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
Directory of Open Access Journals (Sweden)
Bin Jiang
2016-06-01
Full Text Available Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution and the modifiable areal unit problem (MAUP. This paper argues that the confusion and frustration arise from traditional Euclidean geometric thinking, in which locations, directions, and sizes are considered absolute, and it is now time to revise this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, most geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we present topological and scaling analyses illustrated by street-related concepts such as natural streets, street blocks, and natural cities. We further contend that one of the two spatial properties, spatial heterogeneity, is de facto the fractal nature of geographic features, and it should be considered the first effect among the two, because it is global and universal across all scales, which should receive more attention from practitioners of geography.
Prediction of pork quality parameters by applying fractals and data mining on MRI
DEFF Research Database (Denmark)
Caballero, Daniel; Pérez-Palacios, Trinidad; Caro, Andrés
2017-01-01
This work firstly investigates the use of MRI, fractal algorithms and data mining techniques to determine pork quality parameters non-destructively. The main objective was to evaluate the capability of fractal algorithms (Classical Fractal algorithm, CFA; Fractal Texture Algorithm, FTA and One...... Point Fractal Texture Algorithm, OPFTA) to analyse MRI in order to predict quality parameters of loin. In addition, the effect of the sequence acquisition of MRI (Gradient echo, GE; Spin echo, SE and Turbo 3D, T3D) and the predictive technique of data mining (Isotonic regression, IR and Multiple linear...... regression, MLR) were analysed. Both fractal algorithm, FTA and OPFTA are appropriate to analyse MRI of loins. The sequence acquisition, the fractal algorithm and the data mining technique seems to influence on the prediction results. For most physico-chemical parameters, prediction equations with moderate...
Analysis of MRI by fractals for prediction of sensory attributes: A case study in loin
DEFF Research Database (Denmark)
Caballero, Daniel; Antequera, Teresa; Caro, Andrés
2018-01-01
This study investigates the use of fractal algorithms to analyse MRI of meat products, specifically loin, in order to determine sensory parameters of loin. For that, the capability of different fractal algorithms was evaluated (Classical Fractal Algorithm, CFA; Fractal Texture Algorithm, FTA...... was analysed. Results on this study firstly demonstrate the capability of fractal algorithms to analyse MRI from meat product. Different combinations of the analysed techniques can be applied for predicting most sensory attributes of loins adequately (R > 0.5). However, the combination of SE, OPFTA and MLR...... offered the most appropriate results. Thus, it could be proposed as an alternative to the traditional food technology methods....
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.
Development of a New Fractal Algorithm to Predict Quality Traits of MRI Loins
DEFF Research Database (Denmark)
Caballero, Daniel; Caro, Andrés; Amigo, José Manuel
2017-01-01
Traditionally, the quality traits of meat products have been estimated by means of physico-chemical methods. Computer vision algorithms on MRI have also been presented as an alternative to these destructive methods since MRI is non-destructive, non-ionizing and innocuous. The use of fractals...
[Modeling continuous scaling of NDVI based on fractal theory].
Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng
2013-07-01
Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.
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
Generating hierarchical scale free-graphs from fractals
Komjáthy, J.; Simon, K.
2011-01-01
Motivated by the hierarchial network model of E. Ravasz, A.-L. Barabási, and T. Vicsek, we introduce deterministic scale-free networks derived from a graph directed self-similar fractal ¿. With rigorous mathematical results we verify that our model captures some of the most important features of
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 ...
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.
Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E.; Bertoldo, Alessandra
2015-02-01
Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.
International Nuclear Information System (INIS)
Squarcina, Letizia; Bellani, Marcella; De Luca, Alberto; Bertoldo, Alessandra; Brambilla, Paolo; Turkheimer, Federico E
2015-01-01
Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders. (paper)
Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.
Quodbach, Julian; Moussavi, Amir; Tammer, Roland; Frahm, Jens; Kleinebudde, Peter
2014-11-20
An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this case the upper surface of a disintegrating tablet. High-resolution real-time MRI was used to record videos of disintegrating tablets. The acquired video images were processed to depict the upper surface of the tablets and a box-counting algorithm was used to estimate the fractal dimensions. The influence of six different disintegrants, of different relative tablet density, and increasing disintegrant concentration was investigated to evaluate the performance of the novel method. Changing relative densities hardly affect the progression of fractal dimensions, whereas an increase in disintegrant concentration causes increasing fractal dimensions during disintegration, which are also reached quicker. Different disintegrants display only minor differences in the maximal fractal dimension, yet the kinetic in which the maximum is reached allows a differentiation and classification of disintegrants. Copyright © 2014 Elsevier B.V. All rights reserved.
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.
Mouse Activity across Time Scales: Fractal Scenarios
Lima, G. Z. dos Santos; Lobão-Soares, B.; do Nascimento, G. C.; França, Arthur S. C.; Muratori, L.; Ribeiro, S.; Corso, G.
2014-01-01
In this work we devise a classification of mouse activity patterns based on accelerometer data using Detrended Fluctuation Analysis. We use two characteristic mouse behavioural states as benchmarks in this study: waking in free activity and slow-wave sleep (SWS). In both situations we find roughly the same pattern: for short time intervals we observe high correlation in activity - a typical 1/f complex pattern - while for large time intervals there is anti-correlation. High correlation of short intervals ( to : waking state and to : SWS) is related to highly coordinated muscle activity. In the waking state we associate high correlation both to muscle activity and to mouse stereotyped movements (grooming, waking, etc.). On the other side, the observed anti-correlation over large time scales ( to : waking state and to : SWS) during SWS appears related to a feedback autonomic response. The transition from correlated regime at short scales to an anti-correlated regime at large scales during SWS is given by the respiratory cycle interval, while during the waking state this transition occurs at the time scale corresponding to the duration of the stereotyped mouse movements. Furthermore, we find that the waking state is characterized by longer time scales than SWS and by a softer transition from correlation to anti-correlation. Moreover, this soft transition in the waking state encompass a behavioural time scale window that gives rise to a multifractal pattern. We believe that the observed multifractality in mouse activity is formed by the integration of several stereotyped movements each one with a characteristic time correlation. Finally, we compare scaling properties of body acceleration fluctuation time series during sleep and wake periods for healthy mice. Interestingly, differences between sleep and wake in the scaling exponents are comparable to previous works regarding human heartbeat. Complementarily, the nature of these sleep-wake dynamics could lead to a better
Fractals as objects with nontrivial structures at all scales
International Nuclear Information System (INIS)
Lacan, Francis; Tresser, Charles
2015-01-01
Toward the middle of 2001, the authors started arguing that fractals are important when discussing the operational resilience of information systems and related computer sciences issues such as artificial intelligence. But in order to argue along these lines it turned out to be indispensable to define fractals so as to let one recognize as fractals some sets that are very far from being self similar in the (usual) metric sense. This paper is devoted to define (in a loose sense at least) fractals in ways that allow for instance all the Cantor sets to be fractals and that permit to recognize fractality (the property of being fractal) in the context of the information technology issues that we had tried to comprehend. Starting from the meta-definition of a fractal as an “object with non-trivial structure at all scales” that we had used for long, we ended up taking these words seriously. Accordingly we define fractals in manners that depend both on the structures that the fractals are endowed with and the chosen sets of structure compatible maps, i.e., we approach fractals in a category-dependent manner. We expect that this new approach to fractals will contribute to the understanding of more of the fractals that appear in exact and other sciences than what can be handled presently
DEFF Research Database (Denmark)
Bruun Jensen, Casper
2007-01-01
. Instead, I outline a fractal approach to the study of space, society, and infrastructure. A fractal orientation requires a number of related conceptual reorientations. It has implications for thinking about scale and perspective, and (sociotechnical) relations, and for considering the role of the social...... and a fractal social theory....
Geometrical study of astrocytomas through fractals and scaling analysis
International Nuclear Information System (INIS)
Torres H, F.; Baena N, R.; Vergara V, J.; Guerrero M, M.
2017-10-01
The tumor growth is a complex process characterized by the proliferation of uncontrollable cells which invade neighbor tissues. The understanding process of this type of phenomena is very relevant in order to establish diagnosis and proper therapy strategies and to start the valorization of its complexity with proper descriptors produced by the scaling analysis, which define the tumor growth geometry. In this work, obtained results through the scaling analysis for pilocytic astrocytomas, anaplastic and diffuse, are shown, which tumors of primary origin are. On them, it is calculated the fractal dimension and critic exponents of local roughness to characterize in vivo three-dimensional tumor growth. The acquisition of the images for this type of injuries was carried out according to the standard protocol used for brain radiotherapy and radiosurgery, i.e., axial, coronal and sagittal magnetic resonance T1 weighted images and comprising the brain volume for image registration. Image segmentation was performed by the application the K-means procedure upon contrasted images. The results show significant variations of the parameters depending on the tumor stage and its histological origin. (Author)
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 * fractality * 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
Emergence of fractal scale-free networks from stochastic evolution on the Cayley tree
Energy Technology Data Exchange (ETDEWEB)
Chełminiak, Przemysław, E-mail: geronimo@amu.edu.pl
2013-11-29
An unexpected recognition of fractal topology in some real-world scale-free networks has evoked again an interest in the mechanisms stimulating their evolution. To explain this phenomenon a few models of a deterministic construction as well as a probabilistic growth controlled by a tunable parameter have been proposed so far. A quite different approach based on the fully stochastic evolution of the fractal scale-free networks presented in this Letter counterpoises these former ideas. It is argued that the diffusive evolution of the network on the Cayley tree shapes its fractality, self-similarity and the branching number criticality without any control parameter. The last attribute of the scale-free network is an intrinsic property of the skeleton, a special type of spanning tree which determines its fractality.
Fractals and the Large-Scale Structure in the Universe
Indian Academy of Sciences (India)
of fractals. Measuring the Length of a Curve. Consider the problem of measuring the length of a ..... a two dimensional smooth surface embedded in 3 dimen- ... interesting measure of a I-dimensional object is its length and not the volume.
Evolution of atomic-scale surface structures during ion bombardment: A fractal simulation
International Nuclear Information System (INIS)
Shaheen, M.A.; Ruzic, D.N.
1993-01-01
Surfaces of interest in microelectronics have been shown to exhibit fractal topographies on the atomic scale. A model utilizing self-similar fractals to simulate surface roughness has been added to the ion bombardment code TRIM. The model has successfully predicted experimental sputtering yields of low energy (less then 1000 eV) Ar on Si and D on C using experimentally determined fractal dimensions. Under ion bombardment the fractal surface structures evolve as the atoms in the collision cascade are displaced or sputtered. These atoms have been tracked and the evolution of the surface in steps of one monolayer of flux has been determined. The Ar--Si system has been studied for incidence energies of 100 and 500 eV, and incidence angles of 0 degree, 30 degree, and 60 degree. As expected, normally incident ion bombardment tends to reduce the roughness of the surface, whereas large angle ion bombardment increases the degree of surface roughness. Of particular interest though, the surfaces are still locally self-similar fractals after ion bombardment and a steady state fractal dimension is reached, except at large angles of incidence
Fractal properties and small-scale structure of cosmic string networks
International Nuclear Information System (INIS)
Martins, C.J.A.P.; Shellard, E.P.S.
2006-01-01
We present results from a detailed numerical study of the small-scale and loop production properties of cosmic string networks, based on the largest and highest resolution string simulations to date. We investigate the nontrivial fractal properties of cosmic strings, in particular, the fractal dimension and renormalized string mass per unit length, and we also study velocity correlations. We demonstrate important differences between string networks in flat (Minkowski) spacetime and the two very similar expanding cases. For high resolution matter era network simulations, we provide strong evidence that small-scale structure has converged to 'scaling' on all dynamical length scales, without the need for other radiative damping mechanisms. We also discuss preliminary evidence that the dominant loop production size is also approaching scaling
Fractal-Markovian scaling of turbulent bursting process in open channel flow
International Nuclear Information System (INIS)
Keshavarzi, Ali Reza; Ziaei, Ali Naghi; Homayoun, Emdad; Shirvani, Amin
2005-01-01
The turbulent coherent structure of flow in open channel is a chaotic and stochastic process in nature. The coherence structure of the flow or bursting process consists of a series of eddies with a variety of different length scales and it is very important for the entrainment of sediment particles from the bed. In this study, a fractal-Markovian process is applied to the measured turbulent data in open channel. The turbulent data was measured in an experimental flume using three-dimensional acoustic Doppler velocity meter (ADV). A fractal interpolation function (FIF) algorithm was used to simulate more than 500,000 time series data of measured instantaneous velocity fluctuations and Reynolds shear stress. The fractal interpolation functions (FIF) enables to simulate and construct time series of u', v', and u'v' for any particular movement and state in the Markov process. The fractal dimension of the bursting events is calculated for 16 particular movements with the transition probability of the events based on 1st order Markov process. It was found that the average fractal dimensions of the streamwise flow velocity (u') are; 1.73, 1.74, 1.71 and 1.74 with the transition probability of 60.82%, 63.77%, 59.23% and 62.09% for the 1-1, 2-2, 3-3 and 4-4 movements, respectively. It was also found that the fractal dimensions of Reynold stress u'v' for quadrants 1, 2, 3 and 4 are 1.623, 1.623, 1.625 and 1.618, respectively
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.
Directory of Open Access Journals (Sweden)
Yongqing Duan
2017-12-01
Full Text Available Stretchable nanogenerators that directly generate electricity are promising for a wide range of applications in wearable electronics. However, the stretchability of the devices has been a long-standing challenge. Here we present a newly-designed ultra-stretchable nanogenerator based on fractal-inspired piezoelectric nanofibers and liquid metal electrodes that can withstand strain as large as 200%. The large-scale fractal poly(vinylidene fluoride (PVDF micro/nanofibers are fabricated by combination of helix electrohydrodynamic printing (HE-Printing and buckling-driven self-assembly. HE-Printing exploits “whipping/buckling” instability of electrospinning to deposit serpentine fibers with diverse geometries in a programmable, accurately positioned, and individually-controlled manner. Self-organized buckling utilizes the driven force from the prestrained elastomer to assemble serpentine fibers into ultra-stretchable fractal inspired architecture. The nanogenerator with embedded fractal PVDF fibers and liquid-metal microelectrodes demonstrates high stretchability (>200% and electricity (currents >200 nA, it can harvest energy from all directions by arbitrary mechanical motion, and the rectified output has been applied to charge the commercial capacitor and drive LEDs, which enables wearable electronics applications in sensing and energy harvesting.
Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale
Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian
2018-06-01
Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.
Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.
Quodbach, J.; Moussavi, A.; Tammer, R.; Frahm, J.; Kleinebudde, P.
2014-01-01
An efficient disintegrant is capable of breaking up a tablet in the smallest possible particles in the shortest time. Until now, comparative data on the efficacy of different disintegrants is based on dissolution studies or the disintegration time. Extending these approaches, this study introduces a method, which defines the evolution of fractal dimensions of tablets as surrogate parameter for the available surface area. Fractal dimensions are a measure for the tortuosity of a line, in this c...
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.
Directory of Open Access Journals (Sweden)
Miguel Nogueira
Full Text Available The equivalency between the power law behavior of Multiscale Entropy (MSE and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the
Exploring the link between multiscale entropy and fractal scaling behavior in near-surface wind.
Nogueira, Miguel
2017-01-01
The equivalency between the power law behavior of Multiscale Entropy (MSE) and of power spectra opens a promising path for interpretation of complex time-series, which is explored here for the first time for atmospheric fields. Additionally, the present manuscript represents a new independent empirical validation of such relationship, the first one for the atmosphere. The MSE-fractal relationship is verified for synthetic fractal time-series covering the full range of exponents typically observed in the atmosphere. It is also verified for near-surface wind observations from anemometers and CFSR re-analysis product. The results show a ubiquitous β ≈ 5/3 behavior inside the inertial range. A scaling break emerges at scales around a few seconds, with a tendency towards 1/f noise. The presence, extension and fractal exponent of this intermediate range are dependent on the particular surface forcing and atmospheric conditions. MSE shows an identical picture which is consistent with the turbulent energy cascade model: viscous dissipation at the small-scale end of the inertial range works as an information sink, while at the larger (energy-containing) scales the multiple forcings in the boundary layer act as widespread information sources. Another scaling transition occurs at scales around 1-10 days, with an abrupt flattening of the spectrum. MSE shows that this transition corresponds to a maximum of the new information introduced, occurring at the time-scales of the synoptic features that dominate weather patterns. At larger scales, a scaling regime with flatter slopes emerges extending to scales larger than 1 year. MSE analysis shows that the amount of new information created decreases with increasing scale in this low-frequency regime. Additionally, in this region the energy injection is concentrated in two large energy peaks: daily and yearly time-scales. The results demonstrate that the superposition of these periodic signals does not destroy the underlying
Directory of Open Access Journals (Sweden)
Painter Page R
2005-08-01
Full Text Available Abstract Background A prominent theoretical explanation for 3/4-power allometric scaling of metabolism proposes that the nutrient exchange surface of capillaries has properties of a space-filling fractal. The theory assumes that nutrient exchange surface area has a fractal dimension equal to or greater than 2 and less than or equal to 3 and that the volume filled by the exchange surface area has a fractal dimension equal to or greater than 3 and less than or equal to 4. Results It is shown that contradicting predictions can be derived from the assumptions of the model. When errors in the model are corrected, it is shown to predict that metabolic rate is proportional to body mass (proportional scaling. Conclusion The presence of space-filling fractal nutrient exchange surfaces does not provide a satisfactory explanation for 3/4-power metabolic rate scaling.
The fourth dimension of life: fractal geometry and allometric scaling of organisms.
West, G B; Brown, J H; Enquist, B J
1999-06-04
Fractal-like networks effectively endow life with an additional fourth spatial dimension. This is the origin of quarter-power scaling that is so pervasive in biology. Organisms have evolved hierarchical branching networks that terminate in size-invariant units, such as capillaries, leaves, mitochondria, and oxidase molecules. Natural selection has tended to maximize both metabolic capacity, by maximizing the scaling of exchange surface areas, and internal efficiency, by minimizing the scaling of transport distances and times. These design principles are independent of detailed dynamics and explicit models and should apply to virtually all organisms.
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...
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.
Empirical analysis of scaling and fractal characteristics of outpatients
Energy Technology Data Exchange (ETDEWEB)
Zhang, Li-Jiang, E-mail: zljjiang@gmail.com [College of Management and Economics, Tianjin University, Tianjin 300072 (China); Management Institute, Xinxiang Medical University, Xinxiang 453003, Henan (China); Liu, Zi-Xian, E-mail: liuzixian@tju.edu.cn [College of Management and Economics, Tianjin University, Tianjin 300072 (China); Guo, Jin-Li, E-mail: phd5816@163.com [Business School, University of Shanghai for Science and Technology, Shanghai 200093 (China)
2014-01-31
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.
Dynamical properties of fractal networks: Scaling, numerical simulations, and physical realizations
International Nuclear Information System (INIS)
Nakayama, T.; Yakubo, K.; Orbach, R.L.
1994-01-01
This article describes the advances that have been made over the past ten years on the problem of fracton excitations in fractal structures. The relevant systems to this subject are so numerous that focus is limited to a specific structure, the percolating network. Recent progress has followed three directions: scaling, numerical simulations, and experiment. In a happy coincidence, large-scale computations, especially those involving array processors, have become possible in recent years. Experimental techniques such as light- and neutron-scattering experiments have also been developed. Together, they form the basis for a review article useful as a guide to understanding these developments and for charting future research directions. In addition, new numerical simulation results for the dynamical properties of diluted antiferromagnets are presented and interpreted in terms of scaling arguments. The authors hope this article will bring the major advances and future issues facing this field into clearer focus, and will stimulate further research on the dynamical properties of random systems
Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue
Energy Technology Data Exchange (ETDEWEB)
Paggi, Marco [Politecnico di Torino, Department of Structural Engineering and Geotechnics, Corso Duca degli Abruzzi 24, 10129 Torino (Italy)], E-mail: marco.paggi@polito.it; Carpinteri, Alberto [Politecnico di Torino, Department of Structural Engineering and Geotechnics, Corso Duca degli Abruzzi 24, 10129 Torino (Italy)
2009-05-15
The enhanced ability to detect and measure very short cracks, along with a great interest in applying fracture mechanics formulae to smaller and smaller crack sizes, has pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris' constant C are only two notable examples of these anomalous scaling laws. In this framework, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. In this paper, we propose a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue. The limitations of each model are put into evidence and removed. At the end, a new generalized theory based on fractal geometry is proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical formulation. Finally, this approach is herein used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals.
Fractal and multifractal approaches for the analysis of crack-size dependent scaling laws in fatigue
International Nuclear Information System (INIS)
Paggi, Marco; Carpinteri, Alberto
2009-01-01
The enhanced ability to detect and measure very short cracks, along with a great interest in applying fracture mechanics formulae to smaller and smaller crack sizes, has pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The crack-size dependencies of both the fatigue threshold and the Paris' constant C are only two notable examples of these anomalous scaling laws. In this framework, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. In this paper, we propose a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue. The limitations of each model are put into evidence and removed. At the end, a new generalized theory based on fractal geometry is proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical formulation. Finally, this approach is herein used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals.
Directory of Open Access Journals (Sweden)
Howard A Crystal
Full Text Available The fractal dimension of retinal arteries and veins is a measure of the complexity of the vascular tree. We hypothesized that retinal fractal dimension would be associated with brain volume and white matter integrity in HIV-infected women.Nested case-control within longitudinal cohort study.Women were recruited from the Brooklyn site of the Women's Interagency HIV study (WIHS; 34 HIV-infected and 21 HIV-uninfected women with analyzable MRIs and retinal photographs were included. Fractal dimension was determined using the SIVA software program on skeletonized retinal images. The relationship between predictors (retinal vascular measures and outcomes (quantitative MRI measures were analyzed with linear regression models. All models included age, intracranial volume, and both arterial and venous fractal dimension. Some models were adjusted for blood pressure, race/ethnicity, and HIV-infection.The women were 45.6 ± 7.3 years of age. Higher arterial dimension was associated with larger cortical volumes, but higher venous dimension was associated with smaller cortical volumes. In fully adjusted models, venous dimension was significantly associated with fractional anisotropy (standardized β = -0.41, p = 0.009 and total gray matter volume (β = -0.24, p = 0.03, and arterial dimension with mean diffusivity (β = -0.33,.p = 0.04 and fractional anisotropy (β = 0.34, p = 0.03. HIV-infection was not associated with any retinal or MRI measure.Higher venous fractal dimension was associated with smaller cortical volumes and lower fractional anisotropy, whereas higher arterial fractal dimension was associated with the opposite patterns. Longitudinal studies are needed to validate this finding.
Crystal, Howard A; Holman, Susan; Lui, Yvonne W; Baird, Alison E; Yu, Hua; Klein, Ronald; Rojas-Soto, Diana Marcella; Gustafson, Deborah R; Stebbins, Glenn T
2016-01-01
The fractal dimension of retinal arteries and veins is a measure of the complexity of the vascular tree. We hypothesized that retinal fractal dimension would be associated with brain volume and white matter integrity in HIV-infected women. Nested case-control within longitudinal cohort study. Women were recruited from the Brooklyn site of the Women's Interagency HIV study (WIHS); 34 HIV-infected and 21 HIV-uninfected women with analyzable MRIs and retinal photographs were included. Fractal dimension was determined using the SIVA software program on skeletonized retinal images. The relationship between predictors (retinal vascular measures) and outcomes (quantitative MRI measures) were analyzed with linear regression models. All models included age, intracranial volume, and both arterial and venous fractal dimension. Some models were adjusted for blood pressure, race/ethnicity, and HIV-infection. The women were 45.6 ± 7.3 years of age. Higher arterial dimension was associated with larger cortical volumes, but higher venous dimension was associated with smaller cortical volumes. In fully adjusted models, venous dimension was significantly associated with fractional anisotropy (standardized β = -0.41, p = 0.009) and total gray matter volume (β = -0.24, p = 0.03), and arterial dimension with mean diffusivity (β = -0.33,.p = 0.04) and fractional anisotropy (β = 0.34, p = 0.03). HIV-infection was not associated with any retinal or MRI measure. Higher venous fractal dimension was associated with smaller cortical volumes and lower fractional anisotropy, whereas higher arterial fractal dimension was associated with the opposite patterns. Longitudinal studies are needed to validate this finding.
Afshinpour, Babak; Hossein-Zadeh, Gholam-Ali; Soltanian-Zadeh, Hamid
2008-06-30
Unknown low frequency fluctuations called "trend" are observed in noisy time-series measured for different applications. In some disciplines, they carry primary information while in other fields such as functional magnetic resonance imaging (fMRI) they carry nuisance effects. In all cases, however, it is necessary to estimate them accurately. In this paper, a method for estimating trend in the presence of fractal noise is proposed and applied to fMRI time-series. To this end, a partly linear model (PLM) is fitted to each time-series. The parametric and nonparametric parts of PLM are considered as contributions of hemodynamic response and trend, respectively. Using the whitening property of wavelet transform, the unknown components of the model are estimated in the wavelet domain. The results of the proposed method are compared to those of other parametric trend-removal approaches such as spline and polynomial models. It is shown that the proposed method improves activation detection and decreases variance of the estimated parameters relative to the other methods.
WE-E-17A-06: Assessing the Scale of Tumor Heterogeneity by Complete Hierarchical Segmentation On MRI
International Nuclear Information System (INIS)
Gensheimer, M; Trister, A; Ermoian, R; Hawkins, D
2014-01-01
Purpose: In many cancers, intratumoral heterogeneity exists in vascular and genetic structure. We developed an algorithm which uses clinical imaging to interrogate different scales of heterogeneity. We hypothesize that heterogeneity of perfusion at large distance scales may correlate with propensity for disease recurrence. We applied the algorithm to initial diagnosis MRI of rhabdomyosarcoma patients to predict recurrence. Methods: The Spatial Heterogeneity Analysis by Recursive Partitioning (SHARP) algorithm recursively segments the tumor image. The tumor is repeatedly subdivided, with each dividing line chosen to maximize signal intensity difference between the two subregions. This process continues to the voxel level, producing segments at multiple scales. Heterogeneity is measured by comparing signal intensity histograms between each segmented region and the adjacent region. We measured the scales of contrast enhancement heterogeneity of the primary tumor in 18 rhabdomyosarcoma patients. Using Cox proportional hazards regression, we explored the influence of heterogeneity parameters on relapse-free survival (RFS). To compare with existing methods, fractal and Haralick texture features were also calculated. Results: The complete segmentation produced by SHARP allows extraction of diverse features, including the amount of heterogeneity at various distance scales, the area of the tumor with the most heterogeneity at each scale, and for a given point in the tumor, the heterogeneity at different scales. 10/18 rhabdomyosarcoma patients suffered disease recurrence. On contrast-enhanced MRI, larger scale of maximum signal intensity heterogeneity, relative to tumor diameter, predicted for shorter RFS (p=0.05). Fractal dimension, fractal fit, and three Haralick features did not predict RFS (p=0.09-0.90). Conclusion: SHARP produces an automatic segmentation of tumor regions and reports the amount of heterogeneity at various distance scales. In rhabdomyosarcoma, RFS was
Time scale defined by the fractal structure of the price fluctuations in foreign exchange markets
Kumagai, Yoshiaki
2010-04-01
In this contribution, a new time scale named C-fluctuation time is defined by price fluctuations observed at a given resolution. The intraday fractal structures and the relations of the three time scales: real time (physical time), tick time and C-fluctuation time, in foreign exchange markets are analyzed. The data set used is trading prices of foreign exchange rates; US dollar (USD)/Japanese yen (JPY), USD/Euro (EUR), and EUR/JPY. The accuracy of the data is one minute and data within a minute are recorded in order of transaction. The series of instantaneous velocity of C-fluctuation time flowing are exponentially distributed for small C when they are measured by real time and for tiny C when they are measured by tick time. When the market is volatile, for larger C, the series of instantaneous velocity are exponentially distributed.
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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
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
Feng, Guixiang; Ming, Dongping; Wang, Min; Yang, Jianyu
2017-06-01
Scale problems are a major source of concern in the field of remote sensing. Since the remote sensing is a complex technology system, there is a lack of enough cognition on the connotation of scale and scale effect in remote sensing. Thus, this paper first introduces the connotations of pixel-based scale and summarizes the general understanding of pixel-based scale effect. Pixel-based scale effect analysis is essentially important for choosing the appropriate remote sensing data and the proper processing parameters. Fractal dimension is a useful measurement to analysis pixel-based scale. However in traditional fractal dimension calculation, the impact of spatial resolution is not considered, which leads that the scale effect change with spatial resolution can't be clearly reflected. Therefore, this paper proposes to use spatial resolution as the modified scale parameter of two fractal methods to further analyze the pixel-based scale effect. To verify the results of two modified methods (MFBM (Modified Windowed Fractal Brownian Motion Based on the Surface Area) and MDBM (Modified Windowed Double Blanket Method)); the existing scale effect analysis method (information entropy method) is used to evaluate. And six sub-regions of building areas and farmland areas were cut out from QuickBird images to be used as the experimental data. The results of the experiment show that both the fractal dimension and information entropy present the same trend with the decrease of spatial resolution, and some inflection points appear at the same feature scales. Further analysis shows that these feature scales (corresponding to the inflection points) are related to the actual sizes of the geo-object, which results in fewer mixed pixels in the image, and these inflection points are significantly indicative of the observed features. Therefore, the experiment results indicate that the modified fractal methods are effective to reflect the pixel-based scale effect existing in remote sensing
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.
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 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.
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.
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)
International Nuclear Information System (INIS)
Dickau, Jonathan J.
2009-01-01
The use of fractals and fractal-like forms to describe or model the universe has had a long and varied history, which begins long before the word fractal was actually coined. Since the introduction of mathematical rigor to the subject of fractals, by Mandelbrot and others, there have been numerous cosmological theories and analyses of astronomical observations which suggest that the universe exhibits fractality or is by nature fractal. In recent years, the term fractal cosmology has come into usage, as a description for those theories and methods of analysis whereby a fractal nature of the cosmos is shown.
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.
Assessing the scale of tumor heterogeneity by complete hierarchical segmentation of MRI
International Nuclear Information System (INIS)
Gensheimer, Michael F; Ermoian, Ralph P; Hawkins, Douglas S; Trister, Andrew D
2015-01-01
In many cancers, intratumoral heterogeneity has been found in histology, genetic variation and vascular structure. We developed an algorithm to interrogate different scales of heterogeneity using clinical imaging. We hypothesize that heterogeneity of perfusion at coarse scale may correlate with treatment resistance and propensity for disease recurrence. The algorithm recursively segments the tumor image into increasingly smaller regions. Each dividing line is chosen so as to maximize signal intensity difference between the two regions. This process continues until the tumor has been divided into single voxels, resulting in segments at multiple scales. For each scale, heterogeneity is measured by comparing each segmented region to the adjacent region and calculating the difference in signal intensity histograms. Using digital phantom images, we showed that the algorithm is robust to image artifacts and various tumor shapes. We then measured the primary tumor scales of contrast enhancement heterogeneity in MRI of 18 rhabdomyosarcoma patients. Using Cox proportional hazards regression, we explored the influence of heterogeneity parameters on relapse-free survival. Coarser scale of maximum signal intensity heterogeneity was prognostic of shorter survival (p = 0.05). By contrast, two fractal parameters and three Haralick texture features were not prognostic. In summary, our algorithm produces a biologically motivated segmentation of tumor regions and reports the amount of heterogeneity at various distance scales. If validated on a larger dataset, this prognostic imaging biomarker could be useful to identify patients at higher risk for recurrence and candidates for alternative treatment. (paper)
Assessing the scale of tumor heterogeneity by complete hierarchical segmentation of MRI.
