WorldWideScience

Sample records for river networks fractals

  1. River networks and ecological corridors: Reactive transport on fractals, migration fronts, hydrochory

    Science.gov (United States)

    Bertuzzo, E.; Maritan, A.; Gatto, M.; Rodriguez-Iturbe, I.; Rinaldo, A.

    2007-04-01

    Moving from a recent quantitative model of the US colonization in the 19th century that relies on analytical and numerical results of reactive-diffusive transport on fractal river networks, this paper considers its generalization to include an embedded flow direction which biases transport. We explore the properties of biased reaction-dispersal models, in which the reaction rates are described by a logistic equation. The relevance of the work is related to the prediction of the role of hydrologic controls on invasion processes (of species, populations, propagules, or infective agents, depending on the specifics of reaction and transport) occurring in river basins. Exact solutions are obtained along with general numerical solutions, which are applied to fractal constructs like Peano basins and real rivers. We also explore similarities and departures from different one-dimensional invasion models where a bias is added to both the diffusion and the telegraph equations, considering their respective ecological insight. We find that the geometrical constraints imposed by the fractal networks imply strong corrections on the speed of traveling fronts that can be enhanced or smoothed by the bias. Applications to real river networks show that the chief morphological parameters affecting the front speed are those characterizing the node-to-node distances measured along the network structure. The spatial density and number of reactive sites thus prove to be a vital hydrologic control on invasions. We argue that our solutions, currently tied to the validity of the logistic growth, might be relevant to the general study of species' spreading along ecological corridors defined by the river network structure.

  2. Analogies between urban hierarchies and river networks: Fractals, symmetry, and self-organized criticality

    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.

  3. Weighted radial dimension: an improved fractal measurement for highway transportation networks distribution

    Science.gov (United States)

    Feng, Yongjiu; Liu, Miaolong; Tong, Xiaohua

    2007-06-01

    An improved fractal measurement, the weighted radial dimension, is put forward for highway transportation networks distribution. The radial dimension (DL), originated from subway investigation in Stuttgart, is a fractal measurement for transportation systems under ideal assumption considering all the network lines to be homogeneous curves, ignoring the difference on spatial structure, quality and level, especially the highway networks. Considering these defects of radial dimension, an improved fractal measurement called weighted radial dimension (D WL) is introduced and the transportation system in Guangdong province is studied in detail using this novel method. Weighted radial dimensions are measured and calculated, and the spatial structure, intensity and connectivity of transportation networks are discussed in Guangdong province and the four sub-areas: the Pearl River Delta area, the East Costal area, the West Costal area and the Northern Guangdong area. In Guangdong province, the fractal spatial pattern characteristics of transportation system vary remarkably: it is the highest in the Pearl River Delta area, moderate in Costal area and lowest in the Northern Guangdong area. With the Pearl River Delta area as the centre, the weighted radial dimensions decrease with the distance increasing, while the decline level is smaller in the costal area and greater in the Northern Guangdong province. By analysis of the conic of highway density, it is recognized that the density decrease with the distance increasing from the calculation centre (Guangzhou), demonstrating the same trend as weighted radial dimensions shown. Evidently, the improved fractal measurement, weighted radial dimension, is an indictor describing the characteristics of highway transportation system more effectively and accurately.

  4. A geometria fractal da rede de drenagem da bacia hidrográfica do Caeté, Alfredo Wagner-SC Fractal geometry of the drainage network of the Caeté river watershed, Alfredo Wagner-SC

    Directory of Open Access Journals (Sweden)

    Leandro Redin Vestena

    2010-08-01

    Full Text Available Os objetivos deste trabalho foram estimar e avaliar a dimensão fractal da rede de drenagem da bacia hidrográfica do Caeté, em Alfredo Wagner, SC, a partir de diferentes métodos, com o propósito de caracterizar as formas geomorfológicas irregulares. A rede de drenagem apresenta propriedades multifractais. As dimensões fractais para os segmentos individuais (df e para a rede de drenagem inteira (Df foram determinadas por métodos que se fundamentaram nas razões de Horton e pelo método da contagem de caixas (Box-Counting. A rede de drenagem tem característica de autoafinidade. A dimensão fractal proveniente da relação de parâmetros obtidos pelas Leis de Horton apresentou resultados dentro dos limiares da teoria da geometria fractal.The objective of the present work was to evaluate the fractal dimensions of the drainage network of the Caeté river watershed, Alfredo Wagner/SC, with different methods in order to characterize the irregular geomorphologic forms. The drainage network possesses multi-fractal properties. That is why the fractal dimensions for the individual segments (df and for the entire network (Df were evaluated with Horton's Laws and the Box-Counting method. The drainage network has self-affinity characteristics. The fractal dimension obtained through the parameters relationship of Horton's Laws showed the results within the thresholds of the fractal geometry theory.

  5. 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)

  6. Fractal dimension estimations of drainage network in the Carpathian-Pannonian system.

    NARCIS (Netherlands)

    Dombradi, E.; Timar, G.; Bada, G.; Cloetingh, S.A.P.L.; Horvath, F.

    2007-01-01

    The development of drainage network in the intra-Carpathian realm is influenced by a complex Quaternary tectonic evolution manifested with differential vertical motions. The present-day configuration of the left-hand side tributary system of the Tisza river was studied by means of fractal analysis.

  7. 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)

  8. Morphometric relations of fractal-skeletal based channel network model

    Directory of Open Access Journals (Sweden)

    B. S. Daya Sagar

    1998-01-01

    Full Text Available A fractal-skeletal based channel network (F-SCN model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F-SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.

  9. Fractal and multifractal analyses of bipartite networks

    Science.gov (United States)

    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.

  10. From Fractal Trees to Deltaic Networks

    Science.gov (United States)

    Cazanacli, D.; Wolinsky, M. A.; Sylvester, Z.; Cantelli, A.; Paola, C.

    2013-12-01

    Geometric networks that capture many aspects of natural deltas can be constructed from simple concepts from graph theory and normal probability distributions. Fractal trees with symmetrical geometries are the result of replicating two simple geometric elements, line segments whose lengths decrease and bifurcation angles that are commonly held constant. Branches could also have a thickness, which in the case of natural distributary systems is the equivalent of channel width. In river- or wave-dominated natural deltas, the channel width is a function of discharge. When normal variations around the mean values for length, bifurcating angles, and discharge are applied, along with either pruning of 'clashing' branches or merging (equivalent to channel confluence), fractal trees start resembling natural deltaic networks, except that the resulting channels are unnaturally straight. Introducing a bifurcation probability fewer, naturally curved channels are obtained. If there is no bifurcation, the direction of each new segment depends on the direction the previous segment upstream (correlated random walk) and, to a lesser extent, on a general direction of growth (directional bias). When bifurcation occurs, the resulting two directions also depend on the bifurcation angle and the discharge split proportions, with the dominant branch following the direction of the upstream parent channel closely. The bifurcation probability controls the channel density and, in conjunction with the variability of the directional angles, the overall curvature of the channels. The growth of the network in effect is associated with net delta progradation. The overall shape and shape evolution of the delta depend mainly on the bifurcation angle average size and angle variability coupled with the degree of dominant direction dependency (bias). The proposed algorithm demonstrates how, based on only a few simple rules, a wide variety of channel networks resembling natural deltas, can be replicated

  11. 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

  12. Passenger flow analysis of Beijing urban rail transit network using fractal approach

    Science.gov (United States)

    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.

  13. Delay Bound: Fractal Traffic Passes through Network Servers

    Directory of Open Access Journals (Sweden)

    Ming Li

    2013-01-01

    Full Text Available Delay analysis plays a role in real-time systems in computer communication networks. This paper gives our results in the aspect of delay analysis of fractal traffic passing through servers. There are three contributions presented in this paper. First, we will explain the reasons why conventional theory of queuing systems ceases in the general sense when arrival traffic is fractal. Then, we will propose a concise method of delay computation for hard real-time systems as shown in this paper. Finally, the delay computation of fractal traffic passing through severs is presented.

  14. Fractal geometry of two-dimensional fracture networks at Yucca Mountain, southwestern Nevada: proceedings

    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

  15. a Fractal Network Model for Fractured Porous Media

    Science.gov (United States)

    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.

  16. 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.

  17. 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

  18. Fractal gene regulatory networks for robust locomotion control of modular robots

    DEFF Research Database (Denmark)

    Zahadat, Payam; Christensen, David Johan; Schultz, Ulrik Pagh

    2010-01-01

    Designing controllers for modular robots is difficult due to the distributed and dynamic nature of the robots. In this paper fractal gene regulatory networks are evolved to control modular robots in a distributed way. Experiments with different morphologies of modular robot are performed and the ......Designing controllers for modular robots is difficult due to the distributed and dynamic nature of the robots. In this paper fractal gene regulatory networks are evolved to control modular robots in a distributed way. Experiments with different morphologies of modular robot are performed...

  19. Fluvial drainage networks: the fractal approach as an improvement of quantitative geomorphic analyses

    Science.gov (United States)

    Melelli, Laura; Liucci, Luisa; Vergari, Francesca; Ciccacci, Sirio; Del Monte, Maurizio

    2014-05-01

    Drainage basins are primary landscape units for geomorphological investigations. Both hillslopes and river drainage system are fundamental components in drainage basins analysis. As other geomorphological systems, also the drainage basins aim to an equilibrium condition where the sequence of erosion, transport and sedimentation approach to a condition of minimum energy effort. This state is revealed by a typical geometry of landforms and of drainage net. Several morphometric indexes can measure how much a drainage basin is far from the theoretical equilibrium configuration, revealing possible external disarray. In active tectonic areas, the drainage basins have a primary importance in order to highlight style, amount and rate of tectonic impulses, and morphometric indexes allow to estimate the tectonic activity classes of different sectors in a study area. Moreover, drainage rivers are characterized by a self-similarity structure; this promotes the use of fractals theory to investigate the system. In this study, fractals techniques are employed together with quantitative geomorphological analysis to study the Upper Tiber Valley (UTV), a tectonic intermontane basin located in northern Apennines (Umbria, central Italy). The area is the result of different tectonic phases. From Late Pliocene until present time the UTV is strongly controlled by a regional uplift and by an extensional phase with different sets of normal faults playing a fundamental role in basin morphology. Thirty-four basins are taken into account for the quantitative analysis, twenty on the left side of the basin, the others on the right side. Using fractals dimension of drainage networks, Horton's laws results, concavity and steepness indexes, and hypsometric curves, this study aims to obtain an evolutionary model of the UTV, where the uplift is compared to local subsidence induced by normal fault activity. The results highlight a well defined difference between western and eastern tributary basins

  20. Analyzing self-similar and fractal properties of the C. elegans neural network.

    Directory of Open Access Journals (Sweden)

    Tyler M Reese

    Full Text Available The brain is one of the most studied and highly complex systems in the biological world. While much research has concentrated on studying the brain directly, our focus is the structure of the brain itself: at its core an interconnected network of nodes (neurons. A better understanding of the structural connectivity of the brain should elucidate some of its functional properties. In this paper we analyze the connectome of the nematode Caenorhabditis elegans. Consisting of only 302 neurons, it is one of the better-understood neural networks. Using a Laplacian Matrix of the 279-neuron "giant component" of the network, we use an eigenvalue counting function to look for fractal-like self similarity. This matrix representation is also used to plot visualizations of the neural network in eigenfunction coordinates. Small-world properties of the system are examined, including average path length and clustering coefficient. We test for localization of eigenfunctions, using graph energy and spacial variance on these functions. To better understand results, all calculations are also performed on random networks, branching trees, and known fractals, as well as fractals which have been "rewired" to have small-world properties. We propose algorithms for generating Laplacian matrices of each of these graphs.

  1. Spatial-temporal data model and fractal analysis of transportation network in GIS environment

    Science.gov (United States)

    Feng, Yongjiu; Tong, Xiaohua; Li, Yangdong

    2008-10-01

    How to organize transportation data characterized by multi-time, multi-scale, multi-resolution and multi-source is one of the fundamental problems of GIS-T development. A spatial-temporal data model for GIS-T is proposed based on Spatial-temporal- Object Model. Transportation network data is systemically managed using dynamic segmentation technologies. And then a spatial-temporal database is built to integrally store geographical data of multi-time for transportation. Based on the spatial-temporal database, functions of spatial analysis of GIS-T are substantively extended. Fractal module is developed to improve the analyzing in intensity, density, structure and connectivity of transportation network based on the validation and evaluation of topologic relation. Integrated fractal with GIS-T strengthens the functions of spatial analysis and enriches the approaches of data mining and knowledge discovery of transportation network. Finally, the feasibility of the model and methods are tested thorough Guangdong Geographical Information Platform for Highway Project.

  2. An effective fractal-tree closure model for simulating blood flow in large arterial networks.

    Science.gov (United States)

    Perdikaris, Paris; Grinberg, Leopold; Karniadakis, George Em

    2015-06-01

    The aim of the present work is to address the closure problem for hemodynamic simulations by developing a flexible and effective model that accurately distributes flow in the downstream vasculature and can stably provide a physiological pressure outflow boundary condition. To achieve this goal, we model blood flow in the sub-pixel vasculature by using a non-linear 1D model in self-similar networks of compliant arteries that mimic the structure and hierarchy of vessels in the meso-vascular regime (radii [Formula: see text]). We introduce a variable vessel length-to-radius ratio for small arteries and arterioles, while also addressing non-Newtonian blood rheology and arterial wall viscoelasticity effects in small arteries and arterioles. This methodology aims to overcome substantial cut-off radius sensitivities, typically arising in structured tree and linearized impedance models. The proposed model is not sensitive to outflow boundary conditions applied at the end points of the fractal network, and thus does not require calibration of resistance/capacitance parameters typically required for outflow conditions. The proposed model convergences to a periodic state in two cardiac cycles even when started from zero-flow initial conditions. The resulting fractal-trees typically consist of thousands to millions of arteries, posing the need for efficient parallel algorithms. To this end, we have scaled up a Discontinuous Galerkin solver that utilizes the MPI/OpenMP hybrid programming paradigm to thousands of computer cores, and can simulate blood flow in networks of millions of arterial segments at the rate of one cycle per 5 min. The proposed model has been extensively tested on a large and complex cranial network with 50 parent, patient-specific arteries and 21 outlets to which fractal trees where attached, resulting to a network of up to 4,392,484 vessels in total, and a detailed network of the arm with 276 parent arteries and 103 outlets (a total of 702,188 vessels

  3. Topological Vulnerability Evaluation Model Based on Fractal Dimension of Complex Networks.

    Directory of Open Access Journals (Sweden)

    Li Gou

    Full Text Available With an increasing emphasis on network security, much more attentions have been attracted to the vulnerability of complex networks. In this paper, the fractal dimension, which can reflect space-filling capacity of networks, is redefined as the origin moment of the edge betweenness to obtain a more reasonable evaluation of vulnerability. The proposed model combining multiple evaluation indexes not only overcomes the shortage of average edge betweenness's failing to evaluate vulnerability of some special networks, but also characterizes the topological structure and highlights the space-filling capacity of networks. The applications to six US airline networks illustrate the practicality and effectiveness of our proposed method, and the comparisons with three other commonly used methods further validate the superiority of our proposed method.

  4. Fractal physiology and the fractional calculus: a perspective.

    Science.gov (United States)

    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

  5. A fractal analysis of the public transportation system of Paris

    OpenAIRE

    L Benguigui

    1995-01-01

    An analysis of the railway networks of the public transportation system of Paris, based on the notion of fractals, is presented. The two basic networks, (metropolitan and suburban) which have different functions, have also a different fractal dimension: 1.8 for the metropolitan network, and 1.5 for the suburban network. By means of computer simulation, it is concluded that the true dimension of the metro network is probably 2.0. A fractal model of the suburban network, with the same features ...

  6. An inkjet-printed UWB antenna on paper substrate utilizing a novel fractal matching network

    KAUST Repository

    Cook, Benjamin Stassen; Shamim, Atif

    2012-01-01

    In this work, the smallest reported inkjet-printed UWB antenna is proposed that utilizes a fractal matching network to increase the performance of a UWB microstrip monopole. The antenna is inkjet-printed on a paper substrate to demonstrate

  7. Circulating persistent current and induced magnetic field in a fractal network

    Energy Technology Data Exchange (ETDEWEB)

    Saha, Srilekha [Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata 700 064 (India); Maiti, Santanu K., E-mail: santanu.maiti@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700 108 (India); Karmakar, S.N. [Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata 700 064 (India)

    2016-04-29

    We present the overall conductance as well as the circulating currents in individual loops of a Sierpinski gasket (SPG) as we apply bias voltage via the side attached electrodes. SPG being a self-similar structure, its manifestation on loop currents and magnetic fields is examined in various generations of this fractal and it has been observed that for a given configuration of the electrodes, the physical quantities exhibit certain regularity as we go from one generation to another. Also a notable feature is the introduction of anisotropy in hopping causes an increase in magnitude of overall transport current. These features are a subject of interest in this article. - Highlights: • Voltage driven circular current is analyzed in a fractal network. • Current induced magnetic field is strong enough to flip a spin. • Anisotropy in hopping enhances overall transport current.

  8. 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.

  9. An inkjet-printed UWB antenna on paper substrate utilizing a novel fractal matching network

    KAUST Repository

    Cook, Benjamin Stassen

    2012-07-01

    In this work, the smallest reported inkjet-printed UWB antenna is proposed that utilizes a fractal matching network to increase the performance of a UWB microstrip monopole. The antenna is inkjet-printed on a paper substrate to demonstrate the ability to produce small and low-cost UWB antennas with inkjet-printing technology which can enable compact, low-cost, and environmentally friendly wireless sensor network. © 2012 IEEE.

  10. Fast hybrid fractal image compression using an image feature and neural network

    International Nuclear Information System (INIS)

    Zhou Yiming; Zhang Chao; Zhang Zengke

    2008-01-01

    Since fractal image compression could maintain high-resolution reconstructed images at very high compression ratio, it has great potential to improve the efficiency of image storage and image transmission. On the other hand, fractal image encoding is time consuming for the best matching search between range blocks and domain blocks, which limits the algorithm to practical application greatly. In order to solve this problem, two strategies are adopted to improve the fractal image encoding algorithm in this paper. Firstly, based on the definition of an image feature, a necessary condition of the best matching search and FFC algorithm are proposed, and it could reduce the search space observably and exclude most inappropriate domain blocks according to each range block before the best matching search. Secondly, on the basis of FFC algorithm, in order to reduce the mapping error during the best matching search, a special neural network is constructed to modify the mapping scheme for the subblocks, in which the pixel values fluctuate greatly (FNFC algorithm). Experimental results show that the proposed algorithms could obtain good quality of the reconstructed images and need much less time than the baseline encoding algorithm

  11. 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.

  12. Chimera states in brain networks: Empirical neural vs. modular fractal connectivity

    Science.gov (United States)

    Chouzouris, Teresa; Omelchenko, Iryna; Zakharova, Anna; Hlinka, Jaroslav; Jiruska, Premysl; Schöll, Eckehard

    2018-04-01

    Complex spatiotemporal patterns, called chimera states, consist of coexisting coherent and incoherent domains and can be observed in networks of coupled oscillators. The interplay of synchrony and asynchrony in complex brain networks is an important aspect in studies of both the brain function and disease. We analyse the collective dynamics of FitzHugh-Nagumo neurons in complex networks motivated by its potential application to epileptology and epilepsy surgery. We compare two topologies: an empirical structural neural connectivity derived from diffusion-weighted magnetic resonance imaging and a mathematically constructed network with modular fractal connectivity. We analyse the properties of chimeras and partially synchronized states and obtain regions of their stability in the parameter planes. Furthermore, we qualitatively simulate the dynamics of epileptic seizures and study the influence of the removal of nodes on the network synchronizability, which can be useful for applications to epileptic surgery.

  13. 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.

  14. A key heterogeneous structure of fractal networks based on inverse renormalization scheme

    Science.gov (United States)

    Bai, Yanan; Huang, Ning; Sun, Lina

    2018-06-01

    Self-similarity property of complex networks was found by the application of renormalization group theory. Based on this theory, network topologies can be classified into universality classes in the space of configurations. In return, through inverse renormalization scheme, a given primitive structure can grow into a pure fractal network, then adding different types of shortcuts, it exhibits different characteristics of complex networks. However, the effect of primitive structure on networks structural property has received less attention. In this paper, we introduce a degree variance index to measure the dispersion of nodes degree in the primitive structure, and investigate the effect of the primitive structure on network structural property quantified by network efficiency. Numerical simulations and theoretical analysis show a primitive structure is a key heterogeneous structure of generated networks based on inverse renormalization scheme, whether or not adding shortcuts, and the network efficiency is positively correlated with degree variance of the primitive structure.

  15. River network and watershed morphology analysis with potential implications towards basin classification

    Science.gov (United States)

    Bugaets, Andrey; Gartsman, Boris; Bugaets, Nadezhda

    2013-04-01

    Generally, the investigation of river network composition and watersheds morphology (fluvial geomorphology), constituting one of the key patterns of land surface, is a fundamental question of Earth Sciences. Recent ideas in this research field are the equilibrium and optimal, in the sense of minimum energy expenditure, river network evolution under constant or slowly varying conditions (Rodriguez-Iturbe, Rinaldo, 1997). It follows to such network behavior as self-similarity, self-affinity and self-organization. That is to say, under relatively stable conditions the river systems tend to some "good composed" form and vice-versa. Lately appearing global free available detailed DEM covers involve new possibilities in this research field. We develop new methodology and program package for river network structure and watershed morphology detailed analysis on the base of ArcMap tools. Different characteristics of river network (e.g. ordering, coefficients of Horton's laws, Shannon entropy, fractal dimension) and basin morphology (e.g. diagrams of average elevation, slope, width and energy index against distance to outlet along streams) could be calculated to find a good indicators of intensity and non-equilibrium of watershed evolution. Watersheds are non-conservative systems in which energy is dissipated by transporting water and sediment in geomorphic adjustment of the slopes and channels. The problem of estimating the amount of energy expenditure associated with overcoming surface and system resistance is extremely complicated to solve. A simplification on a river network scale is to consider energy expenditure to be primarily associated with friction of the fluid. We propose a new technique to analyze the catchment landforms based on so-called "energy function" that is a distribution of total energy index against distance from outlet. As potential energy of water on the hillslopes is transformed into kinetic energy of the flowing fluid-sediment mixture in the runoff

  16. [Soil particle size distribution and its fractal dimension among degradation sequences of the alpine meadow in the source region of the Yangtze and Yellow River, Qinghai-Tibetan Plateau, China].

    Science.gov (United States)

    Wei, Mao-Hong; Lin, Hui-Long

    2014-03-01

    The alpine meadow in the source region of the Yangtze and Yellow River is suffering serious deterioration. Though great efforts have been put into, the restoration for the degraded grassland is far from being effective, mainly due to poor understanding of the degradation mechanism of alpine meadow in this region. In order to clarify the formation mechanism of degradation grassland and provide the new ideas for restoration, degradation sequences of the alpine meadow in the source region of the Yangtze and Yellow River were taken as target systems to analyze the soil particle size distribution, the fractal dimension of the soil particle size, and the relationship between soil erosion modulus and fractal dimension. The results showed that, with increasing grassland degradation, the percentage contents of clay increased while the percentage contents of silt sand and very fine sand showed a decreasing trend. The fractal dimension presented a positive correlation with clay among the degradation sequences while negative correlations were found with very fine sand and silt sand. The curvilinear regression of fractal dimension and erosion modulus fitted a quadratic function. Judged by the function, fractal dimension 2.81 was the threshold value of soil erosion. The threshold value has an indicative meaning on predicting the breakout of grazing-induced erosion and on restoration of the degraded grassland. Taking fractal dimension of 2.81 as the restoration indicator, adoption of corresponding measures to make fractal dimension less than 2.81, would an effective way to restore the degradation grassland.

  17. Long-term Trend and Fractal of Annual Runoff Process in Mainstream of Tarim River

    Institute of Scientific and Technical Information of China (English)

    XU Jianhua; CHEN Yaning; LI Weihong; DONG Shan

    2008-01-01

    Based on the time series data from the Aral hydrological station for the period of 1958-2005, the paper re-veals the long-term trend and fractal of the annual runoff process in the mainstream of the Tarim River by using thewavelet analysis method and the fractal theory. The main conclusions are as follows: 1) From a large time scale pointof view, i.e. the time scale of 16 (24) years, the annual runoff basically shows a slightly decreasing trend as a wholefrom 1958 to 2005. If the time scale is reduced to 8 (23) or 4 (22) years, the annual runoff still displays the basic trendas the large time scale, but it has fluctuated more obviously during the period. 2) The correlation dimension for theannual runoff process is 3.4307, non-integral, which indicates that the process has both fractal and chaotic characteris-tics. The correlation dimension is above 3, which means that at least four independent variables are needed to describethe dynamics of the annual runoff process. 3) The Hurst exponent for the first period (1958-1973) is 0.5036, whichequals 0.5 approximately and indicates that the annual runoff process is in chaos. The Hurst exponents for the second(1974-1989) and third (1990-2005) periods are both greater than 0.50, which indicate that the annual runoff processshowed a long-enduring characteristic in the two periods. The Hurst exponent for the period from 1990 to 2005 indi-cates that the annual runoffwill show a slightly increasing trend in the 16 years after 2005.

  18. Quantitative evaluation and modeling of two-dimensional neovascular network complexity: the surface fractal dimension

    International Nuclear Information System (INIS)

    Grizzi, Fabio; Russo, Carlo; Colombo, Piergiuseppe; Franceschini, Barbara; Frezza, Eldo E; Cobos, Everardo; Chiriva-Internati, Maurizio

    2005-01-01

    Modeling the complex development and growth of tumor angiogenesis using mathematics and biological data is a burgeoning area of cancer research. Architectural complexity is the main feature of every anatomical system, including organs, tissues, cells and sub-cellular entities. The vascular system is a complex network whose geometrical characteristics cannot be properly defined using the principles of Euclidean geometry, which is only capable of interpreting regular and smooth objects that are almost impossible to find in Nature. However, fractal geometry is a more powerful means of quantifying the spatial complexity of real objects. This paper introduces the surface fractal dimension (D s ) as a numerical index of the two-dimensional (2-D) geometrical complexity of tumor vascular networks, and their behavior during computer-simulated changes in vessel density and distribution. We show that D s significantly depends on the number of vessels and their pattern of distribution. This demonstrates that the quantitative evaluation of the 2-D geometrical complexity of tumor vascular systems can be useful not only to measure its complex architecture, but also to model its development and growth. Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex form of branched anatomical structures, in an attempt to define more appropriate methods of describing them quantitatively. This knowledge can be used to predict the aggressiveness of malignant tumors and design compounds that can halt the process of angiogenesis and influence tumor growth

  19. Paper-based inkjet-printed ultra-wideband fractal antennas

    KAUST Repository

    Maza, Armando Rodriguez; Cook, Benjamin Stassen; Jabbour, Ghassan E.; Shamim, Atif

    2012-01-01

    For the first time, paper-based inkjet-printed ultra-wideband (UWB) fractal antennas are presented. Two new designs, a miniaturised UWB monopole, which utilises a fractal matching network and is the smallest reported inkjet-printed UWB printed

  20. 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

  1. Paper-based inkjet-printed ultra-wideband fractal antennas

    KAUST Repository

    Maza, Armando Rodriguez

    2012-01-01

    For the first time, paper-based inkjet-printed ultra-wideband (UWB) fractal antennas are presented. Two new designs, a miniaturised UWB monopole, which utilises a fractal matching network and is the smallest reported inkjet-printed UWB printed antenna to date, and a fourth-order Koch Snowflake monopole, which utilises a Sierpinski gasket fractal for ink reduction, are demonstrated. It is shown that fractals prove to be a successful method of reducing fabrication costs in inkjet-printed antennas, while retaining or enhancing printed antenna performance. © 2012 The Institution of Engineering and Technology.

  2. 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....

  3. Fractal analysis of urban environment: land use and sewer system

    Science.gov (United States)

    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...).

  4. INTEGRATION OF FRACTAL AND NEURAL NETWORK TECHNOLOGIES IN PEDAGOGICAL MONITORING AND ASSESSMENT OF KNOWLEDGE OF TRAINEES

    Directory of Open Access Journals (Sweden)

    Svetlana N Dvoryatkina

    2017-12-01

    Full Text Available The possibility of statement and solution of the problem of searching of theoretical justification and development of efficient didactic mechanisms of the organization of process of pedagogical monitoring and assessment of level of knowledge of trainees can be based on convergence of the leading psychological and pedagogical, mathematical, and informational technologies with accounting of the modern achievements in science. In the article, the pedagogical expediency of realization of opportunities of means of informational technologies in monitoring and assessment of the composite mathematical knowledge, in the management of cognitive activity of students is proved. The ability to integrate fractal methods and neural network technologies in perfecting of a system of pedagogical monitoring of mathematical knowledge of trainees as a part of the automated training systems (ATS is investigated and realized in practice. It is proved that fractal methods increase the accuracy and depth of estimation of the level of proficiency of students and also complexes of intellectual operations of the integrative qualities allowing to master and apply cross-disciplinary knowledge and abilities in professional activity. Neural network technologies solve a problem of realization of the personal focused tutoring from positions of optimum individualization of mathematical education and self-realization of the person. The technology of projection of integrative system of pedagogical monitoring of knowledge of students includes the following stages: establishment of the required tutoring parameters; definition and preparation of input data for realization of integration of fractal and neural network technologies; development of the diagnostic module as a part of the block of an artificial intelligence of ATS, filling of the databases structured by system; start of system for obtaining the forecast. In development of the integrative automated system of pedagogical

  5. Inter-relationship between scaling exponents for describing self-similar river networks

    Science.gov (United States)

    Yang, Soohyun; Paik, Kyungrock

    2015-04-01

    Natural river networks show well-known self-similar characteristics. Such characteristics are represented by various power-law relationships, e.g., between upstream length and drainage area (exponent h) (Hack, 1957), and in the exceedance probability distribution of upstream area (exponent ɛ) (Rodriguez-Iturbe et al., 1992). It is empirically revealed that these power-law exponents are within narrow ranges. Power-law is also found in the relationship between drainage density (the total stream length divided by the total basin area) and specified source area (the minimum drainage area to form a stream head) (exponent η) (Moussa and Bocquillon, 1996). Considering that above three scaling relationships all refer to fundamental measures of 'length' and 'area' of a given drainage basin, it is natural to hypothesize plausible inter-relationship between these three scaling exponents. Indeed, Rigon et al. (1996) demonstrated the relationship between ɛ and h. In this study, we expand this to a more general ɛ-η-h relationship. We approach ɛ-η relationship in an analytical manner while η-h relationship is demonstrated for six study basins in Korea. Detailed analysis and implications will be presented. References Hack, J. T. (1957). Studies of longitudinal river profiles in Virginia and Maryland. US, Geological Survey Professional Paper, 294. Moussa, R., & Bocquillon, C. (1996). Fractal analyses of tree-like channel networks from digital elevation model data. Journal of Hydrology, 187(1), 157-172. Rigon, R., Rodriguez-Iturbe, I., Maritan, A., Giacometti. A., Tarboton, D. G., & Rinaldo, A. (1996). On Hack's Law. Water Resources Research, 32(11), 3367-3374. Rodríguez-Iturbe, I., Ijjasz-Vasquez, E. J., Bras, R. L., & Tarboton, D. G. (1992). Power law distributions of discharge mass and energy in river basins. Water Resources Research, 28(4), 1089-1093.

  6. Fractal cosmology

    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.

  7. Fractal network dimension and viscoelastic powerlaw behavior: II. An experimental study of structure-mimicking phantoms by magnetic resonance elastography

    International Nuclear Information System (INIS)

    Guo Jing; Posnansky, Oleg; Hirsch, Sebastian; Scheel, Michael; Taupitz, Matthias; Sack, Ingolf; Braun, Juergen

    2012-01-01

    The dynamics of the complex shear modulus, G*, of soft biological tissue is governed by the rigidity and topology of multiscale mechanical networks. Multifrequency elastography can measure the frequency dependence of G* in soft biological tissue, providing information about the structure of tissue networks at multiple scales. In this study, the viscoelastic properties of structure-mimicking phantoms containing tangled paper stripes embedded in agarose gel are investigated by multifrequency magnetic resonance elastography within the dynamic range of 40–120 Hz. The effective media viscoelastic properties are analyzed in terms of the storage modulus (the real part of G*), the loss modulus (the imaginary part of G*) and the viscoelastic powerlaw given by the two-parameter springpot model. Furthermore, diffusion tensor imaging is used for investigating the effect of network structures on water mobility. The following observations were made: the random paper networks with fractal dimensions between 2.481 and 2.755 had no or minor effects on the storage modulus, whereas the loss modulus was significantly increased about 2.2 kPa per fractal dimension unit (R = 0.962, P < 0.01). This structural sensitivity of the loss modulus was significantly correlated with the springpot powerlaw exponent (0.965, P < 0.01), while for the springpot elasticity modulus, a trend was discernable (0.895, P < 0.05). No effect of the paper network on water diffusion was observed. The gel phantoms with embedded paper stripes presented here are a feasible way for experimentally studying the effect of network topology on soft-tissue viscoelastic parameters. In the dynamic range of in vivo elastography, the fractal network dimension primarily correlates to the loss behavior of soft tissue as can be seen from the loss modulus or the powerlaw exponent of the springpot model. These findings represent the experimental underpinning of structure-sensitive elastography for an improved characterization of

  8. Disruption of River Networks in Nature and Models

    Science.gov (United States)

    Perron, J. T.; Black, B. A.; Stokes, M.; McCoy, S. W.; Goldberg, S. L.

