findings to scattering from single scale mass fractals, and respectively to a multiscale fractal representing DNA sequences, and for which an analytic description of the structure factor is not known a priori.
Transport properties of continuous-time quantum walks on Sierpinski fractals.
Darázs, Zoltán; Anishchenko, Anastasiia; Kiss, Tamás; Blumen, Alexander; Mülken, Oliver
2014-09-01
We model quantum transport, described by continuous-time quantum walks (CTQWs), on deterministic Sierpinski fractals, differentiating between Sierpinski gaskets and Sierpinski carpets, along with their dual structures. The transport efficiencies are defined in terms of the exact and the average return probabilities, as well as by the mean survival probability when absorbing traps are present. In the case of gaskets, localization can be identified already for small networks (generations). For carpets, our numerical results indicate a trend towards localization, but only for relatively large structures. The comparison of gaskets and carpets further implies that, distinct from the corresponding classical continuous-time random walk, the spectral dimension does not fully determine the evolution of the CTQW.
Yeh, Jia-Rong; Sun, Wei-Zen; Shieh, Jiann-Shing; Huang, Norden E
2010-06-01
The human heartbeat interval reflects a complicated composition with different underlying modulations and the reactions against environmental inputs. As a result, the human heartbeat interval is a complex time series and its complexity can be scaled using various physical quantifications, such as the property of long-term correlation in detrended fluctuation analysis (DFA). Recently, empirical mode decomposition (EMD) has been shown to be a dyadic filter bank resembling those involved in wavelet decomposition. Moreover, the hierarchy of the extracted modes may be exploited for getting access to the Hurst exponent, which also reflects the property of long-term correlation for a stochastic time series. In this paper, we present significant findings for the dynamic properties of human heartbeat time series by EMD. According to our results, EMD provides a more accurate access to long-term correlation than Hurst exponent does. Moreover, the first intrinsic mode function (IMF 1) is an indicator of orderliness, which reflects the modulation of respiratory sinus arrhythmia (RSA) for healthy subjects or performs a characteristic component similar to that decomposed from a stochastic time series for subjects with congestive heart failure (CHF) and atrial fibrillation (AF). In addition, the averaged amplitude of IMF 1 acts as a parameter of RSA modulation, which reflects significantly negative correlation with aging. These findings lead us to a better understanding of the cardiac system. Copyright 2010 IPEM. Published by Elsevier Ltd. All rights reserved.
Shedding light on fractals: exploration of the Sierpinski carpet optical antenna
Chen, T.L.
2015-01-01
We describe experimental and theoretical investigations of the properties of a fractal optical antenna-the Sierpinski carpet optical antenna. Fractal optical antennas are inspired by fractal antennas designed in radio frequency (RF) region. Shrinking the size of fractal optical antennas from fractal
Determining mean first-passage time on a class of treelike regular fractals.
Lin, Yuan; Wu, Bin; Zhang, Zhongzhi
2010-09-01
Relatively general techniques for computing mean first-passage time (MFPT) of random walks on networks with a specific property are very useful since a universal method for calculating MFPT on general graphs is not available because of their complexity and diversity. In this paper, we present techniques for explicitly determining the partial mean first-passage time (PMFPT), i.e., the average of MFPTs to a given target averaged over all possible starting positions, and the entire mean first-passage time (EMFPT), which is the average of MFPTs over all pairs of nodes on regular treelike fractals. We describe the processes with a family of regular fractals with treelike structure. The proposed fractals include the T fractal and the Peano basin fractal as their special cases. We provide a formula for MFPT between two directly connected nodes in general trees on the basis of which we derive an exact expression for PMFPT to the central node in the fractals. Moreover, we give a technique for calculating EMFPT, which is based on the relationship between characteristic polynomials of the fractals at different generations and avoids the computation of eigenvalues of the characteristic polynomials. Making use of the proposed methods, we obtain analytically the closed-form solutions to PMFPT and EMFPT on the fractals and show how they scale with the number of nodes. In addition, to exhibit the generality of our methods, we also apply them to the Vicsek fractals and the iterative scale-free fractal tree and recover the results previously obtained.
Barbosa, Tiago M; Goh, Wan X; Morais, Jorge E; Costa, Mário J; Pendergast, David
2016-01-01
The aim of this study was to compare the non-linear properties of the four competitive swim strokes. Sixty-eight swimmers performed a set of maximal 4 × 25 m using the four competitive swim strokes. The hip's speed-data as a function of time was collected with a speedo-meter. The speed fluctuation ( dv ), approximate entropy ( ApEn ) and the fractal dimension by Higuchi's method ( D ) were computed. Swimming data exhibited non-linear properties that were different among the four strokes (14.048 ≤ dv ≤ 39.722; 0.682 ≤ ApEn ≤ 1.025; 1.823 ≤ D ≤ 1.919). The ApEn showed the lowest value for front-crawl, followed by breaststroke, butterfly, and backstroke ( P backstroke, followed by butterfly and breaststroke ( P < 0.001). It can be concluded that swimming data exhibits non-linear properties, which are different among the four competitive swimming strokes.
Biomimic design of multi-scale fabric with efficient heat transfer property
Directory of Open Access Journals (Sweden)
Fan Jie
2012-01-01
Full Text Available Wool fiber has a complex hierarchic structure. The multi-scale fibrils are assembled to form a tree-like channel net in wool fiber, providing an efficient heat transfer property. The optimal inner configuration of wool fiber can also be invited to biomimic design of textile fabrics to improve the thermal comfort of cloth. A heat transfer model of biomimic multi-scale fabric using the fractal derivative is established. Theoretical analysis indicates that the heat flux efficiency in the biomimic fabric can be 2 orders of magnitude comparing with that of the continuous medium.
Extended Vicsek fractals: Laplacian spectra and their applications.
Dolgushev, Maxim; Liu, Hongxiao; Zhang, Zhongzhi
2016-11-01
Extended Vicsek fractals (EVF) are the structures constructed by introducing linear spacers into traditional Vicsek fractals. Here we study the Laplacian spectra of the EVF. In particularly, the recurrence relations for the Laplacian spectra allow us to obtain an analytic expression for the sum of all inverse nonvanishing Laplacian eigenvalues. This quantity characterizes the large-scale properties, such as the gyration radius of the polymeric structures, or the global mean-first passage time for the random walk processes. Introduction of the linear spacers leads to local heterogeneities, which reveal themselves, for example, in the dynamics of EVF under external forces.
Directory of Open Access Journals (Sweden)
Naside Ozer
2012-02-01
Full Text Available We analyzed statistical properties of earthquakes in western Anatolia as well as the North Anatolian Fault Zone (NAFZ in terms of spatio-temporal variations of fractal dimensions, p- and b-values. During statistically homogeneous periods characterized by closer fractal dimension values, we propose that occurrence of relatively larger shocks (M >= 5.0 is unlikely. Decreases in seismic activity in such intervals result in spatial b-value distributions that are primarily stable. Fractal dimensions decrease with time in proportion to increasing seismicity. Conversely, no spatiotemporal patterns were observed for p-value changes. In order to evaluate failure probabilities and simulate earthquake occurrence in the western NAFZ, we applied a modified version of the renormalization group method. Assuming an increase in small earthquakes is indicative of larger shocks, we apply the mentioned model to micro-seismic (M<= 3.0 activity, and test our results using San Andreas Fault Zone (SAFZ data. We propose that fractal dimension is a direct indicator of material heterogeneity and strength. Results from a model suggest simulated and observed earthquake occurrences are coherent, and may be used for seismic hazard estimation on creeping strike-slip fault zones.
Fractal analysis: A new remote sensing tool for lava flows
Bruno, B. C.; Taylor, G. J.; Rowland, S. K.; Lucey, P. G.; Self, S.
1992-01-01
Many important quantitative parameters have been developed that relate to the rheology and eruption and emplacement mechanics of lavas. This research centers on developing additional, unique parameters, namely the fractal properties of lava flows, to add to this matrix of properties. There are several methods of calculating the fractal dimension of a lava flow margin. We use the 'structured walk' or 'divider' method. In this method, we measure the length of a given lava flow margin by walking rods of different lengths along the margin. Since smaller rod lengths transverse more smaller-scaled features in the flow margin, the apparent length of the flow outline will increase as the length of the measuring rod decreases. By plotting the apparent length of the flow outline as a function of the length of the measuring rod on a log-log plot, fractal behavior can be determined. A linear trend on a log-log plot indicates that the data are fractal. The fractal dimension can then be calculated from the slope of the linear least squares fit line to the data. We use this 'structured walk' method to calculate the fractal dimension of many lava flows using a wide range of rod lengths, from 1/8 to 16 meters, in field studies of the Hawaiian islands. We also use this method to calculate fractal dimensions from aerial photographs of lava flows, using lengths ranging from 20 meters to over 2 kilometers. Finally, we applied this method to orbital images of extraterrestrial lava flows on Venus, Mars, and the Moon, using rod lengths up to 60 kilometers.
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.
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
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.
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.
Fractal density modeling of crustal heterogeneity from the KTB deep hole
Chen, Guoxiong; Cheng, Qiuming
2017-03-01
Fractal or multifractal concepts have significantly enlightened our understanding of crustal heterogeneity. Much attention has focused on 1/f scaling natures of physicochemical heterogeneity of Earth crust from fractal increment perspective. In this study, fractal density model from fractal clustering point of view is used to characterize the scaling behaviors of heterogeneous sources recorded at German Continental Deep Drilling Program (KTB) main hole, and of special contribution is the local and global multifractal analysis revisited by using Haar wavelet transform (HWT). Fractal density modeling of mass accumulation generalizes the unit of rock density from integer (e.g., g/cm3) to real numbers (e.g., g/cmα), so that crustal heterogeneities with respect to source accumulation are quantified by singularity strength of fractal density in α-dimensional space. From that perspective, we found that the bulk densities of metamorphic rocks exhibit fractal properties but have a weak multifractality, decreasing with the depth. The multiscaling natures of chemical logs also have been evidenced, and the observed distinct fractal laws for mineral contents are related to their different geochemical behaviors within complex lithological context. Accordingly, scaling distributions of mineral contents have been recognized as a main contributor to the multifractal natures of heterogeneous density for low-porosity crystalline rocks. This finally allows us to use de Wijs cascade process to explain the mechanism of fractal density. In practice, the proposed local singularity analysis based on HWT is suggested as an attractive high-pass filtering to amplify weak signatures of well logs as well as to delineate microlithological changes.
Interpreting USANS intensities from computer generated fractal structures
International Nuclear Information System (INIS)
Bertram, W.K.
2003-01-01
Full text: Recent developments in the technique of high resolution Ultra Small Angle Neutron Scattering (USANS) have made this an important tool for investigating the microstructure of a wide variety of materials, in particular those that exhibit scale invariance over a range of scale lengths. The USANS spectrum from a material may show scale invariance that is indicative of a fractal structure in the material but it may also merely reflect the random nature of the sizes and shapes of the scattering entities that make up the material. USANS often allows us to measure the coherent elastic scattering cross sections well into the Guinier region. By analysing the measured scattering intensities using fractal derived models, values are obtained for certain parameters from which certain properties of the material may be obtained. In particular, the porosity can be obtained provided the average volume of the constituents of the material can be calculated. One of the parameters in the analysis is the correlation length, which may be interpreted as the scale length beyond which the material ceases to be fractal. However the relation between this parameter and an average particle size is not at all clear. To throw some light on this, we have used computer simulations to generate a number of fractal-like structures to obtain size distributions and porosities. USANS intensities were calculated from these structures and fitted using a standard fractal model to obtain values for the correlation lengths. The relation between porosity, average particle size and correlation length was investigated. Results are presented that show that the porosity of a fractal system is best calculated using the correlation length parameter to estimate the average particle volume
DEFF Research Database (Denmark)
Mäkikallio, T H; Høiber, S; Køber, L
1999-01-01
variability predict mortality in patients with depressed left ventricular (LV) function after acute myocardial infarction (AMI). Traditional time- and frequency-domain HR variability indexes along with short-term fractal-like correlation properties of RR intervals (exponent alpha) and power-law scaling...... (exponent beta) were studied in 159 patients with depressed LV function (ejection fraction ... variables and LV function. A short-term fractal-like scaling exponent was the most powerful HR variability index in predicting mortality in patients with depressed LV function. Reduction in fractal correlation properties implies more random short-term HR dynamics in patients with increased risk of death...
Laboratory investigation of constitutive property scaling behavior
International Nuclear Information System (INIS)
Tidwell, V.C.
1994-01-01
Because many constitutive rock properties must be measured at one scale but applied at another, scaling behavior is an issue facing many applied disciplines, including the petroleum industry. A research program has been established to investigate and a quantify scaling behavior through systematic physical experimentation, with the aim of developing and testing models that describe scaling behavior in a quantitative manner. Scaling of constitutive rock properties is investigated through physical experimentation involving the collection of gas-permeability data measured over a range of discrete scales. The approach is to systematically isolate those factors that influence property scaling and investigate their relative contributions to overall scaling behavior. Two blocks of rock, each exhibiting differing heterogeneity structure. have recently been examined. The two samples were found to yield different scaling behavior, as exhibited by changes in the distribution functions and semi-variograms. Simple models have been fit to the measured scaling behavior that are of similar functional form but of different magnitude
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.
Guihéneuf, N.; Dausse, A.; de Dreuzy, J. R.; Cherry, J. A.; Parker, B. L.
2016-12-01
Predicting flow in fractured reservoirs remains challenging as it highly depends on hydraulic connectivity of fractures which can vary from point to point. Classical pumping experiments conducted in fractured reservoirs often display fractional flow and anomalous slow diffusion due to bottlenecks or dead zones, characteristic of heterogeneity. In order to investigate reservoir properties at a contaminated site in the Simi Hills (South California, USA), composed by sandstones (dominant calcite cement) inter-bedded with fine-grained formations (shales, siltstones and mudstones), a large scale pumping test was performed in a major fault over 151 days. Deconvolution was applied first to remove the effect of variable flow rates and obtain constant-rate responses of the reservoir. Next, pressure-transients were analyzed both in time and space to get flow dimension, n, through the pressure derivative and extract the anomalous diffusion exponent, dw, as well as the fractal dimension, df. Analysis revealed at least two kinds of responses characterized by flow dimensions of 0.08 and 0.39 and anomalous diffusion exponents of 2.16 and 2.93, respectively. These properties, which can be related to major geological structures (i.e. major faults and surrounding fractures network), shows decreasing hydraulic properties (transmissivity, T, and storativity, S), and consequently, decreasing hydraulic connectivity, with increasing scale of investigation. In particular, the major fault (n = 0.39 ; dw = 2.93) shows a relationship of about T S3 with T r-1.36 and S r-0.43, consistent with flow within a fracture, while the surrounding fractures network (n = 0.08 ; dw = 2.16) displays a relationship which follow T S with T r-1.07 and S r-0.91. This scale-dependence of hydraulic properties may help improve groundwater flow prediction in such fractured reservoirs and could be taken into account for long-term transport of contaminants at this site.
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.
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.
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.
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 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.
Holden, Todd; Gadura, N.; Dehipawala, S.; Cheung, E.; Tuffour, M.; Schneider, P.; Tremberger, G., Jr.; Lieberman, D.; Cheung, T.
2011-10-01
Technologically important extremophiles including oil eating microbes, uranium and rocket fuel perchlorate reduction microbes, electron producing microbes and electrode electrons feeding microbes were compared in terms of their 16S rRNA sequences, a standard targeted sequence in comparative phylogeny studies. Microbes that were reported to have survived a prolonged dormant duration were also studied. Examples included the recently discovered microbe that survives after 34,000 years in a salty environment while feeding off organic compounds from other trapped dead microbes. Shannon entropy of the 16S rRNA nucleotide composition and fractal dimension of the nucleotide sequence in terms of its atomic number fluctuation analyses suggest a selected range for these extremophiles as compared to other microbes; consistent with the experience of relatively mild evolutionary pressure. However, most of the microbes that have been reported to survive in prolonged dormant duration carry sequences with fractal dimension between 1.995 and 2.005 (N = 10 out of 13). Similar results are observed for halophiles, red-shifted chlorophyll and radiation resistant microbes. The results suggest that prolonged dormant duration, in analogous to high salty or radiation environment, would select high fractal 16S rRNA sequences. Path analysis in structural equation modeling supports a causal relation between entropy and fractal dimension for the studied 16S rRNA sequences (N = 7). Candidate choices for high fractal 16S rRNA microbes could offer protection for prolonged spaceflights. BioBrick gene network manipulation could include extremophile 16S rRNA sequences in synthetic biology and shed more light on exobiology and future colonization in shielded spaceflights. Whether the high fractal 16S rRNA sequences contain an asteroidlike extra-terrestrial source could be speculative but interesting.
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.
Scale dependence of effective media properties
International Nuclear Information System (INIS)
Tidwell, V.C.; VonDoemming, J.D.; Martinez, K.
1992-01-01
For problems where media properties are measured at one scale and applied at another, scaling laws or models must be used in order to define effective properties at the scale of interest. The accuracy of such models will play a critical role in predicting flow and transport through the Yucca Mountain Test Site given the sensitivity of these calculations to the input property fields. Therefore, a research programhas been established to gain a fundamental understanding of how properties scale with the aim of developing and testing models that describe scaling behavior in a quantitative-manner. Scaling of constitutive rock properties is investigated through physical experimentation involving the collection of suites of gas permeability data measured over a range of discrete scales. Also, various physical characteristics of property heterogeneity and the means by which the heterogeneity is measured and described are systematically investigated to evaluate their influence on scaling behavior. This paper summarizes the approach that isbeing taken toward this goal and presents the results of a scoping study that was conducted to evaluate the feasibility of the proposed research
Fractal fluctuations in cardiac time series
West, B. J.; Zhang, R.; Sanders, A. W.; Miniyar, S.; Zuckerman, J. H.; Levine, B. D.; Blomqvist, C. G. (Principal Investigator)
1999-01-01
Human heart rate, controlled by complex feedback mechanisms, is a vital index of systematic circulation. However, it has been shown that beat-to-beat values of heart rate fluctuate continually over a wide range of time scales. Herein we use the relative dispersion, the ratio of the standard deviation to the mean, to show, by systematically aggregating the data, that the correlation in the beat-to-beat cardiac time series is a modulated inverse power law. This scaling property indicates the existence of long-time memory in the underlying cardiac control process and supports the conclusion that heart rate variability is a temporal fractal. We argue that the cardiac control system has allometric properties that enable it to respond to a dynamical environment through scaling.
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.
Erdel, Fabian; Baum, Michael; Rippe, Karsten
2015-02-01
The eukaryotic cell nucleus harbours the DNA genome that is organized in a dynamic chromatin network and embedded in a viscous crowded fluid. This environment directly affects enzymatic reactions and target search processes that access the DNA sequence information. However, its physical properties as a reaction medium are poorly understood. Here, we exploit mobility measurements of differently sized inert green fluorescent tracer proteins to characterize the viscoelastic properties of the nuclear interior of a living human cell. We find that it resembles a viscous fluid on small and large scales but appears viscoelastic on intermediate scales that change with protein size. Our results are consistent with simulations of diffusion through polymers and suggest that chromatin forms a random obstacle network rather than a self-similar structure with fixed fractal dimensions. By calculating how long molecules remember their previous position in dependence on their size, we evaluate how the nuclear environment affects search processes of chromatin targets.
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.
Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation
Directory of Open Access Journals (Sweden)
ELNAZ Rezaei abajelu
2017-03-01
Full Text Available Introduction: Soil Hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. In recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (Ks. Fractal models with two subset of two (solid and pore and three phases (solid, pore and soil fractal (PSF are used to estimate the fractal dimension of soil particles. The PSF represents a generalization of the solid and pore mass fractal models. The PSF characterizes both the solid and pore phases of the porous material. It also exhibits self-similarity to some degree, in the sense that where local structure seems to be similar to the whole structure.PSF models can estimate interface fractal dimension using soil pore size distribution data (PSD and soil moisture retention curve (SWRC. The main objective of this study was to evaluate different fractal models to estimate the Ksparameter. Materials and Methods: The Schaapetal data was used in this study. The complex consists of sixty soil samples. Soil texture, soil bulk density, soil saturated hydraulic conductivity and soil particle size distribution curve were measured by hydrometer method, undistributed soil sample, constant head method and wet sieve method, respectively for all soil samples.Soil water retention curve were determined by using pressure plates apparatus.The Ks parameter could be estimated by Ralws model as a function of fractal dimension by seven fractal models. Fractal models included Fuentes at al. (1996, Hunt and Gee (2002, Bird et al. (2000, Huang and Zhang (2005, Tyler and Wheatcraft (1990, Kutlu et al. (2008, Sepaskhah and Tafteh (2013.Therefore The Ks parameter can be estimated as a function of the DS (fractal dimension by seven fractal models (Table 2.Sensitivity analysis of Rawls model was assessed by making changes±10%, ±20% and±30%(in input parameters
Synthesis of the advances in and application of fractal characteristic of traffic flow.
2013-07-01
Fractals are irregular geometric objects that exhibit finite details at all scales, and once magnified, their basic structures remain the same regardless of the scale of magnification. Fractal theory has been successfully applied in different fields ...
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.
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
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.
Two-dimensional fractal geometry, critical phenomena and conformal invariance
International Nuclear Information System (INIS)
Duplantier, B.
1988-01-01
The universal properties of critical geometrical systems in two-dimensions (2D) like the O (n) and Potts models, are described in the framework of Coulomb gas methods and conformal invariance. The conformal spectrum of geometrical critical systems obtained is made of a discrete infinite series of scaling dimensions. Specific applications involve the fractal properties of self-avoiding walks, percolation clusters, and also some non trivial critical exponents or fractal dimensions associated with subsets of the planar Brownian motion. The statistical mechanics of the same critical models on a random 2D lattice (namely in presence of a critically-fluctuating metric, in the so-called 2D quantum gravity) is also addressed, and the above critical geometrical systems are shown to be exactly solvable in this case. The new ''gravitational'' conformal spectrum so derived is found to satisfy the recent Knizhnik, Polyakov and Zamolodchikov quadratic relation which links it to the standard conformal spectrum in the plane
Scaling in topological properties of brain networks
Singh, S.S.; Khundrakpam, B.S.; Reid, A.T.; Lewis, J.D.; Evans, A.C.; Ishrat, R.; Sharma, B.I.; Singh, R.K.B.
2016-01-01
The organization in brain networks shows highly modular features with weak inter-modular interaction. The topology of the networks involves emergence of modules and sub-modules at different levels of constitution governed by fractal laws that are signatures of self-organization in complex networks.
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...
Scaling properties of localized quantum chaos
International Nuclear Information System (INIS)
Izrailev, F.M.
1991-01-01
Statistical properties of spectra and eigenfunctions are studied for the model of quantum chaos in the presence of dynamical localization. The main attention is paid to the scaling properties of localization length and level spacing distribution in the intermediate region between Poissonian and Wigner-Dyson statistics. It is shown that main features of such localized quantum chaos are well described by the introduced ensemble of band random matrices. 28 refs.; 7 figs
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
Fractal nature of hydrocarbon deposits. 2. Spatial distribution
International Nuclear Information System (INIS)
Barton, C.C.; Schutter, T.A; Herring, P.R.; Thomas, W.J.; Scholz, C.H.
1991-01-01
Hydrocarbons are unevenly distributed within reservoirs and are found in patches whose size distribution is a fractal over a wide range of scales. The spatial distribution of the patches is also fractal and this can be used to constrain the design of drilling strategies also defined by a fractal dimension. Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. The authors have performed fractal analyses on the spatial distribution of producing and showing wells combined and of dry wells in 1,600-mi 2 portions of the Denver and Powder River basins that were nearly completely drilled on quarter-mile square-grid spacings. They have limited their analyses to wells drilled to single stratigraphic intervals so that the map pattern revealed by drilling is representative of the spatial patchiness of hydrocarbons at depth. The fractal dimensions for the spatial patchiness of hydrocarbons in the two basins are 1.5 and 1.4, respectively. The fractal dimension for the pattern of all wells drilled is 1.8 for both basins, which suggests a drilling strategy with a fractal dimension significantly higher than the dimensions 1.5 and 1.4 sufficient to efficiently and economically explore these reservoirs. In fact, the fractal analysis reveals that the drilling strategy used in these basins approaches a fractal dimension of 2.0, which is equivalent to random drilling with no geologic input. Knowledge of the fractal dimension of a reservoir prior to drilling would provide a basis for selecting and a criterion for halting a drilling strategy for exploration whose fractal dimension closely matches that of the spatial fractal dimension of the reservoir, such a strategy should prove more efficient and economical than current practice
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.
[Chaos and fractals and their applications in electrocardial signal research].