Gensheimer, Michael F; Hawkins, Douglas S; Ermoian, Ralph P; Trister, Andrew D
2015-02-07
In many cancers, intratumoral heterogeneity has been found in histology, genetic variation and vascular structure. We developed an algorithm to interrogate different scales of heterogeneity using clinical imaging. We hypothesize that heterogeneity of perfusion at coarse scale may correlate with treatment resistance and propensity for disease recurrence. The algorithm recursively segments the tumor image into increasingly smaller regions. Each dividing line is chosen so as to maximize signal intensity difference between the two regions. This process continues until the tumor has been divided into single voxels, resulting in segments at multiple scales. For each scale, heterogeneity is measured by comparing each segmented region to the adjacent region and calculating the difference in signal intensity histograms. Using digital phantom images, we showed that the algorithm is robust to image artifacts and various tumor shapes. We then measured the primary tumor scales of contrast enhancement heterogeneity in MRI of 18 rhabdomyosarcoma patients. Using Cox proportional hazards regression, we explored the influence of heterogeneity parameters on relapse-free survival. Coarser scale of maximum signal intensity heterogeneity was prognostic of shorter survival (p = 0.05). By contrast, two fractal parameters and three Haralick texture features were not prognostic. In summary, our algorithm produces a biologically motivated segmentation of tumor regions and reports the amount of heterogeneity at various distance scales. If validated on a larger dataset, this prognostic imaging biomarker could be useful to identify patients at higher risk for recurrence and candidates for alternative treatment.
McAteer, R. T. James
2015-08-01
My soul is spiraling in frozen fractals all around, And one thought crystallizes like an icy blast, I'm never going back, the past is in the past.Elsa, from Disney’s Frozen, characterizes two fundamental aspects of scale-free processes in Nature: fractals are everywhere in space; fractals can be used to probe changes in time. Self-Organized Criticality provides a powerful set of tools to study scale-free processes. It connects spatial fractals (more generically, multifractals) to temporal evolution. The drawback is that this usually results in scale-free, unit-less, indices, which can be difficult to connect to everyday physics. Here, I show a novel method that connects one of the most powerful SOC tools - the wavelet transform modulus maxima approach to calculating multifractality - to one of the most powerful equations in all of physics - Ampere’s law. In doing so I show how the multifractal spectra can be expressed in terms of current density, and how current density can then be used for the prediction of future energy release from such a system.Our physical understanding of the solar magnetic field structure, and hence our ability to predict solar activity, is limited by the type of data currently available. I show that the multifractal spectrum provides a powerful physical connection between the details of photospheric magnetic gradients of current data and the coronal magnetic structure. By decomposing Ampere’s law and comparing it to the wavelet transform modulus maximum method, I show how the scale-free Holder exponent provides a direct measure of current density across all relevant sizes. The prevalence of this current density across various scales is connected to its stability in time, and hence to the ability of the magnetic structure to store and then release energy. Hence (spatial) multifractals inform us of (future) solar activity.Finally I discuss how such an approach can be used in any study of scale-free processes, and highlight the necessary
Automatic initialization and quality control of large-scale cardiac MRI segmentations.
Albà, Xènia; Lekadir, Karim; Pereañez, Marco; Medrano-Gracia, Pau; Young, Alistair A; Frangi, Alejandro F
2018-01-01
Continuous advances in imaging technologies enable ever more comprehensive phenotyping of human anatomy and physiology. Concomitant reduction of imaging costs has resulted in widespread use of imaging in large clinical trials and population imaging studies. Magnetic Resonance Imaging (MRI), in particular, offers one-stop-shop multidimensional biomarkers of cardiovascular physiology and pathology. A wide range of analysis methods offer sophisticated cardiac image assessment and quantification for clinical and research studies. However, most methods have only been evaluated on relatively small databases often not accessible for open and fair benchmarking. Consequently, published performance indices are not directly comparable across studies and their translation and scalability to large clinical trials or population imaging cohorts is uncertain. Most existing techniques still rely on considerable manual intervention for the initialization and quality control of the segmentation process, becoming prohibitive when dealing with thousands of images. The contributions of this paper are three-fold. First, we propose a fully automatic method for initializing cardiac MRI segmentation, by using image features and random forests regression to predict an initial position of the heart and key anatomical landmarks in an MRI volume. In processing a full imaging database, the technique predicts the optimal corrective displacements and positions in relation to the initial rough intersections of the long and short axis images. Second, we introduce for the first time a quality control measure capable of identifying incorrect cardiac segmentations with no visual assessment. The method uses statistical, pattern and fractal descriptors in a random forest classifier to detect failures to be corrected or removed from subsequent statistical analysis. Finally, we validate these new techniques within a full pipeline for cardiac segmentation applicable to large-scale cardiac MRI databases. The
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.
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.
International Nuclear Information System (INIS)
Wang, Y.D.; Ren, Y.Q.; Hu, T.; Deng, B.; Xiao, T.Q.; Liu, K.Y.; Yang, Y.S.
2016-01-01
Three dimensional (3D) characterization of shales has recently attracted wide attentions in relation to the growing importance of shale oil and gas. Obtaining a complete 3D compositional distribution of shale has proven to be challenging due to its multi-scale characteristics. A combined multi-energy X-ray micro-CT technique and data-constrained modelling (DCM) approach has been used to quantitatively investigate the multi-scale mineral and porosity distributions of a heterogeneous shale from the Junger Basin, northwestern China by sub-sampling. The 3D sub-resolution structures of minerals and pores in the samples are quantitatively obtained as the partial volume fraction distributions, with colours representing compositions. The shale sub-samples from two areas have different physical structures for minerals and pores, with the dominant minerals being feldspar and dolomite, respectively. Significant heterogeneities have been observed in the analysis. The sub-voxel sized pores form large interconnected clusters with fractal structures. The fractal dimensions of the largest clusters for both sub-samples were quantitatively calculated and found to be 2.34 and 2.86, respectively. The results are relevant in quantitative modelling of gas transport in shale reservoirs
Fractals in several electrode materials
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Zhang, Chunyong, E-mail: zhangchy@njau.edu.cn [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); Wu, Jingyu [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Fu, Degang [Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); State Key Laboratory of Bioelectronics, Southeast University, Nanjing 210096 (China)
2014-09-15
Highlights: • Fractal geometry was employed to characterize three important electrode materials. • The surfaces of all studied electrodes were proved to be very rough. • The fractal dimensions of BDD and ACF were scale dependent. • MMO film was more uniform than BDD and ACF in terms of fractal structures. - Abstract: In the present paper, the fractal properties of boron-doped diamond (BDD), mixed metal oxide (MMO) and activated carbon fiber (ACF) electrode have been studied by SEM imaging at different scales. Three materials are self-similar with mean fractal dimension in the range of 2.6–2.8, confirming that they all exhibit very rough surfaces. Specifically, it is found that MMO film is more uniform in terms of fractal structure than BDD and ACF. As a result, the intriguing characteristics make these electrodes as ideal candidates for high-performance decontamination processes.
Saw, Vee-Liem; Chew, Lock Yue
2013-01-01
We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line ...
Peleg, M
1993-01-01
Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.
International Nuclear Information System (INIS)
Jinsheng Wang; Rui Zuo; Yanguo Teng; Zongjian Sun; Qinhong Hu
2010-01-01
Because of the deposit and accumulation from the debris flow, the heterogeneous geological characteristics is obvious for a candidate very low level waste (VLLW) disposal site, with the grain size ranging from tens of microns to 75 cm. Therefore, it is challenging to directly measure the sorption capacity of the media and the distribution coefficient of some radionuclides, such as strontium. We have studies the correlation of the particle mass content with different grade size and the sorption capacity, which is important in the modeling of radionuclide migration in the heterogeneous disposal site. A total of three deep pits and five shallow trenches were excavated, and 21 solid samples were collected for laboratory experiments. The grade and percentage of the different-sized particles were obtained, and the fractal dimension (D) of the media was calculated from the results of sieved experiments. Steady state sorption time and sorption isotherm of strontium was determined in the heterogeneous media, and sorption and distribution of strontium in the heterogeneous media were evaluated by the relationship between the mass percentage and distribution coefficient (K d ) of the fine-particle media, which was comprised of selected particles with a diameter less than 1 mm, and the correlation on the K d and D was regressed fit. The results indicated that fractal dimension bounded from 2.39 to 2.62 in the media, and K d values of strontium ranged between 119 and 126 in the fine-particle media, and corresponding value was 11 and 43 in the original media. The correlation between K d and D was approximately linear. (author)
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation ... involving scaling and memory effects. But most of ..... begin by recalling the definition of the Riemann integral in ordinary calculus [33]. Let g: [a ...
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.)
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
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.
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
Contour fractal analysis of grains
Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB
2017-06-01
Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.
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
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
International Nuclear Information System (INIS)
Li, W.; Bak, P.
1986-01-01
At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D = 1 to the cantorus is governed by an exponent ν = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent
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.
International Nuclear Information System (INIS)
Stemp, W James; Morozov, Mikhail; Key, Alastair J M
2015-01-01
Working load is one factor that affects wear on stone tools. Despite the recognition of the importance of the relationship between working load and the development of microwear on stone tools, there have been few attempts to quantify differences in wear due to changes in load. In a controlled experiment, we used 30 basalt flakes knapped from raw material collected in Olduvai Gorge, Tanzania, Africa, to cut oak branches for the same number of strokes. For each flake, a different loading level was applied starting at 150 g and increasing by increments of 150 g to a maximum load of 4.5 kg. A laser scanning confocal microscope was used to mathematically document the surface texture of the flakes. The worn surface data were compared using area-scale fractal complexity (Asfc), calculated from relative areas, to determine the degree to which variation in loading significantly affected the amount of wear on the flake surfaces. Our results indicate that working load does play a role in the development of lithic microwear on these flakes and that discrimination of two worn flake surfaces, using mean square ratios of Asfc, based on variable load is consistently possible with load differences between ∼100 g and 4.5 kg. However, discrimination of microwear on flake surfaces was not consistent for all load level differences and discrimination became less consistent when working load differences were below ∼100 g. (paper)
Randomness confidence bands of fractal scaling exponents for financial price returns
International Nuclear Information System (INIS)
Ibarra-Valdez, C.; Alvarez, J.; Alvarez-Ramirez, J.
2016-01-01
Highlights: • A robust test for randomness of price returns is proposed. • The DFA scaling exponent is contrasted against confidence bands for random sequences. • The size of the band depends of the sequence length. • Crude oil and USA stock markets have been rarely inefficient. - Abstract: The weak-form of the efficient market hypothesis (EMH) establishes that price returns behave as a pure random process and so their outcomes cannot be forecasted. The detrended fluctuation analysis (DFA) has been widely used to test the weak-form of the EMH by showing that time series of price returns are serially uncorrelated. In this case, the DFA scaling exponent exhibits deviations from the theoretical value of 0.5. This work considers the test of the EMH for DFA implementation on a sliding window, which is an approach that is intended to monitor the evolution of markets. Under these conditions, the scaling exponent exhibits important variations over the scrutinized period that can offer valuable insights in the behavior of the market provided the estimated scaling value is kept within strict statistical tests to verify the presence or not of serial correlations in the price returns. In this work, the statistical tests are based on comparing the estimated scaling exponent with the values obtained from pure Gaussian sequences with the length of the real time series. In this way, the presence of serial correlations can be guaranteed only in terms of the confidence bands of a pure Gaussian process. The crude oil (WTI) and the USA stock (DJIA) markets are used to illustrate the methodology.
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
Alzheimer's Disease Detection in Brain Magnetic Resonance Images Using Multiscale Fractal Analysis
International Nuclear Information System (INIS)
Lahmiri, Salim; Boukadoum, Mounir
2013-01-01
We present a new automated system for the detection of brain magnetic resonance images (MRI) affected by Alzheimer's disease (AD). The MRI is analyzed by means of multiscale analysis (MSA) to obtain its fractals at six different scales. The extracted fractals are used as features to differentiate healthy brain MRI from those of AD by a support vector machine (SVM) classifier. The result of classifying 93 brain MRIs consisting of 51 images of healthy brains and 42 of brains affected by AD, using leave-one-out cross-validation method, yielded 99.18% ± 0.01 classification accuracy, 100% sensitivity, and 98.20% ± 0.02 specificity. These results and a processing time of 5.64 seconds indicate that the proposed approach may be an efficient diagnostic aid for radiologists in the screening for AD
Energy Technology Data Exchange (ETDEWEB)
Ciuciu, P.; Rabrait, C. [CEA, Neuro Spin, Gif Sur Yvette (France); Abry, P.; Wendt, H. [Ecole Normale Super Lyon, Phys Lab, CNRS, UMR 5672, Lyon (France)
2008-07-01
Classical within-subject analysis in functional magnetic resonance imaging (fMRI) relies on a detection step to localize which parts of the brain are activated by a given stimulus type. This is usually achieved using model-based approaches. Here, we propose an alternative exploratory analysis. The originality of this contribution is twofold. First, we propose a synthetic, consistent, and comparative overview of the various stochastic processes and estimation procedures used to model and analyze scale invariance. Notably, it is explained how multifractal models are more versatile to adjust the scaling properties of fMRI data but require more elaborated analysis procedures. Second, we bring evidence of the existence of actual scaling in fMRI time series that are clearly disentangled from putative superimposed non-stationarities. By nature, scaling analysis requires the use of long enough signals with high frequency sampling rate. To this end, we make use of a localized 3-D echo volume imaging (EVI) technique, which has recently emerged in fMRI because it allows very fast acquisitions of successive brain volumes. High temporal resolution EVI fMRI data have been acquired both in resting state and during a slow event-related visual paradigm. A voxel-based systematic multifractal analysis has been performed over both kinds of data. Combining multifractal attribute estimates together with paired statistical tests, we observe significant scaling parameter changes between ongoing and evoked brain activity, which clearly validate an increase in long memory and suggest a global multi-fractality decrease effect under activation. (authors)
International Nuclear Information System (INIS)
Lebedev, D. V.; Filatov, M. V.; Kuklin, A. I.; Islamov, A. Kh.; Stellbrink, J.; Pantina, R. A.; Denisov, Yu. Yu.; Toperverg, B. P.; Isaev-Ivanov, V. V.
2008-01-01
The chromatin organization in chicken erythrocyte nuclei was studied by small-angle neutron scattering in the scattering-vector range from 1.5 x 10 -1 to 10 -4 A -1 with the use of the contrast-variation technique. This scattering-vector range corresponds to linear dimensions from 4 nm to 6 μm and covers the whole hierarchy of chromatin structures, from the nucleosomal structure to the entire nucleus. The results of the present study allowed the following conclusions to be drawn: (1) both the chromatin-protein structure and the structure of the nucleic acid component in chicken erythrocyte nuclei have mass-fractal properties, (2) the structure of the protein component of chromatin exhibits a fractal behavior on scales extending over two orders of magnitude, from the nucleosomal size to the size of an entire nucleus, and (3) the structure of the nucleic acid component of chromatin in chicken erythrocyte nuclei is likewise of a fractal nature and has two levels of organization or two phases with the crossover point at about 300-400 nm
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.
Fractal characterization of the compaction and sintering of ferrites
Glass, H.J.; With, de G.
2001-01-01
A novel parameter, the fractal exponent DE, is derived using the concept of fractal scaling. The fractal exponent DE relates the development of a feature within a material to the development of the size of the material. As an application, structural changes during the compaction and sintering of
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.
2016-10-01
Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the
Applications of fractals in ecology.
Sugihara, G; M May, R
1990-03-01
Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost ... Here a(t) is the cosmic scale factor and it measures the expansion of the Universe. ..... effectively appear as self-conserved dark energy, with a non-trivial ...
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...
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
FELICIA RAMONA BIRAU
2012-01-01
In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and...
Fractal description of fractures
International Nuclear Information System (INIS)
Lung, C.W.
1991-06-01
Recent studies on the fractal description of fractures are reviewed. Some problems on this subject are discussed. It seems hopeful to use the fractal dimension as a parameter for quantitative fractography and to apply fractal structures to the development of high toughness materials. (author). 28 refs, 7 figs
Directory of Open Access Journals (Sweden)
G C Young
Full Text Available We present a method to construct and analyse 3D models of underwater scenes using a single cost-effective camera on a standard laptop with (a free or low-cost software, (b no computer programming ability, and (c minimal man hours for both filming and analysis. This study focuses on four key structural complexity metrics: point-to-point distances, linear rugosity (R, fractal dimension (D, and vector dispersion (1/k. We present the first assessment of accuracy and precision of structure-from-motion (SfM 3D models from an uncalibrated GoPro™ camera at a small scale (4 m2 and show that they can provide meaningful, ecologically relevant results. Models had root mean square errors of 1.48 cm in X-Y and 1.35 in Z, and accuracies of 86.8% (R, 99.6% (D at scales 30-60 cm, 93.6% (D at scales 1-5 cm, and 86.9 (1/k. Values of R were compared to in-situ chain-and-tape measurements, while values of D and 1/k were compared with ground truths from 3D printed objects modelled underwater. All metrics varied less than 3% between independently rendered models. We thereby improve and rigorously validate a tool for ecologists to non-invasively quantify coral reef structural complexity with a variety of multi-scale metrics.
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.
Directory of Open Access Journals (Sweden)
FELICIA RAMONA BIRAU
2012-05-01
Full Text Available In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and of course, the manner in which they interpret that information may be different. Also, Fractal Market Hypothesis refers to the way that liquidity and investment horizons influence the behaviour of financial investors.
DEFF Research Database (Denmark)
Schroeter, Aileen; Rudin, Markus; Gianolio, Eliana
2017-01-01
This chapter discusses principles of nuclear magnetic resonance (NMR) and MRI followed by a survey on the major classes of MRI contrast agents (CA), their modes of action, and some of the most significative applications. The two more established classes of MRI-CA are represented by paramagnetic...... been attained that markedly increase the number and typology of systems with CEST properties. Currently much attention is also devoted to hyperpolarized molecules that display a sensitivity enhancement sufficient for their direct exploitation for the formation of the MR image. A real breakthrough...
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.
Fractal Structure and Entropy Production within the Central Nervous System
Directory of Open Access Journals (Sweden)
Andrew J. E. Seely
2014-08-01
Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.
... the room. Pins, hairpins, metal zippers, and similar metallic items can distort the images. Removable dental work ... an MRI can cause heart pacemakers and other implants not to work as well. The magnets can ...
Classification of radar echoes using fractal geometry
International Nuclear Information System (INIS)
Azzaz, Nafissa; Haddad, Boualem
2017-01-01
Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.
FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY
Directory of Open Access Journals (Sweden)
Ian Parkinson
2011-05-01
Full Text Available A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge. The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals, with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.
Uritskaya, Olga Y.
2005-05-01
Results of fractal stability analysis of daily exchange rate fluctuations of more than 30 floating currencies for a 10-year period are presented. It is shown for the first time that small- and large-scale dynamical instabilities of national monetary systems correlate with deviations of the detrended fluctuation analysis (DFA) exponent from the value 1.5 predicted by the efficient market hypothesis. The observed dependence is used for classification of long-term stability of floating exchange rates as well as for revealing various forms of distortion of stable currency dynamics prior to large-scale crises. A normal range of DFA exponents consistent with crisis-free long-term exchange rate fluctuations is determined, and several typical scenarios of unstable currency dynamics with DFA exponents fluctuating beyond the normal range are identified. It is shown that monetary crashes are usually preceded by prolonged periods of abnormal (decreased or increased) DFA exponent, with the after-crash exponent tending to the value 1.5 indicating a more reliable exchange rate dynamics. Statistically significant regression relations (R=0.99, pcurrency crises and the degree of distortion of monofractal patterns of exchange rate dynamics are found. It is demonstrated that the parameters of these relations characterizing small- and large-scale crises are nearly equal, which implies a common instability mechanism underlying these events. The obtained dependences have been used as a basic ingredient of a forecasting technique which provided correct in-sample predictions of monetary crisis magnitude and duration over various time scales. The developed technique can be recommended for real-time monitoring of dynamical stability of floating exchange rate systems and creating advanced early-warning-system models for currency crisis prevention.
Exploring connectivity with large-scale Granger causality on resting-state functional MRI.
DSouza, Adora M; Abidin, Anas Z; Leistritz, Lutz; Wismüller, Axel
2017-08-01
Large-scale Granger causality (lsGC) is a recently developed, resting-state functional MRI (fMRI) connectivity analysis approach that estimates multivariate voxel-resolution connectivity. Unlike most commonly used multivariate approaches, which establish coarse-resolution connectivity by aggregating voxel time-series avoiding an underdetermined problem, lsGC estimates voxel-resolution, fine-grained connectivity by incorporating an embedded dimension reduction. We investigate application of lsGC on realistic fMRI simulations, modeling smoothing of neuronal activity by the hemodynamic response function and repetition time (TR), and empirical resting-state fMRI data. Subsequently, functional subnetworks are extracted from lsGC connectivity measures for both datasets and validated quantitatively. We also provide guidelines to select lsGC free parameters. Results indicate that lsGC reliably recovers underlying network structure with area under receiver operator characteristic curve (AUC) of 0.93 at TR=1.5s for a 10-min session of fMRI simulations. Furthermore, subnetworks of closely interacting modules are recovered from the aforementioned lsGC networks. Results on empirical resting-state fMRI data demonstrate recovery of visual and motor cortex in close agreement with spatial maps obtained from (i) visuo-motor fMRI stimulation task-sequence (Accuracy=0.76) and (ii) independent component analysis (ICA) of resting-state fMRI (Accuracy=0.86). Compared with conventional Granger causality approach (AUC=0.75), lsGC produces better network recovery on fMRI simulations. Furthermore, it cannot recover functional subnetworks from empirical fMRI data, since quantifying voxel-resolution connectivity is not possible as consequence of encountering an underdetermined problem. Functional network recovery from fMRI data suggests that lsGC gives useful insight into connectivity patterns from resting-state fMRI at a multivariate voxel-resolution. Copyright © 2017 Elsevier B.V. All
Fractal nature of humic materials
International Nuclear Information System (INIS)
Rice, J.A.
1992-01-01
Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this ''disorder within disorder.'' Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fraction has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis
Baryshev, Yuri
2002-01-01
This is the first book to present the fascinating new results on the largest fractal structures in the universe. It guides the reader, in a simple way, to the frontiers of astronomy, explaining how fractals appear in cosmic physics, from our solar system to the megafractals in deep space. It also offers a personal view of the history of the idea of self-similarity and of cosmological principles, from Plato's ideal architecture of the heavens to Mandelbrot's fractals in the modern physical cosmos. In addition, this invaluable book presents the great fractal debate in astronomy (after Luciano Pi
Fractal characterization of brain lesions in CT images
International Nuclear Information System (INIS)
Jauhari, Rajnish K.; Trivedi, Rashmi; Munshi, Prabhat; Sahni, Kamal
2005-01-01
Fractal Dimension (FD) is a parameter used widely for classification, analysis, and pattern recognition of images. In this work we explore the quantification of CT (computed tomography) lesions of the brain by using fractal theory. Five brain lesions, which are portions of CT images of diseased brains, are used for the study. These lesions exhibit self-similarity over a chosen range of scales, and are broadly characterized by their fractal dimensions
Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation
Directory of Open Access Journals (Sweden)
Zhen Yao
2004-12-01
Full Text Available A hybrid 3D compression scheme which combines fractal coding with neighbourhood vector quantisation for video and volume data is reported. While fractal coding exploits the redundancy present in different scales, neighbourhood vector quantisation, as a generalisation of translational motion compensation, is a useful method for removing both intra- and inter-frame coherences. The hybrid coder outperforms most of the fractal coders published to date while the algorithm complexity is kept relatively low.
Cerebellum segmentation in MRI using atlas registration and local multi-scale image descriptors
DEFF Research Database (Denmark)
van der Lijn, F.; de Bruijne, M.; Hoogendam, Y.Y.
2009-01-01
We propose a novel cerebellum segmentation method for MRI, based on a combination of statistical models of the structure's expected location in the brain and its local appearance. The appearance model is obtained from a k-nearest-neighbor classifier, which uses a set of multi-scale local image...
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
Fractal analytical approach of urban form based on spatial correlation function
International Nuclear Information System (INIS)
Chen, Yanguang
2013-01-01
Highlights: ► Many fractal parameter relations of cities can be derived by scaling analysis. ► The area-radius scaling of cities suggests a spatial correlation function. ► Spectral analysis can be used to estimate fractal dimension values of urban form. ► The valid range of fractal dimension of urban form comes between 1.5 and 2. ► The traditional scale concept will be replaced by scaling concept in geography. -- Abstract: Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning
Categorization of fractal plants
International Nuclear Information System (INIS)
Chandra, Munesh; Rani, Mamta
2009-01-01
Fractals in nature are always a result of some growth process. The language of fractals which has been created specifically for the description of natural growth process is called L-systems. Recently, superior iterations (essentially, investigated by Mann [Mann WR. Mean value methods in iteration. Proc Am Math Soc 1953;4:506-10 [MR0054846 (14,988f)
Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L.
1997-01-01
We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.
Thermodynamics for Fractal Statistics
da Cruz, Wellington
1998-01-01
We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Scale-Free Brain-Wave Music from Simultaneously EEG and fMRI Recordings
Lu, Jing; Wu, Dan; Yang, Hua; Luo, Cheng; Li, Chaoyi; Yao, Dezhong
2012-01-01
In the past years, a few methods have been developed to translate human EEG to music. In 2009, PloS One 4 e5915, we developed a method to generate scale-free brainwave music where the amplitude of EEG was translated to music pitch according to the power law followed by both of them, the period of an EEG waveform is translated directly to the duration of a note, and the logarithm of the average power change of EEG is translated to music intensity according to the Fechner's law. In this work, we proposed to adopt simultaneously-recorded fMRI signal to control the intensity of the EEG music, thus an EEG-fMRI music is generated by combining two different and simultaneous brain signals. And most importantly, this approach further realized power law for music intensity as fMRI signal follows it. Thus the EEG-fMRI music makes a step ahead in reflecting the physiological process of the scale-free brain. PMID:23166768
Scale-free brain-wave music from simultaneously EEG and fMRI recordings.
Lu, Jing; Wu, Dan; Yang, Hua; Luo, Cheng; Li, Chaoyi; Yao, Dezhong
2012-01-01
In the past years, a few methods have been developed to translate human EEG to music. In 2009, PloS One 4 e5915, we developed a method to generate scale-free brainwave music where the amplitude of EEG was translated to music pitch according to the power law followed by both of them, the period of an EEG waveform is translated directly to the duration of a note, and the logarithm of the average power change of EEG is translated to music intensity according to the Fechner's law. In this work, we proposed to adopt simultaneously-recorded fMRI signal to control the intensity of the EEG music, thus an EEG-fMRI music is generated by combining two different and simultaneous brain signals. And most importantly, this approach further realized power law for music intensity as fMRI signal follows it. Thus the EEG-fMRI music makes a step ahead in reflecting the physiological process of the scale-free brain.
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.
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 ...
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.
Estimation of brain activation in response to major and minor scales by fMRI
International Nuclear Information System (INIS)
Fujimaki, Takuya; Nemoto, Iku
2011-01-01
We made fMRI measurements of the brain responses to major and minor scales which are the fundamental elements for making melodies in music. In addition, we used an arpeggio of diminished 7th. For a control stimulus, we provided a sequence of repeated single tones. The ascending scales of 12 major and 12 minor keys were made starting from F no.3 to F4. Each scale was 3 s in duration. A 3 s scan was performed 2-3 s (randomized) after a scale has been finished and repeated every 14 s (sparse time scanning). Typically, major scales activated the left inferior frontal gyrus, minor scales the posterior cingulate gyrus and the diminished arpeggio the left auditory cortex. In general, the left hemisphere was more activated than usually seen in responses to music. (author)
Li, Xin; Cai, Yu; Moloney, Brendan; Chen, Yiyi; Huang, Wei; Woods, Mark; Coakley, Fergus V; Rooney, William D; Garzotto, Mark G; Springer, Charles S
2016-08-01
Dynamic-Contrast-Enhanced Magnetic Resonance Imaging (DCE-MRI) has been used widely for clinical applications. Pharmacokinetic modeling of DCE-MRI data that extracts quantitative contrast reagent/tissue-specific model parameters is the most investigated method. One of the primary challenges in pharmacokinetic analysis of DCE-MRI data is accurate and reliable measurement of the arterial input function (AIF), which is the driving force behind all pharmacokinetics. Because of effects such as inflow and partial volume averaging, AIF measured from individual arteries sometimes require amplitude scaling for better representation of the blood contrast reagent (CR) concentration time-courses. Empirical approaches like blinded AIF estimation or reference tissue AIF derivation can be useful and practical, especially when there is no clearly visible blood vessel within the imaging field-of-view (FOV). Similarly, these approaches generally also require magnitude scaling of the derived AIF time-courses. Since the AIF varies among individuals even with the same CR injection protocol and the perfect scaling factor for reconstructing the ground truth AIF often remains unknown, variations in estimated pharmacokinetic parameters due to varying AIF scaling factors are of special interest. In this work, using simulated and real prostate cancer DCE-MRI data, we examined parameter variations associated with AIF scaling. Our results show that, for both the fast-exchange-limit (FXL) Tofts model and the water exchange sensitized fast-exchange-regime (FXR) model, the commonly fitted CR transfer constant (K(trans)) and the extravascular, extracellular volume fraction (ve) scale nearly proportionally with the AIF, whereas the FXR-specific unidirectional cellular water efflux rate constant, kio, and the CR intravasation rate constant, kep, are both AIF scaling insensitive. This indicates that, for DCE-MRI of prostate cancer and possibly other cancers, kio and kep may be more suitable imaging
a Fractal Network Model for Fractured Porous Media
Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung
2016-04-01
The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.
Large-scale Granger causality analysis on resting-state functional MRI
D'Souza, Adora M.; Abidin, Anas Zainul; Leistritz, Lutz; Wismüller, Axel
2016-03-01
We demonstrate an approach to measure the information flow between each pair of time series in resting-state functional MRI (fMRI) data of the human brain and subsequently recover its underlying network structure. By integrating dimensionality reduction into predictive time series modeling, large-scale Granger Causality (lsGC) analysis method can reveal directed information flow suggestive of causal influence at an individual voxel level, unlike other multivariate approaches. This method quantifies the influence each voxel time series has on every other voxel time series in a multivariate sense and hence contains information about the underlying dynamics of the whole system, which can be used to reveal functionally connected networks within the brain. To identify such networks, we perform non-metric network clustering, such as accomplished by the Louvain method. We demonstrate the effectiveness of our approach to recover the motor and visual cortex from resting state human brain fMRI data and compare it with the network recovered from a visuomotor stimulation experiment, where the similarity is measured by the Dice Coefficient (DC). The best DC obtained was 0.59 implying a strong agreement between the two networks. In addition, we thoroughly study the effect of dimensionality reduction in lsGC analysis on network recovery. We conclude that our approach is capable of detecting causal influence between time series in a multivariate sense, which can be used to segment functionally connected networks in the resting-state fMRI.