    2017-12-01

    Many natural systems display especially informative behavior as they respond to perturbations. Landscapes are no exception. For example, longitudinal elevation profiles of rivers responding to changes in uplift rate can reveal differences among erosional mechanisms that are obscured while the profiles are in equilibrium. The responses of erosional river networks to perturbations, including disruption of their network structure by diversion, truncation, resurfacing, or river capture, may be equally revealing. In this presentation, we draw attention to features of disrupted erosional river networks that a general model of landscape evolution should be able to reproduce, including the consequences of different styles of planetary tectonics and the response to heterogeneous bedrock structure and deformation. A comparison of global drainage directions with long-wavelength topography on Earth, Mars, and Saturn's moon Titan reveals the extent to which persistent and relatively rapid crustal deformation has disrupted river networks on Earth. Motivated by this example and others, we ask whether current models of river network evolution adequately capture the disruption of river networks by tectonic, lithologic, or climatic perturbations. In some cases the answer appears to be no, and we suggest some processes that models may be missing.

  9. Fractal geometry of the drainage network of the Caeté river watershed, Alfredo Wagner-SC

    OpenAIRE

    Vestena, Leandro Redin; Kobiyama, Masato

    2010-01-01

    Os objetivos deste trabalho foram estimar e avaliar a dimensão fractal da rede de drenagem da bacia hidrográfica do Caeté, em Alfredo Wagner, SC, a partir de diferentes métodos, com o propósito de caracterizar as formas geomorfológicas irregulares. A rede de drenagem apresenta propriedades multifractais. As dimensões fractais para os segmentos individuais (df) e para a rede de drenagem inteira (Df) foram determinadas por métodos que se fundamentaram nas razões de Horton e pelo método da conta...

  10. L-system fractals

    CERN Document Server

    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

  11. 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

  12. Dynamic network expansion, contraction, and connectivity in the river corridor of mountain stream network

    Science.gov (United States)

    Ward, A. S.; Schmadel, N.; Wondzell, S. M.

    2017-12-01

    River networks are broadly recognized to expand and contract in response to hydrologic forcing. Additionally, the individual controls on river corridor dynamics of hydrologic forcing and geologic setting are well recognized. However, we currently lack tools to integrate our understanding of process dynamics in the river corridor and make predictions at the scale of river networks. In this study, we develop a perceptual model of the river corridor in mountain river networks, translate this into a reduced-complexity mechanistic model, and implement the model in a well-studied headwater catchment. We found that the river network was most sensitive to hydrologic dynamics under the lowest discharges (Qgauge managers of water resources who need to estimate connectivity and flow initiation location along the river corridor over broad, unstudied catchments.

  13. Transport on river networks: A dynamical approach

    OpenAIRE

    Zaliapin, I; Foufoula-Georgiou, E; Ghil, M

    2017-01-01

    This study is motivated by problems related to environmental transport on river networks. We establish statistical properties of a flow along a directed branching network and suggest its compact parameterization. The downstream network transport is treated as a particular case of nearest-neighbor hierarchical aggregation with respect to the metric induced by the branching structure of the river network. We describe the static geometric structure of a drainage network by a tree, referred to as...

  14. The Influence of Water Conservancy Projects on River Network Connectivity, A Case of Luanhe River Basin

    Science.gov (United States)

    Li, Z.; Li, C.

    2017-12-01

    Connectivity is one of the most important characteristics of a river, which is derived from the natural water cycle and determine the renewability of river water. The water conservancy project can change the connectivity of natural river networks, and directly threaten the health and stability of the river ecosystem. Based on the method of Dendritic Connectivity Index (DCI), the impacts from sluices and dams on the connectivity of river network are deeply discussed herein. DCI quantitatively evaluate the connectivity of river networks based on the number of water conservancy facilities, the connectivity of fish and geographical location. The results show that the number of water conservancy facilities and their location in the river basin have a great influence on the connectivity of the river network. With the increase of the number of sluices and dams, DCI is decreasing gradually, but its decreasing range is becoming smaller and smaller. The dam located in the middle of the river network cuts the upper and lower parts of the whole river network, and destroys the connectivity of the river network more seriously. Therefore, this method can be widely applied to the comparison of different alternatives during planning of river basins and then provide a reference for the site selection and design of the water conservancy project and facility concerned.

  15. Automatic River Network Extraction from LIDAR Data

    Science.gov (United States)

    Maderal, E. N.; Valcarcel, N.; Delgado, J.; Sevilla, C.; Ojeda, J. C.

    2016-06-01

    National Geographic Institute of Spain (IGN-ES) has launched a new production system for automatic river network extraction for the Geospatial Reference Information (GRI) within hydrography theme. The goal is to get an accurate and updated river network, automatically extracted as possible. For this, IGN-ES has full LiDAR coverage for the whole Spanish territory with a density of 0.5 points per square meter. To implement this work, it has been validated the technical feasibility, developed a methodology to automate each production phase: hydrological terrain models generation with 2 meter grid size and river network extraction combining hydrographic criteria (topographic network) and hydrological criteria (flow accumulation river network), and finally the production was launched. The key points of this work has been managing a big data environment, more than 160,000 Lidar data files, the infrastructure to store (up to 40 Tb between results and intermediate files), and process; using local virtualization and the Amazon Web Service (AWS), which allowed to obtain this automatic production within 6 months, it also has been important the software stability (TerraScan-TerraSolid, GlobalMapper-Blue Marble , FME-Safe, ArcGIS-Esri) and finally, the human resources managing. The results of this production has been an accurate automatic river network extraction for the whole country with a significant improvement for the altimetric component of the 3D linear vector. This article presents the technical feasibility, the production methodology, the automatic river network extraction production and its advantages over traditional vector extraction systems.

  16. AUTOMATIC RIVER NETWORK EXTRACTION FROM LIDAR DATA

    Directory of Open Access Journals (Sweden)

    E. N. Maderal

    2016-06-01

    Full Text Available National Geographic Institute of Spain (IGN-ES has launched a new production system for automatic river network extraction for the Geospatial Reference Information (GRI within hydrography theme. The goal is to get an accurate and updated river network, automatically extracted as possible. For this, IGN-ES has full LiDAR coverage for the whole Spanish territory with a density of 0.5 points per square meter. To implement this work, it has been validated the technical feasibility, developed a methodology to automate each production phase: hydrological terrain models generation with 2 meter grid size and river network extraction combining hydrographic criteria (topographic network and hydrological criteria (flow accumulation river network, and finally the production was launched. The key points of this work has been managing a big data environment, more than 160,000 Lidar data files, the infrastructure to store (up to 40 Tb between results and intermediate files, and process; using local virtualization and the Amazon Web Service (AWS, which allowed to obtain this automatic production within 6 months, it also has been important the software stability (TerraScan-TerraSolid, GlobalMapper-Blue Marble , FME-Safe, ArcGIS-Esri and finally, the human resources managing. The results of this production has been an accurate automatic river network extraction for the whole country with a significant improvement for the altimetric component of the 3D linear vector. This article presents the technical feasibility, the production methodology, the automatic river network extraction production and its advantages over traditional vector extraction systems.

  17. Statistical Characterization of River and Channel Network Formation in Intermittently Flowing Vortex Systems.

    Science.gov (United States)

    Olson, C. J.; Reichhardt, C.; Nori, F.

    1997-03-01

    Vortices moving in dirty superconductors can form intricate flow patterns, resembling fluid rivers, as they interact with the pinning landscape (F. Nori, Science 271), 1373 (1996).. Weaker pinning produces relatively straight nori>vortex channels, while stronger pinning results in the formation of one or more winding channels that carry all flow. This corresponds to a crossover from elastic flow to plastic flow as the pinning strength is increased. For several pinning parameters, we find the fractal dimension of the channels that form, the vortex trail density, the distance travelled by vortices as they pass through the sample, the branching ratio, the sinuosity, and the size distribution of the rivers, and we compare our rivers with physical rivers that follow Horton's laws.

  18. Synchronisation and stability in river metapopulation networks.

    Science.gov (United States)

    Yeakel, J D; Moore, J W; Guimarães, P R; de Aguiar, M A M

    2014-03-01

    Spatial structure in landscapes impacts population stability. Two linked components of stability have large consequences for persistence: first, statistical stability as the lack of temporal fluctuations; second, synchronisation as an aspect of dynamic stability, which erodes metapopulation rescue effects. Here, we determine the influence of river network structure on the stability of riverine metapopulations. We introduce an approach that converts river networks to metapopulation networks, and analytically show how fluctuation magnitude is influenced by interaction structure. We show that river metapopulation complexity (in terms of branching prevalence) has nonlinear dampening effects on population fluctuations, and can also buffer against synchronisation. We conclude by showing that river transects generally increase synchronisation, while the spatial scale of interaction has nonlinear effects on synchronised dynamics. Our results indicate that this dual stability - conferred by fluctuation and synchronisation dampening - emerges from interaction structure in rivers, and this may strongly influence the persistence of river metapopulations. © 2013 John Wiley & Sons Ltd/CNRS.

  19. Characterisation of human non-proliferativediabetic retinopathy using the fractal analysis

    Directory of Open Access Journals (Sweden)

    Carmen Alina Lupaşcu

    2015-08-01

    Full Text Available AIM:To investigate and quantify changes in the branching patterns of the retina vascular network in diabetes using the fractal analysis method.METHODS:This was a clinic-based prospective study of 172 participants managed at the Ophthalmological Clinic of Cluj-Napoca, Romania, between January 2012 and December 2013. A set of 172 segmented and skeletonized human retinal images, corresponding to both normal (24 images and pathological (148 images states of the retina were examined. An automatic unsupervised method for retinal vessel segmentation was applied before fractal analysis. The fractal analyses of the retinal digital images were performed using the fractal analysis software ImageJ. Statistical analyses were performed for these groups using Microsoft Office Excel 2003 and GraphPad InStat software.RESULTS:It was found that subtle changes in the vascular network geometry of the human retina are influenced by diabetic retinopathy (DR and can be estimated using the fractal geometry. The average of fractal dimensions D for the normal images (segmented and skeletonized versions is slightly lower than the corresponding values of mild non-proliferative DR (NPDR images (segmented and skeletonized versions. The average of fractal dimensions D for the normal images (segmented and skeletonized versions is higher than the corresponding values of moderate NPDR images (segmented and skeletonized versions. The lowest values were found for the corresponding values of severe NPDR images (segmented and skeletonized versions.CONCLUSION:The fractal analysis of fundus photographs may be used for a more complete undeTrstanding of the early and basic pathophysiological mechanisms of diabetes. The architecture of the retinal microvasculature in diabetes can be quantitative quantified by means of the fractal dimension. Microvascular abnormalities on retinal imaging may elucidate early mechanistic pathways for microvascular complications and distinguish patients with

  20. Dynamic hydro-climatic networks in pristine and regulated rivers

    Science.gov (United States)

    Botter, G.; Basso, S.; Lazzaro, G.; Doulatyari, B.; Biswal, B.; Schirmer, M.; Rinaldo, A.

    2014-12-01

    Flow patterns observed at-a-station are the dynamical byproduct of a cascade of processes involving different compartments of the hydro-climatic network (e.g., climate, rainfall, soil, vegetation) that regulates the transformation of rainfall into streamflows. In complex branching rivers, flow regimes result from the heterogeneous arrangement around the stream network of multiple hydrologic cascades that simultaneously occur within distinct contributing areas. As such, flow regimes are seen as the integrated output of a complex "network of networks", which can be properly characterized by its degree of temporal variability and spatial heterogeneity. Hydrologic networks that generate river flow regimes are dynamic in nature. In pristine rivers, the time-variance naturally emerges at multiple timescales from climate variability (namely, seasonality and inter-annual fluctuations), implying that the magnitude (and the features) of the water flow between two nodes may be highly variable across different seasons and years. Conversely, the spatial distribution of river flow regimes within pristine rivers involves scale-dependent transport features, as well as regional climatic and soil use gradients, which in small and meso-scale catchments (A guarantee quite uniform flow regimes and high spatial correlations. Human-impacted rivers, instead, constitute hybrid networks where observed spatio-temporal patterns are dominated by anthropogenic shifts, such as landscape alterations and river regulation. In regulated rivers, the magnitude and the features of water flows from node to node may change significantly through time due to damming and withdrawals. However, regulation may impact river regimes in a spatially heterogeneous manner (e.g. in localized river reaches), with a significant decrease of spatial correlations and network connectivity. Provided that the spatial and temporal dynamics of flow regimes in complex rivers may strongly impact important biotic processes

  1. Generating hierarchical scale free-graphs from fractals

    NARCIS (Netherlands)

    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

  2. Denitrification in the Mississippi River network controlled by flow through river bedforms

    Science.gov (United States)

    Gomez-Velez, Jesus D.; Harvey, Judson W.; Cardenas, M. Bayani; Kiel, Brian

    2015-01-01

    Increasing nitrogen concentrations in the world’s major rivers have led to over-fertilization of sensitive downstream waters1, 2, 3, 4. Flow through channel bed and bank sediments acts to remove riverine nitrogen through microbe-mediated denitrification reactions5, 6, 7, 8, 9, 10. However, little is understood about where in the channel network this biophysical process is most efficient, why certain channels are more effective nitrogen reactors, and how management practices can enhance the removal of nitrogen in regions where water circulates through sediment and mixes with groundwater - hyporheic zones8, 11, 12. Here we present numerical simulations of hyporheic flow and denitrification throughout the Mississippi River network using a hydrogeomorphic model. We find that vertical exchange with sediments beneath the riverbed in hyporheic zones, driven by submerged bedforms, has denitrification potential that far exceeds lateral hyporheic exchange with sediments alongside river channels, driven by river bars and meandering banks. We propose that geomorphic differences along river corridors can explain why denitrification efficiency varies between basins in the Mississippi River network. Our findings suggest that promoting the development of permeable bedforms at the streambed - and thus vertical hyporheic exchange - would be more effective at enhancing river denitrification in large river basins than promoting lateral exchange through induced channel meandering. 

  3. Map of fluid flow in fractal porous medium into fractal continuum flow.

    Science.gov (United States)

    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.

  4. Fractal Bread.

    Science.gov (United States)

    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)

  5. Random a-adic groups and random net fractals

    Energy Technology Data Exchange (ETDEWEB)

    Li Yin [Department of Mathematics, Nanjing University, Nanjing 210093 (China)], E-mail: Lyjerry7788@hotmail.com; Su Weiyi [Department of Mathematics, Nanjing University, Nanjing 210093 (China)], E-mail: suqiu@nju.edu.cn

    2008-08-15

    Based on random a-adic groups, this paper investigates the relationship between the existence conditions of a positive flow in a random network and the estimation of the Hausdorff dimension of a proper random net fractal. Subsequently we describe some particular random fractals for which our results can be applied. Finally the Mauldin and Williams theorem is shown to be very important example for a random Cantor set with application in physics as shown in E-infinity theory.

  6. International trade network: fractal properties and globalization puzzle.

    Science.gov (United States)

    Karpiarz, Mariusz; Fronczak, Piotr; Fronczak, Agata

    2014-12-12

    Globalization is one of the central concepts of our age. The common perception of the process is that, due to declining communication and transport costs, distance becomes less and less important. However, the distance coefficient in the gravity model of trade, which grows in time, indicates that the role of distance increases rather than decreases. This, in essence, captures the notion of the globalization puzzle. Here, we show that the fractality of the international trade system (ITS) provides a simple solution for the puzzle. We argue that the distance coefficient corresponds to the fractal dimension of ITS. We provide two independent methods, the box counting method and spatial choice model, which confirm this statement. Our results allow us to conclude that the previous approaches to solving the puzzle misinterpreted the meaning of the distance coefficient in the gravity model of trade.

  7. Modelling and predicting biogeographical patterns in river networks

    Directory of Open Access Journals (Sweden)

    Sabela Lois

    2016-04-01

    Full Text Available Statistical analysis and interpretation of biogeographical phenomena in rivers is now possible using a spatially explicit modelling framework, which has seen significant developments in the past decade. I used this approach to identify a spatial extent (geostatistical range in which the abundance of the parasitic freshwater pearl mussel (Margaritifera margaritifera L. is spatially autocorrelated in river networks. I show that biomass and abundance of host fish are a likely explanation for the autocorrelation in mussel abundance within a 15-km spatial extent. The application of universal kriging with the empirical model enabled precise prediction of mussel abundance within segments of river networks, something that has the potential to inform conservation biogeography. Although I used a variety of modelling approaches in my thesis, I focus here on the details of this relatively new spatial stream network model, thus advancing the study of biogeographical patterns in river networks.

  8. Infrastructural Fractals

    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....

  9. Organization of complex networks

    Science.gov (United States)

    Kitsak, Maksim

    Many large complex systems can be successfully analyzed using the language of graphs and networks. Interactions between the objects in a network are treated as links connecting nodes. This approach to understanding the structure of networks is an important step toward understanding the way corresponding complex systems function. Using the tools of statistical physics, we analyze the structure of networks as they are found in complex systems such as the Internet, the World Wide Web, and numerous industrial and social networks. In the first chapter we apply the concept of self-similarity to the study of transport properties in complex networks. Self-similar or fractal networks, unlike non-fractal networks, exhibit similarity on a range of scales. We find that these fractal networks have transport properties that differ from those of non-fractal networks. In non-fractal networks, transport flows primarily through the hubs. In fractal networks, the self-similar structure requires any transport to also flow through nodes that have only a few connections. We also study, in models and in real networks, the crossover from fractal to non-fractal networks that occurs when a small number of random interactions are added by means of scaling techniques. In the second chapter we use k-core techniques to study dynamic processes in networks. The k-core of a network is the network's largest component that, within itself, exhibits all nodes with at least k connections. We use this k-core analysis to estimate the relative leadership positions of firms in the Life Science (LS) and Information and Communication Technology (ICT) sectors of industry. We study the differences in the k-core structure between the LS and the ICT sectors. We find that the lead segment (highest k-core) of the LS sector, unlike that of the ICT sector, is remarkably stable over time: once a particular firm enters the lead segment, it is likely to remain there for many years. In the third chapter we study how

  10. Naturaleza fractal en redes de cristales de grasas

    Directory of Open Access Journals (Sweden)

    Gómez Herrera, C.

    2004-06-01

    Full Text Available The determination of the mechanical and rheological characteris­tics of several plastic fats requires a detailed understanding of the microstructure of the fat crystal network aggregates. The (or A fractal approach is useful for the characterization of this micros­tructure. This review begins with information on fractality and statistical self-similar structure. Estimations for fractal dimension by means of equations relating the volume fraction of solid fat to shear elastic modulus G' in linear region are described. The influence of interesterification on fractal dimension decrease (from 2, 46 to 2 ,15 for butterfat-canola oil blends is notable . This influence is not significant for fat blends without butterfat. The need for an increase in research concerning the relationship between fractality and rheology in plastic fats is emphasized.La determinación de las características mecánicas y reológicas de ciertas grasas plásticas requiere conocimientos detallados sobre las microestructuras de los agregados que forman la red de cristales grasos. El estudio de la naturaleza fractal de estas microestructuras resulta útil para su carac­terización. Este artículo de información se inicia con descripciones de la dimensión fractal y de la "autosimilitud estadística". A continuación se describe el cálculo de la dimensión fractal mediante ecuaciones que relacionan la fracción en volumen de grasa sólida con el módulo de recuperación (G' dentro de un comportamiento viscoelástico lineal. Se destaca la influencia que la interesterificación ejerce sobre la dimensión fractal de una mezcla de grasa láctea y aceite de canola (que pasa de 2,64 a 2,15. Esta influencia no se presenta en mezclas sin grasa láctea. Se insiste sobre la necesidad de incrementar las investi­gaciones sobre la relación entre reología y estructura fractal en grasas plásticas.

  11. 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

  12. Flat electronic bands in fractal-kagomé network and the effect of perturbation

    Energy Technology Data Exchange (ETDEWEB)

    Nandy, Atanu, E-mail: atanunandy1989@gmail.com; Chakrabarti, Arunava, E-mail: arunava-chakrabarti@yahoo.co.in [Department of Physics, University of Kalyani, Kalyani, West Bengal - 741235 (India)

    2016-05-06

    We demonstrate an analytical prescription of demonstrating the flat band [FB] states in a fractal incorporated kagomé type network that can give rise to a countable infinity of flat non-dispersive eigenstates with a multitude of localization area. The onset of localization can, in principle, be delayed in space by an appropriate choice of energy regime. The length scale, at which the onset of localization for each mode occurs, can be tuned at will following the formalism developed within the framework of real space renormalization group. This scheme leads to an exact determination of energy eigenvalue for which one can have dispersionless flat electronic bands. Furthermore, we have shown the effect ofuniform magnetic field for the same non-translationally invariant network model that has ultimately led to an‘apparent invisibility’ of such staggered localized states and to generate absolutely continuous sub-bands in the energy spectrum and again an interesting re-entrant behavior of those FB states.

  13. Fractal vector optical fields.

    Science.gov (United States)

    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.

  14. Continuum Model for River Networks

    Science.gov (United States)

    Giacometti, Achille; Maritan, Amos; Banavar, Jayanth R.

    1995-07-01

    The effects of erosion, avalanching, and random precipitation are captured in a simple stochastic partial differential equation for modeling the evolution of river networks. Our model leads to a self-organized structured landscape and to abstraction and piracy of the smaller tributaries as the evolution proceeds. An algebraic distribution of the average basin areas and a power law relationship between the drainage basin area and the river length are found.

  15. Geometry of river networks. I. Scaling, fluctuations, and deviations

    International Nuclear Information System (INIS)

    Dodds, Peter Sheridan; Rothman, Daniel H.

    2001-01-01

    This paper is the first in a series of three papers investigating the detailed geometry of river networks. Branching networks are a universal structure employed in the distribution and collection of material. Large-scale river networks mark an important class of two-dimensional branching networks, being not only of intrinsic interest but also a pervasive natural phenomenon. In the description of river network structure, scaling laws are uniformly observed. Reported values of scaling exponents vary, suggesting that no unique set of scaling exponents exists. To improve this current understanding of scaling in river networks and to provide a fuller description of branching network structure, here we report a theoretical and empirical study of fluctuations about and deviations from scaling. We examine data for continent-scale river networks such as the Mississippi and the Amazon and draw inspiration from a simple model of directed, random networks. We center our investigations on the scaling of the length of a subbasin's dominant stream with its area, a characterization of basin shape known as Hack's law. We generalize this relationship to a joint probability density, and provide observations and explanations of deviations from scaling. We show that fluctuations about scaling are substantial, and grow with system size. We find strong deviations from scaling at small scales which can be explained by the existence of a linear network structure. At intermediate scales, we find slow drifts in exponent values, indicating that scaling is only approximately obeyed and that universality remains indeterminate. At large scales, we observe a breakdown in scaling due to decreasing sample space and correlations with overall basin shape. The extent of approximate scaling is significantly restricted by these deviations, and will not be improved by increases in network resolution

  16. 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.)

  17. A new information dimension of complex networks

    Energy Technology Data Exchange (ETDEWEB)

    Wei, Daijun [School of Computer and Information Science, Southwest University, Chongqing 400715 (China); School of Science, Hubei University for Nationalities, Enshi 445000 (China); Wei, Bo [School of Computer and Information Science, Southwest University, Chongqing 400715 (China); Hu, Yong [Institute of Business Intelligence and Knowledge Discovery, Guangdong University of Foreign Studies, Guangzhou 510006 (China); Zhang, Haixin [School of Computer and Information Science, Southwest University, Chongqing 400715 (China); Deng, Yong, E-mail: ydeng@swu.edu.cn [School of Computer and Information Science, Southwest University, Chongqing 400715 (China); School of Engineering, Vanderbilt University, TN 37235 (United States)

    2014-03-01

    Highlights: •The proposed measure is more practical than the classical information dimension. •The difference of information for box in the box-covering algorithm is considered. •Results indicate the measure can capture the fractal property of complex networks. -- Abstract: The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.

  18. A new information dimension of complex networks

    International Nuclear Information System (INIS)

    Wei, Daijun; Wei, Bo; Hu, Yong; Zhang, Haixin; Deng, Yong

    2014-01-01

    Highlights: •The proposed measure is more practical than the classical information dimension. •The difference of information for box in the box-covering algorithm is considered. •Results indicate the measure can capture the fractal property of complex networks. -- Abstract: The fractal and self-similarity properties are revealed in many complex networks. The classical information dimension is an important method to study fractal and self-similarity properties of planar networks. However, it is not practical for real complex networks. In this Letter, a new information dimension of complex networks is proposed. The nodes number in each box is considered by using the box-covering algorithm of complex networks. The proposed method is applied to calculate the fractal dimensions of some real networks. Our results show that the proposed method is efficient when dealing with the fractal dimension problem of complex networks.

  19. The River Network of Montenegro in the GIS Database

    Directory of Open Access Journals (Sweden)

    Goran Barović

    2017-06-01

    Full Text Available The subject of this paper is the systematization and precise identification of the structure of river networks in Montenegro in both planimetric and hypsometric dimensions, using cartometry. This includes the precise determination of the morphometric parameters of river flows, their numerical display, graphical display, and documentation. This allows for a number of analyses, for example, of individual catchments, the mutual relations of individual watercourses within a higher order catchment, and the classification of flows according to river and sea basins and their relationship to the environment. In addition, there is the potential for expanding the database further, with a view to continuous, systematic, scientific and practical follow-up in all or part of the geographic space. The cartometric analysis of the river network in Montenegro has a special scientific, and also a social value. In the geographical structure of all countries, including Montenegro, rivers occupy a central place as individual elements and integral parts of the whole. There is almost no human activity which is not related to river flows, or related phenomena and processes. The river network as part of a geographic space continues to gain in importance, and therefore studying it must connect with the other structural elements within which it functions. These are the basic relief characteristics, climate, and certain hydrographic characteristics. A complete theoretical and methodological approach to this problem forms the basis for a scientific understanding of the significance of the river network of Montenegro.

  20. Nonlinear random resistor diode networks and fractal dimensions of directed percolation clusters.

    Science.gov (United States)

    Stenull, O; Janssen, H K

    2001-07-01

    We study nonlinear random resistor diode networks at the transition from the nonpercolating to the directed percolating phase. The resistor-like bonds and the diode-like bonds under forward bias voltage obey a generalized Ohm's law V approximately I(r). Based on general grounds such as symmetries and relevance we develop a field theoretic model. We focus on the average two-port resistance, which is governed at the transition by the resistance exponent straight phi(r). By employing renormalization group methods we calculate straight phi(r) for arbitrary r to one-loop order. Then we address the fractal dimensions characterizing directed percolation clusters. Via considering distinct values of the nonlinearity r, we determine the dimension of the red bonds, the chemical path, and the backbone to two-loop order.

  1. Computing representative networks for braided rivers

    NARCIS (Netherlands)

    Kleinhans, M.; van Kreveld, M.J.; Ophelders, T.A.E.; Sonke, W.M.; Speckmann, B.; Verbeek, K.A.B.; Aronov, Boris; Katz, Matthew

    Drainage networks on terrains have been studied extensively from an algorithmic perspective. However, in drainage networks water flow cannot bifurcate and hence they do not model braided rivers (multiple channels which split and join, separated by sediment bars). We initiate the algorithmic study of

  2. Computing Representative Networks for Braided Rivers

    NARCIS (Netherlands)

    Kleinhans, Maarten; van Kreveld, M.J.; Ophelders, Tim; Sonke, Willem; Speckmann, Bettina; Verbeek, Kevin

    2017-01-01

    Drainage networks on terrains have been studied extensively from an algorithmic perspective. However, in drainage networks water flow cannot bifurcate and hence they do not model braided rivers (multiple channels which split and join, separated by sediment bars). We initiate the algorithmic study of

  3. Geometry of river networks. III. Characterization of component connectivity

    International Nuclear Information System (INIS)

    Dodds, Peter Sheridan; Rothman, Daniel H.

    2001-01-01

    Essential to understanding the overall structure of river networks is a knowledge of their detailed architecture. Here we explore the presence of randomness in river network structure and the details of its consequences. We first show that an averaged view of network architecture is provided by a proposed self-similarity statement about the scaling of drainage density, a local measure of stream concentration. This scaling of drainage density is shown to imply Tokunaga's law, a description of the scaling of side branch abundance along a given stream, as well as a scaling law for stream lengths. We then consider fluctuations in drainage density and consequently the numbers of side branches. Data are analyzed for the Mississippi River basin and a model of random directed networks. Numbers of side streams are found to follow exponential distributions, as are intertributary distances along streams. Finally, we derive a joint variation of side stream abundance with stream length, affording a full description of fluctuations in network structure. Fluctuations in side stream numbers are shown to be a direct result of fluctuations in stream lengths. This is the last paper in a series of three on the geometry of river networks

  4. 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.

  5. The Impact of The Fractal Paradigm on Geography

    Science.gov (United States)

    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).

  6. Emergence of complex networks from diffusion on fractal lattices. A special case of the Sierpinski gasket and tetrahedron

    International Nuclear Information System (INIS)

    Chełminiak, Przemysław

    2012-01-01

    A new approach to the assemblage of complex networks displaying the scale-free architecture is proposed. While the growth and the preferential attachment of incoming nodes assure an emergence of such networks according to the Barabási–Albert model, it is argued here that the preferential linking condition needs not to be a principal rule. To assert this statement a simple computer model based on random walks on fractal lattices is introduced. It is shown that the model successfully reproduces the degree distributions, the ultra-small-worldness and the high clustering arising from the topology of scale-free networks. -- Highlights: ► A new mechanism of evolution for scale-free complex networks is proposed. ► The preferential attachment rule is not necessary to construct such networks. ► It is shown that they reveal some basic properties of classical scale-free nets.

  7. Optimal river monitoring network using optimal partition analysis: a case study of Hun River, Northeast China.

    Science.gov (United States)

    Wang, Hui; Liu, Chunyue; Rong, Luge; Wang, Xiaoxu; Sun, Lina; Luo, Qing; Wu, Hao

    2018-01-09

    River monitoring networks play an important role in water environmental management and assessment, and it is critical to develop an appropriate method to optimize the monitoring network. In this study, an effective method was proposed based on the attainment rate of National Grade III water quality, optimal partition analysis and Euclidean distance, and Hun River was taken as a method validation case. There were 7 sampling sites in the monitoring network of the Hun River, and 17 monitoring items were analyzed once a month during January 2009 to December 2010. The results showed that the main monitoring items in the surface water of Hun River were ammonia nitrogen (NH 4 + -N), chemical oxygen demand, and biochemical oxygen demand. After optimization, the required number of monitoring sites was reduced from seven to three, and 57% of the cost was saved. In addition, there were no significant differences between non-optimized and optimized monitoring networks, and the optimized monitoring networks could correctly represent the original monitoring network. The duplicate setting degree of monitoring sites decreased after optimization, and the rationality of the monitoring network was improved. Therefore, the optimal method was identified as feasible, efficient, and economic.

  8. Helicalised fractals

    OpenAIRE

    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 ...

  9. 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 ...

  10. Thinking outside the channel: modeling nitrogen cycling in networked river ecosystems

    Science.gov (United States)

    Ashley M. Helton; Geoffrey C. Poole; Judy L. Meyer; Wilfred M. Wollheim; Bruce J. Peterson; Patrick J. Mulholland; Emily S. Bernhardt; Jack A. Stanford; Clay Arango; Linda R. Ashkenas; Lee W. Cooper; Walter K. Dodds; Stanley V. Gregory; Robert O. Hall; Stephen K. Hamilton; Sherri L. Johnson; William H. McDowell; Jody D. Potter; Jennifer L. Tank; Suzanne M. Thomas; H. Maurice Valett; Jackson R. Webster; Lydia Zeglin

    2011-01-01

    Agricultural and urban development alters nitrogen and other biogeochemical cycles in rivers worldwide. Because such biogeochemical processes cannot be measured empirically across whole river networks, simulation models are critical tools for understanding river-network biogeochemistry. However, limitations inherent in current models restrict our ability to simulate...

  11. 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

  12. 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.

  13. Fractals for Geoengineering

    Science.gov (United States)

    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

  14. Fractals everywhere

    CERN Document Server

    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

  15. Self-similarity and scaling theory of complex networks

    Science.gov (United States)

    Song, Chaoming

    Scale-free networks have been studied extensively due to their relevance to many real systems as diverse as the World Wide Web (WWW), the Internet, biological and social networks. We present a novel approach to the analysis of scale-free networks, revealing that their structure is self-similar. This result is achieved by the application of a renormalization procedure which coarse-grains the system into boxes containing nodes within a given "size". Concurrently, we identify a power-law relation between the number of boxes needed to cover the network and the size of the box defining a self-similar exponent, which classifies fractal and non-fractal networks. By using the concept of renormalization as a mechanism for the growth of fractal and non-fractal modular networks, we show that the key principle that gives rise to the fractal architecture of networks is a strong effective "repulsion" between the most connected nodes (hubs) on all length scales, rendering them very dispersed. We show that a robust network comprised of functional modules, such as a cellular network, necessitates a fractal topology, suggestive of a evolutionary drive for their existence. These fundamental properties help to understand the emergence of the scale-free property in complex networks.

