Analysis of a Model for the Morphological Structure of Renal Arterial Tree: Fractal Structure
Directory of Open Access Journals (Sweden)
Aurora Espinoza-Valdez
2013-01-01
experimental data measurements of the rat kidneys. The fractal dimension depends on the probability of sprouting angiogenesis in the development of the arterial vascular tree of the kidney, that is, of the distribution of blood vessels in the morphology generated by the analytical model. The fractal dimension might determine whether a suitable renal vascular structure is capable of performing physiological functions under appropriate conditions. The analysis can describe the complex structures of the development vasculature in kidney.
Transient flow model and pressure dynamic features of tree-shaped fractal re- servoirs
Institute of Scientific and Technical Information of China (English)
TAN Xiao-hua; LI Xiao-ping
2014-01-01
A transient flow model of tree-shaped fractal reservoirs is built by embedding a fracture network simulated by a tree-shaped fractal network into a matrix system. The model can be solved using the Laplace conversion method. The dimensionless bottom hole pressure can be obtained using the Stehfest numerical inversion method. The bi-logarithmic type curves for the tree-shaped fractal reservoirs are thus obtained. The pressure transient responses under different fractal factors are discussed. The factors with a primary effect on the inter-porosity flow regime include the initial branch numberN, the length ratioα, and the branch angleθ. The diameter ratioβ has a significant effect on the fracture radial flow, the inter-porosity and the total system radial flow regimes. The total branch levelM of the network mainly influences the total system radial flow regime. The model presented in this paper provides a new methodology for analyzing and predicting the pressure dynamic characteristics of naturally fractured reservoirs.
Combinatorial fractal Brownian motion model
Institute of Scientific and Technical Information of China (English)
朱炬波; 梁甸农
2000-01-01
To solve the problem of how to determine the non-scaled interval when processing radar clutter using fractal Brownian motion (FBM) model, a concept of combinatorial FBM model is presented. Since the earth (or sea) surface varies diversely with space, a radar clutter contains several fractal structures, which coexist on all scales. Taking the combination of two FBMs into account, via theoretical derivation we establish a combinatorial FBM model and present a method to estimate its fractal parameters. The correctness of the model and the method is proved by simulation experiments and computation of practial data. Furthermore, we obtain the relationship between fractal parameters when processing combinatorial model with a single FBM model. Meanwhile, by theoretical analysis it is concluded that when combinatorial model is observed on different scales, one of the fractal structures is more obvious.
Counting spanning trees on fractal graphs and their asymptotic complexity
Anema, Jason A.; Tsougkas, Konstantinos
2016-09-01
Using the method of spectral decimation and a modified version of Kirchhoff's matrix-tree theorem, a closed form solution to the number of spanning trees on approximating graphs to a fully symmetric self-similar structure on a finitely ramified fractal is given in theorem 3.4. We show how spectral decimation implies the existence of the asymptotic complexity constant and obtain some bounds for it. Examples calculated include the Sierpiński gasket, a non-post critically finite analog of the Sierpiński gasket, the Diamond fractal, and the hexagasket. For each example, the asymptotic complexity constant is found.
Consequences of the fractal architecture of trees on their structural measures.
Pluciński, Mateusz; Pluciński, Szymon; Rodríguez-Iturbe, Ignacio
2008-03-07
While the mechanics of trees are well known, a systematic and comprehensive study of the mechanical consequences of a tree's fractal structure has been lacking. Here, we analyze the structure of botanical trees using computer modeling and show that many relevant measures of support throughout all the branches of a tree follow specific patterns which can be described by characteristic probability distributions and well-defined spatial relationships. Most notably, moments, forces, and axial and shear stresses throughout the different branches all exhibit power-law distributions. These results suggest a new approach to the study of the mechanics of trees, one accounting for the implications of the above results.
Mayo, Michael; Pfeifer, Peter; Gheorghiu, Stefan
2008-03-01
The acinar airways lie at the periphery of the human lung and are responsible for the transfer of oxygen from air to the blood during respiration. This transfer occurs by the diffusion-reaction of oxygen over the irregular surface of the alveolar membranes lining the acinar airways. We present an exactly solvable diffusion-reaction model on a hierarchically branched tree, allowing a quantitative prediction of the oxygen current over the entire system of acinar airways responsible for the gas exchange. We discuss the effect of diffusional screening, which is strongly coupled to oxygen transport in the human lung. We show that the oxygen current is insensitive to a loss of permeability of the alveolar membranes over a wide range of permeabilities, similar to a ``constant-current source'' in an electric network. Such fault tolerance has been observed in other treatments of the gas exchange in the lung and is obtained here as a fully analytical result.
a Fractal Network Model for Fractured Porous Media
Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung
2016-04-01
The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.
Fractal Models of Earthquake Dynamics
Bhattacharya, Pathikrit; Kamal,; Samanta, Debashis
2009-01-01
Our understanding of earthquakes is based on the theory of plate tectonics. Earthquake dynamics is the study of the interactions of plates (solid disjoint parts of the lithosphere) which produce seismic activity. Over the last about fifty years many models have come up which try to simulate seismic activity by mimicking plate plate interactions. The validity of a given model is subject to the compliance of the synthetic seismic activity it produces to the well known empirical laws which describe the statistical features of observed seismic activity. Here we present a review of two such models of earthquake dynamics with main focus on a relatively new model namely The Two Fractal Overlap Model.
Fractal model of anomalous diffusion.
Gmachowski, Lech
2015-12-01
An equation of motion is derived from fractal analysis of the Brownian particle trajectory in which the asymptotic fractal dimension of the trajectory has a required value. The formula makes it possible to calculate the time dependence of the mean square displacement for both short and long periods when the molecule diffuses anomalously. The anomalous diffusion which occurs after long periods is characterized by two variables, the transport coefficient and the anomalous diffusion exponent. An explicit formula is derived for the transport coefficient, which is related to the diffusion constant, as dependent on the Brownian step time, and the anomalous diffusion exponent. The model makes it possible to deduce anomalous diffusion properties from experimental data obtained even for short time periods and to estimate the transport coefficient in systems for which the diffusion behavior has been investigated. The results were confirmed for both sub and super-diffusion.
Fractal Model of the Spheroidal Graphite
Institute of Scientific and Technical Information of China (English)
Z.Y.HE; K.Z.HWANG
1996-01-01
In this paper,a fractal model about the microstructure of spheroidal-graphite is presented through the research on the surface form and the analysis to microregion.The fractal dimension is calculated and the forming mechanism is also discussed.
Fractal basins in an ecological model
Directory of Open Access Journals (Sweden)
I. Djellit
2013-09-01
Full Text Available Complex dynamics is detected in an ecological model of host-parasitoid interaction. It illustrates fractalization of basins with self-similarity and chaotic attractors. This paper describes these dynamic behaviors, bifurcations, and chaos. Fractals basins are displayed by numerical simulations.
Tikhonov, K. Â. S.; Mirlin, A. Â. D.
2016-11-01
We investigate analytically and numerically eigenfunction statistics in a disordered system on a finite Bethe lattice (Cayley tree). We show that the wave-function amplitude at the root of a tree is distributed fractally in a large part of the delocalized phase. The fractal exponents are expressed in terms of the decay rate and the velocity in a problem of propagation of a front between unstable and stable phases. We demonstrate a crucial difference between a loopless Cayley tree and a locally treelike structure without a boundary (random regular graph) where extended wave functions are ergodic.
Fractal modeling of natural fracture networks
Energy Technology Data Exchange (ETDEWEB)
Ferer, M.; Dean, B.; Mick, C.
1995-06-01
West Virginia University will implement procedures for a fractal analysis of fractures in reservoirs. This procedure will be applied to fracture networks in outcrops and to fractures intersecting horizontal boreholes. The parameters resulting from this analysis will be used to generate synthetic fracture networks with the same fractal characteristics as the real networks. Recovery from naturally fractured, tight-gas reservoirs is controlled by the fracture network. Reliable characterization of the actual fracture network in the reservoir is severely limited. The location and orientation of fractures intersecting the borehole can be determined, but the length of these fractures cannot be unambiguously determined. Because of the lack of detailed information about the actual fracture network, modeling methods must represent the porosity and permeability associated with the fracture network, as accurately as possible with very little a priori information. In the sections following, the authors will (1) present fractal analysis of the MWX site, using the box-counting procedure; (2) review evidence testing the fractal nature of fracture distributions and discuss the advantages of using the fractal analysis over a stochastic analysis; and (3) present an efficient algorithm for producing a self-similar fracture networks which mimic the real MWX outcrop fracture network.
Modeling Fractal Dimension Curve of Urban Growth in Developing Countries
Chen, Yanguang
2016-01-01
The growth curve of fractal dimension of cities can be described with sigmoid function such as Boltzmann's equation and logistic function. The logistic models of fractal dimension curves have been presented for the cities in developed countries. However, these models cannot be well fitted to the observational data of fractal dimension of urban form in developing countries (e.g. China). By statistic experiments of fractal parameters, we find that the quadratic Boltzmann's equation can be used to describe fractal dimension change of Chinese cities. For the normalized fractal dimension values, the Boltzmann's equation can be reduced to a quadratic logistic function. In practice, a fractal dimension dataset of urban growth can be approximately fitted with the quadratic logistic function. Thus, a series of models of fractal dimension curve can be proposed for the cities in developing countries. The models are applied to the city of Beijing, Chinese capital, and yield satisfying trend lines of the observational dat...
Modeling Soil Water Retention Curve with a Fractal Method
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
Many empirical models have been developed to describe the soil water retention curve (SWRC). In this study, a fractal model for SWRC was derived with a specially constructed Menger sponge to describe the fractal scaling behavior of soil; relationships were established among the fractal dimension of SWRC, the fractal dimension of soil mass, and soil texture; and the model was used to estimate SWRC with the estimated results being compared to experimental data for verification. The derived fractal model was in a power-law form, similar to the Brooks-Corey and Campbell empirical functions. Experimental data of particle size distribution (PSD), texture, and soil water retention for 10 soils collected at different places in China were used to estimate the fractal dimension of SWRC and the mass fractal dimension. The fractal dimension of SWRC and the mass fractal dimension were linearly related. Also, both of the fractal dimensions were dependent on soil texture, i.e., clay and sand contents. Expressions were proposed to quantify the relationships. Based on the relationships, four methods were used to determine the fractal dimension of SWRC and the model was applied to estimate soil water content at a wide range of tension values. The estimated results compared well with the measured data having relative errors less than 10% for over 60% of the measurements. Thus, this model, estimating the fractal dimension using soil textural data, offered an alternative for predicting SWRC.
Modelo fractal de substâncias húmicas Fractal model of humic substances
Directory of Open Access Journals (Sweden)
Alessandro Costa da Silva
2001-10-01
Full Text Available A teoria fractal, por meio da determinação da dimensão fractal (D, tem sido considerada como uma alternativa para explicar a conforma��ão de agregados moleculares. Sua utilização no estudo de substâncias húmicas (SH reside na tentativa de descrever (representar a estrutura ramificada ou a superfície rugosa e distorcida destas substâncias. A presença de um modelo fractal por sistemas naturais implica que este pode ser decomposto em partes, em que cada uma, subseqüentemente, é cópia do todo. Do ponto de vista experimental, a dimensão fractal de sistemas húmicos pode ser determinada a partir de técnicas como turbidimetria, raios x, espalhamento de neutrons, dentre outras. Este trabalho pretende facilitar o entendimento sobre a aplicação de fractais ao estudo conformacional de SH, introduzindo conceitos e informações sobre o fundamento dos modelos fractais, bem como sobre o uso da técnica turbidimétrica na determinação do valor D.Fractal theoria application by determination of fractal dimension has been considered an alternative tool to explain the conformation of molecular aggregates. Its utilization in the study of humic substances (HS aims the attempt to describe the limbed structure or the rugous and distorced surface of these substances. The presence of fractal models indicates that the system may be decomposed in parts, each part being a copy of the whole. In the experimental point of view the fractals models of natural systems may be measured through techniques as turbidimetry, x- ray and neutrons scattering. This paper seeks to facilitate the understanding on the application of the fractals in the conformational study of HS, supply information about fractal models foundation and use of the turbidimetry in the determination of fractal dimension.
Fractality à la carte: a general particle aggregation model
Nicolás-Carlock, J. R.; Carrillo-Estrada, J. L.; Dossetti, V.
2016-01-01
In nature, fractal structures emerge in a wide variety of systems as a local optimization of entropic and energetic distributions. The fractality of these systems determines many of their physical, chemical and/or biological properties. Thus, to comprehend the mechanisms that originate and control the fractality is highly relevant in many areas of science and technology. In studying clusters grown by aggregation phenomena, simple models have contributed to unveil some of the basic elements that give origin to fractality, however, the specific contribution from each of these elements to fractality has remained hidden in the complex dynamics. Here, we propose a simple and versatile model of particle aggregation that is, on the one hand, able to reveal the specific entropic and energetic contributions to the clusters’ fractality and morphology, and, on the other, capable to generate an ample assortment of rich natural-looking aggregates with any prescribed fractal dimension.
Fractal Derivative Model for Air Permeability in Hierarchic Porous Media
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Jie Fan
2012-01-01
Full Text Available Air permeability in hierarchic porous media does not obey Fick's equation or its modification because fractal objects have well-defined geometric properties, which are discrete and discontinuous. We propose a theoretical model dealing with, for the first time, a seemingly complex air permeability process using fractal derivative method. The fractal derivative model has been successfully applied to explain the novel air permeability phenomenon of cocoon. The theoretical analysis was in agreement with experimental results.
SANS spectra of the fractal supernucleosomal chromatin structure models
Ilatovskiy, Andrey V.; Lebedev, Dmitry V.; Filatov, Michael V.; Petukhov, Michael G.; Isaev-Ivanov, Vladimir V.
2012-03-01
The eukaryotic genome consists of chromatin—a nucleoprotein complex with hierarchical architecture based on nucleosomes, the organization of higher-order chromatin structures still remains unknown. Available experimental data, including SANS spectra we had obtained for whole nuclei, suggested fractal nature of chromatin. Previously we had built random-walk supernucleosomal models (up to 106 nucleosomes) to interpret our SANS spectra. Here we report a new method to build fractal supernucleosomal structure of a given fractal dimension or two different dimensions. Agreement between calculated and experimental SANS spectra was significantly improved, especially for model with two fractal dimensions—3 and 2.
Modelling Fractal Growth of Bacillus subtilis on Agar Plates
Fogedby, Hans C.
1991-02-01
The observed fractal growth of a bacterial colony of Bacillus subtilis on agar plates is simulated by a simple computer model in two dimensions. Growth morphologies are shown and the fractal dimension is computed. The concentration of nutrients and the time scale ratio of bacterial multiplication and nutrient diffusion are the variable parameters in the model. Fractal growth is observed in the simulations for moderate concentrations and time scale ratios. The simulated morphologies are similar to the ones grown in the biological experiment. The phenomenon is analogous to the fractal morphologies of lipid layers grown on a water surface.
Potts model partition functions on two families of fractal lattices
Gong, Helin; Jin, Xian'an
2014-11-01
The partition function of q-state Potts model, or equivalently the Tutte polynomial, is computationally intractable for regular lattices. The purpose of this paper is to compute partition functions of q-state Potts model on two families of fractal lattices. Based on their self-similar structures and by applying the subgraph-decomposition method, we divide their Tutte polynomials into two summands, and for each summand we obtain a recursive formula involving the other summand. As a result, the number of spanning trees and their asymptotic growth constants, and a lower bound of the number of connected spanning subgraphs or acyclic root-connected orientations for each of such two lattices are obtained.
Fractal Modeling and Scaling in Natural Systems - Editorial
The special issue of Ecological complexity journal on Fractal Modeling and Scaling in Natural Systems contains representative examples of the status and evolution of data-driven research into fractals and scaling in complex natural systems. The editorial discusses contributions to understanding rela...