Willson, Stephen J.
1991-01-01
Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)
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
Mitered fractal trees: constructions and properties
Verhoeff, T.; Verhoeff, K.; Bosch, R.; McKenna, D.; Sarhangi, R.
2012-01-01
Tree-like structures, that is, branching structures without cycles, are attractive for artful expression. Especially interesting are fractal trees, where each subtree is a scaled and possibly otherwise transformed version of the entire tree. Such trees can be rendered in 3D by using beams with a
Fractal-based exponential distribution of urban density and self-affine fractal forms of cities
International Nuclear Information System (INIS)
Chen Yanguang; Feng Jian
2012-01-01
Highlights: ► The model of urban population density differs from the common exponential function. ► Fractal landscape influences the exponential distribution of urban density. ► The exponential distribution of urban population suggests a self-affine fractal. ► Urban space can be divided into three layers with scaling and non-scaling regions. ► The dimension of urban form with characteristic scale can be treated as 2. - Abstract: Urban population density always follows the exponential distribution and can be described with Clark’s model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark’s model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark’s model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.
Energy Technology Data Exchange (ETDEWEB)
Verhagen, Martijn V.; Guit, Gerard L. [Spaarne Gasthuis, Department of Radiology, Haarlem (Netherlands); Hafkamp, Gerrit Jan; Kalisvaart, Kees [Spaarne Gasthuis, Department of Geriatrics, Haarlem (Netherlands)
2016-06-15
Dementia is foremost a clinical diagnosis. However, in diagnosing dementia, it is advocated to perform at least one neuroimaging study. This has two purposes: to rule out potential reversible dementia (PRD), and to help determine the dementia subtype. Our first goal was to establish if MRI combined with visual rating scales changes the clinical diagnosis. The second goal was to demonstrate if MRI contributes to a geriatrician's confidence in the diagnosis. The dementia subtype was determined prior to and after MRI. Scoring scales used were: global cortical atrophy (GCA), medial temporal atrophy (MTA), and white matter hyperintensity measured according to the Fazekas scale. The confidence level of the geriatrician was determined using a visual analogue scale. One hundred and thirty-five patients were included. After MRI, the diagnosis changed in 23.7 % (CI 17.0 %-31.1 %) of patients. Change was due to vascular aetiology in 13.3 % of patients. PRD was found in 2.2 % of all patients. The confidence level in the diagnosis increased significantly after MRI (p = 0.001). MRI, combined with visual rating scales, has a significant impact on dementia subtype diagnosis and on a geriatrician's confidence in the final diagnosis. (orig.)
International Nuclear Information System (INIS)
Verhagen, Martijn V.; Guit, Gerard L.; Hafkamp, Gerrit Jan; Kalisvaart, Kees
2016-01-01
Dementia is foremost a clinical diagnosis. However, in diagnosing dementia, it is advocated to perform at least one neuroimaging study. This has two purposes: to rule out potential reversible dementia (PRD), and to help determine the dementia subtype. Our first goal was to establish if MRI combined with visual rating scales changes the clinical diagnosis. The second goal was to demonstrate if MRI contributes to a geriatrician's confidence in the diagnosis. The dementia subtype was determined prior to and after MRI. Scoring scales used were: global cortical atrophy (GCA), medial temporal atrophy (MTA), and white matter hyperintensity measured according to the Fazekas scale. The confidence level of the geriatrician was determined using a visual analogue scale. One hundred and thirty-five patients were included. After MRI, the diagnosis changed in 23.7 % (CI 17.0 %-31.1 %) of patients. Change was due to vascular aetiology in 13.3 % of patients. PRD was found in 2.2 % of all patients. The confidence level in the diagnosis increased significantly after MRI (p = 0.001). MRI, combined with visual rating scales, has a significant impact on dementia subtype diagnosis and on a geriatrician's confidence in the final diagnosis. (orig.)
Variability of fractal dimension of solar radio flux
Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om
2018-04-01
In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti
2017-08-17
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti; Jiang, Qiu; Mashraei, Yousof; Salama, Khaled N.; Alshareef, Husam N.
2017-01-01
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
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.
Random walk through fractal environments
Isliker, H.; Vlahos, L.
2002-01-01
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...
Fractality and the law of the wall
Xu, Haosen H. A.; Yang, X. I. A.
2018-05-01
Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.
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
DEFF Research Database (Denmark)
Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.
2010-01-01
applications. THz radiation can be employed for various purposes, among them the study of vibrations in biological molecules, motion of electrons in semiconductors and propagation of acoustic shock waves in crystals. We propose here a new THz fractal MTM design that shows very high transmission in the desired...... frequency range as well as a clear differentiation between one polarisation and another. Based on theoretical predictions we fabricated and measured a fractal based THz metamaterial that shows more than 60% field transmission at around 1THz for TE polarized light while the TM waves have almost 80% field...... transmission peak at 0.6THz. One of the main characteristics of this design is its tunability by design: by simply changing the length of the fractal elements one can choose the operating frequency window. The modelling, fabrication and characterisation results will be presented in this paper. Due to the long...
Fractal 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 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....
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.
ABC of multi-fractal spacetimes and fractional sea turtles
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2016-04-15
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)
ABC of multi-fractal spacetimes and fractional sea turtles
International Nuclear Information System (INIS)
Calcagni, Gianluca
2016-01-01
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)
ABC of multi-fractal spacetimes and fractional sea turtles
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.
Fractal and mechanical micro- and nanorange properties of sylvite and halite crystals
Directory of Open Access Journals (Sweden)
Valery N. Aptukov
2017-09-01
Full Text Available This article involves the treatment of micro- and nanorange scanning and indentation data for salt rock crystals obtained with help of the scanning microscope Dimension Icon using the mathematical models. It also describes the basic methods of fractal analysis. It shows the effectiveness of the method of minimal covering which is chosen to research the fractal properties of salt rock crystal surfaces. The article includes the algorithm of this method and the description of its generalization for the two-dimensional case. The values of fractal index and multifractal parameters have been calculated on the basis of the minimal covering method. The article also involves the anisotropy effects for fractal properties, comparison of fractal behavior on different scale levels. It gives the values of hardness for different parts of the crystals and studies the correlation between hardness and fractal index and describes the character of the influence of fractal dimension on roughness.
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...
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.
Miller, Kai J.; Berendsen, Sharon; Seute, Tatjana; Yeom, Kristen; Gephardt, Melanie H.; Grant, Gerald A.; Robe, Pierre A.
2017-01-01
Background: Fractal structure is found throughout many processes in nature, and often arises from sets of simple rules. We examined MRI contrast enhancement patterns from glioblastoma patients for evidence of fractal structure and correlated these with gene expression patterns. Methods: For 39
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...
Directory of Open Access Journals (Sweden)
Luiz Felipe Vasconcellos
2017-01-01
Full Text Available Few studies have evaluated magnetic resonance imaging (MRI visual scales in Parkinson’s disease-Mild Cognitive Impairment (PD-MCI. We selected 79 PD patients and 92 controls (CO to perform neurologic and neuropsychological evaluation. Brain MRI was performed to evaluate the following scales: Global Cortical Atrophy (GCA, Fazekas, and medial temporal atrophy (MTA. The analysis revealed that both PD groups (amnestic and nonamnestic showed worse performance on several tests when compared to CO. Memory, executive function, and attention impairment were more severe in amnestic PD-MCI group. Overall analysis of frequency of MRI visual scales by MCI subtype did not reveal any statistically significant result. Statistically significant inverse correlation was observed between GCA scale and Mini-Mental Status Examination (MMSE, Montreal Cognitive Assessment (MoCA, semantic verbal fluency, Stroop test, figure memory test, trail making test (TMT B, and Rey Auditory Verbal Learning Test (RAVLT. The MTA scale correlated with Stroop test and Fazekas scale with figure memory test, digit span, and Stroop test according to the subgroup evaluated. Visual scales by MRI in MCI should be evaluated by cognitive domain and might be more useful in more severely impaired MCI or dementia patients.
Short-term prediction method of wind speed series based on fractal interpolation
International Nuclear Information System (INIS)
Xiu, Chunbo; Wang, Tiantian; Tian, Meng; Li, Yanqing; Cheng, Yi
2014-01-01
Highlights: • An improved fractal interpolation prediction method is proposed. • The chaos optimization algorithm is used to obtain the iterated function system. • The fractal extrapolate interpolation prediction of wind speed series is performed. - Abstract: In order to improve the prediction performance of the wind speed series, the rescaled range analysis is used to analyze the fractal characteristics of the wind speed series. An improved fractal interpolation prediction method is proposed to predict the wind speed series whose Hurst exponents are close to 1. An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed. The chaos optimization algorithm is used to optimize the function to resolve the optimal vertical scaling factors. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Simulation results show that the fractal interpolation prediction method can get better prediction result than others for the wind speed series with the fractal characteristic, and the prediction performance of the proposed method can be improved further because the fractal characteristic of its iterated function system is similar to that of the predicted wind speed series
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)
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.
A brain MRI bias field correction method created in the Gaussian multi-scale space
Chen, Mingsheng; Qin, Mingxin
2017-07-01
A pre-processing step is needed to correct for the bias field signal before submitting corrupted MR images to such image-processing algorithms. This study presents a new bias field correction method. The method creates a Gaussian multi-scale space by the convolution of the inhomogeneous MR image with a two-dimensional Gaussian function. In the multi-Gaussian space, the method retrieves the image details from the differentiation of the original image and convolution image. Then, it obtains an image whose inhomogeneity is eliminated by the weighted sum of image details in each layer in the space. Next, the bias field-corrected MR image is retrieved after the Υ correction, which enhances the contrast and brightness of the inhomogeneity-eliminated MR image. We have tested the approach on T1 MRI and T2 MRI with varying bias field levels and have achieved satisfactory results. Comparison experiments with popular software have demonstrated superior performance of the proposed method in terms of quantitative indices, especially an improvement in subsequent image segmentation.
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.
Flames in fractal grid generated turbulence
Energy Technology Data Exchange (ETDEWEB)
Goh, K H H; Hampp, F; Lindstedt, R P [Department of Mechanical Engineering, Imperial College, London SW7 2AZ (United Kingdom); Geipel, P, E-mail: p.lindstedt@imperial.ac.uk [Siemens Industrial Turbomachinery AB, SE-612 83 Finspong (Sweden)
2013-12-15
Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values {approx}0.1 and {approx}0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration. (paper)
Effect of noise on fractal structure
Energy Technology Data Exchange (ETDEWEB)
Serletis, Demitre [Division of Neurosurgery, Hospital for Sick Children, 1504-555 University Avenue, Toronto, Ont., M5G 1X8 (Canada)], E-mail: demitre.serletis@utoronto.ca
2008-11-15
In this paper, I investigate the effect of dynamical noise on the estimation of the Hurst exponent and the fractal dimension of time series. Recently, Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on estimation of Lyapunov exponents from a time series. Chaos, Solitons and Fractals, forthcoming] have shown that dynamical noise can make the detection of chaotic dynamics very difficult, and Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on the bifurcation behavior of dynamical systems. Chaos, Solitons and Fractals, forthcoming] have shown that dynamical noise can also shift bifurcation points and produce noise-induced transitions, making the determination of bifurcation boundaries difficult. Here I apply the detrending moving average (DMA) method, recently developed by Alessio et al. [Alessio E, Carbone A, Castelli G, Frappietro V. Second-order moving average and scaling of stochastic time series. The Eur Phys J B 2002;27:197-200] and Carbone et al. [Carbone A, Castelli G, Stanley HE. Time-dependent Hurst exponent in financial time series. Physica A 2004;344:267-71; Carbone A, Castelli G, Stanley HE. Analysis of clusters formed by the moving average of a long-range correlated time series. Phys Rev E 2004;69:026105], to estimate the Hurst exponent of a Brownian walk with a Hurst exponent of 0.5, coupled with low and high intensity noise, and show that dynamical noise has no effect on fractal structure.
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.
Fractal statistics of brittle fragmentation
Directory of Open Access Journals (Sweden)
M. Davydova
2013-04-01
Full Text Available The study of fragmentation statistics of brittle materials that includes four types of experiments is presented. Data processing of the fragmentation of glass plates under quasi-static loading and the fragmentation of quartz cylindrical rods under dynamic loading shows that the size distribution of fragments (spatial quantity is fractal and can be described by a power law. The original experimental technique allows us to measure, apart from the spatial quantity, the temporal quantity - the size of time interval between the impulses of the light reflected from the newly created surfaces. The analysis of distributions of spatial (fragment size and temporal (time interval quantities provides evidence of obeying scaling laws, which suggests the possibility of self-organized criticality in fragmentation.
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
Categorization of new fractal carpets
International Nuclear Information System (INIS)
Rani, Mamta; Goel, Saurabh
2009-01-01
Sierpinski carpet is one of the very beautiful fractals from the historic gallery of classical fractals. Carpet designing is not only a fascinating activity in computer graphics, but it has real applications in carpet industry as well. One may find illusionary delighted carpets designed here, which are useful in real designing of carpets. In this paper, we attempt to systematize their generation and put them into categories. Each next category leads to a more generalized form of the fractal carpet.
Bilipschitz embedding of homogeneous fractals
Lü, Fan; Lou, Man-Li; Wen, Zhi-Ying; Xi, Li-Feng
2014-01-01
In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.
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.
Kiviniemi, Vesa; Remes, Jukka; Starck, Tuomo; Nikkinen, Juha; Haapea, Marianne; Silven, Olli; Tervonen, Osmo
2009-01-01
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(alpha). 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 alpha, fractal dimension D(f), 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 alpha was able to differentiate also blood vessels from grey matter changes. D(f) 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.
FONT DISCRIMINATIO USING FRACTAL DIMENSIONS
Directory of Open Access Journals (Sweden)
S. Mozaffari
2014-09-01
Full Text Available One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dimension was introduced in this paper for the first time. Our feature extraction methods which consider font recognition as texture identification are independent of document content. Experimental results on different pages written by several font types show that fractal geometry can overcome the complexities of font recognition problem.
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.
Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.
2010-01-01
The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103
Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.
Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A
2017-11-28
We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.
3D fully convolutional networks for subcortical segmentation in MRI: A large-scale study.
Dolz, Jose; Desrosiers, Christian; Ben Ayed, Ismail
2018-04-15
This study investigates a 3D and fully convolutional neural network (CNN) for subcortical brain structure segmentation in MRI. 3D CNN architectures have been generally avoided due to their computational and memory requirements during inference. We address the problem via small kernels, allowing deeper architectures. We further model both local and global context by embedding intermediate-layer outputs in the final prediction, which encourages consistency between features extracted at different scales and embeds fine-grained information directly in the segmentation process. Our model is efficiently trained end-to-end on a graphics processing unit (GPU), in a single stage, exploiting the dense inference capabilities of fully CNNs. We performed comprehensive experiments over two publicly available datasets. First, we demonstrate a state-of-the-art performance on the ISBR dataset. Then, we report a large-scale multi-site evaluation over 1112 unregistered subject datasets acquired from 17 different sites (ABIDE dataset), with ages ranging from 7 to 64 years, showing that our method is robust to various acquisition protocols, demographics and clinical factors. Our method yielded segmentations that are highly consistent with a standard atlas-based approach, while running in a fraction of the time needed by atlas-based methods and avoiding registration/normalization steps. This makes it convenient for massive multi-site neuroanatomical imaging studies. To the best of our knowledge, our work is the first to study subcortical structure segmentation on such large-scale and heterogeneous data. Copyright © 2017 Elsevier Inc. All rights reserved.
Electromagnetism on anisotropic fractal media
Ostoja-Starzewski, Martin
2013-04-01
Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.
Fractals and multifractals in physics
International Nuclear Information System (INIS)
Arcangelis, L. de.
1987-01-01
We present a general introduction to the world of fractals. The attention is mainly devoted to stress how fractals do indeed appear in the real world and to find quantitative methods for characterizing their properties. The idea of multifractality is also introduced and it is presented in more details within the framework of the percolation problem
Turbulent wakes of fractal objects
Staicu, A.D.; Mazzi, B.; Vassilicos, J.C.; Water, van de W.
2003-01-01
Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density.
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.
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.
Large-scale functional MRI analysis to accumulate knowledge on brain functions
International Nuclear Information System (INIS)
Schwartz, Yannick
2015-01-01
How can we accumulate knowledge on brain functions? How can we leverage years of research in functional MRI to analyse finer-grained psychological constructs, and build a comprehensive model of the brain? Researchers usually rely on single studies to delineate brain regions recruited by mental processes. They relate their findings to previous works in an informal way by defining regions of interest from the literature. Meta-analysis approaches provide a more principled way to build upon the literature. This thesis investigates three ways to assemble knowledge using activation maps from a large amount of studies. First, we present an approach that uses jointly two similar fMRI experiments, to better condition an analysis from a statistical standpoint. We show that it is a valuable data-driven alternative to traditional regions of interest analyses, but fails to provide a systematic way to relate studies, and thus does not permit to integrate knowledge on a large scale. Because of the difficulty to associate multiple studies, we resort to using a single dataset sampling a large number of stimuli for our second contribution. This method estimates functional networks associated with functional profiles, where the functional networks are interacting brain regions and the functional profiles are a weighted set of cognitive descriptors. This work successfully yields known brain networks and automatically associates meaningful descriptions. Its limitations lie in the unsupervised nature of this method, which is more difficult to validate, and the use of a single dataset. It however brings the notion of cognitive labels, which is central to our last contribution. Our last contribution presents a method that learns functional atlases by combining several datasets. [Henson 2006] shows that forward inference, i.e. the probability of an activation given a cognitive process, is often not sufficient to conclude on the engagement of brain regions for a cognitive process
Fractals: Giant impurity nonlinearities in optics of fractal clusters
International Nuclear Information System (INIS)
Butenko, A.V.; Shalaev, V.M.; Stockman, M.I.
1988-01-01
A theory of nonlinear optical properties of fractals is developed. Giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal. This enhancement occurs if the exciting radiation frequency lies within the absorption band of the fractal. The giant optical nonlinearities are due to existence of high local electric fields in the sites of impurity locations. Such fields are due to the inhomogeneously broadened character of a fractal spectrum, i.e. partial conservation of individuality of fractal-forming particles (monomers). The field enhancement is proportional to the Q-factor of the resonance of a monomer. The effects of coherent anti-Stokes Raman scattering (CARS) and phase conjugation (PC) of light waves are enhanced to a much greater degree than generation of higher harmonics. In a general case the susceptibility of a higher-order is enhanced in the maximum way if the process includes ''subtraction'' of photons (at least one of the strong field frequencies enters the susceptibility with the minus sign). Alternatively, enhancement for the highest-order harmonic generation (when all the photons are ''accumulated'') is minimal. The predicted phenomena bear information on spectral properties of both impurity molecules and a fractal. In particular, in the CARS spectra a narrow (with the natural width) resonant structure, which is proper to an isolated monomer of a fractal, is predicted to be observed. (orig.)
A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions
Zborovský, I.
2018-04-01
Fractal self-similarity of hadron interactions demonstrated by the z-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable z is a function of the momentum fractions x1 and x2 of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions ya and yb of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the z-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.
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)
Fractal geometry in an expanding, one-dimensional, Newtonian universe.
Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel
2007-09-01
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.
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 theory of radon emanation from solids
International Nuclear Information System (INIS)
Semkow, T.M.
1991-01-01
The author developed a fractal theory of Rn emanation from solids, based on α recoil from the α decay of Ra. Range straggling of the recoiling Rn atoms in the solid state is included and the fractal geometry is used to describe the roughness of the emanating surface. A fractal dimension D of the surface and the median projected range become important parameters in calculating the radon emanating power E R from solids. A relation between E R and the specific surface area measured by the gas adsorption is derived for the first time, assuming a uniform distribution of the precursor Ra throughout the samples. It is suggested that the E R measurements can be used to determine D of the surfaces on the scale from tens to hundreds of nm. One obtains, for instance, D = 2.17 ± 0.06 for Lipari volcanic glass and D = 2.83 ± 0.03 for pitchblende. In addition, the author suggests a new process of penetrating recoil and modify the role of indirect recoil. The penetrating recoil may be important for rough surfaces, in which case Rn loses its kinetic energy by penetrating a large number of small surface irregularities. The indirect recoil may be important at the very last stage of energy-loss process, for kinetic energies below ∼ 5 keV
Fractal analysis of sulphidic mineral
Directory of Open Access Journals (Sweden)
Miklúová Viera
2002-03-01
Full Text Available In this paper, the application of fractal theory in the characterization of fragmented surfaces, as well as the mass-size distributions are discussed. The investigated mineral-chalcopyrite of Slovak provenience is characterised after particle size reduction processes-crushing and grinding. The problem how the different size reduction methods influence the surface irregularities of obtained particles is solved. Mandelbrot (1983, introducing the fractal geometry, offered a new way of characterization of surface irregularities by the fractal dimension. The determination of the surface fractal dimension DS consists in measuring the specific surface by the BET method in several fractions into which the comminuted chalcopyrite is sieved. This investigation shows that the specific surface of individual fractions were higher for the crushed sample than for the short-term (3 min ground sample. The surface fractal dimension can give an information about the adsorption sites accessible to molecules of nitrogen and according to this, the value of the fractal dimension is higher for crushed sample.The effect of comminution processes on the mass distribution of particles crushed and ground in air as well as in polar liquids is also discussed. The estimation of fractal dimensions of particles mass distribution is done on the assumption that the particle size distribution is described by the power-law (1. The value of fractal dimension for the mass distribution in the crushed sample is lower than in the sample ground in air, because it is influenced by the energy required for comminution.The sample of chalcopyrite was ground (10min in ethanol and i-butanol [which according to Ikazaki (1991] are characterized by the parameter µ /V, where µ is its dipole moment and V is the molecular volume. The values of µ /V for the used polar liquids are of the same order. That is why the expressive differences in particle size distributions as well as in the values of
Moghilevsky, Débora Estela
2011-01-01
A lo largo de los últimos años del siglo veinte se ha desarrollado la teoría de la complejidad. Este modelo relaciona las ciencias duras tales como la matemática, la teoría del caos, la física cuántica y la geometría fractal con las llamadas seudo ciencias. Dentro de este contexto podemos definir la Psicología Fractal como la ciencia que estudia los aspectos psíquicos como dinámicamente fractales.
Fractal analysis as a potential tool for surface morphology of thin films
Soumya, S.; Swapna, M. S.; Raj, Vimal; Mahadevan Pillai, V. P.; Sankararaman, S.
2017-12-01
Fractal geometry developed by Mandelbrot has emerged as a potential tool for analyzing complex systems in the diversified fields of science, social science, and technology. Self-similar objects having the same details in different scales are referred to as fractals and are analyzed using the mathematics of non-Euclidean geometry. The present work is an attempt to correlate fractal dimension for surface characterization by Atomic Force Microscopy (AFM). Taking the AFM images of zinc sulphide (ZnS) thin films prepared by pulsed laser deposition (PLD) technique, under different annealing temperatures, the effect of annealing temperature and surface roughness on fractal dimension is studied. The annealing temperature and surface roughness show a strong correlation with fractal dimension. From the regression equation set, the surface roughness at a given annealing temperature can be calculated from the fractal dimension. The AFM images are processed using Photoshop and fractal dimension is calculated by box-counting method. The fractal dimension decreases from 1.986 to 1.633 while the surface roughness increases from 1.110 to 3.427, for a change of annealing temperature 30 ° C to 600 ° C. The images are also analyzed by power spectrum method to find the fractal dimension. The study reveals that the box-counting method gives better results compared to the power spectrum method.
Fractal 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...
Fractal analysis reveals reduced complexity of retinal vessels in CADASIL.
Directory of Open Access Journals (Sweden)
Michele Cavallari
2011-04-01
Full Text Available The Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy (CADASIL affects mainly small cerebral arteries and leads to disability and dementia. The relationship between clinical expression of the disease and progression of the microvessel pathology is, however, uncertain as we lack tools for imaging brain vessels in vivo. Ophthalmoscopy is regarded as a window into the cerebral microcirculation. In this study we carried out an ophthalmoscopic examination in subjects with CADASIL. Specifically, we performed fractal analysis of digital retinal photographs. Data are expressed as mean fractal dimension (mean-D, a parameter that reflects complexity of the retinal vessel branching. Ten subjects with genetically confirmed diagnosis of CADASIL and 10 sex and age-matched control subjects were enrolled. Fractal analysis of retinal digital images was performed by means of a computer-based program, and the data expressed as mean-D. Brain MRI lesion volume in FLAIR and T1-weighted images was assessed using MIPAV software. Paired t-test was used to disclose differences in mean-D between CADASIL and control groups. Spearman rank analysis was performed to evaluate potential associations between mean-D values and both disease duration and disease severity, the latter expressed as brain MRI lesion volumes, in the subjects with CADASIL. The results showed that mean-D value of patients (1.42±0.05; mean±SD was lower than control (1.50±0.04; p = 0.002. Mean-D did not correlate with disease duration nor with MRI lesion volumes of the subjects with CADASIL. The findings suggest that fractal analysis is a sensitive tool to assess changes of retinal vessel branching, likely reflecting early brain microvessel alterations, in CADASIL patients.
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.
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
Map of fluid flow in fractal porous medium into fractal continuum flow.
Balankin, Alexander S; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Thermal transport in fractal systems
DEFF Research Database (Denmark)
Kjems, Jørgen
1992-01-01
Recent experiments on the thermal transport in systems with partial fractal geometry, silica aerogels, are reviewed. The individual contributions from phonons, fractons and particle modes, respectively, have been identified and can be described by quantitative models consistent with heat capacity...
Fractal analysis in oral leukoplakia
Directory of Open Access Journals (Sweden)
Prashant Bhai Pandey
2015-01-01
Full Text Available Introduction: Fractal analysis (FA quantifies complex geometric structures by generating a fractal dimension (FD, which can measure the complexity of mucosa. FA is a quantitative tool used to measure the complexity of self-similar or semi-self-similar structures. Aim and Objective: The study was done to perform the FA of oral mucosa with keratotic changes, as it is also made up of self-similar tissues, and thus, its FD can be calculated. Results: In oral leukoplakia, keratinization increases the complexity of mucosa, which denotes fractal geometry. We evaluated and compared pretreated and post-treated oral leukoplakia in 50 patients with clinically proven oral leukoplakia and analyzed the normal oral mucosa and lesional or keratinized mucosa in oral leukoplakia patients through FA using box counting method. Conclusion: FA using the fractal geometry is an efficient, noninvasive prediction tool for early detection of oral leukoplakia and other premalignant conditions in patients.
Energy Technology Data Exchange (ETDEWEB)
Nguyen, N.L.; Reimert, R. [Engler-Bunte-Institut, Bereich Gas, Erdoel und Kohle, Universitaet Karlsruhe (T.H.) (Germany); Hardy, E.H. [Institut fuer Mechanische Verfahrenstechnik und Mechanik, Universitaet Karlsruhe (T.H.) (Germany)
2006-07-15
The influence of fluid dynamics on the hydrodesulfurization (HDS) reactions of a diesel oil in bench-scale reactors was evaluated. The porosities and liquid saturations of catalyst beds were quantified by using the MRI technique. The gas-liquid systems used in the experiments were nitrogen diesel and hydrogen diesel. An apparatus was especially constructed, allowing in situ measurements of gas and liquid distributions in packed beds at elevated pressure and temperature up to 20 bar and 200 C, respectively. The reactor itself had a length of 500 mm and an internal diameter of 19 mm. The packed beds used in this MRI study consisted of: (1) 2 mm diameter nonporous spherical glass beads and (2) 1.3 mm diameter porous Al{sub 2}O{sub 3} trilobes having the same size as the original trilobe catalyst used in HDS bench-scale experiments. The superficial gas and liquid velocities were set within the range of trickle flow, e.g., u{sub 0G} = 20-500 mm/s and u{sub 0L} = 0.1-6 mm/s. In parallel with the MRI experiments, the hydrodesulfurization of a gas oil was investigated in a bench-scale plant. Its reactor had the same dimensions of the trickle-bed column used in the MRI experiments and was filled with original trilobe catalyst. These catalytic experiments were carried out at a wide range of operating conditions (p = 30-80 bar, T = 300-380 C, LHSV = 1-4 h{sup -1}). The results of both fluid dynamic and catalytic reaction experiments were then combined for developing a simulation model to predict the HDS performance by accounting for fluid dynamic nonidealities. (Abstract Copyright [2006], Wiley Periodicals, Inc.)
Fractals in Power Reactor Noise
International Nuclear Information System (INIS)
Aguilar Martinez, O.
1994-01-01
In this work the non- lineal dynamic problem of power reactor is analyzed using classic concepts of fractal analysis as: attractors, Hausdorff-Besikovics dimension, phase space, etc. A new non-linear problem is also analyzed: the discrimination of chaotic signals from random neutron noise signals and processing for diagnosis purposes. The advantages of a fractal analysis approach in the power reactor noise are commented in details
Fractal 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
Persistent fluctuations in stride intervals under fractal auditory stimulation.
Directory of Open Access Journals (Sweden)
Vivien Marmelat
Full Text Available Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.
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.
Random walk through fractal environments
International Nuclear Information System (INIS)
Isliker, H.; Vlahos, L.
2003-01-01
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D F of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D F ≤2 can thus be considered as defective Levy walks. The distribution of jump increments for D F >2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D F F >2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations
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
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.
Fractal markets: Liquidity and investors on different time horizons
Li, Da-Ye; Nishimura, Yusaku; Men, Ming
2014-08-01
In this paper, we propose a new agent-based model to study the source of liquidity and the “emergent” phenomenon in financial market with fractal structure. The model rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stability and liquidity of the financial market the real world market lacks detailed data to bring it to light since it is difficult to identify and distinguish the investors with different time horizons in the empirical approach. results show that in a relatively short period of time fractal market provides liquidity from investors with different horizons and the market gains stability when the market structure changes from uniformity to diversification. In the real world the fractal structure with the finite of horizons can only stabilize the market within limits. With the finite maximum horizons, the greater diversity of the investors and the fractal structure will not necessarily bring more stability to the market which might come with greater fluctuation in large time scale.
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
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...
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.
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.
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-01-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape
A fractal-based image encryption system
Abd-El-Hafiz, S. K.; Radwan, Ahmed Gomaa; Abdel Haleem, Sherif H.; Barakat, Mohamed L.
2014-01-01
single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved
Research on the fractal structure in the Chinese stock market
Zhuang, Xin-tian; Huang, Xiao-yuan; Sha, Yan-li
2004-02-01
Applying fractal theory, this paper probes and discusses self-similarity and scale invariance of the Chinese stock market. It analyses three kinds of scale indexes, i.e., autocorrelation index, Hurst index and the scale index on the basis of detrended fluctuation analysis (DFA) algorithm and promotes DFA into a recursive algorithm. Using the three kinds of scale indexes, we conduct empirical research on the Chinese Shanghai and Shenzhen stock markets. The results indicate that the rate of returns of the two stock markets does not obey the normal distribution. A correlation exists between the stock price indexes over time scales. The stock price indexes exhibit fractal time series. It indicates that the policy guide hidden at the back influences the characteristic of the Chinese stock market.