  16. Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

    Science.gov (United States)

    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

  17. 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.

  18. THE FRACTAL MARKET HYPOTHESIS

    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.

  19. THE FRACTAL MARKET HYPOTHESIS

    OpenAIRE

    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...

  20. Deterministic chaos and fractal complexity in the dynamics of cardiovascular behavior: perspectives on a new frontier.

    Science.gov (United States)

    Sharma, Vijay

    2009-09-10

    Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.

  1. 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

  2. Mapping the temporary and perennial character of whole river networks

    Science.gov (United States)

    González-Ferreras, A. M.; Barquín, J.

    2017-08-01

    Knowledge of the spatial distribution of temporary and perennial river channels in a whole catchment is important for effective integrated basin management and river biodiversity conservation. However, this information is usually not available or is incomplete. In this study, we present a statistically based methodology to classify river segments from a whole river network (Deva-Cares catchment, Northern Spain) as temporary or perennial. This method is based on an a priori classification of a subset of river segments as temporary or perennial, using field surveys and aerial images, and then running Random Forest models to predict classification membership for the rest of the river network. The independent variables and the river network were derived following a computer-based geospatial simulation of riverine landscapes. The model results show high values of overall accuracy, sensitivity, and specificity for the evaluation of the fitted model to the training and testing data set (≥0.9). The most important independent variables were catchment area, area occupied by broadleaf forest, minimum monthly precipitation in August, and average catchment elevation. The final map shows 7525 temporary river segments (1012.5 km) and 3731 perennial river segments (662.5 km). A subsequent validation of the mapping results using River Habitat Survey data and expert knowledge supported the validity of the proposed maps. We conclude that the proposed methodology is a valid method for mapping the limits of flow permanence that could substantially increase our understanding of the spatial links between terrestrial and aquatic interfaces, improving the research, management, and conservation of river biodiversity and functioning.

  3. Fluid temperatures: Modeling the thermal regime of a river network

    Science.gov (United States)

    Rhonda Mazza; Ashley Steel

    2017-01-01

    Water temperature drives the complex food web of a river network. Aquatic organisms hatch, feed, and reproduce in thermal niches within the tributaries and mainstem that comprise the river network. Changes in water temperature can synchronize or asynchronize the timing of their life stages throughout the year. The water temperature fluctuates over time and place,...

  4. 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

  5. Fractals and foods.

    Science.gov (United States)

    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.

  6. Multifractal analysis of complex networks

    International Nuclear Information System (INIS)

    Wang Dan-Ling; Yu Zu-Guo; Anh V

    2012-01-01

    Complex networks have recently attracted much attention in diverse areas of science and technology. Many networks such as the WWW and biological networks are known to display spatial heterogeneity which can be characterized by their fractal dimensions. Multifractal analysis is a useful way to systematically describe the spatial heterogeneity of both theoretical and experimental fractal patterns. In this paper, we introduce a new box-covering algorithm for multifractal analysis of complex networks. This algorithm is used to calculate the generalized fractal dimensions D q of some theoretical networks, namely scale-free networks, small world networks, and random networks, and one kind of real network, namely protein—protein interaction networks of different species. Our numerical results indicate the existence of multifractality in scale-free networks and protein—protein interaction networks, while the multifractal behavior is not clear-cut for small world networks and random networks. The possible variation of D q due to changes in the parameters of the theoretical network models is also discussed. (general)

  7. Fractal systems of central places based on intermittency of space-filling

    International Nuclear Information System (INIS)

    Chen Yanguang

    2011-01-01

    Highlights: → The idea of intermittency is introduced into central place model. → The revised central place model suggests incomplete space filling. → New central place fractals are presented for urban analysis. → The average nearest distance is proposed to estimate the fractal dimension. → The concept of distance-based space is replaced by that of dimension-based space. - Abstract: The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d = 2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D < d = 2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to explain the real patterns of urban places very well. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.

  8. Fractal dust grains in plasma

    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.

  9. Discovery of cosmic fractals

    CERN Document Server

    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

  10. Fractal dimension of the middle meningeal vessels: variation and evolution in Homo erectus, Neanderthals, and modern humans.

    Science.gov (United States)

    Bruner, Emiliano; Mantini, Simone; Perna, Agostino; Maffei, Carlotta; Manzi, Giorgio

    2005-01-01

    The middle meningeal vascular network leaves its traces on the endocranial surface because of the tight relationship between neurocranial development and brain growth. Analysing the endocast of fossil specimens, it is therefore possible to describe the morphology of these structures, leading inferences on the cerebral physiology and metabolism in extinct human groups. In this paper, general features of the meningeal vascular traces are described for specimens included in the Homo erectus, Homo neanderthalensis, and Homo sapiens hypodigms. The complexity of the arterial network is quantified by its fractal dimension, calculated through the box-counting method. Modern humans show significant differences from the other two taxa because of the anterior vascular dominance and the larger fractal dimension. Neither the fractal dimension nor the anterior development are merely associated with cranial size increase. Considering the differences between Neanderthals and modern humans, these results may be interpreted in terms of phylogeny, cerebral functions, or cranial structural network.

  11. Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions

    CERN Document Server

    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...

  12. Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions

    CERN Document Server

    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 ...

  13. Evaluation of statistical methods for quantifying fractal scaling in water-quality time series with irregular sampling

    Directory of Open Access Journals (Sweden)

    Q. Zhang

    2018-02-01

    Full Text Available River water-quality time series often exhibit fractal scaling, which here refers to autocorrelation that decays as a power law over some range of scales. Fractal scaling presents challenges to the identification of deterministic trends because (1 fractal scaling has the potential to lead to false inference about the statistical significance of trends and (2 the abundance of irregularly spaced data in water-quality monitoring networks complicates efforts to quantify fractal scaling. Traditional methods for estimating fractal scaling – in the form of spectral slope (β or other equivalent scaling parameters (e.g., Hurst exponent – are generally inapplicable to irregularly sampled data. Here we consider two types of estimation approaches for irregularly sampled data and evaluate their performance using synthetic time series. These time series were generated such that (1 they exhibit a wide range of prescribed fractal scaling behaviors, ranging from white noise (β  =  0 to Brown noise (β  =  2 and (2 their sampling gap intervals mimic the sampling irregularity (as quantified by both the skewness and mean of gap-interval lengths in real water-quality data. The results suggest that none of the existing methods fully account for the effects of sampling irregularity on β estimation. First, the results illustrate the danger of using interpolation for gap filling when examining autocorrelation, as the interpolation methods consistently underestimate or overestimate β under a wide range of prescribed β values and gap distributions. Second, the widely used Lomb–Scargle spectral method also consistently underestimates β. A previously published modified form, using only the lowest 5 % of the frequencies for spectral slope estimation, has very poor precision, although the overall bias is small. Third, a recent wavelet-based method, coupled with an aliasing filter, generally has the smallest bias and root-mean-squared error among

  14. The global relationship between chromatin physical topology, fractal structure, and gene expression

    DEFF Research Database (Denmark)

    Almassalha, Luay M; Tiwari, A; Ruhoff, P T

    2017-01-01

    in an empty space, but in a highly complex, interrelated, and dense nanoenvironment that profoundly influences chemical interactions. We explored the relationship between the physical nanoenvironment of chromatin and gene transcription in vitro. We analytically show that changes in the fractal dimension, D...... show that the increased heterogeneity of physical structure of chromatin due to increase in fractal dimension correlates with increased heterogeneity of gene networks. These findings indicate that the higher order folding of chromatin topology may act as a molecular-pathway independent code regulating...

  15. Reengineering through natural structures: the fractal factory

    Science.gov (United States)

    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.

  16. Quantum Fractal Eigenstates

    OpenAIRE

    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.

  17. Predicting the distribution of bed material accumulation using river network sediment budgets

    Science.gov (United States)

    Wilkinson, Scott N.; Prosser, Ian P.; Hughes, Andrew O.

    2006-10-01

    Assessing the spatial distribution of bed material accumulation in river networks is important for determining the impacts of erosion on downstream channel form and habitat and for planning erosion and sediment management. A model that constructs spatially distributed budgets of bed material sediment is developed to predict the locations of accumulation following land use change. For each link in the river network, GIS algorithms are used to predict bed material supply from gullies, river banks, and upstream tributaries and to compare total supply with transport capacity. The model is tested in the 29,000 km2 Murrumbidgee River catchment in southeast Australia. It correctly predicts the presence or absence of accumulation in 71% of river links, which is significantly better performance than previous models, which do not account for spatial variability in sediment supply and transport capacity. Representing transient sediment storage is important for predicting smaller accumulations. Bed material accumulation is predicted in 25% of the river network, indicating its importance as an environmental problem in Australia.

  18. Electromagnetism on anisotropic fractal media

    Science.gov (United States)

    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.

  19. Inkjet-Printed Ultra Wide Band Fractal Antennas

    KAUST Repository

    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.

  20. Statistical and Fractal Processing of Phase Images of Human Biological Fluids

    Directory of Open Access Journals (Sweden)

    MARCHUK, Y. I.

    2010-11-01

    Full Text Available Performed in this work are complex statistical and fractal analyses of phase properties inherent to birefringence networks of liquid crystals consisting of optically-thin layers prepared from human bile. Within the framework of a statistical approach, the authors have investigated values and ranges for changes of statistical moments of the 1-st to 4-th orders that characterize coordinate distributions for phase shifts between orthogonal components of amplitudes inherent to laser radiation transformed by human bile with various pathologies. Using the Gramm-Charlie method, ascertained are correlation criteria for differentiation of phase maps describing pathologically changed liquid-crystal networks. In the framework of the fractal approach, determined are dimensionalities of self-similar coordinate phase distributions as well as features of transformation of logarithmic dependences for power spectra of these distributions for various types of human pathologies.

  1. Random walk through fractal environments

    OpenAIRE

    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 ...

  2. Mapping Koch curves into scale-free small-world networks

    International Nuclear Information System (INIS)

    Zhang Zhongzhi; Gao Shuyang; Zhou Shuigeng; Chen Lichao; Zhang Hongjuan; Guan Jihong

    2010-01-01

    The class of Koch fractals is one of the most interesting families of fractals, and the study of complex networks is a central issue in the scientific community. In this paper, inspired by the famous Koch fractals, we propose a mapping technique converting Koch fractals into a family of deterministic networks called Koch networks. This novel class of networks incorporates some key properties characterizing a majority of real-life networked systems-a power-law distribution with exponent in the range between 2 and 3, a high clustering coefficient, a small diameter and average path length and degree correlations. Besides, we enumerate the exact numbers of spanning trees, spanning forests and connected spanning subgraphs in the networks. All these features are obtained exactly according to the proposed generation algorithm of the networks considered. The network representation approach could be used to investigate the complexity of some real-world systems from the perspective of complex networks.

  3. Fractals in several electrode materials

    Energy Technology Data Exchange (ETDEWEB)

    Zhang, Chunyong, E-mail: zhangchy@njau.edu.cn [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); Wu, Jingyu [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Fu, Degang [Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); State Key Laboratory of Bioelectronics, Southeast University, Nanjing 210096 (China)

    2014-09-15

    Highlights: • Fractal geometry was employed to characterize three important electrode materials. • The surfaces of all studied electrodes were proved to be very rough. • The fractal dimensions of BDD and ACF were scale dependent. • MMO film was more uniform than BDD and ACF in terms of fractal structures. - Abstract: In the present paper, the fractal properties of boron-doped diamond (BDD), mixed metal oxide (MMO) and activated carbon fiber (ACF) electrode have been studied by SEM imaging at different scales. Three materials are self-similar with mean fractal dimension in the range of 2.6–2.8, confirming that they all exhibit very rough surfaces. Specifically, it is found that MMO film is more uniform in terms of fractal structure than BDD and ACF. As a result, the intriguing characteristics make these electrodes as ideal candidates for high-performance decontamination processes.

  4. 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.

  5. Fractal Electrochemical Microsupercapacitors

    KAUST Repository

    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.

  6. Fractal Electrochemical Microsupercapacitors

    KAUST Repository

    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.

  7. Combining Biometric Fractal Pattern and Particle Swarm Optimization-Based Classifier for Fingerprint Recognition

    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.

  8. Improved visibility graph fractality with application for the diagnosis of Autism Spectrum Disorder

    Science.gov (United States)

    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.

  9. 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.

  10. Fractals and chaos

    CERN Document Server

    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...

  11. Cumulative Significance of Hyporheic Exchange and Biogeochemical Processing in River Networks

    Science.gov (United States)

    Harvey, J. W.; Gomez-Velez, J. D.

    2014-12-01

    Biogeochemical reactions in rivers that decrease excessive loads of nutrients, metals, organic compounds, etc. are enhanced by hydrologic interactions with microbially and geochemically active sediments of the hyporheic zone. The significance of reactions in individual hyporheic flow paths has been shown to be controlled by the contact time between river water and sediment and the intrinsic reaction rate in the sediment. However, little is known about how the cumulative effects of hyporheic processing in large river basins. We used the river network model NEXSS (Gomez-Velez and Harvey, submitted) to simulate hyporheic exchange through synthetic river networks based on the best available models of network topology, hydraulic geometry and scaling of geomorphic features, grain size, hydraulic conductivity, and intrinsic reaction rates of nutrients and metals in river sediment. The dimensionless reaction significance factor, RSF (Harvey et al., 2013) was used to quantify the cumulative removal fraction of a reactive solute by hyporheic processing. SF scales reaction progress in a single pass through the hyporheic zone with the proportion of stream discharge passing through the hyporheic zone for a specified distance. Reaction progress is optimal where the intrinsic reaction timescale in sediment matches the residence time of hyporheic flow and is less efficient in longer residence time hyporheic flow as a result of the decreasing proportion of river flow that is processed by longer residence time hyporheic flow paths. In contrast, higher fluxes through short residence time hyporheic flow paths may be inefficient because of the repeated surface-subsurface exchanges required to complete the reaction. Using NEXSS we found that reaction efficiency may be high in both small streams and large rivers, although for different reasons. In small streams reaction progress generally is dominated by faster pathways of vertical exchange beneath submerged bedforms. Slower exchange

  12. Comparison of two fractal interpolation methods

    Science.gov (United States)

    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

  13. Statistical and Fractal Approaches on Long Time-Series to Surface-Water/Groundwater Relationship Assessment: A Central Italy Alluvial Plain Case Study

    Directory of Open Access Journals (Sweden)

    Alessandro Chiaudani

    2017-11-01

    Full Text Available In this research, univariate and bivariate statistical methods were applied to rainfall, river and piezometric level datasets belonging to 24-year time series (1986–2009. These methods, which often are used to understand the effects of precipitation on rivers and karstic springs discharge, have been used to assess piezometric level response to rainfall and river level fluctuations in a porous aquifer. A rain gauge, a river level gauge and three wells, located in Central Italy along the lower Pescara River valley in correspondence of its important alluvial aquifer, provided the data. Statistical analysis has been used within a known hydrogeological framework, which has been refined by mean of a photo-interpretation and a GPS survey. Water–groundwater relationships were identified following the autocorrelation and cross-correlation analyses. Spectral analysis and mono-fractal features of time series were assessed to provide information on multi-year variability, data distributions, their fractal dimension and the distribution return time within the historical time series. The statistical–mathematical results were interpreted through fieldwork that identified distinct groundwater flowpaths within the aquifer and enabled the implementation of a conceptual model, improving the knowledge on water resources management tools.

  14. Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales

    Science.gov (United States)

    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.

  15. Towards a physics on fractals: Differential vector calculus in three-dimensional continuum with fractal metric

    Science.gov (United States)

    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.

  16. 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.

  17. Methane emissions from a human-dominated lowland coastal river network (Shanghai, China)

    Science.gov (United States)

    Wang, D.; Yu, Z.

    2017-12-01

    Evasion of methane (CH4) in streams and rivers play a critical role in global carbon (C) cycle, offsetting the C uptake by terrestrial ecosystems. However, little is known about CH4 emissions from lowland coastal rivers profoundly modified by anthropogenic perturbations. Here, we report results from a long-term, large-scale study of CH4 partial pressures (pCH4) and evasion rates in the Shanghai river network. The spatiotemporal variability of pCH4 was examined along a land-use gradient and the annual CH4 evasion were estimated to assess its role in regional C budget. During the study period, the median pCH4 from 87 surveyed rivers was 241 μatm. CH4 was oversaturated throughout the river network, CH4 hotpots were concentrated in the small urban rivers and highly discharge-dependent. The annual median fCH4 for each site ranged from 3.1 mg C•m-2•d-1 to 296.6 mg C•m-2•d-1. The annual CH4 evasion were 105 Gg CO2-eq•yr-1 and 96 Gg CO2-eq•yr-1 for the entire river network and the mainland rivers, respectively. Given the rapid urbanization in global coastal areas, more research is needed to quantify the role of lowland coastal rivers as a major landscape C source in global C budget.

  18. Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.

    Science.gov (United States)

    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.

  19. 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

  20. Nitrous oxide emission from denitrification in stream and river networks

    Science.gov (United States)

    Beaulieu, J.J.; Tank, J.L.; Hamilton, S.K.; Wollheim, W.M.; Hall, R.O.; Mulholland, P.J.; Peterson, B.J.; Ashkenas, L.R.; Cooper, L.W.; Dahm, Clifford N.; Dodds, W.K.; Grimm, N. B.; Johnson, S.L.; McDowell, W.H.; Poole, G.C.; Maurice, Valett H.; Arango, C.P.; Bernot, M.J.; Burgin, A.J.; Crenshaw, C.L.; Helton, A.M.; Johnson, L.T.; O'Brien, J. M.; Potter, J.D.; Sheibley, R.W.; Sobota, D.J.; Thomas, S.M.

    2011-01-01

    Nitrous oxide (N2O) is a potent greenhouse gas that contributes to climate change and stratospheric ozone destruction. Anthropogenic nitrogen (N) loading to river networks is a potentially important source of N 2O via microbial denitrification that converts N to N2O and dinitrogen (N2). The fraction of denitrified N that escapes as N2O rather than N2 (i.e., the N2O yield) is an important determinant of how much N2O is produced by river networks, but little is known about the N2O yield in flowing waters. Here, we present the results of whole-stream 15N-tracer additions conducted in 72 headwater streams draining multiple land-use types across the United States. We found that stream denitrification produces N2O at rates that increase with stream water nitrate (NO3-) concentrations, but that production, but does not increase the N2O yield. In our study, most streams were sources of N2O to the atmosphere and the highest emission rates were observed in streams draining urban basins. Using a global river network model, we estimate that microbial N transformations (e.g., denitrification and nitrification) convert at least 0.68 Tg??y -1 of anthropogenic N inputs to N2O in river networks, equivalent to 10% of the global anthropogenic N2O emission rate. This estimate of stream and river N2O emissions is three times greater than estimated by the Intergovernmental Panel on Climate Change.

  1. mizuRoute version 1: A river network routing tool for a continental domain water resources applications

    Science.gov (United States)

    Mizukami, Naoki; Clark, Martyn P.; Sampson, Kevin; Nijssen, Bart; Mao, Yixin; McMillan, Hilary; Viger, Roland; Markstrom, Steven; Hay, Lauren E.; Woods, Ross; Arnold, Jeffrey R.; Brekke, Levi D.

    2016-01-01

    This paper describes the first version of a stand-alone runoff routing tool, mizuRoute. The mizuRoute tool post-processes runoff outputs from any distributed hydrologic model or land surface model to produce spatially distributed streamflow at various spatial scales from headwater basins to continental-wide river systems. The tool can utilize both traditional grid-based river network and vector-based river network data. Both types of river network include river segment lines and the associated drainage basin polygons, but the vector-based river network can represent finer-scale river lines than the grid-based network. Streamflow estimates at any desired location in the river network can be easily extracted from the output of mizuRoute. The routing process is simulated as two separate steps. First, hillslope routing is performed with a gamma-distribution-based unit-hydrograph to transport runoff from a hillslope to a catchment outlet. The second step is river channel routing, which is performed with one of two routing scheme options: (1) a kinematic wave tracking (KWT) routing procedure; and (2) an impulse response function – unit-hydrograph (IRF-UH) routing procedure. The mizuRoute tool also includes scripts (python, NetCDF operators) to pre-process spatial river network data. This paper demonstrates mizuRoute's capabilities to produce spatially distributed streamflow simulations based on river networks from the United States Geological Survey (USGS) Geospatial Fabric (GF) data set in which over 54 000 river segments and their contributing areas are mapped across the contiguous United States (CONUS). A brief analysis of model parameter sensitivity is also provided. The mizuRoute tool can assist model-based water resources assessments including studies of the impacts of climate change on streamflow.

  2. Contour fractal analysis of grains

    Science.gov (United States)

    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.

  3. Study on multi-fractal fault diagnosis based on EMD fusion in hydraulic engineering

    International Nuclear Information System (INIS)

    Lu, Shibao; Wang, Jianhua; Xue, Yangang

    2016-01-01

    Highlights: • The measured shafting vibration data signal of the hydroelectric generating set is acquired through EMD. • The vibration signal waveform is identified and purified with EMD to obtain approximation coefficient of various fault signals. • The multi-fractal spectrum provides the distributed geometrical or probabilistic information of point. • EMD provides the real information for the next subsequent analysis and recognition. - Abstract: The vibration signal analysis of the hydraulic turbine unit aims at extracting the characteristic information of the unit vibration. The effective signal processing and information extraction are the key to state monitoring and fault diagnosis of the hydraulic turbine unit. In this paper, the vibration fault diagnosis model is established, which combines EMD, multi-fractal spectrum and modified BP neural network; the vibration signal waveform is identified and purified with EMD to obtain approximation coefficient of various fault signals; the characteristic vector of the vibration fault is acquired with the multi-fractal spectrum algorithm, which is classified and identified as input vector of BP neural network. The signal characteristics are extracted through the waveform, the diagnosis and identification are carried out in combination of the multi-fractal spectrum to provide a new method for fault diagnosis of the hydraulic turbine unit. After the application test, the results show that the method can improve the intelligence and humanization of diagnosis, enhance the man–machine interaction, and produce satisfactory identification result.

  4. Mapping mean annual and monthly river discharges: geostatistical developments for incorporating river network dependencies

    International Nuclear Information System (INIS)

    Sauquet, Eric

    2004-01-01

    Regional hydrology is one topic that shows real improvement in partly due to new statistical development and computation facilities. Nevertheless theoretical difficulties for mapping river regime characteristics or recover these features at un gauged location remain because of the nature of the variable under study: river flows are related to a specific area that is defined by the drainage basin, are spatially organised by the river network with upstream-downstream dependencies. Estimations of hydrological descriptors are required for studying links with ecological processes at different spatial scale, from local site where biological or/and water quality data are available to large scale for sustainable development purposes. This presentation aims at describing a method for runoff pattern along the main river network. The approach dedicated to mean annual runoff is based on geostatistical interpolation procedures to which a constraint of water budget has been added. Expansion in Empirical Orthogonal Function has been considered in combination with kriging for interpolating mean monthly discharges. The methodologies are implemented within a Geographical Information System and illustrated by two study cases (two large basins in France). River flow regime descriptors are estimated for basins of more than 50km 2 . Opportunities of collaboration with a partition of France into hydro-eco regions derived from geology and climate considerations is discussed. (Author)

  5. Encounters with chaos and fractals

    CERN Document Server

    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.

  6. Fractal Structures For Fixed Mems Capacitors

    KAUST Repository

    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.

  7. 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....

  8. Fractal Structures For Fixed Mems Capacitors

    KAUST Repository

    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.

  9. Psicodiagnóstico fractal

    OpenAIRE

    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.

  10. Design of LTCC Based Fractal Antenna

    KAUST Repository

    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.

  11. 2-D Fractal Carpet Antenna Design and Performance

    Science.gov (United States)

    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

  12. 2-D Fractal Wire Antenna Design and Performance

    Science.gov (United States)

    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.

  13. 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...

  14. 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.

  15. Fractal-Based Image Analysis In Radiological Applications

    Science.gov (United States)

    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.

  16. Fractal analysis of sulphidic mineral

    Directory of Open Access Journals (Sweden)

    Miklúšová 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

  17. Efficient RF energy harvesting by using a fractal structured rectenna system

    Science.gov (United States)

    Oh, Sechang; Ramasamy, Mouli; Varadan, Vijay K.

    2014-04-01

    A rectenna system delivers, collects, and converts RF energy into direct current to power the electronic devices or recharge batteries. It consists of an antenna for receiving RF power, an input filter for processing energy and impedance matching, a rectifier, an output filter, and a load resistor. However, the conventional rectenna systems have drawback in terms of power generation, as the single resonant frequency of an antenna can generate only low power compared to multiple resonant frequencies. A multi band rectenna system is an optimal solution to generate more power. This paper proposes the design of a novel rectenna system, which involves developing a multi band rectenna with a fractal structured antenna to facilitate an increase in energy harvesting from various sources like Wi-Fi, TV signals, mobile networks and other ambient sources, eliminating the limitation of a single band technique. The usage of fractal antennas effects certain prominent advantages in terms of size and multiple resonances. Even though, a fractal antenna incorporates multiple resonances, controlling the resonant frequencies is an important aspect to generate power from the various desired RF sources. Hence, this paper also describes the design parameters of the fractal antenna and the methods to control the multi band frequency.

  18. Bilipschitz embedding of homogeneous fractals

    OpenAIRE

    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.

  19. Recognition of fractal graphs

    NARCIS (Netherlands)

    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

  20. 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

  1. Chaos and fractals. Applications to nuclear engineering; Caos y fractales. Aplicaciones en ingenieria nuclear

    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).

  2. 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)

  3. Fractal structures and fractal functions as disease indicators

    Science.gov (United States)

    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.

  4. Fractal geometry mathematical foundations and applications

    CERN Document Server

    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

  5. Fractal electrodynamics via non-integer dimensional space approach

    Science.gov (United States)

    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.

  6. Nitrous oxide emission from denitrification in stream and river networks

    OpenAIRE

    Beaulieu, Jake J.; Tank, Jennifer L.; Hamilton, Stephen K.; Wollheim, Wilfred M.; Hall, Robert O.; Mulholland, Patrick J.; Peterson, Bruce J.; Ashkenas, Linda R.; Cooper, Lee W.; Dahm, Clifford N.; Dodds, Walter K.; Grimm, Nancy B.; Johnson, Sherri L.; McDowell, William H.; Poole, Geoffrey C.

    2010-01-01

    Nitrous oxide (N2O) is a potent greenhouse gas that contributes to climate change and stratospheric ozone destruction. Anthropogenic nitrogen (N) loading to river networks is a potentially important source of N2O via microbial denitrification that converts N to N2O and dinitrogen (N2). The fraction of denitrified N that escapes as N2O rather than N2 (i.e., the N2O yield) is an important determinant of how much N2O is produced by river networks, but little is known about the N2O yield in flowi...

  7. A Double-Minded Fractal

    Science.gov (United States)

    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.)

  8. Conference on Fractals and Related Fields III

    CERN Document Server

    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.

  9. Inkjet-Printed Ultra Wide Band Fractal Antennas

    KAUST Repository

    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

  10. 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.

  11. 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.

  12. Fecal Coliform Removal by River Networks

    Science.gov (United States)

    Huang, T.; Wollheim, W. M.; Stewart, R. J.

    2015-12-01

    Bacterial pathogens are a major cause of water quality impairment in the United States. Freshwater ecosystems provide the ecosystem service of reducing pathogen levels by diluting and removing pathogens as water flows from source areas through the river network. However, the integration of field-scale monitoring data and watershed-scale hydrologic models to estimate pathogen loads and removal in varied aquatic ecosystems is still limited. In this study we applied a biogeochemical river network model (the Framework for Aquatic Modeling in the Earth System or FrAMES) and utilized available field data the Oyster R. watershed, a small (51.7 km2) draining coastal New Hampshire (NH, USA), to quantify pathogen removal at the river network scale, using fecal coliform as an indicator. The Oyster R. Watershed is comprised of various land use types, and has had its water quality monitored for fecal coliform, dissolved oxygen, and turbidity since 2001. Water samples were also collected during storm events to account for storm responses. FrAMES was updated to incorporate the dominant processes controlling fecal coliform concentrations in aquatic ecosystems: spatially distributed terrestrial loading, in-stream removal, dilution, and downstream transport. We applied an empirical loading function to estimate the terrestrial loading of fecal coliform across flow conditions. Data was collected from various land use types across a range of hydrologic conditions. The loading relationship includes total daily precipitation, antecedent 24-hour rainfall, air temperature, and catchment impervious surface percentage. Attenuation is due to bacterial "die-off" and dilution processes. Results show that fecal coliform input loads varied among different land use types. At low flow, fecal coliform concentrations were similar among watersheds. However, at high flow the concentrations were significantly higher in urbanized watersheds than forested watersheds. The mainstem had lower fecal coliform

  13. Fractal behaviour of the seismicity in the Southern Iberian Peninsula

    Directory of Open Access Journals (Sweden)

    X. Lana

    2005-01-01

    Full Text Available The fractal behaviour of the seismicity in the Southern Iberian Peninsula is analysed by considering two different series of data: the distance and the elapsed time between consecutive seismic events recorded by the seismic network of the Andalusian Institute of Geophysics (AIG. The fractal analyses have been repeated by considering four threshold magnitudes of 2.5, 3.0, 3.5 and 4.0. The re-scaled analysis lets to determine if the seismicity shows strong randomness or if it is characterised by time-persistence and the cluster dimension indicates the degree of time and spatial clustering of the seismicity. Another analysis, based on the reconstruction theorem, permits to evaluate the minimum number of nonlinear equations describing the dynamical mechanism of the seismicity, its 'loss of memory', its chaotic character and the instability of a possible predicting algorithm. The results obtained depict some differences depending on distances or elapsed times and the different threshold levels of magnitude also lead to slightly different results. Additionally, only a part of the fractal tools, the re-scaled analysis, have been applied to five seismic crises in the same area.

  14. Fractal dimension of turbulent black holes

    Science.gov (United States)

    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.

  15. 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

  16. Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.

    Science.gov (United States)

    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.

  17. Fractal Structures For Mems Variable Capacitors

    KAUST Repository

    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.

  18. Pre-Service Teachers' Concept Images on Fractal Dimension

    Science.gov (United States)

    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…

  19. Fractal THz metamaterials

    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...

  20. 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)

  1. 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.

  2. Bio-inspired patterned networks (BIPS) for development of wearable/disposable biosensors

    Science.gov (United States)

    McLamore, E. S.; Convertino, M.; Hondred, John; Das, Suprem; Claussen, J. C.; Vanegas, D. C.; Gomes, C.

    2016-05-01

    Here we demonstrate a novel approach for fabricating point of care (POC) wearable electrochemical biosensors based on 3D patterning of bionanocomposite networks. To create Bio-Inspired Patterned network (BIPS) electrodes, we first generate fractal network in silico models that optimize transport of network fluxes according to an energy function. Network patterns are then inkjet printed onto flexible substrate using conductive graphene ink. We then deposit fractal nanometal structures onto the graphene to create a 3D nanocomposite network. Finally, we biofunctionalize the surface with biorecognition agents using covalent bonding. In this paper, BIPS are used to develop high efficiency, low cost biosensors for measuring glucose as a proof of concept. Our results on the fundamental performance of BIPS sensors show that the biomimetic nanostructures significantly enhance biosensor sensitivity, accuracy, response time, limit of detection, and hysteresis compared to conventional POC non fractal electrodes (serpentine, interdigitated, and screen printed electrodes). BIPs, in particular Apollonian patterned BIPS, represent a new generation of POC biosensors based on nanoscale and microscale fractal networks that significantly improve electrical connectivity, leading to enhanced sensor performance.

  3. Fractal Analysis of Rock Joint Profiles

    Science.gov (United States)

    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.

  4. A random walk through fractal dimensions

    CERN Document Server

    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

  5. 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.

  6. 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.

  7. A deterministic width function model

    Directory of Open Access Journals (Sweden)

    C. E. Puente

    2003-01-01

    Full Text Available Use of a deterministic fractal-multifractal (FM geometric method to model width functions of natural river networks, as derived distributions of simple multifractal measures via fractal interpolating functions, is reported. It is first demonstrated that the FM procedure may be used to simulate natural width functions, preserving their most relevant features like their overall shape and texture and their observed power-law scaling on their power spectra. It is then shown, via two natural river networks (Racoon and Brushy creeks in the United States, that the FM approach may also be used to closely approximate existing width functions.