Jiao, Qing; Guo, Yongxin; Zhang, Zhengguo
2009-06-01
Chaos and fractals are ubiquitous phenomena of nature. A system with fractal structure usually behaves chaos. As a complicated nonlinear dynamics system, heart has fractals structure and behaves as chaos. The deeper inherent mechanism of heart can be opened out when the chaos and fractals theory is utilized in the research of the electrical activity of heart. Generally a time series of a system was used for describing the status of the strange attractor of the system. The indices include Poincare plot, fractals dimension, Lyapunov exponent, entropy, scaling exponent, Hurst index and so on. In this article, the basic concepts and the methods of chaos and fractals were introduced firstly. Then the applications of chaos and fractals theories in the study of electrocardial signal were expounded with example of how they are used for ventricular fibrillation.
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.
Fractals and spectra related to fourier analysis and function spaces
Triebel, Hans
1997-01-01
Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...
Fractal Structure and Entropy Production within the Central Nervous System
Directory of Open Access Journals (Sweden)
Andrew J. E. Seely
2014-08-01
Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.
Oliveira, Naiara C; Silva, João H; Barros, Olga A; Pinheiro, Allysson P; Santana, William; Saraiva, Antônio A F; Ferreira, Odair P; Freire, Paulo T C; Paula, Amauri J
2015-10-06
We used here a scanning electron microscopy approach that detected backscattered electrons (BSEs) and X-rays (from ionization processes) along a large-field (LF) scan, applied on a Cretaceous fossil of a shrimp (area ∼280 mm(2)) from the Araripe Sedimentary Basin. High-definition LF images from BSEs and X-rays were essentially generated by assembling thousands of magnified images that covered the whole area of the fossil, thus unveiling morphological and compositional aspects at length scales from micrometers to centimeters. Morphological features of the shrimp such as pleopods, pereopods, and antennae located at near-surface layers (undetected by photography techniques) were unveiled in detail by LF BSE images and in calcium and phosphorus elemental maps (mineralized as hydroxyapatite). LF elemental maps for zinc and sulfur indicated a rare fossilization event observed for the first time in fossils from the Araripe Sedimentary Basin: the mineralization of zinc sulfide interfacing to hydroxyapatite in the fossil. Finally, a dimensional analysis of the phosphorus map led to an important finding: the existence of a fractal characteristic (D = 1.63) for the hydroxyapatite-matrix interface, a result of physical-geological events occurring with spatial scale invariance on the specimen, over millions of years.
Nonlinear fractals: applications in physiology and ophthalmology
Directory of Open Access Journals (Sweden)
M. V. Zueva
2014-07-01
Full Text Available Fractal geometry and nonlinear dynamics have applications in the field of biology and medicine. Many complex structures of living systems reveal fractal-like geometry. Among them, nonlinearity of human anatomic structures and physiologic functions are of special interest. Here, we review several multidisciplinary studies that demonstrate multi-scale nonlinear complexity of physiological functions and fractal geometry of anatomical structures of a healthy human including retina. With ageing and diseases, these entities become simpler or more complex. Pathologic conditions contribute to highly periodic dynamics of processes that dominates on a time scale. Nonlinear dynamics application in ophthalmology and physiology of visual system can be promoted by the studies of fractal flickeringbackground and its impact on retina and visual cortex electrical activity. The next step will be the development of novel electrophysiological diagnostics and visual system impairment treatment
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...
Heat kernels and zeta functions on fractals
International Nuclear Information System (INIS)
Dunne, Gerald V
2012-01-01
On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY
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Ian Parkinson
2011-05-01
Full Text Available A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge. The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals, with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.
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
Are Solar Active Regions with Major Flares More Fractal, Multifractal, or Turbulent Than Others?
Georgoulis, Manolis K.
2012-02-01
Multiple recent investigations of solar magnetic-field measurements have raised claims that the scale-free (fractal) or multiscale (multifractal) parameters inferred from the studied magnetograms may help assess the eruptive potential of solar active regions, or may even help predict major flaring activity stemming from these regions. We investigate these claims here, by testing three widely used scale-free and multiscale parameters, namely, the fractal dimension, the multifractal structure function and its inertial-range exponent, and the turbulent power spectrum and its power-law index, on a comprehensive data set of 370 timeseries of active-region magnetograms (17 733 magnetograms in total) observed by SOHO’s Michelson Doppler Imager (MDI) over the entire Solar Cycle 23. We find that both flaring and non-flaring active regions exhibit significant fractality, multifractality, and non-Kolmogorov turbulence but none of the three tested parameters manages to distinguish active regions with major flares from flare-quiet ones. We also find that the multiscale parameters, but not the scale-free fractal dimension, depend sensitively on the spatial resolution and perhaps the observational characteristics of the studied magnetograms. Extending previous works, we attribute the flare-forecasting inability of fractal and multifractal parameters to i) a widespread multiscale complexity caused by a possible underlying self-organization in turbulent solar magnetic structures, flaring and non-flaring alike, and ii) a lack of correlation between the fractal properties of the photosphere and overlying layers, where solar eruptions occur. However useful for understanding solar magnetism, therefore, scale-free and multiscale measures may not be optimal tools for active-region characterization in terms of eruptive ability or, ultimately, for major solar-flare prediction.
Random fractal characters and length uncertainty of the continental ...
Indian Academy of Sciences (India)
A coastline is a random fractal object in a geographical system whose length is uncertain. To determine the coastline length of a country or a region, the scaling region and fractal dimension of the coastline is first calculated, and then, the length of the coastline is measured using the scale at the lower limit or near the limit of ...
Synthesis of the advances in and application of fractal characteristic of traffic flow : [summary].
2013-07-01
Fractals are geometric objects that are self-similar, meaning that their basic structure remains the same regardless of the scale of magnification. Self-similarity is readily seen in nature, for example, in trees, coastlines, clouds, etc. fractal...
Textural characterization of chars using fractal analysis
Energy Technology Data Exchange (ETDEWEB)
Mahamud, Manuel; Lopez, Oscar [Department of Chemical and Environmental Engineering, Faculty of Chemistry, University of Oviedo, Campus de El Cristo, 33071 Oviedo (Spain); Pis, Jose Juan; Pajares, Jesus Alberto [Instituto Nacional del Carbon C.S.I.C., Apartado 73, 33080 Oviedo (Spain)
2004-11-25
The aim of this study is to explore the potential of fractal analysis in helping to understand the textural changes of materials during the manufacture of active carbons. Textural characterization of the chars is carried out in order to obtain a better understanding of the phenomena underlying char formation. The materials selected for study were a series of chars obtained from coals oxidized in air at various temperatures for different periods of time. The data from mercury porosimetry were analyzed using fractal models. The average fractal dimensions for the chars were calculated by using the methods proposed by Friesen and Mikula and that of Zhang and Li. Fractal profiles of the chars obtained by the method of Neimark were compared with the corresponding fractal profiles of the precursor coals. Pore development during carbonization depends-among other factors that are kept constant in this study-on the textural properties of the precursor coal, the devolatilization process and the plastic properties of coals. The evolution of the fractal characteristics of the chars is also studied. At the same time pore volume development is analyzed. These analyses help to clarify the role that various phenomena occurring during carbonization have on the textural properties of the chars.
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 ...
Low field scaling properties of high Tc superconductor glasses
Giovannella, C.; Fruchter, L.; Chappert, C.
We show that the zero field cooling (ZFC) M/H curves of both the YBaCuO and the LaSrCuO granular superconductor glasses (SuG) are subjected to scaling when plotted against the reduced variable t/H1/ψ . The breaking of the scaling for too weak or too strong magnetic fields is discussed and justified by the introduction of a phenomenological fractal picture, describing the behaviour of the disordered intergranular junction network. Nous montrons que les courbes M/H caractéristiques des verres de supraconducteurs granulaires sont sujettes à une loi d'échelle lorsqu'elles sont tracées en fonction de la variable réduite t/H1/ψ. La brisure de la loi d'échelle pour des champs trop forts ou trop faibles est justifiée par l'introduction d'un modèle phénoménologique fractal capable de décrire le comportement d'un réseau désordonné des jonctions.
Fractal analysis of agricultural nozzles spray
Directory of Open Access Journals (Sweden)
Francisco Agüera
2012-02-01
Full Text Available Fractal scaling of the exponential type is used to establish the cumulative volume (V distribution applied through agricultural spray nozzles in size x droplets, smaller than the characteristic size X. From exponent d, we deduced the fractal dimension (Df which measures the degree of irregularity of the medium. This property is known as 'self-similarity'. Assuming that the droplet set from a spray nozzle is self-similar, the objectives of this study were to develop a methodology for calculating a Df factor associated with a given nozzle and to determine regression coefficients in order to predict droplet spectra factors from a nozzle, taking into account its own Df and pressure operating. Based on the iterated function system, we developed an algorithm to relate nozzle types to a particular value of Df. Four nozzles and five operating pressure droplet size characteristics were measured using a Phase Doppler Particle Analyser (PDPA. The data input consisted of droplet size spectra factors derived from these measurements. Estimated Df values showed dependence on nozzle type and independence of operating pressure. We developed an exponential model based on the Df to enable us to predict droplet size spectra factors. Significant coefficients of determination were found for the fitted model. This model could prove useful as a means of comparing the behavior of nozzles which only differ in not measurable geometric parameters and it can predict droplet spectra factors of a nozzle operating under different pressures from data measured only in extreme work pressures.
FRACTAL ANALYSIS OF FRACTURE SYSTEMS IN UPPER TRIASSIC DOLOMITES IN ŽUMBERAK MOUNTAIN, CROATIA
Ivica Pavičić; Ivan Dragičević; Tatjana Vlahović; Tonći Grgasović
2017-01-01
This paper presents results of fractal analysis of fracture systems in upper Triassic dolomites in Žumberak Mountain, Croatia. Mechanical rock characteristics together with structural and diagenetic processes results with fracture systems that can be considered as fractals. They are scale-invariant in specific range of scales. Distribution of fractures can be than described with power law distribution and fractal dimension. Fractal dimension is a measure of how fractures fill the space. Fract...
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)
Directory of Open Access Journals (Sweden)
J. Antonio Paramo
2015-01-01
Full Text Available Hydrozincite (Zn5(OH6(CO32 is, among others, a popular precursor used to synthesize nanoscale ZnO with complex morphologies. For many existing and potential applications utilizing nanostructures, performance is determined by the surface and subsurface properties. Current understanding of the relationship between the morphology and the defect properties of nanocrystalline ZnO and hydrozincite systems is still incomplete. Specifically, for the latter nanomaterial the structure-property correlations are largely unreported in the literature despite the extensive use of hydrozincite in the synthesis applications. In our work, we addressed this issue by studying precipitated nanostructures of Zn5(OH6(CO32 with varying quasi-fractal dimensionalities containing relatively small amounts of a ZnO phase. Crystal morphology of the samples was accurately controlled by the growth time. We observed a strong correlation between the morphology of the samples and their optoelectronic properties. Our results indicate that a substantial increase of the free surface in the nanocrystal samples generates higher relative concentration of defects, consistent with the model of defect-rich surface and subsurface layers.
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.
Critical behavior of the Ising model on random fractals.
Monceau, Pascal
2011-11-01
We study the critical behavior of the Ising model in the case of quenched disorder constrained by fractality on random Sierpinski fractals with a Hausdorff dimension d(f) is approximately equal to 1.8928. This is a first attempt to study a situation between the borderline cases of deterministic self-similarity and quenched randomness. Intensive Monte Carlo simulations were carried out. Scaling corrections are much weaker than in the deterministic cases, so that our results enable us to ensure that finite-size scaling holds, and that the critical behavior is described by a new universality class. The hyperscaling relation is compatible with an effective dimension equal to the Hausdorff one; moreover the two eigenvalues exponents of the renormalization flows are shown to be different from the ones calculated from ε expansions, and from the ones obtained for fourfold symmetric deterministic fractals. Although the space dimensionality is not integer, lack of self-averaging properties exhibits some features very close to the ones of a random fixed point associated with a relevant disorder.
Numerical construction and flow simulation in networks of fractures using fractals
Energy Technology Data Exchange (ETDEWEB)
Yortsos, Y.C.; Acuna, J.A.
1991-11-01
Present models for the representation of naturally fractured systems rely on the double-porosity Warren-Root model or on random arrays of fractures. However, field observation in outcrops has demonstrated the existence of multiple length scales in many naturally fractured media. The existing models fail to capture this important fractal property. In this paper, we use concepts from the theory of fragmentation and from fractal geometry for the numerical construction of networks of fractures that have fractal characteristics. The method is based mainly on the work of Barnsley (1) and allows for great flexibility in the development of patterns. Numerical techniques are developed for the simulation of unsteady single phase flow in such networks. It is found that the pressure transient response of finite fractals behaves according to the analytical predictions of Chang and Yortsos (6), provided that there exists a power law in the mass-radius relationship around the test well location. Otherwise, the finite size effects become significant and interfere severely with the identification of the underlying fractal structure. 21 refs., 13 figs.
Experimental study of circle grid fractal pattern on turbulent intensity in pipe flow
International Nuclear Information System (INIS)
Manshoor, B; Zaman, I; Othman, M F; Khalid, Amir
2013-01-01
Fractal turbulence is deemed much more efficient than grid turbulence in terms of a turbulence generation. In this paper, the hotwire experimental results for the circle grids fractal pattern as a turbulent generator will be presented. The self-similar edge characteristic of the circle grid fractal pattern is thought to play a vital role in the enhancement of turbulent intensity. Three different beta ratios of perforated plates based on circle grids fractal pattern were used in the experimental work and each paired with standard circle grids with similar porosity. The objectives were to study the fractal scaling influence on the flow and also to explore the potential of the circle grids fractal pattern in enhancing the turbulent intensity. The results provided an excellent insight of the fractal generated turbulence and the fractal flow physics. Across the circle grids fractal pattern, the pressure drop was lower but the turbulent intensity was higher than those across the paired standard circle grids
Experimental study of circle grid fractal pattern on turbulent intensity in pipe flow
Manshoor, B.; Zaman, I.; Othman, M. F.; Khalid, Amir
2013-12-01
Fractal turbulence is deemed much more efficient than grid turbulence in terms of a turbulence generation. In this paper, the hotwire experimental results for the circle grids fractal pattern as a turbulent generator will be presented. The self-similar edge characteristic of the circle grid fractal pattern is thought to play a vital role in the enhancement of turbulent intensity. Three different beta ratios of perforated plates based on circle grids fractal pattern were used in the experimental work and each paired with standard circle grids with similar porosity. The objectives were to study the fractal scaling influence on the flow and also to explore the potential of the circle grids fractal pattern in enhancing the turbulent intensity. The results provided an excellent insight of the fractal generated turbulence and the fractal flow physics. Across the circle grids fractal pattern, the pressure drop was lower but the turbulent intensity was higher than those across the paired standard circle grids.
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
Children's separation anxiety scale (CSAS: psychometric properties.
Directory of Open Access Journals (Sweden)
Xavier Méndez
Full Text Available This study describes the psychometric properties of the Children's Separation Anxiety Scale (CSAS, which assesses separation anxiety symptoms in childhood. Participants in Study 1 were 1,908 schoolchildren aged between 8 and 11. Exploratory factor analysis identified four factors: worry about separation, distress from separation, opposition to separation, and calm at separation, which explained 46.91% of the variance. In Study 2, 6,016 children aged 8-11 participated. The factor model in Study 1 was validated by confirmatory factor analysis. The internal consistency (α = 0.82 and temporal stability (r = 0.83 of the instrument were good. The convergent and discriminant validity were evaluated by means of correlations with other measures of separation anxiety, childhood anxiety, depression and anger. Sensitivity of the scale was 85% and its specificity, 95%. The results support the reliability and validity of the CSAS.
Aesthetic Responses to Exact Fractals Driven by Physical Complexity.
Bies, Alexander J; Blanc-Goldhammer, Daryn R; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E
2016-01-01
Fractals are physically complex due to their repetition of patterns at multiple size scales. Whereas the statistical characteristics of the patterns repeat for fractals found in natural objects, computers can generate patterns that repeat exactly. Are these exact fractals processed differently, visually and aesthetically, than their statistical counterparts? We investigated the human aesthetic response to the complexity of exact fractals by manipulating fractal dimensionality, symmetry, recursion, and the number of segments in the generator. Across two studies, a variety of fractal patterns were visually presented to human participants to determine the typical response to exact fractals. In the first study, we found that preference ratings for exact midpoint displacement fractals can be described by a linear trend with preference increasing as fractal dimension increases. For the majority of individuals, preference increased with dimension. We replicated these results for other exact fractal patterns in a second study. In the second study, we also tested the effects of symmetry and recursion by presenting asymmetric dragon fractals, symmetric dragon fractals, and Sierpinski carpets and Koch snowflakes, which have radial and mirror symmetry. We found a strong interaction among recursion, symmetry and fractal dimension. Specifically, at low levels of recursion, the presence of symmetry was enough to drive high preference ratings for patterns with moderate to high levels of fractal dimension. Most individuals required a much higher level of recursion to recover this level of preference in a pattern that lacked mirror or radial symmetry, while others were less discriminating. This suggests that exact fractals are processed differently than their statistical counterparts. We propose a set of four factors that influence complexity and preference judgments in fractals that may extend to other patterns: fractal dimension, recursion, symmetry and the number of segments in a
Evaluation of 3D Printer Accuracy in Producing Fractal Structure.
Kikegawa, Kana; Takamatsu, Kyuuichirou; Kawakami, Masaru; Furukawa, Hidemitsu; Mayama, Hiroyuki; Nonomura, Yoshimune
2017-01-01
Hierarchical structures, also known as fractal structures, exhibit advantageous material properties, such as water- and oil-repellency as well as other useful optical characteristics, owing to its self-similarity. Various methods have been developed for producing hierarchical geometrical structures. Recently, fractal structures have been manufactured using a 3D printing technique that involves computer-aided design data. In this study, we confirmed the accuracy of geometrical structures when Koch curve-like fractal structures with zero to three generations were printed using a 3D printer. The fractal dimension was analyzed using a box-counting method. This analysis indicated that the fractal dimension of the third generation hierarchical structure was approximately the same as that of the ideal Koch curve. These findings demonstrate that the design and production of fractal structures can be controlled using a 3D printer. Although the interior angle deviated from the ideal value, the side length could be precisely controlled.
The influence of frequency on fractal dimension of adsorbed layers
International Nuclear Information System (INIS)
Gasparovic, B.; Risovic, D.; Cosovic, B.; Nelson, A.
2007-01-01
Alternating current (AC) voltammetry and electrochemical impedance spectroscopy are often the methods of choice for use in study of adsorption of organic molecules. The adsorption of organic molecules on interface may result in the formation of fractal structures, whose fractal dimension can be estimated using the method of scaling the hanging mercury drop electrode (HMDE). The aim of present study was to check whether the estimated fractal dimension, D (or for that matter the fractal ordering of the adsorbed layer) shows any correlation (dependence) with change of applied frequency, and second, to check the possibility to extend the method to broad frequency spectrum compatible with impedance spectroscopy. The investigation included two surfactants nonionic Triton-X-100 (T-X-100) and anionic sodium dodecyl sulfate (SDS) and alcohol tert-butanol. All measurements were performed on HMDE at thermodynamic equilibrium employing broad frequency spectrum. The validity of the approach was checked by measurements on pure electrolyte and by comparison with previously obtained results for fractal layers. The results of the investigations show that: (1) the method of scaling the HMDE to obtain the fractal dimension of adsorbed layer is compatible with impedance spectroscopy and the combination of these methods can be used as a powerful tool to investigate fractal aspect of adsorption of organic molecules; (2) fractal ordering of adsorbed layer and the value of fractal dimension is not influenced by the frequency of applied sinusoidal voltage perturbations
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.
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)
Black carbon fractal morphology and short-wave radiative impact: a modelling study
Directory of Open Access Journals (Sweden)
M. Kahnert
2011-11-01
Full Text Available We investigate the impact of the morphological properties of freshly emitted black carbon aerosols on optical properties and on radiative forcing. To this end, we model the optical properties of fractal black carbon aggregates by use of numerically exact solutions to Maxwell's equations within a spectral range from the UVC to the mid-IR. The results are coupled to radiative transfer computations, in which we consider six realistic case studies representing different atmospheric pollution conditions and surface albedos. The spectrally integrated radiative impacts of black carbon are compared for two different fractal morphologies, which brace the range of recently reported experimental observations of black carbon fractal structures. We also gauge our results by performing corresponding calculations based on the homogeneous sphere approximation, which is commonly employed in climate models. We find that at top of atmosphere the aggregate models yield radiative impacts that can be as much as 2 times higher than those based on the homogeneous sphere approximation. An aggregate model with a low fractal dimension can predict a radiative impact that is higher than that obtained with a high fractal dimension by a factor ranging between 1.1–1.6. Although the lower end of this scale seems like a rather small effect, a closer analysis reveals that the single scattering optical properties of more compact and more lacy aggregates differ considerably. In radiative flux computations there can be a partial cancellation due to the opposing effects of different error sources. However, this cancellation effect can strongly depend on atmospheric conditions and is therefore quite unpredictable. We conclude that the fractal morphology of black carbon aerosols and their fractal parameters can have a profound impact on their radiative forcing effect, and that the use of the homogeneous sphere model introduces unacceptably high biases in radiative impact studies. We
Fractal 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 ...
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
In this work the use of fractal scaling exponents for geological mapping was first investigated using theoretical models, and results from the analysis showed that the scaling exponents mapped isolated bodies but did not properly resolve bodies close to each other. However application on real data (the Mamfe basin, the ...
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.
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
Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems
Buffle, J.; Leeuwen, van H.P.
2008-01-01
This book aims to provide the scientific community with a novel and valuable approach based on fractal geometry concepts on the important properties and processes of diverse environmental systems. The interpretation of complex environmental systems using modern fractal approaches is compared and
Estimation of Soil Water Retention Curve Using Fractal Dimension ...
African Journals Online (AJOL)
ADOWIE PERE
2018-02-10
Feb 10, 2018 ... particle size distribution has fractal properties. Hence, fractal model can be used to estimate the soil water retention curve. Thus determining the DSWRC from SWRC experimental data, establishing a relationship among DSWRC and soil readily available characteristics (i.e. clay, silt and sand contents and.
Are fractal dimensions of the spatial distribution of mineral deposits meaningful?
Raines, G.L.
2008-01-01
It has been proposed that the spatial distribution of mineral deposits is bifractal. An implication of this property is that the number of deposits in a permissive area is a function of the shape of the area. This is because the fractal density functions of deposits are dependent on the distance from known deposits. A long thin permissive area with most of the deposits in one end, such as the Alaskan porphyry permissive area, has a major portion of the area far from known deposits and consequently a low density of deposits associated with most of the permissive area. On the other hand, a more equi-dimensioned permissive area, such as the Arizona porphyry permissive area, has a more uniform density of deposits. Another implication of the fractal distribution is that the Poisson assumption typically used for estimating deposit numbers is invalid. Based on datasets of mineral deposits classified by type as inputs, the distributions of many different deposit types are found to have characteristically two fractal dimensions over separate non-overlapping spatial scales in the range of 5-1000 km. In particular, one typically observes a local dimension at spatial scales less than 30-60 km, and a regional dimension at larger spatial scales. The deposit type, geologic setting, and sample size influence the fractal dimensions. The consequence of the geologic setting can be diminished by using deposits classified by type. The crossover point between the two fractal domains is proportional to the median size of the deposit type. A plot of the crossover points for porphyry copper deposits from different geologic domains against median deposit sizes defines linear relationships and identifies regions that are significantly underexplored. Plots of the fractal dimension can also be used to define density functions from which the number of undiscovered deposits can be estimated. This density function is only dependent on the distribution of deposits and is independent of the
Alberti, Tommaso; Lepreti, Fabio; Vecchio, Antonio; Carbone, Vincenzo
2017-04-01
The Earth's climate is an extremely unstable complex system consisting of nonlinear and still rather unknown interactions among atmosphere, land surface, ice and oceans. The system is mainly driven by solar irradiance, even if internal components as volcanic eruptions and human activities affect the atmospheric composition thus acting as a driver for climate changes. Since the extreme climate variability is the result of a set of phenomena operating from daily to multi-millennial timescales, with different correlation times, a study of the scaling properties of the system can evidence non-trivial persistent structures, internal or external physical processes. Recently, the scaling properties of the paleoclimate changes have been analyzed by distinguish between interglacial and glacial climates [Shao and Ditlevsen, 2016]. The results show that the last glacial record (20-120 kyr BP) presents some elements of multifractality, while the last interglacial period (0-10 kyr BP), say the Holocene period, seems to be characterized by a mono-fractal structure. This is associated to the absence of Dansgaard-Oeschger (DO) events in the interglacial climate that could be the cause for the absence of multifractality. This hypothesis is supported by the analysis of the period between 18 and 27 kyr BP, i.e. during the Last Glacial Period, in which a single DO event have been registred. Through the Empirical Mode Decomposition (EMD) we were able to detect a timescale separation within the Last Glacial Period (20-120 kyr BP) in two main components: a high-frequency component, related to the occurrence of DO events, and a low-frequency one, associated to the cooling/warming phase switch [Alberti et al., 2014]. Here, we investigate the scaling properties of the climate fluctuations within the Last Glacial Period, where abrupt climate changes, characterized by fast increase of temperature usually called Dansgaard-Oeschger (DO) events, have been particularly pronounced. By using the
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.