Effects of fractal pore on coal devolatilization
Energy Technology Data Exchange (ETDEWEB)
Chen, Yongli; He, Rong [Tsinghua Univ., Beijing (China). Dept. of Thermal Engineering; Wang, Xiaoliang; Cao, Liyong [Dongfang Electric Corporation, Chengdu (China). Centre New Energy Inst.
2013-07-01
Coal devolatilization is numerically investigated by drop tube furnace and a coal pyrolysis model (Fragmentation and Diffusion Model). The fractal characteristics of coal and char pores are investigated. Gas diffusion and secondary reactions in fractal pores are considered in the numerical simulations of coal devolatilization, and the results show that the fractal dimension is increased firstly and then decreased later with increased coal conversions during devolatilization. The mechanisms of effects of fractal pores on coal devolatilization are analyzed.
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.
2014-08-28
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fan, Jieran; Wang, Di; DeVault, Clayton
2016-01-01
We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure.......We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure....
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
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
Wong, Chung-Ki; Luo, Qingfei; Zotev, Vadim; Phillips, Raquel; Chan, Kam Wai Clifford; Bodurka, Jerzy
2018-03-31
In simultaneous EEG-fMRI, identification of the period of cardioballistic artifact (BCG) in EEG is required for the artifact removal. Recording the electrocardiogram (ECG) waveform during fMRI is difficult, often causing inaccurate period detection. Since the waveform of the BCG extracted by independent component analysis (ICA) is relatively invariable compared to the ECG waveform, we propose a multiple-scale peak-detection algorithm to determine the BCG cycle directly from the EEG data. The algorithm first extracts the high contrast BCG component from the EEG data by ICA. The BCG cycle is then estimated by band-pass filtering the component around the fundamental frequency identified from its energy spectral density, and the peak of BCG artifact occurrence is selected from each of the estimated cycle. The algorithm is shown to achieve a high accuracy on a large EEG-fMRI dataset. It is also adaptive to various heart rates without the needs of adjusting the threshold parameters. The cycle detection remains accurate with the scan duration reduced to half a minute. Additionally, the algorithm gives a figure of merit to evaluate the reliability of the detection accuracy. The algorithm is shown to give a higher detection accuracy than the commonly used cycle detection algorithm fmrib_qrsdetect implemented in EEGLAB. The achieved high cycle detection accuracy of our algorithm without using the ECG waveforms makes possible to create and automate pipelines for processing large EEG-fMRI datasets, and virtually eliminates the need for ECG recordings for BCG artifact removal. Copyright © 2018 The Authors. Published by Elsevier B.V. All rights reserved.
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.
2014-08-28
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape separated by a vertical distance from a lower first metal plate with a complementary fractal shape; and a substrate above which the capacitor body is suspended.
An enhanced fractal image denoising algorithm
International Nuclear Information System (INIS)
Lu Jian; Ye Zhongxing; Zou Yuru; Ye Ruisong
2008-01-01
In recent years, there has been a significant development in image denoising using fractal-based method. This paper presents an enhanced fractal predictive denoising algorithm for denoising the images corrupted by an additive white Gaussian noise (AWGN) by using quadratic gray-level function. Meanwhile, a quantization method for the fractal gray-level coefficients of the quadratic function is proposed to strictly guarantee the contractivity requirement of the enhanced fractal coding, and in terms of the quality of the fractal representation measured by PSNR, the enhanced fractal image coding using quadratic gray-level function generally performs better than the standard fractal coding using linear gray-level function. Based on this enhanced fractal coding, the enhanced fractal image denoising is implemented by estimating the fractal gray-level coefficients of the quadratic function of the noiseless image from its noisy observation. Experimental results show that, compared with other standard fractal-based image denoising schemes using linear gray-level function, the enhanced fractal denoising algorithm can improve the quality of the restored image efficiently
Steady laminar flow of fractal fluids
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)
2017-02-12
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.
Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...
African Journals Online (AJOL)
In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0.......0002) in monozygotic twins than in dizygotic twins (0.108, P = 0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, dominant genetic effects explained 54% of the variation and 46% was individually environmentally determined. Conclusions: In young adult twins...
Towards thermomechanics of fractal media
Ostoja-Starzewski, Martin
2007-11-01
Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.
Large-scale DCMs for resting-state fMRI
Directory of Open Access Journals (Sweden)
Adeel Razi
2017-01-01
Full Text Available This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity. This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI. We use spectral dynamic causal modeling (DCM to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of Bayesian model reduction to discover the most likely sparse graph (or model from a parent (e.g., fully connected graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM—with functional connectivity priors—is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.
Fractal universe and quantum gravity.
Calcagni, Gianluca
2010-06-25
We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
Fractals control in particle's velocity
International Nuclear Information System (INIS)
Zhang Yongping; Liu Shutang; Shen Shulan
2009-01-01
Julia set, a fractal set of the literature of nonlinear physics, has significance for the engineering applications. For example, the fractal structure characteristics of the generalized M-J set could visually reflect the change rule of particle's velocity. According to the real world requirement, the system need show various particle's velocity in some cases. Thus, the control of the nonlinear behavior, i.e., Julia set, has attracted broad attention. In this work, an auxiliary feedback control is introduced to effectively control the Julia set that visually reflects the change rule of particle's velocity. It satisfies the performance requirement of the real world problems.
Taylor dispersion on a fractal
International Nuclear Information System (INIS)
Mazo, R.M.
1998-01-01
Taylor dispersion is the greatly enhanced diffusion in the direction of a fluid flow caused by ordinary diffusion in directions orthogonal to the flow. It is essential that the system be bounded in space in the directions orthogonal to the flow. We investigate the situation where the medium through which the flow occurs has fractal properties so that diffusion in the orthogonal directions is anomalous and non-Fickian. The effective diffusion in the flow direction remains normal; its width grows proportionally with the time. However, the proportionality constant depends on the fractal dimension of the medium as well as its walk dimension. (author)
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
, the retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficients. Falconer's formula and quantitative genetic models were used to determine the genetic component of variation. Results: The mean...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0...
Synergetics and fractals in tribology
Janahmadov, Ahad Kh
2016-01-01
This book examines the theoretical and practical aspects of tribological process using synergy, fractal and multifractal methods, and the fractal and multifractal models of self-similar tribosystems developed on their basis. It provides a comprehensive analysis of their effectiveness, and also considers the method of flicker noise spectroscopy with detailed parameterization of surface roughness friction. All models, problems and solutions are taken and tested on the set of real-life examples of oil-gas industry. The book is intended for researchers, graduate students and engineers specialising in the field of tribology, and also for senior students of technical colleges.
Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review
Energy Technology Data Exchange (ETDEWEB)
Michallek, Florian; Dewey, Marc [Humboldt-Universitaet zu Berlin, Freie Universitaet Berlin, Charite - Universitaetsmedizin Berlin, Medical School, Department of Radiology, Berlin (Germany)
2014-01-15
To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)
Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review
International Nuclear Information System (INIS)
Michallek, Florian; Dewey, Marc
2014-01-01
To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)
Multi-scale radiomic analysis of sub-cortical regions in MRI related to autism, gender and age
Chaddad, Ahmad; Desrosiers, Christian; Toews, Matthew
2017-03-01
We propose using multi-scale image textures to investigate links between neuroanatomical regions and clinical variables in MRI. Texture features are derived at multiple scales of resolution based on the Laplacian-of-Gaussian (LoG) filter. Three quantifier functions (Average, Standard Deviation and Entropy) are used to summarize texture statistics within standard, automatically segmented neuroanatomical regions. Significance tests are performed to identify regional texture differences between ASD vs. TDC and male vs. female groups, as well as correlations with age (corrected p brain imaging data exchange (ABIDE) brain MRI dataset is used to evaluate texture features derived from 31 brain regions from 1112 subjects including 573 typically developing control (TDC, 99 females, 474 males) and 539 Autism spectrum disorder (ASD, 65 female and 474 male) subjects. Statistically significant texture differences between ASD vs. TDC groups are identified asymmetrically in the right hippocampus, left choroid-plexus and corpus callosum (CC), and symmetrically in the cerebellar white matter. Sex-related texture differences in TDC subjects are found in primarily in the left amygdala, left cerebellar white matter, and brain stem. Correlations between age and texture in TDC subjects are found in the thalamus-proper, caudate and pallidum, most exhibiting bilateral symmetry.
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
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.
Molecularly-Limited Fractal Surface Area of Mineral Powders
Directory of Open Access Journals (Sweden)
Petr Jandacka
2016-05-01
Full Text Available The topic of the specific surface area (SSA of powders is not sufficiently described in the literature in spite of its nontrivial contribution to adsorption and dissolution processes. Fractal geometry provides a way to determine this parameter via relation SSA ~ x(D − 3s(2 − D, where x (m is the particle size and s (m is a scale. Such a relation respects nano-, micro-, or macro-topography on the surface. Within this theory, the fractal dimension 2 ≤ D < 3 and scale parameter s plays a significant role. The parameter D may be determined from BET or dissolution measurements on several samples, changing the powder particle sizes or sizes of adsorbate molecules. If the fractality of the surface is high, the SSA does not depend on the particle size distribution and vice versa. In this paper, the SSA parameter is analyzed from the point of view of adsorption and dissolution processes. In the case of adsorption, a new equation for the SSA, depending on the term (2 − D∙(s2 − sBET/sBET, is derived, where sBET and s2 are effective cross-sectional diameters for BET and new adsorbates. Determination of the SSA for the dissolution process appears to be very complicated, since the fractality of the surface may change in the process. Nevertheless, the presented equations have good application potential.
On fractal space-time and fractional calculus
Directory of Open Access Journals (Sweden)
Hu Yue
2016-01-01
Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.
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)
Determination of effective thermal conductivity for polyurethane foam by use of fractal method
Institute of Scientific and Technical Information of China (English)
SHI Mingheng; LI Xiaochuan; CHEN Yongping
2006-01-01
The microstructure of polyurethane foam is disordered, which influences the foam heat conduction process significantly. In this paper foam structure is described by using the local area fractal dimension in a certain small range of length scales. An equivalent element cell is constructed based on the local fractal dimensions along the directions parallel and transverse to the heat flux. By use of fractal void fraction a simplified heat conduction model is proposed to calculate the effective thermal conductivity of polyurethane foam. The predicted effective thermal conductivity agrees well with the experimental data.
Tan, Zhengguo; Hohage, Thorsten; Kalentev, Oleksandr; Joseph, Arun A; Wang, Xiaoqing; Voit, Dirk; Merboldt, K Dietmar; Frahm, Jens
2017-12-01
The purpose of this work is to develop an automatic method for the scaling of unknowns in model-based nonlinear inverse reconstructions and to evaluate its application to real-time phase-contrast (RT-PC) flow magnetic resonance imaging (MRI). Model-based MRI reconstructions of parametric maps which describe a physical or physiological function require the solution of a nonlinear inverse problem, because the list of unknowns in the extended MRI signal equation comprises multiple functional parameters and all coil sensitivity profiles. Iterative solutions therefore rely on an appropriate scaling of unknowns to numerically balance partial derivatives and regularization terms. The scaling of unknowns emerges as a self-adjoint and positive-definite matrix which is expressible by its maximal eigenvalue and solved by power iterations. The proposed method is applied to RT-PC flow MRI based on highly undersampled acquisitions. Experimental validations include numerical phantoms providing ground truth and a wide range of human studies in the ascending aorta, carotid arteries, deep veins during muscular exercise and cerebrospinal fluid during deep respiration. For RT-PC flow MRI, model-based reconstructions with automatic scaling not only offer velocity maps with high spatiotemporal acuity and much reduced phase noise, but also ensure fast convergence as well as accurate and precise velocities for all conditions tested, i.e. for different velocity ranges, vessel sizes and the simultaneous presence of signals with velocity aliasing. In summary, the proposed automatic scaling of unknowns in model-based MRI reconstructions yields quantitatively reliable velocities for RT-PC flow MRI in various experimental scenarios. Copyright © 2017 John Wiley & Sons, Ltd.
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...
Fractals in DNA sequence analysis
Institute of Scientific and Technical Information of China (English)
Yu Zu-Guo(喻祖国); Vo Anh; Gong Zhi-Min(龚志民); Long Shun-Chao(龙顺潮)
2002-01-01
Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance,and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view)to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.
Fractal analysis of urban environment: land use and sewer system
Gires, A.; Ochoa Rodriguez, S.; Van Assel, J.; Bruni, G.; Murla Tulys, D.; Wang, L.; Pina, R.; Richard, J.; Ichiba, A.; Willems, P.; Tchiguirinskaia, I.; ten Veldhuis, M. C.; Schertzer, D. J. M.
2014-12-01
Land use distribution are usually obtained by automatic processing of satellite and airborne pictures. The complexity of the obtained patterns which are furthermore scale dependent is enhanced in urban environment. This scale dependency is even more visible in a rasterized representation where only a unique class is affected to each pixel. A parameter commonly analysed in urban hydrology is the coefficient of imperviousness, which reflects the proportion of rainfall that will be immediately active in the catchment response. This coefficient is strongly scale dependent with a rasterized representation. This complex behaviour is well grasped with the help of the scale invariant notion of fractal dimension which enables to quantify the space occupied by a geometrical set (here the impervious areas) not only at a single scale but across all scales. This fractal dimension is also compared to the ones computed on the representation of the catchments with the help of operational semi-distributed models. Fractal dimensions of the corresponding sewer systems are also computed and compared with values found in the literature for natural river networks. This methodology is tested on 7 pilot sites of the European NWE Interreg IV RainGain project located in France, Belgium, Netherlands, United-Kingdom and Portugal. Results are compared between all the case study which exhibit different physical features (slope, level of urbanisation, population density...).
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.
DSouza, Adora M.; Abidin, Anas Z.; Leistritz, Lutz; Wismüller, Axel
2017-02-01
We investigate the applicability of large-scale Granger Causality (lsGC) for extracting a measure of multivariate information flow between pairs of regional brain activities from resting-state functional MRI (fMRI) and test the effectiveness of these measures for predicting a disease state. Such pairwise multivariate measures of interaction provide high-dimensional representations of connectivity profiles for each subject and are used in a machine learning task to distinguish between healthy controls and individuals presenting with symptoms of HIV Associated Neurocognitive Disorder (HAND). Cognitive impairment in several domains can occur as a result of HIV infection of the central nervous system. The current paradigm for assessing such impairment is through neuropsychological testing. With fMRI data analysis, we aim at non-invasively capturing differences in brain connectivity patterns between healthy subjects and subjects presenting with symptoms of HAND. To classify the extracted interaction patterns among brain regions, we use a prototype-based learning algorithm called Generalized Matrix Learning Vector Quantization (GMLVQ). Our approach to characterize connectivity using lsGC followed by GMLVQ for subsequent classification yields good prediction results with an accuracy of 87% and an area under the ROC curve (AUC) of up to 0.90. We obtain a statistically significant improvement (p<0.01) over a conventional Granger causality approach (accuracy = 0.76, AUC = 0.74). High accuracy and AUC values using our multivariate method to connectivity analysis suggests that our approach is able to better capture changes in interaction patterns between different brain regions when compared to conventional Granger causality analysis known from the literature.
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 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)
Zipf’s law, 1/f noise, and fractal hierarchy
International Nuclear Information System (INIS)
Chen Yanguang
2012-01-01
Highlights: ► I developed a general scaling method based on hierarchies of cites. ► Hierarchy is classified into three types based on monofractal and multifractals. ► Zipf’s law can be used to estimate the capacity dimension of a multifractal set. ► I derive the self-similar hierarchy from the rank-size distribution. ► The hierarchical scaling method can be applied to the 1/f spectra. - Abstract: Fractals, 1/f noise, and Zipf’s laws are frequently observed within the natural living world as well as in social institutions, representing three signatures of complex systems. All these observations are associated with scaling laws and therefore have created much research interest in many diverse scientific circles. However, the inherent relationships between these scaling phenomena are not yet clear. In this paper, theoretical demonstration and mathematical experiments based on urban studies are employed to reveal the analogy between fractal patterns, 1/f spectra, and the Zipf distribution. First, the multifractal process empirically suggests the Zipf distribution. Second, a 1/f spectrum is mathematically identical to Zipf’s law. Third, both 1/f spectra and Zipf’s law can be converted into a self-similar hierarchy. Fourth, fractals, 1/f spectra, Zipf’s law can be rescaled with similar exponential laws and power laws. The self-similar hierarchy is a more general scaling method which can be used to unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/f noise, and rank-size distributions. The mathematical laws of this hierarchical structure can provide us with a holistic perspective of looking at complexity and complex systems.
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
Terahertz response of fractal meta-atoms based on concentric rectangular square resonators
Energy Technology Data Exchange (ETDEWEB)
Song, Zhiqiang; Zhao, Zhenyu, E-mail: zyzhao@shnu.edu.cn; Shi, Wangzhou [Department of Physics, Shanghai Normal University, Shanghai 200234 (China); Peng, Wei [State Key Laboratory of Functional Materials for Informatics, Shanghai Institute of Microsystem and Information Technology, Chinese Academy of Sciences, Shanghai 200050 (China)
2015-11-21
We investigate the terahertz electromagnetic responses of fractal meta-atoms (MAs) induced by different mode coupling mechanisms. Two types of MAs based on concentric rectangular square (CRS) resonators are presented: independent CRS (I-CRS) and junctional-CRS (J-CRS). In I-CRS, each resonator works as an independent dipole so as to result in the multiple resonance modes when the fractal level is above 1. In J-CRS, however, the generated layer is rotated by π/2 radius to the adjacent CRS in one MA. The multiple resonance modes are coupled into a single mode resonance. The fractal level increasing induces resonance modes redshift in I-CRS while blueshift in J-CRS. When the fractal level is below 4, the mode Q factor of J-CRS is in between the two modes of I-CRS; when the fractal level is 4 or above, the mode Q factor of J-CRS exceeds the two modes of I-CRS. Furthermore, the modulation depth (MD) decreases in I-CRS while it increases in J-CRS with the increase in fractal levels. The surface currents analysis reveals that the capacitive coupling of modes in I-CRS results in the modes redshift, while the conductive coupling of modes in J-CRS induces the mode blueshift. A high Q mode with large MD can be achieved via conductive coupling between the resonators of different scales in a fractal MA.
Energy Technology Data Exchange (ETDEWEB)
Chamousis, RL; Chang, LL; Watterson, WJ; Montgomery, RD; Taylor, RP; Moule, AJ; Shaheen, SE; Ilan, B; van de Lagemaat, J; Osterloh, FE
2014-08-21
Living organisms use fractal structures to optimize material and energy transport across regions of differing size scales. Here we test the effect of fractal silver electrodes on light distribution and charge collection in organic semiconducting polymer films made of P3HT and PCBM. The semiconducting polymers were deposited onto electrochemically grown fractal silver structures (5000 nm x 500 nm; fractal dimension of 1.71) with PEDOT:PSS as hole-selective interlayer. The fractal silver electrodes appear black due to increased horizontal light scattering, which is shown to improve light absorption in the polymer. According to surface photovoltage spectroscopy, fractal silver electrodes outperform the flat electrodes when the BHJ film thickness is large (>400 nm, 0.4 V photovoltage). Photocurrents of up to 200 microamperes cm(-2) are generated from the bulk heterojunction (BHJ) photoelectrodes under 435 nm LED (10-20 mW cm(-2)) illumination in acetonitrile solution containing 0.005 M ferrocenium hexafluorophosphate as the electron acceptor. The low IPCE values (0.3-0.7%) are due to slow electron transfer to ferrocenium ion and due to shunting along the large metal-polymer interface. Overall, this work provides an initial assessment of the potential of fractal electrodes for organic photovoltaic cells.
Atypical extended electronic states in an infinite Vicsek fractal: An exact result
International Nuclear Information System (INIS)
Chakrabarti, A.; Bhattacharyya, B.
1996-01-01
We present a class of extended electronic wave functions on a Vicsek fractal. The transmittivity of arbitrarily large fractal lattices corresponding to these particular extended-state eigenvalues exhibits a power-law decay with increasing system size. The eigenvalues corresponding to the above extended states as well as the scaling law for the transmittivity have been exactly calculated using a real-space renormalization-group method. copyright 1996 The American Physical Society
Fractal based observables to probe jet substructure of quarks and gluons
Davighi, Joe; Harris, Philip
2018-04-01
New jet observables are defined which characterize both fractal and scale-dependent contributions to the distribution of hadrons in a jet. These infrared safe observables, named Extended Fractal Observables (EFOs), have been applied to quark-gluon discrimination to demonstrate their potential utility. The EFOs are found to be individually discriminating and only weakly correlated to variables used in existing discriminators. Consequently, their inclusion improves discriminator performance, as here demonstrated with particle level simulation from the parton shower.
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Davis, Ethan, E-mail: ethan.davis4@huskers.unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States); Liu, Ying; Jiang, Lijia; Lu, Yongfeng [Laser Assisted Nano Engineering Lab, Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, 209N Scott Engineering Center, Lincoln, NE 68588-0511 (United States); Ndao, Sidy, E-mail: sndao2@unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States)
2017-01-15
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
International Nuclear Information System (INIS)
Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy
2017-01-01
Highlights: • Hierarchically structured surfaces were fabricated on the micro/nano-scale. • These structures reduced the contact angle of the inherently hydrophilic material. • Similar surfaces have applications in two-phase heat transfer and microfluidics. - Abstract: This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Fractal 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.
Magnetic resonance imaging - cardiac; Magnetic resonance imaging - heart; Nuclear magnetic resonance - cardiac; NMR - cardiac; MRI of the heart; Cardiomyopathy - MRI; Heart failure - MRI; Congenital heart disease - MRI
International Nuclear Information System (INIS)
Chen Yanguang; Lin Jingyi
2009-01-01
This paper demonstrates self-affine fractal structure of city systems by means of theoretical and empirical analyses. A Cobb-Douglas-type function (C-D function) of city systems is derived from a general urban response equation, and the partial scaling exponent of the C-D function proved to be the fractal dimension reflecting the self-affine features of city systems. As a case, the self-affine fractal model is applied to the city of Zhengzhou, China, and the result is satisfying. A fractal parameter equation indicative of structural optimization conditions is then obtained from the C-D function. The equation suggests that priority should be given to the development of the urban element with a lower fractal dimension, or a higher partial scaling exponent, for utility maximization. Moreover, the fractal dimensions of different urban elements tend to become equivalent to each other in the long term. Accordingly, it is self-similar fractals rather than self-affine fractals that represent the optimal structure of city systems under ideal conditions.
Conference on Fractals and Related Fields III
Seuret, Stéphane
2017-01-01
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
Stochastic and fractal analysis of fracture trajectories
Bessendorf, Michael H.
1987-01-01
Analyses of fracture trajectories are used to investigate structures that fall between 'micro' and 'macro' scales. It was shown that fracture trajectories belong to the class of nonstationary processes. It was also found that correlation distance, which may be related to a characteristic size of a fracture process, increases with crack length. An assemblage of crack trajectory processes may be considered as a diffusive process. Chudnovsky (1981-1985) introduced a 'crack diffusion coefficient' d which reflects the ability of the material to deviate the crack trajectory from the most energetically efficient path and thus links the material toughness to its structure. For the set of fracture trajectories in AISI 304 steel, d was found to be equal to 1.04 microns. The fractal dimension D for the same set of trajectories was found to be 1.133.
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.
Chaos, Fractals and Their Applications
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
Fractals, malware, and data models
Jaenisch, Holger M.; Potter, Andrew N.; Williams, Deborah; Handley, James W.
2012-06-01
We examine the hypothesis that the decision boundary between malware and non-malware is fractal. We introduce a novel encoding method derived from text mining for converting disassembled programs first into opstrings and then filter these into a reduced opcode alphabet. These opcodes are enumerated and encoded into real floating point number format and used for characterizing frequency of occurrence and distribution properties of malware functions to compare with non-malware functions. We use the concept of invariant moments to characterize the highly non-Gaussian structure of the opcode distributions. We then derive Data Model based classifiers from identified features and interpolate and extrapolate the parameter sample space for the derived Data Models. This is done to examine the nature of the parameter space classification boundary between families of malware and the general non-malware category. Preliminary results strongly support the fractal boundary hypothesis, and a summary of our methods and results are presented here.
The fractal dimension of architecture
Ostwald, Michael J
2016-01-01
Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along...
Fuzzy fractals, chaos, and noise
Energy Technology Data Exchange (ETDEWEB)
Zardecki, A.
1997-05-01
To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-01-01
reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics
Porosity-dependent fractal nature of the porous silicon surface
Energy Technology Data Exchange (ETDEWEB)
Rahmani, N.; Dariani, R. S., E-mail: dariani@alzahra.ac.ir [Department of Physics, Alzahra University, Tehran, 1993893973 (Iran, Islamic Republic of)
2015-07-15
Porous silicon films with porosity ranging from 42% to 77% were fabricated by electrochemical anodization under different current density. We used atomic force microscopy and dynamic scaling theory for deriving the surface roughness profile and processing the topography of the porous silicon layers, respectively. We first compared the topography of bare silicon surface with porous silicon and then studied the effect of the porosity of porous silicon films on their scaling behavior by using their self-affinity nature. Our work demonstrated that silicon compared to the porous silicon films has the highest Hurst parameter, indicating that the formation of porous layer due to the anodization etching of silicon surface leads to an increase of its roughness. Fractal analysis revealed that the evolution of the nanocrystallites’ fractal dimension along with porosity. Also, we found that both interface width and Hurst parameter are affected by the increase of porosity.
On the fractal characterization of Paretian Poisson processes
Eliazar, Iddo I.; Sokolov, Igor M.
2012-06-01
Paretian Poisson processes are Poisson processes which are defined on the positive half-line, have maximal points, and are quantified by power-law intensities. Paretian Poisson processes are elemental in statistical physics, and are the bedrock of a host of power-law statistics ranging from Pareto's law to anomalous diffusion. In this paper we establish evenness-based fractal characterizations of Paretian Poisson processes. Considering an array of socioeconomic evenness-based measures of statistical heterogeneity, we show that: amongst the realm of Poisson processes which are defined on the positive half-line, and have maximal points, Paretian Poisson processes are the unique class of 'fractal processes' exhibiting scale-invariance. The results established in this paper are diametric to previous results asserting that the scale-invariance of Poisson processes-with respect to physical randomness-based measures of statistical heterogeneity-is characterized by exponential Poissonian intensities.
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
Fractals via iterated functions and multifunctions
International Nuclear Information System (INIS)
Singh, S.L.; Prasad, Bhagwati; Kumar, Ashish
2009-01-01
Fractals have wide applications in biology, computer graphics, quantum physics and several other areas of applied sciences (see, for instance [Daya Sagar BS, Rangarajan Govindan, Veneziano Daniele. Preface - fractals in geophysics. Chaos, Solitons and Fractals 2004;19:237-39; El Naschie MS. Young double-split experiment Heisenberg uncertainty principles and cantorian space-time. Chaos, Solitons and Fractals 1994;4(3):403-09; El Naschie MS. Quantum measurement, information, diffusion and cantorian geodesics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 191-205; El Naschie MS. Iterated function systems, information and the two-slit experiment of quantum mechanics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 185-9; El Naschie MS, Rossler OE, Prigogine I. Forward. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995; El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 2004;19:209-36; El Naschie MS. Fractal black holes and information. Chaos, Solitons and Fractals 2006;29:23-35; El Naschie MS. Superstring theory: what it cannot do but E-infinity could. Chaos, Solitons and Fractals 2006;29:65-8). Especially, the study of iterated functions has been found very useful in the theory of black holes, two-slit experiment in quantum mechanics (cf. El Naschie, as mentioned above). The intent of this paper is to give a brief account of recent developments of fractals arising from IFS. We also discuss iterated multifunctions.
Node insertion in Coalescence Fractal Interpolation Function
International Nuclear Information System (INIS)
Prasad, Srijanani Anurag
2013-01-01
The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed
Fractional hydrodynamic equations for fractal media
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2005-01-01
We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered
Comparison of two fractal interpolation methods
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
Power Load Prediction Based on Fractal Theory
Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song
2015-01-01
The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...
Fractal Metrology for biogeosystems analysis
Directory of Open Access Journals (Sweden)
V. Torres-Argüelles
2010-11-01
Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Directory of Open Access Journals (Sweden)
Zheng eWang
2015-12-01
Full Text Available To investigate whether aberrant interactions between brain structure and function present similarly or differently across probands with psychotic illnesses (schizophrenia (SZ, schizoaffective disorder (SAD, and bipolar I disorder with psychosis (BP and whether these deficits are shared with their first-degree non-psychotic relatives. A total of 1199 subjects were assessed, including 220 SZ, 147 SAD, 180 psychotic BP, 150 first-degree relatives of SZ, 126 SAD relatives, 134 BP relatives and 242 healthy controls. All subjects underwent structural MRI (sMRI and resting-state functional MRI (rs-fMRI scanning. Joint independent analysis (jICA was used to fuse sMRI gray matter (GM and rs-fMRI amplitude of low frequency fluctuations (ALFF data to identify the relationship between the two modalities. Joint ICA revealed two significantly fused components. The association between functional brain alteration in a prefrontal-striatal-thalamic-cerebellar network and structural abnormalities in the default mode network (DMN was found to be common across psychotic diagnoses and correlated with cognitive function, social function and Schizo-Bipolar Scale (SBS scores. The fused alteration in the temporal lobe was unique to SZ and SAD. The above effects were not seen in any relative group (including those with cluster-A personality. Using a multivariate fused approach involving two widely used imaging markers we demonstrate both shared and distinct biological traits across the psychosis spectrum. Further, our results suggest that the above traits are psychosis biomarkers rather than endophenotypes.
Fractal geometry mathematical foundations and applications
Falconer, Kenneth
2013-01-01
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applica
Directory of Open Access Journals (Sweden)
Chia-Hung Lin
2010-01-01
Full Text Available This paper proposes combining the biometric fractal pattern and particle swarm optimization (PSO-based classifier for fingerprint recognition. Fingerprints have arch, loop, whorl, and accidental morphologies, and embed singular points, resulting in the establishment of fingerprint individuality. An automatic fingerprint identification system consists of two stages: digital image processing (DIP and pattern recognition. DIP is used to convert to binary images, refine out noise, and locate the reference point. For binary images, Katz's algorithm is employed to estimate the fractal dimension (FD from a two-dimensional (2D image. Biometric features are extracted as fractal patterns using different FDs. Probabilistic neural network (PNN as a classifier performs to compare the fractal patterns among the small-scale database. A PSO algorithm is used to tune the optimal parameters and heighten the accuracy. For 30 subjects in the laboratory, the proposed classifier demonstrates greater efficiency and higher accuracy in fingerprint recognition.
A simple method for estimating the size of nuclei on fractal surfaces
Zeng, Qiang
2017-10-01
Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.
A variational principle for the Hausdorff dimension of fractal sets
DEFF Research Database (Denmark)
Olsen, Lars; Cutler, Colleen D.