  8. Evaluation of artificial neural network techniques for flow forecasting in the River Yangtze, China

    Directory of Open Access Journals (Sweden)

    C. W. Dawson

    2002-01-01

    Full Text Available While engineers have been quantifying rainfall-runoff processes since the mid-19th century, it is only in the last decade that artificial neural network models have been applied to the same task. This paper evaluates two neural networks in this context: the popular multilayer perceptron (MLP, and the radial basis function network (RBF. Using six-hourly rainfall-runoff data for the River Yangtze at Yichang (upstream of the Three Gorges Dam for the period 1991 to 1993, it is shown that both neural network types can simulate river flows beyond the range of the training set. In addition, an evaluation of alternative RBF transfer functions demonstrates that the popular Gaussian function, often used in RBF networks, is not necessarily the ‘best’ function to use for river flow forecasting. Comparisons are also made between these neural networks and conventional statistical techniques; stepwise multiple linear regression, auto regressive moving average models and a zero order forecasting approach. Keywords: Artificial neural network, multilayer perception, radial basis function, flood forecasting

  9. Band structures in fractal grading porous phononic crystals

    Science.gov (United States)

    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.

  10. 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.

  11. Thermodynamics for Fractal Statistics

    OpenAIRE

    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.

  12. Consistent initial conditions for the Saint-Venant equations in river network modeling

    Directory of Open Access Journals (Sweden)

    C.-W. Yu

    2017-09-01

    Full Text Available Initial conditions for flows and depths (cross-sectional areas throughout a river network are required for any time-marching (unsteady solution of the one-dimensional (1-D hydrodynamic Saint-Venant equations. For a river network modeled with several Strahler orders of tributaries, comprehensive and consistent synoptic data are typically lacking and synthetic starting conditions are needed. Because of underlying nonlinearity, poorly defined or inconsistent initial conditions can lead to convergence problems and long spin-up times in an unsteady solver. Two new approaches are defined and demonstrated herein for computing flows and cross-sectional areas (or depths. These methods can produce an initial condition data set that is consistent with modeled landscape runoff and river geometry boundary conditions at the initial time. These new methods are (1 the pseudo time-marching method (PTM that iterates toward a steady-state initial condition using an unsteady Saint-Venant solver and (2 the steady-solution method (SSM that makes use of graph theory for initial flow rates and solution of a steady-state 1-D momentum equation for the channel cross-sectional areas. The PTM is shown to be adequate for short river reaches but is significantly slower and has occasional non-convergent behavior for large river networks. The SSM approach is shown to provide a rapid solution of consistent initial conditions for both small and large networks, albeit with the requirement that additional code must be written rather than applying an existing unsteady Saint-Venant solver.

  13. Turbulent wakes of fractal objects

    NARCIS (Netherlands)

    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

  14. Fractal geometry and computer graphics

    CERN Document Server

    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...

  15. Delay/Disruption Tolerant Network-Based Message Forwarding for a River Pollution Monitoring Wireless Sensor Network Application.

    Science.gov (United States)

    Velásquez-Villada, Carlos; Donoso, Yezid

    2016-03-25

    Communications from remote areas that may be of interest is still a problem. Many innovative projects applied to remote sites face communications difficulties. The GOLDFISH project was an EU-funded project for river pollution monitoring in developing countries. It had several sensor clusters, with floating WiFi antennas, deployed along a downstream river's course. Sensor clusters sent messages to a Gateway installed on the riverbank. This gateway sent the messages, through a backhaul technology, to an Internet server where data was aggregated over a map. The communication challenge in this scenario was produced by the antennas' movement and network backhaul availability. Since the antennas were floating on the river, communications could be disrupted at any time. Also, 2G/3G availability near the river was not constant. For non-real-time applications, we propose a Delay/Disruption Tolerant Network (DTN)-based solution where all nodes have persistent storage capabilities and DTN protocols to be able to wait minutes or hours to transmit. A mechanical backhaul will periodically visit the river bank where the gateway is installed and it will automatically collect sensor data to be carried to an Internet-covered spot. The proposed forwarding protocol delivers around 98% of the messages for this scenario, performing better than other well-known DTN routing protocols.

  16. Detection and classification of Breast Cancer in Wavelet Sub-bands of Fractal Segmented Cancerous Zones.

    Science.gov (United States)

    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

  17. 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 ...

  18. Fractal characteristic in the wearing of cutting tool

    Science.gov (United States)

    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.

  19. The fractal dimension of cell membrane correlates with its capacitance: A new fractal single-shell model

    Science.gov (United States)

    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

  20. 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.

  1. Assessing Local Communities’ Willingness to Pay for River Network Protection: A Contingent Valuation Study of Shanghai, China

    Directory of Open Access Journals (Sweden)

    Yu Jiang

    2012-10-01

    Full Text Available River networks have experienced serious degradation because of rapid urbanization and population growth in developing countries such as China, and the protection of these networks requires the integration of evaluation with ecology and economics. In this study, a structured questionnaire survey of local residents in Shanghai (China was conducted in urban and suburban areas. The study examined residents’ awareness of the value of the river network, sought their attitude toward the current status, and employed a logistic regression analysis based on the contingent valuation method (CVM to calculate the total benefit and explain the socioeconomic factors influencing the residents’ willingness to pay (WTP. The results suggested that residents in Shanghai had a high degree of recognition of river network value but a low degree of satisfaction with the government’s actions and the current situation. The study also illustrated that the majority of respondents were willing to pay for river network protection. The mean WTP was 226.44 RMB per household per year. The number of years lived in Shanghai, the distance from the home to the nearest river, and the amount of the bid were important factors that influenced the respondents’ WTP. Suggestions for comprehensive management were proposed for the use of policy makers in river network conservation.

  2. Poiseuille equation for steady flow of fractal fluid

    Science.gov (United States)

    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.

  3. On the Mass Fractal Character of Si-Based Structural Networks in Amorphous Polymer Derived Ceramics

    Directory of Open Access Journals (Sweden)

    Sabyasachi Sen

    2015-03-01

    Full Text Available The intermediate-range packing of SiNxC4−x (0 ≤ x ≤ 4 tetrahedra in polysilycarbodiimide and polysilazane-derived amorphous SiCN ceramics is investigated using 29Si spin-lattice relaxation nuclear magnetic resonance (SLR NMR spectroscopy. The SiCN network in the polysilylcarbodiimide-derived ceramic consists predominantly of SiN4 tetrahedra that are characterized by a 3-dimensional spatial distribution signifying compact packing of such units to form amorphous Si3N4 clusters. On the other hand, the SiCN network of the polysilazane-derived ceramic is characterized by mixed bonded SiNxC4−x tetrahedra that are inefficiently packed with a mass fractal dimension of Df ~2.5 that is significantly lower than the embedding Euclidean dimension (D = 3. This result unequivocally confirms the hypothesis that the presence of dissimilar atoms, namely, 4-coordinated C and 3-coordinated N, in the nearest neighbor environment of Si along with some exclusion in connectivity between SiCxN4−x tetrahedra with widely different N:C ratios and the absence of bonding between C and N result in steric hindrance to an efficient packing of these structural units. It is noted that similar inefficiencies in packing are observed in polymer-derived amorphous SiOC ceramics as well as in proteins and binary hard sphere systems.

  4. On the Mass Fractal Character of Si-Based Structural Networks in Amorphous Polymer Derived Ceramics.

    Science.gov (United States)

    Sen, Sabyasachi; Widgeon, Scarlett

    2015-03-17

    The intermediate-range packing of SiN x C 4- x (0 ≤ x ≤ 4) tetrahedra in polysilycarbodiimide and polysilazane-derived amorphous SiCN ceramics is investigated using 29 Si spin-lattice relaxation nuclear magnetic resonance (SLR NMR) spectroscopy. The SiCN network in the polysilylcarbodiimide-derived ceramic consists predominantly of SiN₄ tetrahedra that are characterized by a 3-dimensional spatial distribution signifying compact packing of such units to form amorphous Si₃N₄ clusters. On the other hand, the SiCN network of the polysilazane-derived ceramic is characterized by mixed bonded SiN x C 4- x tetrahedra that are inefficiently packed with a mass fractal dimension of D f ~2.5 that is significantly lower than the embedding Euclidean dimension ( D = 3). This result unequivocally confirms the hypothesis that the presence of dissimilar atoms, namely, 4-coordinated C and 3-coordinated N, in the nearest neighbor environment of Si along with some exclusion in connectivity between SiC x N 4- x tetrahedra with widely different N:C ratios and the absence of bonding between C and N result in steric hindrance to an efficient packing of these structural units. It is noted that similar inefficiencies in packing are observed in polymer-derived amorphous SiOC ceramics as well as in proteins and binary hard sphere systems.

  5. Fractal dimensions the digital art of Eric Hammel

    CERN Document Server

    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

  6. Fractal dimensions the digital art of Eric Hammel

    CERN Document Server

    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

  7. Fractal dimensions the digital art of Eric Hammel

    CERN Document Server

    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

  8. Effect of trap position on the efficiency of trapping in treelike scale-free networks

    International Nuclear Information System (INIS)

    Zhang Zhongzhi; Lin Yuan; Ma Youjun

    2011-01-01

    The conventional wisdom is that the role and impact of nodes on dynamical processes in scale-free networks are not homogenous, because of the presence of highly connected nodes at the tail of their power-law degree distribution. In this paper, we explore the influence of different nodes as traps on the trapping efficiency of the trapping problem taking place on scale-free networks. To this end, we study in detail the trapping problem in two families of deterministically growing scale-free networks with treelike structure: one family is non-fractal, the other is fractal. In the first part of this work, we attack a special case of random walks on the two network families with a perfect trap located at a hub, i.e. node with the highest degree. The second study addresses the case with trap distributed uniformly over all nodes in the networks. For these two cases, we compute analytically the mean trapping time (MTT), a quantitative indicator characterizing the trapping efficiency of the trapping process. We show that in the non-fractal scale-free networks the MTT for both cases follows different scalings with the network order (number of network nodes), implying that trap's position has a significant effect on the trapping efficiency. In contrast, it is presented that for both cases in the fractal scale-free networks, the two leading scalings exhibit the same dependence on the network order, suggesting that the location of trap has no essential impact on the trapping efficiency. We also show that for both cases of the trapping problem, the trapping efficiency is more efficient in the non-fractal scale-free networks than in their fractal counterparts.

  9. 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.

  10. 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.

  11. 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

  12. 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.

  13. Modeling Reservoir-River Networks in Support of Optimizing Seasonal-Scale Reservoir Operations

    Science.gov (United States)

    Villa, D. L.; Lowry, T. S.; Bier, A.; Barco, J.; Sun, A.

    2011-12-01

    HydroSCOPE (Hydropower Seasonal Concurrent Optimization of Power and the Environment) is a seasonal time-scale tool for scenario analysis and optimization of reservoir-river networks. Developed in MATLAB, HydroSCOPE is an object-oriented model that simulates basin-scale dynamics with an objective of optimizing reservoir operations to maximize revenue from power generation, reliability in the water supply, environmental performance, and flood control. HydroSCOPE is part of a larger toolset that is being developed through a Department of Energy multi-laboratory project. This project's goal is to provide conventional hydropower decision makers with better information to execute their day-ahead and seasonal operations and planning activities by integrating water balance and operational dynamics across a wide range of spatial and temporal scales. This presentation details the modeling approach and functionality of HydroSCOPE. HydroSCOPE consists of a river-reservoir network model and an optimization routine. The river-reservoir network model simulates the heat and water balance of river-reservoir networks for time-scales up to one year. The optimization routine software, DAKOTA (Design Analysis Kit for Optimization and Terascale Applications - dakota.sandia.gov), is seamlessly linked to the network model and is used to optimize daily volumetric releases from the reservoirs to best meet a set of user-defined constraints, such as maximizing revenue while minimizing environmental violations. The network model uses 1-D approximations for both the reservoirs and river reaches and is able to account for surface and sediment heat exchange as well as ice dynamics for both models. The reservoir model also accounts for inflow, density, and withdrawal zone mixing, and diffusive heat exchange. Routing for the river reaches is accomplished using a modified Muskingum-Cunge approach that automatically calculates the internal timestep and sub-reach lengths to match the conditions of

  14. Assessment and rationalization of water quality monitoring network: a multivariate statistical approach to the Kabbini River (India).

    Science.gov (United States)

    Mavukkandy, Musthafa Odayooth; Karmakar, Subhankar; Harikumar, P S

    2014-09-01

    The establishment of an efficient surface water quality monitoring (WQM) network is a critical component in the assessment, restoration and protection of river water quality. A periodic evaluation of monitoring network is mandatory to ensure effective data collection and possible redesigning of existing network in a river catchment. In this study, the efficacy and appropriateness of existing water quality monitoring network in the Kabbini River basin of Kerala, India is presented. Significant multivariate statistical techniques like principal component analysis (PCA) and principal factor analysis (PFA) have been employed to evaluate the efficiency of the surface water quality monitoring network with monitoring stations as the evaluated variables for the interpretation of complex data matrix of the river basin. The main objective is to identify significant monitoring stations that must essentially be included in assessing annual and seasonal variations of river water quality. Moreover, the significance of seasonal redesign of the monitoring network was also investigated to capture valuable information on water quality from the network. Results identified few monitoring stations as insignificant in explaining the annual variance of the dataset. Moreover, the seasonal redesign of the monitoring network through a multivariate statistical framework was found to capture valuable information from the system, thus making the network more efficient. Cluster analysis (CA) classified the sampling sites into different groups based on similarity in water quality characteristics. The PCA/PFA identified significant latent factors standing for different pollution sources such as organic pollution, industrial pollution, diffuse pollution and faecal contamination. Thus, the present study illustrates that various multivariate statistical techniques can be effectively employed in sustainable management of water resources. The effectiveness of existing river water quality monitoring

  15. Study of capillary experiments and hydrologic factors under subsurface drip irrigation with fractal theory

    International Nuclear Information System (INIS)

    Zhou, W; Cao, L

    2012-01-01

    Soil spatial variability is one of the primary environmental factors that influences the hydraulic factors and technical indicators of subsurface drip irrigation (SDI), whose emitters are buried in the soil. This paper aimed at evaluating these effects of soil spatial variability on hydrologic factors under SDI. And some SDI emitter and capillary experiments were designed to obtain test data and distribution of pressure and emitter discharge. First, The results of labyrinth non-turbulent mosaic drip emitter test and fractal theory were used to research the fractal and quantitative relationship between single emitter hydrologic factors and soil physical parameters; and then, the capillary experiments and the relationship among hydrologic factors of capillary were used to analyze the fractal and quantitative relationship between hydrologic factors of capillary and soil physical parameters, which explained the inner relationship between spatial variability of soil and hydrologic factors of filed pipeline network under SDI, and provide theory support for the plan, design, management and production of SDI.

  16. 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

  17. Variability of fractal dimension of solar radio flux

    Science.gov (United States)

    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).

  18. 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.

  19. 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

  20. Improving Watershed-Scale Hydrodynamic Models by Incorporating Synthetic 3D River Bathymetry Network

    Science.gov (United States)

    Dey, S.; Saksena, S.; Merwade, V.

    2017-12-01

    Digital Elevation Models (DEMs) have an incomplete representation of river bathymetry, which is critical for simulating river hydrodynamics in flood modeling. Generally, DEMs are augmented with field collected bathymetry data, but such data are available only at individual reaches. Creating a hydrodynamic model covering an entire stream network in the basin requires bathymetry for all streams. This study extends a conceptual bathymetry model, River Channel Morphology Model (RCMM), to estimate the bathymetry for an entire stream network for application in hydrodynamic modeling using a DEM. It is implemented at two large watersheds with different relief and land use characterizations: coastal Guadalupe River basin in Texas with flat terrain and a relatively urban White River basin in Indiana with more relief. After bathymetry incorporation, both watersheds are modeled using HEC-RAS (1D hydraulic model) and Interconnected Pond and Channel Routing (ICPR), a 2-D integrated hydrologic and hydraulic model. A comparison of the streamflow estimated by ICPR at the outlet of the basins indicates that incorporating bathymetry influences streamflow estimates. The inundation maps show that bathymetry has a higher impact on flat terrains of Guadalupe River basin when compared to the White River basin.

  1. THE MORPHOLOGIC PROPERTIES OF MAGNETIC NETWORKS OVER THE SOLAR CYCLE 23

    Energy Technology Data Exchange (ETDEWEB)

    Huang Chong; Yan Yihua; Zhang Yin; Tan Baolin; Li Gang, E-mail: chuang@nao.cas.cn, E-mail: yyh@nao.cas.cn [Key Laboratory of Solar Activity, National Astronomical Observatories of Chinese Academy of Sciences, Beijing 100012 (China)

    2012-11-10

    The morphologic properties of the magnetic networks during Carrington Rotations (CRs) 1955-2091 (from 1999 to 2010) have been analyzed by applying the watershed algorithm to magnetograms observed by the Michelson Doppler Interferometer on board the Solar and Heliospheric Observatory spacecraft. We find that the average area of magnetic cells on the solar surface at lower latitudes (within {+-}50 Degree-Sign ) is smaller than that at higher latitudes (beyond {+-}50 Degree-Sign ). Statistical analysis of these data indicates that the magnetic networks are fractal in nature and the average fractal dimension is D{sub f} = 1.253 {+-} 0.011. We also find that both the fractal dimension and the size of the magnetic networks are anti-correlated with the sunspot area. This is perhaps because a strong magnetic field can suppress spatially modulated oscillation and compress the boundaries of network cells, leading to smoother cell boundaries. The fractal dimension of the cell deviates from that predicted from an isobar of Kolmogorov k {sup -5/3} homogeneous turbulence.

  2. Design of LTCC Based Fractal Antenna

    KAUST Repository

    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

  3. Fractal Structures For Mems Variable Capacitors

    KAUST Repository

    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

  4. A fractal-based image encryption system

    KAUST Repository

    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

  5. 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.

  6. 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.

  7. 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.

  8. 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.

  9. 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.

  10. Monitoring of dry sliding wear using fractal analysis

    NARCIS (Netherlands)

    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

  11. Application of chaos and fractals to computer vision

    CERN Document Server

    Farmer, Michael E

    2014-01-01

    This book provides a thorough investigation of the application of chaos theory and fractal analysis to computer vision. The field of chaos theory has been studied in dynamical physical systems, and has been very successful in providing computational models for very complex problems ranging from weather systems to neural pathway signal propagation. Computer vision researchers have derived motivation for their algorithms from biology and physics for many years as witnessed by the optical flow algorithm, the oscillator model underlying graphical cuts and of course neural networks. These algorithm

  12. 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

  13. 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 ...

  14. 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

  15. International Conference and Workshop on Fractals and Wavelets

    CERN Document Server

    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.

  16. 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

  17. The fourth dimension of life: fractal geometry and allometric scaling of organisms.

    Science.gov (United States)

    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.

  18. 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.

  19. Fractal properties of fractured sandstones of the Guartela Canyon, Parana Basin - Brazil; Propriedades fractais de arenitos fraturados do Canyon Guartela, Formacao Furnas, Bacia do Parana

    Energy Technology Data Exchange (ETDEWEB)

    Souza, Jeferson de; Figueira, Isabela Francoso Rebutini; Santos, Thais Borba [Universidade Federal do Rio Grande do Norte (PPGG/DG/UFRN), Natal (Brazil). Dept. de Geologia. Programa de Pos-Graducao em Geologia; Rostirolla, Sidnei Pires [Universidade Federal do Rio Grande do Norte (DG/UFRN), Natal (Brazil). Dept. de Geologia; Pierin, Andre Ramiro; Spisila, Andre Luis [Universidade Federal do Rio Grande do Norte (DG/UFRN), Natal (Brazil). Dept. de Geologia. Programa de Iniciacao Cientifica

    2008-03-15

    The statistical and geometrical properties of fracture systems were obtained by analyzing remote sense images and outcrop data, in the Region of Guartela Canyon, in the central-eastern of Parana State. The probability distributions of fractures, with their parameters and attributes, were obtained through extensive statistical exploration of data. These parameters were used as input data for generating 3-D stochastic fractures models through the 'discrete fracture network - DFN' method. The modeling is performed by using the code FRED. To study the persistence of statistical parameters in multiple scales were used remote sensing images (SRTM, Landsat TM7 and aerial photos), covering a scale range from outcrops (few meters) to basin scales (hundreds of kilometers). The results indicated the presence of power-law (fractal) statistics for the spatial and size distributions. Fractals distributions were found for all sets studied, in some cases with different fractal exponents. The implications of fractal behavior for the generation of discrete fracture network, and consequently for the hydraulic properties, are briefly discussed. (author)

  20. Chaos and fractals an elementary introduction

    CERN Document Server

    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.

  1. Design of Gravity Survey Network using Fractal Theory to Delineate Hydrocarbon bearing Jabera Structure, Vindhyan Basin, Central India

    Science.gov (United States)

    Dimri, V. P.; Srivastava, R. P.; Vedanti, N.

    2006-12-01

    A gravity survey network was designed using fractal dimension analysis to delineate a domal structure (Jabera dome) reported in southeastern part of the Vindhyan basin, Central India. This area is also regarded as a `high risk-high reward' frontier area for hydrocarbon exploration in previous studies, hence our aim was to delineate shape and lateral extent of the reported domal structure. Based on the synthetic grid, designed using the concept of fractal dimension, gravity data is collected in Jabera-Damoh area of Vindhyan basin. The collected data is random, but the data density is significant, hence the data points are sorted in a way so that they are close to the synthetic grid points of given grid interval. After sorting the data, again the fractal dimension analysis using box counting method has been carried out to avoid the aliasing in the data due to interpolation and also to know the optimum number of data points sufficient for desired quality of Bouguer anomaly maps. Optimization of number of stations takes care of time and cost involved in the survey and the detectibility limit ensures that the data collected is good enough to resolve the target body under study. The fractal dimension analysis gives clue to select these parameters. It showed that it is always preferable to have well distributed station locations instead of clustering the observation points at some geologically known feature because clustering of data points below required station spacing is not going to add much information where as equally distributed observation points add the information. The study area lies in a difficult terrain of Vindhayn basin, hence according to the accessibility, fractal dimension analysis of the real data sorted approximately at regular grid intervals on 2,3, and 4 km has been done and using the concept of optimum gridding interval Bouguer anomaly maps of the region are prepared. The preliminary depth values of the major interfaces in the area were obtained

  2. The carbon commute: Effects of urbanization on dissolved organic carbon quality on a suburban New England river network

    Science.gov (United States)

    Balch, E.; Robison, A.; Wollheim, W. M.

    2017-12-01

    Understanding anthropogenic influence on the sources and fluxes of carbon is necessary for interpreting the carbon cycle and contaminant transport throughout a river system. As urbanization increases worldwide, it is critical to understand how urbanization affects the carbon cycle so that we may be able to predict future changes. Rivers act as both transporters of terrestrial dissolved organic carbon (DOC) to coastal regions, and active transformers of DOC. The character (lability) of the carbon found within a river network is influenced by its sources and fluxes, as determined by the ecological processes, land use, and discharge, which vary throughout the network. We have characterized DOC quantity and quality throughout a suburban New England river network (Ipswich River, MA) in an attempt to provide a detailed picture of how DOC quality varies within a network, and how urbanization influences these changes. We conducted a synoptic survey of 45 sites over two hydrologically similar days in the Ipswich River network in northeast Massachusetts, USA. We collected discrete grab samples for DOC quantity and quality analyses. We also collected dissolved oxygen, conductivity, and nutrients (major anions and cations) as an extension of the synoptic survey. We plan to determine the source of the DOC by using excitation-emission matrices (EEMs), and specific UV absorption (SUVA) at 254 nm. These analyses will provide us with a detailed picture of how DOC quality varies within a network, and how urbanization influences these changes. Using land use data of the Ipswich River watershed, we are able to model the changes in DOC quality throughout the network. In highly urbanized headwaters, through the progressively more forested and wetland dominated main stem reaches, we expect to see the imprint of urbanization throughout the network due to its decreased lability. Studying the imprint of urbanization on DOC throughout a river network helps us complete our understanding of

  3. Electro-chemical manifestation of nanoplasmonics in fractal media

    Science.gov (United States)

    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.

  4. FAST TRACK COMMUNICATION: Weyl law for fat fractals

    Science.gov (United States)

    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.

  5. Effective degrees of freedom of a random walk on a fractal

    Science.gov (United States)

    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.

  6. Self-Similarity of Plasmon Edge Modes on Koch Fractal Antennas.

    Science.gov (United States)

    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.

  7. Power Load Prediction Based on Fractal Theory

    OpenAIRE

    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...

  8. 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.

  9. Use of sEMG in identification of low level muscle activities: features based on ICA and fractal dimension.

    Science.gov (United States)

    Naik, Ganesh R; Kumar, Dinesh K; Arjunan, Sridhar

    2009-01-01

    This paper has experimentally verified and compared features of sEMG (Surface Electromyogram) such as ICA (Independent Component Analysis) and Fractal Dimension (FD) for identification of low level forearm muscle activities. The fractal dimension was used as a feature as reported in the literature. The normalized feature values were used as training and testing vectors for an Artificial neural network (ANN), in order to reduce inter-experimental variations. The identification accuracy using FD of four channels sEMG was 58%, and increased to 96% when the signals are separated to their independent components using ICA.

  10. 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

  11. 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

  12. 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

  13. Fractal Branching in Vascular Trees and Networks by VESsel GENeration Analysis (VESGEN)

    Science.gov (United States)

    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.

  14. Transport properties of electrons in fractal magnetic-barrier structures

    Science.gov (United States)

    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.

  15. Temporal and spatial distribution of isotopes in river water in Central Europe: 50 years experience with the Austrian network of isotopes in rivers.

    Science.gov (United States)

    Rank, Dieter; Wyhlidal, Stefan; Schott, Katharina; Weigand, Silvia; Oblin, Armin

    2018-05-01

    The Austrian network of isotopes in rivers comprises about 15 sampling locations and has been operated since 1976. The Danube isotope time series goes back to 1963. The isotopic composition of river water in Central Europe is mainly governed by the isotopic composition of precipitation in the catchment area; evaporation effects play only a minor role. Short-term and long-term isotope signals in precipitation are thus transmitted through the whole catchment. The influence of climatic changes has become observable in the long-term stable isotope time series of precipitation and surface waters. Environmental 3 H values were around 8 TU in 2015, short-term 3 H pulses up to about 80 TU in the rivers Danube and March were a consequence of releases from nuclear power plants. The complete isotope data series of this network will be included in the Global Network of Isotopes in Rivers database of the International Atomic Energy Agency (IAEA) in 2017. This article comprises a review of 50 years isotope monitoring on rivers and is also intended to provide base information on the (isotope-)hydrological conditions in Central Europe specifically for the end-users of these data, e.g. for modelling hydrological processes. Furthermore, this paper includes the 2006-2015 supplement adding to the Danube isotope set published earlier.

  16. Towards thermomechanics of fractal media

    Science.gov (United States)

    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.

  17. 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

  18. A hydrogeomorphic river network model predicts where and why hyporheic exchange is important in large basins

    Science.gov (United States)

    Gomez-Velez, Jesus D.; Harvey, Judson W.

    2014-09-01

    Hyporheic exchange has been hypothesized to have basin-scale consequences; however, predictions throughout river networks are limited by available geomorphic and hydrogeologic data and by models that can analyze and aggregate hyporheic exchange flows across large spatial scales. We developed a parsimonious but physically based model of hyporheic flow for application in large river basins: Networks with EXchange and Subsurface Storage (NEXSS). We applied NEXSS across a broad range of geomorphic diversity in river reaches and synthetic river networks. NEXSS demonstrates that vertical exchange beneath submerged bed forms rather than lateral exchange through meanders dominates hyporheic fluxes and turnover rates along river corridors. Per kilometer, low-order streams have a biogeochemical potential at least 2 orders of magnitude larger than higher-order streams. However, when biogeochemical potential is examined per average length of each stream order, low- and high-order streams were often found to be comparable. As a result, the hyporheic zone's intrinsic potential for biogeochemical transformations is comparable across different stream orders, but the greater river miles and larger total streambed area of lower order streams result in the highest cumulative impact from low-order streams. Lateral exchange through meander banks may be important in some cases but generally only in large rivers.

  19. A hydrogeomorphic river network model predicts where and why hyporheic exchange is important in large basins

    Science.gov (United States)

    Gomez-Velez, Jesus D.; Harvey, Judson

    2014-01-01

    Hyporheic exchange has been hypothesized to have basin-scale consequences; however, predictions throughout river networks are limited by available geomorphic and hydrogeologic data and by models that can analyze and aggregate hyporheic exchange flows across large spatial scales. We developed a parsimonious but physically based model of hyporheic flow for application in large river basins: Networks with EXchange and Subsurface Storage (NEXSS). We applied NEXSS across a broad range of geomorphic diversity in river reaches and synthetic river networks. NEXSS demonstrates that vertical exchange beneath submerged bed forms rather than lateral exchange through meanders dominates hyporheic fluxes and turnover rates along river corridors. Per kilometer, low-order streams have a biogeochemical potential at least 2 orders of magnitude larger than higher-order streams. However, when biogeochemical potential is examined per average length of each stream order, low- and high-order streams were often found to be comparable. As a result, the hyporheic zone's intrinsic potential for biogeochemical transformations is comparable across different stream orders, but the greater river miles and larger total streambed area of lower order streams result in the highest cumulative impact from low-order streams. Lateral exchange through meander banks may be important in some cases but generally only in large rivers.

  20. Undergraduate Experiment with Fractal Diffraction Gratings

    Science.gov (United States)

    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…

  1. 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.

  2. Variation of the fractal dimension anisotropy of two major Cenozoic normal fault systems over space and time around the Snake River Plain, Idaho and SW Montana

    Science.gov (United States)

    Davarpanah, A.; Babaie, H. A.

    2012-12-01

    The interaction of the thermally induced stress field of the Yellowstone hotspot (YHS) with existing Basin and Range (BR) fault blocks, over the past 17 m.y., has produced a new, spatially and temporally variable system of normal faults around the Snake River Plain (SRP) in Idaho and Wyoming-Montana area. Data about the trace of these new cross faults (CF) and older BR normal faults were acquired from a combination of satellite imageries, DEM, and USGS geological maps and databases at scales of 1:24,000, 1:100,000, 1:250,000, 1:1000, 000, and 1:2,500, 000, and classified based on their azimuth in ArcGIS 10. The box-counting fractal dimension (Db) of the BR fault traces, determined applying the Benoit software, and the anisotropy intensity (ellipticity) of the fractal dimensions, measured with the modified Cantor dust method applying the AMOCADO software, were measured in two large spatial domains (I and II). The Db and anisotropy of the cross faults were studied in five temporal domains (T1-T5) classified based on the geologic age of successive eruptive centers (12 Ma to recent) of the YHS along the eastern SRP. The fractal anisotropy of the CF system in each temporal domain was also spatially determined in the southern part (domain S1), central part (domain S2), and northern part (domain S3) of the SRP. Line (fault trace) density maps for the BR and CF polylines reveal a higher linear density (trace length per unit area) for the BR traces in the spatial domain I, and a higher linear density of the CF traces around the present Yellowstone National Park (S1T5) where most of the seismically active faults are located. Our spatio-temporal analysis reveals that the fractal dimension of the BR system in domain I (Db=1.423) is greater than that in domain II (Db=1.307). It also shows that the anisotropy of the fractal dimension in domain I is less eccentric (axial ratio: 1.242) than that in domain II (1.355), probably reflecting the greater variation in the trend of the BR

  3. The analysis of the influence of fractal structure of stimuli on fractal dynamics in fixational eye movements and EEG signal

    Science.gov (United States)

    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.

  4. Fractal dimension analysis of complexity in Ligeti piano pieces

    Science.gov (United States)

    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.

  5. Delay/Disruption Tolerant Network-Based Message Forwarding for a River Pollution Monitoring Wireless Sensor Network Application

    Directory of Open Access Journals (Sweden)

    Carlos Velásquez-Villada

    2016-03-01

    Full Text Available Communications from remote areas that may be of interest is still a problem. Many innovative projects applied to remote sites face communications difficulties. The GOLDFISH project was an EU-funded project for river pollution monitoring in developing countries. It had several sensor clusters, with floating WiFi antennas, deployed along a downstream river’s course. Sensor clusters sent messages to a Gateway installed on the riverbank. This gateway sent the messages, through a backhaul technology, to an Internet server where data was aggregated over a map. The communication challenge in this scenario was produced by the antennas’ movement and network backhaul availability. Since the antennas were floating on the river, communications could be disrupted at any time. Also, 2G/3G availability near the river was not constant. For non-real-time applications, we propose a Delay/Disruption Tolerant Network (DTN-based solution where all nodes have persistent storage capabilities and DTN protocols to be able to wait minutes or hours to transmit. A mechanical backhaul will periodically visit the river bank where the gateway is installed and it will automatically collect sensor data to be carried to an Internet-covered spot. The proposed forwarding protocol delivers around 98% of the messages for this scenario, performing better than other well-known DTN routing protocols.