A fractal model of the Universe
Gottlieb, Ioan
The book represents a revisioned, extended, completed and translated version of the book "Superposed Universes. A scientific novel and a SF story" (1995). The book contains a hypothesis by the author concerning the complexity of the Nature. An introduction to the theories of numbers, manyfolds and topology is given. The possible connection with the theory of evolution of the Universe is discussed. The book contains also in the last chapter a SF story based on the hypothesis presented. A connection with fractals theory is given. A part of his earlier studies (1955-1956) were subsequently published without citation by Ali Kyrala (Phys. Rev. vol.117, No.5, march 1, 1960). The book contains as an important appendix the early papers (some of which are published in the coauthoprship with his scientific advisors): 1) T.T. Vescan, A. Weiszmann and I.Gottlieb, Contributii la studiul problemelor geometrice ale teoriei relativitatii restranse. Academia R.P.R. Baza Timisoara. Lucrarile consfatuirii de geometrie diferentiala din 9-12 iunie 1955. In this paper the authors show a new method of the calculation of the metrics. 2) Jean Gottlieb, L'hyphotese d'un modele de la structure de la matiere, Revista Matematica y Fisica Teorica, Serie A, Volumen XY, No.1, y.2, 1964 3) I. Gottlieb, Some hypotheses on space, time and gravitation, Studies in Gravitation Theory, CIP Press, Bucharest, 1988, pp.227-234 as well as some recent papers (published in the coauthorship with his disciples): 4)M. Agop, Gottlieb speace-time. A fractal axiomatic model of the Universe. in Particles and Fields, Editors: M.Agop and P.D. Ioannou, Athens University Press, 2005, pp. 59-141 5) I. Gottlieb, M.Agop and V.Enache, Games with Cantor's dust. Chaos, Solitons and Fractals, vol.40 (2009) pp. 940-945 6) I. Gottlieb, My picture over the World, Bull. of the Polytechnic Institute of Iasi. Tom LVI)LX, Fasc. 1, 2010, pp. 1-18. The book contains also a dedication to father Vasile Gottlieb and wife Cleopatra
A MIXED LUBRICATION MODEL MODIFIED BY SURFACES' FRACTAL CHARACTERISTICS
Institute of Scientific and Technical Information of China (English)
孟凡明; 张有云
2003-01-01
Fractal characteristics are introduced into solving lubrication problems. Based on the analysis of the relationship between roughness and engineering surfaces' fractal characteristics and by introducing fractal parameters into the mixed lubrication equation, the relationship between flow factors and fractal dimensions is analyzed. The results show that the pressure flow factors' values increase, while the shear flow factor decreases, with the increasing length to width ratio of a representative asperity γ at the same fractal dimension. It can be also found that these factors experience more irregular and significant variations and show the higher resolution and the local optimal and the worst fractal dimensions, by a fractal dimension D, compared with the oil film thickness to roughness ratio h/Rq. As an example of application of the model to solve the lubrication of the piston skirt in an engine, the frictional force and the load capacity of the oil film in a cylinder were analyzed. The results reveal that the oil film frictional force and the load capacity fluctuate with increasing fractal dimension, showing big values at the small D and smaller ones and slightly variable in the range of bigger one, at the same crank angle.
Fractal Evolving Theory and Growing Model of Olefin Polymerization Process
Institute of Scientific and Technical Information of China (English)
霍超; 任晓红; 等
2003-01-01
The surface morphology of Ti-Mg supported catalyst and the polyethylene particles are studied using scanning electron microscope(SEM) technology.The results show that either the catalyst's surface or polymer particle's surface is irregular and has fractal characteristics,which can be described by fractal parameter.The more interesting discovery is that the surface fractal dimension values of the polymer particles vary periodically with the polymerization time.We call this phenomenon fractal evolution,which can be divided into the "revolution" stage and the "evolution" stage,And then we present polymerization fractal growing model(PFGM),and successfully describe and /or predict the whole evolving process of the polyethylene particle morphology under the different slurry polymerization(including pre-polymerization) conditions without H2.
Structural Equation Model Trees
Brandmaier, Andreas M.; von Oertzen, Timo; McArdle, John J.; Lindenberger, Ulman
2013-01-01
In the behavioral and social sciences, structural equation models (SEMs) have become widely accepted as a modeling tool for the relation between latent and observed variables. SEMs can be seen as a unification of several multivariate analysis techniques. SEM Trees combine the strengths of SEMs and the decision tree paradigm by building tree…
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.
Chen, Yanguang
2015-01-01
An analogy between the fractal nature of networks of arteries and that of systems of rivers has been drawn in the previous works. However, the deep structure of the hierarchy of blood vessels has not yet been revealed. This paper is devoted to researching the fractals, allometric scaling, and hierarchy of blood vessels. By analogy with Horton-Strahler's laws of river composition, three exponential laws have been put forward. These exponential laws can be reconstructed and transformed into three linear scaling laws, which can be named composition laws of blood vessels network. From these linear scaling laws it follows a set of power laws, including the three-parameter Zipf's law on the rank-size distribution of blood vessel length and the allometric scaling law on the length-diameter relationship of blood vessels in different orders. The models are applied to the observed data on human beings and animals early given by other researchers, and an interesting finding is that human bodies more conform to natural r...
Fractal Basins in the Lorenz Model
Institute of Scientific and Technical Information of China (English)
I.Djellit; J.C.Sprott; M. R. Ferchichi
2011-01-01
@@ The Lorenz mapping is a discretization of a pair of differential equations.It illustrates the pertinence of compu- tational chaos.We describe complex dynamics, bifurcations, and chaos in the map.Fractal basins are displayed by numerical simulation.%The Lorenz mapping is a discretization of a pair of differential equations. It illustrates the pertinence of computational chaos. We describe complex dynamics, bifurcations, and chaos in the map. Fractal basins are displayed by numerical simulation.
Directory of Open Access Journals (Sweden)
Iasef Md Rian
2014-09-01
Full Text Available The shapes of trees are complex and fractal-like, and they have a set of physical, mechanical and biological functions. The relation between them always draws attention of human beings throughout history and, focusing on the relation between shape and structural strength, architects have designed a number of treelike structures, referred as dendriforms. The replication and adoption of the treelike patterns for constructing architectural structures have been varied in different time periods based on the existing and advanced knowledge and available technologies. This paper, by briefly discussing the biological functions and the mechanical properties of trees with regard to their shapes, overviews and investigates the chronological evolution and advancements of dendriform and arboreal structures in architecture referring to some important historical as well as contemporary examples.
Directory of Open Access Journals (Sweden)
Jordan P. Sinclair
2015-04-01
Full Text Available Fractal symmetry is symmetry across scale. If one looks at a branch of a tree its branching pattern is reminiscent of the tree as a whole. Plants exhibit a number of different symmetries, including bilateral, rotational, translational, and fractal; deviations from each of these types has been associated with organisms developing in stressful environments. Here, we explore the utilization and meaning of fractal analysis on annual growth ring production in woody plants. Early detection of stress in plants is difficult and the compounding effects of multiple or severe stressors can lead to irreversible damage or death. Annual wood production was used to produce a time series for individuals from stands classified as either high vigor or low vigor (a general measure of health. As a measure of symmetry over time, the fractal dimension of each time series was determined and compared among vigor classes. We found that individuals obtained from low vigor sites had a significantly lower fractal dimension than those from high vigor sites. These results agree with patterns found in a variety of other organisms, and we argue that the reduced fractal dimension is related to a loss in system complexity of stressed individuals.
Random curds as mathematical models of fractal rhythm in architecture
Directory of Open Access Journals (Sweden)
Ćirović Ivana
2014-01-01
Full Text Available The author Carl Bovill has suggested and described a method for generating rhythm in architecture with the help of random curds, as they are the mathematical models of unpredictable and uneven groupings which he recognizes in natural shapes and in natural processes. He specified the rhythm generated in this way as the fractal rhythm. Random curds can be generated by a simple process of curdling, as suggested by B. Mandelbrot. This paper examines the way in which the choice of probability for every stage or level of the curdling process, and the number of stages in the procedure of curdling, affect the characteristics of the obtained fractal object as a potential mathematical model of rhythm in the design process. At the same time, this paper examines the characteristics of rhythm in architecture which determine whether the obtained fractal object will be accepted as an appropriate mathematical model of the observed rhythm.
A user-friendly modified pore-solid fractal model
Dian-yuan Ding; Ying Zhao; Hao Feng; Bing-cheng Si; Robert Lee Hill
2016-01-01
The primary objective of this study was to evaluate a range of calculation points on water retention curves (WRC) instead of the singularity point at air-entry suction in the pore-solid fractal (PSF) model, which additionally considered the hysteresis effect based on the PSF theory. The modified pore-solid fractal (M-PSF) model was tested using 26 soil samples from Yangling on the Loess Plateau in China and 54 soil samples from the Unsaturated Soil Hydraulic Database. The derivation results s...
Fractal properties of the lattice Lotka-Volterra model.
Tsekouras, G A; Provata, A
2002-01-01
The lattice Lotka-Volterra (LLV) model is studied using mean-field analysis and Monte Carlo simulations. While the mean-field phase portrait consists of a center surrounded by an infinity of closed trajectories, when the process is restricted to a two-dimensional (2D) square lattice, local inhomogeneities/fluctuations appear. Spontaneous local clustering is observed on lattice and homogeneous initial distributions turn into clustered structures. Reactions take place only at the interfaces between different species and the borders adopt locally fractal structure. Intercluster surface reactions are responsible for the formation of local fluctuations of the species concentrations. The box-counting fractal dimension of the LLV dynamics on a 2D support is found to depend on the reaction constants while the upper bound of fractality determines the size of the local oscillators. Lacunarity analysis is used to determine the degree of clustering of homologous species. Besides the spontaneous clustering that takes place on a regular 2D lattice, the effects of fractal supports on the dynamics of the LLV are studied. For supports of dimensionality D(s)<2 the lattice can, for certain domains of the reaction constants, adopt a poisoned state where only one of the species survives. By appropriately selecting the fractal dimension of the substrate, it is possible to direct the system into a poisoned or oscillatory steady state at will.
Magnetic critical behavior of the Ising model on fractal structures
Monceau, Pascal; Perreau, Michel; Hébert, Frédéric
1998-09-01
The critical temperature and the set of critical exponents (β,γ,ν) of the Ising model on a fractal structure, namely the Sierpiński carpet, are calculated from a Monte Carlo simulation based on the Wolff algorithm together with the histogram method and finite-size scaling. Both cases of periodic boundary conditions and free edges are investigated. The calculations have been done up to the seventh iteration step of the fractal structure. The results show that, although the structure is not translationally invariant, the scaling behavior of thermodynamical quantities is conserved, which gives a meaning to the finite-size analysis. Although some discrepancies in the values of the critical exponents occur between periodic boundary conditions and free edges, the effective dimension obtained through the Rushbrooke and Josephson's scaling law have the same value in both cases. This value is slightly but significantly different from the fractal dimension.
Chaos, solitons and fractals in hidden symmetry models
Energy Technology Data Exchange (ETDEWEB)
Maccari, Attilio [Technical Institute ' G. Cardano' , Piazza della Resistenza 1, 00015 Monterotondo, Rome (Italy)] e-mail: solitone@yahoo.it
2006-01-01
A spontaneous symmetry breaking (or hidden symmetry) model is reduced to a system nonlinear evolution equations integrable via an appropriate change of variables, by means of the asymptotic perturbation (AP) method, based on spatio-temporal rescaling and Fourier expansion. It is demonstrated the existence of coherent solutions as well as chaotic and fractal patterns, due to the possibility of selecting appropriately some arbitrary functions. Dromion, lump, breather, instanton and ring soliton solutions are derived and the interaction between these coherent solutions are completely elastic, because they pass through each other and preserve their shapes and velocities, the only change being a phase shift. Finally, one can construct lower dimensional chaotic patterns such as chaotic-chaotic patterns, periodic-chaotic patterns, chaotic soliton and dromion patterns. In a similar way, fractal dromion and lump patterns as well as stochastic fractal excitations can appear in the solution.
A user-friendly modified pore-solid fractal model
Ding, Dian-Yuan; Zhao, Ying; Feng, Hao; Si, Bing-Cheng; Hill, Robert Lee
2016-12-01
The primary objective of this study was to evaluate a range of calculation points on water retention curves (WRC) instead of the singularity point at air-entry suction in the pore-solid fractal (PSF) model, which additionally considered the hysteresis effect based on the PSF theory. The modified pore-solid fractal (M-PSF) model was tested using 26 soil samples from Yangling on the Loess Plateau in China and 54 soil samples from the Unsaturated Soil Hydraulic Database. The derivation results showed that the M-PSF model is user-friendly and flexible for a wide range of calculation point options. This model theoretically describes the primary differences between the soil moisture desorption and the adsorption processes by the fractal dimensions. The M-PSF model demonstrated good performance particularly at the calculation points corresponding to the suctions from 100 cm to 1000 cm. Furthermore, the M-PSF model, used the fractal dimension of the particle size distribution, exhibited an accepted performance of WRC predictions for different textured soils when the suction values were ≥100 cm. To fully understand the function of hysteresis in the PSF theory, the role of allowable and accessible pores must be examined.
Critical Exponents of Ferromagnetic Ising Model on Fractal Lattices
Hsiao, Pai-Yi
2001-04-01
We review the value of the critical exponents ν-1, β/ν, and γ/ν of ferromagnetic Ising model on fractal lattices of Hausdorff dimension between one and three. They are obtained by Monte Carlo simulation with the help of Wolff algorithm. The results are accurate enough to show that the hyperscaling law df = 2β/ν + γ/ν is satisfied in non-integer dimension. Nevertheless, the discrepancy between the simulation results and the γ-expansion studies suggests that the strong universality should be adapted for the fractal lattices.
Fractal Model for Acoustic Absorbing of Porous Fibrous Metal Materials
Directory of Open Access Journals (Sweden)
Weihua Chen
2016-01-01
Full Text Available To investigate the changing rules between sound absorbing performance and geometrical parameters of porous fibrous metal materials (PFMMs, this paper presents a fractal acoustic model by incorporating the static flow resistivity based on Biot-Allard model. Static flow resistivity is essential for an accurate assessment of the acoustic performance of the PFMM. However, it is quite difficult to evaluate the static flow resistivity from the microstructure of the PFMM because of a large number of disordered pores. In order to overcome this difficulty, we firstly established a static flow resistivity formula for the PFMM based on fractal theory. Secondly, a fractal acoustic model was derived on the basis of the static flow resistivity formula. The sound absorption coefficients calculated by the presented acoustic model were validated by the values of Biot-Allard model and experimental data. Finally, the variation of the surface acoustic impedance, the complex wave number, and the sound absorption coefficient with the fractal dimensions were discussed. The research results can reveal the relationship between sound absorption and geometrical parameters and provide a basis for improving the sound absorption capability of the PFMMs.
A New Model of Urban Population Density Indicating Latent Fractal Structure
Chen, Yanguang
2016-01-01
Fractal structure of a system suggests the optimal way in which parts arranged or put together to form a whole. The ideas from fractals have a potential application to the researches on urban sustainable development. To characterize fractal cities, we need the measure of fractional dimension. However, if the fractal organization is concealed in the complex spatial distributions of geographical phenomena, the common methods of evaluating fractal parameter will be disabled. In this article, a new model is proposed to describe urban density and estimate fractal dimension of urban form. If urban density takes on quasi-fractal pattern or the self-similar pattern is hidden in the negative exponential distribution, the generalized gamma function may be employed to model the urban landscape and estimate its latent fractal dimension. As a case study, the method is applied to the city of Hangzhou, China. The results show that urban form evolves from simple to complex structure with time.
[Modeling continuous scaling of NDVI based on fractal theory].
Luan, Hai-Jun; Tian, Qing-Jiu; Yu, Tao; Hu, Xin-Li; Huang, Yan; Du, Ling-Tong; Zhao, Li-Min; Wei, Xi; Han, Jie; Zhang, Zhou-Wei; Li, Shao-Peng
2013-07-01
Scale effect was one of the very important scientific problems of remote sensing. The scale effect of quantitative remote sensing can be used to study retrievals' relationship between different-resolution images, and its research became an effective way to confront the challenges, such as validation of quantitative remote sensing products et al. Traditional up-scaling methods cannot describe scale changing features of retrievals on entire series of scales; meanwhile, they are faced with serious parameters correction issues because of imaging parameters' variation of different sensors, such as geometrical correction, spectral correction, etc. Utilizing single sensor image, fractal methodology was utilized to solve these problems. Taking NDVI (computed by land surface radiance) as example and based on Enhanced Thematic Mapper Plus (ETM+) image, a scheme was proposed to model continuous scaling of retrievals. Then the experimental results indicated that: (a) For NDVI, scale effect existed, and it could be described by fractal model of continuous scaling; (2) The fractal method was suitable for validation of NDVI. All of these proved that fractal was an effective methodology of studying scaling of quantitative remote sensing.
A Fractal Model for the Effective Thermal Conductivity of Granular Flow with Non-uniform Particles
Institute of Scientific and Technical Information of China (English)
ZHANG Duan-Ming; LEI Ya-Jie; YU Bo-Ming; ZHANG Mei-Jun; HUANG Ming-Tao; LI Zhi-Hua; GUAN Li
2002-01-01
The equipartition of energy applied in binary mixture of granular flow is extended to granular flow withnon-uniform particles. Based on the fractal characteristic of granular flow with non-uniform particles as well as energyequipartition, a fractal velocity distribution function and a fractal model of effective thermal conductivity are derived.Thermal conduction resulted from motions of particles in the granular flow, as well as the effect of fractal dimension oneffective thermal conductivity, is discussed.
An Introduction to Flow and Transport in Fractal Models of Porous Media: Part I
Cai, Jianchao; San José Martínez, Fernando; Martín, Miguel Angel; Perfect, Edmund
2014-09-01
This special issue gathers together a number of recent papers on fractal geometry and its applications to the modeling of flow and transport in porous media. The aim is to provide a systematic approach for analyzing the statics and dynamics of fluids in fractal porous media by means of theory, modeling and experimentation. The topics covered include lacunarity analyses of multifractal and natural grayscale patterns, random packing's of self-similar pore/particle size distributions, Darcian and non-Darcian hydraulic flows, diffusion within fractals, models for the permeability and thermal conductivity of fractal porous media and hydrophobicity and surface erosion properties of fractal structures.