1994-01-01
Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)......Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)...
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-05-01
In this work, Paper-based inkjet-printed Ultra-wide band (UWB) fractal antennas are presented. Three new designs, a combined UWB fractal monopole based on the fourth order Koch Snowflake fractal which utilizes a Sierpinski Gasket fractal for ink reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics. It is shown that fractals prove to be a successful method of reducing fabrication cost in inkjet printed antennas while retaining or enhancing printed antenna performance.
Ducharme, Scott W; Liddy, Joshua J; Haddad, Jeffrey M; Busa, Michael A; Claxton, Laura J; van Emmerik, Richard E A
2018-04-01
Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5-10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50-100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking
Visual assessment of posterior atrophy development of a MRI rating scale
Energy Technology Data Exchange (ETDEWEB)
Koedam, Esther L.G.E.; Scheltens, Philip; Pijnenburg, Yolande A.L. [VU University Medical Centre, Department of Neurology and Alzheimer Centre, PO Box 7057, MB, Amsterdam (Netherlands); Lehmann, Manja; Fox, Nick [UCL Institute of Neurology, Dementia Research Centre, London (United Kingdom); Flier, Wiesje M. van der [VU University Medical Centre, Department of Neurology and Alzheimer Centre, PO Box 7057, MB, Amsterdam (Netherlands); VU University Medical Centre, Department Epidemiology and Biostatistics, PO Box 7057, MB, Amsterdam (Netherlands); Barkhof, Frederik; Wattjes, Mike P. [VU University Medical Centre, Department of Radiology, PO Box 7057, MB, Amsterdam (Netherlands)
2011-12-15
To develop a visual rating scale for posterior atrophy (PA) assessment and to analyse whether this scale aids in the discrimination between Alzheimer's disease (AD) and other dementias. Magnetic resonance imaging of 118 memory clinic patients were analysed for PA (range 0-3), medial temporal lobe atrophy (MTA) (range 0-4) and global cortical atrophy (range 0-3) by different raters. Weighted-kappas were calculated for inter- and intra-rater agreement. Relationships between PA and MTA with the MMSE and age were estimated with linear-regression analysis. Intra-rater agreement ranged between 0.93 and 0.95 and inter-rater agreement between 0.65 and 0.84. Mean PA scores were higher in AD compared to controls (1.6 {+-} 0.9 and 0.6 {+-} 0.7, p < 0.01), and other dementias (0.8 {+-} 0.8, p < 0.01). PA was not associated with age compared to MTA (B = 1.1 (0.8) versus B = 3.1 (0.7), p < 0.01). PA and MTA were independently negatively associated with the MMSE (B = -1.6 (0.5), p < 0.01 versus B = -1.4 (0.5), p < 0.01). This robust and reproducible scale for PA assessment conveys independent information in a clinical setting and may be useful in the discrimination of AD from other dementias. (orig.)
Visual assessment of posterior atrophy development of a MRI rating scale
International Nuclear Information System (INIS)
Koedam, Esther L.G.E.; Scheltens, Philip; Pijnenburg, Yolande A.L.; Lehmann, Manja; Fox, Nick; Flier, Wiesje M. van der; Barkhof, Frederik; Wattjes, Mike P.
2011-01-01
To develop a visual rating scale for posterior atrophy (PA) assessment and to analyse whether this scale aids in the discrimination between Alzheimer's disease (AD) and other dementias. Magnetic resonance imaging of 118 memory clinic patients were analysed for PA (range 0-3), medial temporal lobe atrophy (MTA) (range 0-4) and global cortical atrophy (range 0-3) by different raters. Weighted-kappas were calculated for inter- and intra-rater agreement. Relationships between PA and MTA with the MMSE and age were estimated with linear-regression analysis. Intra-rater agreement ranged between 0.93 and 0.95 and inter-rater agreement between 0.65 and 0.84. Mean PA scores were higher in AD compared to controls (1.6 ± 0.9 and 0.6 ± 0.7, p < 0.01), and other dementias (0.8 ± 0.8, p < 0.01). PA was not associated with age compared to MTA (B = 1.1 (0.8) versus B = 3.1 (0.7), p < 0.01). PA and MTA were independently negatively associated with the MMSE (B = -1.6 (0.5), p < 0.01 versus B = -1.4 (0.5), p < 0.01). This robust and reproducible scale for PA assessment conveys independent information in a clinical setting and may be useful in the discrimination of AD from other dementias. (orig.)
Fractals and Forecasting in Earthquakes and Finance
Rundle, J. B.; Holliday, J. R.; Turcotte, D. L.
2011-12-01
It is now recognized that Benoit Mandelbrot's fractals play a critical role in describing a vast range of physical and social phenomena. Here we focus on two systems, earthquakes and finance. Since 1942, earthquakes have been characterized by the Gutenberg-Richter magnitude-frequency relation, which in more recent times is often written as a moment-frequency power law. A similar relation can be shown to hold for financial markets. Moreover, a recent New York Times article, titled "A Richter Scale for the Markets" [1] summarized the emerging viewpoint that stock market crashes can be described with similar ideas as large and great earthquakes. The idea that stock market crashes can be related in any way to earthquake phenomena has its roots in Mandelbrot's 1963 work on speculative prices in commodities markets such as cotton [2]. He pointed out that Gaussian statistics did not account for the excessive number of booms and busts that characterize such markets. Here we show that both earthquakes and financial crashes can both be described by a common Landau-Ginzburg-type free energy model, involving the presence of a classical limit of stability, or spinodal. These metastable systems are characterized by fractal statistics near the spinodal. For earthquakes, the independent ("order") parameter is the slip deficit along a fault, whereas for the financial markets, it is financial leverage in place. For financial markets, asset values play the role of a free energy. In both systems, a common set of techniques can be used to compute the probabilities of future earthquakes or crashes. In the case of financial models, the probabilities are closely related to implied volatility, an important component of Black-Scholes models for stock valuations. [2] B. Mandelbrot, The variation of certain speculative prices, J. Business, 36, 294 (1963)
Fractal analysis of polar bear hairs
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Wang Qing-Li
2015-01-01
Full Text Available Hairs of a polar bear (Ursus maritimus are of superior properties such as the excellent thermal protection. Why do polar bears can resist such cold environment? The paper concludes that its fractal porosity plays an important role, and its fractal dimensions are very close to the golden mean, 1.618, revealing the possible optimal structure of polar bear hair.
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-09-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP; SCHWARZ, UJ
1991-01-01
To study the structure of interstellar clouds we used the so-called perimeter-area relation to estimate fractal dimensions. We studied the reliability of the method by applying it to artificial fractals and discuss some of the problems and pitfalls. Results for two different cloud types
Fractal Image Coding with Digital Watermarks
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Z. Klenovicova
2000-12-01
Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
1994-01-01
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
Undergraduate Experiment with Fractal Diffraction Gratings
Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.
2011-01-01
We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
Clausse, A.; Delmastro, D.F.
1990-01-01
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es
Fractal behaviour of the seismicity in the Southern Iberian Peninsula
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X. Lana
2005-01-01
Full Text Available The fractal behaviour of the seismicity in the Southern Iberian Peninsula is analysed by considering two different series of data: the distance and the elapsed time between consecutive seismic events recorded by the seismic network of the Andalusian Institute of Geophysics (AIG. The fractal analyses have been repeated by considering four threshold magnitudes of 2.5, 3.0, 3.5 and 4.0. The re-scaled analysis lets to determine if the seismicity shows strong randomness or if it is characterised by time-persistence and the cluster dimension indicates the degree of time and spatial clustering of the seismicity. Another analysis, based on the reconstruction theorem, permits to evaluate the minimum number of nonlinear equations describing the dynamical mechanism of the seismicity, its 'loss of memory', its chaotic character and the instability of a possible predicting algorithm. The results obtained depict some differences depending on distances or elapsed times and the different threshold levels of magnitude also lead to slightly different results. Additionally, only a part of the fractal tools, the re-scaled analysis, have been applied to five seismic crises in the same area.
The Impact of The Fractal Paradigm on Geography
De Cola, L.
2001-12-01
Being itself somewhat fractal, Benoit Mandelbrot's magnum opus THE FRACTAL GEOMETRY OF NATURE may be deconstructed in many ways, including geometrically, systematically, and epistemologically. Viewed as a work of geography it may be used to organize the major topics of interest to scientists preoccupied with the understanding of real-world space in astronomy, geology, meteorology, hydrology, and biology. We shall use it to highlight such recent geographic accomplishments as automated feature detection, understanding urban growth, and modeling the spread of disease in space and time. However, several key challenges remain unsolved, among them: 1. It is still not possible to move continuously from one map scale to another so that objects change their dimension smoothly. I.e. as a viewer zooms in on a map the zero-dimensional location of a city should gradually become a 2-dimensional polygon, then a network of 1-dimensional streets, then 3-dimensional buildings, etc. 2. Spatial autocorrelation continues to be regarded more as an econometric challenge than as a problem of scaling. Similarities of values among closely-spaced observation is not so much a problem to be overcome as a source of information about spatial structure. 3. Although the fractal paradigm is a powerful model for data analysis, its ideas and techniques need to be brought to bear on the problems of understanding such hierarchies as ecosystems (the flow networks of energy and matter), taxonomies (biological classification), and knowledge (hierarchies of bureaucratic information, networks of linked data, etc).
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
Dielectric dispersion of porous media as a fractal phenomenon
Thevanayagam, S.
1997-09-01
It is postulated that porous media is made up of fractal solid skeleton structure and fractal pore surface. The model thus developed satisfies measured anomalous dielectric behavior of three distinctly different porous media: kaolin, montmorillonite, and shaly sand rock. It is shown that the underlying mechanism behind dielectric dispersion in the kHz range to high MHz range is indeed Maxwell-Wagner mechanism but modified to take into account the multiphase nature of the porous media as opposed to the traditional two-phase Maxwell-Wagner charge accumulation effect. The conductivity of the surface water associated with the solid surface and charge accumulation across the surface irregularities, asperity, and bridging between particles at the micro-scale-level pores are shown to contribute to this modified Maxwell-Wagner mechanism. The latter is dominant at low frequencies. The surface water thickness is calculated to be about 2-6 nm for a variety of porous media.
Surface structures of equilibrium restricted curvature model on two fractal substrates
International Nuclear Information System (INIS)
Song Li-Jian; Tang Gang; Zhang Yong-Wei; Han Kui; Xun Zhi-Peng; Xia Hui; Hao Da-Peng; Li Yan
2014-01-01
With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature (ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension d f , but possess different dynamic exponents of random walk z rw . The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension d f , but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk z rw . The ERC model growing on the two substrates follows the well-known Family—Vicsek scaling law and satisfies the scaling relations 2α + d f ≍ z ≍ 2z rw . In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins—Herring equation. (general)
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.
A random walk through fractal dimensions
Kaye, Brian H
2008-01-01
Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science.From reviews of the first edition:''...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.'' MRS Bulletin
Stochastic self-similar and fractal universe
International Nuclear Information System (INIS)
Iovane, G.; Laserra, E.; Tortoriello, F.S.
2004-01-01
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical structures by using a comparison between quantum quantities and astrophysical ones. We present the observed segregated Universe as the result of a fundamental self-similar law, which generalizes the Compton wavelength relation. It appears that the Universe has a memory of its quantum origin as suggested by R. Penrose with respect to quasi-crystal. A more accurate analysis shows that the present theory can be extended from the astrophysical to the nuclear scale by using generalized (stochastically) self-similar random process. This transition is connected to the relevant presence of the electromagnetic and nuclear interactions inside the matter. In this sense, the presented rule is correct from a subatomic scale to an astrophysical one. We discuss the near full agreement at organic cell scale and human scale too. Consequently the Universe, with its structures at all scales (atomic nucleus, organic cell, human, planet, solar system, galaxy, clusters of galaxy, super clusters of galaxy), could have a fundamental quantum reason. In conclusion, we analyze the spatial dimensions of the objects in the Universe as well as space-time dimensions. The result is that it seems we live in an El Naschie's E-infinity Cantorian space-time; so we must seriously start considering fractal geometry as the geometry of nature, a type of arena where the laws of physics appear at each scale in a self-similar way as advocated long ago by the Swedish school of astrophysics
The Role of Resolution in the Estimation of Fractal Dimension Maps From SAR Data
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Gerardo Di Martino
2017-12-01
Full Text Available This work is aimed at investigating the role of resolution in fractal dimension map estimation, analyzing the role of the different surface spatial scales involved in the considered estimation process. The study is performed using a data set of actual Cosmo/SkyMed Synthetic Aperture Radar (SAR images relevant to two different areas, the region of Bidi in Burkina Faso and the city of Naples in Italy, acquired in stripmap and enhanced spotlight modes. The behavior of fractal dimension maps in the presence of areas with distinctive characteristics from the viewpoint of land-cover and surface features is discussed. Significant differences among the estimated maps are obtained in the presence of fine textural details, which significantly affect the fractal dimension estimation for the higher resolution spotlight images. The obtained results show that if we are interested in obtaining a reliable estimate of the fractal dimension of the observed natural scene, stripmap images should be chosen in view of both economic and computational considerations. In turn, the combination of fractal dimension maps obtained from stripmap and spotlight images can be used to identify areas on the scene presenting non-fractal behavior (e.g., urban areas. Along this guideline, a simple example of stripmap-spotlight data fusion is also presented.
Directory of Open Access Journals (Sweden)
Alireza Keshavarzi
2017-07-01
Full Text Available In this study, the fractal dimensions of velocity fluctuations and the Reynolds shear stresses propagation for flow around a circular bridge pier are presented. In the study reported herein, the fractal dimension of velocity fluctuations (u′, v′, w′ and the Reynolds shear stresses (u′v′ and u′w′ of flow around a bridge pier were computed using a Fractal Interpolation Function (FIF algorithm. The velocity fluctuations of flow along a horizontal plane above the bed were measured using Acoustic Doppler Velocity meter (ADV and Particle Image Velocimetry (PIV. The PIV is a powerful technique which enables us to attain high resolution spatial and temporal information of turbulent flow using instantaneous time snapshots. In this study, PIV was used for detection of high resolution fractal scaling around a bridge pier. The results showed that the fractal dimension of flow fluctuated significantly in the longitudinal and transverse directions in the vicinity of the pier. It was also found that the fractal dimension of velocity fluctuations and shear stresses increased rapidly at vicinity of pier at downstream whereas it remained approximately unchanged far downstream of the pier. The higher value of fractal dimension was found at a distance equal to one times of the pier diameter in the back of the pier. Furthermore, the average fractal dimension for the streamwise and transverse velocity fluctuations decreased from the centreline to the side wall of the flume. Finally, the results from ADV measurement were consistent with the result from PIV, therefore, the ADV enables to detect turbulent characteristics of flow around a circular bridge pier.
Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study
Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana
2016-04-01
The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with
Fractales y series de datos geofísicos
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Montes Vides Luis Alfredo
1993-10-01
Full Text Available
There is a new Geometry which provides a potentially tool for the characterization of geophysical data: The Fractal Geometry. Generally, Geophysical data consist of records in time or data series, for example yearly records of temperature, and they show a random behavior or variation on both a short and a long-term time scale. The trace of a record is a curve with a fractal dimension D, and it is characterized by an exponent H. In this paper, the Hurt's rescaled range analysis method is used to determine the fractal dimension of a geophysical data serie D and H, his self-affinity measure.
La geometría de fractales ha surgido como una herramienta potencialmente útil para la caracterización de datos en Geofísica. Comúnmente, los datos geofísicos conforman series de tiempo, que exhiben un comportamiento aleatorio o variación a corto y a largo plazo. Un ejemplo típico son los registros anuales de temperatura. La traza de un registro es una curva con una dimensión fractal D, caracterizada por un exponente H.
En el presente trabajo se utiliza el método de análisis de rango en cambios de escala, creado por H. E. Hurst, para determinar la dimensión fractal de una serie de datos geofísicos, y su medida de auto-afinidad.
Pre-Service Teachers' Concept Images on Fractal Dimension
Karakus, Fatih
2016-01-01
The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…
Morphometric relations of fractal-skeletal based channel network model
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B. S. Daya Sagar
1998-01-01
Full Text Available A fractal-skeletal based channel network (F-SCN model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F-SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.
Bifurcation and Fractal of the Coupled Logistic Map
Wang, Xingyuan; Luo, Chao
The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Fractal dimensions from a 3-dimensional intermittency analysis in e+e- annihilation
International Nuclear Information System (INIS)
Behrend, H.J.; Criegee, L.; Field, J.H.; Franke, G.; Jung, H.; Meyer, J.; Podobrin, O.; Schroeder, V.; Winter, G.G.; Bussey, P.J.; Campbell, A.J.; Hendry, D.; Lumsdon, S.J.; Skillicorn, I.O.; Ahme, J.; Blobel, V.; Feindt, M.; Fenner, H.; Harjes, J.; Koehne, J.H.; Peters, J.H.; Spitzer, H.; Weihrich, T.; Boer, W. de; Buschhorn, G.; Grindhammer, G.; Gunderson, B.; Kiesling, C.; Kotthaus, R.; Kroha, H.; Lueers, D.; Oberlack, H.; Schacht, P.; Scholz, S.; Wiedenmann, W.; Davier, M.; Grivaz, J.F.; Haissinski, J.; Journe, V.; Le Diberder, F.; Veillet, J.J.; Cozzika, G.; Ducros, Y.; Alexander, G.; Beck, A.; Bella, G.; Grunhaus, J.; Klatchko, A.; Levy, A.; Milstene, C.
1990-10-01
The intermittency structure of multihadronic e + e - annihilation is analyzed by evaluating the factorial moments F 2 -F 5 in 3-dimensional Lorentz invariant phase space as a function of the resolution scale. We interpret our data in the language of fractal objects. It turns out that the fractal dimension depends on the resolution scale in a way that can be attributed to geometrical resolution effects and dynamical effects, such as the π 0 Dalitz decay. The LUND 7.2 hadronization model provides an excellent description of the data. There is no indication of unexplained multiplicity fluctuations in small phase space regions. (orig.)
Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael
2016-02-01
One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.
Undergraduate experiment with fractal diffraction gratings
International Nuclear Information System (INIS)
Monsoriu, Juan A; Furlan, Walter D; Pons, Amparo; Barreiro, Juan C; Gimenez, Marcos H
2011-01-01
We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics laboratories and compared with those obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. Good agreement is obtained between experimental and numerical results.
Directory of Open Access Journals (Sweden)
María Eugenia Torres
2007-01-01
Full Text Available En este trabajo comparamos tres métodos diferentes utilizados para estimar el exponente de Hurst, y analizamos su eficiencia cuando son aplicados a series de datos de diferentes longitudes. Se analizan series temporales de fBm sintetizada pura y con tendencias sinusoidales superpuestas. Mostraremos que los tres métodos aquí discutidos, DFA, basado en wavelets y de variaciones discretas, no sólo son altamente dependientes de la longitud de la señal, sino también del orden o número de los momentos (polinómico, regularidad wavelet o variaciones discretas. Para longitudes de datos suficientemente grandes (superiores a 212, los métodos basados en wavelets y de variaciones discretas mostraron ser menos sesgados y más estables para señales fBm simuladas. Mostraremos que el método de DFA, más utilizado en el ambiente biomédico, es el que proporciona peores estimaciones, arrojando resultados ambiguos cuando son aplicados a señales biológicas de diferentes longitudes o con diferentes parámetros de estimación, sin que pueda considerarse a ninguno de los otros dos como métodos confiables en el momento de desear obtener resultados de relevancia física o fisiológica. Los resultados obtenidos indican que debería procederse con más cautela cuando se trata de obtener conclusiones fisiológicas a partir de estimaciones realizadas a partir de señales reales.
International Nuclear Information System (INIS)
Tokarev, M.V.; Aparin, A.A.; Zborovsky, I.
2014-01-01
The concept of z-scaling previously developed for analysis of inclusive reactions in proton-proton collisions is applied for description of processes with polarized protons at the planned Spin Physics Detector NICA in Dubna. A hypothesis of self-similarity and fractality of the proton spin structure is discussed. The possibilities to extract information on spin-dependent fractal dimensions of hadrons and fragmentation process from asymmetries and coefficients of polarization transfer are justified. The double longitudinal spin asymmetry A LL of π 0 -meson production and the coefficient of the polarization transfer D LL of Λ hyperon production in proton-proton collisions measured at RHIC are analyzed in the framework of z-scaling. The spin-dependent fractal dimensions of proton and fragmentation process with polarized Λ hyperon are estimated. A study of the spin-dependent constituent energy loss as a function of transverse momentum of the inclusive hadron and collision energy is suggested.
Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications
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Alexandru Grigorovici
2017-03-01
Full Text Available In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoretical model, such as the scale relativity theory or the extended scale relativity theory. Thus, using the last theory, fractal entropy through non-differentiable Lie groups was established and, moreover, the pairs generating mechanisms through fractal entanglement states were explained. Our model has implications in the dynamics of biological structures, in the form of the “chameleon-like” behavior of cholesterol.
DEFF Research Database (Denmark)
Laustsen, Christoffer
The basic idea was to use MRI to produce a sequence of 3D gray scale image slices of various animals, subsequentlyimaged with a clinical CT system. For this purpose, these animals were used: toad, lungfish, python snake and a horseshoe crab. Each animal was sacrificed according to standard...... visually inspected, both in 2D and 3D, and compared with photographs and anatomy atlases found at library and on the internet....
International Nuclear Information System (INIS)
Barton, C.C.; Larsen, E.
1985-01-01
Fracture traces exposed on three 214- to 260-m 2 pavements in the same Miocene ash-flow tuff at Yucca Mountain, southwestern Nevada, have been mapped at a scale of 1:50. The maps are two-dimensional sections through the three-dimensional network of strata-bound fractures. All fractures with trace lengths greater than 0.20 m were mapped. The distribution of fracture-trace lengths is log-normal. The fractures do not exhibit well-defined sets based on orientation. Since fractal characterization of such complex fracture-trace networks may prove useful for modeling fracture flow and mechanical responses of fractured rock, an analysis of each of the three maps was done to test whether such networks are fractal. These networks proved to be fractal and the fractal dimensions (D) are tightly clustered (1.12, 1.14, 1.16) for three laterally separated pavements, even though visually the fracture networks appear quite different. The fractal analysis also indicates that the network patterns are scale independent over two orders of magnitude for trace lengths ranging from 0.20 to 25 m. 7 refs., 7 figs
Model of fractal aggregates induced by shear
Directory of Open Access Journals (Sweden)
Wan Zhanhong
2013-01-01
Full Text Available It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.
A Parallel Approach to Fractal Image Compression
Lubomir Dedera
2004-01-01
The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
Random walks of oriented particles on fractals
International Nuclear Information System (INIS)
Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko
2014-01-01
Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features. (paper)
Designing a fractal antenna of 2400 MHz
International Nuclear Information System (INIS)
Miranda Hamburger, Fabio
2012-01-01
The design of a fractal antenna with 2400 MHz of frequency has been studied. The fractal used is described by Waclaw Spierpi.ski. The initial figure, also known as seed, is divided using equilateral triangles with the aim of obtaining a perimeter similar to a meaningful portion of wave length. The use of λ to establish an ideal perimeter has reduced the radiation resistance. The adequate number of iterations needed to design the antenna is calculated based on λ. (author) [es
Fractal effects on excitations in diluted ferromagnets
International Nuclear Information System (INIS)
Kumar, D.
1981-08-01
The low energy spin-wave like excitations in diluted ferromagnets near percolation threshold are studied. For this purpose an explicit use of the fractal model for the backbone of the infinite percolating cluster due to Kirkpatrick is made. Three physical effects are identified, which cause the softening of spin-waves as the percolation point is approached. The importance of fractal effects in the calculation of density of states and the low temperature thermodynamics is pointed out. (author)
A fractal-like resistive network
International Nuclear Information System (INIS)
Saggese, A; De Luca, R
2014-01-01
The equivalent resistance of a fractal-like network is calculated by means of approaches similar to those employed in defining the equivalent resistance of an infinite ladder. Starting from an elementary triangular circuit, a fractal-like network, named after Saggese, is developed. The equivalent resistance of finite approximations of this network is measured, and the didactical implications of the model are highlighted. (paper)
Heat kernels and zeta functions on fractals
International Nuclear Information System (INIS)
Dunne, Gerald V
2012-01-01
On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
International Nuclear Information System (INIS)
Lim, Sin Liang; Koo, Voon Chet; Daya Sagar, B.S.
2009-01-01
Multiscale convexity analysis of certain fractal binary objects-like 8-segment Koch quadric, Koch triadic, and random Koch quadric and triadic islands-is performed via (i) morphologic openings with respect to recursively changing the size of a template, and (ii) construction of convex hulls through half-plane closings. Based on scale vs convexity measure relationship, transition levels between the morphologic regimes are determined as crossover scales. These crossover scales are taken as the basis to segment binary fractal objects into various morphologically prominent zones. Each segmented zone is characterized through normalized morphologic complexity measures. Despite the fact that there is no notably significant relationship between the zone-wise complexity measures and fractal dimensions computed by conventional box counting method, fractal objects-whether they are generated deterministically or by introducing randomness-possess morphologically significant sub-zones with varied degrees of spatial complexities. Classification of realistic fractal sets and/or fields according to sub-zones possessing varied degrees of spatial complexities provides insight to explore links with the physical processes involved in the formation of fractal-like phenomena.
Pulse regime in formation of fractal fibers
Energy Technology Data Exchange (ETDEWEB)
Smirnov, B. M., E-mail: bmsmirnov@gmail.com [Joint Institute for High Temperatures (Russian Federation)
2016-11-15
The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gas flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.
Decoding the Margins: What Can the Fractal Geometry of Basaltic Flow Margins Tell Us?
Schaefer, E. I.; Hamilton, C.; Neish, C.; Beard, S. P.; Bramson, A. M.; Sori, M.; Rader, E. L.
2016-12-01
Studying lava flows on other planetary bodies is essential to characterizing eruption styles and constraining the bodies' thermal evolution. Although planetary basaltic flows are common, many key features are not resolvable in orbital imagery. We are thus developing a technique to characterize basaltic flow type, sub-meter roughness, and sediment mantling from these data. We will present the results from upcoming fieldwork at Craters of the Moon National Monument and Preserve with FINESSE (August) and at Hawai'i Volcanoes National Park (September). We build on earlier work that showed that basaltic flow margins are approximately fractal [Bruno et al., 1992; Gaonac'h et al., 1992] and that their fractal dimensions (D) have distinct `a`ā and pāhoehoe ranges under simple conditions [Bruno et al., 1994]. Using a differential GPS rover, we have recently shown that the margin of Iceland's 2014 Holuhraun flow exhibits near-perfect (R2=0.9998) fractality for ≥24 km across dm to km scales [Schaefer et al., 2016]. This finding suggests that a fractal-based technique has significant potential to characterize flows at sub-resolution scales. We are simultaneously seeking to understand how margin fractality can be modified. A preliminary result for an `a'ā flow in Hawaii's Ka'ū Desert suggests that although aeolian mantling obscures the original flow margin, the apparent margin (i.e., sediment-lava interface) remains fractal [Schaefer et al., 2015]. Further, the apparent margin's D is likely significantly modified from that of the original margin. Other factors that we are exploring include erosion, transitional flow types, and topographic confinement. We will also rigorously test the intriguing possibility that margin D correlates with the sub-meter Hurst exponent H of the flow surface, a common metric of roughness scaling [e.g., Shepard et al., 2001]. This hypothesis is based on geometric arguments [Turcotte, 1997] and is qualitatively consistent with all results so far.
On the Lipschitz condition in the fractal calculus
International Nuclear Information System (INIS)
Golmankhaneh, Alireza K.; Tunc, Cemil
2017-01-01
In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.
Band structures in fractal grading porous phononic crystals
Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin
2018-05-01
In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.
Fractal 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.
Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions
Lapidus, Michael L
1999-01-01
A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...
Fractal Markets Hypothesis and the Global Financial Crisis: Wavelet Power Evidence
Kristoufek, Ladislav
2013-10-01
We analyze whether the prediction of the fractal markets hypothesis about a dominance of specific investment horizons during turbulent times holds. To do so, we utilize the continuous wavelet transform analysis and obtained wavelet power spectra which give the crucial information about the variance distribution across scales and its evolution in time. We show that the most turbulent times of the Global Financial Crisis can be very well characterized by the dominance of short investment horizons which is in hand with the assertions of the fractal markets hypothesis.
Fractal Shapes Description with Parametric L-systems and Turtle Algebra
Ikbal Zammouri; Béchir Ayeb
2007-01-01
In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel betw...
Fractal and multifractal analyses of bipartite networks
Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua
2017-03-01
Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.
Fractal analysis of cervical intraepithelial neoplasia.
Directory of Open Access Journals (Sweden)
Markus Fabrizii
Full Text Available INTRODUCTION: Cervical intraepithelial neoplasias (CIN represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. METHODS: Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods. RESULTS: Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. CONCLUSION: Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.
From dendrimers to fractal polymers and beyond
Directory of Open Access Journals (Sweden)
Charles N. Moorefield
2013-01-01
Full Text Available The advent of dendritic chemistry has facilitated materials research by allowing precise control of functional component placement in macromolecular architecture. The iterative synthetic protocols used for dendrimer construction were developed based on the desire to craft highly branched, high molecular weight, molecules with exact mass and tailored functionality. Arborols, inspired by trees and precursors of the utilitarian macromolecules known as dendrimers today, were the first examples to employ predesigned, 1 → 3 C-branched, building blocks; physical characteristics of the arborols, including their globular shapes, excellent solubilities, and demonstrated aggregation, combined to reveal the inherent supramolecular potential (e.g., the unimolecular micelle of these unique species. The architecture that is a characteristic of dendritic materials also exhibits fractal qualities based on self-similar, repetitive, branched frameworks. Thus, the fractal design and supramolecular aspects of these constructs are suggestive of a larger field of fractal materials that incorporates repeating geometries and are derived by complementary building block recognition and assembly. Use of terpyridine-M2+-terpyridine (where, M = Ru, Zn, Fe, etc connectivity in concert with mathematical algorithms, such as forms the basis for the Seirpinski gasket, has allowed the beginning exploration of fractal materials construction. The propensity of the fractal molecules to self-assemble into higher order architectures adds another dimension to this new arena of materials and composite construction.
Multirate diversity strategy of fractal modulation
International Nuclear Information System (INIS)
Yuan Yong; Shi Si-Hong; Luo Mao-Kang
2011-01-01
Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters are unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment. (general)
On the arithmetic of fractal dimension using hyperhelices
International Nuclear Information System (INIS)
Toledo-Suarez, Carlos D.
2009-01-01
A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension
Poiseuille equation for steady flow of fractal fluid
Tarasov, Vasily E.
2016-07-01
Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.
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
Fitting the Generic Multi-Parameter Crossover Model: Towards Realistic Scaling Estimates
Z.R. Struzik; E.H. Dooijes; F.C.A. Groen; M.M. Novak; T. G. Dewey
1997-01-01
textabstractThe primary concern of fractal metrology is providing a means of reliable estimation of scaling exponents such as fractal dimension, in order to prove the null hypothesis that a particular object can be regarded as fractal. In the particular context to be discussed in this contribution,
Investigation into How 8th Grade Students Define Fractals
Karakus, Fatih
2015-01-01
The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…
Generalized Warburg impedance on realistic self-affine fractals ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals.