  6. 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)

  7. Monitoring Isotopes in Rivers: Creation of the Global Network of Isotopes in Rivers (GNIR). Results of a Coordinated Research Project 2002-2006

    International Nuclear Information System (INIS)

    2012-03-01

    River runoff plays a key role in human development in all societies through the provision of water for agriculture, industry and domestic use. Although the monitoring of water availability and our understanding of the main hydrological processes at the catchment scale are relatively good, many important aspects, especially those related to the interaction of runoff and groundwater, remain poorly understood. Additionally, the impact of human activities - such as the construction of large reservoirs and diversions, and the redirection of rivers to supply drinking water or water for irrigation or hydropower - are highly relevant and, together with the predicted impact of climate change, are likely to heavily impact local water cycles. The effects of such changes include: limited availability of water; changes in flood or drought frequency; changes in water quality, sediment load and groundwater recharge; and biodiversity loss in riparian environments. Additionally, political disputes may result as water resources become affected in terms of availability and/or quality. In most instances, stable isotopes and other water tracers provide a deeper insight into hydrological processes, especially in aspects related to water pathways, interconnections, transport of water and pollutants, and the transit time of water. To explore the contribution of these techniques in more detail, the IAEA has launched a monitoring programme, the Global Network of Isotopes in Rivers (GNIR), aimed at regular analysis of the isotope composition of runoff in large rivers. This isotope monitoring network complements an earlier precipitation network, the Global Network of Isotopes in Precipitation (GNIP). To prepare for GNIR, the IAEA launched a coordinated research project (CRP) called Design Criteria for a Network to Monitor Isotope Compositions of Runoff in Large Rivers. The main aim of the CRP was to develop a scientific rationale and a protocol for the operation of such a network, as well as

  8. Quantitative assessment of early diabetic retinopathy using fractal analysis.

    Science.gov (United States)

    Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y

    2009-01-01

    Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.

  9. Fractals and spectra related to fourier analysis and function spaces

    CERN Document Server

    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 (…) ...

  10. 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.

  11. Heterogeneity of cerebral blood flow: a fractal approach

    International Nuclear Information System (INIS)

    Kuikka, J.T.; Hartikainen, P.

    2000-01-01

    Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and single-photon emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (=coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17±0.05 (mean±SD) for the left hemisphere and 1.15±0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04±0.03 than in healthy controls. (orig.) [de

  12. Using Peano Curves to Construct Laplacians on Fractals

    Science.gov (United States)

    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.

  13. 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.)

  14. 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.)

  15. ABC of multi-fractal spacetimes and fractional sea turtles

    Science.gov (United States)

    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.

  16. Simulation of extreme ground water flow in the fractal crack structure of Earth's crust - impact on catastrophic floods

    Science.gov (United States)

    Bukharov, Dmitriy; Aleksey, Kucherik; Tatyana, Trifonova

    2014-05-01

    Recently, the contribution of groundwater in catastrophic floods is the question under discussion [1,2]. The principal problem in such an approach - to analyze the transportation ways for groundwater in dynamics, and especially - the reasons of exit it on land surface. The crackness, being a characteristic property for all rocks, should be associated with the process in respect of unified dynamic system as a river water basin is, taking into account fundamental phenomena of the 3D-crack network development/modification (up to faults) as a transport groundwater system [3]. 2. In the system of fractal cracks (connected with the main channel for groundwater) the formation of extreme flow is possible, i.e. a devastating case occurs by instantaneous flash mechanism. The development of such a process is related to two factors. First, within the main channel of propagation of the groundwater when a motion is turbulent. In accordance with the theory of Kolmogorov [4], we assume that such a turbulence is isotropic. The fact means that both velocity and pressure fields in the water flow have pulsations related to the non-linear energy transfer between the vortices. This approach allows us to determine both that a maximum possible size of the vortices defined by characteristic dimensions of the underground channel and another - a minimum size of their due to process of dissipation. Energy transfer in the eddies formed near a border, is a complex nonlinear process, which we described by using a modernized Prandtl semi-empirical model [5]. Second, the mechanism of groundwater propagation in the system of cracks extending from the main underground channel is described in the frames of the fractal geometry methods [6]. The approach allows to determine the degree of similarity in the crack system, i.e. the ratio of mean diameters and lengths of cracks/faults for each step of decomposition. The fact results in integrated quantitative characteristics of 3D-network in all, by fractal

  17. 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...

  18. Skin inspired fractal strain sensors using a copper nanowire and graphite microflake hybrid conductive network.

    Science.gov (United States)

    Jason, Naveen N; Wang, Stephen J; Bhanushali, Sushrut; Cheng, Wenlong

    2016-09-22

    This work demonstrates a facile "paint-on" approach to fabricate highly stretchable and highly sensitive strain sensors by combining one-dimensional copper nanowire networks with two-dimensional graphite microflakes. This paint-on approach allows for the fabrication of electronic skin (e-skin) patches which can directly replicate with high fidelity the human skin surface they are on, regardless of the topological complexity. This leads to high accuracy for detecting biometric signals for applications in personalised wearable sensors. The copper nanowires contribute to high stretchability and the graphite flakes offer high sensitivity, and their hybrid coating offers the advantages of both. To understand the topological effects on the sensing performance, we utilized fractal shaped elastomeric substrates and systematically compared their stretchability and sensitivity. We could achieve a high stretchability of up to 600% and a maximum gauge factor of 3000. Our simple yet efficient paint-on approach enabled facile fine-tuning of sensitivity/stretchability simply by adjusting ratios of 1D vs. 2D materials in the hybrid coating, and the topological structural designs. This capability leads to a wide range of biomedical sensors demonstrated here, including pulse sensors, prosthetic hands, and a wireless ankle motion sensor.

  19. 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.

  20. Fractal characterization of the compaction and sintering of ferrites

    NARCIS (Netherlands)

    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

  1. Distinctive fingerprints of erosional regimes in terrestrial channel networks

    Science.gov (United States)

    Grau Galofre, A.; Jellinek, M.

    2017-12-01

    Satellite imagery and digital elevation maps capture the large scale morphology of channel networks attributed to long term erosional processes, such as fluvial, glacial, groundwater sapping and subglacial erosion. Characteristic morphologies associated with each of these styles of erosion have been studied in detail, but there exists a knowledge gap related to their parameterization and quantification. This knowledge gap prevents a rigorous analysis of the dominant processes that shaped a particular landscape, and a comparison across styles of erosion. To address this gap, we use previous morphological descriptions of glaciers, rivers, sapping valleys and tunnel valleys to identify and measure quantitative metrics diagnostic of these distinctive styles of erosion. From digital elevation models, we identify four geometric metrics: The minimum channel width, channel aspect ratio (longest length to channel width at the outlet), presence of undulating longitudinal profiles, and tributary junction angle. We also parameterize channel network complexity in terms of its stream order and fractal dimension. We then perform a statistical classification of the channel networks using a Principal Component Analysis on measurements of these six metrics on a dataset of 70 channelized systems. We show that rivers, glaciers, groundwater seepage and subglacial meltwater erode the landscape in rigorously distinguishable ways. Our methodology can more generally be applied to identify the contributions of different processes involved in carving a channel network. In particular, we are able to identify transitions from fluvial to glaciated landscapes or vice-versa.

  2. A Tutorial Review on Fractal Spacetime and Fractional Calculus

    Science.gov (United States)

    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.

  3. Biological signatures of dynamic river networks from a coupled landscape evolution and neutral community model

    Science.gov (United States)

    Stokes, M.; Perron, J. T.

    2017-12-01

    Freshwater systems host exceptionally species-rich communities whose spatial structure is dictated by the topology of the river networks they inhabit. Over geologic time, river networks are dynamic; drainage basins shrink and grow, and river capture establishes new connections between previously separated regions. It has been hypothesized that these changes in river network structure influence the evolution of life by exchanging and isolating species, perhaps boosting biodiversity in the process. However, no general model exists to predict the evolutionary consequences of landscape change. We couple a neutral community model of freshwater organisms to a landscape evolution model in which the river network undergoes drainage divide migration and repeated river capture. Neutral community models are macro-ecological models that include stochastic speciation and dispersal to produce realistic patterns of biodiversity. We explore the consequences of three modes of speciation - point mutation, time-protracted, and vicariant (geographic) speciation - by tracking patterns of diversity in time and comparing the final result to an equilibrium solution of the neutral model on the final landscape. Under point mutation, a simple model of stochastic and instantaneous speciation, the results are identical to the equilibrium solution and indicate the dominance of the species-area relationship in forming patterns of diversity. The number of species in a basin is proportional to its area, and regional species richness reaches its maximum when drainage area is evenly distributed among sub-basins. Time-protracted speciation is also modeled as a stochastic process, but in order to produce more realistic rates of diversification, speciation is not assumed to be instantaneous. Rather, each new species must persist for a certain amount of time before it is considered to be established. When vicariance (geographic speciation) is included, there is a transient signature of increased

  4. Where and why hyporheic exchange is important: Inferences from a parsimonious, physically-based river network model

    Science.gov (United States)

    Gomez-Velez, J. D.; Harvey, J. W.

    2014-12-01

    Hyporheic exchange has been hypothesized to have basin-scale consequences; however, predictions throughout river networks are limited by available geomorphic and hydrogeologic data as well as models that can analyze and aggregate hyporheic exchange flows across large spatial scales. We developed a parsimonious but physically-based model of hyporheic flow for application in large river basins: Networks with EXchange and Subsurface Storage (NEXSS). At the core of NEXSS is a characterization of the channel geometry, geomorphic features, and related hydraulic drivers based on scaling equations from the literature and readily accessible information such as river discharge, bankfull width, median grain size, sinuosity, channel slope, and regional groundwater gradients. Multi-scale hyporheic flow is computed based on combining simple but powerful analytical and numerical expressions that have been previously published. We applied NEXSS across a broad range of geomorphic diversity in river reaches and synthetic river networks. NEXSS demonstrates that vertical exchange beneath submerged bedforms dominates hyporheic fluxes and turnover rates along the river corridor. Moreover, the hyporheic zone's potential for biogeochemical transformations is comparable across stream orders, but the abundance of lower-order channels results in a considerably higher cumulative effect for low-order streams. Thus, vertical exchange beneath submerged bedforms has more potential for biogeochemical transformations than lateral exchange beneath banks, although lateral exchange through meanders may be important in large rivers. These results have implications for predicting outcomes of river and basin management practices.

  5. COMPLEX NETWORK SIMULATION OF FOREST NETWORK SPATIAL PATTERN IN PEARL RIVER DELTA

    Directory of Open Access Journals (Sweden)

    Y. Zeng

    2017-09-01

    Full Text Available Forest network-construction uses for the method and model with the scale-free features of complex network theory based on random graph theory and dynamic network nodes which show a power-law distribution phenomenon. The model is suitable for ecological disturbance by larger ecological landscape Pearl River Delta consistent recovery. Remote sensing and GIS spatial data are available through the latest forest patches. A standard scale-free network node distribution model calculates the area of forest network’s power-law distribution parameter value size; The recent existing forest polygons which are defined as nodes can compute the network nodes decaying index value of the network’s degree distribution. The parameters of forest network are picked up then make a spatial transition to GIS real world models. Hence the connection is automatically generated by minimizing the ecological corridor by the least cost rule between the near nodes. Based on scale-free network node distribution requirements, select the number compared with less, a huge point of aggregation as a future forest planning network’s main node, and put them with the existing node sequence comparison. By this theory, the forest ecological projects in the past avoid being fragmented, scattered disorderly phenomena. The previous regular forest networks can be reduced the required forest planting costs by this method. For ecological restoration of tropical and subtropical in south China areas, it will provide an effective method for the forest entering city project guidance and demonstration with other ecological networks (water, climate network, etc. for networking a standard and base datum.

  6. Synthetic Minority Oversampling Technique and Fractal Dimension for Identifying Multiple Sclerosis

    Science.gov (United States)

    Zhang, Yu-Dong; Zhang, Yin; Phillips, Preetha; Dong, Zhengchao; Wang, Shuihua

    Multiple sclerosis (MS) is a severe brain disease. Early detection can provide timely treatment. Fractal dimension can provide statistical index of pattern changes with scale at a given brain image. In this study, our team used susceptibility weighted imaging technique to obtain 676 MS slices and 880 healthy slices. We used synthetic minority oversampling technique to process the unbalanced dataset. Then, we used Canny edge detector to extract distinguishing edges. The Minkowski-Bouligand dimension was a fractal dimension estimation method and used to extract features from edges. Single hidden layer neural network was used as the classifier. Finally, we proposed a three-segment representation biogeography-based optimization to train the classifier. Our method achieved a sensitivity of 97.78±1.29%, a specificity of 97.82±1.60% and an accuracy of 97.80±1.40%. The proposed method is superior to seven state-of-the-art methods in terms of sensitivity and accuracy.

  7. 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.

  8. 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

  9. Investigation into How 8th Grade Students Define Fractals

    Science.gov (United States)

    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…

  10. Fractal Image Coding with Digital Watermarks

    Directory of Open Access Journals (Sweden)

    Z. Klenovicova

    2000-12-01

    Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.

  11. 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)

  12. Fractal dimension of cantori

    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

  13. 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.

  14. River networks as ecological corridors: A coherent ecohydrological perspective

    Science.gov (United States)

    Rinaldo, Andrea; Gatto, Marino; Rodriguez-Iturbe, Ignacio

    2018-02-01

    This paper draws together several lines of argument to suggest that an ecohydrological framework, i.e. laboratory, field and theoretical approaches focused on hydrologic controls on biota, has contributed substantially to our understanding of the function of river networks as ecological corridors. Such function proves relevant to: the spatial ecology of species; population dynamics and biological invasions; the spread of waterborne disease. As examples, we describe metacommunity predictions of fish diversity patterns in the Mississippi-Missouri basin, geomorphic controls imposed by the fluvial landscape on elevational gradients of species' richness, the zebra mussel invasion of the same Mississippi-Missouri river system, and the spread of proliferative kidney disease in salmonid fish. We conclude that spatial descriptions of ecological processes in the fluvial landscape, constrained by their specific hydrologic and ecological dynamics and by the ecosystem matrix for interactions, i.e. the directional dispersal embedded in fluvial and host/pathogen mobility networks, have already produced a remarkably broad range of significant results. Notable scientific and practical perspectives are thus open, in the authors' view, to future developments in ecohydrologic research.

  15. Constructing and applying the fractal pied de poule (houndstooth)

    NARCIS (Netherlands)

    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

  16. 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)

  17. Physical heterogeneity and aquatic community function in river networks: A case study from the Kanawha River Basin, USA

    Science.gov (United States)

    Thoms, M. C.; Delong, M. D.; Flotemersch, J. E.; Collins, S. E.

    2017-08-01

    The geomorphological character of a river network provides the template upon which evolution acts to create unique biological communities. Deciphering commonly observed patterns and processes within riverine landscapes resulting from the interplay between physical and biological components is a central tenet for the interdisciplinary field of river science. Relationships between the physical heterogeneity and food web character of functional process zones (FPZs) - large tracts of river with a similar geomorphic character -in the Kanawha River (West Virginia, USA) are examined in this study. Food web character was measured as food chain length (FCL), which reflects ecological community structure and ecosystem function. Our results show that the same basal resources were present throughout the Kanawha River but that their assimilation into the aquatic food web by primary consumers differed between FPZs. Differences in the trophic position of higher consumers (fish) were also recorded between FPZs. Overall, the morphological heterogeneity and heterogeneity of the river bed sediment of FPZs were significantly correlated with FCL. Specifically, FCL increases with greater FPZ physical heterogeneity. The result of this study does not support the current paradigm that ecosystem size is the primary determinant of food web character in river ecosystems.

  18. 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.

  19. Testing statistical self-similarity in the topology of river networks

    Science.gov (United States)

    Troutman, Brent M.; Mantilla, Ricardo; Gupta, Vijay K.

    2010-01-01

    Recent work has demonstrated that the topological properties of real river networks deviate significantly from predictions of Shreve's random model. At the same time the property of mean self-similarity postulated by Tokunaga's model is well supported by data. Recently, a new class of network model called random self-similar networks (RSN) that combines self-similarity and randomness has been introduced to replicate important topological features observed in real river networks. We investigate if the hypothesis of statistical self-similarity in the RSN model is supported by data on a set of 30 basins located across the continental United States that encompass a wide range of hydroclimatic variability. We demonstrate that the generators of the RSN model obey a geometric distribution, and self-similarity holds in a statistical sense in 26 of these 30 basins. The parameters describing the distribution of interior and exterior generators are tested to be statistically different and the difference is shown to produce the well-known Hack's law. The inter-basin variability of RSN parameters is found to be statistically significant. We also test generator dependence on two climatic indices, mean annual precipitation and radiative index of dryness. Some indication of climatic influence on the generators is detected, but this influence is not statistically significant with the sample size available. Finally, two key applications of the RSN model to hydrology and geomorphology are briefly discussed.

  20. 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

  1. Fractal analysis of polar bear hairs

    Directory of Open Access Journals (Sweden)

    Wang Qing-Li

    2015-01-01

    Full Text Available Hairs of a polar bear (Ursus maritimus are of superior properties such as the excellent thermal protection. Why do polar bears can resist such cold environment? The paper concludes that its fractal porosity plays an important role, and its fractal dimensions are very close to the golden mean, 1.618, revealing the possible optimal structure of polar bear hair.

  2. Fractal tomography and its application in 3D vision

    Science.gov (United States)

    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.

  3. Nitrous oxide emission from denitrification in stream and river networks

    Science.gov (United States)

    Nitrous oxide (N2O) is a potent greenhouse gas that contributes to climate change and stratospheric ozone destruction. Anthropogenic nitrogen (N) loading to river networks is a potentially important source of N2O via microbial denitrification which converts N to N2O and dinitrog...

  4. Wetting characteristics of 3-dimensional nanostructured fractal surfaces

    Science.gov (United States)

    Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy

    2017-01-01

    This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.

  5. Teaching about Fractals.

    Science.gov (United States)

    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)

  6. 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.

  7. 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.

  8. Fractal characteristics investigation on electromagnetic scattering from 2-D Weierstrass fractal dielectric rough surface

    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)

  9. USING ARTIFICIAL NEURAL NETWORKS (ANNs FOR SEDIMENT LOAD FORECASTING OF TALKHEROOD RIVER MOUTH

    Directory of Open Access Journals (Sweden)

    Vahid Nourani

    2009-01-01

    Full Text Available Without a doubt the carried sediment load by a river is the most important factor in creating and formation of the related Delta in the river mouth. Therefore, accurate forecasting of the river sediment load can play a significant role for study on the river Delta. However considering the complexity and non-linearity of the phenomenon, the classic experimental or physical-based approaches usually could not handle the problem so well. In this paper, Artificial Neural Network (ANN as a non-linear black box interpolator tool is used for modeling suspended sediment load which discharges to the Talkherood river mouth, located in northern west Iran. For this purpose, observed time series of water discharge at current and previous time steps are used as the model input neurons and the model output neuron will be the forecasted sediment load at the current time step. In this way, various schemes of the ANN approach are examined in order to achieve the best network as well as the best architecture of the model. The obtained results are also compared with the results of two other classic methods (i.e., linear regression and rating curve methods in order to approve the efficiency and ability of the proposed method.

  10. Fractal Interfaces for Stimulating and Recording Neural Implants

    Science.gov (United States)

    Watterson, William James

    From investigating movement in an insect to deciphering cognition in a human brain to treating Parkinson's disease, hearing loss, or even blindness, electronic implants are an essential tool for understanding the brain and treating neural diseases. Currently, the stimulating and recording resolution of these implants remains low. For instance, they can record all the neuron activity associated with movement in an insect, but are quite far from recording, at an individual neuron resolution, the large volumes of brain tissue associated with cognition. Likewise, there is remarkable success in the cochlear implant restoring hearing due to the relatively simple anatomy of the auditory nerves, but are failing to restore vision to the blind due to poor signal fidelity and transmission in stimulating the more complex anatomy of the visual nerves. The critically important research needed to improve the resolution of these implants is to optimize the neuron-electrode interface. This thesis explores geometrical and material modifications to both stimulating and recording electrodes which can improve the neuron-electrode interface. First, we introduce a fractal electrode geometry which radically improves the restored visual acuity achieved by retinal implants and leads to safe, long-term operation of the implant. Next, we demonstrate excellent neuron survival and neurite outgrowth on carbon nanotube electrodes, thus providing a safe biomaterial which forms a strong connection between the electrode and neurons. Additional preliminary evidence suggests carbon nanotubes patterned into a fractal geometry will provide further benefits in improving the electrode-neuron interface. Finally, we propose a novel implant based off field effect transistor technology which utilizes an interconnecting fractal network of semiconducting carbon nanotubes to record from thousands of neurons simutaneously at an individual neuron resolution. Taken together, these improvements have the potential to

  11. Fractal Dimension of Fracture Surface in Rock Material after High Temperature

    Directory of Open Access Journals (Sweden)

    Z. Z. Zhang

    2015-01-01

    Full Text Available Experiments on granite specimens after different high temperature under uniaxial compression were conducted and the fracture surfaces were observed by scanning electron microscope (SEM. The fractal dimensions of the fracture surfaces with increasing temperature were calculated, respectively. The fractal dimension of fracture surface is between 1.44 and 1.63. Its value approximately goes up exponentially with the increase of temperature. There is a quadratic polynomial relationship between the rockburst tendency and fractal dimension of fracture surface; namely, a fractal dimension threshold can be obtained. Below the threshold value, a positive correlativity shows between rockburst tendency and fractal dimension; when the fractal dimension is greater than the threshold value, it shows an inverse correlativity.

  12. Evaluation of peri-implant bone using fractal analysis

    International Nuclear Information System (INIS)

    Jung, Yun Hoa

    2005-01-01

    The purpose of this study was to investigate whether the fractal dimension of successive panoramic radiographs of bone after implant placement is useful in the characterization of structural change in alveolar bone. Twelve subjects with thirty-five implants were retrospectively followed-up from one week to six months after implantation. Thirty-six panoramic radiographs from twelve patients were classified into 1 week. 1-2 months and 3-6 months after implantation and digitized. The windows of bone apical and mesial or distal to the implant were defined as peri apical region of interest (ROI) and inter dental ROI; the fractal dimension of the image was calculated. There was not a statistically significant difference in fractal dimensions during the period up to 6 months after implantation. The fractal dimensions were higher in 13 and 15 mm than 10 and 11.5 mm implant length at inter dental ROIs in 3-6 months after implantation (p<0.01). Longer fixtures showed the higher fractal dimension of bone around implant. This investigation needs further exploration with large numbers of implants for longer follow-up periods.

  13. Fractal analysis for studying the evolution of forests

    International Nuclear Information System (INIS)

    Andronache, Ion C.; Ahammer, Helmut; Jelinek, Herbert F.; Peptenatu, Daniel; Ciobotaru, Ana-M.; Draghici, Cristian C.; Pintilii, Radu D.; Simion, Adrian G.

    2016-01-01

    Highlights: • Legal and illegal deforestation is investigated by fractal analysis. • A new fractal fragmentation index FFI is proposed. • Differences in shapes of forest areas indicate the type of deforestation. • Support of ecological management. - Abstract: Deforestation is an important phenomenon that may create major imbalances in ecosystems. In this study we propose a new mathematical analysis of the forest area dynamic, enabling qualitative as well as quantitative statements and results. Fractal dimensions of the area and the perimeter of a forest were determined using digital images. The difference between fractal dimensions of the area and the perimeter images turned out to be a crucial quantitative parameter. Accordingly, we propose a new fractal fragmentation index, FFI, which is based on this difference and which highlights the degree of compaction or non-compaction of the forest area in order to interpret geographic features. Particularly, this method was applied to forests, where large areas have been legally or illegally deforested. However, these methods can easily be used for other ecological or geographical investigations based on digital images, including deforestation of rainforests.

  14. MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS

    NARCIS (Netherlands)

    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

  15. River Networks As Ecological Corridors for Species, Populations and Pathogens of Water-Borne Disease

    Science.gov (United States)

    Rinaldo, A.

    2014-12-01

    River basins are a natural laboratory for the study of the integration of hydrological, ecological and geomorphological processes. Moving from morphological and functional analyses of dendritic geometries observed in Nature over a wide range of scales, this Lecture addresses essential ecological processes that take place along dendritic structures, hydrology-driven and controlled, like e.g.: population migrations and human settlements, that historically proceeded along river networks to follow water supply routes; riparian ecosystems composition that owing to their positioning along streams play crucial roles in their watersheds and in the loss of biodiversity proceeding at unprecedented rates; waterborne disease spreading, like epidemic cholera that exhibits epidemic patterns that mirror those of watercourses and of human mobility and resurgences upon heavy rainfall. Moreover, the regional incidence of Schistosomiasis, a parasitic waterborne disease, and water resources developments prove tightly related, and proliferative kidney disease in fish thrives differently in pristine and engineered watercourses: can we establish quantitatively the critical linkages with hydrologic drivers and controls? How does connectivity within a river network affect community composition or the spreading mechanisms? Does the river basin act as a template for biodiversity or for species' persistence? Are there hydrologic controls on epidemics of water-borne disease? Here, I shall focus on the noteworthy scientific perspectives provided by spatially explicit eco-hydrological studies centered on river networks viewed as ecological corridors for species, populations and pathogens of waterborne disease. A notable methodological coherence is granted by the mathematical description of river networks as the support for reactive transport. The Lecture overviews a number of topics idiosyncratically related to my own research work but ideally aimed at a coherent body of materials and methods. A

  16. Fractal Geometry and Stochastics V

    CERN Document Server

    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...

  17. CHNTRN: a CHaNnel TRaNsport model for simulating sediment and chemical distribution in a stream/river network

    Energy Technology Data Exchange (ETDEWEB)

    Yeh, G.T.

    1983-09-01

    This report presents the development of a CHaNnel TRaNsport model for simulating sediment and chemical distribution in a stream/river network. A particular feature of the model is its capability to deal with the network system that may consist of any number of joined and branched streams/rivers of comparable size. The model employs a numerical method - an integrated compartment method (ICM) - which greatly facilitates the setup of the matrix equation for the discrete field approximating the corresponding continuous field. Most of the possible boundary conditions that may be anticipated in real-world problems are considered. These include junctions, prescribed concentration, prescribed dispersive flux, and prescribed total flux. The model is applied to two case studies: (1) a single river and (2) a five-segment river in a watershed. Results indicate that the model can realistically simulate the behavior of the sediment and chemical variations in a stream/river network. 11 references, 10 figures, 3 tables.

  18. Elasticity of fractal materials using the continuum model with non-integer dimensional space

    Science.gov (United States)

    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.

  19. Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method

    Science.gov (United States)

    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.

  20. 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...

  1. Fractal characteristics of fracture morphology of steels irradiated with high-energy ions

    Energy Technology Data Exchange (ETDEWEB)

    Xian, Yongqiang; Liu, Juan [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); University of Chinese Academy of Science, Beijing 100049 (China); Zhang, Chonghong, E-mail: c.h.zhang@impcas.ac.cn [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China); Chen, Jiachao [Paul Scherrer Institute, Villigen PSI (Switzerland); Yang, Yitao; Zhang, Liqing; Song, Yin [Institute of Modern Physics, Chinese Academy of Science, Lanzhou 730000 (China)

    2015-06-15

    Highlights: • Fractal dimensions of fracture surfaces of steels before and after irradiation were calculated. • Fractal dimension can effectively describe change of fracture surfaces induced by irradiation. • Correlation of change of fractal dimension with embrittlement of irradiated steels is discussed. - Abstract: A fractal analysis of fracture surfaces of steels (a ferritic/martensitic steel and an oxide-dispersion-strengthened ferritic steel) before and after the irradiation with high-energy ions is presented. Fracture surfaces were acquired from a tensile test and a small-ball punch test (SP). Digital images of the fracture surfaces obtained from scanning electron microscopy (SEM) were used to calculate the fractal dimension (FD) by using the pixel covering method. Boundary of binary image and fractal dimension were determined with a MATLAB program. The results indicate that fractal dimension can be an effective parameter to describe the characteristics of fracture surfaces before and after irradiation. The rougher the fracture surface, the larger the fractal dimension. Correlation of the change of fractal dimension with the embrittlement of the irradiated steels is discussed.

  2. International Conference on Advances of Fractals and Related Topics

    CERN Document Server

    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.   

  3. A new numerical approximation of the fractal ordinary differential equation

    Science.gov (United States)

    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.

  4. Evaluation of 3D Printer Accuracy in Producing Fractal Structure.

    Science.gov (United States)

    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.

  5. MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS

    NARCIS (Netherlands)

    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

  6. MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS

    NARCIS (Netherlands)

    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

  7. 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

  8. The ordered network structure and its prediction for the big floods of the Changjiang River Basins

    Energy Technology Data Exchange (ETDEWEB)

    Men, Ke-Pei; Zhao, Kai; Zhu, Shu-Dan [Nanjing Univ. of Information Science and Technology, Nanjing (China). College of Mathematics and Statistics

    2013-12-15

    According to the latest statistical data of hydrology, a total of 21 floods took place over the Changjiang (Yangtze) River Basins from 1827 to 2012 and showed an obvious commensurable orderliness. In the guidance of the information forecasting theory of Wen-Bo Weng, based on previous research results, combining ordered analysis with complex network technology, we focus on the summary of the ordered network structure of the Changjiang floods, supplement new information, further optimize networks, construct the 2D- and 3D-ordered network structure and make prediction research. Predictions show that the future big deluges will probably occur over the Changjiang River Basin around 2013-2014, 2020-2021, 2030, 2036, 2051, and 2058. (orig.)

  9. The ordered network structure and its prediction for the big floods of the Changjiang River Basins

    International Nuclear Information System (INIS)

    Men, Ke-Pei; Zhao, Kai; Zhu, Shu-Dan

    2013-01-01

    According to the latest statistical data of hydrology, a total of 21 floods took place over the Changjiang (Yangtze) River Basins from 1827 to 2012 and showed an obvious commensurable orderliness. In the guidance of the information forecasting theory of Wen-Bo Weng, based on previous research results, combining ordered analysis with complex network technology, we focus on the summary of the ordered network structure of the Changjiang floods, supplement new information, further optimize networks, construct the 2D- and 3D-ordered network structure and make prediction research. Predictions show that the future big deluges will probably occur over the Changjiang River Basin around 2013-2014, 2020-2021, 2030, 2036, 2051, and 2058. (orig.)

  10. 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.

  11. Where Does the River Run? Lessons from a Semi-Arid River

    Science.gov (United States)

    Meixner, T.; Soto, C. D.; Richter, H.; Uhlman, K.

    2009-12-01

    Spatial data sets to assess the nature of stream groundwater interactions and the resulting power law/fractal structure of travel time distributions are rare. Spatial data sets can be collected using high technology or by use of a large number of field assistants. The labor intensive way is expensive unless the public can be enlisted as citizen scientists to gather large, robust, spatial data sets robustly and cheaply. Such an effort requires public interest and the ability of a few to organize such an effort at a basin if not regional scale. The San Pedro basin offers such an opportunity for citizen science due to the water resource restrictions of the basins semi-arid climate. Since 1999 The Nature Conservancy, in cooperation with the Upper San Pedro Partnership, the public at large and various university and federal science agency participants, has been mapping where the San Pedro River has water present versus where it is dry. This mapping has used an army of volunteers armed with GPS units, clipboards and their eyes to make the determination if a given 10m reach of the river is wet or dry. These wet/dry mapping data now exist for 11 different annual surveys. These data are unique and enable an investigation of the hydrologic connectedness of flowing waters within this system. Analysis of these data reveals several important findings. The total river area that is wet is strongly correlated with stream flow as observed at three USGS gauges. The correlation is strongest however for 90 day and 1 year average flows rather than more local in time observations such as the daily, 7 day or monthly mean flow at the gauges. This result indicates that where the river is flowing depends on long term hydrologic conditions. The length of river reach that is mapped as wet or dry is indicative of the travel distance and thus time that water travels in the surface (wet) and subsurface (dry) of the river system. The reach length that is mapped as wet follows a power law function

  12. Persistent fluctuations in stride intervals under fractal auditory stimulation.

    Science.gov (United States)

    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.

  13. Interaction of Aquifer and River-Canal Network near Well Field.

    Science.gov (United States)

    Ghosh, Narayan C; Mishra, Govinda C; Sandhu, Cornelius S S; Grischek, Thomas; Singh, Vikrant V

    2015-01-01

    The article presents semi-analytical mathematical models to asses (1) enhancements of seepage from a canal and (2) induced flow from a partially penetrating river in an unconfined aquifer consequent to groundwater withdrawal in a well field in the vicinity of the river and canal. The nonlinear exponential relation between seepage from a canal reach and hydraulic head in the aquifer beneath the canal reach is used for quantifying seepage from the canal reach. Hantush's (1967) basic solution for water table rise due to recharge from a rectangular spreading basin in absence of pumping well is used for generating unit pulse response function coefficients for water table rise in the aquifer. Duhamel's convolution theory and method of superposition are applied to obtain water table position due to pumping and recharge from different canal reaches. Hunt's (1999) basic solution for river depletion due to constant pumping from a well in the vicinity of a partially penetrating river is used to generate unit pulse response function coefficients. Applying convolution technique and superposition, treating the recharge from canal reaches as recharge through conceptual injection wells, river depletion consequent to variable pumping and recharge is quantified. The integrated model is applied to a case study in Haridwar (India). The well field consists of 22 pumping wells located in the vicinity of a perennial river and a canal network. The river bank filtrate portion consequent to pumping is quantified. © 2014, National GroundWater Association.