International Nuclear Information System (INIS)
Achik, I.; Boughaleb, Y.; Hader, A.; Sbiaai, K.; Hajjaji, A.
2013-01-01
The aim of the present work was to study numerically the scaling behavior and the morphological properties of the interfaces generated by the multilayer deposition process. We have noticed that, in the case where the ratio of the surface diffusion coefficient to the deposition rate reaches high values D/F > > 1, the interface consists of mound structures. By using the dynamic scaling, we have shown that the height–height correlation function scales with time t and length l as G(l,t) ∼ l α f(t/l α/β ) with β = 0.25 ± 0.05 and α = 0.51 ± 0.02. These exponent values are equal to the ones predicted by the Edwards–Wilkinson approach. Besides, our results are in agreement with the growth system of Cu/Cu(100) at 300 K which has been characterized in more detail by a combined scanning tunneling microscopy and spot profile analysis — low energy electronic diffusion study. Moreover, by considering two different methods, we have examined the fractal aspect of the obtained interfaces. - Highlights: • The adlayer interfaces present mound morphologies. • The adlayer interfaces scale with the Family–Vicsek law. • The critical exponents (α, β) are in agreement with those of Edwards–Wilkinson approach
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.
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.
Scale Invariant Properties in Heart Rate Signals
Makowiec, D.; Dudkowska, A.; Zwierz, M.; Galaska, R.; Rynkiewicz, A.
2006-05-01
The rate of heart beat is controlled by autonomic nervous system: accelerated by the sympathetic system and slowed by the parasympathetic system. Scaling properties in heart rate are usually related to the intrinsic dynamics of this physiological regulatory system. The two packages calculating local exponent spectra: Wavelet Transform Modulus Maxima and Multifractal Detrended Fluctuation Analysis (accessible from Physionet home page http://circ.ahajournals.org/cgi/content/full/101/23/e215) are tested, and then used to investigate the spectrum of singularity exponents in series of heart rates obtained from patients suffering from reduced left ventricle systolic function. It occurs that this state of a heart could be connected to some perturbation in the regulatory system, because the heart rate appears to be less controlled than in a healthy human heart. The multifractality in the heart rate signal is weakened: the spectrum is narrower and moved to higher values what indicate the higher activity of the sympatethic nervous system.
Stemp, W James; Lerner, Harry J; Kristant, Elaine H
2013-01-01
Although previous use-wear studies involving quartz and quartzite have been undertaken by archaeologists, these are comparatively few in number. Moreover, there has been relatively little effort to quantify use-wear on stone tools made from quartzite. The purpose of this article is to determine the effectiveness of a measurement system, laser scanning confocal microscopy (LSCM), to document the surface roughness or texture of experimental Mistassini quartzite scrapers used on two different contact materials (fresh and dry deer hide). As in previous studies using LSCM on chert, flint, and obsidian, this exploratory study incorporates a mathematical algorithm that permits the discrimination of surface roughness based on comparisons at multiple scales. Specifically, we employ measures of relative area (RelA) coupled with the F-test to discriminate used from unused stone tool surfaces, as well as surfaces of quartzite scrapers used on dry and fresh deer hide. Our results further demonstrate the effect of raw material variation on use-wear formation and its documentation using LSCM and RelA. © Wiley Periodicals, Inc.
Methods of nanoassembly of a fractal polymer and materials formed thereby
Newkome, George R [Medina, OH; Moorefield, Charles N [Akron, OH
2012-07-24
The invention relates to the formation of synthesized fractal constructs and the methods of chemical self-assembly for the preparation of a non-dendritic, nano-scale, fractal constructs or molecules. More particularly, the invention relates to fractal constructs formed by molecular self-assembly, to create synthetic, nanometer-scale fractal shapes. In an embodiment, a nanoscale Sierpinski hexagonal gasket is formed. This non-dendritic, perfectly self-similar fractal macromolecule is comprised of bisterpyridine building blocks that are bound together by coordination to 36 Ru and 6 Fe ions to form a nearly planar array of increasingly larger hexagons around a hollow center.
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.
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.
Fractal and multifractal analyses of bipartite networks
Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua
2017-03-01
Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.
The Fractal Nature of Wood Revealed by Drying
2000-01-01
The materials for this investigation came from two species, one was a 37-year- old plantation-grown Ginkgo ( Ginkgo biloba ) and the other was a 48-year...bacterial colonies, tumor cells, axon termi- nals, tree crown properties , and so on. Wood is a typical porous material that exhibits interconnected...a set of fractal dimensions. But there was no explanation leading to the characterization of wood properties . A typical property of fractals relates
International Nuclear Information System (INIS)
Yuan Deyou; Du Shude; Cheng Zhengxing
2009-01-01
The notion of vector-valued wavelets associated with an orthogonal vector-valued scaling function with 3-scale is introduced. The existence of orthogonal vector-valued wavelets is discussed and a necessary and sufficient condition is presented by means of the theory of vector-valued multiresolution analysis and paraunitary vector filter bank theory. An algorithm for constructing a class of orthogonal vector-valued wavelets with compact support is proposed. The concept of vector-valued wavelet packets is introduced and their properties are characterized by virtue of operator theory, time-frequency analysis method. Moreover, it is shown how to construct various orthonormal bases of space L 2 (R,C μ )(2≤μ element of Z) from these wavelet packets. Relation to some physical theories such as fractal theory and E-infinity theory is also discussed.
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 ...
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.
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.
Incomplete information and fractal phase space
International Nuclear Information System (INIS)
Wang, Qiuping A.
2004-01-01
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter ω which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of ω on the basis of fractal phase space. ω is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process
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.
Quantum waveguide theory of a fractal structure
International Nuclear Information System (INIS)
Lin Zhiping; Hou Zhilin; Liu Youyan
2007-01-01
The electronic transport properties of fractal quantum waveguide networks in the presence of a magnetic field are studied. A Generalized Eigen-function Method (GEM) is used to calculate the transmission and reflection coefficients of the studied systems unto the fourth generation Sierpinski fractal network with node number N=123. The relationship among the transmission coefficient T, magnetic flux Φ and wave vector k is investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux Φ are observed and discussed, and compared with the results of the tight-binding model
Random walk statistics on fractal structures
Rammal, R.
1984-09-01
We consider some statistical properties of simple random walks on fractal structures viewed as networks of sites and bonds: range, renewal theory, mean first passage time, etc. Asymptotic behaviors are shown to be controlled by the fractal ( ¯d) and spectral ( ¯d) dimensionalities of the considered structure. A simple decimation procedure giving the value of ( ¯d) is outlined and illustrated in the case of the Sierpinski gaskets. Recent results for the trapping problem, the self-avoiding walk, and the true-self-avoiding walk are briefly reviewed. New numerical results for diffusion on percolation clusters are also presented.
Fractal Rock Slope Dynamics Anticipating a Collapse
Czech Academy of Sciences Publication Activity Database
Paluš, Milan; Novotná, Dagmar; Zvelebil, Jiří
2004-01-01
Roč. 70 (2004), 036212 ISSN 1063-651X R&D Projects: GA ČR GA205/00/1055 Institutional research plan: CEZ:AV0Z1030915 Keywords : fractal * scaling * unstable rock slope * collapse prediction * engineering geology Subject RIV: BA - General Mathematics Impact factor: 2.352, year: 2004
Physiological Heterogeneity: Fractals Link Determinism and Randomness in Structures and Functions
Bassingthwaighte, James B.
2010-01-01
Spatial variation in concentrations or flows within an organ and temporal variation in reaction rates or flows appear to broaden as one refines the scale of observation. How can we characterize heterogeneity independently of scale? Fractals come to our rescue! A system is fractal if its features adhere to the same rules through a succession of different scales. Fractals efficiently describe many types of observations, geometric and kinetic, and help to integrate physiological knowledge. PMID:20871797
Fractal structures and intermittency in QCD
International Nuclear Information System (INIS)
Gustafson, Goesta.
1990-04-01
New results are presented for fractal structures and intermittency in QCD parton showers. A geometrical interpretation of the anomalous dimension in QCD is given. It is shown that model predications for factorial moments in the PEP-PETRA energy range are increased. if the properties of directly produced pions are more carefully taken into account
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.
Intergranular area microalloyed aluminium-silicate ceramics fractal analysis
Directory of Open Access Journals (Sweden)
Purenović J.
2013-01-01
Full Text Available Porous aluminium-silicate ceramics, modified by alloying with magnesium and microalloying with alluminium belongs to a group of advanced multifunctional ceramics materials. This multiphase solid-solid system has predominantly amorphous microstructure and micro morphology. Intergranular and interphase areas are very complex, because they represent areas, where numbered processes and interactions take place, making new boundaries and regions with fractal nature. Fractal analysis of intergranular microstructure has included determination of ceramic grain fractal dimension by using Richardson method. Considering the fractal nature of intergranular contacts, it is possible to establish correlation between material electrical properties and fractal analysis, as a tool for future correlation with microstructure characterization. [Projekat Ministarstva nauke Republike Srbije, br. ON 172057 i br. III 45012
Variability of fractal dimension of solar radio flux
Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om
2018-04-01
In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).
Self-organization of In2S3 quantum dots into fractal nanostructures by electrophoretic deposition.
Vigneashwari, B; Tyagi, A K; Dash, S; Shankar, P; Manna, I; Suthanthiraraj, S Austin
2009-09-01
This paper describes the assembly of In2S3 quantum dots by electrophoretic deposition (EPD) and their subsequent self-organization into fractal nanostructures over ITO substrates. The surface morphology and the organization of these dots into nanostructures were analyzed using SEM, HRSEM and AFM techniques. These analyses reveal the existence, under appropriate conditions, of very unique nanoscale structural motifs and scale invariance associated with the assembly. Formation of such a well correlated assembly, although seems to be electric field driven, appears to be dominated by self-organizing mechanism. Such self-organized nano-scale structures consisting of cavities are likely to have fascinating condensed phase transport properties. The paper reports microscopic study of such fractal assemblies using SEM, HTSEM and AFM.
Hausdorff, J. M.; Mitchell, S. L.; Firtion, R.; Peng, C. K.; Cudkowicz, M. E.; Wei, J. Y.; Goldberger, A. L.
1997-01-01
Fluctuations in the duration of the gait cycle (the stride interval) display fractal dynamics and long-range correlations in healthy young adults. We hypothesized that these stride-interval correlations would be altered by changes in neurological function associated with aging and certain disease states. To test this hypothesis, we compared the stride-interval time series of 1) healthy elderly subjects and young controls and of 2) subjects with Huntington's disease and healthy controls. Using detrended fluctuation analysis we computed alpha, a measure of the degree to which one stride interval is correlated with previous and subsequent intervals over different time scales. The scaling exponent alpha was significantly lower in elderly subjects compared with young subjects (elderly: 0.68 +/- 0.14; young: 0.87 +/- 0.15; P elderly subjects and in subjects with Huntington's disease. Abnormal alterations in the fractal properties of gait dynamics are apparently associated with changes in central nervous system control.
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.
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.
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.
Childhood Career Development Scale: Scale Construction and Psychometric Properties
Schultheiss, Donna E. Palladino; Stead, Graham B.
2004-01-01
The purpose of this investigation was to construct a theoretically driven and psychometrically sound childhood career development scale to measure career progress in fourth-through sixth-grade children. Super's nine dimensions (i.e., curiosity, exploration, information, key figures, interests, locus of control, time perspective, self-concept, and…
Våge, Selina; Thingstad, T Frede
2015-01-01
Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities. Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurring at different trophic levels and levels of phylogenetic resolution, we present a theoretical perspective on this enormous biodiversity, discussing in particular self-similar aspects of pelagic microbial food web organization. Fractal methods have been used to describe a variety of natural phenomena, with studies of habitat structures being an application in ecology. In contrast to mathematical fractals where pattern generating rules are readily known, however, identifying mechanisms that lead to natural fractals is not straight-forward. Here we put forward the hypothesis that trophic interactions between pelagic microbes may be organized in a fractal-like manner, with the emergent network resembling the structure of the Sierpinski triangle. We discuss a mechanism that could be underlying the formation of repeated patterns at different trophic levels and discuss how this may help understand characteristic biomass size-spectra that hint at scale-invariant properties of the pelagic environment. If the idea of simple underlying principles leading to a fractal-like organization of the pelagic food web could be formalized, this would extend an ecologists mindset on how biological complexity could be accounted for. It may furthermore benefit ecosystem modeling by facilitating adequate model resolution across multiple scales.
Directory of Open Access Journals (Sweden)
Selina eVåge
2015-12-01
Full Text Available Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities . Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurring at different trophic levels and levels of phylogenetic resolution, we present a theoretical perspective on this enormous biodiversity, discussing in particular self-similar aspects of pelagic microbial food web organization. Fractal methods have been used to describe a variety of natural phenomena, with studies of habitat structures being an application in ecology. In contrast to mathematical fractals where pattern generating rules are readily known, however, identifying mechanisms that lead to natural fractals is not straight-forward. Here we put forward the hypothesis that trophic interactions between pelagic microbes may be organized in a fractal-like manner, with the emergent network resembling the structure of the Sierpinski triangle. We discuss a mechanism that could be underlying the formation of repeated patterns at different trophic levels and discuss how this may help understand characteristic biomass size-spectra that hint at scale-invariant properties of the pelagic environment. If the idea of simple underlying principles leading to a fractal-like organization of the pelagic food web could be formalized, this would extend an ecologists mindset on how biological complexity could be accounted for. It may furthermore benefit ecosystem modeling by facilitating adequate model resolution across multiple scales.
Våge, Selina; Thingstad, T. Frede
2015-01-01
Trophic interactions are highly complex and modern sequencing techniques reveal enormous biodiversity across multiple scales in marine microbial communities. Within the chemically and physically relatively homogeneous pelagic environment, this calls for an explanation beyond spatial and temporal heterogeneity. Based on observations of simple parasite-host and predator-prey interactions occurring at different trophic levels and levels of phylogenetic resolution, we present a theoretical perspective on this enormous biodiversity, discussing in particular self-similar aspects of pelagic microbial food web organization. Fractal methods have been used to describe a variety of natural phenomena, with studies of habitat structures being an application in ecology. In contrast to mathematical fractals where pattern generating rules are readily known, however, identifying mechanisms that lead to natural fractals is not straight-forward. Here we put forward the hypothesis that trophic interactions between pelagic microbes may be organized in a fractal-like manner, with the emergent network resembling the structure of the Sierpinski triangle. We discuss a mechanism that could be underlying the formation of repeated patterns at different trophic levels and discuss how this may help understand characteristic biomass size-spectra that hint at scale-invariant properties of the pelagic environment. If the idea of simple underlying principles leading to a fractal-like organization of the pelagic food web could be formalized, this would extend an ecologists mindset on how biological complexity could be accounted for. It may furthermore benefit ecosystem modeling by facilitating adequate model resolution across multiple scales. PMID:26648929
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 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
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.
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
Self-similarity and scaling theory of complex networks
Song, Chaoming
Scale-free networks have been studied extensively due to their relevance to many real systems as diverse as the World Wide Web (WWW), the Internet, biological and social networks. We present a novel approach to the analysis of scale-free networks, revealing that their structure is self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a self-similar exponent, which classifies fractal and non-fractal networks. By using the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks, we show that the key principle that gives rise to the fractal architecture of networks is a strong effective "repulsion" between the most connected nodes (hubs) on all length scales, rendering them very dispersed. We show that a robust network comprised of functional modules, such as a cellular network, necessitates a fractal topology, suggestive of a evolutionary drive for their existence. These fundamental properties help to understand the emergence of the scale-free property in complex networks.
Development and Psychometric Properties of the Homophobic Bullying Scale
Prati, Gabriele
2012-01-01
The study aimed to develop the Homophobic Bullying Scale and to investigate its psychometric properties. The items of the Homophobic Bullying Scale were created to measure high school students' bullying behaviors motivated by homophobia, including verbal bullying, relational bullying, physical bullying, property bullying, sexual harassment, and…
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...
Scaling properties of the transverse mass spectra
International Nuclear Information System (INIS)
Schaffner-Bielich, J.
2002-01-01
Motivated from the formation of an initial state of gluon-saturated matter, we discuss scaling relations for the transverse mass spectra at BNL's relativistic heavy-ion collider (RHIC). We show on linear plots, that the transverse mass spectra for various hadrons can be described by an universal function in m t . The transverse mass spectra for different centralities can be rescaled into each other. Finally, we demonstrate that m t -scaling is also present in proton-antiproton collider data and compare it to m t -scaling at RHIC. (orig.)
Fractal physiology and the fractional calculus: a perspective
Directory of Open Access Journals (Sweden)
Bruce J West
2010-10-01
Full Text Available This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. We review the allometric aggregation approach to the processing of physiologic time series as a way of determining the fractal character of the underlying phenomena. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. Fractional operators acting on fractal functions yield fractal functions, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine. Allometric control incorporates long-time memory, inverse power-law (IPL correlations, and long-range interactions in complex phenomena as manifest by IPL distributions. We hypothesize that allometric control, rather than homeostatic control, maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can be described using the fractional calculus to capture the dynamics of complex physiologic networks. This hypothesis is supported by a number of physiologic time series data.
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....
Pikkujamsa, S. M.; Makikallio, T. H.; Sourander, L. B.; Raiha, I. J.; Puukka, P.; Skytta, J.; Peng, C. K.; Goldberger, A. L.; Huikuri, H. V.
1999-01-01
BACKGROUND: New methods of R-R interval variability based on fractal scaling and nonlinear dynamics ("chaos theory") may give new insights into heart rate dynamics. The aims of this study were to (1) systematically characterize and quantify the effects of aging from early childhood to advanced age on 24-hour heart rate dynamics in healthy subjects; (2) compare age-related changes in conventional time- and frequency-domain measures with changes in newly derived measures based on fractal scaling and complexity (chaos) theory; and (3) further test the hypothesis that there is loss of complexity and altered fractal scaling of heart rate dynamics with advanced age. METHODS AND RESULTS: The relationship between age and cardiac interbeat (R-R) interval dynamics from childhood to senescence was studied in 114 healthy subjects (age range, 1 to 82 years) by measurement of the slope, beta, of the power-law regression line (log power-log frequency) of R-R interval variability (10(-4) to 10(-2) Hz), approximate entropy (ApEn), short-term (alpha(1)) and intermediate-term (alpha(2)) fractal scaling exponents obtained by detrended fluctuation analysis, and traditional time- and frequency-domain measures from 24-hour ECG recordings. Compared with young adults (fractal correlation properties (alpha(1), alpha(2), beta) of R-R interval dynamics despite lower spectral and time-domain measures. Progressive loss of complexity (decreased ApEn, r=-0.69, Pfractal-like heart rate behavior (increased alpha(2), r=0.63, decreased beta, r=-0.60, P60 years, n=29). CONCLUSIONS: Cardiac interbeat interval dynamics change markedly from childhood to old age in healthy subjects. Children show complexity and fractal correlation properties of R-R interval time series comparable to those of young adults, despite lower overall heart rate variability. Healthy aging is associated with R-R interval dynamics showing higher regularity and altered fractal scaling consistent with a loss of complex variability.
Passenger flow analysis of Beijing urban rail transit network using fractal approach
Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia
2018-04-01
To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.
DEFF Research Database (Denmark)
Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.
1989-01-01
temperature are studied as functions of temperature, time, and concentration. At zero temperature and high dilution, the growing solid is found to have a fractal morphology and the effective fractal exponent D varies with concentration and ratio of time scales of the two dynamical processes. The mechanism...... responsible for forming the fractal solid is shown to be a buildup of a locally high vacancy concentration in the active growth zone. The growth-probability measure of the fractals is analyzed in terms of multifractality by calculating the f(α) spectrum. It is shown that the basic ideas of relating...... probability measures of static fractal objects to the growth-probability distribution during formation of the fractal apply to the present model. The f(α) spectrum is found to be in the universality class of diffusion-limited aggregation. At finite temperatures, the fractal solid domains become metastable...
[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.
Scaling properties of pure-quartic solitons
DEFF Research Database (Denmark)
Blanco-Redondo, Andrea; Lo, Chih Wei; Stefani, Alessio
2017-01-01
We demonstrate, by experiments and analytical developments, that the recently discovered pure-quartic solitons significantly outperform conventional solitons for high-energy ultrafast pulses. This is due to the favorable scaling of their energy and their Kelly sidebands.......We demonstrate, by experiments and analytical developments, that the recently discovered pure-quartic solitons significantly outperform conventional solitons for high-energy ultrafast pulses. This is due to the favorable scaling of their energy and their Kelly sidebands....
Fractal tiles associated with shift radix systems.
Berthé, Valérie; Siegel, Anne; Steiner, Wolfgang; Surer, Paul; Thuswaldner, Jörg M
2011-01-15
Shift radix systems form a collection of dynamical systems depending on a parameter r which varies in the d -dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings. In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters r these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (non-monic) expanding polynomials. We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter r of the shift radix system, these tiles provide multiple tilings and even tilings of the d -dimensional real vector space. These tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above. Such a tiling may consist of tiles having infinitely many different shapes. Moreover, the tiles need not be self-affine (or graph directed self-affine).
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. .
The application of fractals to Xiazhuang uranium ore field
International Nuclear Information System (INIS)
Li She; Guan Taiyang; Chinese Academy of Sciences, Guiyang; Pan Jiayong; Cao Shuanglin; Nanjing Univ., Nanjing
2006-01-01
Fractal theory is utilized to study spatial distribution features of uranium deposits in Xiazhuang region. The results show that the spatial distribution of uranium deposits has self-similarity statistically and the distribution regularity of uranium deposits can be quantitatively described with fractal dimension. The fractal dimension value of spatial distribution of uranium deposits are calculated with counting box method. The dimension value of different metallogenic regions are compared. The results show that the number of box correlates well to the scale with a correlation coefficient of more than 0.98. (authors)
Shower fractal dimension analysis in a highly-granular calorimeter
Ruan, M
2014-01-01
We report on an investigation of the self-similar structure of particle showers recorded at a highly-granular calorimeter. On both simulated and experimental data, a strong correlation between the number of hits and the spatial scale of the readout channels is observed, from which we define the shower fractal dimension. The measured fractal dimension turns out to be strongly dependent on particle type, which enables new approaches for particle identification. A logarithmic dependence of the particle energy on the fractal dimension is also observed.
Design of inside cut von koch fractal UWB MIMO antenna
Tharani, V.; Shanmuga Priya, N.; Rajesh, A.
2017-11-01
An Inside Cut Hexagonal Von Koch fractal MIMO antenna is designed for UWB applications and its characteristics behaviour are studied. Self-comparative and space filling properties of Koch fractal structure are utilized in the antenna design which leads to the desired miniaturization and wideband characteristics. The hexagonal shaped Von Koch Fractal antenna with Defected Ground Structure (DGS) is designed on FR4 substrate with a compact size of 30mm x 20mm x 1.6mm. The antenna achieves a maximum of -44dB and -51dB at 7.1GHz for 1-element and 2-element case respectively.
Quantifying inhomogeneity in fractal sets
Fraser, Jonathan M.; Todd, Mike
2018-04-01
An inhomogeneous fractal set is one which exhibits different scaling behaviour at different points. The Assouad dimension of a set is a quantity which finds the ‘most difficult location and scale’ at which to cover the set and its difference from box dimension can be thought of as a first-level overall measure of how inhomogeneous the set is. For the next level of analysis, we develop a quantitative theory of inhomogeneity by considering the measure of the set of points around which the set exhibits a given level of inhomogeneity at a certain scale. For a set of examples, a family of -invariant subsets of the 2-torus, we show that this quantity satisfies a large deviations principle. We compare members of this family, demonstrating how the rate function gives us a deeper understanding of their inhomogeneity.
Psychometric properties of Sternberg love scale | Askarpour ...
African Journals Online (AJOL)
Introduction: The aim of study was to evaluate the psychometric indices Sternberg love scale on married men and women in Iranian society. Methods: The study type is correlation (factor analysis). In this research factor analysis was used that is an exploratory and confirmatory technique to study the structure of a set of data, ...
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...
Random-fractal Ansatz for the configurations of two-dimensional critical systems.