Fractal tomography and its application in 3D vision
Trubochkina, N.
2018-01-01
A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.
Constructing and applying the fractal pied de poule (houndstooth)
Feijs, L.M.G.; Toeters, M.J.; Hart, G.; Sarhangi, R.
2013-01-01
Time is ready for a fractal version of pied de poule; it is almost "in the air". Taking inspiration from the Cantor set, and using the analysis of the classical pattern, we obtain a family of elegant new fractal Pied de Poules. We calculate the fractal dimension and develop an attractive fashion
Monitoring of dry sliding wear using fractal analysis
Zhang, Jindang; Regtien, Paulus P.L.; Korsten, Maarten J.
2005-01-01
Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power
Generalized Warburg impedance on realistic self-affine fractals
Indian Academy of Sciences (India)
We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals. The information about the ...
Direct numerical simulation of fractal-generated turbulence
International Nuclear Information System (INIS)
Suzuki, H; Hasegawa, Y; Ushijima, T; Nagata, K; Sakai, Y; Hayase, T
2013-01-01
We simulate fractal-generated turbulence (Hurst and Vassilicos 2007 Phys. Fluids 19 035103)) by means of a direct numerical simulation and address its fundamental characteristics. We examine whether the fractal-generated turbulence in the upstream region has a nature similar to that of a wake. We propose an equation for predicting peak values of the velocity fluctuation intensity and devise a method for formulating the functional form of the quantity of interest by focusing on the time scale of decaying turbulence, and we examine those forms for the turbulent kinetic energy and rms of pressure fluctuation through this method. By using the method, both of these functional forms are found to be power-law functions in the downstream region, even though these profiles follow exponential functions around these peaks. In addition, decay exponents of these quantities are estimated. The integral length scales of velocity fluctuations for transverse as well as streamwise directions are essentially constant in the downstream direction. Decaying turbulence having both these characteristics conflicts with decaying turbulence described by the theory predicting exponential decay. We discuss a factor causing the difference by focusing on the functional form of the transfer function of homogeneous, isotropic turbulence. (paper)
Inspecting plastic deformation of Pd by means of fractal geometry
International Nuclear Information System (INIS)
Eftekhari, Ali
2007-01-01
The influence of phase transformation-induced plastic deformation in Pd|H system on the electrode surface was investigated. Since the Pd surface is subject of severe plastic deformation during this process, the structure and roughness of the electrode surface significantly change. Quantitative analysis of the electrode surfaces for comparative study of such changes is a valuable tool to inspect the plastic deformation induced. Fractal dimension can be used as a quantitative measure for this purpose. Since inappropriate methods may lead to significant errors, an appropriate approach was proposed for the determination of fractal dimensions in such systems. It was demonstrated that the surface roughness generated is mainly due to the plastic deformation induced, not the other side processes, as the electrodes were coated with a uniform layer of gold with thickness smaller than 10 nm. Since plastic deformation is due to hydrogen insertion/extraction and occurs in atomic-scale, it is necessary to divide structural changes appeared in nano- and micro-scale
Lectures on fractal geometry and dynamical systems
Pesin, Yakov
2009-01-01
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular "chaotic" motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples o...
Computer Security: The dilemma of fractal defence
Stefan Lueders, Computer Security Team
2015-01-01
Aren’t mathematical fractals just beautiful? The Mandelbrot set and the Julia set, the Sierpinski gasket, the Menger sponge, the Koch curve (see here)… Based on very simple mathematical rules, they quickly develop into a mosaic of facets slightly different from each other. More and more features appear the closer you zoom into a fractal and expose similar but not identical features of the overall picture. Computer security is like these fractals, only much less pretty: simple at first glance, but increasingly complex and complicated when you look more closely at the details. The deeper you dig, the more and more possibilities open up for malicious people as the attack surface grows, just like that of “Koch’s snowflakes”, where the border length grows exponentially. Consequently, the defensive perimeter also increases when we follow the bits and bytes layer by layer from their processing in the CPU, trickling up the software stack thro...
Fractal design concepts for stretchable electronics.
Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A
2014-01-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
On Nonextensive Statistics, Chaos and Fractal Strings
Castro, C
2004-01-01
Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics ( with a non-additive $ q$-entropy ) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...
A fractal-based image encryption system
Abd-El-Hafiz, S. K.
2014-12-01
This study introduces a novel image encryption system based on diffusion and confusion processes in which the image information is hidden inside the complex details of fractal images. A simplified encryption technique is, first, presented using a single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved through several parameters: feedback delay, multiplexing and independent horizontal or vertical shifts. The effect of each parameter is studied separately and, then, they are combined to illustrate their influence on the encryption quality. The encryption quality is evaluated using different analysis techniques such as correlation coefficients, differential attack measures, histogram distributions, key sensitivity analysis and the National Institute of Standards and Technology (NIST) statistical test suite. The obtained results show great potential compared to other techniques.
Fractal design concepts for stretchable electronics
Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.
2014-02-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
Spalek, Klara; Fastenrath, Matthias; Ackermann, Sandra; Auschra, Bianca; Coynel, David; Frey, Julia; Gschwind, Leo; Hartmann, Francina; van der Maarel, Nadine; Papassotiropoulos, Andreas; de Quervain, Dominique; Milnik, Annette
2015-01-01
Extensive evidence indicates that women outperform men in episodic memory tasks. Furthermore, women are known to evaluate emotional stimuli as more arousing than men. Because emotional arousal typically increases episodic memory formation, the females' memory advantage might be more pronounced for emotionally arousing information than for neutral information. Here, we report behavioral data from 3398 subjects, who performed picture rating and memory tasks, and corresponding fMRI data from up ...
Hall, Andrew; Mundell, Victoria J; Blanco-Andujar, Cristina; Bencsik, Martin; McHale, Glen; Newton, Michael I; Cave, Gareth W V
2010-04-14
Superparamagnetic iron oxide nanometre scale particles have been utilised as contrast agents to image staked target binding oligonucleotide arrays using MRI to correlate the signal intensity and T(2)* relaxation times in different NMR fluids.
Spalek, Klara; Fastenrath, Matthias; Ackermann, Sandra; Auschra, Bianca; Coynel, David; Frey, Julia; Gschwind, Leo; Hartmann, Francina; van der Maarel, Nadine; Papassotiropoulos, Andreas; de Quervain, Dominique; Milnik, Annette
2015-01-21
Extensive evidence indicates that women outperform men in episodic memory tasks. Furthermore, women are known to evaluate emotional stimuli as more arousing than men. Because emotional arousal typically increases episodic memory formation, the females' memory advantage might be more pronounced for emotionally arousing information than for neutral information. Here, we report behavioral data from 3398 subjects, who performed picture rating and memory tasks, and corresponding fMRI data from up to 696 subjects. We were interested in the interaction between sex and valence category on emotional appraisal, memory performances, and fMRI activity. The behavioral results showed that females evaluate in particular negative (p pictures, as emotionally more arousing (pinteraction recall females outperformed males not only in positive (p picture recall (p pictures (pinteraction memory advantage during free recall was absent in a recognition setting. We identified activation differences in fMRI, which corresponded to the females' stronger appraisal of especially negative pictures, but no activation differences that reflected the interaction effect in the free recall memory task. In conclusion, females' valence-category-specific memory advantage is only observed in a free recall, but not a recognition setting and does not depend on females' higher emotional appraisal. Copyright © 2015 the authors 0270-6474/15/350920-16$15.00/0.
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
The virtual education fractality: nature and organization
Directory of Open Access Journals (Sweden)
Osbaldo Turpo Gebera
2013-04-01
Full Text Available The potential generated by ICT in education raises reflect on the underlying frameworks. In this sense, the fractal is an opportunity to explain how it organizes and manages virtual education.This approach recognizes that educational dynamics are recursive and iterative processes instituted as progressive sequences, by way of fractals. This understanding enables becoming as mediated and articulated successive levels. In each dimension are embodied own activities and in turn, involves the recurrence of subsequent levels as possible solving of problem situations. Thus, the knowledge built in response to a collaborative action, participation in networks, ranging from autonomous to the cultural level or conversely.
Directory of Open Access Journals (Sweden)
K. Gotoh
2003-01-01
Full Text Available In our recent papers we applied fractal methods to extract the earthquake precursory signatures from scaling characteristics of the ULF geomagnetic data, obtained in a seismic active region of Guam Island during the large earthquake of 8 August 1993. We found specific dynamics of their fractal characteristics (spectral exponents and fractal dimensions before the earthquake: appearance of the flicker-noise signatures and increase of the time series fractal dimension. Here we analyze ULF geomagnetic data obtained in a seismic active region of Izu Peninsula, Japan during a swarm of the strong nearby earthquakes of June–August 2000 and compare the results obtained in both regions. We apply the same methodology of data processing using the FFT procedure, Higuchi method and Burlaga-Klein approach to calculate the spectral exponents and fractal dimensions of the ULF time series. We found the common features and specific peculiarities in the behavior of fractal characteristics of the ULF time series before Izu and Guam earthquakes. As a common feature, we obtained the same increase of the ULF time series fractal dimension before the earthquakes, and as specific peculiarity – this increase appears to be sharp for Izu earthquake in comparison with gradual increase of the ULF time series fractal dimension for Guam earthquake. The results obtained in both regions are discussed on the basis of the SOC (self-organized criticality concept taking into account the differences in the depths of the earthquake focuses. On the basis of the peculiarities revealed, we advance methodology for extraction of the earthquake precursory signatures. As an adjacent step, we suggest the combined analysis of the ULF time series in the parametric space polarization ratio – fractal dimension. We reason also upon the advantage of the multifractal approach with respect to the mono-fractal analysis for study of the earthquake preparation dynamics.
Transport properties of electrons in fractal magnetic-barrier structures
Sun, Lifeng; Fang, Chao; Guo, Yong
2010-09-01
Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volume 1 of Eric Hammel's Fractal Dimensions, Volume 2 is filled wit
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1, 2, and 3 of Eric Hammel's Fractal Dimensions, Volume 4 is
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1 and 2 of Eric Hammel's Fractal Dimensions, Volume 3 is fil
A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer.
Canning, Sara; Walker, Alan J; Roach, Paul A
2016-12-17
Piezoelectric ultrasonic transducers have the potential to operate as both a sensor and as an actuator of ultrasonic waves. Currently, manufactured transducers operate effectively over narrow bandwidths as a result of their regular structures which incorporate a single length scale. To increase the operational bandwidth of these devices, consideration has been given in the literature to the implementation of designs which contain a range of length scales. In this paper, a mathematical model of a novel Sierpinski tetrix fractal-inspired transducer for sensor applications is presented. To accompany the growing body of research based on fractal-inspired transducers, this paper offers the first sensor design based on a three-dimensional fractal. The three-dimensional model reduces to an effective one-dimensional model by allowing for a number of assumptions of the propagating wave in the fractal lattice. The reception sensitivity of the sensor is investigated. Comparisons of reception force response (RFR) are performed between this novel design along with a previously investigated Sierpinski gasket-inspired device and standard Euclidean design. The results indicate that the proposed device surpasses traditional design sensors.
Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.
Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2018-01-22
We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.
Energy Technology Data Exchange (ETDEWEB)
Clausse, A; Delmastro, D F
1991-12-31
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author). [Espanol] En este trabajo se presenta una descripcion de las lineas de investigacion que los autores estan llevando a cabo en teoria de caos y fractales orientadas al campo nuclear. Es de especial importancia las posibilidades que se abren en el area de la seguridad nuclear, en donde la informacion proveniente de las tecnicas de caos y fractales pueden ayudar al desarrollo de mejores criterios y disenos mas confiables. (Autor).
International Nuclear Information System (INIS)
Pagnozzi, Alex M.; Fiori, Simona; Boyd, Roslyn N.; Guzzetta, Andrea; Doecke, James; Rose, Stephen; Dowson, Nicholas; Gal, Yaniv
2016-01-01
Several scoring systems for measuring brain injury severity have been developed to standardize the classification of MRI results, which allows for the prediction of functional outcomes to help plan effective interventions for children with cerebral palsy. The aim of this study is to use statistical techniques to optimize the clinical utility of a recently proposed template-based scoring method by weighting individual anatomical scores of injury, while maintaining its simplicity by retaining only a subset of scored anatomical regions. Seventy-six children with unilateral cerebral palsy were evaluated in terms of upper limb motor function using the Assisting Hand Assessment measure and injuries visible on MRI using a semiquantitative approach. This cohort included 52 children with periventricular white matter injury and 24 with cortical and deep gray matter injuries. A subset of the template-derived cerebral regions was selected using a data-driven region selection algorithm. Linear regression was performed using this subset, with interaction effects excluded. Linear regression improved multiple correlations between MRI-based and Assisting Hand Assessment scores for both periventricular white matter (R squared increased to 0.45 from 0, P < 0.0001) and cortical and deep gray matter (0.84 from 0.44, P < 0.0001) cohorts. In both cohorts, the data-driven approach retained fewer than 8 of the 40 template-derived anatomical regions. The equal or better prediction of the clinically meaningful Assisting Hand Assessment measure using fewer anatomical regions highlights the potential of these developments to enable enhanced quantification of injury and prediction of patient motor outcome, while maintaining the clinical expediency of the scoring approach. (orig.)
Pagnozzi, Alex M; Fiori, Simona; Boyd, Roslyn N; Guzzetta, Andrea; Doecke, James; Gal, Yaniv; Rose, Stephen; Dowson, Nicholas
2016-02-01
Several scoring systems for measuring brain injury severity have been developed to standardize the classification of MRI results, which allows for the prediction of functional outcomes to help plan effective interventions for children with cerebral palsy. The aim of this study is to use statistical techniques to optimize the clinical utility of a recently proposed template-based scoring method by weighting individual anatomical scores of injury, while maintaining its simplicity by retaining only a subset of scored anatomical regions. Seventy-six children with unilateral cerebral palsy were evaluated in terms of upper limb motor function using the Assisting Hand Assessment measure and injuries visible on MRI using a semiquantitative approach. This cohort included 52 children with periventricular white matter injury and 24 with cortical and deep gray matter injuries. A subset of the template-derived cerebral regions was selected using a data-driven region selection algorithm. Linear regression was performed using this subset, with interaction effects excluded. Linear regression improved multiple correlations between MRI-based and Assisting Hand Assessment scores for both periventricular white matter (R squared increased to 0.45 from 0, P < 0.0001) and cortical and deep gray matter (0.84 from 0.44, P < 0.0001) cohorts. In both cohorts, the data-driven approach retained fewer than 8 of the 40 template-derived anatomical regions. The equal or better prediction of the clinically meaningful Assisting Hand Assessment measure using fewer anatomical regions highlights the potential of these developments to enable enhanced quantification of injury and prediction of patient motor outcome, while maintaining the clinical expediency of the scoring approach.
Energy Technology Data Exchange (ETDEWEB)
Pagnozzi, Alex M. [Royal Brisbane and Women' s Hospital, CSIRO Digital Productivity and Services Flagship, The Australian e-Health Research Centre, Herston, QLD (Australia); The University of Queensland, School of Medicine, Brisbane (Australia); Fiori, Simona [Stella Maris Scientific Institute, Pisa (Italy); Boyd, Roslyn N. [The University of Queensland, Queensland Cerebral Palsy and Rehabilitation Research Centre, School of Medicine, Brisbane (Australia); Guzzetta, Andrea [Stella Maris Scientific Institute, Pisa (Italy); University of Pisa, Department of Clinical and Experimental Medicine, Pisa (Italy); Doecke, James; Rose, Stephen; Dowson, Nicholas [Royal Brisbane and Women' s Hospital, CSIRO Digital Productivity and Services Flagship, The Australian e-Health Research Centre, Herston, QLD (Australia); Gal, Yaniv [The University of Queensland, Centre for Medical Diagnostic Technologies in Queensland, Brisbane (Australia)
2016-02-15
Several scoring systems for measuring brain injury severity have been developed to standardize the classification of MRI results, which allows for the prediction of functional outcomes to help plan effective interventions for children with cerebral palsy. The aim of this study is to use statistical techniques to optimize the clinical utility of a recently proposed template-based scoring method by weighting individual anatomical scores of injury, while maintaining its simplicity by retaining only a subset of scored anatomical regions. Seventy-six children with unilateral cerebral palsy were evaluated in terms of upper limb motor function using the Assisting Hand Assessment measure and injuries visible on MRI using a semiquantitative approach. This cohort included 52 children with periventricular white matter injury and 24 with cortical and deep gray matter injuries. A subset of the template-derived cerebral regions was selected using a data-driven region selection algorithm. Linear regression was performed using this subset, with interaction effects excluded. Linear regression improved multiple correlations between MRI-based and Assisting Hand Assessment scores for both periventricular white matter (R squared increased to 0.45 from 0, P < 0.0001) and cortical and deep gray matter (0.84 from 0.44, P < 0.0001) cohorts. In both cohorts, the data-driven approach retained fewer than 8 of the 40 template-derived anatomical regions. The equal or better prediction of the clinically meaningful Assisting Hand Assessment measure using fewer anatomical regions highlights the potential of these developments to enable enhanced quantification of injury and prediction of patient motor outcome, while maintaining the clinical expediency of the scoring approach. (orig.)
Fractal characteristic in the wearing of cutting tool
Mei, Anhua; Wang, Jinghui
1995-11-01
This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.
Fractal electrodynamics via non-integer dimensional space approach
Tarasov, Vasily E.
2015-09-01
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.
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 (…) ...
de Bartolo, S.; Fallico, C.; Straface, S.; Troisi, S.; Veltri, M.
2009-04-01
fractal dimension of the area of the pores (Df) or of the fractal dimension of capillary tortuosity (DT), very similar to those reported in literature (Yu and Cheng, 2002; Yu and Liu, 2004; Yu, 2005) and falling in the range of definition (1 well as the invariability of, due to the homogeneity of the considered porous media. The linear scaling law of the permeability (k) close to scale length was investigated furnishing more reliable results. However for a better definition of a law of scale for Df, DT and k several number of scale length are need and a greater number of experimental data should be carried out. For this purpose the considered experimental apparatus is limited from its restricted dimensions and geometric bounds; therefore further investigations in experimental field are desirable. Bibliografy Bouwer, H. & Rice, R. C. 1976. A Slug Test for Hydraulic Conductivity of Unconfined Aquifers With Completely or Partially Penetrating Wells, Water Resources Research, 12(3). De Bartolo, S., Fallico, C., Straface, S., Troisi, S. & Veltri M. (in review). Scaling of the hydraulic conductivity measurements by a fractal analysis on an unconfined aquifer reproduced in a laboratory facility, Geoderma Special Issue 2008. Neuman, S.P. 1972. Theory of flow in unconfined aquifers considering delayed response of the water table, Water Resources Research, 8(4), 1031-1045. Yu, B.M. 2005. Fractal Character for Tortuous Streamtubes in Porous Media, Chin. Phis. Lett., 22(1), 158. Yu, B.M. & Cheng, P. 2002. A Fractal Permeability Model for Bi-Dispersed Porous Media, Int. J. Heat Mass Transfer 45(14), 2983. Yu, B.M. & Liu W. 2004. Fractal Analysis of Permeabilities for Porous Media, American Institute of Chemical Engineers 50(1), 46-57.
A Parallel Approach to Fractal Image Compression
Directory of Open Access Journals (Sweden)
Lubomir Dedera
2004-01-01
Full Text Available The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
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
Design of silicon-based fractal antennas
Ghaffar, Farhan A.
2012-11-20
This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.
Fractal geometry of high temperature superconductors
International Nuclear Information System (INIS)
Mosolov, A.B.
1989-01-01
Microstructural geometry of superconducting structural composites of Ag-Yba 2 Cu 3 O x system with a volumetric shave of silver from 0 to 60% is investigated by light and electron microscopy methods. It is ascertained that the structure of cermets investigated is characterized by fractal geometry which is sufficient for describing the electrical and mechanical properties of these materials
Design of silicon-based fractal antennas
Ghaffar, Farhan A.; Shamim, Atif
2012-01-01
This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.
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.
On the oscillatory dynamical behaviour of epidemic spreading in fractal media
International Nuclear Information System (INIS)
Bab, M A; Albano, E V
2008-01-01
We present numerical evidence that dynamical physical processes that develop a time-dependent characteristic length, and take place in fractal media exhibiting spatial discrete scale invariance (DSI) with fundamental scaling ratio b, may become coupled to the topology of the fractal leading to the observation of time DSI. The hallmark of time DSI is the observation of a log-periodic modulation of the dynamic or kinetic observables, which is characterized by a well-defined fundamental time scaling ratio (τ). Both fundamental scaling ratios are linked according to b = τ 1/z , where z is the dynamic exponent characteristic of the physical process. Specifically, we have studied the epidemic behaviour of the contact process (CP) in Sierpinski Carpets. The CP exhibits second-order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility. We observed that relevant dynamic observables, such as the number of active sites, the survival probability of the epidemics and the mean square displacement of the epidemic from the origin (R 2 (t)), exhibit log-periodic modulations. By fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents. Since, at criticality, one has that R 2 (t) ∼ t 2/z , an independent estimation of the dynamic exponent can be performed, in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and τ
On the oscillatory dynamical behaviour of epidemic spreading in fractal media
Energy Technology Data Exchange (ETDEWEB)
Bab, M A; Albano, E V [Instituto de Investigaciones FisicoquImicas Teoricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, UNLP, CONICET, Casilla de Correo 16, Sucursal 4 (1900) La Plata (Argentina)
2008-02-01
We present numerical evidence that dynamical physical processes that develop a time-dependent characteristic length, and take place in fractal media exhibiting spatial discrete scale invariance (DSI) with fundamental scaling ratio b, may become coupled to the topology of the fractal leading to the observation of time DSI. The hallmark of time DSI is the observation of a log-periodic modulation of the dynamic or kinetic observables, which is characterized by a well-defined fundamental time scaling ratio ({tau}). Both fundamental scaling ratios are linked according to b = {tau}{sup 1/z}, where z is the dynamic exponent characteristic of the physical process. Specifically, we have studied the epidemic behaviour of the contact process (CP) in Sierpinski Carpets. The CP exhibits second-order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility. We observed that relevant dynamic observables, such as the number of active sites, the survival probability of the epidemics and the mean square displacement of the epidemic from the origin (R{sup 2}(t)), exhibit log-periodic modulations. By fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents. Since, at criticality, one has that R{sup 2}(t) {approx} t{sup 2/z}, an independent estimation of the dynamic exponent can be performed, in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and {tau}.
Segmentation of time series with long-range fractal correlations
Bernaola-Galván, P.; Oliver, J.L.; Hackenberg, M.; Coronado, A.V.; Ivanov, P.Ch.; Carpena, P.
2012-01-01
Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome. PMID:23645997
Fractales para la arqueología: un nuevo lenguaje
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Rodríguez Alcalde, Angel
1995-06-01
Full Text Available In this paper we propose an evolutionary model of systems in which their elements are articulated through the relationships that involve an exchange of information. When analysing these relationships we use the concept of percolation. The result is a set of dynamic systems self-organized towards a critical state, as the consequence of the iteration of time-space events at a small scale. The network of relationships follows a fractal structure. As an example we tackle the problem of the expansion of domestic species in the Mediterranean basin, proposing an alternative model to that of demic diffusion.
Se propone un modelo de evolución de sistemas en los que sus elementos se articulan mediante relaciones que implican intercambio de información. Éstas se analizan a partir del concepto de percolación. El resultado son sistemas dinámicos que se auto-organizan hacia un estado crítico. como consecuencia de la iteración de sucesos espacio-temporales a pequeña escala. La red de relaciones presenta estructura fractal. Como ejemplo se aborda el problema de la expansión de las especies domésticas en la cuenca mediterránea, proponiendo un modelo alternativo a la difusión démica.
Mass and charge transport in IPMC actuators with fractal interfaces
Chang, Longfei; Wu, Yucheng; Zhu, Zicai; Li, Heng
2016-04-01
Ionic Polymer-Metal Composite (IPMC) actuators have been attracting a growing interest in extensive applications, which consequently raises the demands on the accuracy of its theoretical modeling. For the last few years, rough landscape of the interface between the electrode and the ionic membrane of IPMC has been well-documented as one of the key elements to ensure a satisfied performance. However, in most of the available work, the interface morphology of IPMC was simplified with structural idealization, which lead to perplexity in the physical interpretation on its interface mechanism. In this paper, the quasi-random rough interface of IPMC was described with fractal dimension and scaling parameters. And the electro-chemical field was modeled by Poisson equation and a properly simplified Nernst-Planck equation set. Then, by simulation with Finite Element Method, a comprehensive analysis on he inner mass and charge transportation in IPMC actuators with different fractal interfaces was provided, which may be further adopted to instruct the performance-oriented interface design for ionic electro-active actuators. The results also verified that rough interface can impact the electrical and mechanical response of IPMC, not only from the respect of the real surface increase, but also from mass distribution difference caused by the complexity of the micro profile.
FRACTAL DIMENSION OF URBAN EXPANSION BASED ON REMOTE SENSING IMAGES
Directory of Open Access Journals (Sweden)
IACOB I. CIPRIAN
2012-11-01
Full Text Available Fractal Dimension of Urban Expansion Based on Remote Sensing Images: In Cluj-Napoca city the process of urbanization has been accelerated during the years and implication of local authorities reflects a relevant planning policy. A good urban planning framework should take into account the society demands and also it should satisfy the natural conditions of local environment. The expansion of antropic areas it can be approached by implication of 5D variables (time as a sequence of stages, space: with x, y, z and magnitude of phenomena into the process, which will allow us to analyse and extract the roughness of city shape. Thus, to improve the decision factor we take a different approach in this paper, looking at geometry and scale composition. Using the remote sensing (RS and GIS techniques we manage to extract a sequence of built-up areas (from 1980 to 2012 and used the result as an input for modelling the spatialtemporal changes of urban expansion and fractal theory to analysed the geometric features. Taking the time as a parameter we can observe behaviour and changes in urban landscape, this condition have been known as self-organized – a condition which in first stage the system was without any turbulence (before the antropic factor and during the time tend to approach chaotic behaviour (entropy state without causing an disequilibrium in the main system.
Segmentation of time series with long-range fractal correlations.
Bernaola-Galván, P; Oliver, J L; Hackenberg, M; Coronado, A V; Ivanov, P Ch; Carpena, P
2012-06-01
Segmentation is a standard method of data analysis to identify change-points dividing a nonstationary time series into homogeneous segments. However, for long-range fractal correlated series, most of the segmentation techniques detect spurious change-points which are simply due to the heterogeneities induced by the correlations and not to real nonstationarities. To avoid this oversegmentation, we present a segmentation algorithm which takes as a reference for homogeneity, instead of a random i.i.d. series, a correlated series modeled by a fractional noise with the same degree of correlations as the series to be segmented. We apply our algorithm to artificial series with long-range correlations and show that it systematically detects only the change-points produced by real nonstationarities and not those created by the correlations of the signal. Further, we apply the method to the sequence of the long arm of human chromosome 21, which is known to have long-range fractal correlations. We obtain only three segments that clearly correspond to the three regions of different G + C composition revealed by means of a multi-scale wavelet plot. Similar results have been obtained when segmenting all human chromosome sequences, showing the existence of previously unknown huge compositional superstructures in the human genome.
Chockanathan, Udaysankar; DSouza, Adora M.; Abidin, Anas Z.; Schifitto, Giovanni; Wismüller, Axel
2018-02-01
Resting-state functional MRI (rs-fMRI), coupled with advanced multivariate time-series analysis methods such as Granger causality, is a promising tool for the development of novel functional connectivity biomarkers of neurologic and psychiatric disease. Recently large-scale Granger causality (lsGC) has been proposed as an alternative to conventional Granger causality (cGC) that extends the scope of robust Granger causal analyses to high-dimensional systems such as the human brain. In this study, lsGC and cGC were comparatively evaluated on their ability to capture neurologic damage associated with HIV-associated neurocognitive disorders (HAND). Functional brain network models were constructed from rs-fMRI data collected from a cohort of HIV+ and HIV- subjects. Graph theoretic properties of the resulting networks were then used to train a support vector machine (SVM) model to predict clinically relevant parameters, such as HIV status and neuropsychometric (NP) scores. For the HIV+/- classification task, lsGC, which yielded a peak area under the receiver operating characteristic curve (AUC) of 0.83, significantly outperformed cGC, which yielded a peak AUC of 0.61, at all parameter settings tested. For the NP score regression task, lsGC, with a minimum mean squared error (MSE) of 0.75, significantly outperformed cGC, with a minimum MSE of 0.84 (p < 0.001, one-tailed paired t-test). These results show that, at optimal parameter settings, lsGC is better able to capture functional brain connectivity correlates of HAND than cGC. However, given the substantial variation in the performance of the two methods at different parameter settings, particularly for the regression task, improved parameter selection criteria are necessary and constitute an area for future research.
Electron spin-lattice relaxation in fractals
International Nuclear Information System (INIS)
Shrivastava, K.N.
1986-08-01
We have developed the theory of the spin-fracton interaction for paramagnetic ions in fractal structures. The interaction is exponentially damped by the self-similarity length of the fractal and by the range dimensionality d Φ . The relaxation time of the spin due to the absorption and emission of the fracton has been calculated for a general dimensionality called the Raman dimensionality d R , which for the fractons differs from the Hausdorff (fractal) dimensionality, D, as well as from the Euclidean dimensionality, d. The exponent of the energy level separation in the relaxation rate varies with d R d Φ /D. We have calculated the spin relaxation rate due to a new type of Raman process in which one fracton is absorbed to affect a spin transition from one electronic level to another and later another fracton is emitted along with a spin transition such that the difference in the energies of the two fractons is equal to the electronic energy level separation. The temperature and the dimensionality dependence of such a process has been found in several approximations. In one of the approximations where the van Vleck relaxation rate for a spin in a crystal is known to vary with temperature as T 9 , our calculated variation for fractals turns out to be T 6.6 , whereas the experimental value for Fe 3+ in frozen solutions of myoglobin azide is T 6.3 . Since we used d R =4/3 and the fracton range dimensionality d Φ =D/1.8, we expect to measure the dimensionalities of the problem by measuring the temperature dependence of the relaxation times. We have also calculated the shift of the paramagnetic resonance transition for a spin in a fractal for general dimensionalities. (author)
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 (60 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.