Institute of Scientific and Technical Information of China (English)
TAO GaoLiang; ZHANG JiRu
2009-01-01
Based on the Sierpinski carpet and Menger sponge models, two categories of fractal models of rock and soil which are composed of the volume fractal model of pores, the volume fractal model of grains, pore-size or particle-size distribution fractal models are established and their relations are clarified in this paper. Through comparison and analysis, it is found that previous models can be unified by the two categories of fractal models, so the unified fractal models are formed. Experimental results presented by Katz indicate that the first category of fractal models can be used to express the fractal behavior of sandstone. A scanning electron microscope (SEM) will be used to study the microstructure of soft clay and it will be testified that the fractal behavior of soft clay suits the second category of fractal models.
Theoretical study of statistical fractal model with applications to mineral resource prediction
Wei, Shen; Pengda, Zhao
2002-04-01
The statistical estimation of fractal dimensions is an important topic of investigation. Current solutions emphsize visual straight-line fitting, but nonlinear statistical modeling has the potential of making valuable contributions in this field. In this paper, we present the concepts of generalized fractal models and generalized fractal dimension and conclude that many geological models are special cases of the generalized models. We show that the power-function distribution possesses the fractal property of scaling invariance under upper truncation, which may help in lead statistical fractal modeling. A new method is developed on the basis of nonlinear regression to estimate fractal parameters. This method has advantages with respect to the traditional method based on linear regression for estimating the fractal dimension. Finally, the new method is illustrated by means of application to a real data set.
Fractal dimension of critical clusters in the Φ44 model
Jansen, K.; Lang, C. B.
1991-06-01
We study the d=4 O(4) symmetric nonlinear sigma model at the pseudocritical points for 84-284 lattices. The Fortuin-Kasteleyn-Coniglio-Klein clusters are shown to have fractal dimension df~=3-in accordance with the conjectured scaling relation involving the odd critical exponent δ. For the one cluster algorithm introduced recently by Wolff the dynamical critical exponent z comes out to be compatible with zero in this model.
Analysis of Texture Using the Fractal Model
Navas, William; Espinosa, Ramon Vasquez
1997-01-01
Properties such as the fractal dimension (FD) can be used for feature extraction and classification of regions within an image. The FD measures the degree of roughness of a surface, so this number is used to characterize a particular region, in order to differentiate it from another. There are two basic approaches discussed in the literature to measure FD: the blanket method, and the box counting method. Both attempt to measure FD by estimating the change in surface area with respect to the change in resolution. We tested both methods but box counting resulted computationally faster and gave better results. Differential Box Counting (DBC) was used to segment a collage containing three textures. The FD is independent of directionality and brightness so five features were used derived from the original image to account for directionality and gray level biases. FD can not be measured on a point, so we use a window that slides across the image giving values of FD to the pixel on the center of the window. Windowing blurs the boundaries of adjacent classes, so an edge-preserving, feature-smoothing algorithm is used to improve classification within segments and to make the boundaries sharper. Segmentation using DBC was 90.8910 accurate.
Fractal model for simulation of frost formation and growth
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
A planar fractal model for simulation of frost formation and growth was proposed based on diffusion limited aggregation(DLA)model and the computational simulation was carried out in this paper.By changing the times of program running circulation and the ratio of random particles generated,the simulation figures were gained under different conditions.A microscope is used to observe the shape and structure of frost layer and a digital camera with high resolution is used to record the pattern of frost layer at different time.Through comparing the simulation figures with the experimental images,we find that the simulation results agree well with the experimental images in shape and the fractal dimension of simulation figures is nearly equal to that of experimental images.The results indicate that it is reasonable to represent frost layer growth time with the program circulation times and to simulate the frost layer density variation during its growth process by reducing the random particle generation probability.The feasibility of using the suggested model to simulate the process of frost formation and growth was justified.The insufficiencies and its causes of this fractal model are also discussed.
MODELING OF THE EMULSION STABILITY USING FRACTAL DIMENSIONS
Directory of Open Access Journals (Sweden)
PREDRAG JOVANIĆ
2008-09-01
Full Text Available There are many developed strategies in the emulsion stability evaluation, for purpose of determining the life circle of emulsions. Most of them are based on the reological properties of the emulsions. There are very few which relay on the direct emulsion observations. In this paper we present the developed method for the emulsion stability evaluation by the direct observation of optical properties. As the stability quantification measure we propose the fractal dimension approach. The method is based on the measure of the emulsion transmittance properties, which are directly dependent on the emulsion stability at the moment of measurement. As the test emulsion the oil in the water emulsion was used. The system is classified as the stable emulsion and our intention was to find the moment when the emulsion starts to break. The emulsion transmittance properties were measured using an acquisition system, consisting of a CCD camera and a fast PC configuration equipped with the capturing software. The fractal dimensions were determined by the so called box counting method. The experimental emulsions were measured continuously within the period of 1200 h, from the moment of the emulsion creation. The changes of fractal dimensions were observed which indicates that the emulsion changed its state and therefore the stability during the time. Three regions of the emulsion life circle were divided according to the fractal dimensions measurement, which can be connected with the stable, unstable, and meta-stable states of the emulsion life circle. In the end, the model of the emulsion behavior was developed for the purpose of quantifying the changes in the experimental emulsion.
Error Assessment in Modeling with Fractal Brownian Motions
Qiao, Bingqiang
2013-01-01
To model a given time series $F(t)$ with fractal Brownian motions (fBms), it is necessary to have appropriate error assessment for related quantities. Usually the fractal dimension $D$ is derived from the Hurst exponent $H$ via the relation $D=2-H$, and the Hurst exponent can be evaluated by analyzing the dependence of the rescaled range $\\langle|F(t+\\tau)-F(t)|\\rangle$ on the time span $\\tau$. For fBms, the error of the rescaled range not only depends on data sampling but also varies with $H$ due to the presence of long term memory. This error for a given time series then can not be assessed without knowing the fractal dimension. We carry out extensive numerical simulations to explore the error of rescaled range of fBms and find that for $0
A Fractal Model for the Transverse Thermal Dispersion Conductivity in Porous Media
Institute of Scientific and Technical Information of China (English)
郁伯铭; 李建华
2004-01-01
A quasi-analytical model, i.e. the fractal model, for the transverse thermal dispersion conductivity in porous media is presented based on the fractal characteristics of tortuous flow paths/streamlines in porous media. The fractal dimension of tortuous flow paths, the spatial deviation velocity and the transverse thermal dispersion conductivity are derived. The proposed model is expressed as functions of the fractal dimension of tortuous flow paths/streamlines, Peclet number, porosity and structural parameters. The present results are compared with those from the existing correlation, and good agreement is found between the present model predictions and those from the existing correlation.
A fractal growth model: Exploring the connection pattern of hubs in complex networks
Li, Dongyan; Wang, Xingyuan; Huang, Penghe
2017-04-01
Fractal is ubiquitous in many real-world networks. Previous researches showed that the strong disassortativity between the hub-nodes on all length scales was the key principle that gave rise to the fractal architecture of networks. Although fractal property emerged in some models, there were few researches about the fractal growth model and quantitative analyses about the strength of the disassortativity for fractal model. In this paper, we proposed a novel inverse renormalization method, named Box-based Preferential Attachment (BPA), to build the fractal growth models in which the Preferential Attachment was performed at box level. The proposed models provided a new framework that demonstrated small-world-fractal transition. Also, we firstly demonstrated the statistical characteristic of connection patterns of the hubs in fractal networks. The experimental results showed that, given proper growing scale and added edges, the proposed models could clearly show pure small-world or pure fractal or both of them. It also showed that the hub connection ratio showed normal distribution in many real-world networks. At last, the comparisons of connection pattern between the proposed models and the biological and technical networks were performed. The results gave useful reference for exploring the growth principle and for modeling the connection patterns for real-world networks.
Hermann, Philipp; Mrkvička, Tomáš; Mattfeldt, Torsten; Minárová, Mária; Helisová, Kateřina; Nicolis, Orietta; Wartner, Fabian; Stehlík, Milan
2015-08-15
Fractals are models of natural processes with many applications in medicine. The recent studies in medicine show that fractals can be applied for cancer detection and the description of pathological architecture of tumors. This fact is not surprising, as due to the irregular structure, cancerous cells can be interpreted as fractals. Inspired by Sierpinski carpet, we introduce a flexible parametric model of random carpets. Randomization is introduced by usage of binomial random variables. We provide an algorithm for estimation of parameters of the model and illustrate theoretical and practical issues in generation of Sierpinski gaskets and Hausdorff measure calculations. Stochastic geometry models can also serve as models for binary cancer images. Recently, a Boolean model was applied on the 200 images of mammary cancer tissue and 200 images of mastopathic tissue. Here, we describe the Quermass-interaction process, which can handle much more variations in the cancer data, and we apply it to the images. It was found out that mastopathic tissue deviates significantly stronger from Quermass-interaction process, which describes interactions among particles, than mammary cancer tissue does. The Quermass-interaction process serves as a model describing the tissue, which structure is broken to a certain level. However, random fractal model fits well for mastopathic tissue. We provide a novel discrimination method between mastopathic and mammary cancer tissue on the basis of complex wavelet-based self-similarity measure with classification rates more than 80%. Such similarity measure relates to Hurst exponent and fractional Brownian motions. The R package FractalParameterEstimation is developed and introduced in the paper.
Modelling tree biomasses in Finland
Energy Technology Data Exchange (ETDEWEB)
Repola, J.
2013-06-01
Biomass equations for above- and below-ground tree components of Scots pine (Pinus sylvestris L), Norway spruce (Picea abies [L.] Karst) and birch (Betula pendula Roth and Betula pubescens Ehrh.) were compiled using empirical material from a total of 102 stands. These stands (44 Scots pine, 34 Norway spruce and 24 birch stands) were located mainly on mineral soil sites representing a large part of Finland. The biomass models were based on data measured from 1648 sample trees, comprising 908 pine, 613 spruce and 127 birch trees. Biomass equations were derived for the total above-ground biomass and for the individual tree components: stem wood, stem bark, living and dead branches, needles, stump, and roots, as dependent variables. Three multivariate models with different numbers of independent variables for above-ground biomass and one for below-ground biomass were constructed. Variables that are normally measured in forest inventories were used as independent variables. The simplest model formulations, multivariate models (1) were mainly based on tree diameter and height as independent variables. In more elaborated multivariate models, (2) and (3), additional commonly measured tree variables such as age, crown length, bark thickness and radial growth rate were added. Tree biomass modelling includes consecutive phases, which cause unreliability in the prediction of biomass. First, biomasses of sample trees should be determined reliably to decrease the statistical errors caused by sub-sampling. In this study, methods to improve the accuracy of stem biomass estimates of the sample trees were developed. In addition, the reliability of the method applied to estimate sample-tree crown biomass was tested, and no systematic error was detected. Second, the whole information content of data should be utilized in order to achieve reliable parameter estimates and applicable and flexible model structure. In the modelling approach, the basic assumption was that the biomasses of
Brown, D J
1996-07-01
A mathematical model is described, based on linear transmission line theory, for the computation of hydraulic input impedance spectra in complex, dichotomously branching networks similar to mammalian arterial systems. Conceptually, the networks are constructed from a discretized set of self-similar compliant tubes whose dimensions are described by an integer power law. The model allows specification of the branching geometry, i.e., the daughter-parent branch area ratio and the daughter-daughter area asymmetry ratio, as functions of vessel size. Characteristic impedances of individual vessels are described by linear theory for a fully constrained thick-walled elastic tube. Besides termination impedances and fluid density and viscosity, other model parameters included relative vessel length and phase velocity, each as a function of vessel size (elastic nonuniformity). The primary goal of the study was to examine systematically the effect of fractal branching asymmetry, both degree and location within the network, on the complex input impedance spectrum and reflection coefficient. With progressive branching asymmetry, fractal model spectra exhibit some of the features inherent in natural arterial systems such as the loss of prominent, regularly-occurring maxima and minima; the effect is most apparent at higher frequencies. Marked reduction of the reflection coefficient occurs, due to disparities in wave path length, when branching is asymmetric. Because of path length differences, branching asymmetry near the system input has a far greater effect on minimizing spectrum oscillations and reflections than downstream asymmetry. Fractal-like constructs suggest a means by which arterial trees of realistic complexity might be described, both structurally and functionally.
Holographic, new agegraphic and ghost dark energy models in fractal cosmology
Karami, K; Ghaffari, S; Fahimi, K
2013-01-01
We investigate the holographic, new agegraphic and ghost dark energy models in the framework of fractal cosmology. We consider a fractal FRW universe filled with the dark energy and dark matter. We obtain the equation of state parameters of the selected dark energy models in the ultraviolet regime and discuss on their implications.
National Research Council Canada - National Science Library
Goodwin, Adrian N
2009-01-01
A flexible tree taper model based on a cubic polynomial is described. It is algebraically invertible and integrable, and can be constrained by one or two diameters, neither of which need be diameter at breast height (DBH...
A multiple fractal model for estimating permeability of dual-porosity media
Li, Bo; Liu, Richeng; Jiang, Yujing
2016-09-01
A multiple fractal model that considers the fractal properties of both porous matrices and fracture networks is proposed for the permeability of dual-porosity media embedded with randomly distributed fractures. In this model, the aperture distribution is verified to follow the fractal scaling law, and the porous matrix is assumed to comprise a bundle of tortuous capillaries that also follow the fractal scaling law. Analytical expressions for fractal aperture distribution, total flow rate, total equivalent permeability, and dimensionless permeability are established, where the dimensionless permeability is defined as the ratio of permeability of the porous matrices to that of the fracture networks. The dimensionless permeability is closely correlated to the structural parameters (i.e., α, θ, Dtf, Dtp, De, Dp, emax, λmax) of the dual-porosity media, and it is more sensitive to the fractal dimension for the size distribution of fracture aperture than to that for the size distribution of pore/capillary diameter. The maximum pore/capillary diameter has a greater impact on the dimensionless permeability than that of the maximum fracture aperture. The dimensionless permeability of fracture networks constructed by the fractal aperture distribution has close values with those of models with lognormal aperture distribution. The proposed multiple fractal model does not involve any empirical constants that do not have clear physical meanings, which could serve as a quick estimation method for assessing permeability of dual-porosity media.
Tree Modeling with Real Tree-Parts Examples.
Xie, Ke; Yan, Feilong; Sharf, Andrei; Deussen, Oliver; Huang, Hui; Chen, Baoquan
2016-12-01
We introduce a 3D tree modeling technique that utilizes examples of real trees to enhance tree creation with realistic structures and fine-level details. In contrast to previous works that use smooth generalized cylinders to represent tree branches, our method generates realistic looking tree models with complex branching geometry by employing an exemplar database consisting of real-life trees reconstructed from scanned data. These trees are sliced into representative parts (denoted as tree-cuts), representing trunk logs and branching structures. In the modeling process, tree-cuts are positioned in space in an intuitive manner, serving as efficient proxies that guide the creation of the complete tree. Allometry rules are taken into account to ensure reasonable relations between adjacent branches. Realism is further enhanced by automatically transferring geometric textures from our database onto tree branches as well as by guided growing of foliage. Our results demonstrate the complexity and variety of trees that can be generated with our method within few minutes. We carry a user study to test the effectiveness of our modeling technique.
2011-01-01
Objective The aim of this study was to use fractal dimension (FD) analysis on multidetector CT (MDCT) images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension (PH). Materials and Methods Fourteen patients with PH and 17 patients without PH as controls were studied. All of the patients underwent contrast-enhanced helical CT and transthoracic echocardiography. The pulmonary artery trees were generated using post-processing software, a...
Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation
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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
Fractal Branching in Vascular Trees and Networks by VESsel GENeration Analysis (VESGEN)
Parsons-Wingerter, Patricia A.
2016-01-01
Vascular patterning offers an informative multi-scale, fractal readout of regulatory signaling by complex molecular pathways. Understanding such molecular crosstalk is important for physiological, pathological and therapeutic research in Space Biology and Astronaut countermeasures. When mapped out and quantified by NASA's innovative VESsel GENeration Analysis (VESGEN) software, remodeling vascular patterns become useful biomarkers that advance out understanding of the response of biology and human health to challenges such as microgravity and radiation in space environments.
Fractal and Multifractal Models Applied to Porous Media - Editorial
Given the current high level of interest in the use of fractal geometry to characterize natural porous media, a special issue of the Vadose Zone Journal was organized in order to expose established fractal analysis techniques and cutting-edge new developments to a wider Earth science audience. The ...