  14. Potential of commercial microwave link network derived rainfall for river runoff simulations

    Science.gov (United States)

    Smiatek, Gerhard; Keis, Felix; Chwala, Christian; Fersch, Benjamin; Kunstmann, Harald

    2017-03-01

    Commercial microwave link networks allow for the quantification of path integrated precipitation because the attenuation by hydrometeors correlates with rainfall between transmitter and receiver stations. The networks, operated and maintained by cellphone companies, thereby provide completely new and country wide precipitation measurements. As the density of traditional precipitation station networks worldwide is significantly decreasing, microwave link derived precipitation estimates receive increasing attention not only by hydrologists but also by meteorological and hydrological services. We investigate the potential of microwave derived precipitation estimates for streamflow prediction and water balance analyses, exemplarily shown for an orographically complex region in the German Alps (River Ammer). We investigate the additional value of link derived rainfall estimations combined with station observations compared to station and weather radar derived values. Our river runoff simulation system employs a distributed hydrological model at 100 × 100 m grid resolution. We analyze the potential of microwave link derived precipitation estimates for two episodes of 30 days with typically moderate river flow and an episode of extreme flooding. The simulation results indicate the potential of this novel precipitation monitoring method: a significant improvement in hydrograph reproduction has been achieved in the extreme flooding period that was characterized by a large number of local strong precipitation events. The present rainfall monitoring gauges alone were not able to correctly capture these events.

  15. Interplay between spatially explicit sediment sourcing, hierarchical river-network structure, and in-channel bed material sediment transport and storage dynamics

    Science.gov (United States)

    Czuba, Jonathan A.; Foufoula-Georgiou, Efi; Gran, Karen B.; Belmont, Patrick; Wilcock, Peter R.

    2017-05-01

    Understanding how sediment moves along source to sink pathways through watersheds—from hillslopes to channels and in and out of floodplains—is a fundamental problem in geomorphology. We contribute to advancing this understanding by modeling the transport and in-channel storage dynamics of bed material sediment on a river network over a 600 year time period. Specifically, we present spatiotemporal changes in bed sediment thickness along an entire river network to elucidate how river networks organize and process sediment supply. We apply our model to sand transport in the agricultural Greater Blue Earth River Basin in Minnesota. By casting the arrival of sediment to links of the network as a Poisson process, we derive analytically (under supply-limited conditions) the time-averaged probability distribution function of bed sediment thickness for each link of the river network for any spatial distribution of inputs. Under transport-limited conditions, the analytical assumptions of the Poisson arrival process are violated (due to in-channel storage dynamics) where we find large fluctuations and periodicity in the time series of bed sediment thickness. The time series of bed sediment thickness is the result of dynamics on a network in propagating, altering, and amalgamating sediment inputs in sometimes unexpected ways. One key insight gleaned from the model is that there can be a small fraction of reaches with relatively low-transport capacity within a nonequilibrium river network acting as "bottlenecks" that control sediment to downstream reaches, whereby fluctuations in bed elevation can dissociate from signals in sediment supply.

  16. Applications of fractals in ecology.

    Science.gov (United States)

    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.

  17. Using Geoscience and Geostatistics to Optimize Groundwater Monitoring Networks at the Savannah River Site

    International Nuclear Information System (INIS)

    Tuckfield, R.C.

    2001-01-01

    A team of scientists, engineers, and statisticians was assembled to review the operation efficiency of groundwater monitoring networks at US Department of Energy Savannah River Site (SRS). Subsequent to a feasibility study, this team selected and conducted an analysis of the A/M area groundwater monitoring well network. The purpose was to optimize the number of groundwater wells requisite for monitoring the plumes of the principal constituent of concern, viz., trichloroethylene (TCE). The project gathered technical expertise from the Savannah River Technology Center (SRTC), the Environmental Restoration Division (ERD), and the Environmental Protection Department (EPD) of SRS

  18. Assessment of textural differentiations in forest resources in Romania using fractal analysis

    DEFF Research Database (Denmark)

    Andronache, Ion; Fensholt, Rasmus; Ahammer, Helmut

    2017-01-01

    regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis.We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas......, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested...... and compact organization) in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters). Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby...

  19. 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.

  20. 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.

  1. An approach to study of methods for urban analysis and urban fabric renewal in observation of a city as a multiple fractal structure

    Directory of Open Access Journals (Sweden)

    Bogdanov Ana

    2007-01-01

    Full Text Available Urban forms and processes can be observed as fractal structures since in their seemingly chaotic development and complexity it can be noticed an internal order and regularity, which could be quantified and described by the methods of fractal analysis. With determination of fractal dimension it is possible to quantify the level of irregularity, the complexity and hierarchy of the urban structures, as well as the level of urban transformations in various time intersections. The fractal geometry method has been used in analyses of spatial distribution of population, networks and utilities because it corresponds more than deterministic methods to the nature of urban settlements as open, non-linear and dynamic systems. In that sense, fractal geometry becomes the means to grasp a complex morphological urban structure of urban settlements in general, the interrelationships between the inner spatial elements, and to predict future development possibilities. Moreover on the basis of urban pattern analysis by means of fractal geometry, it is possible to evaluate the growth and development process and to perform a comparative analysis of development in spatially and temporarily different settlement settings. Having in view that complex urban fabric presumes tight connections and diversity, which is in contrast to sprawl and monotony which increasingly characterize urban growth and development, this paper is a contribution to research of potential for modern urban settlements to regain the spirit of spontaneity and human dimension through application of development models that are fractal geometry based.

  2. Fractal studies on the positron annihilation in metals

    International Nuclear Information System (INIS)

    Lung, C.W.

    1994-06-01

    Traditionally, the Euclidean lines, circles and spheres have served as the basis of the intuitive understanding of the geometry of nature. Recently, the concept of fractals has caught the imagination of scientists in many fields. This paper is to continue our previous work on position annihilation near fractal surfaces to demonstrate that the concept of fractals provides a powerful tool for understanding the structure and properties of defects and rough surfaces in relation to positron annihilation studies. Some problems on Berry geometrical phase have also been discussed. (author). 15 refs, fig., 1 tab

  3. Comparison of the Gen Expression Programming, Nonlinear Time Series and Artificial Neural Network in Estimating the River Daily Flow (Case Study: The Karun River

    Directory of Open Access Journals (Sweden)

    R. Zamani

    2015-06-01

    Full Text Available Today, the daily flow forecasting of rivers is an important issue in hydrology and water resources and thus can be used the results of daily river flow modeling in water resources management, droughts and floods monitoring. In this study, due to the importance of this issue, using nonlinear time series models and artificial intelligence (Artificial Neural Network and Gen Expression Programming, the daily flow modeling has been at the time interval (1981-2012 in the Armand hydrometric station on the Karun River. Armand station upstream basin is one of the most basins in the North Karun basin and includes four sub basins (Vanak, Middle Karun, Beheshtabad and Kohrang.The results of this study shown that artificial intelligence models have superior than nonlinear time series in flow daily simulation in the Karun River. As well as, modeling and comparison of artificial intelligence models showed that the Gen Expression Programming have evaluation criteria better than artificial neural network.

  4. 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

  5. Fine-resolution Modeling of Urban-Energy Systems' Water Footprint in River Networks

    Science.gov (United States)

    McManamay, R.; Surendran Nair, S.; Morton, A.; DeRolph, C.; Stewart, R.

    2015-12-01

    Characterizing the interplay between urbanization, energy production, and water resources is essential for ensuring sustainable population growth. In order to balance limited water supplies, competing users must account for their realized and virtual water footprint, i.e. the total direct and indirect amount of water used, respectively. Unfortunately, publicly reported US water use estimates are spatially coarse, temporally static, and completely ignore returns of water to rivers after use. These estimates are insufficient to account for the high spatial and temporal heterogeneity of water budgets in urbanizing systems. Likewise, urbanizing areas are supported by competing sources of energy production, which also have heterogeneous water footprints. Hence, a fundamental challenge of planning for sustainable urban growth and decision-making across disparate policy sectors lies in characterizing inter-dependencies among urban systems, energy producers, and water resources. A modeling framework is presented that provides a novel approach to integrate urban-energy infrastructure into a spatial accounting network that accurately measures water footprints as changes in the quantity and quality of river flows. River networks (RNs), i.e. networks of branching tributaries nested within larger rivers, provide a spatial structure to measure water budgets by modeling hydrology and accounting for use and returns from urbanizing areas and energy producers. We quantify urban-energy water footprints for Atlanta, GA and Knoxville, TN (USA) based on changes in hydrology in RNs. Although water intakes providing supply to metropolitan areas were proximate to metropolitan areas, power plants contributing to energy demand in Knoxville and Atlanta, occurred 30 and 90km outside the metropolitan boundary, respectively. Direct water footprints from urban landcover primarily comprised smaller streams whereas indirect footprints from water supply reservoirs and energy producers included

  6. An efficient fractal image coding algorithm using unified feature and DCT

    International Nuclear Information System (INIS)

    Zhou Yiming; Zhang Chao; Zhang Zengke

    2009-01-01

    Fractal image compression is a promising technique to improve the efficiency of image storage and image transmission with high compression ratio, however, the huge time consumption for the fractal image coding is a great obstacle to the practical applications. In order to improve the fractal image coding, efficient fractal image coding algorithms using a special unified feature and a DCT coder are proposed in this paper. Firstly, based on a necessary condition to the best matching search rule during fractal image coding, the fast algorithm using a special unified feature (UFC) is addressed, and it can reduce the search space obviously and exclude most inappropriate matching subblocks before the best matching search. Secondly, on the basis of UFC algorithm, in order to improve the quality of the reconstructed image, a DCT coder is combined to construct a hybrid fractal image algorithm (DUFC). Experimental results show that the proposed algorithms can obtain good quality of the reconstructed images and need much less time than the baseline fractal coding algorithm.

  7. 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.

  8. Fractal dimension evolution and spatial replacement dynamics of urban growth

    International Nuclear Information System (INIS)

    Chen Yanguang

    2012-01-01

    Highlights: ► The fractal dimension growth can be modeled by Boltzmann’s equation. ► Boltzmann’s model suggests urban spatial replacement dynamics. ► If the rate of urban growth is too high, periodic oscillations or chaos will arise. ► Chaos is associated with fractals by the fractal dimension evolution model. ► The fractal dimension of urban form implies the space-filling ratio of a city. - Abstract: This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to interpret the fractal dimension of urban form. The fractal dimension evolution of urban growth can be empirically modeled with Boltzmann’s equation. For the normalized data, Boltzmann’s equation is just equivalent to the logistic function. The logistic equation can be transformed into the well-known 1-dimensional logistic map, which is based on a 2-dimensional map suggesting spatial replacement dynamics of city development. The 2-dimensional recurrence relations can be employed to generate the nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is thus made in this article that, for the fractal dimension growth following the logistic curve, the normalized dimension value is the ratio of space filling. If the rate of spatial replacement (urban growth) is too high, the periodic oscillations and chaos will arise. The spatial replacement dynamics can be extended to general replacement dynamics, and bifurcation and chaos mirror a process of complex replacement.

  9. Vortex-ring-fractal Structure of Atom and Molecule

    International Nuclear Information System (INIS)

    Osmera, Pavel

    2010-01-01

    This chapter is an attempt to attain a new and profound model of the nature's structure using a vortex-ring-fractal theory (VRFT). Scientists have been trying to explain some phenomena in Nature that have not been explained so far. The aim of this paper is the vortex-ring-fractal modeling of elements in the Mendeleev's periodic table, which is not in contradiction to the known laws of nature. We would like to find some acceptable structure model of the hydrogen as a vortex-fractal-coil structure of the proton and a vortex-fractal-ring structure of the electron. It is known that planetary model of the hydrogen atom is not right, the classical quantum model is too abstract. Our imagination is that the hydrogen is a levitation system of the proton and the electron. Structures of helium, oxygen, and carbon atoms and a hydrogen molecule are presented too.

  10. Fractal analysis of bone architecture at distal radius

    International Nuclear Information System (INIS)

    Tomomitsu, Tatsushi; Mimura, Hiroaki; Murase, Kenya; Sone, Teruki; Fukunaga, Masao

    2005-01-01

    Bone strength depends on bone quality (architecture, turnover, damage accumulation, and mineralization) as well as bone mass. In this study, human bone architecture was analyzed using fractal image analysis, and the clinical relevance of this method was evaluated. The subjects were 12 healthy female controls and 16 female patients suspected of having osteoporosis (age range, 22-70 years; mean age, 49.1 years). High-resolution CT images of the distal radius were acquired and analyzed using a peripheral quantitative computed tomography (pQCT) system. On the same day, bone mineral densities of the lumbar spine (L-BMD), proximal femur (F-BMD), and distal radius (R-BMD) were measured by dual-energy X-ray absorptiometry (DXA). We examined the correlation between the fractal dimension and six bone mass indices. Subjects diagnosed with osteopenia or osteoporosis were divided into two groups (with and without vertebral fracture), and we compared measured values between these two groups. The fractal dimension correlated most closely with L-BMD (r=0.744). The coefficient of correlation between the fractal dimension and L-BMD was very similar to the coefficient of correlation between L-BMD and F-BMD (r=0.783) and the coefficient of correlation between L-BMD and R-BMD (r=0.742). The fractal dimension was the only measured value that differed significantly between both the osteopenic and the osteoporotic subjects with and without vertebral fracture. The present results suggest that the fractal dimension of the distal radius can be reliably used as a bone strength index that reflects bone architecture as well as bone mass. (author)

  11. Graph Theory-Based Technique for Isolating Corrupted Boundary Conditions in Continental-Scale River Network Hydrodynamic Simulation

    Science.gov (United States)

    Yu, C. W.; Hodges, B. R.; Liu, F.

    2017-12-01

    Development of continental-scale river network models creates challenges where the massive amount of boundary condition data encounters the sensitivity of a dynamic nu- merical model. The topographic data sets used to define the river channel characteristics may include either corrupt data or complex configurations that cause instabilities in a numerical solution of the Saint-Venant equations. For local-scale river models (e.g. HEC- RAS), modelers typically rely on past experience to make ad hoc boundary condition adjustments that ensure a stable solution - the proof of the adjustment is merely the sta- bility of the solution. To date, there do not exist any formal methodologies or automated procedures for a priori detecting/fixing boundary conditions that cause instabilities in a dynamic model. Formal methodologies for data screening and adjustment are a critical need for simulations with a large number of river reaches that draw their boundary con- dition data from a wide variety of sources. At the continental scale, we simply cannot assume that we will have access to river-channel cross-section data that has been ade- quately analyzed and processed. Herein, we argue that problematic boundary condition data for unsteady dynamic modeling can be identified through numerical modeling with the steady-state Saint-Venant equations. The fragility of numerical stability increases with the complexity of branching in river network system and instabilities (even in an unsteady solution) are typically triggered by the nonlinear advection term in Saint-Venant equations. It follows that the behavior of the simpler steady-state equations (which retain the nonlin- ear term) can be used to screen the boundary condition data for problematic regions. In this research, we propose a graph-theory based method to isolate the location of corrupted boundary condition data in a continental-scale river network and demonstrate its utility with a network of O(10^4) elements. Acknowledgement

  12. Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects

    Science.gov (United States)

    Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.

    2013-04-01

    This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to

  13. A transfer matrix method for the analysis of fractal quantum potentials

    International Nuclear Information System (INIS)

    Monsoriu, Juan A; Villatoro, Francisco R; Marin, Maria J; UrchueguIa, Javier F; Cordoba, Pedro Fernandez de

    2005-01-01

    The scattering properties of quantum particles on a sequence of potentials converging towards a fractal one are obtained by means of the transfer matrix method. The reflection coefficients for both the fractal potential and finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal potential has a self-similar structure associated with the fractal distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function

  14. Speculations on self-avoiding surfaces in fractals. A mean field treatment

    International Nuclear Information System (INIS)

    Pandey, R.B.; Kumar, N.; Stauffer, D.

    1984-08-01

    We estimate the exponents characterizing the self-avoiding surfaces using an approximation in the framework of a Flory-type theory. We find for planar self-avoiding surfaces embedded randomly in a fractal of dimensionality D':theta=3/(4+D'); for random surfaces of fractal dimension D embedded in a Euclidian space of dimensionality d:theta=3/(2D+d-2); and for fractal surfaces embedded in a structure of fractal dimensionality D':theta=3/(2D+D'-2). (author)

  15. A transfer matrix method for the analysis of fractal quantum potentials

    Energy Technology Data Exchange (ETDEWEB)

    Monsoriu, Juan A [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Villatoro, Francisco R [Departamento de Lenguajes y Ciencias de la Computacion, Universidad de Malaga, E-29071 Malaga (Spain); Marin, Maria J [Departamento de Termodinamica, Universitat de Valencia, E-46100 Burjassot (Spain); UrchueguIa, Javier F [Departamento de Fisica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain); Cordoba, Pedro Fernandez de [Departamento de Matematica Aplicada, Universidad Politecnica de Valencia, E-46022 Valencia (Spain)

    2005-07-01

    The scattering properties of quantum particles on a sequence of potentials converging towards a fractal one are obtained by means of the transfer matrix method. The reflection coefficients for both the fractal potential and finite periodic potential are calculated and compared. It is shown that the reflection coefficient for the fractal potential has a self-similar structure associated with the fractal distribution of the potential whose degree of self-similarity has been quantified by means of the correlation function.

  16. 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...

  17. Ulam method and fractal Weyl law for Perron-Frobenius operators

    Science.gov (United States)

    Ermann, L.; Shepelyansky, D. L.

    2010-06-01

    We use the Ulam method to study spectral properties of the Perron-Frobenius operators of dynamical maps in a chaotic regime. For maps with absorption we show numerically that the spectrum is characterized by the fractal Weyl law recently established for nonunitary operators describing poles of quantum chaotic scattering with the Weyl exponent ν = d-1, where d is the fractal dimension of corresponding strange set of trajectories nonescaping in future times. In contrast, for dissipative maps we numerically find the Weyl exponent ν = d/2 where d is the fractal dimension of strange attractor. The Weyl exponent can be also expressed via the relation ν = d0/2 where d0 is the fractal dimension of the invariant sets. We also discuss the properties of eigenvalues and eigenvectors of such operators characterized by the fractal Weyl law.

  18. 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.

  19. 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)

  20. Fractal universe and quantum gravity.

    Science.gov (United States)

    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.

  1. 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.

  2. Synergetics and fractals in tribology

    CERN Document Server

    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.

  3. 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

  4. A fractal-based image encryption system

    KAUST Repository

    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.

  5. 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.

  6. a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution

    Science.gov (United States)

    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.

  7. An investigation of fractal characteristics of mesoporous carbon electrodes with various pore structures

    International Nuclear Information System (INIS)

    Pyun, Su-Il; Rhee, Chang-Kyu

    2004-01-01

    Fractal characteristics of mesoporous carbon electrodes were investigated with various pore structures using the N 2 gas adsorption method and the transmission electron microscopy (TEM) image analysis method. The mesoporous carbons with various pore structures were prepared by imprinting mesophase pitch used as a carbonaceous precursor with different colloidal silica particles. All imprinted mesoporous carbons were composed of two groups of pores produced from the carbonisation of mesophase pitch and from the silica imprinting. The overall surface fractal dimensions of the carbon specimens were determined from the analyses of the N 2 gas adsorption isotherms. In order to distinguish the surface fractal dimension of the carbonisation-induced pore surface from that fractal dimension of the silica-imprinted pore surface, the individual surface fractal dimensions were determined from the image analyses of the TEM images. From the comparison of the overall surface fractal dimension with the individual surface fractal dimensions, it was recognised that the overall surface fractal dimension is crucially influenced by the individual surface fractal dimension of the silica-imprinted pore surface. Moreover, from the fact that the silica-imprinted pore surface with broad relative pore size distribution (PSD) gave lower value of the individual surface fractal dimension than that pore surface with narrow relative PSD, it is concluded that as the silica-imprinted pores comprising the carbon specimen agglomerate, the individual surface fractal dimension of that pore surface decreases

  8. FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY

    Directory of Open Access Journals (Sweden)

    Hynek Lauschmann

    2011-05-01

    Full Text Available The morphology of fatigue fracture surface (caused by constant cycle loading is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness. Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.

  9. Fractal aspects and convergence of Newton`s method

    Energy Technology Data Exchange (ETDEWEB)

    Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)

    1996-12-31

    Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.

  10. 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)

  11. Launching the chaotic realm of iso-fractals: A short remark

    Energy Technology Data Exchange (ETDEWEB)

    O' Schmidt, Nathan [Department of Mathematics, Boise State University, 1910 University Drive, Boise, ID 83725 (United States); Katebi, Reza [Department of Physics, California State University in Fullerton, 800 North State College Boulevard, Fullerton, CA 92831 (United States); Corda, Christian [Institute for Theoretical Physics and Advanced Mathematics Einstein-Galilei (IFM), Via Santa Gonda 14, 59100 Prato (Italy)

    2015-03-10

    In this brief note, we introduce the new, emerging sub-discipline of iso-fractals by highlighting and discussing the preliminary results of recent works. First, we note the abundance of fractal, chaotic, non-linear, and self-similar structures in nature while emphasizing the importance of studying such systems because fractal geometry is the language of chaos. Second, we outline the iso-fractal generalization of the Mandelbrot set to exemplify the newly generated Mandelbrot iso-sets. Third, we present the cutting-edge notion of dynamic iso-spaces and explain how a mathematical space can be iso-topically lifted with iso-unit functions that (continuously or discretely) change; in the discrete case examples, we mention that iteratively generated sequences like Fibonacci’s numbers and (the complex moduli of) Mandelbrot’s numbers can supply a deterministic chain of iso-units to construct an ordered series of (magnified and/or de-magnified) iso-spaces that are locally iso-morphic. Fourth, we consider the initiation of iso-fractals with Inopin’s holographic ring (IHR) topology and fractional statistics for 2D and 3D iso-spaces. In total, the reviewed iso-fractal results are a significant improvement over traditional fractals because the application of Santilli’s iso-mathematics arms us an extra degree of freedom for attacking problems in chaos. Finally, we conclude by proposing some questions and ideas for future research work.

  12. Fractals as macroscopic manifestation of squeezed coherent states and brain dynamics

    International Nuclear Information System (INIS)

    Vitiello, Giuseppe

    2012-01-01

    Recent results on the relation between self-similarity and squeezed coherent states are presented. I consider fractals which are generated iteratively according to a prescribed recipe, the so-called deterministic fractals. Fractal properties are incorporated in the framework of the theory of the entire analytical functions and deformed coherent states. Conversely, fractal properties of squeezed coherent states are recognized. This sheds some light on the understanding of the dynamical origin of fractals and their global nature emerging from local deformation processes. The self-similarity in brain background activity suggested by laboratory observations of power-law distributions of power spectral densities of electrocorticograms is also discussed and accounted in the frame of the dissipative many-body model of brain.

  13. Fractal Dimension and Maximum Sunspot Number in Solar Cycle

    Directory of Open Access Journals (Sweden)

    R.-S. Kim

    2006-09-01

    Full Text Available The fractal dimension is a quantitative parameter describing the characteristics of irregular time series. In this study, we use this parameter to analyze the irregular aspects of solar activity and to predict the maximum sunspot number in the following solar cycle by examining time series of the sunspot number. For this, we considered the daily sunspot number since 1850 from SIDC (Solar Influences Data analysis Center and then estimated cycle variation of the fractal dimension by using Higuchi's method. We examined the relationship between this fractal dimension and the maximum monthly sunspot number in each solar cycle. As a result, we found that there is a strong inverse relationship between the fractal dimension and the maximum monthly sunspot number. By using this relation we predicted the maximum sunspot number in the solar cycle from the fractal dimension of the sunspot numbers during the solar activity increasing phase. The successful prediction is proven by a good correlation (r=0.89 between the observed and predicted maximum sunspot numbers in the solar cycles.

  14. 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

  15. Species turnover and geographic distance in an urban river network

    DEFF Research Database (Denmark)

    Rouquette, James R.; Dallimer, Martin; Armsworth, Paul R.

    2013-01-01

    AimUnderstanding the relationships between species turnover, environmental features and the geographic distance between sites can provide important insights into the processes driving species diversity. This is particularly relevant where the effective distance between sites may be a function...... patterns of species turnover and to determine whether these patterns differ between different taxonomic groups. LocationSheffield area, UK. MethodsAquatic (macroinvertebrates, diatoms) and terrestrial (birds, plants, butterflies) organisms were surveyed at 41 sites across an urban river network. We...... of the geographic distance measures, although network distance remained significant for birds and some plant groups after removing the effect of environmental distance. Water-dispersed and neophyte plant groups were significantly related to network and flow distance. Main conclusionsThe results suggest that aquatic...

  16. Human physiological benefits of viewing nature: EEG responses to exact and statistical fractal patterns.

    Science.gov (United States)

    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.

  17. Pulmonary vasculature in dogs assessed by three-dimensional fractal analysis and chemometrics

    DEFF Research Database (Denmark)

    Müller, Anna V; Marschner, Clara B; Kristensen, Annemarie T

    2017-01-01

    Fractal analysis of canine pulmonary vessels could allow quantification of their space-filling properties. Aims of this prospective, analytical, cross-sectional study were to describe methods for reconstructing three dimensional pulmonary arterial vascular trees from computed tomographic pulmonary...... angiogram, applying fractal analyses of these vascular trees in dogs with and without diseases that are known to predispose to thromboembolism, and testing the hypothesis that diseased dogs would have a different fractal dimension than healthy dogs. A total of 34 dogs were sampled. Based on computed...... for each dog using a semiautomated segmentation technique. Vascular three-dimensional reconstructions were then evaluated using fractal analysis. Fractal dimensions were analyzed, by group, using analysis of variance and principal component analysis. Fractal dimensions were significantly different among...

  18. A Coupled Model of the 1D River Network and 3D Estuary Based on Hydrodynamics and Suspended Sediment Simulation

    Directory of Open Access Journals (Sweden)

    Wei Zhang

    2014-01-01

    Full Text Available River networks and estuaries are very common in coastal areas. Runoff from the upper stream interacts with tidal current from open sea in these two systems, leading to a complex hydrodynamics process. Therefore, it is necessary to consider the two systems as a whole to study the flow and suspended sediment transport. Firstly, a 1D model is established in the Pearl River network and a 3D model is applied in its estuary. As sufficient mass exchanges between the river network and its estuary, a strict mathematical relationship of water level at the interfaces can be adopted to couple the 1D model with the 3D model. By doing so, the coupled model does not need to have common nested grids. The river network exchanges the suspended sediment with its estuary by adding the continuity conditions at the interfaces. The coupled model is, respectively, calibrated in the dry season and the wet season. The results demonstrate that the coupled model works excellently in simulating water level and discharge. Although there are more errors in simulating suspended sediment concentration due to some reasons, the coupled model is still good enough to evaluate the suspended sediment transport in river network and estuary systems.

  19. Fractal character of structural control on uranium mineralization in south china

    International Nuclear Information System (INIS)

    Zhou Quanyu; Tan Kaixuan; Xie Yanshi

    2009-01-01

    South China is the most important uranium producer in the country. Most uranium ore deposits in south China are strictly controlled by NE-NNE trending regional fracture structure. Fractal analyses on spatial distribution of uranium ore deposits and regional fracture structure in south China have been done in this paper. It indicates that the spatial distribution of both uranium ore deposits and regional fracture structure in south China show fractal character. The fractal dimension D=1.414 2 for the spatial distribution of regional fracture structure in the whole area indicate a higher ripening degree in the fracture structure evolution and an advantages to fluid flow and uranium mineralization. The fractal dimension D=1.052 7 for the spatial distribution of uranium ore deposits in south China show a lower complexity than regional fracture structure. The fractal dimensions in three sub-areas in south China on spatial distribution of uranium ore deposits show a positive correlation to which of regional fracture structure. The fractal spatial distribution of uranium ore deposits in south China is the result of the evolution of the fractal fracture structure system. (authors)

  20. Anisotropic fractal media by vector calculus in non-integer dimensional space

    Energy Technology Data Exchange (ETDEWEB)

    Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru [Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Moscow 119991 (Russian Federation)

    2014-08-15

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

  1. Anisotropic fractal media by vector calculus in non-integer dimensional space

    Science.gov (United States)

    Tarasov, Vasily E.

    2014-08-01

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media.

  2. Anisotropic fractal media by vector calculus in non-integer dimensional space

    International Nuclear Information System (INIS)

    Tarasov, Vasily E.

    2014-01-01

    A review of different approaches to describe anisotropic fractal media is proposed. In this paper, differentiation and integration non-integer dimensional and multi-fractional spaces are considered as tools to describe anisotropic fractal materials and media. We suggest a generalization of vector calculus for non-integer dimensional space by using a product measure method. The product of fractional and non-integer dimensional spaces allows us to take into account the anisotropy of the fractal media in the framework of continuum models. The integration over non-integer-dimensional spaces is considered. In this paper differential operators of first and second orders for fractional space and non-integer dimensional space are suggested. The differential operators are defined as inverse operations to integration in spaces with non-integer dimensions. Non-integer dimensional space that is product of spaces with different dimensions allows us to give continuum models for anisotropic type of the media. The Poisson's equation for fractal medium, the Euler-Bernoulli fractal beam, and the Timoshenko beam equations for fractal material are considered as examples of application of suggested generalization of vector calculus for anisotropic fractal materials and media

  3. Design of silicon-based fractal antennas

    KAUST Repository

    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.

  4. Design of silicon-based fractal antennas

    KAUST Repository

    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.

  5. Estimating extreme river discharges in Europe through a Bayesian network

    Science.gov (United States)

    Paprotny, Dominik; Morales-Nápoles, Oswaldo

    2017-06-01

    Large-scale hydrological modelling of flood hazards requires adequate extreme discharge data. In practise, models based on physics are applied alongside those utilizing only statistical analysis. The former require enormous computational power, while the latter are mostly limited in accuracy and spatial coverage. In this paper we introduce an alternate, statistical approach based on Bayesian networks (BNs), a graphical model for dependent random variables. We use a non-parametric BN to describe the joint distribution of extreme discharges in European rivers and variables representing the geographical characteristics of their catchments. Annual maxima of daily discharges from more than 1800 river gauges (stations with catchment areas ranging from 1.4 to 807 000 km2) were collected, together with information on terrain, land use and local climate. The (conditional) correlations between the variables are modelled through copulas, with the dependency structure defined in the network. The results show that using this method, mean annual maxima and return periods of discharges could be estimated with an accuracy similar to existing studies using physical models for Europe and better than a comparable global statistical model. Performance of the model varies slightly between regions of Europe, but is consistent between different time periods, and remains the same in a split-sample validation. Though discharge prediction under climate change is not the main scope of this paper, the BN was applied to a large domain covering all sizes of rivers in the continent both for present and future climate, as an example. Results show substantial variation in the influence of climate change on river discharges. The model can be used to provide quick estimates of extreme discharges at any location for the purpose of obtaining input information for hydraulic modelling.

  6. 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.

  7. Return to axi-symmetry for pipe flows generated after a fractal orifice

    Energy Technology Data Exchange (ETDEWEB)

    Nicolleau, F C G A, E-mail: F.Nicolleau@Sheffield.ac.uk [SFMG, Department of Mechanical Engineering, University of Sheffield, Mappin Street, Sheffield S1 3JD (United Kingdom)

    2013-12-15

    We present experimental results obtained from pipe flows generated by fractal shaped orifices or openings. We compare different fractal orifices and their efficiencies to re-generate axi-symmetric flows and to return to the standard flow generated by a perforated plate or a circular orifice plate. We consider two families of fractal openings: mono-orifice and complex orifice and emphasize the differences between the two fractal families. For the Reynolds number we used, we found that there is an optimum iteration for the fractal level above which no improvement for practical applications such as flowmetering is to be expected. The main parameters we propose for the characterization of the fractal orifice are the connexity parameter, the symmetry angle and the gap to the wall {delta}*{sub g}. The results presented here are among the first for flows forced through fractal openings and will serve as a reference for future studies and benchmarks for numerical applications. (paper)

  8. Return to axi-symmetry for pipe flows generated after a fractal orifice

    International Nuclear Information System (INIS)

    Nicolleau, F C G A

    2013-01-01

    We present experimental results obtained from pipe flows generated by fractal shaped orifices or openings. We compare different fractal orifices and their efficiencies to re-generate axi-symmetric flows and to return to the standard flow generated by a perforated plate or a circular orifice plate. We consider two families of fractal openings: mono-orifice and complex orifice and emphasize the differences between the two fractal families. For the Reynolds number we used, we found that there is an optimum iteration for the fractal level above which no improvement for practical applications such as flowmetering is to be expected. The main parameters we propose for the characterization of the fractal orifice are the connexity parameter, the symmetry angle and the gap to the wall δ* g . The results presented here are among the first for flows forced through fractal openings and will serve as a reference for future studies and benchmarks for numerical applications. (paper)

  9. Turbulent premixed flames on fractal-grid-generated turbulence

    Energy Technology Data Exchange (ETDEWEB)

    Soulopoulos, N; Kerl, J; Sponfeldner, T; Beyrau, F; Hardalupas, Y; Taylor, A M K P [Mechanical Engineering Department, Imperial College London, London SW7 2AZ (United Kingdom); Vassilicos, J C, E-mail: ns6@ic.ac.uk [Department of Aeronautics, Imperial College London, London SW7 2AZ (United Kingdom)

    2013-12-15

    A space-filling, low blockage fractal grid is used as a novel turbulence generator in a premixed turbulent flame stabilized by a rod. The study compares the flame behaviour with a fractal grid to the behaviour when a standard square mesh grid with the same effective mesh size and solidity as the fractal grid is used. The isothermal gas flow turbulence characteristics, including mean flow velocity and rms of velocity fluctuations and Taylor length, were evaluated from hot-wire measurements. The behaviour of the flames was assessed with direct chemiluminescence emission from the flame and high-speed OH-laser-induced fluorescence. The characteristics of the two flames are considered in terms of turbulent flame thickness, local flame curvature and turbulent flame speed. It is found that, for the same flow rate and stoichiometry and at the same distance downstream of the location of the grid, fractal-grid-generated turbulence leads to a more turbulent flame with enhanced burning rate and increased flame surface area. (paper)

  10. 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.