Lee, Ching Hua; Ozaki, Dai; Matsueda, Hiroaki
2016-12-01
Critical systems have always intrigued physicists and precipitated the development of new techniques. Recently, there has been renewed interest in the information contained in the configurations of classical critical systems, whose computation do not require full knowledge of the wave function. Inspired by holographic duality, we investigated the entanglement properties of the classical configurations (snapshots) of the Potts model by introducing an Ansatz ensemble of random fractal images. By virtue of the central limit theorem, our Ansatz accurately reproduces the entanglement spectra of actual Potts snapshots without any fine tuning of parameters or artificial restrictions on ensemble choice. It provides a microscopic interpretation of the results of previous studies, which established a relation between the scaling behavior of snapshot entropy and the critical exponent. More importantly, it elucidates the role of ensemble disorder in restoring conformal invariance, an aspect previously ignored. Away from criticality, the breakdown of scale invariance leads to a renormalization of the parameter Σ in the random fractal Ansatz, whose variation can be used as an alternative determination of the critical exponent. We conclude by providing a recipe for the explicit construction of fractal unit cells consistent with a given scaling exponent.
A TUTORIAL INTRODUCTION TO ADAPTIVE FRACTAL ANALYSIS
Directory of Open Access Journals (Sweden)
Michael A Riley
2012-09-01
Full Text Available The authors present a tutorial description of adaptive fractal analysis (AFA. AFA utilizes an adaptive detrending algorithm to extract globally smooth trend signals from the data and then analyzes the scaling of the residuals to the fit as a function of the time scale at which the fit is computed. The authors present applications to synthetic mathematical signals to verify the accuracy of AFA and demonstrate the basic steps of the analysis. The authors then present results from applying AFA to time series from a cognitive psychology experiment on repeated estimation of durations of time to illustrate some of the complexities of real-world data. AFA shows promise in dealing with many types of signals, but like any fractal analysis method there are special challenges and considerations to take into account, such as determining the presence of linear scaling regions.
Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions
Lapidus, Michel L; Žubrinić, Darko
2017-01-01
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the f...
On claimed ULF seismogenic fractal signatures in the geomagnetic field
Masci, Fabrizio
2010-10-01
During the last ten years, fractal analysis of ultra low frequency (ULF) geomagnetic field components has been proposed as one of the most promising tools to highlight magnetic precursory signals possibly generated by the preparation processes of earthquakes. Several papers claim seismogenic changes in the fractal features of the geomagnetic field some months before earthquakes occur. The target of the present paper is to put forth a qualitative investigation on the fractal characteristics of ULF magnetic signatures that previous authors have claimed to be related without doubt to strong earthquakes. This analysis takes into account both the temporal evolution of the geomagnetic field fractal parameters reported in previous researches and the temporal evolution of global geomagnetic activity. Running averages of the geomagnetic indices ΣKp and Ap are plotted into the original figures from the previous publications. This simple analysis shows that the fractal features of the ULF geomagnetic field are closely related to the geomagnetic activity both before and after the earthquake occurs. The correlation between the geomagnetic field fractal parameters and geomagnetic activity is clearly shown over both long and short time scales. In light of this, the present paper shows that fractal behaviors of previously claimed seismogenic ULF magnetic signatures depend mainly on geomagnetic activity due to solar-terrestrial interaction. Therefore, previously reported association with the preparation process of the earthquake is dubious.
Semiflexible crossing-avoiding trails on plane-filling fractals
International Nuclear Information System (INIS)
Živić, I.; Elezović-Hadžić, S.; Milošević, S.
2015-01-01
We have studied the statistics of semiflexible polymer chains modeled by crossing-avoiding trails (CAT) situated on the family of plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension d f is equal to 2 for all members of the fractal family. By applying the exact and Monte Carlo real-space renormalization group method we have calculated the critical exponent ν, which governs the scaling behavior of the end-to-end distance of the polymer, as well as the entropic critical exponent γ, for a large set of fractals, and various values of polymer flexibility. Our results, obtained for CAT model on PF fractals, show that both critical exponents depend on the polymer flexibility, in such a way that less flexible polymer chains display enlarged values of ν, and diminished values of γ. We have compared the obtained results for CAT model with the known results for the self-avoiding walk and self-avoiding trail models and discussed the influence of excluded volume effect on the values of semiflexible polymer critical exponents, for a large set of studied compact fractals.
Nonlinear internal friction, chaos, fractal and musical instruments
International Nuclear Information System (INIS)
Sun, Z.Q.; Lung, C.W.
1995-08-01
Nonlinear and structure sensitive internal friction phenomena in materials are used for characterizing musical instruments. It may be one of the most important factors influencing timbre of instruments. As a nonlinear dissipated system, chaos and fractals are fundamental peculiarities of sound spectra. It is shown that the concept of multi range fractals can be used to decompose the frequency spectra of melody. New approaches are suggested to improve the fabrication, property characterization and physical understanding of instruments. (author). 18 refs, 4 figs
Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals
Steinhurst, Benjamin; Teplyaev, Alexander
2012-01-01
We show that if a Barlow-Evans Markov process on a vermiculated space is symmetric, then one can study the spectral properties of the corresponding Laplacian using projective limits. For some examples, such as the Laakso spaces and a Spierpinski P\\^ate \\`a Choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. Also, one can construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhu...
Shape characteristics of equilibrium and non-equilibrium fractal clusters.
Mansfield, Marc L; Douglas, Jack F
2013-07-28
It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other
Temporal fractals in movies and mind.
Cutting, James E; DeLong, Jordan E; Brunick, Kaitlin L
2018-01-01
Fractal patterns are seemingly everywhere. They can be analyzed through Fourier and power analyses, and other methods. Cutting, DeLong, and Nothelfer (2010) analyzed as time-series data the fluctuations of shot durations in 150 popular movies released over 70 years. They found that these patterns had become increasingly fractal-like and concluded that they might be linked to those found in the results of psychological tasks involving attention. To explore this possibility further, we began by analyzing the shot patterns of almost twice as many movies released over a century. The increasing fractal-like nature of shot patterns is affirmed, as determined by both a slope measure and a long-range dependence measure, neither of which is sensitive to the vector lengths of their inputs within the ranges explored here. But the main reason for increased long-range dependence is related to, but not caused by, the increasing vector length of the shot-series samples. It appears that, in generating increasingly fractal-like patterns, filmmakers have systematically explored dimensions that are important for holding our attention-shot durations, scene durations, motion, and sound amplitude-and have crafted fluctuations in them like those of our endogenous attention patterns. Other dimensions-luminance, clutter, and shot scale-are important to film style but their variations seem not to be important to holding viewers' moment-to-moment attention and have not changed in their fractional dimension over time.
Small-angle scattering from generalized self-similar Vicsek fractals
International Nuclear Information System (INIS)
Cherny, Alexander Yu; Anitas, Eugen M; Osipov, Vladimir A; Kuklin, Alexander I
2012-01-01
An analytical approach for calculating the small-angle X-ray or neutron scattering (SAXS/SANS) from generalized self-similar Vicsek fractals (GSSVF) is presented; each fractal consists of spherical subunits. The system considered is a mass-fractal, generated iteratively from a regular 3D Vicsek fractal structure. Its fractal dimension is controllable and increases with increasing the value of the scaling factor. Small-angle scattering (SAS) intensity is determined from a set of non-interacting, randomly oriented and uniformly distributed GSSVF fractals. It is shown that in the fractal region, the curve I(q)q D is approximately log-periodic with the period equal to the scaling factor of fractal; here D and I(q) are the fractal dimension and the SAS intensity, respectively. In particular, the positions of deepest minima and highest maxima are log-periodic, and their number coincides with the number of fractal iterations. The log-periodicity of the scattering curves is a consequence of the self-similarity of GSSVF.
Relating Silica Scaling in Reverse Osmosis to Membrane Surface Properties.
Tong, Tiezheng; Zhao, Song; Boo, Chanhee; Hashmi, Sara M; Elimelech, Menachem
2017-04-18
We investigated the relationship between membrane surface properties and silica scaling in reverse osmosis (RO). The effects of membrane hydrophilicity, free energy for heterogeneous nucleation, and surface charge on silica scaling were examined by comparing thin-film composite polyamide membranes grafted with a variety of polymers. Results show that the rate of silica scaling was independent of both membrane hydrophilicity and free energy for heterogeneous nucleation. In contrast, membrane surface charge demonstrated a strong correlation with the extent of silica scaling (R 2 > 0.95, p scaling, whereas a more negative membrane surface charge led to reduced scaling. This observation suggests that deposition of negatively charged silica species on the membrane surface plays a critical role in silica scale formation. Our findings provide fundamental insights into the mechanisms governing silica scaling in reverse osmosis and highlight the potential of membrane surface modification as a strategy to reduce silica scaling.
Coskun, Aycan; Sonmez, Harun; Ercin Kasapoglu, K.; Ozge Dinc, S.; Celal Tunusluoglu, M.
2010-05-01
of granular materials. Engineering Geology 48, 231-244. Kahraman, S., Alber, M., Fener, M. and Gunaydin, O. 2008. Evaluating the geomechanical properties of Misis fault breccia (Turkey). Int. J. Rock Mech. Min. Sci, 45, (8), 1469-1479. Kolay, E., Kayabali, K., 2006. Investigation of the effect of aggregate shape and surface roughness on the slake durability index using the fractal dimension approach. Engineering Geology 86, 271-294. Kruhl, J.H., Nega, M., 1996. The fractal shape of sutured quartz grain boundaries: application as a geothermometer. Geologische Rundschau 85, 38-43. Lindquist E.S. 1994. The strength, deformation properties of melange. PhD thesis, University of California, Berkeley, 1994. 264p. Lindquist E.S. and Goodman R.E. 1994. The strength and deformation properties of the physical model m!elange. In: Nelson PP, Laubach SE, editors. Proceedings of the First North American Rock Mechanics Conference (NARMS), Austin, Texas. Rotterdam: AA Balkema; 1994. Pardini, G., 2003. Fractal scaling of surface roughness in artificially weathered smectite rich soil regoliths. Geoderma 117, 157-167. Sezer E., 2009. A computer program for fractal dimension (FRACEK) with application on type of mass movement characterization. Computers and Geosciences (doi:10.1016/j.cageo.2009.04.006). Sonmez H, Tuncay E, and Gokceoglu C., 2004. Models to predict the uniaxial compressive strength and the modulus of elasticity for Ankara Agglomerate. Int. J. Rock Mech. Min. Sci., 41 (5), 717-729. Sonmez, H., Gokceoglu, C., Medley, E.W., Tuncay, E., and Nefeslioglu, H.A., 2006. Estimating the uniaxial compressive strength of a volcanic bimrock. Int. J. Rock Mech. Min. Sci., 43 (4), 554-561. Zorlu K., 2008. Description of the weathering states of building stones by fractal geometry and fuzzy inference system in the Olba ancient city (Southern Turkey). Engineering Geology 101 (2008) 124-133.
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
Psychometric properties of Frustration Discomfort Scale in a Turkish sample.
Ozer, Bilge Uzun; Demir, Ayhan; Harrington, Neil
2012-08-01
The present study assessed the psychometric properties of the Frustration Discomfort Scale for Turkish college students. The Frustration Discomfort Scale (FDS), Procrastination Assessment Scale-Student, and Rosenberg Self-Esteem Scale were administered to a sample of 171 (98 women, 73 men) Turkish college students. The results of the confirmatory factor analysis yielded fit index values demonstrating viability of the four-dimensional solution as in the original. Findings also revealed that, as predicted, the Discomfort Intolerance subscale of Turkish FDS was most strongly correlated with procrastination. Overall results provided evidence for the factor validity and reliability of the Turkish version of the scale for use in a Turkish population.
Fractal Tempo Fluctuation and Pulse Prediction.
Rankin, Summer K; Large, Edward W; Fink, Philip W
2009-06-01
WE INVESTIGATED PEOPLES' ABILITY TO ADAPT TO THE fluctuating tempi of music performance. In Experiment 1, four pieces from different musical styles were chosen, and performances were recorded from a skilled pianist who was instructed to play with natural expression. Spectral and rescaled range analyses on interbeat interval time-series revealed long-range (1/ f type) serial correlations and fractal scaling in each piece. Stimuli for Experiment 2 included two of the performances from Experiment 1, with mechanical versions serving as controls. Participants tapped the beat at ¼- and ⅛-note metrical levels, successfully adapting to large tempo fluctuations in both performances. Participants predicted the structured tempo fluctuations, with superior performance at the ¼-note level. Thus, listeners may exploit long-range correlations and fractal scaling to predict tempo changes in music.
Psychometric Properties of the Revised Teachers' Attitude toward Inclusion Scale
Monsen, Jeremy J.; Ewing, Donna L.; Boyle, James
2015-01-01
This paper presents the psychometric properties of a questionnaire measure that updates and extends Larrivee and Cook's (1979) Opinions Relative to Mainstreaming Scale in terms of structure, terminology, and language. The revised scale was tested using a sample of 106 teachers based in inclusive mainstream schools. Using Principal Component…
Properties of Some Partial Dynamic Equations on Time Scales
Directory of Open Access Journals (Sweden)
Deepak B. Pachpatte
2013-01-01
Full Text Available The main objective of the paper is to study the properties of the solution of a certain partial dynamic equation on time scales. The tools employed are based on the application of the Banach fixed-point theorem and a certain integral inequality with explicit estimates on time scales.
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.
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
Long-range correlations and fractal dynamics in C. elegans: Changes with aging and stress
Alves, Luiz G. A.; Winter, Peter B.; Ferreira, Leonardo N.; Brielmann, Renée M.; Morimoto, Richard I.; Amaral, Luís A. N.
2017-08-01
Reduced motor control is one of the most frequent features associated with aging and disease. Nonlinear and fractal analyses have proved to be useful in investigating human physiological alterations with age and disease. Similar findings have not been established for any of the model organisms typically studied by biologists, though. If the physiology of a simpler model organism displays the same characteristics, this fact would open a new research window on the control mechanisms that organisms use to regulate physiological processes during aging and stress. Here, we use a recently introduced animal-tracking technology to simultaneously follow tens of Caenorhabdits elegans for several hours and use tools from fractal physiology to quantitatively evaluate the effects of aging and temperature stress on nematode motility. Similar to human physiological signals, scaling analysis reveals long-range correlations in numerous motility variables, fractal properties in behavioral shifts, and fluctuation dynamics over a wide range of timescales. These properties change as a result of a superposition of age and stress-related adaptive mechanisms that regulate motility.
Fern leaves and cauliflower curds are not fractals.
Lev-Yadun, Simcha
2012-05-01
The popular demonstration of drawing a mature fern leaf as expressed by Barnsley's fractal method is mathematically and visually very attractive but anatomically and developmentally misleading, and thus has limited, if any, biological significance. The same is true for the fractal demonstration of the external features of cauliflower curds. Actual fern leaves and cauliflower curds have a very small number of anatomically variable and non-iterating bifurcations, which superficially look self-similar, but do not allow for scaling down of their structure as real fractals do. Moreover, fern leaves and cauliflower curds develop from the inside out through a process totally different from fractal drawing procedures. The above cases demonstrate a general problem of using mathematical tools to investigate or illustrate biological phenomena in an irrelevant manner. A realistic set of mathematical equations to describe fern leaf or cauliflower curd development is needed.
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.
Fractal based curves in musical creativity: A critical annotation
Georgaki, Anastasia; Tsolakis, Christos
In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.
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...
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!
Aero-acoustic performance of Fractal Spoilers
Nedic, J.; Ganapathisubramani, B.; Vassilicos, C.; Boree, J.; Brizzi, L.; Spohn, A.
2010-11-01
One of the major environmental problems facing the aviation industry is that of aircraft noise. The work presented in this paper, done as part of the OPENAIR Project, looks at reducing spoiler noise through means of large-scale fractal porosity. It is hypothesised that the highly turbulent flow generated by these grids, which have multi-length-scales, would remove the re-circulation region and with it, the low frequency noise it generates. In its place, a higher frequency noise is introduced which is susceptible to atmospheric attenuation, and would be deemed less offensive to the human ear. A total of nine laboratory scaled spoilers were looked at, seven of which had a fractal design, one conventionally porous and one solid for reference. All of the spoilers were mounted on a flat plate and inclined at 30^o to the horizontal. Far-field, microphone array and PIV measurements were taken in an anechoic chamber to determine the acoustic performance and to study the flow coming through the spoilers. A significant reduction in sound pressure level is recorded and is found to be very sensitive to small changes in fractal grid parameters. Wake and drag force measurements indicated that the spoilers increase the drag whilst having minimal effect on the lift.
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
Scaling laws and properties of compositional data
Buccianti, Antonella; Albanese, Stefano; Lima, AnnaMaria; Minolfi, Giulia; De Vivo, Benedetto
2016-04-01
Many random processes occur in geochemistry. Accurate predictions of the manner in which elements or chemical species interact each other are needed to construct models able to treat presence of random components. Geochemical variables actually observed are the consequence of several events, some of which may be poorly defined or imperfectly understood. Variables tend to change with time/space but, despite their complexity, may share specific common traits and it is possible to model them stochastically. Description of the frequency distribution of the geochemical abundances has been an important target of research, attracting attention for at least 100 years, starting with CLARKE (1889) and continued by GOLDSCHMIDT (1933) and WEDEPOHL (1955). However, it was AHRENS (1954a,b) who focussed on the effect of skewness distributions, for example the log-normal distribution, regarded by him as a fundamental law of geochemistry. Although modeling of frequency distributions with some probabilistic models (for example Gaussian, log-normal, Pareto) has been well discussed in several fields of application, little attention has been devoted to the features of compositional data. When compositional nature of data is taken into account, the most typical distribution models for compositions are the Dirichlet and the additive logistic normal (or normal on the simplex) (AITCHISON et al. 2003; MATEU-FIGUERAS et al. 2005; MATEU-FIGUERAS and PAWLOWSKY-GLAHN 2008; MATEU-FIGUERAS et al. 2013). As an alternative, because compositional data have to be transformed from simplex space to real space, coordinates obtained by the ilr transformation or by application of the concept of balance can be analyzed by classical methods (EGOZCUE et al. 2003). In this contribution an approach coherent with the properties of compositional information is proposed and used to investigate the shape of the frequency distribution of compositional data. The purpose is to understand data-generation processes
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.
Fractal-like image statistics in visual art: similarity to natural scenes.
Redies, Christoph; Hasenstein, Jens; Denzler, Joachim
2007-01-01
Both natural scenes and visual art are often perceived as esthetically pleasing. It is therefore conceivable that the two types of visual stimuli share statistical properties. For example, natural scenes display a Fourier power spectrum that tends to fall with spatial frequency according to a power-law. This result indicates that natural scenes have fractal-like, scale-invariant properties. In the present study, we asked whether visual art displays similar statistical properties by measuring their Fourier power spectra. Our analysis was restricted to graphic art from the Western hemisphere. For comparison, we also analyzed images, which generally display relatively low or no esthetic quality (household and laboratory objects, parts of plants, and scientific illustrations). Graphic art, but not the other image categories, resembles natural scenes in showing fractal-like, scale-invariant statistics. This property is universal in our sample of graphic art; it is independent of cultural variables, such as century and country of origin, techniques used or subject matter. We speculate that both graphic art and natural scenes share statistical properties because visual art is adapted to the structure of the visual system which, in turn, is adapted to process optimally the image statistics of natural scenes.
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 ...
Psychometric Properties of Fear of Happiness Scale Turkish Form
Directory of Open Access Journals (Sweden)
Tugba Turk
2017-03-01
Full Text Available The aim of this study was to examine psychometric properties of Fear of Happiness Scale in Turkish university students. The sample consisted of 500 university students from Trakya University whose ages ranged from 18-33. At first, linguistic equivalence of the scale was performed. After that validity and reliability analyses were conducted. Besides Fear of Happiness Scale, Life Satisfaction Scale was administered to the students. For criterion validity, Pearson Correlation coefficient was calculated between Fear of Happiness Scale and Life Satisfaction Scale. Cronbach Alpha was computed for reliability analysis. Exploratory and confirmatory factor analysis revealed that the structure of the original scale was acceptable for the Turkish sample. Internal consistency of the scale was found to be .89. Confirmatory factor analysis provides good fit values for this scale. There is negative relationship between Fear of Happiness Scale and Life Satisfaction Scale. The results of data analysis showed that the Fear of Happiness Scale is a valid and reliable measure for Turkish university students. [Psikiyatride Guncel Yaklasimlar - Current Approaches in Psychiatry 2017; 9(1.000: 1-12
Pulmonary vasculature in dogs assessed by three-dimensional fractal analysis and chemometrics
DEFF Research Database (Denmark)
Müller, Anna V; Marschner, Clara B; Kristensen, Annemarie T
2017-01-01
Fractal analysis of canine pulmonary vessels could allow quantification of their space-filling properties. Aims of this prospective, analytical, cross-sectional study were to describe methods for reconstructing three dimensional pulmonary arterial vascular trees from computed tomographic pulmonary...... angiogram, applying fractal analyses of these vascular trees in dogs with and without diseases that are known to predispose to thromboembolism, and testing the hypothesis that diseased dogs would have a different fractal dimension than healthy dogs. A total of 34 dogs were sampled. Based on computed...... for each dog using a semiautomated segmentation technique. Vascular three-dimensional reconstructions were then evaluated using fractal analysis. Fractal dimensions were analyzed, by group, using analysis of variance and principal component analysis. Fractal dimensions were significantly different among...
FRACTAL ANALYSIS OF FRACTURE SYSTEMS IN UPPER TRIASSIC DOLOMITES IN ŽUMBERAK MOUNTAIN, CROATIA
Directory of Open Access Journals (Sweden)
Ivica Pavičić
2017-01-01
Full Text Available This paper presents results of fractal analysis of fracture systems in upper Triassic dolomites in Žumberak Mountain, Croatia. Mechanical rock characteristics together with structural and diagenetic processes results with fracture systems that can be considered as fractals. They are scale-invariant in specific range of scales. Distribution of fractures can be than described with power law distribution and fractal dimension. Fractal dimension is a measure of how fractures fill the space. Fractal dimension can be estimated form photographs of outcrops by converting photographs to binary photographs. In binary photo there is only black (rock or fractures and white (fractures or rock. Fractal dimension is then estimated based on box-counting method. In this paper we present results of fractal analysis from three outcrops. Results are very similar to previous published results from outcrops of dolomites in Slovenia. Obtained fractal dimensions are in range 2,69-2,78 and it depends on how fracture systems are distributed in the outcrop. Lower values indicate smaller number of fractures and higher significance of larger fractures. Higher values indicate distribution of more similar sized fractures throughout whole outcrop. Fractal dimension is very significant parameter in rock fracture system characterisation sense it describes how fractures are distributed in the outcrop. It can be used in discrete fracture network modelling if spatial distribution of fractures is represented with power law distribution.
Generation of fractals from complex logistic map
Energy Technology Data Exchange (ETDEWEB)
Rani, Mamta [Galgotias College of Engg. and Technology, Greater Noida (India)], E-mail: mamtarsingh@rediffmail.com; Agarwal, Rashi [IEC College of Engg. and Tech., Greater Noida (India)], E-mail: agarwal_rashi@yahoo.com
2009-10-15
Remarkably benign looking logistic transformations x{sub n+1} = r x{sub n}(1 - x{sub n}) for choosing x{sub 0} between 0 and 1 and 0 < r {<=} 4 have found a celebrated place in chaos, fractals and discrete dynamics. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck [Beck C. Physical meaning for Mandelbrot and Julia sets. Physica D 1999;125(3-4):171-182. Zbl0988.37060] to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter case. The purpose of this paper is to study the bounded behavior of the complex logistic map using superior iterates and generate fractals from the same. The analysis in this paper shows that many beautiful properties of the logistic map are extendable for a larger value of r.
Generation of fractals from complex logistic map
International Nuclear Information System (INIS)
Rani, Mamta; Agarwal, Rashi
2009-01-01
Remarkably benign looking logistic transformations x n+1 = r x n (1 - x n ) for choosing x 0 between 0 and 1 and 0 < r ≤ 4 have found a celebrated place in chaos, fractals and discrete dynamics. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck [Beck C. Physical meaning for Mandelbrot and Julia sets. Physica D 1999;125(3-4):171-182. Zbl0988.37060] to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter case. The purpose of this paper is to study the bounded behavior of the complex logistic map using superior iterates and generate fractals from the same. The analysis in this paper shows that many beautiful properties of the logistic map are extendable for a larger value of r.
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.
Creating a fractal-based quality management infrastructure.