Pelletier, J D
1997-01-01
The power spectrum S of linear transects of the earth's topography is often observed to be a power-law function of wave number k with exponent close to -2: S(k) is proportional to k^-2. In addition, river networks are fractal trees that satisfy many power-law or fractal relationships between their morphologic components. A model equation for the evolution of the earth's topography by erosional processes which produces fractal topography and fractal river networks is presented and its solutions compared in detail to real topography. The model is the diffusion equation for sediment transport on hillslopes and channels with the local diffusivity proportional to the square of the discharge. The dependence of diffusivity on discharge follows from fundamental equations of sediment transport. We study the model in two ways. In the first analysis the diffusivity is parameterized as a function of relief and a Taylor expansion procedure is carried out to obtain a differential equation for the landform elevation which i...
An Active Region Model for Capturing Fractal Flow Patterns inUnsaturated Soils: Model Development
Energy Technology Data Exchange (ETDEWEB)
Liu, Hui-Hai; Zhang, R.; Bodvarsson, Gudmundur S.
2005-06-11
Preferential flow commonly observed in unsaturated soils allows rapid movement of solute from the soil surface or vadose zone to the groundwater, bypassing a significant volume of unsaturated soil and increasing the risk of groundwater contamination. A variety of evidence indicates that complex preferential patterns observed from fields are fractals. In this study, we developed a relatively simple active region model to incorporate the fractal flow pattern into the continuum approach. In the model, the flow domain is divided into active and inactive regions. Flow occurs preferentially in the active region (characterized by fractals), and inactive region is simply bypassed. A new constitutive relationship (the portion of the active region as a function of saturation) was derived. The validity of the proposed model is demonstrated by the consistency between field observations and the new constitutive relationship.
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
The fractal globule as a model of chromatin architecture in the cell.
Mirny, Leonid A
2011-01-01
The fractal globule is a compact polymer state that emerges during polymer condensation as a result of topological constraints which prevent one region of the chain from passing across another one. This long-lived intermediate state was introduced in 1988 (Grosberg et al. 1988) and has not been observed in experiments or simulations until recently (Lieberman-Aiden et al. 2009). Recent characterization of human chromatin using a novel chromosome conformational capture technique brought the fractal globule into the spotlight as a structural model of human chromosome on the scale of up to 10 Mb (Lieberman-Aiden et al. 2009). Here, we present the concept of the fractal globule, comparing it to other states of a polymer and focusing on its properties relevant for the biophysics of chromatin. We then discuss properties of the fractal globule that make it an attractive model for chromatin organization inside a cell. Next, we connect the fractal globule to recent studies that emphasize topological constraints as a primary factor driving formation of chromosomal territories. We discuss how theoretical predictions, made on the basis of the fractal globule model, can be tested experimentally. Finally, we discuss whether fractal globule architecture can be relevant for chromatin packing in other organisms such as yeast and bacteria.
A Fractal Model for the Capacitance of Lunar Dust and Lunar Dust Aggregates
Collier, Michael R.; Stubbs, Timothy J.; Keller, John W.; Farrell, William M.; Marshall, John; Richard, Denis Thomas
2011-01-01
Lunar dust grains and dust aggregates exhibit clumping, with an uneven mass distribution, as well as features that span many spatial scales. It has been observed that these aggregates display an almost fractal repetition of geometry with scale. Furthermore, lunar dust grains typically have sharp protrusions and jagged features that result from the lack of aeolian weathering (as opposed to space weathering) on the Moon. A perfectly spherical geometry, frequently used as a model for lunar dust grains, has none of these characteristics (although a sphere may be a reasonable proxy for the very smallest grains and some glasses). We present a fractal model for a lunar dust grain or aggregate of grains that reproduces (1) the irregular clumpy nature of lunar dust, (2) the presence of sharp points, and (3) dust features that span multiple scale lengths. We calculate the capacitance of the fractal lunar dust analytically assuming fixed dust mass (i.e. volume) for an arbitrary number of fractal levels and compare the capacitance to that of a non-fractal object with the same volume, surface area, and characteristic width. The fractal capacitance is larger than that of the equivalent non-fractal object suggesting that for a given potential, electrostatic forces on lunar dust grains and aggregates are greater than one might infer from assuming dust grains are sphericaL Consequently, electrostatic transport of lunar dust grains, for example lofting, appears more plausible than might be inferred by calculations based on less realistic assumptions about dust shape and associated capacitance.
Xiao, Boqi; Tu, Xing; Ren, Wen; Wang, Zongchi
2015-06-01
In this study, the analytical expressions for the hydraulic permeability and Kozeny-Carman (KC) constant of porous nanofibers are derived based on fractal theory. In the present approach, the permeability is explicitly related to the porosity and the area fractal dimensions of porous nanofibers. The proposed fractal models for KC constant is also found to be a function of the microstructural parameters (porosity, area fractal dimensions). Besides, the present model clearly indicates that KC constant is not a constant and increases with porosity. However, KC constant is close to a constant value which is 18 for ϕ > 0.8. Every parameter of the proposed formulas of calculating permeability and KC constant has clear physical meaning. The model predictions are compared with the existing experimental data, and fair agreement between the model predictions and experimental data is found for different porosities.
Component-based Discrete Event Simulation Using the Fractal Component Model
Dalle, Olivier
2007-01-01
In this paper we show that Fractal, a generic component model coming from the Component-Based Software Engineering (CBSE) community, meets most of the functional expectations identified so far in the simulation community for component-based modeling and simulation. We also demonstrate that Fractal offers additional features that have not yet been identified in the simulation community despite their potential usefulness. Eventually we describe our ongoing work on such a new simulation architec...
Approximating the Ising model on fractal lattices of dimension less than two
DEFF Research Database (Denmark)
Codello, Alessandro; Drach, Vincent; Hietanen, Ari
2015-01-01
We construct periodic approximations to the free energies of Ising models on fractal lattices of dimension smaller than two, in the case of a zero external magnetic field, based on the combinatorial method of Feynman and Vdovichenko. We show that the procedure is applicable to any fractal obtained...... with, possibly, arbitrary accuracy and paves the way for determination Tc of any fractal of dimension less than two. Critical exponents are more diffcult to determine since the free energy of any periodic approximation still has a logarithmic singularity at the critical point implying α = 0. We also...
Modeling of movement-related potentials using a fractal approach.
Uşakli, Ali Bülent
2010-06-01
In bio-signal applications, classification performance depends greatly on feature extraction, which is also the case for electroencephalogram (EEG) based applications. Feature extraction, and consequently classification of EEG signals is not an easy task due to their inherent low signal-to-noise ratios and artifacts. EEG signals can be treated as the output of a non-linear dynamical (chaotic) system in the human brain and therefore they can be modeled by their dimension values. In this study, the variance fractal dimension technique is suggested for the modeling of movement-related potentials (MRPs). Experimental data sets consist of EEG signals recorded during the movements of right foot up, lip pursing and a simultaneous execution of these two tasks. The experimental results and performance tests show that the proposed modeling method can efficiently be applied to MRPs especially in the binary approached brain computer interface applications aiming to assist severely disabled people such as amyotrophic lateral sclerosis patients in communication and/or controlling devices.
Scaling law and fractality concepts in models of turbulent diffusion
Energy Technology Data Exchange (ETDEWEB)
Bakunin, O G [Russian Research Center ' Kurchatov Institute' , Nuclear Fusion Institute, Kurchatova Sq., Moscow, 123182 (Russian Federation); FOM Instituut voor Plasmafysica ' Rijnhuizen' , Associate Euroatom-FOM, 3430 BE Nieuwegein (Netherlands)
2003-10-01
A large variety of plasma instabilities lead to the development of different types of plasma turbulences. This paper discusses the Dreizin-Dykhne model of random flows, the Kadomtsev-Pogutse approach to describe 'braided' magnetic field and transport estimates in systems with convective cells. The important role of correlation effects and anisotropy is shown. The variety of forms require not only special description methods, but also an analysis of the general mechanisms for different turbulence types. One such mechanism is the percolation transport. Its description is based on the idea of long-range correlations, taken from the theory of phase transitions and the percolation theory. This approach is based on fractality ideas. This paper discusses several different models of the percolation transport. The similar characters of used approaches are pointed out. The detailed analysis of the more important results obtained in this domain is presented in this paper. The aim of this paper is to make these results clear and not only for theoreticians.
A fractal model for nuclear organization: current evidence and biological implications.
Bancaud, Aurélien; Lavelle, Christophe; Huet, Sébastien; Ellenberg, Jan
2012-10-01
Chromatin is a multiscale structure on which transcription, replication, recombination and repair of the genome occur. To fully understand any of these processes at the molecular level under physiological conditions, a clear picture of the polymorphic and dynamic organization of chromatin in the eukaryotic nucleus is required. Recent studies indicate that a fractal model of chromatin architecture is consistent with both the reaction-diffusion properties of chromatin interacting proteins and with structural data on chromatin interminglement. In this study, we provide a critical overview of the experimental evidence that support a fractal organization of chromatin. On this basis, we discuss the functional implications of a fractal chromatin model for biological processes and propose future experiments to probe chromatin organization further that should allow to strongly support or invalidate the fractal hypothesis.
Crossover and thermodynamic representation in the extended η model for fractal growth
Nagatani, Takashi; Stanley, H. Eugene
1990-10-01
The η model for the dielectric breakdown is extended to the case where double power laws apply. It is shown that a crossover phenomenon between the diffusion-limited aggregation (DLA) fractal and the η fractal occurs in the extended η model. Through the use of the dimensional analysis, a dimensionless parameter is found to govern the crossover. It is shown that when η1 the inverse crossover from the η fractal to the DLA fractal appears. It is also shown that the crossover radius is controlled by changing the applied field. The global flow diagram in the two-parameter space is obtained by using a two-parameter position-space renormalization-group approach. The crossover exponent and the crossover radius are calculated. The crossover phenomenon is described in terms of a thermodynamic representation of the two-phase equilibrium.
About wave field modeling in hierarchic medium with fractal inclusions
Hachay, Olga; Khachay, Andrey
2014-05-01
The processes of oil gaseous deposits outworking are linked with moving of polyphase multicomponent media, which are characterized by no equilibrium and nonlinear rheological features. The real behavior of layered systems is defined as complicated rheology moving liquids and structural morphology of porous media. It is eargently needed to account those factors for substantial description of the filtration processes. Additionally we must account also the synergetic effects. That allows suggesting new methods of control and managing of complicated natural systems, which can research these effects. Thus our research is directed to the layered system, from which we have to outwork oil and which is a complicated hierarchic dynamical system with fractal inclusions. In that paper we suggest the algorithm of modeling of 2-d seismic field distribution in the heterogeneous medium with hierarchic inclusions. Also we can compare the integral 2-D for seismic field in a frame of local hierarchic heterogeneity with a porous inclusion and pure elastic inclusion for the case when the parameter Lame is equal to zero for the inclusions and the layered structure. For that case we can regard the problem for the latitude and longitudinal waves independently. Here we shall analyze the first case. The received results can be used for choosing criterions of joined seismic methods for high complicated media research.If the boundaries of the inclusion of the k rank are fractals, the surface and contour integrals in the integral equations must be changed to repeated fractional integrals of Riman-Liuvill type .Using the developed earlier 3-d method of induction electromagnetic frequency geometric monitoring we showed the opportunity of defining of physical and structural features of hierarchic oil layer structure and estimating of water saturating by crack inclusions. For visualization we had elaborated some algorithms and programs for constructing cross sections for two hierarchic structural
Teaching as a fractal: from experience to model
Directory of Open Access Journals (Sweden)
Patricia COMPAÑ-ROSIQUE
2015-12-01
Full Text Available The aim of this work is to improve students’ learning by designing a teaching model that seeks to increase student motivation to acquire new knowledge. To design the model, the methodology is based on the study of the students’ opinion on several aspects we think importantly affect the quality of teaching (such as the overcrowded classrooms, time intended for the subject or type of classroom where classes are taught, and on our experience when performing several experimental activities in the classroom (for instance, peer reviews and oral presentations. Besides the feedback from the students, it is essential to rely on the experience and reflections of lecturers who have been teaching the subject several years. This way we could detect several key aspects that, in our opinion, must be considered when designing a teaching proposal: motivation, assessment, progressiveness and autonomy. As a result we have obtained a teaching model based on instructional design as well as on the principles of fractal geometry, in the sense that different levels of abstraction for the various training activities are presented and the activities are self-similar, that is, they are decomposed again and again. At each level, an activity decomposes into a lower level tasks and their corresponding evaluation. With this model the immediate feedback and the student motivation are encouraged. We are convinced that a greater motivation will suppose an increase in the student’s working time and in their performance. Although the study has been done on a subject, the results are fully generalizable to other subjects.
Fractal behavior in the headway fluctuation simulated by the NaSch model
Zhu, H. B.; Gao, J. B.
2014-03-01
The fractal behavior of traffic flow is studied by the adaptive fractal analysis method on the basis of the vehicle headway time series, which are obtained from the numerical simulation of the NaSch model. We find that the vehicle headway time series has a fractal behavior that is similar to the standard Brownian motion (BM) over a wide range of scales when the density is low. As the density increases well-defined sharp spectral peaks, corresponding to the stop-and-go waves, appear while the scale range showing BM-like behavior rapidly shrinks. In the high density regime, a new type of fractal behavior with long-range correlations appears, accompanying the worsening of traffic congestions. The underlying dynamics of traffic flow is analyzed, and some meaningful results are obtained.
Use of fractal models in the Earth's remote sensing of the arctic zone
Berg, D. B.; Medvedev, A. N.; Manzhurov, I. L.; Taubaev, A. A.
2016-12-01
The development and practical application of new mathematical methods of processing, image analysis and pattern recognition has significant prospects for mapping the Earth from space. In the paper, it is proposed to use the fractal model of the surface contamination distribution, previously developed by the authors, for the analysis of color multispectral satellite images on the example of the territory of the Polar Urals. The research has shown the following: 1) The brightness distribution on remote sensing snapshot has a fractal character. 2) The values of fractal dimension of the territory images in different spectral ranges significantly differ. 3) The hierarchy of geomorphological structures in the range of 13-1700 m may be considered as self-similar. Thus, the proposed method of calculating the fractal dimension value of the snapshot may become one of the informative attributes for remote sensing images interpretation.
Field Fractal Cosmological Model As an Example of Practical Cosmology Approach
Baryshev, Yu V
2008-01-01
The idea of the global gravitational effect as the source of cosmological redshift was considered by de Sitter (1916, 1917), Eddington (1923), Tolman (1929) and Bondi (1947), also Hubble (1929) called the discovered distance-redshift relation as "De Sitter effect". For homogeneous matter distribution cosmological gravitational redshift is proportional to square of distance: z_grav ~ r^2. However for a fractal matter distribution having the fractal dimension D=2 the global gravitational redshift is the linear function of distance: z_grav ~ r, which gives possibility for interpretation of the Hubble law without the space expansion. Here the field gravity fractal cosmological model (FGF) is presented, which based on two initial principles. The first assumption is that the field gravity theory describes the gravitational interaction within the conceptual unity of all fundamental physical interactions. The second hypothesis is that the spatial distribution of matter is a fractal at all scales up to the Hubble radi...
Logistic Models of Fractal Dimension Growth for Spatio-Temporal Dynamics of Urban Morphology
Chen, Yanguang
2016-01-01
Urban form and growth can be described with fractal dimension, which is a measurement of space filling of urban evolution. Based on empirical analyses, a discovery is made that the time series of fractal dimension of urban form can be treated as a sigmoid function of time. Among various sigmoid functions, the logistic function is the most probable selection. However, how to use the model of fractal dimension growth to explain and predict urban growth is a pending problem remaining to be solved. This paper is devoted to modeling fractal dimension evolution of different types of cities. A interesting discovery is as follows: for the cities in developed countries such as UK, USA and Israel, the comparable fractal dimension values of a city's morphology in different years can be fitted to the logistic function; while for the cities in developing countries such as China, the fractal dimension data of urban form can be fitted to a quadratic logistic function. A generalized logistic function is thus proposed to mode...
Fractal Aggregation Under Rotation
Institute of Scientific and Technical Information of China (English)
WU Feng-Min; WU Li-Li; LU Hang-Jun; LI Qiao-Wen; YE Gao-Xiang
2004-01-01
By means of the Monte Carlo simulation, a fractal growth model is introduced to describe diffusion-limited aggregation (DLA) under rotation. Patterns which are different from the classical DLA model are observed and the fractal dimension of such clusters is calculated. It is found that the pattern of the clusters and their fractal dimension depend strongly on the rotation velocity of the diffusing particle. Our results indicate the transition from fractal to non-fractal behavior of growing cluster with increasing rotation velocity, i.e. for small enough angular velocity ω the fractal dimension decreases with increasing ω, but then, with increasing rotation velocity, the fractal dimension increases and the cluster becomes compact and tends to non-fractal.
Figaro, S; Avril, J P; Brouers, F; Ouensanga, A; Gaspard, S
2009-01-30
Adsorption kinetic of molasses wastewaters after anaerobic digestion (MSWD) and melanoidin respectively on activated carbon was studied at different pH. The kinetic parameters could be determined using classical kinetic equations and a recently published fractal kinetic equation. A linear form of this equation can also be used to fit adsorption data. Even with lower correlation coefficients the fractal kinetic equation gives lower normalized standard deviation values than the pseudo-second order model generally used to fit adsorption kinetic data, indicating that the fractal kinetic model is much more accurate for describing the kinetic adsorption data than the pseudo-second order kinetic model.