Void analysis of target residues at SPS energy -evidence of correlation with fractal behaviour
International Nuclear Information System (INIS)
Ghosh, Dipak; Deb, Argha; Das, Rupa . E-mail : dipakghosh_in@yahoo.com
2007-01-01
This paper presents an analysis of the target residues in 32 S -AgBr and 16 0 -AgBr interactions at 200 AGeV and 60AGeV respectively in terms of fractal moment by Takagi method and void probability scaling. The study reveals an interesting feature of the production process. In 16 O- AgBr interactions multifractal behaviour is present in both hemispheres and void probability does not show a scaling behaviour, but at high energy the situation changes. In 32 S -AgBr interactions for both hemisphere monofractal behaviour is indicated by that data and void probability also shows good scaling behaviour. This suggests that a possible correlation of void probability with fractal behaviour of target residues. (author)
Kelty-Stephen, Damian G; Dixon, James A
2014-12-01
Intermodal integration required for perceptual learning tasks is rife with individual differences. Participants vary in how they use perceptual information to one modality. One participant alone might change her own response over time. Participants vary further in their use of feedback through one modality to inform another modality. Two experiments test the general hypothesis that perceptual-motor fluctuations reveal both information use within modality and coordination among modalities. Experiment 1 focuses on perceptual learning in dynamic touch, in which participants use exploratory hand-wielding of unseen objects to make visually guided length judgments and use visual feedback to rescale their judgments of the same mechanical information. Previous research found that the degree of fractal temporal scaling (i.e., "fractality") in hand-wielding moderates the use of mechanical information. Experiment 1 shows that head-sway fractality moderates the use of visual information. Further, experience with feedback increases head-sway fractality and prolongs its effect on later hand-wielding fractality. Experiment 2 replicates effects of head-sway fractality moderating use of visual information in a purely visual-judgment task. Together, these findings suggest that fractal fluctuations may provide a modal-general window onto not just how participants use perceptual information but also how well they may integrate information among different modalities. PsycINFO Database Record (c) 2014 APA, all rights reserved.
Kamada, Ray; Decaria, Alex Joseph
1992-01-01
We present DA, a self-affine, multi-fractal which may become the first routine wave/turbulence discriminant for time series data. Using nocturnal atmospheric data, we show the advantages of D A over self-similar fractals and standard turbulence measures such as FFTs, Richardson number, Brunt-Vaisala frequency, buoyancy length scale, variances, turbulent kinetic energy, and phase averaging. DA also shows promise in resolving "wave-break" events. Since it uses local basis functions, DA may be...
a Predictive Model of Permeability for Fractal-Based Rough Rock Fractures during Shear
Huang, Na; Jiang, Yujing; Liu, Richeng; Li, Bo; Zhang, Zhenyu
This study investigates the roles of fracture roughness, normal stress and shear displacement on the fluid flow characteristics through three-dimensional (3D) self-affine fractal rock fractures, whose surfaces are generated using the modified successive random additions (SRA) algorithm. A series of numerical shear-flow tests under different normal stresses were conducted on rough rock fractures to calculate the evolutions of fracture aperture and permeability. The results show that the rough surfaces of fractal-based fractures can be described using the scaling parameter Hurst exponent (H), in which H = 3 - Df, where Df is the fractal dimension of 3D single fractures. The joint roughness coefficient (JRC) distribution of fracture profiles follows a Gauss function with a negative linear relationship between H and average JRC. The frequency curves of aperture distributions change from sharp to flat with increasing shear displacement, indicating a more anisotropic and heterogeneous flow pattern. Both the mean aperture and permeability of fracture increase with the increment of surface roughness and decrement of normal stress. At the beginning of shear, the permeability increases remarkably and then gradually becomes steady. A predictive model of permeability using the mean mechanical aperture is proposed and the validity is verified by comparisons with the experimental results reported in literature. The proposed model provides a simple method to approximate permeability of fractal-based rough rock fractures during shear using fracture aperture distribution that can be easily obtained from digitized fracture surface information.
International Nuclear Information System (INIS)
Ogura, Tatsuo; Miyamoto, Masanori; Budiyono, Agung; Nakamura, Katsuhiro
2007-01-01
Fractal magnetoconductance fluctuations are often observed in experiments on ballistic quantum dots. Although the analysis of the exact self-affine fractal has been given by the semiclassical theory using self-similar periodic orbits in systems with a soft-walled potential with a saddle, there has been no corresponding quantum mechanical investigation. We numerically calculate the quantum conductance with use of the recursive Green's function method applied to open cavities characterized by a Henon-Heiles type potential. The conductance fluctuations show exact self-affinity just as in some of the experimental observations. The enlargement factor for the horizontal axis can be explained by the scaling factor of the area of self-similar periodic orbits, and therefore be attributed to the curvature of the saddle in the cavity potential. The fractal dimension obtained through the box counting method agrees with those evaluated with use of the Hurst exponent, and coincides with the semiclassical prediction. We further investigate the variation of the fractal dimension by changing the control parameters between the classical and quantum domains. (fast track communication)
Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors.
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Núbia Rosa da Silva
Full Text Available The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification.
Queiros-Conde, D.; Foucher, F.; Mounaïm-Rousselle, C.; Kassem, H.; Feidt, M.
2008-12-01
Multi-scale features of turbulent flames near a wall display two kinds of scale-dependent fractal features. In scale-space, an unique fractal dimension cannot be defined and the fractal dimension of the front is scale-dependent. Moreover, when the front approaches the wall, this dependency changes: fractal dimension also depends on the wall-distance. Our aim here is to propose a general geometrical framework that provides the possibility to integrate these two cases, in order to describe the multi-scale structure of turbulent flames interacting with a wall. Based on the scale-entropy quantity, which is simply linked to the roughness of the front, we thus introduce a general scale-entropy diffusion equation. We define the notion of “scale-evolutivity” which characterises the deviation of a multi-scale system from the pure fractal behaviour. The specific case of a constant “scale-evolutivity” over the scale-range is studied. In this case, called “parabolic scaling”, the fractal dimension is a linear function of the logarithm of scale. The case of a constant scale-evolutivity in the wall-distance space implies that the fractal dimension depends linearly on the logarithm of the wall-distance. We then verified experimentally, that parabolic scaling represents a good approximation of the real multi-scale features of turbulent flames near a wall.
Closed contour fractal dimension estimation by the Fourier transform
International Nuclear Information System (INIS)
Florindo, J.B.; Bruno, O.M.
2011-01-01
Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.
Tijera, Manuel; Maqueda, Gregorio; Cano, José L.; López, Pilar; Yagüe, Carlos
2010-05-01
The wind velocity series of the atmospheric turbulent flow in the planetary boundary layer (PBL), in spite of being highly erratic, present a self-similarity structure (Frisch, 1995; Peitgen et., 2004; Falkovich et., 2006). So, the wind velocity can be seen as a fractal magnitude. We calculate the fractal dimension (Komolgorov capacity or box-counting dimension) of the wind perturbation series (u' = u- ) in the physical spaces (namely velocity-time). It has been studied the time evolution of the fractal dimension along different days and at three levels above the ground (5.8 m, 13.5 m, 32 m). The data analysed was recorded in the experimental campaign SABLES-98 (Cuxart et al., 2000) at the Research Centre for the Lower Atmosphere (CIBA) located in Valladolid (Spain). In this work the u, v and w components of wind velocity series have been measured by sonic anemometers (20 Hz sampling rate). The fractal dimension versus the integral length scales of the mean wind series have been studied, as well as the influence of different turbulent parameters. A method for estimating these integral scales is developed using the normalized autocorrelation function and a Gaussian fit. Finally, it will be analysed the variation of the fractal dimension versus stability parameters (as Richardson number) in order to explain some of the dominant features which are likely immersed in the fractal nature of these turbulent flows. References - Cuxart J, Yagüe C, Morales G, Terradellas E, Orbe J, Calvo J, Fernández A, Soler MR, Infante C, Buenestado P, Espinalt A, Joergensen HE, Rees JM, Vilá J, Redondo JM, Cantalapiedra IR and Conangla L (2000) Stable atmospheric boundary-layer experiment in Spain (SABLES98): a report. Boundary- Layer Meteorol 96:337-370 - Falkovich G and Kattepalli R. Sreenivasan (2006) Lessons from Hidrodynamic Turbulence. Physics Today 59: 43-49 - Frisch U (1995) Turbulence the legacy of A.N. Kolmogorov Cambridge University Press 269pp - Peitgen H, Jürgens H and
Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.
Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K
2014-08-01
Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.
Fractal analysis of fractures and microstructures in rocks
International Nuclear Information System (INIS)
Merceron, T.; Nakashima, S.; Velde, B.; Badri, A.
1991-01-01
Fractal geometry was used to characterize the distribution of fracture fields in rocks, which represent main pathways for material migration such as groundwater flow. Fractal investigations of fracture distribution were performed on granite along Auriat and Shikoku boreholes. Fractal dimensions range between 0.3 and 0.5 according to the different sets of fracture planes selected for the analyses. Shear, tension and compressional modes exhibit different fractal values while the composite fracture patterns are also fractal but with a different, median, fractal value. These observations indicate that the fractal method can be used to distinguish fracture types of different origins in a complex system. Fractal results for Shikoku borehole also correlate with geophysical parameters recorded along, drill-holes such as resistivity and possibly permeability. These results represent the first steps of the fractal investigation along drill-holes. Future studies will be conducted to verify relationships between fractal dimensions and permeability by using available geophysical data. Microstructures and microcracks were analysed in the Inada granite. Microcrack patterns are fractal but fractal dimensions values vary according to both mineral type and orientations of measurement within the mineral. Microcracks in quartz are characterized by more irregular distribution (average D = 0.40) than those in feldspars (D = 0.50) suggesting a different mode of rupture. Highest values of D are reported along main cleavage planes for feldspars or C axis for quartz. Further fractal investigations of microstructure in granite will be used to characterize the potential pathways for fluid migration and diffusion in the rock matrix. (author)
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...
Fractal dimension analysis of complexity in Ligeti piano pieces
Bader, Rolf
2005-04-01
Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.
A new numerical approximation of the fractal ordinary differential equation
Atangana, Abdon; Jain, Sonal
2018-02-01
The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.
Evaluation of 3D Printer Accuracy in Producing Fractal Structure.
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.
... resonance imaging - chest; NMR - chest; MRI of the thorax; Thoracic MRI Patient Instructions ... Gotway MB, Panse PM, Gruden JF, Elicker BM. Thoracic radiology. In: Broaddus VC, Mason RJ, Ernst JD, et ...
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.
Fractal Adaptive Web Service for Mobile Learning
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Ichraf Tirellil
2006-06-01
Full Text Available This paper describes our proposition for adaptive web services which is based on configurable, re-usable adaptive/personalized services. To realize our ideas, we have developed an approach for designing, implementing and maintaining personal service. This approach enables the user to accomplish an activity with a set of services answering to his preferences, his profiles and to a personalized context. In this paper, we describe the principle of our approach that we call fractal adaptation approach, and we discuss the implementation of personalization services in the context of mobile and collaborative scenario of learning. We have realized a platform in this context -a platform for mobile and collaborative learning- based on fractal adaptable web services. The platform is tested with a population of students and tutors, in order to release the gaps and the advantages of the approach suggested.
Fractal Analysis of Stealthy Pathfinding Aesthetics
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Ron Coleman
2009-01-01
Full Text Available This paper uses a fractal model to analyze aesthetic values of a new class of obstacle-prone or “stealthy” pathfinding which seeks to avoid detection, exposure, openness, and so forth in videogames. This study is important since in general the artificial intelligence literature has given relatively little attention to aesthetic outcomes in pathfinding. The data we report, according to the fractal model, suggests that stealthy paths are statistically significantly unique in relative aesthetic value when compared to control paths. We show furthermore that paths generated with different stealth regimes are also statistically significantly unique. These conclusions are supported by statistical analysis of model results on experimental trials involving pathfinding in randomly generated, multiroom virtual worlds.
Reengineering through natural structures: the fractal factory
Sihn, Wilfried
1995-08-01
Many branches of European industry have had to recognize that their lead in the world market has been caught up with, particularly through Asian competition. In many cases a deficit of up to 30% in costs and productivity already exists. The reasons are rigid, Tayloristic company structures. The companies are not in a position to react flexibly to constantly changing environmental conditions. This article illustrates the methods of the `fractal company' which are necessary to solve the structure crisis. The fractal company distinguishes itself through its dynamics and its vitality, as well as its independent reaction to the changing circumstances. The developed methods, procedures, and framework conditions such as company structuring, human networking, hierarchy formation, and models for renumeration and working time are explained. They are based on practical examples from IPA's work with the automobile industry, their suppliers, and the engineering industry.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fang, Jieran; Wang, Di; DeVault, Clayton T
2017-01-01
Graphene has been demonstrated to be a promising photodetection material because of its ultrabroadband optical absorption, compatibility with CMOS technology, and dynamic tunability in optical and electrical properties. However, being a single atomic layer thick, graphene has intrinsically small...... optical absorption, which hinders its incorporation with modern photodetecting systems. In this work, we propose a gold snowflake-like fractal metasurface design to realize broadband and polarization-insensitive plasmonic enhancement in graphene photodetector. We experimentally obtain an enhanced...... photovoltage from the fractal metasurface that is an order of magnitude greater than that generated at a plain gold-graphene edge and such an enhancement in the photovoltage sustains over the entire visible spectrum. We also observed a relatively constant photoresponse with respect to polarization angles...
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.
Tumor cells diagnostic through fractal dimensions
International Nuclear Information System (INIS)
Timbo, Christiano dos Santos
2004-01-01
This method relies on the application of an algorithm for the quantitative and statistic differentiation of a sample of cells stricken by a certain kind of pathology and a sample of healthy cells. This differentiation is made by applying the principles of fractal dimension to digital images of the cells. The algorithm was developed using the the concepts of Object- Oriented Programming, resulting in a simple code, divided in 5 distinct procedures, and a user-friendly interface. To obtain the fractal dimension of the images of the cells, the program processes the image, extracting its border, and uses it to characterize the complexity of the form of the cell in a quantitative way. In order to validate the code, it was used a digitalized image found in an article by W. Bauer, developer of an analog method. The result showed a difference of 6% between the value obtained by Bauer and the value obtained the algorithm developed in this work. (author)
Fractal dimension and vessel complexity in patients with cerebral arteriovenous malformations.
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Gernot Reishofer
Full Text Available The fractal dimension (FD can be used as a measure for morphological complexity in biological systems. The aim of this study was to test the usefulness of this quantitative parameter in the context of cerebral vascular complexity. Fractal analysis was applied on ten patients with cerebral arteriovenous malformations (AVM and ten healthy controls. Maximum intensity projections from Time-of-Flight MRI scans were analyzed using different measurements of FD, the Box-counting dimension, the Minkowski dimension and generalized dimensions evaluated by means of multifractal analysis. The physiological significance of this parameter was investigated by comparing values of FD first, with the maximum slope of contrast media transit obtained from dynamic contrast-enhanced MRI data and second, with the nidus size obtained from X-ray angiography data. We found that for all methods, the Box-counting dimension, the Minkowski dimension and the generalized dimensions FD was significantly higher in the hemisphere with AVM compared to the hemisphere without AVM indicating that FD is a sensitive parameter to capture vascular complexity. Furthermore we found a high correlation between FD and the maximum slope of contrast media transit and between FD and the size of the central nidus pointing out the physiological relevance of FD. The proposed method may therefore serve as an additional objective parameter, which can be assessed automatically and might assist in the complex workup of AVMs.
a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution
Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin
Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.
Esteban, Francisco J; Padilla, Nelly; Sanz-Cortés, Magdalena; de Miras, Juan Ruiz; Bargalló, Núria; Villoslada, Pablo; Gratacós, Eduard
2010-12-01
In the search for a useful parameter to detect and quantify subtle brain abnormalities in infants with intrauterine growth restriction (IUGR), we hypothesised that the analysis of the structural complexity of grey matter (GM) and white matter (WM) using the fractal dimension (FD), a measurement of the topological complexity of an object, could be established as a useful tool for quantitative studies of infant brain morphology. We studied a sample of 18 singleton IUGR premature infants, (12.72 months corrected age (CA), range: 12 months-14 months), 15 preterm infants matched one-to-one for gestational age (GA) at delivery (12.6 months; range: 12 months-14 months), and 15 neonates born at term (12.4 months; range: 11 months-14 months). The neurodevelopmental outcome was assessed in all subjects at 18 months CA according to the Bayley Scale for Infant and Toddler Development - Third edition (BSID-III). For MRI acquisition and processing, the infants were scanned at 12 months CA, in a TIM TRIO 3T scanner, sleeping naturally. Images were pre-processed using the SPM5 toolbox, the GM and WM segmented under the VBM5 toolbox, and the box-counting method was applied for FD calculation of normal and skeletonized segmented images. The results showed a significant decrease of the FD of the brain GM and WM in the IUGR group when compared to the preterm or at-term controls. We also identified a significant linear tendency of both GM and WM FD from IUGR to preterm and term groups. Finally, multiple linear analyses between the FD of the GM or WM and the neurodevelopmental scales showed a significant regression of the language and motor scales with the FD of the GM. In conclusion, a decreased FD of the GM and WM in IUGR infants could be a sensitive indicator for the investigation of structural brain abnormalities in the IUGR population at 12 months of age, which can also be related to functional disorders. Copyright © 2010 Elsevier Inc. All rights reserved.
FRACTAL DIMENSIONALITY ANALYSIS OF MAMMARY GLAND THERMOGRAMS
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Yu. E. Lyah
2016-06-01
Full Text Available Thermography may enable early detection of a cancer tumour within a mammary gland at an early, treatable stage of the illness, but thermogram analysis methods must be developed to achieve this goal. This study analyses the feasibility of applying the Hurst exponent readings algorithm for evaluation of the high dimensionality fractals to reveal any possible difference between normal thermograms (NT and malignant thermograms (MT.
A short history of fractal-Cantorian space-time
International Nuclear Information System (INIS)
Marek-Crnjac, L.
2009-01-01
The article attempts to give a short historical overview of the discovery of fractal-Cantorian space-time starting from the 17th century up to the present. In the last 25 years a great number of scientists worked on fractal space-time notably Garnet Ord in Canada, Laurent Nottale in France and Mohamed El Naschie in England who gave an exact mathematical procedure for the derivation of the dimensionality and curvature of fractal space-time fuzzy manifold.
Enhancement of critical temperature in fractal metamaterial superconductors
Energy Technology Data Exchange (ETDEWEB)
Smolyaninov, Igor I., E-mail: smoly@umd.edu [Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 (United States); Smolyaninova, Vera N. [Department of Physics Astronomy and Geosciences, Towson University, 8000 York Road, Towson, MD 21252 (United States)
2017-04-15
Fractal metamaterial superconductor geometry has been suggested and analyzed based on the recently developed theoretical description of critical temperature increase in epsilon near zero (ENZ) metamaterial superconductors. Considerable enhancement of critical temperature has been predicted in such materials due to appearance of large number of additional poles in the inverse dielectric response function of the fractal. Our results agree with the recent observation (Fratini et al. Nature 466, 841 (2010)) that fractal defect structure promotes superconductivity.
Optical diffraction from fractals with a structural transition
International Nuclear Information System (INIS)
Perez Rodriguez, F.; Canessa, E.
1994-04-01
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and biharmonic equations and are compared to more 'regular' irreversible clusters such as diffusion limited and Laplacian aggregates. The optical diffraction method enables to identify a decrease of the fractal dimension above the structural point. (author). 19 refs, 6 figs
Password Authentication Based on Fractal Coding Scheme
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Nadia M. G. Al-Saidi
2012-01-01
Full Text Available Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.
Wavelets, vibrations and scalings
Meyer, Yves
1997-01-01
Physicists and mathematicians are intensely studying fractal sets of fractal curves. Mandelbrot advocated modeling of real-life signals by fractal or multifractal functions. One example is fractional Brownian motion, where large-scale behavior is related to a corresponding infrared divergence. Self-similarities and scaling laws play a key role in this new area. There is a widely accepted belief that wavelet analysis should provide the best available tool to unveil such scaling laws. And orthonormal wavelet bases are the only existing bases which are structurally invariant through dyadic dilations. This book discusses the relevance of wavelet analysis to problems in which self-similarities are important. Among the conclusions drawn are the following: 1) A weak form of self-similarity can be given a simple characterization through size estimates on wavelet coefficients, and 2) Wavelet bases can be tuned in order to provide a sharper characterization of this self-similarity. A pioneer of the wavelet "saga", Meye...
Fractal Branching in Vascular Trees and Networks by VESsel GENeration Analysis (VESGEN)
Parsons-Wingerter, Patricia A.
2016-01-01
Vascular patterning offers an informative multi-scale, fractal readout of regulatory signaling by complex molecular pathways. Understanding such molecular crosstalk is important for physiological, pathological and therapeutic research in Space Biology and Astronaut countermeasures. When mapped out and quantified by NASA's innovative VESsel GENeration Analysis (VESGEN) software, remodeling vascular patterns become useful biomarkers that advance out understanding of the response of biology and human health to challenges such as microgravity and radiation in space environments.
Fusion of multiscale wavelet-based fractal analysis on retina image for stroke prediction.
Che Azemin, M Z; Kumar, Dinesh K; Wong, T Y; Wang, J J; Kawasaki, R; Mitchell, P; Arjunan, Sridhar P
2010-01-01
In this paper, we present a novel method of analyzing retinal vasculature using Fourier Fractal Dimension to extract the complexity of the retinal vasculature enhanced at different wavelet scales. Logistic regression was used as a fusion method to model the classifier for 5-year stroke prediction. The efficacy of this technique has been tested using standard pattern recognition performance evaluation, Receivers Operating Characteristics (ROC) analysis and medical prediction statistics, odds ratio. Stroke prediction model was developed using the proposed system.
International Conference on Advances of Fractals and Related Topics
Lau, Ka-Sing
2014-01-01
This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
Fractal-Based Image Analysis In Radiological Applications
Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.
1987-10-01
We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.
FAST TRACK COMMUNICATION: Weyl law for fat fractals
Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos
2010-10-01
It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.
Electro-chemical manifestation of nanoplasmonics in fractal media
Baskin, Emmanuel; Iomin, Alexander
2013-06-01
Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.
Fractal characteristic study of shearer cutter cutting resistance curves
Energy Technology Data Exchange (ETDEWEB)
Liu, C. [Heilongjiang Scientific and Technical Institute, Haerbin (China). Dept of Mechanical Engineering
2004-02-01
The cutting resistance curve is the most useful tool for reflecting the overall cutting performance of a cutting machine. The cutting resistance curve is influenced by many factors such as the pick structure and arrangement, the cutter operation parameters, coal quality and geologic conditions. This paper discusses the use of fractal geometry to study the properties of the cutting resistance curve, and the use of fractal dimensions to evaluate cutting performance. On the basis of fractal theory, the general form and calculation method of fractal characteristics are given. 4 refs., 3 figs., 1 tab.
Directory of Open Access Journals (Sweden)
Sari Bahagiarti Kusumayudha
2009-11-01
Full Text Available The Gunungsewu area is a karst terrain with water scarcity, located in the Yogyakarta Special Province, adjacent to the open sea of Indian Ocean in the South. Shorelines of the Gunungsewu southern parts show fractal geometry phenomenon, and there can be found some groundwater outlets discharging to the Indian Ocean. One of the coastal outlets exists at the Baron Beach.The amount of water discharge from this spring reaches 20,000 l/sec in wet season, and approximately 9000 in dry season. In order to find other potential coastal springs, shoreline of the south coast is divided into some segments. By applying fractal analysis utilizing air photo of 1 : 30,000 scale, the fractal dimension of every shore line segment is determined, and then the fractal dimension value is correlated to the existence of spring in the segment being analyzed. The results inform us that shoreline segments having fractal dimension (D > 1.300 are potential for the occurrence of coastal springs.
DEFF Research Database (Denmark)
Pedersen, Knud B; Broe, Rebecca; Grauslund, Jakob
2016-01-01
PURPOSE: To investigate inter-eye agreement in retinal vascular fractal dimension (FD) in patients with type 1 diabetes. METHODS: In a cross-sectional study, both eyes were exained in 178 patients with type 1 diabetes. All vessels in a zone 0.5-2.0 disc diameters from the optic disc were traced...... and FD calculated with the box-counting method using SIVA-Fractal semiautomatic software. The modified Early Treatment Diabetic Retinopathy Study (ETDRS) scale was used to grade diabetic retinopathy (DR). Pitman's test of difference in variance was used to calculated inter-eye agreement in FD according...
An Explanation for the Arctic Sea Ice Melt Pond Fractal Transition
Popovic, P.; Abbot, D. S.
2016-12-01
As Arctic sea ice melts during the summer, pools of melt water form on its surface. This decreases the ice's albedo, which signifcantly impacts its subsequent evolution. Understanding this process is essential for buiding accurate sea ice models in GCMs and using them to forecast future changes in sea ice. A feature of melt ponds that helps determine their impact on ice albedo is that they often form complex geometric shapes. One characteristic of their shape, the fractal dimension of the pond boundaries, D, has been shown to transition between the two fundamental limits of D = 1 and D = 2 at some critical pond size. Here, we provide an explanation for this behavior. First, using aerial photographs taken during the SHEBA mission, we show how this fractal transition curve changes with time, and show that there is a qualitative difference in the pond shape as ice transitions from impermeable to permeable. While ice is impermeable, the maximum fractal dimension is less than 2, whereas after it becomes permeable, the maximum fractal dimension becomes very close to 2. We then show how the fractal dimension of the boundary of a collection of overlapping circles placed randomly on a plane also transitions from D = 1 to D = 2 at a size equal to the average size of a single circle. We, therefore, conclude that this transition is a simple geometric consequence of regular shapes connecting. The one physical parameter that can be extracted from the fractal transition curve is the length scale at which transition occurs. Previously, this length scale has been associated with the typical size of snow dunes created on the ice surface during winter. We provide an alternative explanation by noting that the flexural wavelength of the ice poses a fundamental limit on the size of melt ponds on permeable ice. If this is true, melt ponds could be used as a proxy for ice thickness. Finally, we provide some remarks on how to observationally distinguish between the two ideas for what
International Nuclear Information System (INIS)
Ren Xincheng; Guo Lixin
2008-01-01
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)
Homayoun as a Persian Music Scale on Non-Musician’s Brain: an fMRI Study
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Farzaneh Pouladi
2011-10-01
Full Text Available Introduction: The aim of this study was to get to a neurological evaluation of one of the Persian music scales, Homayoun, on brain activation of non-musician subjects. We selected this scale because Homayoun is one of the main scales in Persian classical music which is similar to minor mode in western scales. Methods: This study was performed on 19 right handed subjects, Aging 22-31. Here some pieces from Homayoun Dastgah are used in both rhythmic and non-rhythmic. Result: The results of this study revealed the brain activities for each of rhythmic and non-rhythmic versions of Homayoun Dastgah. The activated regions for non-rhythmic Homayoun contained: right and left Subcallosal Cortex, left Medial Frontal cortex, left anterior Cingulate Gyrus, left Frontal Pole and for rhythmic Homayoun contained: left Precentral Gyrus, left Precuneous Cortex, left anterior Supramarginal, left Superior Parietal Lobule, left Postcentral Gyrus. Also, we acquired amygdala area in both pieces of music. Discussion: Based on arousal effects of rhythm and Damasio's somatic marker hypothesis, non-rhythmic Homayoun activates regions related to emotion and thinking while activity of rhythmic Homayoun is related to areas of movement and motion.
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.
Lambert, Simon A.; Näsholm, Sven Peter; Nordsletten, David; Michler, Christian; Juge, Lauriane; Serfaty, Jean-Michel; Bilston, Lynne; Guzina, Bojan; Holm, Sverre; Sinkus, Ralph
2015-08-01
Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5 μ m in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.
Fractal dimension algorithms and their application to time series associated with natural phenomena
International Nuclear Information System (INIS)
La Torre, F Cervantes-De; González-Trejo, J I; Real-Ramírez, C A; Hoyos-Reyes, L F
2013-01-01
Chaotic invariants like the fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of systems, because it contains information about their geometrical structure at multiple scales. In this work, three algorithms are applied to non-linear time series: spectral analysis, rescaled range analysis and Higuchi's algorithm. The analyzed time series are associated with natural phenomena. The disturbance storm time (Dst) is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a self-similar behavior, which depends on the time scale of measurements. It is also observed that fractal dimensions, D, calculated with Higuchi's method may not be constant over-all time scales. This work shows that during 2001, D reaches its lowest values in March and November. The possibility that D recovers a change pattern arising from self-organized critical phenomena is also discussed
Single-Image Super-Resolution Based on Rational Fractal Interpolation.
Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming
2018-08-01
This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.
Pore Structure and Fractal Characteristics of Niutitang Shale from China
Directory of Open Access Journals (Sweden)
Zhaodong Xi
2018-04-01
Full Text Available A suite of shale samples from the Lower Cambrian Niutitang Formation in northwestern Hunan Province, China, were investigated to better understand the pore structure and fractal characteristics of marine shale. Organic geochemistry, mineralogy by X-ray diffraction, porosity, permeability, mercury intrusion and nitrogen adsorption and methane adsorption experiments were conducted for each sample. Fractal dimension D was obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH model. The relationships between total organic carbon (TOC content, mineral compositions, pore structure parameters and fractal dimension are discussed, along with the contributions of fractal dimension to shale gas reservoir evaluation. Analysis of the results showed that Niutitang shale samples featured high TOC content (2.51% on average, high thermal maturity (3.0% on average, low permeability and complex pore structures, which are highly fractal. TOC content and mineral compositions are two major factors affecting pore structure but they have different impacts on the fractal dimension. Shale samples with higher TOC content had a larger specific surface area (SSA, pore volume (PV and fractal dimension, which enhanced the heterogeneity of the pore structure. Quartz content had a relatively weak influence on shale pore structure, whereas SSA, PV and fractal dimension decreased with increasing clay mineral content. Shale with a higher clay content weakened pore structure heterogeneity. The permeability and Langmuir volume of methane adsorption were affected by fractal dimension. Shale samples with higher fractal dimension had higher adsorption capacity but lower permeability, which is favorable for shale gas adsorption but adverse to shale gas seepage and diffusion.
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 dimension of the fractured surface of materials
International Nuclear Information System (INIS)
Lung, C.W.; Zhang, S.Z.
1989-05-01
Fractal dimension of the fractured surface of materials is discussed to show that the origin of the negative correlation between D F and toughness lies in the method of fractal dimension measurement with perimeter-area relation and also in the physical mechanism of crack propagation. (author). 8 refs, 4 figs, 1 tab
Three-dimensional fractal geometry for gas permeation in microchannels
Malankowska, Magdalena; Schlautmann, Stefan; Berenschot, Erwin J.W.; Tiggelaar, Roald M.; Pina, Maria Pilar; Mallada, Reyes; Tas, Niels R.; Gardeniers, Han
2018-01-01
The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The
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
Fractal sets generated by chemical reactions discrete chaotic dynamics
International Nuclear Information System (INIS)
Gontar, V.; Grechko, O.
2007-01-01
Fractal sets composed by the parameters values of difference equations derived from chemical reactions discrete chaotic dynamics (DCD) and corresponding to the sequences of symmetrical patterns were obtained in this work. Examples of fractal sets with the corresponding symmetrical patterns have been presented
Fractal Dimension analysis for seismicity spatial and temporal ...
Indian Academy of Sciences (India)
23
The research can further promote the application of fractal theory in the study ... spatial-temporal propagation characteristics of seismic activities, fractal theory is not ... provide a theoretical basis for the prevention and control of earthquakes. 2. ... random self-similar structure of the earthquake in the time series and the spatial.
Experiencia en el aula de secundaria con fractales
Gallardo, Sandra; Martínez-Santaolalla, Manuel José; Molina, Marta; Peñas, María; Cañadas, María C.; Crisóstomo, Edson
2006-01-01
Presentamos una experiencia docente en un aula de 2º ESO en la que trabajamos los fractales mediante el uso de material de carácter manipulativo. La metodología seguida se basa en la construcción de casos particulares con el fin de llegar al concepto de fractal.