Pronovost, Peter J; Marsteller, Jill A
2014-01-01
The purpose of this paper is to describe how a fractal-based quality management infrastructure could benefit quality improvement (QI) and patient safety efforts in health care. The premise for this infrastructure comes from the QI work with health care professionals and organizations. The authors used the fractal structure system in a health system initiative, a statewide collaborative, and several countrywide efforts to improve quality of care. It is responsive to coordination theory and this infrastructure is responsive to coordination theory and repeats specific characteristics at every level of an organization, with vertical and horizontal connections among these levels to establish system-wide interdependence. The fractal system infrastructure helped a health system achieve 96 percent compliance on national core measures, and helped intensive care units across the USA, Spain, and England to reduce central line-associated bloodstream infections. The fractal system approach organizes workers around common goals, links all hospital levels and, supports peer learning and accountability, grounds solutions in local wisdom, and effectively uses available resources. The fractal structure helps health care organizations meet their social and ethical obligations as learning organizations to provide the highest possible quality of care and safety for patients using their services. The concept of deliberately creating an infrastructure to manage QI and patient safety work and support organizational learning is new to health care. This paper clearly describes how to create a fractal infrastructure that can scale up or down to a department, hospital, health system, state, or country.
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.
Fractal tiles associated with shift radix systems☆
Berthé, Valérie; Siegel, Anne; Steiner, Wolfgang; Surer, Paul; Thuswaldner, Jörg M.
2011-01-01
Shift radix systems form a collection of dynamical systems depending on a parameter r which varies in the d-dimensional real vector space. They generalize well-known numeration systems such as beta-expansions, expansions with respect to rational bases, and canonical number systems. Beta-numeration and canonical number systems are known to be intimately related to fractal shapes, such as the classical Rauzy fractal and the twin dragon. These fractals turned out to be important for studying properties of expansions in several settings. In the present paper we associate a collection of fractal tiles with shift radix systems. We show that for certain classes of parameters r these tiles coincide with affine copies of the well-known tiles associated with beta-expansions and canonical number systems. On the other hand, these tiles provide natural families of tiles for beta-expansions with (non-unit) Pisot numbers as well as canonical number systems with (non-monic) expanding polynomials. We also prove basic properties for tiles associated with shift radix systems. Indeed, we prove that under some algebraic conditions on the parameter r of the shift radix system, these tiles provide multiple tilings and even tilings of the d-dimensional real vector space. These tilings turn out to have a more complicated structure than the tilings arising from the known number systems mentioned above. Such a tiling may consist of tiles having infinitely many different shapes. Moreover, the tiles need not be self-affine (or graph directed self-affine). PMID:24068835
Acceptance of Dating Violence Scale: Checking its psychometric properties
Pimentel, Carlos Eduardo; Moura, Giovanna Barroca de; Cavalcanti, Jaqueline Gomes
2017-01-01
Abstract Violence by intimate partners is a cause of concern in several countries, including Brazil. Although some instruments that measure this phenomenon have been found, the Acceptance of Couple Violence Scale (ACVS) has proven to be a brief measure with satisfactory psychometric properties. For this reason, we have sought to investigate its psychometric properties in Brazilian samples. The ACVS was subjected to two studies. Study 1 indicated a two-factor structure with satisfactory intern...
Psychometric properties of Conversion Disorder Scale- Revised (CDS) for children.
Ijaz, Tazvin; Nasir, Attikah; Sarfraz, Naema; Ijaz, Shirmeen
2017-05-01
To revise conversion disorder scale and to establish the psychometric properties of the revised scale. This case-control study was conducted from February to June, 2014, at the Government College University, Lahore, Pakistan, and comprised schoolchildren and children with conversion disorder. In order to generate items for revised version of conversion disorder scale, seven practising mental health professionals were consulted. A list of 42 items was finalised for expert ratings. After empirical validation, a scale of 40 items was administered on the participants and factor analysis was conducted. Of the240 participants, 120(50%) were schoolchildren (controls group) and 120(50%)were children with conversion disorder (clinical group).The results of factor analysis revealed five factors (swallowing and speech symptoms, motor symptoms, sensory symptoms, weakness and fatigue, and mixed symptoms) and retention of all 40 items of revised version of conversion disorder scale. Concurrent validity of the revised scale was found to be 0.81 which was significantly high. Similarly, discriminant validity of the scale was also high as both clinical and control groups had significant difference (pconversion disorder scale was 76% sensitive to predicting conversion disorder while specificity showed that the scale was 73% accurate in specifying participants of the control group. The revised version of conversion disorder scale was a reliable and valid tool to be used for screening of children with conversion disorder.
Fractal Simulations of African Design in Pre-College Computing Education
Eglash, Ron; Krishnamoorthy, Mukkai; Sanchez, Jason; Woodbridge, Andrew
2011-01-01
This article describes the use of fractal simulations of African design in a high school computing class. Fractal patterns--repetitions of shape at multiple scales--are a common feature in many aspects of African design. In African architecture we often see circular houses grouped in circular complexes, or rectangular houses in rectangular…
Properties of proxy-derived modified Rankin Scale assessment.
McArthur, Kate; Beagan, Michael L C; Degnan, Andrew; Howarth, Rosanne C; Mitchell, Kirsten A; McQuaige, Fiona B; Shannon, Mary Ann C; Stott, D J; Quinn, Terence J
2013-08-01
Cognitive or communication issues may preclude direct modified Rankin Scale interview, necessitating interview with a suitable surrogate. The clinimetric properties of this proxy modified Rankin Scale assessment have not been described. To describe reliability of proxy-derived modified Rankin Scale and compare with traditional direct patient interview. Researchers assessed consenting stroke inpatients and their proxies using a nonstructured modified Rankin Scale approach. Paired interviewers (trained in modified Rankin Scale) performed independent and blinded modified Rankin Scale assessment of patients and appropriate proxies. Interobserver variability and agreement between patient and proxy modified Rankin Scale were described using kappa statistics (k, 95% confidence interval) and percentage agreement. Ninety-seven stroke survivors were assessed. Proxies were family members (n = 29), nurses (n = 50), or physiotherapists (n = 25). Median modified Rankin Scale from both patient and proxies was 3 [interquartile range (IQR): 2-4]. Reliability for patient modified Rankin Scale interview was weighted kappa = 0·70 (95% confidence interval: 0·30-1·00). Reliability for proxy modified Rankin Scale weighted kappa = 0·62 (95% confidence interval: 0·34-0·90). Subgroup analysis of various proxy information sources were as follows: family weighted kappa = 0·61; nurse weighted kappa = 0·58; therapist weighted kappa = 0·58. There was disagreement between patient-derived modified Rankin Scale and corresponding proxy modified Rankin Scale weighted kappa = 0·64 (95% CI: 0·42-0·86). There is potential for substantial interobserver variability in proxy modified Rankin Scale and validity of certain proxy assessments is questionable. Direct modified Rankin Scale interview is preferred. © 2012 The Authors. International Journal of Stroke © 2012 World Stroke Organization.
Attractive critical point from weak antilocalization on fractals
Sticlet, D.C.; Akhmerov, A.R.
2016-01-01
We report an attractive critical point occurring in the Anderson localization scaling flow of symplectic models on fractals. The scaling theory of Anderson localization predicts that in disordered symplectic two-dimensional systems weak-antilocalization effects lead to a metal-insulator
Maggi, F.
2007-01-01
While the fractal dimension of suspended flocs of cohesive sediment is known to vary with the shear rate, electrochemical properties of the sediment and environment, geometrical restructuring, and presence of organic matter, experimental data presented in this work suggest changes in fractal
Tan, Wanyu; Li, Yongmei; Tan, Kaixuan; Duan, Xianzhe; Liu, Dong; Liu, Zehua
2016-12-01
Radon diffusion and transport through different media is a complex process affected by many factors. In this study, the fractal theories and field covering experiments were used to study the fractal characteristics of particle size distribution (PSD) of six kinds of geotechnical materials (e.g., waste rock, sand, laterite, kaolin, mixture of sand and laterite, and mixture of waste rock and laterite) and their effects on radon diffusion. In addition, the radon diffusion coefficient and diffusion length were calculated. Moreover, new formulas for estimating diffusion coefficient and diffusion length functional of fractal dimension d of PSD were proposed. These results demonstrate the following points: (1) the fractal dimension d of the PSD can be used to characterize the property of soils and rocks in the studies of radon diffusion behavior; (2) the diffusion coefficient and diffusion length decrease with increasing fractal dimension of PSD; and (3) the effectiveness of final covers in reducing radon exhalation of uranium tailings impoundments can be evaluated on the basis of the fractal dimension of PSD of materials.
Fractals and the birth of Gothic: reflections on the biologic basis of creativity.
Goldberger, A L
1996-05-01
The birth of Gothic, one of the great triumphs of human spiritual and artistic expression, would appear to be a topic remote from the enterprise of contemporary neurobiology. The intent of this brief essay is to explore the possibility that this singular architectural movement may have important implications for understanding the nonlinear dynamics of the brain. We explore the hypothesis that the Gothic cathedral, with its porous, scale-free structures, may represent an externalization of the fractal properties of our physiology in general, and of our neural architectures and neuro-dynamics, in particular.
Balankin, Alexander S; Horta Rangel, Antonio; García Pérez, Gregorio; Gayosso Martinez, Felipe; Sanchez Chavez, Hugo; Martínez-González, Claudia L
2013-05-01
We study the static and dynamic properties of networks of crumpled creases formed in hand crushed sheets of paper. The fractal dimensionalities of crumpling networks in the unfolded (flat) and folded configurations are determined. Some other noteworthy features of crumpling networks are established. The physical implications of these findings are discussed. Specifically, we state that self-avoiding interactions introduce a characteristic length scale of sheet crumpling. A framework to model the crumpling phenomena is suggested. Mechanics of sheet crushing under external confinement is developed. The effect of compaction geometry on the crushing mechanics is revealed.
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
Analysis of the Psychometric Properties of a Parental Alienation Scale
Directory of Open Access Journals (Sweden)
Paula Inez Cunha Gomide
Full Text Available Abstract The development of forensic evaluation scales is fundamental. This study's purpose was to explore the psychometric properties of a parental alienation scale. Forensic technicians completed 193 scales concerning parents involved in a lawsuit: 48 families with at least one parent indicated as the alienator (group A and 48 families with no parental alienation claim (group B. The scale consisted of five categories and 69 items: denying access to the child; derogatory comparisons; emotional manipulation; behavior of parent and child during assessment. The results show Cronbach's alpha = .965 and split-half = .745; KMO = .884 and Bartlett's sphericity test ( p < .001. Concurrent criterion validity applied to data showed that the scale is able to distinguish between the alienator and target parent. The results showed significant and consistent standards in the instrument's psychometric characteristics.
The psychometric properties of hopelessness scale among children
Directory of Open Access Journals (Sweden)
Mojtaba Habibi
2017-07-01
Full Text Available Hopelessness, or negative expectations toward the future, is considered to be a central feature of depression. This can affect individual’s personal, familial, occupational, educational and social functions negatively. The current research aimed to study the psychometric properties of hopelessness scale in children within the age range of 12-19. After translating items of HSC to Persian, a sample of 603 guidance and high school students (300 girls and 303 boys were selected from all students of Tehran. To measure divergent/convergent validity of the scale, children depression scale (CDI and adolescent’s self-efficacy scale (SEQ-C were performed in parallel. A first-order Confirmatory factor analysis was used to measure hopelessness scale in children (HSC questionnaire. Cronbach’s alpha coefficient of HSC in students was calculated 77% and was relatively satisfactory. The Factor analysis of HSC was confirmed by confirmatory factor analysis. An analysis of correlation coefficients has revealed that HSC has a significant positive relation with depression scale and a significant negative relation with self-efficacy scale which indicates that there is a convergent validity between HSC and depression scale in children and a divergent validity between it and self-efficacy in adolescents. First-order confirmatory factor analysis of HSC scale has shown a better fitness with observed data. The confirmatory factor structure, validity and reliability of HSC were relatively satisfactory for research purposes and clinical diagnoses.
Contrasting scaling properties of interglacial and glacial climates.
Shao, Zhi-Gang; Ditlevsen, Peter D
2016-03-16
Understanding natural climate variability is essential for assessments of climate change. This is reflected in the scaling properties of climate records. The scaling exponents of the interglacial and the glacial climates are fundamentally different. The Holocene record is monofractal, with a scaling exponent H∼0.7. On the contrary, the glacial record is multifractal, with a significantly higher scaling exponent H∼1.2, indicating a longer persistence time and stronger nonlinearities in the glacial climate. The glacial climate is dominated by the strong multi-millennial Dansgaard-Oeschger (DO) events influencing the long-time correlation. However, by separately analysing the last glacial maximum lacking DO events, here we find the same scaling for that period as for the full glacial period. The unbroken scaling thus indicates that the DO events are part of the natural variability and not externally triggered. At glacial time scales, there is a scale break to a trivial scaling, contrasting the DO events from the similarly saw-tooth-shaped glacial cycles.
Homework Emotion Regulation Scale: Psychometric Properties for Middle School Students
Xu, Jianzhong; Fan, Xitao; Du, Jianxia
2016-01-01
The goal of the present investigation is to evaluate the psychometric properties of the Homework Emotion Regulation Scale (HERS) using 796 middle school students in China. Confirmatory factor analyses (CFAs) supported the existence of two distinct yet related subscales for the HERS: Emotion Management and Cognitive Reappraisal. Concerning the…
Scaling properties of net information measures for bound states of ...
Indian Academy of Sciences (India)
Using dimensional analyses, the scaling properties of the Heisenberg uncertainty relationship as well as the various information theoretical uncertainty-like relationships are derived for the bound states corresponding to the superposition of the power potential of the form () = + $^{n_{i}}, where , , , ...
Global scaling properties of the spectrum for the Fibonacci chains
Zheng, W. M.
1987-02-01
By means of the approximate renormalization approach of Niu and Nori [Phys. Rev. Lett. 57, 2057 (1986)] the widths of subband segments in the spectrum and the occupation probabilities on subbands are obtained to the lowest order for the two-value Fibonacci chains. The global scaling properties of the spectrum are then analytically calculated.
Scaling relations for galaxy clusters: Properties and evolution
Giodini, S.; Lovisari, L.; Pointecouteau, E.; Ettori, S.; Reiprich, T.H.; Hoekstra, H.
2013-01-01
Well-calibrated scaling relations between the observable properties and the total masses of clusters of galaxies are important for understanding the physical processes that give rise to these relations. They are also a critical ingredient for studies that aim to constrain cosmological parameters
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.
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.
Multispectral image fusion based on fractal features
Tian, Jie; Chen, Jie; Zhang, Chunhua
2004-01-01
they can be dealt with special rules. There has been various fusion rules developed with each one aiming at a special problem. These rules have different performance, so it is very important to select an appropriate rule during the design of an image fusion system. Recent research denotes that the rule should be adjustable so that it is always suitable to extrude the features of targets and to preserve the pixels of useful information. In this paper, owing to the consideration that fractal dimension is one of the main features to distinguish man-made targets from natural objects, the fusion rule was defined that if the studied region of image contains man-made target, the pixels of the source image whose fractal dimension is minimal are saved to be the pixels of the fused image, otherwise, a weighted average operator is adopted to avoid loss of information. The main idea of this rule is to store the pixels with low fractal dimensions, so it can be named Minimal Fractal dimensions (MFD) fusion rule. This fractal-based algorithm is compared with a common weighted average fusion algorithm. An objective assessment is taken to the two fusion results. The criteria of Entropy, Cross-Entropy, Peak Signal-to-Noise Ratio (PSNR) and Standard Gray Scale Difference are defined in this paper. Reversely to the idea of constructing an ideal image as the assessing reference, the source images are selected to be the reference in this paper. It can be deemed that this assessment is to calculate how much the image quality has been enhanced and the quantity of information has been increased when the fused image is compared with the source images. The experimental results imply that the fractal-based multi-spectral fusion algorithm can effectively preserve the information of man-made objects with a high contrast. It is proved that this algorithm could well preserve features of military targets because that battlefield targets are most man-made objects and in common their images differ from
An Examination of Psychometric Properties of Positive Functional Attitudes Scale
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Saide Umut ZEYBEK
2017-08-01
Full Text Available The aim of this study is to investigate the applicability of Coping Attitudes Scale: Measure of Positive Attitudes in Depression (CAS among Turkish young adult community sample and determine the psychometric properties (validity and reliability of this scale. This study was conducted with 419 students attending different departments in Mugla Sitki Kocman University, Faculty of Education in the spring semester of academic year of 2015-2016. Positive Functional Attitudes Scale, Beck Depression Scale, Beck Hopelessness Scale, Automatic Thoughts Scale, Positivity Scale and Developed Automatic Thoughts Scale.were used as data collection tools. Confirmatory factor analysis (CFA were used for investigation of the psychometric properties of the PFAS. Also, criterion-related validity, test-retest validity, and internal consistency were used calculated. The CFA results showed that standardized item estimates of the CAS ranged between 0.45 and 0.47. Also the CFA results showed that the original factor structure of the PFAS confirmed on the Turkish sample. internal consistency was calculated using the total community samples PFAS score. Cronbachs alpha coefficient ort he total scale (.93 was high. Test-retest results of the subscales were 0.76. The findings showed that factor structures of the PFAS life perspective, personal accomplishment, positive future, self-worth, coping with problems had psychometric quality in Turkish version. As a result of the study, the Turkish version of PFAS has good validity and reliability for young adult community sample. [JCBPR 2017; 6(2.000: 59-66
Fractal analysis of sulphidic mineral
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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
Fractal spectra in generalized Fibonacci one-dimensional magnonic quasicrystals
Energy Technology Data Exchange (ETDEWEB)
Costa, C.H.O. [Departamento de Fisica Teorica e Experimental, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Vasconcelos, M.S., E-mail: manoelvasconcelos@yahoo.com.br [Escola de Ciencias e Tecnologia, Universidade Federal do Rio grande do Norte, 59072-970 Natal-RN (Brazil); Barbosa, P.H.R.; Barbosa Filho, F.F. [Departamento de Fisica, Universidade Federal do Piaui, 64049-550 Teresina-Pi (Brazil)
2012-07-15
In this work we carry out a theoretical analysis of the spectra of magnons in quasiperiodic magnonic crystals arranged in accordance with generalized Fibonacci sequences in the exchange regime, by using a model based on a transfer-matrix method together random-phase approximation (RPA). The generalized Fibonacci sequences are characterized by an irrational parameter {sigma}(p,q), which rules the physical properties of the system. We discussed the magnonic fractal spectra for first three generalizations, i.e., silver, bronze and nickel mean. By varying the generation number, we have found that the fragmentation process of allowed bands makes possible the emergence of new allowed magnonic bulk bands in spectra regions that were magnonic band gaps before, such as which occurs in doped semiconductor devices. This interesting property arises in one-dimensional magnonic quasicrystals fabricated in accordance to quasiperiodic sequences, without the need to introduce some deferent atomic layer or defect in the system. We also make a qualitative and quantitative investigations on these magnonic spectra by analyzing the distribution and magnitude of allowed bulk bands in function of the generalized Fibonacci number F{sub n} and as well as how they scale as a function of the number of generations of the sequences, respectively. - Highlights: Black-Right-Pointing-Pointer Quasiperiodic magnonic crystals are arranged in accordance with the generalized Fibonacci sequence. Black-Right-Pointing-Pointer Heisenberg model in exchange regime is applied. Black-Right-Pointing-Pointer We use a theoretical model based on a transfer-matrix method together random-phase approximation. Black-Right-Pointing-Pointer Fractal spectra are characterized. Black-Right-Pointing-Pointer We analyze the distribution of allowed bulk bands in function of the generalized Fibonacci number.
Fractal Characteristics Analysis of Blackouts in Interconnected Power Grid
DEFF Research Database (Denmark)
Wang, Feng; Li, Lijuan; Li, Canbing
2018-01-01
The power failure models are a key to understand the mechanism of large scale blackouts. In this letter, the similarity of blackouts in interconnected power grids (IPGs) and their sub-grids is discovered by the fractal characteristics analysis to simplify the failure models of the IPG. The distri......The power failure models are a key to understand the mechanism of large scale blackouts. In this letter, the similarity of blackouts in interconnected power grids (IPGs) and their sub-grids is discovered by the fractal characteristics analysis to simplify the failure models of the IPG....... The distribution characteristics of blackouts in various sub-grids are demonstrated based on the Kolmogorov-Smirnov (KS) test. The fractal dimensions (FDs) of the IPG and its sub-grids are then obtained by using the KS test and the maximum likelihood estimation (MLE). The blackouts data in China were used...
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.
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
Beyond Fractals and 1/f Noise: Multifractal Analysis of Complex Physiological Time Series
Ivanov, Plamen Ch.; Amaral, Luis A. N.; Ashkenazy, Yosef; Stanley, H. Eugene; Goldberger, Ary L.; Hausdorff, Jeffrey M.; Yoneyama, Mitsuru; Arai, Kuniharu
2001-03-01
We investigate time series with 1/f-like spectra generated by two physiologic control systems --- the human heartbeat and human gait. We show that physiological fluctuations exhibit unexpected ``hidden'' structures often described by scaling laws. In particular, our studies indicate that when analyzed on different time scales the heartbeat fluctuations exhibit cascades of branching patterns with self-similar (fractal) properties, characterized by long-range power-law anticorrelations. We find that these scaling features change during sleep and wake phases, and with pathological perturbations. Further, by means of a new wavelet-based technique, we find evidence of multifractality in the healthy human heartbeat even under resting conditions, and show that the multifractal character and nonlinear properties of the healthy heart are encoded in the Fourier phases. We uncover a loss of multifractality for a life-threatening condition, congestive heart failure. In contrast to the heartbeat, we find that the interstride interval time series of healthy human gait, a voluntary process under neural regulation, is described by a single fractal dimension (such as classical 1/f noise) indicating monofractal behavior. Thus our approach can help distinguish physiological and physical signals with comparable frequency spectra and two-point correlations, and guide modeling of their control mechanisms.
Fractal Globule as a model of DNA folding in eukaryotes
Imakaev, Maksim; Mirny, Leonid
2012-02-01
A recent study (Lieberman-Aiden et al., Science, 2009) observed that the structure of the genome, on the scale of a few megabases, is consistent with a fractal globule. The fractal globule is a quasi-equilibrium state of a polymer after a rapid collapse. First proposed theoretically in 1988, this structure had never been simulated. Fractal globule was seen as a state, in which each subchain is compact, and doesn't mix with other subchains due to their mutual unentanglement (topological constraints). We use GPU-assisted dynamics to create fractal globules of different sizes and observe their dynamics. Our simulations confirm that a polymer after rapid collapse has compact subchains. We measure the scaling of looping probability of a subchain with it's length, and observe the remarkably robust inverse proportionality. Dynamic simulation of the equilibration of this state show that it exhibits Rose type subdiffusion. Due to diffusion, fractal globule quickly degrades to a quasi-equilibrium state, in which subchains of a polymer are mixed, but topologically unentangled. We propose that separation of spatial and topological equilibration of a polymer chain might have implications in different fields of physics.
Fractal gases of zero momentum with respect to all inertial frames
Moore, Guy S. M.
1990-06-01
Unlike gases containing molecules obeying Maxwell-Boltzmann statistics, ``fractal gases'' obey the fundamental axiom that their linear momentum is zero when resolved in any direction with respect to all inertial frames of reference. In contrast to speculation, the properties of fractal gases obeying Newtonian mechanics, or special or general relativity can be investigated in a way similar to the logic of geometry. They have the following properties: (1) An entire fractal gas cannot decay into a Maxwell-Boltzmann distribution, but is in a state of overall equilibrium. (2) Localities tend toward localized equilibrium, upset later by collision with other localities. (3) Fractal gases contain temperature differences that are a source of temporary order. (4) The appearance of a fractal gas to a hypothetical observer would suggest creation in an initial discontinuity.
Fractal dimension analysis for spike detection in low SNR extracellular signals.
Salmasi, Mehrdad; Büttner, Ulrich; Glasauer, Stefan
2016-06-01
Many algorithms have been suggested for detection and sorting of spikes in extracellular recording. Nevertheless, it is still challenging to detect spikes in low signal-to-noise ratios (SNR). We propose a spike detection algorithm that is based on the fractal properties of extracellular signals and can detect spikes in low SNR regimes. Semi-intact spikes are low-amplitude spikes whose shapes are almost preserved. The detection of these spikes can significantly enhance the performance of multi-electrode recording systems. Semi-intact spikes are simulated by adding three noise components to a spike train: thermal noise, inter-spike noise, and spike-level noise. We show that simulated signals have fractal properties which make them proper candidates for fractal analysis. Then we use fractal dimension as the main core of our spike detection algorithm and call it fractal detector. The performance of the fractal detector is compared with three frequently used spike detectors. We demonstrate that in low SNR, the fractal detector has the best performance and results in the highest detection probability. It is shown that, in contrast to the other three detectors, the performance of the fractal detector is independent of inter-spike noise power and that variations in spike shape do not alter its performance. Finally, we use the fractal detector for spike detection in experimental data and similar to simulations, it is shown that the fractal detector has the best performance in low SNR regimes. The detection of low-amplitude spikes provides more information about the neural activity in the vicinity of the recording electrodes. Our results suggest using the fractal detector as a reliable and robust method for detecting semi-intact spikes in low SNR extracellular signals.