Fractal Modeling of Pore Structure and Ionic Diffusivity for Cement Paste
Directory of Open Access Journals (Sweden)
Yun Gao
2016-01-01
Full Text Available Pore structure in cement based composites is of paramount importance to ionic diffusivity. In this paper, pore structure in cement paste is modeled by means of the recently proposed solid mass fractal model. Moreover, an enhanced Maxwell homogenization method that incorporates the solid mass fractal model is proposed to determine the associated ionic diffusivity. Experiments are performed to validate the modeling, that is, mercury intrusion porosimetry and rapid chloride migration. Results indicate that modeling agrees well with those obtained from experiments.
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter. PMID:28117325
Hashemi, S. M.; Jagodič, U.; Mozaffari, M. R.; Ejtehadi, M. R.; Muševič, I.; Ravnik, M.
2017-01-01
Fractals are remarkable examples of self-similarity where a structure or dynamic pattern is repeated over multiple spatial or time scales. However, little is known about how fractal stimuli such as fractal surfaces interact with their local environment if it exhibits order. Here we show geometry-induced formation of fractal defect states in Koch nematic colloids, exhibiting fractal self-similarity better than 90% over three orders of magnitude in the length scales, from micrometers to nanometres. We produce polymer Koch-shaped hollow colloidal prisms of three successive fractal iterations by direct laser writing, and characterize their coupling with the nematic by polarization microscopy and numerical modelling. Explicit generation of topological defect pairs is found, with the number of defects following exponential-law dependence and reaching few 100 already at fractal iteration four. This work demonstrates a route for generation of fractal topological defect states in responsive soft matter.
A Parallel Implementation of Improved Fractal Image Coding Based on Tree Topology
Institute of Scientific and Technical Information of China (English)
SUNYunda,; ZHAOYao; YUANBaozong
2003-01-01
One of the main drawbacks of fractai im-age coding (FIC) is its time-consuming encoding process.So how to speed up the encoding process is a challenging issue of FIC research. As both sequential solutions and parallel ones have their advantages and disadvantages, we combine them together to further speed up the encoding phase. In this paper a derivative tree topology is first pro-posed to provide support for complex parallelism. Then a dual-classification technique is designed for speeding up the fractai image coding with Same-Sized Block Mapping,which improves the decoded image quality. Finally, some experimental results with good performance are presented.
Monceau, Pascal
2006-09-01
The extension of the phase diagram of the q -state Potts model to noninteger dimension is investigated by means of Monte Carlo simulations on Sierpinski and Menger fractal structures. Both multicanonical and canonical simulations have been carried out with the help of the Wang-Landau and the Wolff cluster algorithms. Lower bounds are provided for the critical values qc of q where a first-order transition is expected in the cases of two structures whose fractal dimension is smaller than 2: The transitions associated with the seven-state and ten-state Potts models on Sierpinski carpets with fractal dimensions df≃1.8928 and df≃1.7925 , respectively, are shown to be second-order ones, the renormalization eigenvalue exponents yh are calculated, and bounds are provided for the renormalization eigenvalue exponents yt and the critical temperatures. Moreover, the results suggest that second-order transitions are expected to occur for very large values of q when the fractal dimension is lowered below 2—that is, in the case of hierarchically weakly connected systems with an infinite ramification order. At last, the transition associated with the four-state Potts model on a fractal structure with a dimension df≃2.631 is shown to be a weakly first-order one.
Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields
Institute of Scientific and Technical Information of China (English)
LI Ying; KONG Xiang-Mu; HUANG Jia-Yin
2003-01-01
Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Soil water retention characteristics are the key information required in hydrological modeling. Frac-tal models provide a practical alternative for indirectly estimating soil water retention characteristics fromparticle-size distribution data. Predictive capabilities of three fractal models, i.e, Tyler-Wheatcraft model,Rieu-Sposito model, and Brooks-Corey model, were fully evaluated in this work using experimental datafrom an international database and literature. Particle-size distribution data were firstly interpolated into20 classes using a van Genuchten-type equation. Fractal dimensions of the tortuous pore wall and the poresurface were then calculated from the detailed particle-size distribution and incorporated as a parameter infractal water retention models. Comparisons between measured and model-estimated water retention cha-racteristics indicated that these three models were applicable to relatively different soil textures and pressurehead ranges. Tyler-Wheatcraft and Brooks-Corey models led to reasonable agreements for both coarse- andmedium-textured soils, while the latter showed applicability to a broader texture range. In contrast, Rieu-Sposito model was more suitable for fine-textured soils. Fractal models produced a better estimation of watercontents at low pressure heads than at high pressure heads.
Site effect classification based on microtremor data analysis using concentration–area fractal model
Directory of Open Access Journals (Sweden)
A. Adib
2014-07-01
Full Text Available The aim of this study is to classify the site effect using concentration–area (C–A fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log–log plots of the frequency, amplification and vulnerability index (k-g indicate a multifractal nature for the parameters in the area. The results obtained from the C–A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1 hard soil and weak rock with frequency of 6.2 to 8 Hz, (2 stiff soil with frequency of about 4.9 to 6.2 Hz, (3 moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4 soft soil with the frequency lower than 2.4 Hz.
Adib, A.; Afzal, P.; Heydarzadeh, K.
2015-01-01
The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modelling reveal that proper soil types are located around the central city. The results derived via the fractal modelling were utilized to improve the Nogoshi and Igarashi (1970, 1971) classification results in the Meybod city. The resulting categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.
Site effect classification based on microtremor data analysis using concentration-area fractal model
Adib, A.; Afzal, P.; Heydarzadeh, K.
2014-07-01
The aim of this study is to classify the site effect using concentration-area (C-A) fractal model in Meybod city, Central Iran, based on microtremor data analysis. Log-log plots of the frequency, amplification and vulnerability index (k-g) indicate a multifractal nature for the parameters in the area. The results obtained from the C-A fractal modeling reveal that proper soil types are located around the central city. The results derived via the fractal modeling were utilized to improve the Nogoshi's classification results in the Meybod city. The resulted categories are: (1) hard soil and weak rock with frequency of 6.2 to 8 Hz, (2) stiff soil with frequency of about 4.9 to 6.2 Hz, (3) moderately soft soil with the frequency of 2.4 to 4.9 Hz, and (4) soft soil with the frequency lower than 2.4 Hz.
Enzymatic saccharification of acid pretreated corn stover: Empirical and fractal kinetic modelling.
Wojtusik, Mateusz; Zurita, Mauricio; Villar, Juan C; Ladero, Miguel; Garcia-Ochoa, Felix
2016-11-01
Enzymatic hydrolysis of corn stover was studied at agitation speeds from 50 to 500rpm in a stirred tank bioreactor, at high solid concentrations (20% w/w dry solid/suspension), 50°C and 15.5mgprotein·gglucane(-1). Two empirical kinetic models have been fitted to empirical data, namely: a potential model and a fractal one. For the former case, the global order dramatically decreases from 13 to 2 as agitation speed increases, suggesting an increment in the access of enzymes to cellulose in terms of chemisorption followed by hydrolysis. For its part, the fractal kinetic model fits better to data, showing its kinetic constant a constant augmentation with increasing agitation speed up to a constant value at 250rpm and above, when mass transfer limitations are overcome. In contrast, the fractal exponent decreases with rising agitation speed till circa 0.19, suggesting higher accessibility of enzymes to the substrate.
Kalauzi, Aleksandar; Bojić, Tijana; Vuckovic, Aleksandra
2012-07-01
The exact mathematical relationship between FFT spectrum and fractal dimension (FD) of an experimentally recorded signal is not known. In this work, we tried to calculate signal FD directly from its Fourier amplitudes. First, dependence of Higuchi's FD of mathematical sinusoids on their individual frequencies was modeled with a two-parameter exponential function. Next, FD of a finite sum of sinusoids was found to be a weighted average of their FDs, weighting factors being their Fourier amplitudes raised to a fractal degree. Exponent dependence on frequency was modeled with exponential, power and logarithmic functions. A set of 280 EEG signals and Weierstrass functions were analyzed. Cross-validation was done within EEG signals and between them and Weierstrass functions. Exponential dependence of fractal exponents on frequency was found to be the most accurate. In this work, signal FD was for the first time expressed as a fractal weighted average of FD values of its Fourier components, also allowing researchers to perform direct estimation of signal fractal dimension from its FFT spectrum.
两种新型树状结构的分形天线研究%Study on Two Novel Tree-shaped Fractal Antennas
Institute of Scientific and Technical Information of China (English)
周文平; 张卫; 刘金梅; 王小良
2012-01-01
结合分形技术的优点,研究了2种新型分形天线.分别对这2种天线进行了0阶、1阶、2阶仿真分析比较.其中一种新型树状分形结构应用于传统印刷偶极子天线,研究表明2阶分形天线的工作频点相对于0阶工作频点下降了59.7％,具有非常好的尺寸减缩性.另一种将圆弧应用于单极子天线中,具有良好的多频性,相邻谐振频点的比值是变化的,这也使得天线设计更加灵活.这2种树状分形结构具有设计简单、易制作,对于天线的小型化和多频性的研究和设计提供了较好的参考价值.%Two novel treeshaped fractal antennas are proposed which are based on the theory of Fractal . Two different antennas are investigated by simulating analysis which the help of electromagnetic simulation software. One of the antennas was developed by the applying of a novel tree-shaped fractal structure to the dipole antenna which could be used in printing The resonant frequency of the two-iterative fractal antenna is 59. 7% that is lower than that of the zero-iterative fractal one. It can be shown that it has a good size-reduction feature. The other one of the antenna was developed by the applying of arc branch to the monopole antenna. The simulation analysis results show that it has the good multi-band characteristics. The adjacent of resonance frequency ratio is changing. It also makes the antenna design more flexible. The both of two fractal tree structures have the features of simplification and valuable easier to produce. For the miniaturization of antenna and the multi-band antenna design the paper provide a good reference.
Modeling and fabrication of an RF MEMS variable capacitor with a fractal geometry
Elshurafa, Amro M.
2013-08-16
In this paper, we model, fabricate, and measure an electrostatically actuated MEMS variable capacitor that utilizes a fractal geometry and serpentine-like suspension arms. Explicitly, a variable capacitor that possesses a top suspended plate with a specific fractal geometry and also possesses a bottom fixed plate complementary in shape to the top plate has been fabricated in the PolyMUMPS process. An important benefit that was achieved from using the fractal geometry in designing the MEMS variable capacitor is increasing the tuning range of the variable capacitor beyond the typical ratio of 1.5. The modeling was carried out using the commercially available finite element software COMSOL to predict both the tuning range and pull-in voltage. Measurement results show that the tuning range is 2.5 at a maximum actuation voltage of 10V.
Topologiacl Models of 2D Fractal Cellular Structures
Le Caër, G.; Delannay, R.
1995-11-01
In space-filling 2D cellular structures with trivalent vertices and in which each cell is constrained to share at most one side with any cell and no side with itself, the maximum fraction of three-sided cells is produced by a decoration of vertices of any initial structure by three-sided cells. Fractal cellular structures are obtained if the latter decoration process is iterated indefinitely. Other methods of constructions of fractal structures are also described. The probability distribution P(n) of the number n of cell sides and some two-cell topological properties of a 2D fractal cellular structure constructed from the triangular Sierpinski gasket are investigated. On the whole, the repartition of cells in 2D structures with n geq 3 and P(3) ne 0 evolve regularly when topological disorder, conveniently measured by the variance μ2 of P(n), increases. The strong correlations which exist among cells, in particular in natural structures (μ2lesssim 5), decrease progressively when μ2 increases, a cell repartition close to a random one being reached for μ2sim 12. We argue that the structures finally evolve to fractal structures (for which μ2 is infinite) but we have not characterized the latter transition. Dans des structures cellulaires 2D à sommets trivalents qui remplissent l'espace et dans lesquelles une cellule partage au plus un côté avec toute autre cellule et aucun avec elle-même, la proportion maximum admissible de cellules à trois côtés est obtenue par une décoration de tous les sommets d'une structure initiale quelconque par des cellules à trois côtés. Des structures cellulaires “fractales” 2D sont ainsi engendrées si le processus précédent est répété à l'infini. D'autres méthodes de constructions de structures fractales sont également décrites. La distribution de probabilité P(n) du nombre n de côtés des cellules ainsi que des corrélations de paires sont étudiées pour une structure cellulaire fractale construite à partir
Fractal Aggregation Under Rotation
Institute of Scientific and Technical Information of China (English)
WUFeng-Min; WULi-Li; LUHang-Jun; LIQiao-Wen; YEGao-Xiang
2004-01-01
By means of the Monte Carlo simulation, a fractal growth model is introduced to describe diffusion-limited aggregation (DLA) under rotation. Patterns which are different from the classical DLA model are observed and the fractal dimension of such clusters is calculated. It is found that the pattern of the clusters and their fractal dimension depend strongly on the rotation velocity of the diffusing particle. Our results indicate the transition from fractal to non-fractal behavior of growing cluster with increasing rotation velocity, i.e. for small enough angular velocity ω; thefractal dimension decreases with increasing ω;, but then, with increasing rotation velocity, the fractal dimension increases and the cluster becomes compact and tends to non-fractal.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fan, Jieran; Wang, Di; DeVault, Clayton
2016-01-01
We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure.......We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure....
Fractal modeling of natural fracture networks. Final report, June 1994--June 1995
Energy Technology Data Exchange (ETDEWEB)
Ferer, M.V.; Dean, B.H.; Mick, C.
1996-04-01
Recovery from naturally fractured, tight-gas reservoirs is controlled by the fracture network. Reliable characterization of the actual fracture network in the reservoir is severely limited. The location and orientation of fractures intersecting the borehole can be determined, but the length of these fractures cannot be unambiguously determined. Fracture networks can be determined for outcrops, but there is little reason to believe that the network in the reservoir should be identical because of the differences in stresses and history. Because of the lack of detailed information about the actual fracture network, modeling methods must represent the porosity and permeability associated with the fracture network, as accurately as possible with very little apriori information. Three rather different types of approaches have been used: (1) dual porosity simulations; (2) `stochastic` modeling of fracture networks, and (3) fractal modeling of fracture networks. Stochastic models which assume a variety of probability distributions of fracture characteristics have been used with some success in modeling fracture networks. The advantage of these stochastic models over the dual porosity simulations is that real fracture heterogeneities are included in the modeling process. In the sections provided in this paper the authors will present fractal analysis of the MWX site, using the box-counting procedure; (2) review evidence testing the fractal nature of fracture distributions and discuss the advantages of using their fractal analysis over a stochastic analysis; (3) present an efficient algorithm for producing a self-similar fracture networks which mimic the real MWX outcrop fracture network.
Chen, Yun; Yang, Hui
2016-08-01
Engineered and natural systems often involve irregular and self-similar geometric forms, which is called fractal geometry. For instance, precision machining produces a visually flat surface, while which looks like a rough mountain in the nanometer scale under the microscope. Human heart consists of a fractal network of muscle cells, Purkinje fibers, arteries and veins. Cardiac electrical activity exhibits highly nonlinear and fractal behaviors. Although space-time dynamics occur on the fractal geometry, e.g., chemical etching on the surface of machined parts and electrical conduction in the heart, most of existing works modeled space-time dynamics (e.g., reaction, diffusion and propagation) on the Euclidean geometry (e.g., flat planes and rectangular volumes). This brings inaccurate approximation of real-world dynamics, due to sensitive dependence of nonlinear dynamical systems on initial conditions. In this paper, we developed novel methods and tools for the numerical simulation and pattern recognition of spatiotemporal dynamics on fractal surfaces of complex systems, which include (1) characterization and modeling of fractal geometry, (2) fractal-based simulation and modeling of spatiotemporal dynamics, (3) recognizing and quantifying spatiotemporal patterns. Experimental results show that the proposed methods outperform traditional modeling approaches based on the Euclidean geometry, and provide effective tools to model and characterize space-time dynamics on fractal surfaces of complex systems.
On a fractal LC-electric circuit modeled by local fractional calculus
Yang, Xiao-Jun; Machado, J. A. Tenreiro; Cattani, Carlo; Gao, Feng
2017-06-01
A non-differentiable model of the LC-electric circuit described by a local fractional differential equation of fractal dimensional order is addressed in this article. From the fractal electrodynamics point of view, the relaxation oscillator, defined on Cantor sets in LC-electric circuit, and its exact solution using the local fractional Laplace transform are obtained. Comparative results among local fractional derivative, Riemann-Liouville fractional derivative and conventional derivative are discussed. Local fractional calculus is proposed as a new tool suitable for the study of a large class of electric circuits.
Modelling Applicability of Fractal Analysis to Efficiency of Soil Exploration by Roots
Walk, Thomas C.; van Erp, Erik; Lynch, Jonathan P.