Growth of fractal structures in flames with silicon admixture
Smirnov, B. M.; Dutka, M.; van Essen, V. M.; Gersen, S.; Visser, P.; Vainchtein, D.; De Hosson, J. Th. M.; Levinsky, H. B.; Mokhov, A. V.
Transmission electron microscopy (TEM) measurements and theoretical analysis are combined to construct the physical picture of formation of SiO2 fractal aggregates in a methane/hexamethyldisiloxane/air atmospheric pressure flame. The formation of SiO2 fractal aggregates is described as a multistage
Evaluation of surface quality by Fractal Dimension and Volume ...
African Journals Online (AJOL)
Experimental and simulation results have enabled to show than the large diameter ball under low loads and medium feed speeds, favors the elimination of peaks and reduction of fractal dimension whence quality improvement of surface. Keywords: burnishing, volume parameters, fractal dimension, experimental designs ...
Bouguer correction density determination from fractal analysis using ...
African Journals Online (AJOL)
In this work, Bouguer density is determined using the fractal approach. This technique was applied to the gravity data of the Kwello area of the Basement Complex, north-western Nigeria. The density obtained using the fractal approach is 2500 kgm which is lower than the conventional value of 2670 kgm used for average ...
Usefulness of fractal analysis for the diagnosis of periodontitis
Energy Technology Data Exchange (ETDEWEB)
Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung [Dankook Univ. School of Dentistry, Seoul (Korea, Republic of)
2001-03-15
To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979{+-}0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006{+-}0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.
Separation in Data Mining Based on Fractal Nature of Data
Czech Academy of Sciences Publication Activity Database
Jiřina, Marcel; Jiřina jr., M.
2013-01-01
Roč. 3, č. 1 (2013), s. 44-60 ISSN 2225-658X Institutional support: RVO:67985807 Keywords : nearest neighbor * fractal set * multifractal * IINC method * correlation dimension Subject RIV: JC - Computer Hardware ; Software http://sdiwc.net/digital-library/separation-in-data-mining-based-on-fractal-nature-of-data.html
Fractal Dimension Of CT Images Of Normal Parotid Glands
International Nuclear Information System (INIS)
Lee, Sang Jin; Heo, Min Suk; You, Dong Soo
1999-01-01
This study was to investigate the age and sex differences of the fractal dimension of the normal parotid glands in the digitized CT images. The six groups, which were composed of 42 men and women from 20's, 40's and 60's and over were picked. Each group contained seven people of the same sex. The normal parotid CT images were digitized, and their fractal dimensions were calculated using Scion Image PC program. The mean of fractal dimensions in males was 1.7292 (+/-0.0588) and 1.6329 (+/-0.0425) in females. The mean of fractal dimensions in young males was 1.7617, 1.7328 in middle males, and 1.6933 in old males. The mean of fractal dimensions in young females was 1.6318, 1.6365 in middle females, and 1.6303 in old females. There was no statistical difference in fractal dimension between left and right parotid gland of the same subject (p>0.05). Fractal dimensions in male were decreased in older group (p 0.05). The fractal dimension of parotid glands in the digitized CT images will be useful to evaluate the age and sex differences.
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
Fractal Information by Means of Harmonic Mappings and Some Physical Implications
Directory of Open Access Journals (Sweden)
Maricel Agop
2016-04-01
Full Text Available Considering that the motions of the complex system structural units take place on continuous, but non-differentiable curves, in the frame of the extended scale relativity model (in its Schrödinger-type variant, it is proven that the imaginary part of a scalar potential of velocities can be correlated with the fractal information and, implicitly, with a tensor of “tensions”, which is fundamental in the construction of the constitutive laws of material. In this way, a specific differential geometry based on a Poincaré-type metric of the Lobachevsky plane (which is invariant to the homographic group of transformations and also a specific variational principle (whose field equations represent an harmonic map from the usual space into the Lobachevsky plane are generated. Moreover, fractal information (which is made explicit at any scale resolution is produced, so that the field variables define a gravitational field. This latter situation is specific to a variational principle in the sense of Matzner–Misner and to certain Ernst-type field equations, the fractal information being contained in the material structure and, thus, in its own space associated with it.
Theory and discretization of ideal magnetohydrodynamic equilibria with fractal pressure profiles
Kraus, B. F.; Hudson, S. R.
2017-09-01
In three-dimensional ideal magnetohydrodynamics, closed flux surfaces cannot maintain both rational rotational-transform and pressure gradients, as these features together produce unphysical, infinite currents. A proposed set of equilibria nullifies these currents by flattening the pressure on sufficiently wide intervals around each rational surface. Such rational surfaces exist at every scale, which characterizes the pressure profile as self-similar and thus fractal. The pressure profile is approximated numerically by considering a finite number of rational regions and analyzed mathematically by classifying the irrational numbers that support gradients into subsets. Applying these results to a given rotational-transform profile in cylindrical geometry, we find magnetic field and current density profiles compatible with the fractal pressure.
Pore-Fractal Structure in Porous Carbons Made from Corn and Wheat
Kapoor, Y. M.; Schmidt, P. W.; Rice, Randall D.; Shulse, Laural; Voss, D. J.; Venkatraman, A.; Fan, L. T.; Walawender, W. P.; Rieker, T. P.
1998-03-01
Small-angle X-ray scattering has been used in a study of the pore structure of some porous and activated carbons on length scales between about 5 and 10^4 ÅThe carbons were obtained by pyrolysis and activation of wheat and American corn (maize). The scattering data showed that in each carbon there are at least two of the following four types of pores: (1) pores with diameters of at least 10^4 Åpores with smooth or fractal surfaces and diameters of at least 5 x 10^3 Åpore-fractals with diameters of no more than about 10^3 Åand (4) pores with diameters no larger than 100 ÅThe relation between the pore structure and the procedure used to obtain the carbon and will be discussed.
Fractal ventilation enhances respiratory sinus arrhythmia
Directory of Open Access Journals (Sweden)
Girling Linda G
2005-05-01
Full Text Available Abstract Background Programming a mechanical ventilator with a biologically variable or fractal breathing pattern (an example of 1/f noise improves gas exchange and respiratory mechanics. Here we show that fractal ventilation increases respiratory sinus arrhythmia (RSA – a mechanism known to improve ventilation/perfusion matching. Methods Pigs were anaesthetised with propofol/ketamine, paralysed with doxacurium, and ventilated in either control mode (CV or in fractal mode (FV at baseline and then following infusion of oleic acid to result in lung injury. Results Mean RSA and mean positive RSA were nearly double with FV, both at baseline and following oleic acid. At baseline, mean RSA = 18.6 msec with CV and 36.8 msec with FV (n = 10; p = 0.043; post oleic acid, mean RSA = 11.1 msec with CV and 21.8 msec with FV (n = 9, p = 0.028; at baseline, mean positive RSA = 20.8 msec with CV and 38.1 msec with FV (p = 0.047; post oleic acid, mean positive RSA = 13.2 msec with CV and 24.4 msec with FV (p = 0.026. Heart rate variability was also greater with FV. At baseline the coefficient of variation for heart rate was 2.2% during CV and 4.0% during FV. Following oleic acid the variation was 2.1 vs. 5.6% respectively. Conclusion These findings suggest FV enhances physiological entrainment between respiratory, brain stem and cardiac nonlinear oscillators, further supporting the concept that RSA itself reflects cardiorespiratory interaction. In addition, these results provide another mechanism whereby FV may be superior to conventional CV.
A fractal nature for polymerized laminin.
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Camila Hochman-Mendez
Full Text Available Polylaminin (polyLM is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM, scanning electron microscopy (SEM and atomic force microscopy (AFM to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.
A fractal nature for polymerized laminin.
Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana
2014-01-01
Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.
Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method
Zhu, Fanglong; Li, Kejing
2010-03-01
In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.
Fractal analysis for heat extraction in geothermal system
Directory of Open Access Journals (Sweden)
Shang Xiaoji
2017-01-01
Full Text Available Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy’s velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.
International Conference and Workshop on Fractals and Wavelets
Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod
2014-01-01
Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
Vibration modes of 3n-gaskets and other fractals
Energy Technology Data Exchange (ETDEWEB)
Bajorin, N; Chen, T; Dagan, A; Emmons, C; Hussein, M; Khalil, M; Mody, P; Steinhurst, B; Teplyaev, A [Department of Mathematics, University of Connecticut, Storrs CT 06269 (United States)
2008-01-11
We rigorously study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals, which include the Sierpinski gasket and other 3n-gaskets. We consider the classical Laplacian on fractals which generalizes the usual one-dimensional second derivative, is the generator of the self-similar diffusion process, and has possible applications as the quantum Hamiltonian. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations. Our analysis, in particular, allows the computation of the spectral zeta function on fractals and the limiting distribution of eigenvalues (i.e., integrated density of states). We consider such examples as the level-3 Sierpinski gasket, a fractal 3-tree, and the diamond fractal.
Band structures in Sierpinski triangle fractal porous phononic crystals
International Nuclear Information System (INIS)
Wang, Kai; Liu, Ying; Liang, Tianshu
2016-01-01
In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.
Determination of fish gender using fractal analysis of ultrasound images
DEFF Research Database (Denmark)
McEvoy, Fintan J.; Tomkiewicz, Jonna; Støttrup, Josianne
2009-01-01
The gender of cod Gadus morhua can be determined by considering the complexity in their gonadal ultrasonographic appearance. The fractal dimension (DB) can be used to describe this feature in images. B-mode gonadal ultrasound images in 32 cod, where gender was known, were collected. Fractal...... by subjective analysis alone. The mean (and standard deviation) of the fractal dimension DB for male fish was 1.554 (0.073) while for female fish it was 1.468 (0.061); the difference was statistically significant (P=0.001). The area under the ROC curve was 0.84 indicating the value of fractal analysis in gender...... result. Fractal analysis is useful for gender determination in cod. This or a similar form of analysis may have wide application in veterinary imaging as a tool for quantification of complexity in images...
Band structures in Sierpinski triangle fractal porous phononic crystals
Energy Technology Data Exchange (ETDEWEB)
Wang, Kai; Liu, Ying, E-mail: yliu5@bjtu.edu.cn; Liang, Tianshu
2016-10-01
In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.
A Tutorial Review on Fractal Spacetime and Fractional Calculus
He, Ji-Huan
2014-11-01
This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.
Using Peano Curves to Construct Laplacians on Fractals
Molitor, Denali; Ott, Nadia; Strichartz, Robert
2015-12-01
We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.
Insulator Contamination Forecasting Based on Fractal Analysis of Leakage Current
Directory of Open Access Journals (Sweden)
Bing Luo
2012-07-01
Full Text Available In this paper, an artificial pollution test is carried out to study the leakage current of porcelain insulators. Fractal theory is adopted to extract the characteristics hidden in leakage current waveforms. Fractal dimensions of the leakage current for the security, forecast and danger zones are analyzed under four types of degrees of contamination. The mean value and the standard deviation of the fractal dimension in the forecast zone are calculated to characterize the differences. The analysis reveals large differences in the fractal dimension of leakage current under different contamination discharge stages and degrees. The experimental and calculation results suggest that the fractal dimension of a leakage current waveform can be used as a new indicator of the discharge process and contamination degree of insulators. The results provide new methods and valid indicators for forecasting contamination flashovers.
Fractal solutions of recirculation tubular chemical reactors
International Nuclear Information System (INIS)
Berezowski, Marek
2003-01-01
Three kinds of fractal solutions of model of recirculation non-adiabatic tubular chemical reactors are presented. The first kind concerns the structure of Feigenbaum's diagram on the limit of chaos. The second kind and the third one concern the effect of initial conditions on the dynamic solutions of models. In the course of computations two types of recirculation were considered, viz. the recirculation of mass (return of a part of products' stream) and recirculation of heat (heat exchange in the external heat exchanger)
Seuront, Laurent
2015-08-01
Fractal analysis is increasingly used to describe, and provide further understanding to, zooplankton swimming behavior. This may be related to the fact that fractal analysis and the related fractal dimension D have the desirable properties to be independent of measurement scale and to be very sensitive to even subtle behavioral changes that may be undetectable to other behavioral variables. As early claimed by Coughlin et al. (1992), this creates "the need for fractal analysis" in behavioral studies, which has hence the potential to become a valuable tool in zooplankton behavioral ecology. However, this paper stresses that fractal analysis, as well as the more elaborated multifractal analysis, is also a risky business that may lead to irrelevant results, without paying extreme attention to a series of both conceptual and practical steps that are all likely to bias the results of any analysis. These biases are reviewed and exemplified on the basis of the published literature, and remedial procedures are provided not only for geometric and stochastic fractal analyses, but also for the more complicated multifractal analysis. The concept of multifractals is finally introduced as a direct, objective and quantitative tool to identify models of motion behavior, such as Brownian motion, fractional Brownian motion, ballistic motion, Lévy flight/walk and multifractal random walk. I finally briefly review the state of this emerging field in zooplankton behavioral research.
International Nuclear Information System (INIS)
Imai, Kuniharu; Ikeda, Mitsuru; Enchi, Yukihiro; Niimi, Takanaga
2008-01-01
Purpose: To confirm whether or not the influence of anatomic noise on the detection of nodules in digital chest radiography can be evaluated by the fractal-feature distance. Materials and methods: We used the square images with and without a simulated nodule which were generated in our previous observer performance study; the simulated nodule was located on the upper margin of a rib, the inside of a rib, the lower margin of a rib, or the central region between two adjoining ribs. For the square chest images, fractal analysis was conducted using the virtual volume method. The fractal-feature distances between the considered and the reference images were calculated using the pseudo-fractal dimension and complexity, and the square images without the simulated nodule were employed as the reference images. We compared the fractal-feature distances with the observer's confidence level regarding the presence of a nodule in plain chest radiograph. Results: For all square chest images, the relationships between the length of the square boxes and the mean of the virtual volumes were linear on a log-log scale. For all types of the simulated nodules, the fractal-feature distance was the highest for the simulated nodules located on the central region between two adjoining ribs and was the lowest for those located in the inside of a rib. The fractal-feature distance showed a linear relation to an observer's confidence level. Conclusion: The fractal-feature distance would be useful for evaluating the influence of anatomic noise on the detection of nodules in digital chest radiography
Fractal characteristics of an asphaltene deposited heterogeneous surface
International Nuclear Information System (INIS)
Amin, J. Sayyad; Ayatollahi, Sh.; Alamdari, A.
2009-01-01
Several methods have been employed in recent years to investigate homogeneous surface topography based on image analysis, such as AFM (atomic force microscopy) and SEM (scanning electron microscopy). Fractal analysis of the images provides fractal dimension of the surface which is used as one of the most common surface indices. Surface topography has generally been considered to be mono-fractal. On the other hand, precipitation of organic materials on a rough surface and its irregular growth result in morphology alteration and converts a homogeneous surface to a heterogeneous one. In this case a mono-fractal description of the surface does not completely describe the nature of the altered surface. This work aims to investigate the topography alteration of a glass surface as a result of asphaltene precipitation and its growth at various pressures using a bi-fractal approach. The experimental results of the deposited surfaces were clearly indicating two regions of micro- and macro-asperities namely, surface types I and II, respectively. The fractal plots were indicative of bi-fractal behavior and for each surface type one fractal dimension was calculated. The topography information of the surfaces was obtained by two image analyses, AFM and SEM imaging techniques. Results of the bi-fractal analysis demonstrated that topography alteration in surface type II (macro-asperities) is more evident than that in surface type I (micro-asperities). Compared to surface type II, a better correlation was observed between the fractal dimensions inferred from the AFM images (D A ) and those of the SEM images (D S ) in surface type I.
Directory of Open Access Journals (Sweden)
Silvester Tursiloadi
2010-06-01
Full Text Available A technique to determine the surface fractal dimension of mesoporous TiO2 using a dynamic flow adsorption instrument is described. Fractal dimension is an additional technique to characterize surface morphology. Surface fractal dimension, a quantitative measurement of surface ruggedness, can be determined by adsorbing a homologous series of adsorbates onto an adsorbent sample of mesoporous TiO2. Titania wet gel prepared by hydrolysis of Ti-alkoxide was immersed in the flow of supercritical CO2 at 60 °C and the solvent was extracted. Mesoporous TiO2 consists of anatase nano-particles, about 5nm in diameter, have been obtained. After calcination at 600 °C, the average pore size of the extracted gel, about 20nm in diameter, and the pore volume, about 0.35cm3g-1, and the specific surface area, about 58 m2g-1. Using the N2 adsorption isotherm, the surface fractal dimension, DS, has been estimated according to the Frenkel-Halsey-Hill (FHH theory. The N2 adsorption isotherm for the as-extracted aerogel indicates the mesoporous structure. Two linear regions are found for the FHH plot of the as-extracted aerogel. The estimated surface fractal dimensions are about 2.49 and 2.68. Both of the DS values indicate rather complex surface morphology. The TEM observation shows that there are amorphous and crystalline particles. Two values of DS may be attributed to these two kinds of particles. The two regions are in near length scales, and the smaller DS, DS =2.49, for the smaller region. This result indicates that there are two kinds of particles, probably amorphous and anatase particles as shown by the TEM observation. Keywords: surface fractal dimensions, CO2 supercritically extraction, sol-gel, aerogel, titania
Sierpinski triangles as a tool to introduce fractal geometry to children and their parents
Gires, Auguste; Schertzer, Daniel
2017-04-01
There are currently two somehow contradictory trends in the public debates involving scientific issues. On the one hand there is a need to address topics of increasing complexity, while on the other hand simple(istic) solutions are suggested by numerous people (including high level ones). Meanwhile there seems to be growing defiance towards science findings. Such problems are faced in numerous fields including geosciences where famous examples are the debates dealing with climate change, or water / air contamination. Such unfortunate trends means that the input of scientists in the society and public debates is strongly required. Although it not actually their job, scientists should get involved as a citizens. They should try to explain the complexity of the issues at stake, and take the necessary time to achieve this; not all problems can be explained with the help of a 140 characters tweet! Rather than hiding the uncertainties, they should try to explain this notion often not well understood, and admit the current limitations of knowledge. In the meantime it would be positive if this dialogue could help children and their parents to get familiarized with science and scientists, show that science is not obscure and actually present in everyday life. Scientists obviously also have the hope of fostering a desire for understanding, enhancing scientific culture and even promoting careers in this field. Fractals and fractal geometry are actually a rather good tool to achieve this. Indeed through numerous iterations of a simple process, one can easily obtain a rather complex shape, exhibiting some of the features observed in the nature. Fractal shapes are scale invariant, i.e. the more you zoom in, the more details you see; a portion of the shape is similar to the full one. This paper aims at presenting a series of activities presenting fractals to young people developed primarily around the famous Sierpinski triangles. Two types of activities were carefully designed
Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.
2012-04-01
In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe
Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin
2016-05-01
One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.
Street, Nichola; Forsythe, Alexandra M.; Reilly, Ronan; Taylor, Richard; Helmy, Mai S.
2016-01-01
Fractal patterns offer one way to represent the rough complexity of the natural world. Whilst they dominate many of our visual experiences in nature, little large-scale perceptual research has been done to explore how we respond aesthetically to these patterns. Previous research (Taylor et al., 2011) suggests that the fractal patterns with mid-range fractal dimensions (FDs) have universal aesthetic appeal. Perceptual and aesthetic responses to visual complexity have been more varied with findings suggesting both linear (Forsythe et al., 2011) and curvilinear (Berlyne, 1970) relationships. Individual differences have been found to account for many of the differences we see in aesthetic responses but some, such as culture, have received little attention within the fractal and complexity research fields. This two-study article aims to test preference responses to FD and visual complexity, using a large cohort (N = 443) of participants from around the world to allow universality claims to be tested. It explores the extent to which age, culture and gender can predict our preferences for fractally complex patterns. Following exploratory analysis that found strong correlations between FD and visual complexity, a series of linear mixed-effect models were implemented to explore if each of the individual variables could predict preference. The first tested a linear complexity model (likelihood of selecting the more complex image from the pair of images) and the second a mid-range FD model (likelihood of selecting an image within mid-range). Results show that individual differences can reliably predict preferences for complexity across culture, gender and age. However, in fitting with current findings the mid-range models show greater consistency in preference not mediated by gender, age or culture. This article supports the established theory that the mid-range fractal patterns appear to be a universal construct underlying preference but also highlights the fragility of
(Multi)fractality of Earthquakes by use of Wavelet Analysis
Enescu, B.; Ito, K.; Struzik, Z. R.
2002-12-01
The fractal character of earthquakes' occurrence, in time, space or energy, has by now been established beyond doubt and is in agreement with modern models of seismicity. Moreover, the cascade-like generation process of earthquakes -with one "main" shock followed by many aftershocks, having their own aftershocks- may well be described through multifractal analysis, well suited for dealing with such multiplicative processes. The (multi)fractal character of seismicity has been analysed so far by using traditional techniques, like the box-counting and correlation function algorithms. This work introduces a new approach for characterising the multifractal patterns of seismicity. The use of wavelet analysis, in particular of the wavelet transform modulus maxima, to multifractal analysis was pioneered by Arneodo et al. (1991, 1995) and applied successfully in diverse fields, such as the study of turbulence, the DNA sequences or the heart rate dynamics. The wavelets act like a microscope, revealing details about the analysed data at different times and scales. We introduce and perform such an analysis on the occurrence time of earthquakes and show its advantages. In particular, we analyse shallow seismicity, characterised by a high aftershock "productivity", as well as intermediate and deep seismic activity, known for its scarcity of aftershocks. We examine as well declustered (aftershocks removed) versions of seismic catalogues. Our preliminary results show some degree of multifractality for the undeclustered, shallow seismicity. On the other hand, at large scales, we detect a monofractal scaling behaviour, clearly put in evidence for the declustered, shallow seismic activity. Moreover, some of the declustered sequences show a long-range dependent (LRD) behaviour, characterised by a Hurst exponent, H > 0.5, in contrast with the memory-less, Poissonian model. We demonstrate that the LRD is a genuine characteristic and is not an effect of the time series probability
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.
Elasticity of fractal materials using the continuum model with non-integer dimensional space
Tarasov, Vasily E.
2015-01-01
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.
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
International Nuclear Information System (INIS)
Tanaka, Manabu
1993-01-01
The effects of microstructural aspects, such as grain size and grain boundary configuration, and creep conditions on the fractal dimension of the grain boundary fracture were examined using several heat-resistant alloys, principally in an analysis scale range between one grain boundary length and specimen size. Grain boundary fracture surface profiles in the heat-resistant alloys exhibited a fractal nature in the scale range between one grain boundary length and specimen size as well as in the scale range below one grain boundary length. The fractal dimension of the grain boundary fracture slightly increased with decreasing grain size and was generally a little larger in the specimens with serrated grain boundaries than in those with straight grain boundaries. The fractal dimension of the grain boundary and the number of grain boundary microcracks which affected the grain boundary fracture patterns were a little larger in the specimen with the smaller grain size, and were also larger in the specimen with serrated grain boundaries. The fractal dimension of the grain boundary fracture increased with decreasing creep stress in the temperature range from 973 to 1422 K in these alloys, since more grain boundary microcracks existed in the specimens ruptured under the lower stresses at the higher temperatures. (orig.) [de
Effective degrees of freedom of a random walk on a fractal
Balankin, Alexander S.
2015-12-01
We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.
Directory of Open Access Journals (Sweden)
Ries A.
2010-10-01
Full Text Available A numerical analysis of elementary particle masses on the logarithmic number line revealed systematic mass gaps of 2e, e, e/2, e/4, e/8 and e/16. Also in abundance data of the chemical elements, a repeated abundance gap of e/2 could be detected. This lead us to modify a fractal scaling model originally published by Müller in this journal, interpreting elementary particles as proton resonances. We express a set of 78 accurately determined particle masses on the logarithmic scale in a continued fraction form where all numerators are Euler’s number.
Quantitative characteristics of the Indian Ocean seafloor relief using fractal dimension
Digital Repository Service at National Institute of Oceanography (India)
Chakraborty, B.; Mahale, V.; Shashikumar, K.; Srinivas, K.
on the basis that the topographic profiles are self- affine and concluded that different depth profiles may be characterized by different fractal dimension (D). Using regression technique4, the power law on a logarithmic scale can be written as: log10 PH...-S profiles (J and K) are situated along west and eastern end. It has been observed that, the western region of the site C is comparatively shallower than the eastern side and the seafioor morphology varies from medium to large scale and has E-W trending...
Convergence of trajectories in fractal interpolation of stochastic processes
International Nuclear Information System (INIS)
MaIysz, Robert
2006-01-01
The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation
Scales are a visible peeling or flaking of outer skin layers. These layers are called the stratum ... Scales may be caused by dry skin, certain inflammatory skin conditions, or infections. Examples of disorders that ...
Transition in the fractal geometry of Arctic melt ponds
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C. Hohenegger
2012-10-01
Full Text Available During the Arctic melt season, the sea ice surface undergoes a remarkable transformation from vast expanses of snow covered ice to complex mosaics of ice and melt ponds. Sea ice albedo, a key parameter in climate modeling, is determined by the complex evolution of melt pond configurations. In fact, ice–albedo feedback has played a major role in the recent declines of the summer Arctic sea ice pack. However, understanding melt pond evolution remains a significant challenge to improving climate projections. By analyzing area–perimeter data from hundreds of thousands of melt ponds, we find here an unexpected separation of scales, where pond fractal dimension D transitions from 1 to 2 around a critical length scale of 100 m^{2} in area. Pond complexity increases rapidly through the transition as smaller ponds coalesce to form large connected regions, and reaches a maximum for ponds larger than 1000 m^{2}, whose boundaries resemble space-filling curves, with D ≈ 2. These universal features of Arctic melt pond evolution are similar to phase transitions in statistical physics. The results impact sea ice albedo, the transmitted radiation fields under melting sea ice, the heat balance of sea ice and the upper ocean, and biological productivity such as under ice phytoplankton blooms.
Fractal Folding and Medium Viscoelasticity Contribute Jointly to Chromosome Dynamics
Polovnikov, K. E.; Gherardi, M.; Cosentino-Lagomarsino, M.; Tamm, M. V.
2018-02-01
Chromosomes are key players of cell physiology, their dynamics provides valuable information about its physical organization. In both prokaryotes and eukaryotes, the short-time motion of chromosomal loci has been described with a Rouse model in a simple or viscoelastic medium. However, little emphasis has been put on the influence of the folded organization of chromosomes on the local dynamics. Clearly, stress propagation, and thus dynamics, must be affected by such organization, but a theory allowing us to extract such information from data, e.g., on two-point correlations, is lacking. Here, we describe a theoretical framework able to answer this general polymer dynamics question. We provide a scaling analysis of the stress-propagation time between two loci at a given arclength distance along the chromosomal coordinate. The results suggest a precise way to assess folding information from the dynamical coupling of chromosome segments. Additionally, we realize this framework in a specific model of a polymer whose long-range interactions are designed to make it fold in a fractal way and immersed in a medium characterized by subdiffusive fractional Langevin motion with a tunable scaling exponent. This allows us to derive explicit analytical expressions for the correlation functions.
Invited Article: Plasmonic growth of patterned metamaterials with fractal geometry
Directory of Open Access Journals (Sweden)
Nobuyuki Takeyasu
2016-08-01
Full Text Available Large-scale metallic three-dimensional (3D structures composed of sub-wavelength fine details, called metamaterials, have attracted optical scientists and materials scientists because of their unconventional and extraordinary optical properties that are not seen in nature. However, existing nano-fabrication technologies including two-photon fabrication, e-beam, focused ion-beam, and probe microscopy are not necessarily suitable for fabricating such large-scale 3D metallic nanostructures. In this article, we propose a different method of fabricating metamaterials, which is based on a bottom-up approach. We mimicked the generation of wood forest under the sunlight and rain in nature. In our method, a silver nano-forest is grown from the silver seeds (nanoparticles placed on the glass substrate in silver-ion solution. The metallic nano-forest is formed only in the area where ultraviolet light is illuminated. The local temperature increases at nano-seeds and tips of nano-trees and their branches due to the plasmonic heating as a result of UV light excitation of localized mode of surface plasmon polaritons. We have made experiments of growth of metallic nano-forest patterned by the light distribution. The experimental results show a beautiful nano-forest made of silver with self-similarity. Fractal dimension and spectral response of the grown structure are discussed. The structures exhibit a broad spectral response from ultraviolet to infrared, which was used for surface-enhanced Raman detection of molecules.
Fractality of profit landscapes and validation of time series models for stock prices
Yi, Il Gu; Oh, Gabjin; Kim, Beom Jun
2013-08-01
We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters p and q, and the sell (buy) decision is made when the log return is larger (smaller) than p (-q). We discretize the unit square (p,q) ∈ [0,1] × [0,1] into the N × N square grid and the profit Π(p,q) is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: the number M of local maxima follows the power-law form M ˜ Na, but the scaling exponent a is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent a ≈ 1.6 observed for real stock markets. We suggest that the fractality of profit landscape characterized by a ≈ 1.6 can be a useful measure to validate time series model for stock prices.
International Nuclear Information System (INIS)
Chen Yanguang
2009-01-01
A pair of nonlinear programming models is built to explain the fractal structure of systems of cities and those of rivers. The hierarchies of cities can be characterized by a set of exponential functions, which is identical in form to the Horton-Strahler's laws of the river networks. Four power laws can be derived from these exponential functions. The evolution of both systems of cities and rivers are then represented as nonlinear dual programming models: to maximize information entropy subject to a certain energy use or to minimize energy dissipation subject to certain information capacity. The optimal solutions of the programming problems are just the exponential equations associated with scaling relations. By doing so, fractals and the self-organized criticality marked by the power laws are interpreted using the idea from the entropy-maximization principle, which gives further weight to the suggestion that optimality of the system as a whole defines the dynamical origin of fractal forms in both nature and society.
Fractal analysis of fracture increasing spontaneous imbibition in porous media with gas-saturated
Cai, Jianchao; Sun, Shuyu
2013-01-01
Spontaneous imbibition (SI) of wetting liquid into matrix blocks due to capillary pressure is regarded as an important recovery mechanism in low permeability fractured reservoir. In this paper, an analytical model is proposed for characterizing SI horizontally from a single plane fracture into gas-saturated matrix blocks. The presented model is based on the fractal character of pores in porous matrix, with gravity force included in the entire imbibition process. The accumulated mass of wetting liquid imbibed into matrix blocks is related to a number of factors such as contact area, pore fractal dimension, tortuosity, maximum pore size, porosity, liquid density and viscosity, surface tension, contact angle, as well as height and tilt angle of the fracture. The mechanism of fracture-enhanced SI is analyzed accordingly. Because of the effect of fracture, the gravity force is positive to imbibition process. Additionally, the farther away from the fracture top of the pore, the more influential the hydrostatic pressure is upon the imbibition action. The presented fractal analysis of horizontal spontaneous imbibition from a single fracture could also shed light on the scaling study of the mass transfer function between matrix and fracture system of fractured reservoirs. © 2013 World Scientific Publishing Company.
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.