Properties Important To Mixing For WTP Large Scale Integrated Testing
International Nuclear Information System (INIS)
Koopman, D.; Martino, C.; Poirier, M.
2012-01-01
Large Scale Integrated Testing (LSIT) is being planned by Bechtel National, Inc. to address uncertainties in the full scale mixing performance of the Hanford Waste Treatment and Immobilization Plant (WTP). Testing will use simulated waste rather than actual Hanford waste. Therefore, the use of suitable simulants is critical to achieving the goals of the test program. External review boards have raised questions regarding the overall representativeness of simulants used in previous mixing tests. Accordingly, WTP requested the Savannah River National Laboratory (SRNL) to assist with development of simulants for use in LSIT. Among the first tasks assigned to SRNL was to develop a list of waste properties that matter to pulse-jet mixer (PJM) mixing of WTP tanks. This report satisfies Commitment 5.2.3.1 of the Department of Energy Implementation Plan for Defense Nuclear Facilities Safety Board Recommendation 2010-2: physical properties important to mixing and scaling. In support of waste simulant development, the following two objectives are the focus of this report: (1) Assess physical and chemical properties important to the testing and development of mixing scaling relationships; (2) Identify the governing properties and associated ranges for LSIT to achieve the Newtonian and non-Newtonian test objectives. This includes the properties to support testing of sampling and heel management systems. The test objectives for LSIT relate to transfer and pump out of solid particles, prototypic integrated operations, sparger operation, PJM controllability, vessel level/density measurement accuracy, sampling, heel management, PJM restart, design and safety margin, Computational Fluid Dynamics (CFD) Verification and Validation (V and V) and comparison, performance testing and scaling, and high temperature operation. The slurry properties that are most important to Performance Testing and Scaling depend on the test objective and rheological classification of the slurry (i
Breakdown coefficients and scaling properties of rain fields
Directory of Open Access Journals (Sweden)
D. Harris
1998-01-01
Full Text Available The theory of scale similarity and breakdown coefficients is applied here to intermittent rainfall data consisting of time series and spatial rain fields. The probability distributions (pdf of the logarithm of the breakdown coefficients are the principal descriptor used. Rain fields are distinguished as being either multiscaling or multiaffine depending on whether the pdfs of breakdown coefficients are scale similar or scale dependent, respectively. Parameter estimation techniques are developed which are applicable to both multiscaling and multiaffine fields. The scale parameter (width, σ, of the pdfs of the log-breakdown coefficients is a measure of the intermittency of a field. For multiaffine fields, this scale parameter is found to increase with scale in a power-law fashion consistent with a bounded-cascade picture of rainfall modelling. The resulting power-law exponent, H, is indicative of the smoothness of the field. Some details of breakdown coefficient analysis are addressed and a theoretical link between this analysis and moment scaling analysis is also presented. Breakdown coefficient properties of cascades are also investigated in the context of parameter estimation for modelling purposes.
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...
Scale-dependent Hausdorff dimensions in 2d gravity
Directory of Open Access Journals (Sweden)
J. Ambjørn
2014-09-01
Full Text Available By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized causal dynamical triangulations and ordinary dynamical triangulations. We study the fractal properties of the associated continuum geometries and identify both global and local Hausdorff dimensions.
Scale-dependent Hausdorff dimensions in 2d gravity
Energy Technology Data Exchange (ETDEWEB)
Ambjørn, J., E-mail: ambjorn@nbi.dk [Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark); Institute for Mathematics, Astrophysics and Particle Physics (IMAPP), Radbaud University Nijmegen, Heyendaalseweg 135, 6525 AJ, Nijmegen (Netherlands); Budd, T., E-mail: budd@nbi.dk [Niels Bohr Institute, Copenhagen University, Blegdamsvej 17, DK-2100 Copenhagen Ø (Denmark); Watabiki, Y., E-mail: watabiki@th.phys.titech.ac.jp [Tokyo Institute of Technology, Dept. of Physics, High Energy Theory Group, 2-12-1 Oh-okayama, Meguro-ku, Tokyo 152-8551 (Japan)
2014-09-07
By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized) causal dynamical triangulations and ordinary dynamical triangulations. We study the fractal properties of the associated continuum geometries and identify both global and local Hausdorff dimensions.
Persistent fluctuations in stride intervals under fractal auditory stimulation.
Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J; Daffertshofer, Andreas
2014-01-01
Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.
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
Psychometric properties of a scale to measure alexithymia.
Blanchard, E B; Arena, J G; Pallmeyer, T P
1981-01-01
Four studies were conducted on a sample of 230 undergraduates to determine the psychometric properties of a measure of alexithymia, the Schalling-Sifneos Scale. In the first study it was found that scores on the scale are approximately normally distributed for each sex with 8.2% of males and 1.8% of females in the alexithymia range. In the second study a factor analysis of the scale revealed three distinct factors: (1) 'difficulty in expression of feelings'; (2) 'the importance of feelings especially about people'; (3) 'day-dreaming or introspection'. In the second factor analytic study, scores from several standard psychological tests on the same subjects were introduced with the scale items. Two factors in this analysis were comprised almost entirely of the other test scores: a 'general psychological distress factor' and a 'concerns about physical symptoms factor'. The other two factors were similar to factors 1 and 2 above in terms of items. The Rathus Assertiveness Scale loaded positively on the equivalent of factor 1. In the lst study, it was shown that Schalling-Sifneos Scale score is relatively orthogonal to other psychological tests with the exception of a Psychosomatic Symptom Checklist and thus is measuring something other than depression, anxiety, etc.
Fractal symmetry of protein interior: what have we learned?
Banerji, Anirban; Ghosh, Indira
2011-08-01
The application of fractal dimension-based constructs to probe the protein interior dates back to the development of the concept of fractal dimension itself. Numerous approaches have been tried and tested over a course of (almost) 30 years with the aim of elucidating the various facets of symmetry of self-similarity prevalent in the protein interior. In the last 5 years especially, there has been a startling upsurge of research that innovatively stretches the limits of fractal-based studies to present an array of unexpected results on the biophysical properties of protein interior. In this article, we introduce readers to the fundamentals of fractals, reviewing the commonality (and the lack of it) between these approaches before exploring the patterns in the results that they produced. Clustering the approaches in major schools of protein self-similarity studies, we describe the evolution of fractal dimension-based methodologies. The genealogy of approaches (and results) presented here portrays a clear picture of the contemporary state of fractal-based studies in the context of the protein interior. To underline the utility of fractal dimension-based measures further, we have performed a correlation dimension analysis on all of the available non-redundant protein structures, both at the level of an individual protein and at the level of structural domains. In this investigation, we were able to separately quantify the self-similar symmetries in spatial correlation patterns amongst peptide-dipole units, charged amino acids, residues with the π-electron cloud and hydrophobic amino acids. The results revealed that electrostatic environments in the interiors of proteins belonging to 'α/α toroid' (all-α class) and 'PLP-dependent transferase-like' domains (α/β class) are highly conducive. In contrast, the interiors of 'zinc finger design' ('designed proteins') and 'knottins' ('small proteins') were identified as folds with the least conducive electrostatic
The small-scale clustering properties of dwarf galaxies
Vader, J. P.; Sandage, Allan
1991-01-01
Two results on the small-scale clustering properties of dwarf galaxies are reported, which were identified in the vicinity of early-type Shapley-Ames galaxies on high-resolution photographic plates. The first result indicates that dwarf galaxies display the same trend of stronger clustering toward earlier morphological type on small scales as their giant counterparts on larger scales. It is suggested that early-type dwarfs can be used as dynamical probes of dark halos around early-type giant galaxies and as tracers of the dynamical evolution of such halos in dense environments. The second result pertains to the trend of increasing early-type dwarf frequency per early-type giant with environment richness previously established for rich groups. It is found that a minimum value of isolated early-type galaxies is approximately 0.25, as compared to a maximum of approximately 8 in rich environments like the Virgo Cluster.
[Psychometric properties of the Activities Daily Life Scale (ADL)].
Boyer, L; Murcia, A; Belzeaux, R; Loundou, A; Azorin, J-M; Chabannes, J-M; Dassa, D; Naudin, J; Samuelian, J-C; Lancon, C
2010-10-01
Deficits in social functioning are an important core feature of mental health. Recently in France, the Activities Daily Life (ADL) scale has been proposed by the French authorities to assess social functioning for all hospitalized patients in a psychiatric ward. The perspective is to use this scale in the financing and organization of mental health services in France. The ADL scale is a 6-item (dressing/undressing, walking/mobility, eating/drinking, using toilets, behaviour, relationships/communication) heteroquestionnaire completed by a health care professional at the beginning of each hospitalization, assessing functioning of patients suffering from mental health diseases. However, limited consensus exists on this scale. The psychometric properties of the ADL scale have not been assessed. There is a pressing need for detailed examination of its performance. The aim of this study was to explore ADL psychometric properties in a sample of hospitalized patients in a psychiatric ward. We retrospectively analyzed data for all episodes of care delivered to hospitalized patients in a psychiatric ward in our French Public Hospital from January 1, 2008 to June 30, 2008. The study involved retrospective review of administrative and medical databases. The following data were collected: age, gender, diagnoses based on the International Classification of Diseases - 10th version, ADL scale and Assessment of Social Self-Sufficiency scale (ASSS). The psychometric properties were examined using construct validity, reliability, external validity, reproducibility and sensitivity to change. Data analysis was performed using SPSS 15.0 and WINSTEP software. A total of 1066 patients completed the ADL scale. Among them, 49.7% were male, mean age was 36.5 ± 10.8, and 83.5% were single. Schizophrenia, schizotypal and delusional disorders (40.0%), mood disorders (27.9%) and mental and behavioural disorders due to psychoactive substance use (12%) were the most common diagnoses. Factor
Assessing organizational climate: psychometric properties of the CLIOR Scale.
Peña-Suárez, Elsa; Muñiz, José; Campillo-Álvarez, Angela; Fonseca-Pedrero, Eduardo; García-Cueto, Eduardo
2013-02-01
Organizational climate is the set of perceptions shared by workers who occupy the same workplace. The main goal of this study is to develop a new organizational climate scale and to determine its psychometric properties. The sample consisted of 3,163 Health Service workers. A total of 88.7% of participants worked in hospitals, and 11.3% in primary care; 80% were women and 20% men, with a mean age of 51.9 years (SD= 6.28). The proposed scale consists of 50 Likert-type items, with an alpha coefficient of 0.97, and an essentially one-dimensional structure. The discrimination indexes of the items are greater than 0.40, and the items show no differential item functioning in relation to participants' sex. A short version of the scale was developed, made up of 15 items, with discrimination indexes higher than 0.40, an alpha coefficient of 0.94, and its structure was clearly one-dimensional. These results indicate that the new scale has adequate psychometric properties, allowing a reliable and valid assessment of organizational climate.
Development and psychometric properties of the Inner Strength Scale.
Lundman, Berit; Viglund, Kerstin; Aléx, Lena; Jonsén, Elisabeth; Norberg, Astrid; Fischer, Regina Santamäki; Strandberg, Gunilla; Nygren, Björn
2011-10-01
Four dimensions of inner strength were previously identified in a meta-theoretical analysis: firmness, creativity, connectedness, and flexibility. The aim of this study was to develop an Inner Strength Scale (ISS) based on those four dimensions and to evaluate its psychometric properties. An initial version of ISS was distributed for validation purpose with the Rosenberg Self-Esteem Scale, the resilience scale, and the sense of Coherence Scale. A convenience sample of 391 adults, aged 19-90 years participated. Principal component analysis (PCA) and confirmatory factor analysis (CFA) were used in the process of exploring, evaluating, and reducing the 63-item ISS to the 20-item ISS. Cronbach's alpha and test-retest were used to measure reliability. CFA showed satisfactory goodness-of-fit for the 20-item ISS. The analysis supported a fourfactor solution explaining 51% of the variance. Cronbach's alpha on the 20-item ISS was 0.86, and the test-retest showed stability over time (r=0.79). The ISS was found to be a valid and reliable instrument for capturing a multifaceted understanding of inner strength. Further tests of psychometric properties of the ISS will be performed in forthcoming studies. Copyright © 2011 Elsevier Ltd. All rights reserved.
The Metacognitions about Online Gaming Scale: Development and psychometric properties.
Spada, Marcantonio M; Caselli, Gabriele
2017-01-01
Recent research has suggested that metacognitions may play a role across the spectrum of addictive behaviours. The goal of our studies was to develop the first self-report scale of metacognitions about online gaming. We conducted two studies with samples of online gamers (n=225, n=348) to test the structure and psychometric properties of the Metacognitions about Online Gaming Scale and examined its capacity to predict weekly online gaming hours and Internet addiction. Exploratory and confirmatory factor analyses supported a three-factor solution: positive metacognitions about online gaming, negative metacognitions about the uncontrollability of online gaming, and negative metacognitions about the dangers of online gaming. Internal consistency, predictive and divergent validity were acceptable. All the factors of the Metacognitions about Online Gaming Scale correlated positively with weekly online gaming hours and Internet addiction. Regression analyses showed that negative metacognitions about the uncontrollability of online gaming and levels of Internet addiction were the only significant predictors of weekly online gaming hours, and that positive metacognitions about online gaming and negative metacognitions about the uncontrollability of online gaming were the only significant predictors of Internet addiction. The Metacognitions about Online Gaming Scale was shown to possess good psychometric properties, as well as predictive and divergent validity within the populations that were tested. Copyright © 2015 Elsevier Ltd. All rights reserved.
Wei Shen
2011-01-01
The self-similar is a common phenomena arising in the field of geology. It has been shown that geochemical element data, mineral deposits, and spacial distribution conform to a fractal structure. A fractal distribution requires that the number of objects larger than a specified size have a power-law dependence on size. This paper shows that a number of distributions, including power-function, Pareto, lognormal, and Zipf, display fractal properties under certain conditions and that this may be...
A Esmailpour; N Mostoufi; R Zarghami
2016-01-01
A study has been conducted to determine the effects of operating conditions such as vibration frequency, vibration amplitude on the fractal structure of silica (SiO2) nanoparticle agglomerate in a vibro-fluidized bed. An improved model was proposed by assimilation of fractal theory, Richardson-Zaki equation and mass balance. This model has been developed to predict the properties of nanoparticle agglomerate, such as fractal dimension and its size. It has been found out the vibration intensity...
Fractal Characteristics Analysis of Blackouts in Interconnected Power Grid
Wang, Feng; Li, Lijuan; Li, Canbing; Wu, Qiuwei; Cao, Yijia; Zhou, Bin; Fang, Baling
2018-01-01
The power failure models are a key to understand the mechanism of large scale blackouts. In this letter, the similarity of blackouts in interconnected power grids (IPGs) and their sub-grids is discovered by the fractal characteristics analysis to simplify the failure models of the IPG. The distribution characteristics of blackouts in various sub-grids are demonstrated based on the Kolmogorov-Smirnov (KS) test. The fractal dimensions (FDs) of the IPG and its sub-grids are then obtained by usin...
Towards Video Quality Metrics Based on Colour Fractal Geometry
Directory of Open Access Journals (Sweden)
Richard Noël
2010-01-01
Full Text Available Vision is a complex process that integrates multiple aspects of an image: spatial frequencies, topology and colour. Unfortunately, so far, all these elements were independently took into consideration for the development of image and video quality metrics, therefore we propose an approach that blends together all of them. Our approach allows for the analysis of the complexity of colour images in the RGB colour space, based on the probabilistic algorithm for calculating the fractal dimension and lacunarity. Given that all the existing fractal approaches are defined only for gray-scale images, we extend them to the colour domain. We show how these two colour fractal features capture the multiple aspects that characterize the degradation of the video signal, based on the hypothesis that the quality degradation perceived by the user is directly proportional to the modification of the fractal complexity. We claim that the two colour fractal measures can objectively assess the quality of the video signal and they can be used as metrics for the user-perceived video quality degradation and we validated them through experimental results obtained for an MPEG-4 video streaming application; finally, the results are compared against the ones given by unanimously-accepted metrics and subjective tests.
Controlling the efficiency of trapping in treelike fractals.
Wu, Bin; Zhang, Zhongzhi
2013-07-14
Efficiently controlling the trapping process, especially the trapping efficiency, is central in the study of trap problem in complex systems, since it is a fundamental mechanism for diverse other dynamic processes. Thus, it is of theoretical and practical significance to study the control technique for trapping problem. In this paper, we study the trapping problem in a family of proposed directed fractals with a deep trap at a central node. The directed fractals are a generalization of previous undirected fractals by introducing the directed edge weights dominated by a parameter. We characterize all the eigenvalues and their degeneracies for an associated matrix governing the trapping process. The eigenvalues are provided through an exact recursive relation deduced from the self-similar structure of the fractals. We also obtain the expressions for the smallest eigenvalue and the mean first-passage time (MFPT) as a measure of trapping efficiency, which is the expected time for the walker to first visit the trap. The MFPT is evaluated according to the proved fact that it is approximately equal to reciprocal of the smallest eigenvalue. We show that the MFPT is controlled by the weight parameter by modifying which the MFPT can scale superlinealy, linearly, or sublinearly with the system size. Thus, this work paves a way to delicately controlling the trapping process in the fractals.
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 new modified fast fractal image compression algorithm
DEFF Research Database (Denmark)
Salarian, Mehdi; Nadernejad, Ehsan; MiarNaimi, Hossein
2013-01-01
In this paper, a new fractal image compression algorithm is proposed, in which the time of the encoding process is considerably reduced. The algorithm exploits a domain pool reduction approach, along with the use of innovative predefined values for contrast scaling factor, S, instead of searching...
A fractal model for intergranular fractures in nanocrystals
International Nuclear Information System (INIS)
Lung, C.W.; Xiong, L.Y.; Zhou, X.Z.
1993-09-01
A fractal model for intergranular fractures in nanocrystals is proposed to explain the dependence of fracture toughness with grain size in this range of scale. Based on positron annihilation and internal friction experimental results, we point out that the assumption of a constant grain boundary thickness in previous models is too simplified to be true. (author). 7 refs, 6 figs
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
Multiscale Fractal Characterization of Hierarchical Heterogeneity in Sandstone Reservoirs
Liu, Yanfeng; Liu, Yuetian; Sun, Lu; Liu, Jian
2016-07-01
Heterogeneities affecting reservoirs often develop at different scales. Previous studies have described these heterogeneities using different parameters depending on their size, and there is no one comprehensive method of reservoir evaluation that considers every scale. This paper introduces a multiscale fractal approach to quantify consistently the hierarchical heterogeneities of sandstone reservoirs. Materials taken from typical depositional pattern and aerial photography are used to represent three main types of sandstone reservoir: turbidite, braided, and meandering river system. Subsequent multiscale fractal dimension analysis using the Bouligand-Minkowski method characterizes well the hierarchical heterogeneity of the sandstone reservoirs. The multiscale fractal dimension provides a curve function that describes the heterogeneity at different scales. The heterogeneity of a reservoir’s internal structure decreases as the observational scale increases. The shape of a deposit’s facies is vital for quantitative determination of the sedimentation type, and thus enhanced oil recovery. Characterization of hierarchical heterogeneity by multiscale fractal dimension can assist reservoir evaluation, geological modeling, and even the design of well patterns.
Cathodic Arcs From Fractal Spots to Energetic Condensation
Anders, Andre
2009-01-01
Emphasizes the fractal character of cathode spots, and describes strongly fluctuating plasma properties such as the presence of multiply charged ions that move with supersonic velocity. This book also deals with issues, such as arc source construction, and macroparticle removal. It is intended for scientists, practitioners, and students alike
From quantum fields to fractal structures: intermittency in particle physics
International Nuclear Information System (INIS)
Peschanski, R.
1991-01-01
Some features and theoretical interpretations of the intermittency phenomenon observed in high-energy multi-particle production are recalled. One develops on the various connections found with fractal structuration of fluctuations in turbulence, spin-glass physics and aggregation phenomena described by the non-linear Smoluchowski equation. This may lead to a new approach to quantum field properties
Estimation of soil water retention curve using fractal dimension ...
African Journals Online (AJOL)
The soil water retention curve (SWRC) is a fundamental hydraulic property majorly used to study flow transport in soils and calculate plant-available water. Since, direct measurement of SWRC is time-consuming and expensive, different models have been developed to estimate SWRC. In this study, a fractal-based model ...
Colloid-facilitated contaminant transport in fractal media
Bolshov, Leonid A.; Kondratenko, Peter S.; Matveev, Leonid V.
2011-10-01
We investigate colloid-facilitated contaminant advection in strongly heterogeneous geological medium with fractal properties. Transport regimes and asymptotic behavior at large distances are studied for different relationships between sorption parameters and characteristics of percolation medium. Crossover times between transport regimes are determined.
Magnetic Reconnection Rate in Space Plasmas: A Fractal Approach
International Nuclear Information System (INIS)
Materassi, Massimo; Consolini, Giuseppe
2007-01-01
Magnetic reconnection is generally discussed via a fluid description. Here, we evaluate the reconnection rate assuming a fractal topology of the reconnection region. The central idea is that the fluid hypothesis may be violated at the scales where reconnection takes place. The reconnection rate, expressed as the Alfven Mach number of the plasma moving toward the diffusion region, is shown to depend on the fractal dimension and on the sizes of the reconnection or diffusion region. This mechanism is more efficient than prediction of the Sweet-Parker model and even Petschek's model for finite magnetic Reynolds number. A good agreement also with rates given by Hall MHD models is found. A discussion of the fractal assumption on the diffusion region in terms of current microstructures is proposed. The comparison with in-situ satellite observations suggests the reconnection region to be a filamentary domain
arXiv Generalized Fragmentation Functions for Fractal Jet Observables
Elder, Benjamin T.; Thaler, Jesse; Waalewijn, Wouter J.; Zhou, Kevin
2017-06-15
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phen...
Navigation performance in virtual environments varies with fractal dimension of landscape.
Juliani, Arthur W; Bies, Alexander J; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E
2016-09-01
Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.
Validation and psychometric properties of the State Impulsivity Scale (SIS).
Iribarren, M M; Jiménez-Giménez, M; García-de Cecilia, J M; Rubio-Valladolid, G
2011-01-01
Impulsivity is a complex phenomenon that can be evaluated from a trait or state perspective. Impulsive trait is a predisposition relatively stable over time, but not always perceptible by behavior. However, the impulsivity state covers transient variations on impulsivity levels that are dependent on environmental or biologic conditions. This study has aimed to validate a scale to assess impulsivity as a state in a Spanish sample. State Impulsivity Scale (SIS) was designed based on three experimental models: Reward, Automatism and Attentional. All the items in the SIS explore the presence and frequency of impulsive behaviors. Statistical analyses of reliability and validity were done. Convergent validity was examined by means of correlations among SIS and Barratt Impulsiveness Scale (BIS-11), Sensitivity to the punishment and sensitivity to the reward questionnaire (SPSRQ) and Sensations Seeking Scale type V (SSS). We used a Spanish sample of 70 patients who had at least one diagnosis of Impulse Control Disorder (IP), 73 psychiatric patients without impulsive disorders (NIP) and 150 control subjects (CS). The values obtained reveal the high reliability of the SIS (Cronbach's alpha coefficients 0.884), factor analysis confirmed the theoretical three-dimensional structure and convergent validity was excellent. SIS also demonstrated its capacity for discrimination among IP group and NIP and CS groups. SIS is a new impulsive behavior assessment instrument validated in Spanish population. The results obtained indicate adequate psychometric properties for its use in the clinical and research fields. Key Words: State Impulsivity, Trait, Evaluation, Scale.
Asymmetric multi-fractality in the U.S. stock indices using index-based model of A-MFDFA
International Nuclear Information System (INIS)
Lee, Minhyuk; Song, Jae Wook; Park, Ji Hwan; Chang, Woojin
2017-01-01
Highlights: • ‘Index-based A-MFDFA’ model is proposed to assess the asymmetric multi-fractality. • The asymmetric multi-fractality in the U.S. stock indices are investigated using ‘Index-based’ and ‘Return-based’ A-MFDFA. • The asymmetric feature is more significantly identified by ‘Index-based’ model than ‘return-based’ model. • Source of multi-fractality and time-varying features are analyzed. - Abstract: We detect the asymmetric multi-fractality in the U.S. stock indices based on the asymmetric multi-fractal detrended fluctuation analysis (A-MFDFA). Instead using the conventional return-based approach, we propose the index-based model of A-MFDFA where the trend based on the evolution of stock index rather than stock price return plays a role for evaluating the asymmetric scaling behaviors. The results show that the multi-fractal behaviors of the U.S. stock indices are asymmetric and the index-based model detects the asymmetric multi-fractality better than return-based model. We also discuss the source of multi-fractality and its asymmetry and observe that the multi-fractal asymmetry in the U.S. stock indices has a time-varying feature where the degree of multi-fractality and asymmetry increase during the financial crisis.