2004-01-01
• Background and Aims Fractal analysis allows calculation of fractal dimension, fractal abundance and lacunarity. Fractal analysis of plant roots has revealed correlations of fractal dimension with age, topology or genotypic variation, while fractal abundance has been associated with root length. Lacunarity is associated with heterogeneity of distribution, and has yet to be utilized in analysis of roots. In this study, fractal analysis was applied to the study of root architecture and acquisi...
Energy Technology Data Exchange (ETDEWEB)
Bessagnet, B.
2000-07-01
Most generally, atmospheric aerosol particles are ideally modelled as spheres for which it is easy to calculate geometrical properties (diameter, surface, and volume) and ensuing radiative, dynamical and chemical characteristics. However, the particles issued in particular from combustion processes display a large range of structures, from linear cluster structures to quasi spherical ones. These various shapes result in quite different physical and chemical characteristics for these particles. Thus, the processes of absorption, coagulation and deposition are strongly affected by the fractal nature of aerosols. Whereas only one discretization parameter (diameter) is required in the spectral distribution of spherical particles, it is necessary to use a 2-D distribution n(v,a) for fractal ones, v and a respectively representing the volume and the surface of the particle. The governing aerosol population balance equation not only involves a coagulation term but also a coalescence contribution describing the surface evolution. With this new model, surface fractal dimensions are associated with varying particle morphologies. This model has been applied to a plume study. First, the gas phase is treated using a gas phase chemistry model, then the fractal aerosol module is used for the particulate phase.
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)
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)
A fractal model for the effective thermal conductivity of nanoparticle suspensions
Institute of Scientific and Technical Information of China (English)
WANG Buxuan; ZHOU Leping; PENG Xiaofeng
2004-01-01
Extending the effective medium approximation with the fractal theory for describing nanoparticle clusters and their radius distribution, a predictive model is proposed for the effective thermal conductivity of nanoparticle suspension, combined with the consideration of size effect and surface adsorption effect of nanoparticles.The predicted effective thermal conductivity of nanoparticle suspension is consistent with experimental data in the dilute limit.
Rough electricity: a new fractal multi-factor model of electricity spot prices
DEFF Research Database (Denmark)
Bennedsen, Mikkel
We introduce a new mathematical model of electricity spot prices which accounts for the most important stylized facts of these time series: seasonality, spikes, stochastic volatility and mean reversion. Empirical studies have found a possible fifth stylized fact, fractality, and our approach...
Modelling the afforested system: the forest/tree model
Heil, G.W.; Deursen, van W.; Elemans, M.; Mol, J.; Kros, H.
2007-01-01
A forest/tree model has been developed of which the main growth processes are based on the CENW model. The model links the flows of carbon (C)), energy, nutrients and water in trees and soil organic matter. Modelled tree growth depends on physiological plant factors, the size of plant pools, such as
Elastoplastic contact mechanics model of rough surface based on fractal theory
Yuan, Yuan; Gan, Li; Liu, Kai; Yang, Xiaohui
2017-01-01
Because the result of the MB fractal model contradicts with the classical contact mechanics, a revised elastoplastic contact model of a single asperity is developed based on fractal theory. The critical areas of a single asperity are scale dependent, with an increase in the contact load and contact area, a transition from elastic, elastoplastic to full plastic deformation takes place in this order. In considering the size distribution function, analytic expression between the total contact load and the real contact area on the contact surface is obtained. The elastic, elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity. The results show that a rough surface is firstly in elastic deformation. As the load increases, elastoplastic or full plastic deformation takes place. For constant characteristic length scale G, the slope of load-area relation is proportional to fractal dimension D. For constant fractal dimension D, the slope of load-area relation is inversely proportional to G. For constant D and G, the slope of load-area relation is inversely proportional to property of the material ϕ, namely with the same load, the material of rough surface is softer, and the total contact area is larger. The contact mechanics model provides a foundation for study of the friction, wear and seal performance of rough surfaces.
Elastoplastic Contact Mechanics Model of Rough Surface Based on Fractal Theory
Institute of Scientific and Technical Information of China (English)
YUAN Yuan; GAN Li; LIU Kai; YANG Xiaohui
2017-01-01
Because the result of the MB fractal model contradicts with the classical contact mechanics,a revised elastoplastic contact model of a single asperity is developed based on fractal theory.The critical areas of a single asperity are scale dependent,with an increase in the contact load and contact area,a transition from elastic,elastoplastic to full plastic deformation takes place in this order.In considering the size distribution function,analytic expression between the total contact load and the real contact area on the contact surface is obtained.The elastic,elastoplastic and full plastic contact load are obtained by the critical elastic contact area of the biggest asperity and maximun contact area of a single asperity.The results show that a rough surface is firstly in elastic deformation.As the load increases,elastoplastic or full plastic deformation takes place.For constant characteristic length scale G,the slope of load-area relation is proportional to fractal dimension D.For constant fractal dimension D,the slope of load-area relation is inversely proportional to G.For constant D and G,the slope of load-area relation is inversely proportional to property of the material φ,namely with the same load,the material of rough surface is softer,and the total contact area is larger.The contact mechanics model provides a foundation for study of the friction,wear and seal performance of rough surfaces.
Black carbon fractal morphology and short-wave radiative impact: a modelling study
Directory of Open Access Journals (Sweden)
M. Kahnert
2011-11-01
Full Text Available We investigate the impact of the morphological properties of freshly emitted black carbon aerosols on optical properties and on radiative forcing. To this end, we model the optical properties of fractal black carbon aggregates by use of numerically exact solutions to Maxwell's equations within a spectral range from the UVC to the mid-IR. The results are coupled to radiative transfer computations, in which we consider six realistic case studies representing different atmospheric pollution conditions and surface albedos. The spectrally integrated radiative impacts of black carbon are compared for two different fractal morphologies, which brace the range of recently reported experimental observations of black carbon fractal structures. We also gauge our results by performing corresponding calculations based on the homogeneous sphere approximation, which is commonly employed in climate models. We find that at top of atmosphere the aggregate models yield radiative impacts that can be as much as 2 times higher than those based on the homogeneous sphere approximation. An aggregate model with a low fractal dimension can predict a radiative impact that is higher than that obtained with a high fractal dimension by a factor ranging between 1.1–1.6. Although the lower end of this scale seems like a rather small effect, a closer analysis reveals that the single scattering optical properties of more compact and more lacy aggregates differ considerably. In radiative flux computations there can be a partial cancellation due to the opposing effects of different error sources. However, this cancellation effect can strongly depend on atmospheric conditions and is therefore quite unpredictable. We conclude that the fractal morphology of black carbon aerosols and their fractal parameters can have a profound impact on their radiative forcing effect, and that the use of the homogeneous sphere model introduces unacceptably high biases in radiative impact studies. We
Black carbon fractal morphology and short-wave radiative impact: a modelling study
Directory of Open Access Journals (Sweden)
M. Kahnert
2011-08-01
Full Text Available We investigate the impact of the morphological properties of freshly emitted black carbon aerosols on optical properties and on radiative forcing. To this end, we model the optical properties of fractal black carbon aggregates by use of numerically exact solutions to Maxwell's equations within a spectral range from the UVC to the mid-IR. The results are coupled to radiative transfer computations, in which we consider six realistic case studies representing different atmospheric pollution conditions and surface albedos. The spectrally integrated radiative impacts of black carbon are compared for two different fractal morphologies, which brace the range of recently reported experimental observations of black carbon fractal structures. We also gauge our results by performing corresponding calculations based on the homogeneous sphere approximation, which is commonly employed in climate models. We find that at top of atmosphere the aggregate models yield radiative impacts that can be as much as 2 times higher than those based on the homogeneous sphere approximation. An aggregate model with a low fractal dimension can predict a radiative impact that is higher than that obtained with a high fractal dimension by a factor ranging between 1.1–1.6. Although the lower end of this scale seems like a rather small effect, a closer analysis reveals that the single scattering optical properties of more compact and more lacy aggregates differ considerably. In radiative flux computations there can be a partial cancellation due to the opposing effects of differences in the optical cross sections and asymmetry parameters. However, this cancellation effect can strongly depend on atmospheric conditions and is therefore quite unpredictable. We conclude that the fractal morphology of black carbon aerosols and their fractal parameters can have a profound impact on their radiative forcing effect, and that the use of the homogeneous sphere model introduces unacceptably
Modelling, fabrication and characterisation of THz fractal meta-materials
DEFF Research Database (Denmark)
Xiao, S.; Zhou, L.; Malureanu, Radu
2011-01-01
We present theoretical predictions, fabrication procedure and characterisation results of fractal metamaterials for the THz frequency range. The characterisation results match well the predicted response thus validating both the fabrication procedure as well as the simulation one. Such systems show...... the possibility of fabricating new THz devices like polarisers, polarising beam splitters etc. We set a goal to develop a method which is unambiguous but at the same time simple and straightforward. We assume that this can be done by observing the wave propagation inside a metamaterial slab thick enough to avoid......] of the field inside the metamaterial slab when it is illuminated with a plane wave incident from vacuum. Then we determine the effective refractive index from the propagation constant of the dominating (fundamental) Bloch mode. The Bloch and wave impedances are determined by definition as the proportionality...
Liang, Yingjie; Ye, Allen Q.; Chen, Wen; Gatto, Rodolfo G.; Colon-Perez, Luis; Mareci, Thomas H.; Magin, Richard L.
2016-10-01
Non-Gaussian (anomalous) diffusion is wide spread in biological tissues where its effects modulate chemical reactions and membrane transport. When viewed using magnetic resonance imaging (MRI), anomalous diffusion is characterized by a persistent or 'long tail' behavior in the decay of the diffusion signal. Recent MRI studies have used the fractional derivative to describe diffusion dynamics in normal and post-mortem tissue by connecting the order of the derivative with changes in tissue composition, structure and complexity. In this study we consider an alternative approach by introducing fractal time and space derivatives into Fick's second law of diffusion. This provides a more natural way to link sub-voxel tissue composition with the observed MRI diffusion signal decay following the application of a diffusion-sensitive pulse sequence. Unlike previous studies using fractional order derivatives, here the fractal derivative order is directly connected to the Hausdorff fractal dimension of the diffusion trajectory. The result is a simpler, computationally faster, and more direct way to incorporate tissue complexity and microstructure into the diffusional dynamics. Furthermore, the results are readily expressed in terms of spectral entropy, which provides a quantitative measure of the overall complexity of the heterogeneous and multi-scale structure of biological tissues. As an example, we apply this new model for the characterization of diffusion in fixed samples of the mouse brain. These results are compared with those obtained using the mono-exponential, the stretched exponential, the fractional derivative, and the diffusion kurtosis models. Overall, we find that the order of the fractal time derivative, the diffusion coefficient, and the spectral entropy are potential biomarkers to differentiate between the microstructure of white and gray matter. In addition, we note that the fractal derivative model has practical advantages over the existing models from the
Species Tree Inference Using a Mixture Model.
Ullah, Ikram; Parviainen, Pekka; Lagergren, Jens
2015-09-01
Species tree reconstruction has been a subject of substantial research due to its central role across biology and medicine. A species tree is often reconstructed using a set of gene trees or by directly using sequence data. In either of these cases, one of the main confounding phenomena is the discordance between a species tree and a gene tree due to evolutionary events such as duplications and losses. Probabilistic methods can resolve the discordance by coestimating gene trees and the species tree but this approach poses a scalability problem for larger data sets. We present MixTreEM-DLRS: A two-phase approach for reconstructing a species tree in the presence of gene duplications and losses. In the first phase, MixTreEM, a novel structural expectation maximization algorithm based on a mixture model is used to reconstruct a set of candidate species trees, given sequence data for monocopy gene families from the genomes under study. In the second phase, PrIME-DLRS, a method based on the DLRS model (Åkerborg O, Sennblad B, Arvestad L, Lagergren J. 2009. Simultaneous Bayesian gene tree reconstruction and reconciliation analysis. Proc Natl Acad Sci U S A. 106(14):5714-5719), is used for selecting the best species tree. PrIME-DLRS can handle multicopy gene families since DLRS, apart from modeling sequence evolution, models gene duplication and loss using a gene evolution model (Arvestad L, Lagergren J, Sennblad B. 2009. The gene evolution model and computing its associated probabilities. J ACM. 56(2):1-44). We evaluate MixTreEM-DLRS using synthetic and biological data, and compare its performance with a recent genome-scale species tree reconstruction method PHYLDOG (Boussau B, Szöllősi GJ, Duret L, Gouy M, Tannier E, Daubin V. 2013. Genome-scale coestimation of species and gene trees. Genome Res. 23(2):323-330) as well as with a fast parsimony-based algorithm Duptree (Wehe A, Bansal MS, Burleigh JG, Eulenstein O. 2008. Duptree: a program for large-scale phylogenetic
Workflow Fault Tree Generation Through Model Checking
DEFF Research Database (Denmark)
Herbert, Luke Thomas; Sharp, Robin
2014-01-01
We present a framework for the automated generation of fault trees from models of realworld process workflows, expressed in a formalised subset of the popular Business Process Modelling and Notation (BPMN) language. To capture uncertainty and unreliability in workflows, we extend this formalism...... of the system being modelled. From these calculations, a comprehensive fault tree is generated. Further, we show that annotating the model with rewards (data) allows the expected mean values of reward structures to be calculated at points of failure....
Tao, Xie; Shang-Zhuo, Zhao; William, Perrie; He, Fang; Wen-Jin, Yu; Yi-Jun, He
2016-06-01
To study the electromagnetic backscattering from a one-dimensional drifting fractal sea surface, a fractal sea surface wave-current model is derived, based on the mechanism of wave-current interactions. The numerical results show the effect of the ocean current on the wave. Wave amplitude decreases, wavelength and kurtosis of wave height increase, spectrum intensity decreases and shifts towards lower frequencies when the current occurs parallel to the direction of the ocean wave. By comparison, wave amplitude increases, wavelength and kurtosis of wave height decrease, spectrum intensity increases and shifts towards higher frequencies if the current is in the opposite direction to the direction of ocean wave. The wave-current interaction effect of the ocean current is much stronger than that of the nonlinear wave-wave interaction. The kurtosis of the nonlinear fractal ocean surface is larger than that of linear fractal ocean surface. The effect of the current on skewness of the probability distribution function is negligible. Therefore, the ocean wave spectrum is notably changed by the surface current and the change should be detectable in the electromagnetic backscattering signal. Project supported by the National Natural Science Foundation of China (Grant No. 41276187), the Global Change Research Program of China (Grant No. 2015CB953901), the Priority Academic Development Program of Jiangsu Higher Education Institutions (PAPD), Program for the Innovation Research and Entrepreneurship Team in Jiangsu Province, China, the Canadian Program on Energy Research and Development, and the Canadian World Class Tanker Safety Service.
Testing models of tree canopy structure
Energy Technology Data Exchange (ETDEWEB)
Martens, S.N. (Los Alamos National Laboratory, NM (United States))
1994-06-01
Models of tree canopy structure are difficult to test because of a lack of data which are suitability detailed. Previously, I have made three-dimensional reconstructions of individual trees from measured data. These reconstructions have been used to test assumptions about the dispersion of canopy elements in two- and three-dimensional space. Lacunarity analysis has also been used to describe the texture of the reconstructed canopies. Further tests regarding models of the nature of tree branching structures have been made. Results using probability distribution functions for branching measured from real trees show that branching in Juglans is not Markovian. Specific constraints or rules are necessary to achieve simulations of branching structure which are faithful to the originally measured trees.
A Fractal and Scale-free Model of Complex Networks with Hub Attraction Behaviors
Kuang, Li; Li, Deyi; Li, Yuanxiang; Sun, Yu
2013-01-01
It is widely believed that fractality of complex networks origins from hub repulsion behaviors (anticorrelation or disassortativity), which means large degree nodes tend to connect with small degree nodes. This hypothesis was demonstrated by a dynamical growth model, which evolves as the inverse renormalization procedure proposed by Song et al. Now we find that the dynamical growth model is based on the assumption that all the cross-boxes links has the same probability e to link to the most connected nodes inside each box. Therefore, we modify the growth model by adopting the flexible probability e, which makes hubs have higher probability to connect with hubs than non-hubs. With this model, we find some fractal and scale-free networks have hub attraction behaviors (correlation or assortativity). The results are the counter-examples of former beliefs.
Fractal Potential Flows as an Exact Model for Fully Developed Turbulence
Vass, József
2013-01-01
Fully Developed Turbulence (FDT) occurs at the infinite extreme of the Reynolds spectrum. It is a theoretical phenomenon which can only be approximated experimentally or computationally, and thus its precise properties are only hypothetical, though widely accepted. It is considered to be a chaotic yet steady flow field, with self-similar fractalline features. A number of approximate models exist, often exploiting this self-similarity. We hereby present the exact mathematical model of Fractal Potential Flows, and link it philosophically to the phenomenon of FDT, building on its experimental characteristics. The model hinges on the recursive iteration of a fluid dynamical transfer operator. We show the existence of its unique attractor in an appropriate function space - called the invariant flow - which will serve as our model for the FDT flow field. Its sink singularities are shown to form an IFS fractal, resolving Mandelbrot's Conjecture. Meanwhile we present an isometric isomorphism between flows and probabi...