  11. 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.

  12. Self-stabilized Fractality of Sea-coasts Through Damped Erosion

    Science.gov (United States)

    Sapoval, B.; Baldassari, A.; Gabrielli, A.

    2004-05-01

    Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).

  13. An Efficient Method for Mapping High-Resolution Global River Discharge Based on the Algorithms of Drainage Network Extraction

    Directory of Open Access Journals (Sweden)

    Jiaye Li

    2018-04-01

    Full Text Available River discharge, which represents the accumulation of surface water flowing into rivers and ultimately into the ocean or other water bodies, may have great impacts on water quality and the living organisms in rivers. However, the global knowledge of river discharge is still poor and worth exploring. This study proposes an efficient method for mapping high-resolution global river discharge based on the algorithms of drainage network extraction. Using the existing global runoff map and digital elevation model (DEM data as inputs, this method consists of three steps. First, the pixels of the runoff map and the DEM data are resampled into the same resolution (i.e., 0.01-degree. Second, the flow direction of each pixel of the DEM data (identified by the optimal flow path method used in drainage network extraction is determined and then applied to the corresponding pixel of the runoff map. Third, the river discharge of each pixel of the runoff map is calculated by summing the runoffs of all the pixels in the upstream of this pixel, similar to the upslope area accumulation step in drainage network extraction. Finally, a 0.01-degree global map of the mean annual river discharge is obtained. Moreover, a 0.5-degree global map of the mean annual river discharge is produced to display the results with a more intuitive perception. Compared against the existing global river discharge databases, the 0.01-degree map is of a generally high accuracy for the selected river basins, especially for the Amazon River basin with the lowest relative error (RE of 0.3% and the Yangtze River basin within the RE range of ±6.0%. However, it is noted that the results of the Congo and Zambezi River basins are not satisfactory, with RE values over 90%, and it is inferred that there may be some accuracy problems with the runoff map in these river basins.

  14. Fractal Geometry in the Arts: AN Overview across the Different Cultures

    Science.gov (United States)

    Sala, Nicoletta

    Fractal, in mathematics, is a geometric shape that is complex and detailed in structure at any level of magnification. The word "fractal" was coined less than thirty years ago by one of history's most creative and mathematicians, Benoit Mandelbrot, whose work, The Fractal Geometry of Nature, first introduced and explained concepts underlying this new vision of the geometry. Although other mathematical thinkers like Georg Cantor (1845-1918), Felix Hausdorff (1868-1942), Gaston Julia (1893-1978), Helge von Koch (1870-1924), Giuseppe Peano (1858-1932), Lewis Richardson (1891-1953), Waclaw Sierpinski (1882-1969) and others had attained isolated insights of fractal understanding, such ideas were largely ignored until Mandelbrot's genius forged them at a single blow into a gorgeously coherent and fascinating discipline. Fractal geometry is applied in different field now: engineering, physics, chemistry, biology, and architecture. The aim of this paper is to introduce an approach where the arts are analysed using a fractal point of view.

  15. 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)...

  16. Fractal analysis as a potential tool for surface morphology of thin films

    Science.gov (United States)

    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.

  17. Fractal based curves in musical creativity: A critical annotation

    Science.gov (United States)

    Georgaki, Anastasia; Tsolakis, Christos

    In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.

  18. Study on Conversion Between Momentum and Contrarian Based on Fractal Game

    Science.gov (United States)

    Wu, Xu; Song, Guanghui; Deng, Yan; Xu, Lin

    2015-06-01

    Based on the fractal game which is performed by the majority and the minority, the fractal market theory (FMT) is employed to describe the features of investors' decision-making. Accordingly, the process of fractal games is formed in order to analyze the statistical features of conversion between momentum and contrarian. The result shows that among three fractal game mechanisms, the statistical feature of simulated return rate series is much more similar to log returns on actual series. In addition, the conversion between momentum and contrarian is also extremely similar to real situation, which can reflect the effectiveness of using fractal game in analyzing the conversion between momentum and contrarian. Moreover, it also provides decision-making reference which helps investors develop effective investment strategy.

  19. Arctic sea ice melt pond fractal dimension - explained

    Science.gov (United States)

    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.

  20. Fractal Nanotechnology

    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.

  1. Fractal design concepts for stretchable electronics.

    Science.gov (United States)

    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.

  2. Fractal design concepts for stretchable electronics

    Science.gov (United States)

    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.

  3. 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

  4. Fractal growth in impurity-controlled solidification in lipid monolayers

    DEFF Research Database (Denmark)

    Fogedby, Hans C.; Sørensen, Erik Schwartz; Mouritsen, Ole G.

    1987-01-01

    A simple two-dimensional microscopic model is proposed to describe solidifcation processes in systems with impurities which are miscible only in the fluid phase. Computer simulation of the model shows that the resulting solids are fractal over a wide range of impurity concentrations and impurity...... diffusional constants. A fractal-forming mechanism is suggested for impurity-controlled solidification which is consistent with recent experimental observations of fractal growth of solid phospholipid domains in monolayers. The Journal of Chemical Physics is copyrighted by The American Institute of Physics....

  5. Shower fractal dimension analysis in a highly-granular calorimeter

    CERN Document Server

    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.

  6. 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.

  7. Experiencia en el aula de secundaria con fractales

    OpenAIRE

    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.

  8. A fractal view of Chernobyl fallout in Northern Italy and Europe

    International Nuclear Information System (INIS)

    Salvadori, G.; Ratti, S.P.; Belli, G.; Quinto, E.

    1996-01-01

    Fractals are associated with irregularity and represent a powerful tool for investigating phenomena featuring a complex behaviour, as it is the case of the atmospheric processes playing a role in spreading the radioactive pollution of Chernobyl in the environment. The introduction of fractals in environmental sciences is quite recent. Fractals may account for the presence of strong fluctuations and for the high variability characterising the natural events involved in the Chernobyl fallout: the geographical sparseness of pollutant and the presence of 'hot spots' make it advisable to use fractals as a theoretical framework for modelling

  9. Fractal Dimension of Particle Showers Measured in a Highly Granular Calorimeter

    CERN Document Server

    Ruan, Manqi; Bourdy, Vincent; Brients, Jean-Claude; Videau, Henri

    2014-01-01

    fractal dimension of showers measured in a high granularity calorimeter designed for a future lepton collider. The shower fractal dimension reveals detailed information of the spatial configuration of the shower. It is found to be characteristic of the type of interaction and highly sensitive to the nature of the incident particle. Using the shower fractal dimension, we demonstrate a particle identification algorithm that can efficiently separate electromagnetic showers, hadronic showers and non-showering tracks. We also find a logarithmic dependence of the shower fractal dimension on the particle energy.

  10. A family of fractal sets with Hausdorff dimension 0.618

    Energy Technology Data Exchange (ETDEWEB)

    Zhong Ting [Information Management and Engineering Institute, Jishou University, Zhangjiajie 427000, Hunan (China)], E-mail: zhongting_2005@126.com

    2009-10-15

    In this paper, we introduce a class of fractal sets, which can be recursively constructed by two sequences {l_brace}n{sub k}{r_brace}{sub k{>=}}{sub 1} and {l_brace}c{sub k}{r_brace}{sub k{>=}}{sub 1}. We obtain the exact Hausdorff dimensions of these types of fractal sets using the continued fraction map. Connection of continued fraction with El Naschie's fractal spacetime is also illustrated. Furthermore, we restrict one sequence {l_brace}c{sub k}{r_brace}{sub k{>=}}{sub 1} to make every irrational number {alpha} element of (0, 1) correspond to only one of the above fractal sets called {alpha}-Cantor sets, and we found that almost all {alpha}-Cantor sets possess a common Hausdorff dimension of 0.618, which is also the Hausdorff dimension of the one-dimensional random recursive Cantor set and it is the foundation stone of E-infinity fractal spacetime theory.

  11. 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

  12. Effect of watershed urbanization on N2O emissions from the Chongqing metropolitan river network, China

    Science.gov (United States)

    He, Yixin; Wang, Xiaofeng; Chen, Huai; Yuan, Xingzhong; Wu, Ning; Zhang, Yuewei; Yue, Junsheng; Zhang, Qiaoyong; Diao, Yuanbin; Zhou, Lilei

    2017-12-01

    Watershed urbanization, an integrated anthropogenic perturbation, is another considerable global concern in addition to that of global warming and may significantly enrich the N loadings of watersheds, which then greatly influences the nitrous oxide (N2O) production and fluxes of these aquatic systems. However, little is known about the N2O dynamics in human-dominated metropolitan river networks. In this study, we present the temporal and spatial variations in N2O saturation and emission in the Chongqing metropolitan river network, which is undergoing intensified urbanization. The N2O saturation and fluxes at 84 sampling sites ranged from 126% to 10536% and from 4.5 to 1566.8 μmol N2O m-2 d-1, with means of 1780% and 261 μmol N2O m-2 d-1. The riverine N2O saturation and fluxes increased along with the urbanization gradient and urbanization rate, with disproportionately higher values in urban rivers due to the N2O-rich sewage inputs and enriched in situ N substrates. We found a clear seasonal pattern of N2O saturation, which was co-regulated by both water temperature and precipitation. Regression analysis indicated that the N substrates and dissolved oxygen (DO) that controlled nitrogen metabolism acted as good predictors of the N2O emissions of urban river networks. Particularly, phosphorus (P) and hydromorphological factors (water velocity, river size and bottom substrate) had stronger relationships with the N2O saturation and could also be used to predict the N2O emission hotspots in regions with rapid urbanization. In addition, the default emission factors (EF5-r) used in the Intergovernmental Panel on Climate Change (IPCC) methodology may need revision given the differences among the physical and chemical factors in different rivers, especially urban rivers.

  13. 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

  14. Form in the Natural Environment: Fractal Computer Graphics and Wassily Kandinsky.

    Science.gov (United States)

    Geake, John; Porter, Jim

    1992-01-01

    Reports on study of use of fractal geometry in a computer graphics program to improve the perception of intermediate grade level students in their paintings. Finds that students are more likely to use changing shapes and colors after viewing slides of fractal computer graphics. Concludes that fractal computer graphics would make highly engaging…

  15. 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...

  16. Are Equilibrium Multichannel Networks Predictable? the Case of the Indus River, Pakistan

    Science.gov (United States)

    Darby, S. E.; Carling, P. A.

    2017-12-01

    Focusing on the specific case of the Indus River, we argue that the equilibrium planform network structure of large, multi-channel, rivers is predictable. Between Chashma and Taunsa, Pakistan, the Indus is a 264 km long multiple-channel reach. Remote sensing imagery, including a period of time that encompasses the occurrence of major floods in 2007 and 2010, shows that Indus has a minimum of two and a maximum of nine channels, with on average four active channels during the dry season and five during the monsoon. We show that the network structure, if not detailed planform, remains stable, even for the record 2010 flood (27,100 m3s-1; recurrence interval > 100 years). Bankline recession is negligible for discharges less than a peak annual discharge of 6,000 m3s-1 ( 80% of mean annual flow). Maximum Flow Efficiency (MFE) principle demonstrates the channel network is insensitive to the monsoon floods, which typically peak at 13,200 m3s-1. Rather, the network is in near-equilibrium with the mean annual flood (7,530 m3s-1). MFE principle indicates stable networks have three to four channels, thus the observed stability in the number of active channels accords with the presence of a near-equilibrium reach-scale channel network. Insensitivity to the annual hydrological cycle demonstrates that the time-scale for network adjustment is much longer than the time-scale of the monsoon hydrograph, with the annual excess water being stored on floodplains, rather than being conveyed in an enlarged channel network. The analysis explains the lack of significant channel adjustment following the largest flood in 40 years and the extensive Indus flooding experienced on an annual basis, with its substantial impacts on the populace and agricultural production.

  17. Fractal markets: Liquidity and investors on different time horizons

    Science.gov (United States)

    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.

  18. Plot-slope soil erosion using 7Be measurement and rill fractal dimension

    International Nuclear Information System (INIS)

    Zhang Fengbao; Yang Mingyi

    2010-01-01

    In this study, we intended to use 7 Be measurement and fractal theory to quantify soil erosion process on slope. The results showed that contribution rate of inter rill erosion was more than that of rill erosion during early stage of rainfall. When it rained, contribution rate of rill erosion began to be higher than inter rill erosion and become the main part of erosion during medium stage of rainfall. The trend of contribution rate of inter rill erosion was growing and the rill erosion was lowering during late stage of rainfall. Rill fractal dimension on the plot slope was almost growing larger during rainfall,growing quickly during early stage of rainfall and slowly during the late stage. Correlations was positive between rill fractal dimension and total erosion amount, also positive between rill fractal dimension and rill erosion. The correlations was positive between rill fractal dimension variation and total erosion amount, also was positive between rill fractal dimension variation and rill erosion amount. The best correlation was observed between rill fractal dimension and rill erosion amount. These results indicated that the rill fractal dimension on the plot slope could represent the development process of rill,the complex degree of rill and the variation of soil erosion intensity on the entire slope. (authors)

  19. 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

  20. A variable-order fractal derivative model for anomalous diffusion

    Directory of Open Access Journals (Sweden)

    Liu Xiaoting

    2017-01-01

    Full Text Available This paper pays attention to develop a variable-order fractal derivative model for anomalous diffusion. Previous investigations have indicated that the medium structure, fractal dimension or porosity may change with time or space during solute transport processes, results in time or spatial dependent anomalous diffusion phenomena. Hereby, this study makes an attempt to introduce a variable-order fractal derivative diffusion model, in which the index of fractal derivative depends on temporal moment or spatial position, to characterize the above mentioned anomalous diffusion (or transport processes. Compared with other models, the main advantages in description and the physical explanation of new model are explored by numerical simulation. Further discussions on the dissimilitude such as computational efficiency, diffusion behavior and heavy tail phenomena of the new model and variable-order fractional derivative model are also offered.

  1. Moisture diffusivity in structure of random fractal fiber bed

    Energy Technology Data Exchange (ETDEWEB)

    Zhu, Fanglong, E-mail: zhufanglong_168@163.com [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); The Chinese People' s Armed Police Forces Academy, Langfan City (China); Zhou, Yu; Feng, Qianqian [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); Xia, Dehong [School of Mechanical Engineering, University of Science and Technology, Beijing (China)

    2013-11-08

    A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.

  2. An Efficient Computational Technique for Fractal Vehicular Traffic Flow

    Directory of Open Access Journals (Sweden)

    Devendra Kumar

    2018-04-01

    Full Text Available In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.

  3. Fractal corrections of BaTiO3-ceramic sintering parameters

    Directory of Open Access Journals (Sweden)

    Mitić V.V.

    2014-01-01

    Full Text Available Morphology of ceramics grains and pores as well as Brownian character of particle dynamics inside ceramics specimen contributes to better understanding of the sintering process. BaTiO3-ceramics, studied in this paper, has light fractal form and it is emanated in three aspects. First, the surface of grains, even in starting green body as well as distribution of grains shows fractal behavior. Second, existence of pores and their distribution follow the rules of fractal geometry. Third, movement of particles inside viscous flow underlies the rule of Brownian motion, which is essentially a fractal category. These three elements, each in its domain influence sintering dynamics, and can be described by dimensionless quantitative factors, αs αp and αm, being normalized to the interval [0,1]. Following sintering process, the associate formulae of Frenkel, Scherer and Mackenzie-Shuttleworth are shown from the angle of view of ceramics fractal dimension changing that approaches to 3. Also, it is shown that the energy balance is not violated after applying fractal correction to quasi equilibrium of the energy emanating from surface area reduction ES and energy adopted by viscous flow Ef .[Projekat Ministarstva nauke Republike Srbije, br. 172057: Directed synthesis, structure and properties of multifunctional materials

  4. Exploring the relationship between fractal features and bacterial essential genes

    International Nuclear Information System (INIS)

    Yu Yong-Ming; Yang Li-Cai; Zhao Lu-Lu; Liu Zhi-Ping; Zhou Qian

    2016-01-01

    Essential genes are indispensable for the survival of an organism in optimal conditions. Rapid and accurate identifications of new essential genes are of great theoretical and practical significance. Exploring features with predictive power is fundamental for this. Here, we calculate six fractal features from primary gene and protein sequences and then explore their relationship with gene essentiality by statistical analysis and machine learning-based methods. The models are applied to all the currently available identified genes in 27 bacteria from the database of essential genes (DEG). It is found that the fractal features of essential genes generally differ from those of non-essential genes. The fractal features are used to ascertain the parameters of two machine learning classifiers: Naïve Bayes and Random Forest. The area under the curve (AUC) of both classifiers show that each fractal feature is satisfactorily discriminative between essential genes and non-essential genes individually. And, although significant correlations exist among fractal features, gene essentiality can also be reliably predicted by various combinations of them. Thus, the fractal features analyzed in our study can be used not only to construct a good essentiality classifier alone, but also to be significant contributors for computational tools identifying essential genes. (paper)

  5. 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)

  6. 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.

  7. 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 ...

  8. Thermal properties of bodies in fractal and cantorian physics

    International Nuclear Information System (INIS)

    Zmeskal, Oldrich; Buchnicek, Miroslav; Vala, Martin

    2005-01-01

    Fundamental laws describing the heat diffusion in fractal environment are discussed. It is shown that for the three-dimensional space the heat radiation process occur in structures with fractal dimension D element of heat conduction and convection have the upper hand (generally in the real gases). To describe the heat diffusion a new law has been formulated. Its validity is more general than the Plank's radiation law based on the quantum heat diffusion theory. The energy density w = f (K, D), where K is the fractal measure and D is the fractal dimension exhibit typical dependency peaking with agreement with Planck's radiation law and with the experimental data for the absolutely black body in the energy interval kT m m kT m ∼ 1.5275. The agreement of the fractal model with the experimental outcomes is documented for the spectral characteristics of the Sun. The properties of stellar objects (black holes, relict radiation, etc.) and the elementary particles fields and interactions between them (quarks, leptons, mesons, baryons, bosons and their coupling constants) will be discussed with the help of the described mathematic apparatus in our further contributions. The general gas law for real gases in its more applicable form than the widely used laws (e.g. van der Waals, Berthelot, Kammerlingh-Onnes) has been also formulated. The energy density, which is in this case represented by the gas pressure p = f (K, D), can gain generally complex value and represents the behaviour of real (cohesive) gas in interval D element of (1,3>. The gas behaves as the ideal one only for particular values of the fractal dimensions (the energy density is real-valued). Again, it is shown that above the critical temperature (kT > K h c) and for fractal dimension D m > 2.0269 the results are comparable to the kinetics theory of real (ideal) gas (van der Waals equation of state, compressibility factor, Boyle's temperature). For the critical temperature (K h c = kT r ) the compressibility

  9. Toward a new “Fractals-General Science”

    Directory of Open Access Journals (Sweden)

    Hassen Taher Dorrah

    2014-09-01

    Full Text Available A recent study has shown that everywhere real systems follow common “fractals-general stacking behavior” during their change pathways (or evolutionary life cycles. This fact leads to the emergence of the new discipline “Fractals-General Science” as a mother-discipline (and acting as upper umbrella of existing natural and applied sciences to commonly handle their fractals-general change behavior. It is, therefore, the main targets of this short communication are to present the motives, objectives, relations with other existing sciences, and the development map of such new science. It is discussed that there are many foreseen illustrative applications in geology, archeology, astronomy, life sciences, ecology, environmental science, hydrology, agronomy, engineering, materials sciences, chemistry, nanotechnology, biology, medicine, psychiatry, sociology, humanities, education, and arts that could effectively lead the implementation and experimentation of such new science. It is highlighted that the new “Fractals-General Science” could provide through multi-stacking representations the necessary platforms for investigating interactions and mutual changes between real life systems belonging to several sciences and disciplines. Examples are handling problems of the processing of basic formation and changes of matter and substances, propagation of combined corrosion, creep, fatigue and sedimentation of engineering and industrial systems, and the progressing of humans’ evolutionary life cycles.

  10. Evaluation of Spatial Pattern of Altered Flow Regimes on a River Network Using a Distributed Hydrological Model.

    Science.gov (United States)

    Ryo, Masahiro; Iwasaki, Yuichi; Yoshimura, Chihiro; Saavedra V, Oliver C

    2015-01-01

    Alteration of the spatial variability of natural flow regimes has been less studied than that of the temporal variability, despite its ecological importance for river ecosystems. Here, we aimed to quantify the spatial patterns of flow regime alterations along a river network in the Sagami River, Japan, by estimating river discharge under natural and altered flow conditions. We used a distributed hydrological model, which simulates hydrological processes spatiotemporally, to estimate 20-year daily river discharge along the river network. Then, 33 hydrologic indices (i.e., Indicators of Hydrologic Alteration) were calculated from the simulated discharge to estimate the spatial patterns of their alterations. Some hydrologic indices were relatively well estimated such as the magnitude and timing of maximum flows, monthly median flows, and the frequency of low and high flow pulses. The accuracy was evaluated with correlation analysis (r > 0.4) and the Kolmogorov-Smirnov test (α = 0.05) by comparing these indices calculated from both observed and simulated discharge. The spatial patterns of the flow regime alterations varied depending on the hydrologic indices. For example, both the median flow in August and the frequency of high flow pulses were reduced by the maximum of approximately 70%, but these strongest alterations were detected at different locations (i.e., on the mainstream and the tributary, respectively). These results are likely caused by different operational purposes of multiple water control facilities. The results imply that the evaluation only at discharge gauges is insufficient to capture the alteration of the flow regime. Our findings clearly emphasize the importance of evaluating the spatial pattern of flow regime alteration on a river network where its discharge is affected by multiple water control facilities.

  11. Metacommunity theory as a multispecies, multiscale framework for studying the influence of river network structure on riverine communities and ecosystems

    Science.gov (United States)

    Brown, B.L.; Swan, C.M.; Auerbach, D.A.; Campbell, Grant E.H.; Hitt, N.P.; Maloney, K.O.; Patrick, C.

    2011-01-01

    Explaining the mechanisms underlying patterns of species diversity and composition in riverine networks is challenging. Historically, community ecologists have conceived of communities as largely isolated entities and have focused on local environmental factors and interspecific interactions as the major forces determining species composition. However, stream ecologists have long embraced a multiscale approach to studying riverine ecosystems and have studied both local factors and larger-scale regional factors, such as dispersal and disturbance. River networks exhibit a dendritic spatial structure that can constrain aquatic organisms when their dispersal is influenced by or confined to the river network. We contend that the principles of metacommunity theory would help stream ecologists to understand how the complex spatial structure of river networks mediates the relative influences of local and regional control on species composition. From a basic ecological perspective, the concept is attractive because new evidence suggests that the importance of regional processes (dispersal) depends on spatial structure of habitat and on connection to the regional species pool. The role of local factors relative to regional factors will vary with spatial position in a river network. From an applied perspective, the long-standing view in ecology that local community composition is an indicator of habitat quality may not be uniformly applicable across a river network, but the strength of such bioassessment approaches probably will depend on spatial position in the network. The principles of metacommunity theory are broadly applicable across taxa and systems but seem of particular consequence to stream ecology given the unique spatial structure of riverine systems. By explicitly embracing processes at multiple spatial scales, metacommunity theory provides a foundation on which to build a richer understanding of stream communities.

  12. 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

  13. [Formation and changes of regulated trihalomethanes and haloacetic acids in raw water of Yangtze River, Huangpu River and different treatment processes and pipelines network].

    Science.gov (United States)

    Chen, Xin; Zhang, Dong; Lu, Yin-hao; Zheng, Wei-wei; Wu, Yu-xin; Wei, Xiao; Tian, Da-jun; Wang, Xia; Zhang, Hao; Guo, Shuai; Jiang, Song-hui; Qu, Wei-dong

    2010-10-01

    To investigate the pollutant levels of regulated disinfection by-products trihalomethanes (THMs) and haloacetic acids (HAAs) in raw water from the Huangpu River, the Yangtze River and different treatment processes and finished water, and to explore the changes tendency in transmission and distribution pipeline network. A total of 65 ml water samples with two replicates were collected from different raw water, corresponding treatment processes, finished water and six national surveillance points in main network of transmission and distribution, water source for A water plant and B, C water plant was the Huangpu River and the Yangtze River, respectively. Regulated THMs and HAAs above water samples were detected by gas chromatography. The total trihalomethanes (THM(4)) concentration in different treatment processes of A water plant was ND-9.64 µg/L, dichlorobromomethane was the highest (6.43 µg/L). The THM(4) concentration in B and C water plant was ND to 38.06 µg/L, dibromochloromethane (12.24 µg/L) and bromoform (14.07 µg/L) were the highest in the B and the C water plant respectively. In addition to trichloroacetic acid in A water plant from the raw water, the other HAAs came from different treatment processes. The total haloacetic acids (HAA(6)) concentration of different treated processes in A water plant was 3.21 - 22.97 µg/L, mobromoacetic acid (10.40 µg/L) was the highest. Dibromoacetic acid was the highest both in B (8.25 µg/L) and C (8.84 µg/L) water plant, HAA(6) concentration was ND to 27.18 µg/L. The highest and the lowest concentration of THM(4) were found from the main distribution network of C and A water plant respectively, but the concentration of HAA(6) in the main water pipes network of A water plant was the highest, and the lowest in C water plant. The THMs concentration was 21.11 - 31.18 µg/L in C water plant and 6.72 - 8.51 µg/L in A water plant. The concentration of HAA(6) was 25.02 - 37.31 µg/L in A water plant and 18.69 - 23

  14. Analysis of fractal dimensions of rat bones from film and digital images

    Science.gov (United States)

    Pornprasertsuk, S.; Ludlow, J. B.; Webber, R. L.; Tyndall, D. A.; Yamauchi, M.

    2001-01-01

    OBJECTIVES: (1) To compare the effect of two different intra-oral image receptors on estimates of fractal dimension; and (2) to determine the variations in fractal dimensions between the femur, tibia and humerus of the rat and between their proximal, middle and distal regions. METHODS: The left femur, tibia and humerus from 24 4-6-month-old Sprague-Dawley rats were radiographed using intra-oral film and a charge-coupled device (CCD). Films were digitized at a pixel density comparable to the CCD using a flat-bed scanner. Square regions of interest were selected from proximal, middle, and distal regions of each bone. Fractal dimensions were estimated from the slope of regression lines fitted to plots of log power against log spatial frequency. RESULTS: The fractal dimensions estimates from digitized films were significantly greater than those produced from the CCD (P=0.0008). Estimated fractal dimensions of three types of bone were not significantly different (P=0.0544); however, the three regions of bones were significantly different (P=0.0239). The fractal dimensions estimated from radiographs of the proximal and distal regions of the bones were lower than comparable estimates obtained from the middle region. CONCLUSIONS: Different types of image receptors significantly affect estimates of fractal dimension. There was no difference in the fractal dimensions of the different bones but the three regions differed significantly.

  15. Metapopulation modelling of riparian tree species persistence in river networks under climate change.

    Science.gov (United States)

    Van Looy, Kris; Piffady, Jérémy

    2017-11-01

    Floodplain landscapes are highly fragmented by river regulation resulting in habitat degradation and flood regime perturbation, posing risks to population persistence. Climate change is expected to pose supplementary risks in this context of fragmented landscapes, and especially for river systems adaptation management programs are developed. The association of habitat quality and quantity with the landscape dynamics and resilience to human-induced disturbances is still poorly understood in the context of species survival and colonization processes, but essential to prioritize conservation and restoration actions. We present a modelling approach that elucidates network connectivity and landscape dynamics in spatial and temporal context to identify vital corridors and conservation priorities in the Loire river and its tributaries. Alteration of flooding and flow regimes is believed to be critical to population dynamics in river ecosystems. Still, little is known of critical levels of alteration both spatially and temporally. We applied metapopulation modelling approaches for a dispersal-limited tree species, white elm; and a recruitment-limited tree species, black poplar. In different model steps the connectivity and natural dynamics of the river landscape are confronted with physical alterations (dams/dykes) to species survival and then future scenarios for climatic changes and potential adaptation measures are entered in the model and translated in population persistence over the river basin. For the two tree species we highlighted crucial network zones in relation to habitat quality and connectivity. Where the human impact model already shows currently restricted metapopulation development, climate change is projected to aggravate this persistence perspective substantially. For both species a significant drawback to the basin population is observed, with 1/3 for elm and ¼ for poplar after 25 years already. But proposed adaptation measures prove effective to even

  16. Insights and issues with simulating terrestrial DOC loading of Arctic river networks.

    Science.gov (United States)

    Kicklighter, David W; Hayes, Daniel J; McClelland, James W; Peterson, Bruce J; McGuire, A David; Melillo, Jerry M

    2013-12-01

    Terrestrial carbon dynamics influence the contribution of dissolved organic carbon (DOC) to river networks in addition to hydrology. In this study, we use a biogeochemical process model to simulate the lateral transfer of DOC from land to the Arctic Ocean via riverine transport. We estimate that, over the 20th century, the pan-Arctic watershed has contributed, on average, 32 Tg C/yr of DOC to river networks emptying into the Arctic Ocean with most of the DOC coming from the extensive area of boreal deciduous needle-leaved forests and forested wetlands in Eurasian watersheds. We also estimate that the rate of terrestrial DOC loading has been increasing by 0.037 Tg C/yr2 over the 20th century primarily as a result of climate-induced increases in water yield. These increases have been offset by decreases in terrestrial DOC loading caused by wildfires. Other environmental factors (CO2 fertilization, ozone pollution, atmospheric nitrogen deposition, timber harvest, agriculture) are estimated to have relatively small effects on terrestrial DOC loading to Arctic rivers. The effects of the various environmental factors on terrestrial carbon dynamics have both offset and enhanced concurrent effects on hydrology to influence terrestrial DOC loading and may be changing the relative importance of terrestrial carbon dynamics on this carbon flux. Improvements in simulating terrestrial DOC loading to pan-Arctic rivers in the future will require better information on the production and consumption of DOC within the soil profile, the transfer of DOC from land to headwater streams, the spatial distribution of precipitation and its temporal trends, carbon dynamics of larch-dominated ecosystems in eastern Siberia, and the role of industrial organic effluents on carbon budgets of rivers in western Russia.

  17. Insights and issues with simulating terrestrial DOC loading of Arctic river networks

    Science.gov (United States)

    Kicklighter, David W.; Hayes, Daniel J.; McClelland, James W.; Peterson, Bruce J.; McGuire, A. David; Melillo, Jerry M.

    2013-01-01

    Terrestrial carbon dynamics influence the contribution of dissolved organic carbon (DOC) to river networks in addition to hydrology. In this study, we use a biogeochemical process model to simulate the lateral transfer of DOC from land to the Arctic Ocean via riverine transport. We estimate that, over the 20th century, the pan-Arctic watershed has contributed, on average, 32 Tg C/yr of DOC to river networks emptying into the Arctic Ocean with most of the DOC coming from the extensive area of boreal deciduous needle-leaved forests and forested wetlands in Eurasian watersheds. We also estimate that the rate of terrestrial DOC loading has been increasing by 0.037 Tg C/yr2 over the 20th century primarily as a result of climate-induced increases in water yield. These increases have been offset by decreases in terrestrial DOC loading caused by wildfires. Other environmental factors (CO2 fertilization, ozone pollution, atmospheric nitrogen deposition, timber harvest, agriculture) are estimated to have relatively small effects on terrestrial DOC loading to Arctic rivers. The effects of the various environmental factors on terrestrial carbon dynamics have both offset and enhanced concurrent effects on hydrology to influence terrestrial DOC loading and may be changing the relative importance of terrestrial carbon dynamics on this carbon flux. Improvements in simulating terrestrial DOC loading to pan-Arctic rivers in the future will require better information on the production and consumption of DOC within the soil profile, the transfer of DOC from land to headwater streams, the spatial distribution of precipitation and its temporal trends, carbon dynamics of larch-dominated ecosystems in eastern Siberia, and the role of industrial organic effluents on carbon budgets of rivers in western Russia.