Synthesis of the advance in and application of fractal characteristics of traffic flow : summary.
2013-07-01
Fractals are geometric objects that are selfsimilar, meaning that their basic structure : remains the same regardless of the scale of : magnification. Self-similarity is readily seen in : nature, for example, in trees, coastlines, clouds, : etc. ...
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.
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.
Directory of Open Access Journals (Sweden)
N. Yonaiguchi
2007-08-01
Full Text Available The VHF electromagnetic noise intensity data at several stations in the Tohoku area of Japan during the period of a rather large (with magnitude of 7.2 earthquake (Miyagi-ken oki earthquake taken place on 16 August 2005, are analyzed by means of different fractal analysis methods, including (1 spectral slope estimation, (2 multi-fractal detrended fluctuation analysis and (3 multi-fractal wavelet transform modulus maxima method. It seems to the authors that there is no definite analysis method for the analysis of any seismogenic phenomenon, so that the only way we have to take, is to apply different methods to the same data for the detailed comparison of the results. This comparison enables us to deduce the properties commonly observed by the above methods. Because the most important feature common to these three methods, is that significant changes in fractal scaling characteristics are observed just during the earthquake (mainly before the earthquake only at one station of Kunimi. Finally, we can come to the definite conclusion on the self-organization of VHF emissions only at one station in the present case.
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.
The number of elementary particles in a fractal M-theory of 11.2360667977 dimensions
International Nuclear Information System (INIS)
He, J.-H.
2007-01-01
It is generally accepted that there are 60 experimentally found particles. The standard model strongly predicts two more hypothetical particles, the Higgs and the graviton. This paper reveals other possible scenario for predicting 69 particles at different energy scales in 11+φ 3 fractal dimensions of a fractal M theory, where φ=(5-1)/2. A modified Newton's law is suggested to experimentally verify our predictions at extremely small quantum scales. The modified Newton's law is in harmony with Heisenberg's uncertainty principle
Multiscale analysis of depth images from natural scenes: Scaling in the depth of the woods
International Nuclear Information System (INIS)
Chéné, Yann; Belin, Étienne; Rousseau, David; Chapeau-Blondeau, François
2013-01-01
We analyze an ensemble of images from outdoor natural scenes and consisting of pairs of a standard gray-level luminance image associated with a depth image of the same scene, delivered by a recently introduced low-cost sensor for joint imaging of depth and luminance. We specially focus on statistical analysis of multiscale and fractal properties in the natural images. Two methodologies are implemented for this purpose, and examining the distribution of contrast upon coarse-graining at increasing scales, and the orientationally averaged power spectrum tied to spatial frequencies. Both methodologies confirm, on another independent dataset here, the presence of fractal scale invariance in the luminance natural images, as previously reported. Both methodologies here also reveal the presence of fractal scale invariance in the novel data formed by depth images from natural scenes. The multiscale analysis is confronted on luminance images and on the novel depth images together with an analysis of their statistical correlation. The results, especially the new results on the multiscale analysis of depth images, consolidate the importance and extend the multiplicity of aspects of self-similarity and fractal scale invariance properties observable in the constitution of images from natural scenes. Such results are useful to better understanding and modeling of the (multiscale) structure of images from natural scenes, with relevance to image processing algorithms and to visual perception. The approach also contains potentialities for the fractal characterization of three-dimensional natural structures and their interaction with light
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.
Evaluating the psychometric properties of the Jacelon Attributed Dignity Scale.
Jacelon, Cynthia S; Choi, Jeungok
2014-09-01
To develop and psychometrically test the Jacelon Attributed Dignity Scale (JADS). The JADS was designed to measure self-perceived attributed dignity in community-dwelling older adults. Attributed dignity was conceived of as a state characteristic of the self. The JADS is a short, positively scored, norm-referenced, evaluation index designed to measure self-perceived attributed dignity during the last week. Instrument development and testing including psychometric properties, internal consistency, factor structure, temporal stability and construct validity. Using a quota sample, 289 older adults (65-99 years old) were recruited from senior centres in western New England to complete the JADS, demographic information, the Self-Esteem Scale and the Social Desirability Scale during 2010-2011. Descriptive statistics, exploratory factor analysis, construct validity and temporal stability were evaluated. The resulting positively scored 18-item scale has four factors with high internal consistency for each factor and the entire scale. Construct validity was established by examining correlations with instruments that measured self-esteem and social desirability. Attributed dignity is a unique concept that is stable over time. The JADS is an 18-item Likert-scaled instrument designed to measure attributed dignity. Attributed dignity is a concept with four factors and is defined as a cognitive component of the self-connoting self-value, perceived value from others, self in relation to others and behaving with respect. The importance of attributed dignity for older adults in relation to health, function, independence, quality of life and successful ageing can now be evaluated. © 2014 John Wiley & Sons Ltd.
Crystalline metamaterials for topological properties at subwavelength scales.
Yves, Simon; Fleury, Romain; Berthelot, Thomas; Fink, Mathias; Lemoult, Fabrice; Lerosey, Geoffroy
2017-07-18
The exciting discovery of topological condensed matter systems has lately triggered a search for their photonic analogues, motivated by the possibility of robust backscattering-immune light transport. However, topological photonic phases have so far only been observed in photonic crystals and waveguide arrays, which are inherently physically wavelength scaled, hindering their application in compact subwavelength systems. In this letter, we tackle this problem by patterning the deep subwavelength resonant elements of metamaterials onto specific lattices, and create crystalline metamaterials that can develop complex nonlocal properties due to multiple scattering, despite their very subwavelength spatial scale that usually implies to disregard their structure. These spatially dispersive systems can support subwavelength topological phases, as we demonstrate at microwaves by direct field mapping. Our approach gives a straightforward tabletop platform for the study of photonic topological phases, and allows to envision applications benefiting the compactness of metamaterials and the amazing potential of topological insulators.
Psychometric properties of a pictorial scale measuring correct condom use.
Li, Qing; Li, Xiaoming; Stanton, Bonita; Wang, Bo
2011-02-01
This study was designed to assess the psychometric properties of a pictorial scale of correct condom use (PSCCU) using data from female sex workers (FSWs) in China. The psychometric properties assessed in this study include construct validity by correlations and known-group validation. The study sample included 396 FSWs in Guangxi, China. The results demonstrate adequate validity of the PSCCU among the study population. FSWs with a higher level of education scored significantly higher on the PSCCU than those with a lower level of education. FSWs who self-reported appropriate condom use with stable partners scored significantly higher on PSCCU than their counterparts. The PSCCU should provide HIV/STI prevention researchers and practitioners with a valid alternative assessment tool among high-risk populations, especially in resource-limited settings.
Mechanical Properties of Materials with Nanometer Scale Microstructures
Energy Technology Data Exchange (ETDEWEB)
William D. Nix
2004-10-31
We have been engaged in research on the mechanical properties of materials with nanometer-scale microstructural dimensions. Our attention has been focused on studying the mechanical properties of thin films and interfaces and very small volumes of material. Because the dimensions of thin film samples are small (typically 1 mm in thickness, or less), specialized mechanical testing techniques based on nanoindentation, microbeam bending and dynamic vibration of micromachined structures have been developed and used. Here we report briefly on some of the results we have obtained over the past three years. We also give a summary of all of the dissertations, talks and publications completed on this grant during the past 15 years.
Psychometric Properties of the Dutch Rosenberg Self-Esteem Scale
Directory of Open Access Journals (Sweden)
Erik Franck
2008-01-01
Full Text Available Interest in self-esteem has been fuelled by the suggestion that level of self-esteem is associated with psychological well-being. In the present study, we translated the Rosenberg Self-Esteem Scale (RSES into the Dutch language and evaluated its psychometric properties in a sample of 442 adults. The results of both exploratory and confirmatory factor analyses confirmed that a single-factor solution provides the best fit. In addition, the Dutch RSES showed high internal consistency as well as high congruent validity. Overall, these findings support the usefulness of the Dutch RSES as a measure for global self-esteem.
Psychometric Properties of the Dutch Rosenberg Self-Esteem Scale
Franck, Erik; De Raedt, Rudi; Barbez, Catherine; Rosseel, Yves
2008-01-01
Interest in self-esteem has been fuelled by the suggestion that level of self-esteem is associated with psychological well-being. In the present study, we translated the Rosenberg Self-Esteem Scale (RSES) into the Dutch language and evaluated its psychometric properties in a sample of 442 adults. The results of both exploratory and confirmatory factor analyses confirmed that a single-factor solution provides the best fit. In addition, the Dutch RSES showed high internal consistency as well as...
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.
Impacts of Irrigation on Soil Moisture Scaling Properties and Downscaling
Ko, A.; Mascaro, G.; Vivoni, E. R.
2015-12-01
Soil moisture (θ) exhibits high spatial variability due to the combined effect of natural and anthropogenic factors. Among the latter group, irrigation can introduce significant heterogeneity in the spatial variability of θ, thus modifying the statistical properties typically observed in natural landscapes. This, in turn, can affect the application of downscaling models of coarse satellite θ products based on the hypothesis of spatial homogeneity of θ distribution. In this study, the impact of irrigation on the scale invariance properties of θ and the application of a multifractal downscaling algorithm are analyzed using ground- and aircraft-based θ measurements from the National Airborne Field Experiments 2005 (NAFE05) and 2006 (NAFE06) campaigns conducted in two sites in Australia. After identifying irrigated areas through vegetation indices derived from Landsat 5 Thematic Mapper scenes, we investigate the presence of scale invariance from 32 km to 1 km in three scenarios, including (1) the original θ fields and in cases where θ in irrigated pixels was (2) replaced with missing data or (3) interpolated from neighboring pixels. We found that irrigation has a larger impact on the scale invariance properties in a large and compact agricultural district in the NAFE06 region, while it has a negligible influence on the sparser districts of NAFE05. The θ fields of scenario 3 are then used to calibrate a downscaling model based on spatially-homogeneous multifractal cascades as a function of coarse predictors. The model capability to reproduce the θ variability across scales is assessed by comparing ensembles of disaggregated field with the small-scale θ airborne observations and, for the first time, with ground θ measurements. Model performances are adequate in most cases in both experiments, although some deficiencies are found in regions with a larger presence of irrigated fields, suggesting the need to further refine the technique for detection of
Fractal Analysis of Drainage Basins on Mars
Stepinski, T. F.; Marinova, M. M.; McGovern, P. J.; Clifford, S. M.
2002-01-01
We used statistical properties of drainage networks on Mars as a measure of martian landscape morphology and an indicator of landscape evolution processes. We utilize the Mars Orbiter Laser Altimeter (MOLA) data to construct digital elevation maps (DEMs) of several, mostly ancient, martian terrains. Drainage basins and channel networks are computationally extracted from DEMs and their structures are analyzed and compared to drainage networks extracted from terrestrial and lunar DEMs. We show that martian networks are self-affine statistical fractals with planar properties similar to terrestrial networks, but vertical properties similar to lunar networks. The uniformity of martian drainage density is between those for terrestrial and lunar landscapes. Our results are consistent with the roughening of ancient martian terrains by combination of rainfall-fed erosion and impacts, although roughening by other fluvial processes cannot be excluded. The notion of sustained rainfall in recent Mars history is inconsistent with our findings.
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 characterization of the coal surface
Directory of Open Access Journals (Sweden)
Miklúová Viera
1998-09-01
Full Text Available The aim of this paper is to point up to the characterization of the brown coal using the fractal theory. On the base of BET measurements on the adsorption surface, the surface fractal dimension of crushed and milled coal samples have been determined. These values of the fractal dimension are used in the estimation of the processes by the energy input.
Fractal 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
Dynamics and Scaling Properties of Fractures in clay-like Materials
Energy Technology Data Exchange (ETDEWEB)
Walmann, Thomas
1998-12-31
Computer models that can help oil companies predict realistic and physically correct fracture patterns are important. To verify such a model, experiments described in this thesis were undertaken, using wet clay and powder. The main focus was on extensional fractures, but other types of fractures were also studied. High resolution digital images of the fracture patterns were recorded and analyzed using statistical physics and fractal geometry. The characteristic shapes and size distributions of individual fractures and the overall fracture patterns obtained from laboratory model studies were compared to results from aerial photographs of a fracture pattern in a collapsed glacier that had undergone a similar deformation. A new scaling relation (a power-law) between the length of a fracture and the projected area is derived for fractures formed during clay model experiments. This scaling relation is found also in a field study of a fracture pattern in a glacier. The forms of the different distributions that characterizes fractures in clay experiments are discussed. Several characteristic lengths are associated with the laboratory experiments. They are related to the sample size and shape, the model material and the nature of the imposed deformation. The roughness of the fracture traces obtained from powder experiments was found to have a self-affine form. The roughness, or Hurst exponent, was found to have the value 0.73, plus or minus 0.09. A large number of interacting fractures were formed in the systems studied, and under such conditions the fluctuations about the direction perpendicular to the principle strain direction are influenced by neighbouring fractures. As expected, an upper cutoff for the scaling range was observed. But the length at which the crossover from a self-affine shape to a flat shape took place did not depend systematically on any of the experimental parameters or characteristic length scales. The total fracture trace patterns could not be
Scale invariance in road networks.
Kalapala, Vamsi; Sanwalani, Vishal; Clauset, Aaron; Moore, Cristopher
2006-02-01
We study the topological and geographic structure of the national road networks of the United States, England, and Denmark. By transforming these networks into their dual representation, where roads are vertices and an edge connects two vertices if the corresponding roads ever intersect, we show that they exhibit both topological and geographic scale invariance. That is, we show that for sufficiently large geographic areas, the dual degree distribution follows a power law with exponent 2.2< or = alpha < or =2.4, and that journeys, regardless of their length, have a largely identical structure. To explain these properties, we introduce and analyze a simple fractal model of road placement that reproduces the observed structure, and suggests a testable connection between the scaling exponent and the fractal dimensions governing the placement of roads and intersections.
The complexity of sequences generated by the arc-fractal system.
Directory of Open Access Journals (Sweden)
Hoai Nguyen Huynh
Full Text Available We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even though they are constructed from very simple rules. Second by employing the ϵ-machine approach developed by Crutchfield and Young, we measure the complexity and randomness of the sequences and show that they are indeed complex, i.e. neither periodic nor random, with the value of complexity measure being significant as compared to the known example of logistic map at the edge of chaos. The complexity and randomness of the sequences are then discussed in relation with the properties of associated fractal objects, such as their fractal dimension, symmetry and orientations of the arcs.
The Complexity of Sequences Generated by the Arc-Fractal System
Huynh, Hoai Nguyen; Pradana, Andri; Chew, Lock Yue
2015-01-01
We study properties of the symbolic sequences extracted from the fractals generated by the arc-fractal system introduced earlier by Huynh and Chew. The sequences consist of only a few symbols yet possess several nontrivial properties. First using an operator approach, we show that the sequences are not periodic, even though they are constructed from very simple rules. Second by employing the ϵ-machine approach developed by Crutchfield and Young, we measure the complexity and randomness of the sequences and show that they are indeed complex, i.e. neither periodic nor random, with the value of complexity measure being significant as compared to the known example of logistic map at the edge of chaos. The complexity and randomness of the sequences are then discussed in relation with the properties of associated fractal objects, such as their fractal dimension, symmetry and orientations of the arcs. PMID:25700034
Development and application of 3-D fractal reservoir model based on collage theorem
Energy Technology Data Exchange (ETDEWEB)
Kim, I.K.; Kim, K.S.; Sung, W.M. [Hanyang Univ., Seoul (Korea, Republic of)
1995-04-30
Reservoir characterization is the essential process to accurately evaluate the reservoir and has been conducted by geostatistical method, SRA algorithm, and etc. The characterized distribution of heterogeneous property by these methods shows randomly distributed phenomena, and does not present anomalous shape of property variation at discontinued space as compared with the observed shape in nature. This study proposed a new algorithm of fractal concept based on collage theorem, which can virtually present not only geometric shape of irregular and anomalous pore structures or coastlines, but also property variation for discontinuously observed data. With a basis of fractal concept, three dimensional fractal reservoir model was developed to more accurately characterize the heterogeneous reservoir. We performed analysis of pre-predictable hypothetically observed permeability data by using the fractal reservoir model. From the results, we can recognize that permeability distributions in the areal view or the cross-sectional view were consistent with the observed data. (author). 8 refs., 1 tab., 6 figs.
Large Scale Emerging Properties from Non Hamiltonian Complex Systems
Directory of Open Access Journals (Sweden)
Marco Bianucci
2017-06-01
Full Text Available The concept of “large scale” depends obviously on the phenomenon we are interested in. For example, in the field of foundation of Thermodynamics from microscopic dynamics, the spatial and time large scales are order of fraction of millimetres and microseconds, respectively, or lesser, and are defined in relation to the spatial and time scales of the microscopic systems. In large scale oceanography or global climate dynamics problems the time scales of interest are order of thousands of kilometres, for space, and many years for time, and are compared to the local and daily/monthly times scales of atmosphere and ocean dynamics. In all the cases a Zwanzig projection approach is, at least in principle, an effective tool to obtain class of universal smooth “large scale” dynamics for few degrees of freedom of interest, starting from the complex dynamics of the whole (usually many degrees of freedom system. The projection approach leads to a very complex calculus with differential operators, that is drastically simplified when the basic dynamics of the system of interest is Hamiltonian, as it happens in Foundation of Thermodynamics problems. However, in geophysical Fluid Dynamics, Biology, and in most of the physical problems the building block fundamental equations of motions have a non Hamiltonian structure. Thus, to continue to apply the useful projection approach also in these cases, we exploit the generalization of the Hamiltonian formalism given by the Lie algebra of dissipative differential operators. In this way, we are able to analytically deal with the series of the differential operators stemming from the projection approach applied to these general cases. Then we shall apply this formalism to obtain some relevant results concerning the statistical properties of the El Niño Southern Oscillation (ENSO.
Paar, Vladimir; Pavin, Nenad; Rubčić, Antun; Rubčić, Jasna
2002-01-01
We show that stable isotopes display a fractal pattern in the N,Z-chart and abundance-weighted chart of isotopes with the fractal dimension df ≈ 1.2. On this basis a scale invariant power law for atomic and molecular weights can be introduced and applied to systematics of Chemical elements and compounds.
Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder
Ahmadlou, Mehran; Adeli, Hojjat; Adeli, Amir
2012-10-01
Recently, the visibility graph (VG) algorithm was proposed for mapping a time series to a graph to study complexity and fractality of the time series through investigation of the complexity of its graph. The visibility graph algorithm converts a fractal time series to a scale-free graph. VG has been used for the investigation of fractality in the dynamic behavior of both artificial and natural complex systems. However, robustness and performance of the power of scale-freeness of VG (PSVG) as an effective method for measuring fractality has not been investigated. Since noise is unavoidable in real life time series, the robustness of a fractality measure is of paramount importance. To improve the accuracy and robustness of PSVG to noise for measurement of fractality of time series in biological time-series, an improved PSVG is presented in this paper. The proposed method is evaluated using two examples: a synthetic benchmark time series and a complicated real life Electroencephalograms (EEG)-based diagnostic problem, that is distinguishing autistic children from non-autistic children. It is shown that the proposed improved PSVG is less sensitive to noise and therefore more robust compared with PSVG. Further, it is shown that using improved PSVG in the wavelet-chaos neural network model of Adeli and c-workers in place of the Katz fractality dimension results in a more accurate diagnosis of autism, a complicated neurological and psychiatric disorder.
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
In order to explore the effect of changes in plant communities and land use on soil properties, as a result of anthropogenic disturbances, we apply the theory of fractals and soil physics as a means to better quantify changes in particle-size distribution (PSD) and soil porosity. Fractal dimension a...
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.
Psychometric properties and refinement of the Reproductive Coercion Scale.
McCauley, Heather L; Silverman, Jay G; Jones, Kelley A; Tancredi, Daniel J; Decker, Michele R; McCormick, Marie C; Austin, S Bryn; Anderson, Heather A; Miller, Elizabeth
2017-03-01
Identification and refinement of psychometric properties of the Reproductive Coercion Scale (RCS) for use in survey research and clinical practice. Young women aged 16-29 years seeking services in 24 Pennsylvania and 5 California family planning clinics completed questionnaires. Data were pooled for analysis (n=4674), and underlying domains were assessed using Horn's Parallel Analysis and Exploratory Factor Analysis. Multidimensional Item Response Theory was used to refine the scale and assess reliability and validity of a short-form RCS. The full, nine-item RCS had two underlying domains: pregnancy coercion and condom manipulation. Five items were retained in the short form: three about pregnancy coercion (e.g., "told you not to use birth control…") and two for condom manipulation (e.g., "taken off the condom while you were having sex…"; one of these items is the combination of two original items on damaging the condom that were combined because of similar statistical properties and face validity and a third item on removing the condom was retained on its own). Recent reproductive coercion was reported by 6.7% and 6.3% of the sample with the full and short-form RCS, respectively. Characteristics of women reporting reproductive coercion were similar with both forms. Findings indicate that reproductive coercion includes pregnancy coercion and deliberate manipulation of condoms to promote pregnancy. Moreover, women experience reproductive coercion across a continuum of severity. We selected items that varied in RC severity and discrimination to generate a five-item short-form RCS for survey research and clinical practice. This study assesses the psychometric properties of the RCS, identifying pregnancy coercion and condom manipulation as underlying domains of reproductive coercion. Recommendations for using the RCS in research and clinical practice are discussed. Copyright © 2016 Elsevier Inc. All rights reserved.
Invited Article: Plasmonic growth of patterned metamaterials with fractal geometry
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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.
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.
Molecularly-Limited Fractal Surface Area of Mineral Powders
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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.
Fractal physiology for physicists: Lévy statistics
West, Bruce J.; Deering, William
1994-10-01
The biomedical applications of fractal concepts have led to a wealth of new insights in biology and physiology, including a new formulation of the concept of health. Herein we review how over the past decade the complexity inherent in physiological structures and processes has been described by random fractals. In particular we argue that the scaling observed in these biological data sets is a consequence of the Lévy statistics of the underlying processes. This review interleaves arguments from renormalization group theory, fractal scaling and Lévy stable distributions in various physiological contexts including the mammalian lung, the beating of the heart, DNA sequencing, the dendritic branching of neurons and blood vessels, the dynamics of proteins, ion channel gating and radioactive clearance curves from the body in order to reveal an underlying unity to physiological processes. Wiebel promotes the use of fractal geometry as a design principle for living organisms, herein we suggest that Lévy stable statistics in being more inclusive may be an even more useful design principle.
Exploring scaling laws in surface topography
International Nuclear Information System (INIS)
Abedini, M.J.; Shaghaghian, M.R.
2009-01-01
Surface topography affects many soil properties and processes, particularly surface water storage and runoff. Application of fractal analysis helps understand the scaling laws inherent in surface topography at a wide range of spatial scales and climatic regimes. In this research, a high resolution digital elevation model with a 3 mm resolution on one side of the spectrum and large scale DEMs, with a 500 m spatial resolution on the other side were used to explore scaling laws in surface topography. With appropriate exploratory spatial data analysis of both types of data sets, two conventional computational procedures - variogram and Box Counting Methods (BCM) - address scaling laws in surface topography. The results respect scaling laws in surface topography to some extent as neither the plot treatment nor the direction treatment has a significant impact on fractal dimension variability. While in the variogram method, the change in slope in Richardson's plots appears to be the norm rather than the exception; Richardson's plots resulting from box counting implementation lack such mathematical behavior. These breaks in slope might have useful implications for delineating homogeneous hydrologic units and detecting change in trend in hydrologic time series. Furthermore, it is shown that fractal dimension cannot be used to capture anisotropic variabilities both within and among micro-plots. In addition, its numerical value remains insignificant at the 5% level in moving from one direction to another and also from one spatial scale to another while the ordinate intercept could discriminate the surface roughness variability from one spatial scale to another.
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.
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)
The distribution function of a probability measure on a space with a fractal structure
Energy Technology Data Exchange (ETDEWEB)
Sanchez-Granero, M.A.; Galvez-Rodriguez, J.F.