Khokhlov, D L
1999-01-01
The model of the universe is considered in which background of the universe is not defined by the matter but is a priori specified as a homogenous and isotropic flat space. The scale factor of the universe follows the linear law. The scale of mass changes proportional to the scale factor. This leads to that the universe has the fractal structure with a power index of 2.
Xi, Jinxiang; Si, Xiuhua A.; Kim, JongWon; Mckee, Edward; Lin, En-Bing
2014-01-01
Background Exhaled aerosol patterns, also called aerosol fingerprints, provide clues to the health of the lung and can be used to detect disease-modified airway structures. The key is how to decode the exhaled aerosol fingerprints and retrieve the lung structural information for a non-invasive identification of respiratory diseases. Objective and Methods In this study, a CFD-fractal analysis method was developed to quantify exhaled aerosol fingerprints and applied it to one benign and three malign conditions: a tracheal carina tumor, a bronchial tumor, and asthma. Respirations of tracer aerosols of 1 µm at a flow rate of 30 L/min were simulated, with exhaled distributions recorded at the mouth. Large eddy simulations and a Lagrangian tracking approach were used to simulate respiratory airflows and aerosol dynamics. Aerosol morphometric measures such as concentration disparity, spatial distributions, and fractal analysis were applied to distinguish various exhaled aerosol patterns. Findings Utilizing physiology-based modeling, we demonstrated substantial differences in exhaled aerosol distributions among normal and pathological airways, which were suggestive of the disease location and extent. With fractal analysis, we also demonstrated that exhaled aerosol patterns exhibited fractal behavior in both the entire image and selected regions of interest. Each exhaled aerosol fingerprint exhibited distinct pattern parameters such as spatial probability, fractal dimension, lacunarity, and multifractal spectrum. Furthermore, a correlation of the diseased location and exhaled aerosol spatial distribution was established for asthma. Conclusion Aerosol-fingerprint-based breath tests disclose clues about the site and severity of lung diseases and appear to be sensitive enough to be a practical tool for diagnosis and prognosis of respiratory diseases with structural abnormalities. PMID:25105680
Numerical Modelling of Ore-forming Dynamics of Fractal Dispersive Fluid Systems
Institute of Scientific and Technical Information of China (English)
邓军; 方云; 杨立强; 杨军臣; 孙忠实; 王建平; 丁式江; 王庆飞
2001-01-01
Based on an analysis of the fractal structures and mass transport mechanism of typical shear-fluid-ore formation system, the fractal dispersion theory of the fluid system was used in the dynamic study of the ore formation system. The model of point-source diffusive illuviation of the shear-fluid-ore formation system was constructed, and the numerical simulation of dynamics of the ore formation system was finished. The result shows that: (1) The metallogenic system have nested fractal structure. Different fractal dimension values in different systems show unbalance and inhomogeneity of ore-forming processes in the geohistory. It is an important parameter to symbolize the process of remobilization and accumulation of ore-forming materials. Also it can indicate the dynamics of the metallogenic system quantitatively to some extent. (2) In essence, the fractal dispersive ore-forming dynamics is a combination of multi-processes dominated by fluid dynamics and supplemented by molecule dispersion in fluids and fluid-rock interaction. It changes components and physico-chemical properties of primary rocks and fluids, favouring deposition and mineralization of ore-forming materials. (3) Gold ore-forming processes in different types of shear zones are quite different. (1) In a metallogenic system with inhomogeneous volumetric change and inhomogeneous shear, mineralization occurs in structural barriers in the centre of a shear zone and in geochemical barriers in the shear zone near its boundaries. But there is little possibility of mineralization out of the shear zone. (2) As to a metallogenic system with inhomogeneous volumetric change and simple shear, mineralization may occur only in structural barriers near the centre of the shear zone. (3) In a metallogenic system with homogeneous volumetric change and inhomogeneous shear, mineralization may occur in geochemical barriers both within and out of the shear zone.
Directory of Open Access Journals (Sweden)
Jinxiang Xi
Full Text Available Exhaled aerosol patterns, also called aerosol fingerprints, provide clues to the health of the lung and can be used to detect disease-modified airway structures. The key is how to decode the exhaled aerosol fingerprints and retrieve the lung structural information for a non-invasive identification of respiratory diseases.In this study, a CFD-fractal analysis method was developed to quantify exhaled aerosol fingerprints and applied it to one benign and three malign conditions: a tracheal carina tumor, a bronchial tumor, and asthma. Respirations of tracer aerosols of 1 µm at a flow rate of 30 L/min were simulated, with exhaled distributions recorded at the mouth. Large eddy simulations and a Lagrangian tracking approach were used to simulate respiratory airflows and aerosol dynamics. Aerosol morphometric measures such as concentration disparity, spatial distributions, and fractal analysis were applied to distinguish various exhaled aerosol patterns.Utilizing physiology-based modeling, we demonstrated substantial differences in exhaled aerosol distributions among normal and pathological airways, which were suggestive of the disease location and extent. With fractal analysis, we also demonstrated that exhaled aerosol patterns exhibited fractal behavior in both the entire image and selected regions of interest. Each exhaled aerosol fingerprint exhibited distinct pattern parameters such as spatial probability, fractal dimension, lacunarity, and multifractal spectrum. Furthermore, a correlation of the diseased location and exhaled aerosol spatial distribution was established for asthma.Aerosol-fingerprint-based breath tests disclose clues about the site and severity of lung diseases and appear to be sensitive enough to be a practical tool for diagnosis and prognosis of respiratory diseases with structural abnormalities.
When human walking becomes random walking: fractal analysis and modeling of gait rhythm fluctuations
Hausdorff, Jeffrey M.; Ashkenazy, Yosef; Peng, Chang-K.; Ivanov, Plamen Ch.; Stanley, H. Eugene; Goldberger, Ary L.
2001-12-01
We present a random walk, fractal analysis of the stride-to-stride fluctuations in the human gait rhythm. The gait of healthy young adults is scale-free with long-range correlations extending over hundreds of strides. This fractal scaling changes characteristically with maturation in children and older adults and becomes almost completely uncorrelated with certain neurologic diseases. Stochastic modeling of the gait rhythm dynamics, based on transitions between different “neural centers”, reproduces distinctive statistical properties of the gait pattern. By tuning one model parameter, the hopping (transition) range, the model can describe alterations in gait dynamics from childhood to adulthood - including a decrease in the correlation and volatility exponents with maturation.
Tao, Xie; William, Perrie; Shang-Zhuo, Zhao; He, Fang; Wen-Jin, Yu; Yi-Jun, He
2016-07-01
Sea surface current has a significant influence on electromagnetic (EM) backscattering signals and may constitute a dominant synthetic aperture radar (SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section (NRCS) discrepancies between the model for a coupled wave-current fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle, as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface. Project supported by the National Natural Science Foundation of China (Grant No. 41276187), the Global Change Research Program of China (Grant No. 2015CB953901), the Priority Academic Program Development of Jiangsu Higher Education Institutions, China, the Program for the Innovation Research and Entrepreneurship Team in Jiangsu Province, China, the Canadian Program on Energy Research and Development, and the Canadian World Class Tanker Safety Service Program.
Directory of Open Access Journals (Sweden)
WAN Xin
2006-02-01
Full Text Available Under vacuum, heat transfer in porous corundum shell of investment casting depends on the characteristics of the solid materials and the spatial arrangement of solids and pores. In this study, we present a modified fractal approach to model the pore structure of corundum shell and to describe its influence on the thermal conductivity. We assumed that there is no heat convection in the shell. A sectioned view of porous corundum shell was studied and used to describe the geometric structure and to calculate the fractal dimension d. Based on the fractal dimension d, we obtained the relationship between volumetric solid content and pore arrangement in different measure scales. A heat transfer model was thus established using a network of resistors in which we applied an equivalent approach to calculate the effective thermal conductivity of real porous corundum shell that include the effects of heat conduction and heat radiation of solid. From the obtained results we discuss these effects on the effective thermal conductivity including the scale of measurement, the structure of pore and the temperature. At last these results were compared with other empirical model, which computed by assuming even porosity in which effect of pore structure was not being considered. Though the thermal conductivity calculated essentially in agreement with that obtained from empirical model, model used in this study is more close to the real heat transfer process.
Institute of Scientific and Technical Information of China (English)
谢涛; William Perrie; 赵尚卓; 方贺; 于文金; 何宜军
2016-01-01
Sea surface current has a significant influence on electromagnetic (EM) backscattering signals and may constitute a dominant synthetic aperture radar (SAR) imaging mechanism. An effective EM backscattering model for a one-dimensional drifting fractal sea surface is presented in this paper. This model is used to simulate EM backscattering signals from the drifting sea surface. Numerical results show that ocean currents have a significant influence on EM backscattering signals from the sea surface. The normalized radar cross section (NRCS) discrepancies between the model for a coupled wave-current fractal sea surface and the model for an uncoupled fractal sea surface increase with the increase of incidence angle, as well as with increasing ocean currents. Ocean currents that are parallel to the direction of the wave can weaken the EM backscattering signal intensity, while the EM backscattering signal is intensified by ocean currents propagating oppositely to the wave direction. The model presented in this paper can be used to study the SAR imaging mechanism for a drifting sea surface.
Critical behavior of the Gaussian model on fractal lattices in external magnetic field
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
For inhomogeneous lattices we generalize the classical Gaussian model, i.e. it is proposed that the Gaussian type distribution constant and the external magnetic field of site i in this model depend on the coordination number qi of site i, and that the relation bqi/bqj=qi/qj holds among bqi's, where bqi is the Gaussian type distribution constant of site i. Using the decimation real-space renormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierarchical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site i can be expressed in the form K*=bqi/qi and h*qi=0, respectively. It is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices, and if the fractal dimensionality df=4, the Gaussian model and the mean field theories give the same results.
Fractals a very short introduction
Falconer, Kenneth
2013-01-01
Many are familiar with the beauty and ubiquity of fractal forms within nature. Unlike the study of smooth forms such as spheres, fractal geometry describes more familiar shapes and patterns, such as the complex contours of coastlines, the outlines of clouds, and the branching of trees. In this Very Short Introduction, Kenneth Falconer looks at the roots of the 'fractal revolution' that occurred in mathematics in the 20th century, presents the 'new geometry' of fractals, explains the basic concepts, and explores the wide range of applications in science, and in aspects of economics.This is esse
Tahavvor, Ali Reza
2016-06-01
In the present study artificial neural network and fractal geometry are used to predict frost thickness and density on a cold flat plate having constant surface temperature under forced convection for different ambient conditions. These methods are very applicable in this area because phase changes such as melting and solidification are simulated by conventional methods but frost formation is a most complicated phase change phenomenon consists of coupled heat and mass transfer. Therefore conventional mathematical techniques cannot capture the effects of all parameters on its growth and development because this process influenced by many factors and it is a time dependent process. Therefore, in this work soft computing method such as artificial neural network and fractal geometry are used to do this manner. The databases for modeling are generated from the experimental measurements. First, multilayer perceptron network is used and it is found that the back-propagation algorithm with Levenberg-Marquardt learning rule is the best choice to estimate frost growth properties due to accurate and faster training procedure. Second, fractal geometry based on the Von-Koch curve is used to model frost growth procedure especially in frost thickness and density. Comparison is performed between experimental measurements and soft computing methods. Results show that soft computing methods can be used more efficiently to determine frost properties over a flat plate. Based on the developed models, wide range of frost formation over flat plates can be determined for various conditions.
Tahavvor, Ali Reza
2017-03-01
In the present study artificial neural network and fractal geometry are used to predict frost thickness and density on a cold flat plate having constant surface temperature under forced convection for different ambient conditions. These methods are very applicable in this area because phase changes such as melting and solidification are simulated by conventional methods but frost formation is a most complicated phase change phenomenon consists of coupled heat and mass transfer. Therefore conventional mathematical techniques cannot capture the effects of all parameters on its growth and development because this process influenced by many factors and it is a time dependent process. Therefore, in this work soft computing method such as artificial neural network and fractal geometry are used to do this manner. The databases for modeling are generated from the experimental measurements. First, multilayer perceptron network is used and it is found that the back-propagation algorithm with Levenberg-Marquardt learning rule is the best choice to estimate frost growth properties due to accurate and faster training procedure. Second, fractal geometry based on the Von-Koch curve is used to model frost growth procedure especially in frost thickness and density. Comparison is performed between experimental measurements and soft computing methods. Results show that soft computing methods can be used more efficiently to determine frost properties over a flat plate. Based on the developed models, wide range of frost formation over flat plates can be determined for various conditions.
Argolo, C.; Barros, P.; Tomé, T.; Arashiro, E.; Gleria, Iram; Lyra, M. L.
2016-08-01
We investigate a stochastic lattice model describing a predator-prey system in a fractal scale-free landscape, mimicked by the fractal Sierpinski carpet. We determine the threshold of species coexistence, that is, the critical phase boundary related to the transition between an active state, where both species coexist and an absorbing state where one of the species is extinct. We show that the predators must live longer in order to persist in a fractal habitat. We further performed a finite-size scaling analysis in the vicinity of the absorbing-state phase transition to compute a set of stationary and dynamical critical exponents. Our results indicate that the transition belongs to the directed percolation universality class exhibited by the usual contact process model on the same fractal landscape.
Zhao, Leihong; Yang, Lining; Lin, Hongjun; Zhang, Meijia; Yu, Haiying; Liao, Bao-Qiang; Wang, Fangyuan; Zhou, Xiaoling; Li, Renjie
2016-12-01
While the adsorptive fouling in membrane bioreactors (MBRs) is highly dependent of the surface morphology, little progress has been made on modeling biocake layer surface morphology. In this study, a novel method, which combined static light scattering method for fractal dimension (Df) measurement with fractal method represented by the modified two-variable Weierstrass-Mandelbrot function, was proposed to model biocake layer surface in a MBR. Characterization by atomic force microscopy showed that the biocake surface was stochastic, disorder, self-similarity, and with non-integer dimension, illustrating obvious fractal features. Fractal dimension (Df) of sludge suspension experienced a significant change with operation of the MBR. The constructed biocake layer surface by the proposed method was quite close to the real surface, showing the feasibility of the proposed method. It was found that Df was the critical factor affecting surface morphology, while other factors exerted moderate or minor effects on the roughness of biocake layer.
The fractal universe, preon structure of particles, and the familon model of dark matter
Burdyuzha, V. V.
2014-06-01
The consequences of the preon structure of matter are discussed. The table of elementary particles is presented in its preon version, in which quarks, leptons and gauge bosons are considered to be composite particles. The preon model provides a natural explanation for dark matter, which consists of pseudo-Goldstone familon bosons with a mass m ˜ 10-3-10-5 eV. It has been shown that phase transitions could occur at various temperatures in a medium of familons formed of up and down quarks of different generations, leading to fractal fragmentation of the medium and the formation of "distinguished scales" in the Universe. The role of particle families is elucidatied. Fractality is also briefly discussed.
Nonlinear extensions of a fractal-multifractal approach for environmental modeling
Energy Technology Data Exchange (ETDEWEB)
Cortis, A.; Puente, C.E.; Sivakumar, B.
2008-10-15
We present the extension of a deterministic fractal geometric procedure aimed at representing the complexity of the spatio-temporal patterns encountered in environmental applications. The original procedure, which is based on transformations of multifractal distributions via fractal functions, is extended through the introduction of nonlinear perturbations to the underlying iterated linear maps. We demonstrate how the nonlinear perturbations generate yet a richer collection of patterns by means of various simulations that include evolutions of patterns based on changes in their parameters and in their statistical and multifractal properties. It is shown that the nonlinear extensions yield structures that closely resemble complex hydrologic temporal data sets, such as rainfall and runoff time series, and width-functions of river networks as a function of distance from the basin outlet. The implications of this nonlinear approach for environmental modeling and prediction are discussed.
Energy Technology Data Exchange (ETDEWEB)
Sun, Haitao; Li, Ning; Guo, Lijun; Gao, Fei; Liu, Cheng [Shandong University, Shandong Medical Imaging Research Institute, Shandong (Korea, Republic of)
2011-06-15
The aim of this study was to use fractal dimension (FD) analysis on multidetector CT (MDCT) images for quantifying the morphological changes of the pulmonary artery tree in patients with pulmonary hypertension (PH). Fourteen patients with PH and 17 patients without PH as controls were studied. All of the patients underwent contrast-enhanced helical CT and transthoracic echocardiography. The pulmonary artery trees were generated using post-processing software, and the FD and projected image area of the pulmonary artery trees were determined with Image J software in a personal computer. The FD, the projected image area and the pulmonary artery pressure (PAP) were statistically evaluated in the two groups. The FD, the projected image area and the PAP of the patients with PH were higher than those values of the patients without PH (p < 0.05, t-test). There was a high correlation of FD with the PAP (r = 0.82, p < 0.05, partial correlation analysis). There was a moderate correlation of FD with the projected image area (r = 0.49, p < 0.05, partial correlation analysis). There was a correlation of the PAP with the projected image area (r = 0.65, p < 0.05, Pearson correlation analysis). The FD of the pulmonary arteries in the PH patients was significantly higher than that of the controls. There is a high correlation of FD with the PAP.