  18. Integration of Fractal Biosensor in a Digital Microfluidic Platform

    KAUST Repository

    Mashraei, Yousof

    2016-06-08

    The digital microfluidic (DMF) platform introduces many applications in biomedical assays. If it is to be commercially available to the public, it needs to have the essential features of smart sensing and a compact size. In this work, we report on a fractal electrode biosensor that is used for both droplet actuation and sensing C-reactive protein (CRP) concentration levels to assess cardiac disease risk. Our proposed electrode is the first two-terminal electrode design to be integrated into DMF platforms. A simulation of the electrical field distribution shows reduced peak intensities and uniform distribution of the field. When compared to a V-notch square electrode, the fractal electrode shows a superior performance in both aspects, i.e. field uniformity and intensity. These improvements are translated into a successful and responsive actuation of a water droplet with 100V. Likewise, the effective dielectric strength is improved by a 33% increase in the fractal electrode breakdown voltage. Additionally, the capability of the fractal electrode to work as a capacitive biosensor is evaluated with CRP quantification test. Selected fractal electrodes undergo a surface treatment to immobilize anti-CRP antibodies on their surface. The measurement shows a response to the added CRP in capacitance within three minutes. When the untreated electrodes were used for quantification, there was no significant change in capacitance, and this suggested that immobilization was necessary. The electrodes configuration in the fabricated DMF platform allows the fractal electrodes to be selectively used as biosensors, which means the device could be integrated into point-of-care applications.

  19. 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.

  20. Some fractal properties of the percolating backbone in two dimensions

    International Nuclear Information System (INIS)

    Laidlaw, D.; MacKay, G.; Jan, N.

    1987-01-01

    A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that fractal dimensionality of the backbone is d/sub f//sup BB/ = 1.61 +/- 0.01, the chemical dimensionality is d/sub t/ = 1.40 +/- 0.01, and the fractal dimension of the minimum path d/sub min/ = 1.15 +/- 0.02 for the two-dimensional triangular lattice

  1. Assessment of Textural Differentiations in Forest Resources in Romania Using Fractal Analysis

    Directory of Open Access Journals (Sweden)

    Ion Andronache

    2017-02-01

    Full Text Available Deforestation and forest degradation have several negative effects on the environment including a loss of species habitats, disturbance of the water cycle and reduced ability to retain CO2, with consequences for global warming. We investigated the evolution of forest resources from development regions in Romania affected by both deforestation and reforestation using a non-Euclidean method based on fractal analysis. We calculated four fractal dimensions of forest areas: the fractal box-counting dimension of the forest areas, the fractal box-counting dimension of the dilated forest areas, the fractal dilation dimension and the box-counting dimension of the border of the dilated forest areas. Fractal analysis revealed morpho-structural and textural differentiations of forested, deforested and reforested areas in development regions with dominant mountain relief and high hills (more forested and compact organization in comparison to the development regions dominated by plains or low hills (less forested, more fragmented with small and isolated clusters. Our analysis used the fractal analysis that has the advantage of analyzing the entire image, rather than studying local information, thereby enabling quantification of the uniformity, fragmentation, heterogeneity and homogeneity of forests.

  2. Solving fractal steady heat-transfer problems with the local fractional Sumudu transform

    Directory of Open Access Journals (Sweden)

    Wang Yi

    2015-01-01

    Full Text Available In this paper the linear oscillator problem in fractal steady heat-transfer is studied within the local fractional theory. In particular, the local fractional Sumudu transform (LFST will be used to solve both the homogeneous and the non-homogeneous local fractional oscillator equations (LFOEs under fractal steady heat-transfer. It will be shown that the obtained non-differentiable solutions characterize the fractal phenomena with and without the driving force in fractal steady heat transfer at low excess temperatures.

  3. 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 ...

  4. Growth of fractal structures in flames with silicon admixture

    NARCIS (Netherlands)

    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

  5. 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.

  6. 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.

  7. Temporal fractals in seabird foraging behaviour: diving through the scales of time

    Science.gov (United States)

    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.

  8. Research on evaluation of degree of complexity of mining fault network based on GIS

    Energy Technology Data Exchange (ETDEWEB)

    Hua Zhang; Yun-jia Wang; Chuan-zhi Liu [China University of Mining and Technology, Jiangsu (China). School of Environment Science and Spatial Informatics

    2007-03-15

    A large number of spatial and attribute data are involved in coal resource evaluation. Databases are a relatively advanced data management technology, but their major defects are the poor graphic and spatial data functions, from which it is difficult to realize scientific management of evaluation data with spatial characteristics and evaluation result maps. On account of these deficiencies, the evaluation of degree of complexity of mining fault network based on a geographic information system (GIS) is proposed which integrates management of spatial and attribute data. A fractal is an index which can reflect the comprehensive information of faults' number, density, size, composition and dynamics mechanism. A fractal dimension is used as the quantitative evaluation index. Evaluation software has been developed based on a component GIS-MapX, with which the degree of complexity of fault network is evaluated quantitatively using the quantitative index of fractal dimensions in Liuqiao No.2 coal mine as an example. Results show that it is effective in acquiring model parameters and enhancing the definition of data and evaluation results with the application of GIS technology. The fault network is a system with fractal structure and its complexity can be described reasonably and accurately by fractal dimension, which provides an effective method for coal resource evaluation. 9 refs., 6 figs., 2 tabs.

  9. Fractales para la arqueología: un nuevo lenguaje

    Directory of Open Access Journals (Sweden)

    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.

  10. An Investigation of Fractal Characteristics of Marine Shales in the Southern China from Nitrogen Adsorption Data

    Directory of Open Access Journals (Sweden)

    Jian Xiong

    2015-01-01

    Full Text Available We mainly focus on the Permian, Lower Cambrian, Lower Silurian, and Upper Ordovician Formation; the fractal dimensions of marine shales in southern China were calculated using the FHH fractal model based on the low-pressure nitrogen adsorption analysis. The results show that the marine shales in southern China have the dual fractal characteristics. The fractal dimension D1 at low relative pressure represents the pore surface fractal characteristics, whereas the fractal dimension D2 at higher relative pressure describes the pore structure fractal characteristics. The fractal dimensions D1 range from 2.0918 to 2.718 with a mean value of 2.4762, and the fractal dimensions D2 range from 2.5842 to 2.9399 with a mean value of 2.8015. There are positive relationships between fractal dimension D1 and specific surface area and total pore volume, whereas the fractal dimensions D2 have negative correlation with average pore size. The larger the value of the fractal dimension D1 is, the rougher the pore surface is, which could provide more adsorption sites, leading to higher adsorption capacity for gas. The larger the value of the fractal dimension D2 is, the more complicated the pore structure is, resulting in the lower flow capacity for gas.

  11. Fractal Dimension Analysis of Texture Formation of Whey Protein-Based Foods

    Directory of Open Access Journals (Sweden)

    Robi Andoyo

    2018-01-01

    Full Text Available Whey protein in the form of isolate or concentrate is widely used in food industries due to its functionality to form gel under certain condition and its nutritive value. Controlling or manipulating the formation of gel aggregates is used often to evaluate food texture. Many researchers made use of fractal analysis that provides the quantitative data (i.e., fractal dimension for fundamentally and rationally analyzing and designing whey protein-based food texture. This quantitative analysis is also done to better understand how the texture of whey protein-based food is formed. Two methods for fractal analysis were discussed in this review: image analysis (microscopy and rheology. These methods, however, have several limitations which greatly affect the accuracy of both fractal dimension values and types of aggregation obtained. This review therefore also discussed problem encountered and ways to reduce the potential errors during fractal analysis of each method.

  12. 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)

  13. Three-dimensional fractal geometry for gas permeation in microchannels

    NARCIS (Netherlands)

    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

  14. On Nonextensive Statistics, Chaos and Fractal Strings

    CERN Document Server

    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...

  15. Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors

    Science.gov (United States)

    Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.

    2017-11-01

    Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.

  16. Fractality and the law of the wall

    Science.gov (United States)

    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.

  17. Fractal Image Coding Based on a Fitting Surface

    Directory of Open Access Journals (Sweden)

    Sheng Bi

    2014-01-01

    Full Text Available A no-search fractal image coding method based on a fitting surface is proposed. In our research, an improved gray-level transform with a fitting surface is introduced. One advantage of this method is that the fitting surface is used for both the range and domain blocks and one set of parameters can be saved. Another advantage is that the fitting surface can approximate the range and domain blocks better than the previous fitting planes; this can result in smaller block matching errors and better decoded image quality. Since the no-search and quadtree techniques are adopted, smaller matching errors also imply less number of blocks matching which results in a faster encoding process. Moreover, by combining all the fitting surfaces, a fitting surface image (FSI is also proposed to speed up the fractal decoding. Experiments show that our proposed method can yield superior performance over the other three methods. Relative to range-averaged image, FSI can provide faster fractal decoding process. Finally, by combining the proposed fractal coding method with JPEG, a hybrid coding method is designed which can provide higher PSNR than JPEG while maintaining the same Bpp.

  18. Vector calculus in non-integer dimensional space and its applications to fractal media

    Science.gov (United States)

    Tarasov, Vasily E.

    2015-02-01

    We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are defined. For simplification we consider scalar and vector fields that are independent of angles. We formulate a generalization of vector calculus for rotationally covariant scalar and vector functions. This generalization allows us to describe fractal media and materials in the framework of continuum models with non-integer dimensional space. As examples of application of the suggested calculus, we consider elasticity of fractal materials (fractal hollow ball and fractal cylindrical pipe with pressure inside and outside), steady distribution of heat in fractal media, electric field of fractal charged cylinder. We solve the correspondent equations for non-integer dimensional space models.

  19. Fractal apertures in waveguides, conducting screens and cavities analysis and design

    CERN Document Server

    Ghosh, Basudeb; Kartikeyan, M V

    2014-01-01

    This book deals with the design and analysis of fractal apertures in waveguides, conducting screens and cavities using numerical electromagnetics and field-solvers. The aim is to obtain design solutions with improved accuracy for a wide range of applications. To achieve this goal, a few diverse problems are considered. The book is organized with adequate space dedicated for the design and analysis of fractal apertures in waveguides, conducting screens, and cavities, microwave/millimeter wave applications followed by detailed case-study problems to infuse better insight and understanding of the subject. Finally, summaries and suggestions are given for future work. Fractal geometries were widely used in electromagnetics, specifically for antennas and frequency selective surfaces (FSS). The self-similarity of fractal geometry gives rise to a multiband response, whereas the  space-filling nature of the fractal geometries makes it an efficient element in antenna and FSS unit cell miniaturization. Until now, no e...

  20. 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)

  1. Navigation performance in virtual environments varies with fractal dimension of landscape.

    Science.gov (United States)

    Juliani, Arthur W; Bies, Alexander J; Boydston, Cooper R; Taylor, Richard P; Sereno, Margaret E

    2016-09-01

    Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans' ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D. In Experiment 2, participants completed a map-reading and location-judgment task in separate sets of fractal landscapes. In both experiments, task performance was highest at the low-to-mid range of D, which was previously reported as most preferred and discriminable in studies of fractal aesthetics and discrimination, respectively, supporting a theory of visual fluency. The applicability of these findings to architecture, urban planning, and the general design of constructed spaces is discussed.

  2. 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

  3. Retinal vascular fractals predict long-term microvascular complications in type 1 diabetes mellitus

    DEFF Research Database (Denmark)

    Broe, Rebecca; Rasmussen, Malin L; Frydkjaer-Olsen, Ulrik

    2014-01-01

    : We included 180 patients with type 1 diabetes in a 16 year follow-up study. In baseline retinal photographs (from 1995), all vessels in a zone 0.5-2.0 disc diameters from the disc margin were traced using Singapore Institute Vessel Assessment-Fractal image analysis software. Artefacts were removed......AIMS/HYPOTHESIS: Fractal analysis of the retinal vasculature provides a global measure of the complexity and density of retinal vessels summarised as a single variable: the fractal dimension. We investigated fractal dimensions as long-term predictors of microvasculopathy in type 1 diabetes. METHODS....... Retinal fractal analysis therefore is a potential tool for risk stratification in type 1 diabetes....

  4. 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

  5. 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)

  6. Spatial patterns of aquatic habitat richness in the Upper Mississippi River floodplain, USA

    Science.gov (United States)

    De Jager, Nathan R.; Rohweder, Jason J.

    2012-01-01

    Interactions among hydrology and geomorphology create shifting mosaics of aquatic habitat patches in large river floodplains (e.g., main and side channels, floodplain lakes, and shallow backwater areas) and the connectivity among these habitat patches underpins high levels of biotic diversity and productivity. However, the diversity and connectivity among the habitats of most floodplain rivers have been negatively impacted by hydrologic and structural modifications that support commercial navigation and control flooding. We therefore tested the hypothesis that the rate of increase in patch richness (# of types) with increasing scale reflects anthropogenic modifications to habitat diversity and connectivity in a large floodplain river, the Upper Mississippi River (UMR). To do this, we calculated the number of aquatic habitat patch types within neighborhoods surrounding each of the ≈19 million 5-m aquatic pixels of the UMR for multiple neighborhood sizes (1–100 ha). For all of the 87 river-reach focal areas we examined, changes in habitat richness (R) with increasing neighborhood length (L, # pixels) were characterized by a fractal-like power function R = Lz (R2 > 0.92 (P z) measures the rate of increase in habitat richness with neighborhood size and is related to a fractal dimension. Variation in z reflected fundamental changes to spatial patterns of aquatic habitat richness in this river system. With only a few exceptions, z exceeded the river-wide average of 0.18 in focal areas where side channels, contiguous floodplain lakes, and contiguous shallow-water areas exceeded 5%, 5%, and 10% of the floodplain respectively. In contrast, z was always less than 0.18 for focal areas where impounded water exceeded 40% of floodplain area. Our results suggest that rehabilitation efforts that target areas with <5% of the floodplain in side channels, <5% in floodplain lakes, and/or <10% in shallow-water areas could improve habitat diversity across multiple scales in the UMR.

  7. 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 ...

  8. Fractales y series de datos geofísicos

    Directory of Open Access Journals (Sweden)

    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.

  9. Fractal dimensions of silica gels generated using reactive molecular dynamics simulations

    International Nuclear Information System (INIS)

    Bhattacharya, Sudin; Kieffer, John

    2005-01-01

    We have used molecular dynamics simulations based on a three-body potential with charge transfer to generate nanoporous silica aerogels. Care was taken to reproduce the sol-gel condensation reaction that forms the gel backbone as realistically as possible and to thereby produce credible gel structures. The self-similarity of aerogel structures was investigated by evaluating their fractal dimension from geometric correlations. For comparison, we have also generated porous silica glasses by rupturing dense silica and computed their fractal dimension. The fractal dimension of the porous silica structures was found to be process dependent. Finally, we have determined that the effect of supercritical drying on the fractal nature of condensed silica gels is not appreciable

  10. Bony change of apical lesion healing process using fractal analysis

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo [Yonsei University College of Medicine, Seoul (Korea, Republic of)

    2005-06-15

    To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L{sub 0}) is 0.940 {+-} 0.361 and that of normal area (N{sub 0}) is 1.186 {+-} 0.727 (p<0.05). Fractal dimension at apical lesion of 6 months after endodontic treatment (L{sub 1}) is 1.076 {+-} 0.069 and that of normal area (N{sub 1}) is 1.192 {+-} 0.055 (p<0.05). Fractal dimension at apical lesion of 1 year after endodontic treatment (L{sub 2}) is 1.163 {+-} 0.074 and that of normal area (N{sub 2}) is 1.225 {+-} 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.

  11. 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.)

  12. 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.)

  13. A simple method for estimating the size of nuclei on fractal surfaces

    Science.gov (United States)

    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.

  14. Fractal Globule as a model of DNA folding in eukaryotes

    Science.gov (United States)

    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.

  15. Aqueous synthesis of LiFePO4 with Fractal Granularity

    Science.gov (United States)

    Cabán-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; Gómez-Romero, Pedro

    2016-06-01

    Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to high tap density electrodes, which is beneficial for energy density. These intricate structures could be easily and effectively coated with a thin and uniform carbon layer for increased conductivity, as it is well established for simpler microstructures. Materials and electrodes were studied by means of XRD, SEM, TEM, SAED, XPS, Raman and TGA. Last but not least, lithium transport through fractal LiFePO4 electrodes was investigated based upon fractal theory. These water-made fractal electrodes lead to high-performance lithium cells (even at high rates) tested by CV and galvanostatic charge-discharge, their performance is comparable to state of the art (but less environmentally friendly) electrodes.

  16. Electrical conductivity modeling in fractal non-saturated porous media

    Science.gov (United States)

    Wei, W.; Cai, J.; Hu, X.; Han, Q.

    2016-12-01

    The variety of electrical conductivity in non-saturated conditions is important to study electric conduction in natural sedimentary rocks. The electrical conductivity in completely saturated porous media is a porosity-function representing the complex connected behavior of single conducting phases (pore fluid). For partially saturated conditions, the electrical conductivity becomes even more complicated since the connectedness of pore. Archie's second law is an empirical electrical conductivity-porosity and -saturation model that has been used to predict the formation factor of non-saturated porous rock. However, the physical interpretation of its parameters, e.g., the cementation exponent m and the saturation exponent n, remains questionable. On basis of our previous work, we combine the pore-solid fractal (PSF) model to build an electrical conductivity model in non-saturated porous media. Our theoretical porosity- and saturation-dependent models contain endmember properties, such as fluid electrical conductivities, pore fractal dimension and tortuosity fractal dimension (representing the complex degree of electrical flowing path). We find the presented model with non-saturation-dependent electrical conductivity datasets indicate excellent match between theory and experiments. This means the value of pore fractal dimension and tortuosity fractal dimension change from medium to medium and depends not only on geometrical properties of pore structure but also characteristics of electrical current flowing in the non-saturated porous media.

  17. Fractal geometry in an expanding, one-dimensional, Newtonian universe.

    Science.gov (United States)

    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.

  18. Computer Security: The dilemma of fractal defence

    CERN Multimedia

    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...

  19. Lectures on fractal geometry and dynamical systems

    CERN Document Server

    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...

  20. Comprehensive model-based prediction of micropollutants from diffuse sources in the Swiss river network

    Science.gov (United States)

    Strahm, Ivo; Munz, Nicole; Braun, Christian; Gälli, René; Leu, Christian; Stamm, Christian

    2014-05-01

    Water quality in the Swiss river network is affected by many micropollutants from a variety of diffuse sources. This study compares, for the first time, in a comprehensive manner the diffuse sources and the substance groups that contribute the most to water contamination in Swiss streams and highlights the major regions for water pollution. For this a simple but comprehensive model was developed to estimate emission from diffuse sources for the entire Swiss river network of 65 000 km. Based on emission factors the model calculates catchment specific losses to streams for more than 15 diffuse sources (such as crop lands, grassland, vineyards, fruit orchards, roads, railways, facades, roofs, green space in urban areas, landfills, etc.) and more than 130 different substances from 5 different substance groups (pesticides, biocides, heavy metals, human drugs, animal drugs). For more than 180 000 stream sections estimates of mean annual pollutant loads and mean annual concentration levels were modeled. This data was validated with a set of monitoring data and evaluated based on annual average environmental quality standards (AA-EQS). Model validation showed that the estimated mean annual concentration levels are within the range of measured data. Therefore simulations were considered as adequately robust for identifying the major sources of diffuse pollution. The analysis depicted that in Switzerland widespread pollution of streams can be expected. Along more than 18 000 km of the river network one or more simulated substances has a concentration exceeding the AA-EQS. In single stream sections it could be more than 50 different substances. Moreover, the simulations showed that in two-thirds of small streams (Strahler order 1 and 2) at least one AA-EQS is always exceeded. The highest number of substances exceeding the AA-EQS are in areas with large fractions of arable cropping, vineyards and fruit orchards. Urban areas are also of concern even without considering

  1. Assessment of disintegrant efficacy with fractal dimensions from real-time MRI.

    Science.gov (United States)

    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.

  2. Potential interaction between transport and stream networks over the lowland rivers in Eastern India.

    Science.gov (United States)

    Roy, Suvendu; Sahu, Abhay Sankar

    2017-07-15

    Extension of transport networks supports good accessibility and associated with the development of a region. However, transport lines have fragmented the regional landscape and disturbed the natural interplay between rivers and their floodplains. Spatial analysis using multiple buffers provides information about the potential interaction between road and stream networks and their impact on channel morphology of a small watershed in the Lower Gangetic Plain. Present study is tried to understand the lateral and longitudinal disconnection in headwater stream by rural roads with the integration of geoinformatics and field survey. Significant (p development, delineation of stream corridor, regular monitoring and engineering efficiency for the construction of road and road-stream crossing might be effective in managing river geomorphology and riverine landscape. Copyright © 2017 Elsevier Ltd. All rights reserved.

  3. 'HYDROTELERAY-MINITEL', the French national network for the radiological survey of the rivers

    International Nuclear Information System (INIS)

    Linden, G.

    1998-01-01

    The HYDROTELERAY network allows the continuous measurement of radioactivity in the rivers stream. It currently comprises five measuring stations. Each one includes: an autonomous measuring line; a probe immersed in a 25-litre stainless steel tank; the tank is supplied with water from the river; an hydro-collector allowing to take a sample of water directly from the tank if an alarm happens; a PC containing an 'ACCUSPEC INa PLUS' data acquisition card for the INa measurements as well as a MODEM card to transmit data to the central managing unit. (R.P.)

  4. Fractal fluctuations in spatiotemporal variables when walking on a self-paced treadmill.

    Science.gov (United States)

    Choi, Jin-Seung; Kang, Dong-Won; Seo, Jeong-Woo; Tack, Gye-Rae

    2017-12-08

    This study investigated the fractal dynamic properties of stride time (ST), stride length (SL) and stride speed (SS) during walking on a self-paced treadmill (STM) in which the belt speed is automatically controlled by the walking speed. Twelve healthy young subjects participated in the study. The subjects walked at their preferred walking speed under four conditions: STM, STM with a metronome (STM+met), fixed-speed (conventional) treadmill (FTM), and FTM with a metronome (FTM+met). To compare the fractal dynamics between conditions, the mean, variability, and fractal dynamics of ST, SL, and SS were compared. Moreover, the relationship among the variables was examined under each walking condition using three types of surrogates. The mean values of all variables did not differ between the two treadmills, and the variability of all variables was generally larger for STM than for FTM. The use of a metronome resulted in a decrease in variability in ST and SS for all conditions. The fractal dynamic characteristics of SS were maintained with STM, in contrast to FTM, and only the fractal dynamic characteristics of ST disappeared when using a metronome. In addition, the fractal dynamic patterns of the cross-correlated surrogate results were identical to those of all variables for the two treadmills. In terms of the fractal dynamic properties, STM walking was generally closer to overground walking than FTM walking. Although further research is needed, the present results will be useful in research on gait fractal dynamics and rehabilitation. Copyright © 2017 Elsevier Ltd. All rights reserved.

  5. Fractal Hypothesis of the Pelagic Microbial Ecosystem—Can Simple Ecological Principles Lead to Self-Similar Complexity in the Pelagic Microbial Food Web?

    Science.gov (United States)

    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

  6. Multi-fractal analysis of highway traffic data

    Institute of Scientific and Technical Information of China (English)

    Shang Peng-Jian; Shen Jin-Sheng

    2007-01-01

    The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwise H(o)lder exponent of a function is calculated by developing an algorithm for the numerical evaluation of H(o)lder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.

  7. Fractal Theory for Permeability Prediction, Venezuelan and USA Wells

    Science.gov (United States)

    Aldana, Milagrosa; Altamiranda, Dignorah; Cabrera, Ana

    2014-05-01

    Inferring petrophysical parameters such as permeability, porosity, water saturation, capillary pressure, etc, from the analysis of well logs or other available core data has always been of critical importance in the oil industry. Permeability in particular, which is considered to be a complex parameter, has been inferred using both empirical and theoretical techniques. The main goal of this work is to predict permeability values on different wells using Fractal Theory, based on a method proposed by Pape et al. (1999). This approach uses the relationship between permeability and the geometric form of the pore space of the rock. This method is based on the modified equation of Kozeny-Carman and a fractal pattern, which allows determining permeability as a function of the cementation exponent, porosity and the fractal dimension. Data from wells located in Venezuela and the United States of America are analyzed. Employing data of porosity and permeability obtained from core samples, and applying the Fractal Theory method, we calculated the prediction equations for each well. At the beginning, this was achieved by training with 50% of the data available for each well. Afterwards, these equations were tested inferring over 100% of the data to analyze possible trends in their distribution. This procedure gave excellent results in all the wells in spite of their geographic distance, generating permeability models with the potential to accurately predict permeability logs in the remaining parts of the well for which there are no core samples, using even porority logs. Additionally, empirical models were used to determine permeability and the results were compared with those obtained by applying the fractal method. The results indicated that, although there are empirical equations that give a proper adjustment, the prediction results obtained using fractal theory give a better fit to the core reference data.

  8. The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction.

    Science.gov (United States)

    Najafi, Elham; Darooneh, Amir H

    2015-01-01

    A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.

  9. The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction

    Science.gov (United States)

    Najafi, Elham; Darooneh, Amir H.

    2015-01-01

    A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction. PMID:26091207

  10. Contextualizing Wetlands Within a River Network to Assess Nitrate Removal and Inform Watershed Management

    Science.gov (United States)

    Czuba, Jonathan A.; Hansen, Amy T.; Foufoula-Georgiou, Efi; Finlay, Jacques C.

    2018-02-01

    Aquatic nitrate removal depends on interactions throughout an interconnected network of lakes, wetlands, and river channels. Herein, we present a network-based model that quantifies nitrate-nitrogen and organic carbon concentrations through a wetland-river network and estimates nitrate export from the watershed. This model dynamically accounts for multiple competing limitations on nitrate removal, explicitly incorporates wetlands in the network, and captures hierarchical network effects and spatial interactions. We apply the model to the Le Sueur Basin, a data-rich 2,880 km2 agricultural landscape in southern Minnesota and validate the model using synoptic field measurements during June for years 2013-2015. Using the model, we show that the overall limits to nitrate removal rate via denitrification shift between nitrate concentration, organic carbon availability, and residence time depending on discharge, characteristics of the waterbody, and location in the network. Our model results show that the spatial context of wetland restorations is an important but often overlooked factor because nonlinearities in the system, e.g., deriving from switching of resource limitation on denitrification rate, can lead to unexpected changes in downstream biogeochemistry. Our results demonstrate that reduction of watershed-scale nitrate concentrations and downstream loads in the Le Sueur Basin can be most effectively achieved by increasing water residence time (by slowing the flow) rather than by increasing organic carbon concentrations (which may limit denitrification). This framework can be used toward assessing where and how to restore wetlands for reducing nitrate concentrations and loads from agricultural watersheds.

  11. Model to estimate fractal dimension for ion-bombarded materials

    Energy Technology Data Exchange (ETDEWEB)

    Hu, A., E-mail: hu77@purdue.edu; Hassanein, A.

    2014-03-15

    Comprehensive fractal Monte Carlo model ITMC-F (Hu and Hassanein, 2012 [1]) is developed based on the Monte Carlo ion bombardment simulation code, i.e., Ion Transport in Materials and Compounds (ITMC) code (Hassanein, 1985 [2]). The ITMC-F studies the impact of surface roughness on the angular dependence of sputtering yield. Instead of assuming material surfaces to be flat or composed of exact self-similar fractals in simulation, we developed a new method to describe the surface shapes. Random fractal surfaces which are generated by midpoint displacement algorithm and support vector machine algorithm are combined with ITMC. With this new fractal version of ITMC-F, we successfully simulated the angular dependence of sputtering yield for various ion-target combinations, with the input surface roughness exponent directly depicted from experimental data (Hu and Hassanein, 2012 [1]). The ITMC-F code showed good agreement with the experimental data. In advanced, we compare other experimental sputtering yield with the results from ITMC-F to estimate the surface roughness exponent for ion-bombarded material in this research.

  12. [Modeling continuous scaling of NDVI based on fractal theory].

    Science.gov (United States)

    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.

  13. Evolution of fractality in space plasmas of interest to geomagnetic activity

    Science.gov (United States)

    Muñoz, Víctor; Domínguez, Macarena; Alejandro Valdivia, Juan; Good, Simon; Nigro, Giuseppina; Carbone, Vincenzo

    2018-03-01

    We studied the temporal evolution of fractality for geomagnetic activity, by calculating fractal dimensions from the Dst data and from a magnetohydrodynamic shell model for turbulent magnetized plasma, which may be a useful model to study geomagnetic activity under solar wind forcing. We show that the shell model is able to reproduce the relationship between the fractal dimension and the occurrence of dissipative events, but only in a certain region of viscosity and resistivity values. We also present preliminary results of the application of these ideas to the study of the magnetic field time series in the solar wind during magnetic clouds, which suggest that it is possible, by means of the fractal dimension, to characterize the complexity of the magnetic cloud structure.

  14. Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems

    NARCIS (Netherlands)

    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

  15. Navigation performance in virtual environments varies with fractal dimension of landscape

    OpenAIRE

    Juliani, Arthur W.; Bies, Alexander J.; Boydston, Cooper R.; Taylor, Richard P.; Sereno, Margaret E.

    2016-01-01

    Fractal geometry has been used to describe natural and built environments, but has yet to be studied in navigational research. In order to establish a relationship between the fractal dimension (D) of a natural environment and humans’ ability to navigate such spaces, we conducted two experiments using virtual environments that simulate the fractal properties of nature. In Experiment 1, participants completed a goal-driven search task either with or without a map in landscapes that varied in D...

  16. Effect of exposure time and image resolution on fractal dimension

    International Nuclear Information System (INIS)

    An, Byung Mo; Heo, Min Suk; Lee, Seung Pyo; Lee, Sam Sun; Choi, Soon Chul; Park, Tae Won; Kim, Jong Dae

    2002-01-01

    To evaluate the effect of exposure time and image resolution on fractal dimension calculations for determining the optimal range of these two variances. Thirty-one radiographs of the mandibular angle area of sixteen human dry mandibles were taken at different exposure times (0.01, 0.08, 0.16, 0.25, 0.40, 0.64, and 0.80 s). Each radiograph was digitized at 1200 dpi, 8 bit, 256 gray level using a film scanner. We selected an Region of Interest (ROI) that corresponded to the same region as in each radiograph, but the resolution of ROI was degraded to 1000, 800, 600, 500, 400, 300, 200, and 100 dpi. The fractal dimension was calculated by using the tile-counting method for each image, and the calculated values were then compared statistically. As the exposure time and the image resolution increased, the mean value of the fractal dimension decreased, except the case where exposure time was set at 0.01 seconds (alpha = 0.05). The exposure time and image resolution affected the fractal dimension by interaction (p<0.001). When the exposure time was set to either 0.64 seconds or 0.80 seconds, the resulting fractal dimensions were lower, irrespective of image resolution, than at shorter exposure times (alpha = 0.05). The optimal range for exposure time and resolution was determined to be 0.08-0.40 seconds and from 400-1000 dpi, respectively. Adequate exposure time and image resolution is essential for acquiring the fractal dimension using tile-counting method for evaluation of the mandible.

  17. Fractal-Based Analysis of the Influence of Music on Human Respiration

    Science.gov (United States)

    Reza Namazi, H.

    An important challenge in respiration related studies is to investigate the influence of external stimuli on human respiration. Auditory stimulus is an important type of stimuli that influences human respiration. However, no one discovered any trend, which relates the characteristics of the auditory stimuli to the characteristics of the respiratory signal. In this paper, we investigate the correlation between auditory stimuli and respiratory signal from fractal point of view. We found out that the fractal structure of respiratory signal is correlated with the fractal structure of the applied music. Based on the obtained results, the music with greater fractal dimension will result in respiratory signal with smaller fractal dimension. In order to verify this result, we benefit from approximate entropy. The results show the respiratory signal will have smaller approximate entropy by choosing the music with smaller approximate entropy. The method of analysis could be further investigated to analyze the variations of different physiological time series due to the various types of stimuli when the complexity is the main concern.

  18. 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

  19. Fractals and humor

    Science.gov (United States)

    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...

  20. Removal of terrestrial DOC in aquatic ecosystems of a temperate river network

    Science.gov (United States)

    Wollheim, W.M.; Stewart, R. J.; Aiken, George R.; Butler, Kenna D.; Morse, Nathaniel B.; Salisbury, J.

    2015-01-01

    Surface waters play a potentially important role in the global carbon balance. Dissolved organic carbon (DOC) fluxes are a major transfer of terrestrial carbon to river systems, and the fate of DOC in aquatic systems is poorly constrained. We used a unique combination of spatially distributed sampling of three DOC fractions throughout a river network and modeling to quantify the net removal of terrestrial DOC during a summer base flow period. We found that aquatic reactivity of terrestrial DOC leading to net loss is low, closer to conservative chloride than to reactive nitrogen. Net removal occurred mainly from the hydrophobic organic acid fraction, while hydrophilic and transphilic acids showed no net change, indicating that partitioning of bulk DOC into different fractions is critical for understanding terrestrial DOC removal. These findings suggest that river systems may have only a modest ability to alter the amounts of terrestrial DOC delivered to coastal zones.