2017-07-01
In this work we show how to define a probability measure with the help of a fractal structure. One of the keys of this approach is to use the completion of the fractal structure. Then we use the theory of a cumulative distribution function on a Polish ultrametric space and describe it in this context. Finally, with the help of fractal structures, we prove that a function satisfying the properties of a cumulative distribution function on a Polish ultrametric space is a cumulative distribution function with respect to some probability measure on the space. (Author)
Directory of Open Access Journals (Sweden)
Vesa J Kiviniemi
2009-07-01
Full Text Available Temporal blood oxygen level dependent (BOLD contrast signals in functional MRI during rest may be characterized by power spectral distribution (PSD trends of the form 1/f α. Trends with 1/f characteristics comprise fractal properties with repeating oscillation patterns in multiple time scales. Estimates of the fractal properties enable the quantification of phenomena that may otherwise be difficult to measure, such as transient, non-linear changes. In this study it was hypothesized that the fractal metrics of 1/f BOLD signal trends can map changes related to dynamic, multi-scale alterations in cerebral blood flow (CBF after a transient hyperventilation challenge. Twenty-three normal adults were imaged in a resting-state before and after hyperventilation. Different variables (1/f trend constant α, fractal dimension Df, and, Hurst exponent H characterizing the trends were measured from BOLD signals. The results show that fractal metrics of the BOLD signal follow the fractional Gaussian noise model, even during the dynamic CBF change that follows hyperventilation. The most dominant effect on the fractal metrics was detected in grey matter, in line with previous hyperventilation vaso-reactivity studies. The α was able to differentiate also blood vessels from grey matter changes. Df was most sensitive to grey matter. H correlated with default mode network areas before hyperventilation but this pattern vanished after hyperventilation due to a global increase in H. In the future, resting-state fMRI combined with fractal metrics of the BOLD signal may be used for analyzing multi-scale alterations of cerebral blood flow.
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...
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
Fractal profit landscape of the stock market.
Grönlund, Andreas; Yi, Il Gu; Kim, Beom Jun
2012-01-01
We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.
Fractal analysis of heart rate variability and mortality after an acute myocardial infarction
DEFF Research Database (Denmark)
Tapanainen, Jari M; Thomsen, Poul Erik Bloch; Køber, Lars
2002-01-01
The recently developed fractal analysis of heart rate (HR) variability has been suggested to provide prognostic information about patients with heart failure. This prospective multicenter study was designed to assess the prognostic significance of fractal and traditional HR variability parameters...... in a large, consecutive series of survivors of an acute myocardial infarction (AMI). A consecutive series of 697 patients were recruited to participate 2 to 7 days after an AMI in 3 Nordic university hospitals. The conventional time-domain and spectral parameters and the newer fractal scaling indexes of HR...... variability were analyzed from 24-hour RR interval recordings. During the mean follow-up of 18.4 +/- 6.5 months, 49 patients (7.0%) died. Of all the risk variables, a reduced short-term fractal scaling exponent (alpha(1)
Fractal behavior in the headway fluctuation simulated by the NaSch model
Zhu, H. B.; Gao, J. B.
2014-03-01
The fractal behavior of traffic flow is studied by the adaptive fractal analysis method on the basis of the vehicle headway time series, which are obtained from the numerical simulation of the NaSch model. We find that the vehicle headway time series has a fractal behavior that is similar to the standard Brownian motion (BM) over a wide range of scales when the density is low. As the density increases well-defined sharp spectral peaks, corresponding to the stop-and-go waves, appear while the scale range showing BM-like behavior rapidly shrinks. In the high density regime, a new type of fractal behavior with long-range correlations appears, accompanying the worsening of traffic congestions. The underlying dynamics of traffic flow is analyzed, and some meaningful results are obtained.
Psychometric properties of the Revised Cheek and Buss Shyness Scale.
Hopko, Derek R; Stowell, Jessica; Jones, Warren H; Armento, Maria E A; Cheek, Jonathan M
2005-04-01
Although the Revised Cheek and Buss Shyness Scale (RCBS; Cheek, 1983) is widely used, its psychometric properties largely are unknown. In this investigation, we examined the normative data, factor structure, internal consistency, test-retest reliability, and convergent/discriminant validity of the RCBS using a sample of 261 university students. Results provided strong support for the stability of normative data over time, reliability of the measure, and its predicted associations with contemporary measures of shyness, social anxiety, and related constructs. Although support was obtained for a unifactorial conceptualization of shyness, an exploratory factor analysis revealed an alternative 3-factor solution that was supportive of a previously proposed meta-analytic model of shyness (Jones, Briggs, & Smith, 1986) and was consistent with other prominent shyness theories (Buss, 1980; Pilkonis, 1977a, 1977b; Zimbardo, 1977). This factor model was replicable on a holdout sample, and there were some data to support the discriminant validity of factors.
The psychometric properties of the Schutte Emotional Intelligence Scale
Directory of Open Access Journals (Sweden)
Cara S. Jonker
2008-10-01
Full Text Available the objective of this study was to investigate the psychometric properties of the Schutte Emotional Intelligence Scale (SEiS. the psychometric soundness of the SEiS was tested. A cross-sectional survey design was used for this study. A sample (n = 341 was taken from Economical Science students from a higher-education institution. The results obtained using the cross-sectional design supported a six- dimensional factor structure of the SEiS. the six factors are Positive Affect, Emotion-Others, happy Emotions, Emotions-Own, Non-verbal Emotions and Emotional Management. A multi-analysis of variance (MANOVA was used to determine differences in terms of biographical data. the results indicated signifcant differences between gender and language groups.
Magnetic Properties of Large-Scale Nanostructured Graphene Systems
DEFF Research Database (Denmark)
Gregersen, Søren Schou
The on-going progress in two-dimensional (2D) materials and nanostructure fabrication motivates the study of altered and combined materials. Graphene—the most studied material of the 2D family—displays unique electronic and spintronic properties. Exceptionally high electron mobilities, that surpass...... those in conventional materials such as silicon, make graphene a very interesting material for high-speed electronics. Simultaneously, long spin-diffusion lengths and spin-life times makes graphene an eligible spin-transport channel. In this thesis, we explore fundamental features of nanostructured...... graphene systems using large-scale modeling techniques. Graphene perforations, or antidots, have received substantial interest in the prospect of opening large band gaps in the otherwise gapless graphene. Motivated by recent improvements of fabrication processes, such as forming graphene antidots and layer...
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
Properties and effects of remaining carbon from waste plastics gasifying on iron scale reduction.
Zhang, Chongmin; Chen, Shuwen; Miao, Xincheng; Yuan, Hao
2011-06-01
The carbonous activities of three kinds of carbon-bearing materials gasified from plastics were tested with coal coke as reference. The results showed that the carbonous activities of these remaining carbon-bearing materials were higher than that of coal-coke. Besides, the fractal analyses showed that the porosities of remaining carbon-bearing materials were higher than that of coal-coke. It revealed that these kinds of remaining carbon-bearing materials are conducive to improve the kinetics conditions of gas-solid phase reaction in iron scale reduction. Copyright © 2011 The Research Centre for Eco-Environmental Sciences, Chinese Academy of Sciences. Published by Elsevier B.V. All rights reserved.
Svartdal, Frode
2017-01-01
Procrastination has been defined in different ways. Two instruments--the Irrational Procrastination Scale (IPS) and the Pure Procrastination Scale (PPS)--focus on a core problem in procrastination--the irrational delay of intended behavior. The present paper examined the psychometric properties of the Norwegian translations of these scales. In…
The magnetic properties of mill scale-derived permanent magnet
International Nuclear Information System (INIS)
Woon, H.S.; Hashim, M.M.; Yahya, N.; Zakaria, A.; Lim, K.P.
2005-01-01
In the permanent magnet SrO-FeO-Fe 2 O 3 system, there exist several magnetically ordered compounds with a stable phase at room temperature. The most important are the M(SrFe 12 O 19 ), X(SrFe 15 O 23 ) and W(SrFe 18 O 27 ) phases with hexagonal close packed structure. In this project, M(SrFe 12 O 19 ) was prepared using mill scale, a steel-maker byproduct, as raw material. The Malaysia steel industry generates approximately 30,000 metric tons of waste products such as mill scale every year. Transportation and disposal of the byproducts are costly and the environmental regulations are becoming stricter. Hence, local steel mills are to find new ways to recycle the waste as a feedstock for the steel-making process or as a saleable product. The M(SrFe 12 O 19 ) was synthesized using the conventional ceramic process. The formation of the SrFe 12 O 19 was confirmed by X-ray diffraction. The magnetic properties such as the energy product (BH)max, coercive force (iHc) and remanence (Br) were also reported in this paper. (Author)
Multi-fractal measures of city-size distributions based on the three-parameter Zipf model
International Nuclear Information System (INIS)
Chen Yanguang; Zhou Yixing
2004-01-01
A multi-fractal framework of urban hierarchies is presented to address the rank-size distribution of cities. The three-parameter Zipf model based on a pair of exponential-type scaling laws is generalized to multi-scale fractal measures. Then according to the equivalent relationship between Zipf's law and Pareto distribution, a set of multi-fractal equations are derived using dual conversion and the Legendre transform. The US city population data coming from the 2000 census are employed to verify the multi-fractal models and the results are satisfying. The multi-fractal measures reveal some strange symmetry regularity of urban systems. While explaining partially the remains of the hierarchical step-like frequency distribution of city sizes suggested by central place theory, the mathematical framework can be interpreted with the entropy-maximizing principle and some related ideas from self-organization
Psychometric properties of the Chinese Internet Gaming Disorder Scale.
Sigerson, Leif; Li, Angel Y-L; Cheung, Mike W-L; Luk, Jeremy W; Cheng, Cecilia
2017-11-01
To develop a consensus on the definition and measurement of Internet gaming disorder (IGD), several recent studies have used the DSM-5's proposed criteria for IGD as the basis in scale construction. This study contributes to this emerging consensus by developing and validating a new Chinese Internet Gaming Disorder Scale (C-IGDS) based on the DSM-5 criteria. A representative sample of Hong Kong community adults (n=502, 50% men, mean age=37.1, age range=18-60) was recruited for a telephone survey with random digit dialing. Various statistical techniques were used to assess the psychometric properties of the C-IGDS. The C-IGDS had good reliability (Cronbach's α=0.91) and structural validity (CFA model fit: RMSEA=0.027, CFI=0.991, TLI=0.988) in our sample. Moderate to moderately strong correlations with depressive symptoms (r=0.617, pgaming hours (r=0.412, p<0.001) supported the criterion validity of the C-IGDS. In addition, the C-IGDS exhibited strict measurement invariance for sex and at least strong measurement invariance for age. In addition to providing the first Chinese scale for measuring IGD based on the DSM-5's proposed criteria, this study provides empirical support for the validity of these diagnostic criteria as the basis for a universal measure of IGD. Most important, this study is the first to reveal the criteria's measurement invariance, thereby indicating their suitability for use with diverse demographic groups. Copyright © 2017 Elsevier Ltd. All rights reserved.
Baka, Łukasz
2017-10-17
Self-efficacy refers to different spheres of human functioning and to different tasks, including teaching activity. It is regarded as an important personal resource related to coping with stress. This paper was aimed at presenting psychometric properties of the Norwegian Teachers Self-Efficacy Scale (NTSES), related to these beliefs in the group of teachers. Psychometric properties of the scale were evaluated on the basis of the data obtained from 404 teachers of elementary and middle schools. Our analyses of exploratory and confirmatory factor revealed a 3-dimensional structure, but not a 6-dimensional structure of NTSES as obtained in the original Norwegian study. They also showed high reliability and construct validity coefficients. Teachers self-efficacy was positively correlated with general self-efficacy, internal locus of control and negatively with job burnout. Although NTSES can be used in the study of Polish teachers, this should be done with great caution and the measure of global index of NTSES should be used. Additional studies on a larger sample of teachers are recommended. Med Pr 2017;68(6):743-755. This work is available in Open Access model and licensed under a CC BY-NC 3.0 PL license.
Norwegian Teacher Self-Efficacy Scale – Psychometric properties of the Polish version of the scale
Directory of Open Access Journals (Sweden)
Łukasz Baka
2017-12-01
Full Text Available Background: Self-efficacy refers to different spheres of human functioning and to different tasks, including teaching activity. It is regarded as an important personal resource related to coping with stress. This paper was aimed at presenting psychometric properties of the Norwegian Teachers Self-Efficacy Scale (NTSES, related to these beliefs in the group of teachers. Material and Methods: Psychometric properties of the scale were evaluated on the basis of the data obtained from 404 teachers of elementary and middle schools. Results: Our analyses of exploratory and confirmatory factor revealed a 3-dimensional structure, but not a 6-dimensional structure of NTSES as obtained in the original Norwegian study. They also showed high reliability and construct validity coefficients. Teachers self-efficacy was positively correlated with general self-efficacy, internal locus of control and negatively with job burnout. Conclusions: Although NTSES can be used in the study of Polish teachers, this should be done with great caution and the measure of global index of NTSES should be used. Additional studies on a larger sample of teachers are recommended. Med Pr 2017;68(6:743–755
Fractal Dimension Analysis of Transient Visual Evoked Potentials: Optimisation and Applications.
Boon, Mei Ying; Henry, Bruce Ian; Chu, Byoung Sun; Basahi, Nour; Suttle, Catherine May; Luu, Chi; Leung, Harry; Hing, Stephen
2016-01-01
The visual evoked potential (VEP) provides a time series signal response to an external visual stimulus at the location of the visual cortex. The major VEP signal components, peak latency and amplitude, may be affected by disease processes. Additionally, the VEP contains fine detailed and non-periodic structure, of presently unclear relevance to normal function, which may be quantified using the fractal dimension. The purpose of this study is to provide a systematic investigation of the key parameters in the measurement of the fractal dimension of VEPs, to develop an optimal analysis protocol for application. VEP time series were mathematically transformed using delay time, τ, and embedding dimension, m, parameters. The fractal dimension of the transformed data was obtained from a scaling analysis based on straight line fits to the numbers of pairs of points with separation less than r versus log(r) in the transformed space. Optimal τ, m, and scaling analysis were obtained by comparing the consistency of results using different sampling frequencies. The optimised method was then piloted on samples of normal and abnormal VEPs. Consistent fractal dimension estimates were obtained using τ = 4 ms, designating the fractal dimension = D2 of the time series based on embedding dimension m = 7 (for 3606 Hz and 5000 Hz), m = 6 (for 1803 Hz) and m = 5 (for 1000Hz), and estimating D2 for each embedding dimension as the steepest slope of the linear scaling region in the plot of log(C(r)) vs log(r) provided the scaling region occurred within the middle third of the plot. Piloting revealed that fractal dimensions were higher from the sampled abnormal than normal achromatic VEPs in adults (p = 0.02). Variances of fractal dimension were higher from the abnormal than normal chromatic VEPs in children (p = 0.01). A useful analysis protocol to assess the fractal dimension of transformed VEPs has been developed.
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.
Separating Fractal and Oscillatory Components in the Power Spectrum of Neurophysiological Signal.
Wen, Haiguang; Liu, Zhongming
2016-01-01
Neurophysiological field-potential signals consist of both arrhythmic and rhythmic patterns indicative of the fractal and oscillatory dynamics arising from likely distinct mechanisms. Here, we present a new method, namely the irregular-resampling auto-spectral analysis (IRASA), to separate fractal and oscillatory components in the power spectrum of neurophysiological signal according to their distinct temporal and spectral characteristics. In this method, we irregularly resampled the neural signal by a set of non-integer factors, and statistically summarized the auto-power spectra of the resampled signals to separate the fractal component from the oscillatory component in the frequency domain. We tested this method on simulated data and demonstrated that IRASA could robustly separate the fractal component from the oscillatory component. In addition, applications of IRASA to macaque electrocorticography and human magnetoencephalography data revealed a greater power-law exponent of fractal dynamics during sleep compared to wakefulness. The temporal fluctuation in the broadband power of the fractal component revealed characteristic dynamics within and across the eyes-closed, eyes-open and sleep states. These results demonstrate the efficacy and potential applications of this method in analyzing electrophysiological signatures of large-scale neural circuit activity. We expect that the proposed method or its future variations would potentially allow for more specific characterization of the differential contributions of oscillatory and fractal dynamics to distributed neural processes underlying various brain functions.
Psychometric properties of an African symptoms check list scale: the Ndetei-Othieno-Kathuku scale.
Ndetei, D M; Othieno, C J; Mutiso, V; Ongecha, F A; Kokonya, D A; Omar, A; Gakinya, B; Mwangi, J
2006-05-01
To profile and quantify the psychometric properties of the NOK (Ndetei-Othieno-Kathuku) scale against internationally used Gold-standards and benchmarks for mild psychiatric disorders and post-traumatic stress disorders and to provide a potential easy to administer culture sensitive instrument for screening and assessing those with possible psychiatric disorders for the Kenyan and similar social-cultural situations. Cross-Sectional quantitative study. A psychiatric clinical consultation setting and Kyanguli Secondary School psychotrauma counselling clinical set-up. Survivors of the Nairobi USA Embassy bombing who were referred for psychiatric treatment and survivors of a fire disaster from a rural Kenyan school (Kyanguli School fire disaster) including students, parents of the diseased children and staff members. Positive correlation was found between the NOK and all the instruments. The highest correlations were between the NOK and the BDI and SCL-90 (r = 0.557 to 0.786). The differences between the NOK scores among the different groups were statistically significant (F ratio = 13.54 to 160.34, p < 0.01). The reliability coefficient (internal consistency) of the scale, alpha = 0.9733. Other item statistics and correlations of the scale are discussed. It is concluded that the NOK has high concurrent and discriminant validity as well as a high internal consistency and that it can be used for the rapid assessment of psychotrauma victims of all age groups; and stress in general in similar age groups in the local setting. It is culture appropriate and sensitive.
Robustness of the fractal regime for the multiple-scattering structure factor
Katyal, Nisha; Botet, Robert; Puri, Sanjay
2016-08-01
In the single-scattering theory of electromagnetic radiation, the fractal regime is a definite range in the photon momentum-transfer q, which is characterized by the scaling-law behavior of the structure factor: S(q) ∝ 1 /q df. This allows a straightforward estimation of the fractal dimension df of aggregates in Small-Angle X-ray Scattering (SAXS) experiments. However, this behavior is not commonly studied in optical scattering experiments because of the lack of information on its domain of validity. In the present work, we propose a definition of the multiple-scattering structure factor, which naturally generalizes the single-scattering function S(q). We show that the mean-field theory of electromagnetic scattering provides an explicit condition to interpret the significance of multiple scattering. In this paper, we investigate and discuss electromagnetic scattering by three classes of fractal aggregates. The results obtained from the TMatrix method show that the fractal scaling range is divided into two domains: (1) a genuine fractal regime, which is robust; (2) a possible anomalous scaling regime, S(q) ∝ 1 /qδ, with exponent δ independent of df, and related to the way the scattering mechanism uses the local morphology of the scatterer. The recognition, and an analysis, of the latter domain is of importance because it may result in significant reduction of the fractal regime, and brings into question the proper mechanism in the build-up of multiple-scattering.
Osberg, Timothy M; Haseley, Erin N; Kamas, Michele M
2008-01-01
We examined the psychometric properties of the Restructured Clinical (RC) scales (Tellegen et al., 2003) of the MMPI-2 (Butcher, Dahlstrom, Graham, Tellegen, & Kaemmer, 1989) in a large sample (N = 744) of 18-year-old college freshman. We found that the RC scales demonstrated good convergence with their Clinical scale counterparts and were more distinctive than the Clinical scales. The patterns of discriminant correlations for the RC scales were slightly clearer than those of the Clinical scales and a set of other existing MMPI-2 scales. Diagnostic efficiency statistics based on Clinical and RC scale elevation status did not differ appreciably. However, the diagnostic efficiency statistics of cutoff scores derived from mean RC and Clinical scale T scores improved on the traditional scale elevation measures. We consider the clinical implications of these findings.
Thermal Properties of Unusual Local-Scale Features on Vesta
Capria, M.; DeSanctis, M.; Palomba, E.; Grassi, D.; Capaccioni, F.; Ammannito, E.; Combe, J.; Sunshine, J. M.; Titus, T. N.; Mittlefehldt, D. W.;
2012-01-01
On Vesta, the thermal behavior of areas of unusual albedo seen at the local scale can be related to physical properties that can provide information about the origin of those materials. We used Dawn s Visible and Infrared Mapping Spectrometer (VIR) hyperspectral cubes to retrieve surface temperatures and emissivities, with high accuracy as long as temperatures are greater than 180 K. Data acquired in the Survey phase (23 July through 29 August 2011) show several unusual surface features: 1) high-albedo (bright) and low-albedo (dark) material deposits, 2) spectrally distinct ejecta and pitted materials, 3) regions suggesting finer-grained materials. Some of the unusual dark and bright features were reobserved by VIR in the subsequent High-Altitude Mapping Orbit (HAMO) and Low- Altitude Mapping Orbit (LAMO) phases at increased pixel resolution. In this work we present temperature maps and emissivities of several local-scale features that were observed by Dawn under different illumination conditions and different local solar times. Data from VIR's IR channel show that bright regions generally correspond to regions with lower thermal emission, i.e. lower temperature, while dark regions correspond to areas with higher thermal emission, i.e. higher temperature. This behavior confirms that many of the dark appearances in the VIS mainly reflect albedo variations, and not, for example, shadowing. During maximum daily insolation, dark features in the equatorial region may rise to temperatures greater than 270 K, while brightest features stop at roughly 258 K, local solar time being similar. However, pitted materials, showing relatively low reflectance, have significantly lower temperatures, as a result of differences in composition and/or structure (e.g, average grain size of the surface regolith, porosity, etc.). To complement this work, we provide preliminary values of thermal inertia for some bright and dark features.
Iron phosphate glasses: Bulk properties and atomic scale structure
Energy Technology Data Exchange (ETDEWEB)
Joseph, Kitheri; Stennett, Martin C.; Hyatt, Neil C.; Asuvathraman, R.; Dube, Charu L.; Gandy, Amy S.; Govindan Kutty, K. V.; Jolley, Kenny; Vasudeva Rao, P. R.; Smith, Roger
2017-10-01
Bulk properties such as glass transition temperature, density and thermal expansion of iron phosphate glass compositions, with replacement of Cs by Ba, are investigated as a surrogate for the transmutation of 137Cs to 137Ba, relevant to the immobilisation of Cs in glass. These studies are required to establish the appropriate incorporation rate of 137Cs in iron phosphate glass. Density and glass transition temperature increases with the addition of BaO indicating the shrinkage and reticulation of the iron phosphate glass network. The average thermal expansion coefficient reduces from 19.8 × 10-6 K-1 to 13.4 × 10-6 K-1, when 25 wt. % of Cs2O was replaced by 25 wt. % of BaO in caesium loaded iron phosphate glass. In addition to the above bulk properties, the role of Ba as a network modifier in the structure of iron phosphate glass is examined using various spectroscopic techniques. The FeII content and average coordination number of iron in the glass network was estimated using Mössbauer spectroscopy. The FeII content in the un-doped iron phosphate glass and barium doped iron phosphate glasses was 20, 21 and 22 ± 1% respectively and the average Fe coordination varied from 5.3 ± 0.2 to 5.7 ± 0.2 with increasing Ba content. The atomic scale structure was further probed by Fe K-edge X-ray absorption spectroscopy. The average coordination number provided by extended X-ray absorption fine structure spectroscopy and X-ray absorption near edge structure was in good agreement with that given by the Mössbauer data.
Small scale variability of snow properties on Antarctic sea ice
Wever, Nander; Leonard, Katherine; Paul, Stephan; Jacobi, Hans-Werner; Proksch, Martin; Lehning, Michael
2016-04-01
Snow on sea ice plays an important role in air-ice-sea interactions, as snow accumulation may for example increase the albedo. Snow is also able to smooth the ice surface, thereby reducing the surface roughness, while at the same time it may generate new roughness elements by interactions with the wind. Snow density is a key property in many processes, for example by influencing the thermal conductivity of the snow layer, radiative transfer inside the snow as well as the effects of aerodynamic forcing on the snowpack. By comparing snow density and grain size from snow pits and snow micro penetrometer (SMP) measurements, highly resolved density and grain size profiles were acquired during two subsequent cruises of the RV Polarstern in the Weddell Sea, Antarctica, between June and October 2013. During the first cruise, SMP measurements were done along two approximately 40 m transects with a horizontal resolution of approximately 30 cm. During the second cruise, one transect was made with approximately 7.5 m resolution over a distance of 500 m. Average snow densities are about 300 kg/m3, but the analysis also reveals a high spatial variability in snow density on sea ice in both horizontal and vertical direction, ranging from roughly 180 to 360 kg/m3. This variability is expressed by coherent snow structures over several meters. On the first cruise, the measurements were accompanied by terrestrial laser scanning (TLS) on an area of 50x50 m2. The comparison with the TLS data indicates that the spatial variability is exhibiting similar spatial patterns as deviations in surface topology. This suggests a strong influence from surface processes, for example wind, on the temporal development of density or grain size profiles. The fundamental relationship between variations in snow properties, surface roughness and changes therein as investigated in this study is interpreted with respect to large-scale ice movement and the mass balance.
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.