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
Habib Abedi; Mustafa Salti
2015-04-01
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. This correspondence allows us to reconstruct the potential and the dynamics of a fractal canonical scalar field (the fractal quintessence) according to the evolution of ghost dark energy density.
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 i
More general capillary pressure and relative permeability models from fractal geometry.
Li, Kewen
2010-01-15
More general capillary pressure and relative permeability models were derived theoretically from fractal modeling of a porous medium. It was found that the new capillary pressure model could be reduced to the frequently-used Brooks-Corey capillary pressure model and the Li-Horne imbibition model when the fractal dimension of a porous medium takes specific values. This also demonstrates that the Brooks-Corey model and the Li-Horne model have a further confirmed theoretical basis. Capillary pressure data measured using mercury intrusion techinque were used to verify the model. The results demonstrated that the new capillary pressure model could represent the capillary pressure curves in those rocks with fracures or with great heterogeneity while the existing models cannot. The new relative permeability models can be reduced to the Brooks-Corey relative permeability model in a specific case. It has been proved theoretically that the relative permeability of each phase in a smooth fracture is only a linear function of its own saturation. Relative permeability data were calculated using the new models and the model results were compared with experimental data measured using a steady-state technique. The comparison demonstrated that the relative permeability models and experimental results were consistent with each other.
Directory of Open Access Journals (Sweden)
Franceschini Barbara
2005-02-01
Full Text Available Abstract Background 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. Methods This paper introduces the surface fractal dimension (Ds 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. Results We show that Ds 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. Conclusions 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.
A Fractal Model for the Shear Behaviour of Large-Scale Opened Rock Joints
Li, Y.; Oh, J.; Mitra, R.; Canbulat, I.
2017-01-01
This paper presents a joint constitutive model that represents the shear behaviour of a large-scale opened rock joint. Evaluation of the degree of opening is made by considering the ratio between the joint wall aperture and the joint amplitude. Scale dependence of the surface roughness is investigated by approximating a natural joint profile to a fractal curve patterned in self-affinity. Developed scaling laws show the slopes of critical waviness and critical unevenness tend to flatten with increased sampling length. Geometrical examination of four 400-mm joint profiles agrees well with the suggested formulations involving multi-order asperities and fractal descriptors. Additionally, a fractal-based formulation is proposed to estimate the peak shear displacements of rock joints at varying scales, which shows a good correlation with experimental data taken from the literature. Parameters involved in the constitutive law can be acquired by inspecting roughness features of sampled rock joints. Thus, the model can be implemented in numerical software for the stability analysis of the rock mass with opened joints.
Bouligand, C.; Glen, J.M.G.; Blakely, R.J.
2009-01-01
We have revisited the problem of mapping depth to the Curie temperature isotherm from magnetic anomalies in an attempt to provide a measure of crustal temperatures in the western United States. Such methods are based on the estimation of the depth to the bottom of magnetic sources, which is assumed to correspond to the temperature at which rocks lose their spontaneous magnetization. In this study, we test and apply a method based on the spectral analysis of magnetic anomalies. Early spectral analysis methods assumed that crustal magnetization is a completely uncorrelated function of position. Our method incorporates a more realistic representation where magnetization has a fractal distribution defined by three independent parameters: the depths to the top and bottom of magnetic sources and a fractal parameter related to the geology. The predictions of this model are compatible with radial power spectra obtained from aeromagnetic data in the western United States. Model parameters are mapped by estimating their value within a sliding window swept over the study area. The method works well on synthetic data sets when one of the three parameters is specified in advance. The application of this method to western United States magnetic compilations, assuming a constant fractal parameter, allowed us to detect robust long-wavelength variations in the depth to the bottom of magnetic sources. Depending on the geologic and geophysical context, these features may result from variations in depth to the Curie temperature isotherm, depth to the mantle, depth to the base of volcanic rocks, or geologic settings that affect the value of the fractal parameter. Depth to the bottom of magnetic sources shows several features correlated with prominent heat flow anomalies. It also shows some features absent in the map of heat flow. Independent geophysical and geologic data sets are examined to determine their origin, thereby providing new insights on the thermal and geologic crustal
Martelloni, Gianluca; Guarino, Alessio
2016-01-01
We present a three-dimensional model, based on cohesive spherical particles, of rain-induced landslides. The rainwater infiltration into the soil follow the either the fractional or the fractal diffusion equations. We solve analytically the fractal diffusion partial differential equation (PDE) with particular boundary conditions to simulate a rainfall event. Then, for the PDE, we developed a numerical integration scheme that we integrate with MD (Molecular Dynamics) algorithm for the triggering and propagation of the simulated landslide. Therefore we test the numerical integration scheme of fractal diffusion equation with the analytical solution. We adopt the fractal diffusion equation in term of gravimetric water content that we use as input of triggering scheme based on Mohr-Coulomb limit-equilibrium criterion, adapted to particle level. Moreover, taking into account an interacting force Lennard-Jones inspired, we use a standard MD algorithm to update particle positions and velocities. Then we present resul...
Fractal analysis of alveolarization in hyperoxia-induced rat models of bronchopulmonary dysplasia.
Porzionato, Andrea; Guidolin, Diego; Macchi, Veronica; Sarasin, Gloria; Grisafi, Davide; Tortorella, Cinzia; Dedja, Arben; Zaramella, Patrizia; De Caro, Raffaele
2016-04-01
No papers are available about potentiality of fractal analysis in quantitative assessment of alveolarization in bronchopulmonary dysplasia (BPD). Thus, we here performed a comparative analysis between fractal [fractal dimension (D) and lacunarity] and stereological [mean linear intercept (Lm), total volume of alveolar air spaces, total number of alveoli, mean alveolar volume, total volume and surface area of alveolar septa, and mean alveolar septal thickness] parameters in experimental hyperoxia-induced models of BPD. At birth, rats were distributed between the following groups: 1) rats raised in ambient air for 2 wk; 2) rats exposed to 60% oxygen for 2 wk; 3) rats raised in normoxia for 6 wk; and 4) rats exposed to 60% hyperoxia for 2 wk and to room air for further 4 wk. Normoxic 6-wk rats showed increased D and decreased lacunarity with respect to normoxic 2-wk rats, together with changes in all stereological parameters except for mean alveolar volume. Hyperoxia-exposed 2-wk rats showed significant changes only in total number of alveoli, mean alveolar volume, and lacunarity with respect to equal-in-age normoxic rats. In the comparison between 6-wk rats, the hyperoxia-exposed group showed decreased D and increased lacunarity, together with changes in all stereological parameters except for septal thickness. Analysis of receiver operating characteristic curves showed a comparable discriminatory power of D, lacunarity, and total number of alveoli; Lm and mean alveolar volume were less discriminative. D and lacunarity did not show significant changes when different segmentation thresholds were applied, suggesting that the fractal approach may be fit to automatic image analysis. Copyright © 2016 the American Physiological Society.
Modeling Fractal Structure of Systems of Cities Using Spatial Correlation Function
Chen, Yanguang
2016-01-01
This paper proposes a new method to analyze the spatial structure of urban systems using ideas from fractals. Regarding a system of cities as a set of "particles" distributed randomly on a triangular lattice, we construct a spatial correlation function of cities. Suppose that the spatial correlation follows the power law. It can be proved that the correlation exponent is the second order generalized dimension. The spatial correlation model is applied to the system of cities in China. The results show that the Chinese urban system can be described by the correlation dimension ranging from 1.3 to 1.6. The fractality of self-organized network of cities in both the conventional geographic space and the "time" space is revealed with the empirical evidence. The spatial correlation analysis is significant in that it is applicable to both large and small sizes of samples and can be used to link different fractal dimensions in urban study, including box dimension and radial dimension.
Mathematical Models Arising in the Fractal Forest Gap via Local Fractional Calculus
Directory of Open Access Journals (Sweden)
Chun-Ying Long
2014-01-01
Full Text Available The forest new gap models via local fractional calculus are investigated. The JABOWA and FORSKA models are extended to deal with the growth of individual trees defined on Cantor sets. The local fractional growth equations with local fractional derivative and difference are discussed. Our results are first attempted to show the key roles for the nondifferentiable growth of individual trees.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
The Tsallis distribution and the stretched exponential distribution were successfully used to fit the experimental data of turbulence particle acceleration published in Nature (2001), which manifested a clear departure from the normal distribution. These studies, however, fall short of a clear physical mechanism behind the statistical phenomenological description. In this study, we propose a multi- scale diffusion model which considers both normal diffusion in molecular-scale and anomalous diffu- sion in vortex-scale, and the latter is described by a novel fractal derivative modeling approach. This multi-scale model gives rise to a new probability density function which fits experimental data very well.
Institute of Scientific and Technical Information of China (English)
SUN HongGuang; CHEN Wen
2009-01-01
The Tsallis distribution and the stretched exponential distribution were successfully used to fit the experimental data of turbulence particle acceleration published in Nature (2001), which manifested a clear departure from the normal distribution. These studies, however, fall short of a clear physical mechanism behind the statistical phenomenological description. In this study, we propose a multi-scale diffusion model which considers both normal diffusion in molecular-scale and anomalous diffu-sion in vortex-scale, and the latter is described by a novel fractal derivative modeling approach. This multi-scale model gives rise to a new probability density function which fits experimental data very well.
Energy Technology Data Exchange (ETDEWEB)
Bhattacharya, Pathikrit; Kamal [Department of Earth Sciences, Indian Institute of Technology, Roorkee, Uttarakhand, 247 667 (India); Chakrabarti, Bikas K, E-mail: pathikri@princeton.edu, E-mail: bikask.chakrabarti@saha.ac.in, E-mail: kamalfes@iitr.ernet.in [Theoretical Condensed Matter Physics Division and Centre for Applied Mathematics and Computational Science, Saha Institute of Nuclear Physics, Kolkata, West Bengal, 700064 (India)
2011-09-15
Our understanding of earthquakes is based on the theory of plate tectonics. Earthquake dynamics is the study of the interactions of plates (solid disjoint parts of the lithosphere) which produce seismic activity. Over the last about fifty years many models have come up which try to simulate seismic activity by mimicking plate plate interactions. The validity of a given model is subject to the compliance of the synthetic seismic activity it produces to the well known empirical laws which describe the statistical features of observed seismic activity. Here we present a review of one such, purely geometric, model of earthquake dynamics, namely The Two Fractal Overlap Model. The model tries to emulate the stick-slip dynamics of lithospheric plates with fractal surfaces by evaluating the time-evolution of overlap lengths of two identical Cantor sets sliding over each other. As we show later in the text, some statistical aspects of natural seismicity are naturally captured by this simple model. More importantly, however, this model also reveals a new statistical feature of aftershock sequences which we have verified to be present in nature as well. We show that, both in the model as well as in nature, the cumulative integral of aftershock magnitudes over time is a remarkable straight line with a characteristic slope. This slope is closely related to the fractal geometry of the fault surface that produces most of thee aftershocks. We also go on to discuss the implications that this feature may have in possible predictions of aftershock magnitudes or times of occurrence.
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....
Guideliness for system modeling: fault tree [analysis
Energy Technology Data Exchange (ETDEWEB)
Lee, Yoon Hwan; Yang, Joon Eon; Kang, Dae Il; Hwang, Mee Jeong
2004-07-01
This document, the guidelines for system modeling related to Fault Tree Analysis(FTA), is intended to provide the guidelines with the analyzer to construct the fault trees in the level of the capability category II of ASME PRA standard. Especially, they are to provide the essential and basic guidelines and the related contents to be used in support of revising the Ulchin 3 and 4 PSA model for risk monitor within the capability category II of ASME PRA standard. Normally the main objective of system analysis is to assess the reliability of system modeled by Event Tree Analysis (ETA). A variety of analytical techniques can be used for the system analysis, however, FTA method is used in this procedures guide. FTA is the method used for representing the failure logic of plant systems deductively using AND, OR or NOT gates. The fault tree should reflect all possible failure modes that may contribute to the system unavailability. This should include contributions due to the mechanical failures of the components, Common Cause Failures (CCFs), human errors and outages for testing and maintenance. This document identifies and describes the definitions and the general procedures of FTA and the essential and basic guidelines for reving the fault trees. Accordingly, the guidelines for FTA will be capable to guide the FTA to the level of the capability category II of ASME PRA standard.
A New Model of Ultracapacitors Based on Fractal Fundamentals
Directory of Open Access Journals (Sweden)
Xiaodong Zhang
2014-01-01
Full Text Available An intuitive model is proposed in this paper to describe the electrical behavior of certain ultracapacitors. The model is based on a simple expression that can be fully characterized by five real numbers. In this paper, the measured impedances of three ultracapacitors as a function of frequency are compared to model results. There is good agreement between the model and measurements. Results presented in a previous study are also reviewed and the paper demonstrates that those results are also consistent with the newly described model.
A Lattice Boltzmann Model for Fluid-Solid Coupling Heat Transfer in Fractal Porous Media
Institute of Scientific and Technical Information of China (English)
CAI Jun; HUAI Xiu-Lan
2009-01-01
We report a lattice Boltzmann model that can be used to simulate fluid-solid coupling heat transfer in fractal porous media.A numerical simulation is conducted to investigate the temperature evolution under different ratios of thermal conductivity of solid matrix of porous media to that of fluid.The accordance of our simulation results with the solutions from the conventional CFD method indicates the feasibility and the reliability for the developed lattice Boltzmann model to reveal the phenomena and rules of fluid-solid coupling heat transfer in complex porous structures.
Do Fractal Models of Clouds Produces the Right 3D Radiative Effects?
Varnai, Tamas; Marshak, Alexander; Einaudi, Franco (Technical Monitor)
2001-01-01
Stochastic fractal models of clouds are often used to study 3D radiative effects and their influence on the remote sensing of cloud properties. Since it is important that the cloud models produce a correct radiative response, some researchers require the model parameters to match observed cloud properties such as scale-independent optical thickness variability. Unfortunately, matching these properties does not necessarily imply that the cloud models will cause the right 3D radiative effects. First, the matched properties alone only influence the 3D effects but do not completely determine them. Second, in many cases the retrieved cloud properties have been already biased by 3D radiative effects, and so the models may not match the true real clouds. Finally, the matched cloud properties cannot be considered independent from the scales at which they have been retrieved. This paper proposes an approach that helps ensure that fractal cloud models are realistic and produce the right 3D effects. The technique compares the results of radiative transfer simulations for the model clouds to new direct observations of 3D radiative effects in satellite images.
Concept Tree Based Information Retrieval Model
Directory of Open Access Journals (Sweden)
Chunyan Yuan
2014-05-01
Full Text Available This paper proposes a novel concept-based query expansion technique named Markov concept tree model (MCTM, discovering term relationship through the concept tree deduced by term markov network. We address two important issues for query expansion: the selection and the weighting of expansion search terms. In contrast to earlier methods, queries are expanded by adding those terms that are most similar to the concept of the query, rather than selecting terms that are similar to a signal query terms. Utilizing Markov network which is constructed according to the co-occurrence information of the terms in collection, it generate concept tree for each original query term, remove the redundant and irrelevant nodes in concept tree, then adjust the weight of original query and the weight of expansion term based on a pruning algorithm. We use this model for query expansion and evaluate the effectiveness of the model by examining the accuracy and robustness of the expansion methods, Compared with the baseline model, the experiments on standard dataset reveal that this method can achieve a better query quality
Modeling huanglongbing transmission within a citrus tree.
Chiyaka, Christinah; Singer, Burton H; Halbert, Susan E; Morris, J Glenn; van Bruggen, Ariena H C
2012-07-24
The citrus disease huanglongbing (HLB), associated with an uncultured bacterial pathogen, is threatening the citrus industry worldwide. A mathematical model of the transmission of HLB between its psyllid vector and citrus host has been developed to characterize the dynamics of the vector and disease development, focusing on the spread of the pathogen from flush to flush (a newly developing cluster of very young leaves on the expanding terminal end of a shoot) within a tree. This approach differs from that of prior models for vector-transmitted plant diseases where the entire plant is the unit of analysis. Dynamics of vector and host populations are simulated realistically as the flush population approaches complete infection. Model analysis indicates that vector activity is essential for initial infection but is not necessary for continued infection because infection can occur from flush to flush through internal movement in the tree. Flush production, within-tree spread, and latent period are the most important parameters influencing HLB development. The model shows that the effect of spraying of psyllids depends on time of initial spraying, frequency, and efficacy of the insecticides. Similarly, effects of removal of symptomatic flush depend on the frequency of removal and the time of initiation of this practice since the start of the epidemic. Within-tree resistance to spread, possibly affected by inherent or induced resistance, is a major factor affecting epidemic development, supporting the notion that alternate routes of transmission besides that by the vector can be important for epidemic development.
Mostafa, Mostafa E.
2009-04-01
The finite cube elements method (FCEM) is a numerical tool designed for modelling gravity anomalies and estimating structural index (SI) of solid and fractal bodies with defined boundaries, tilted or in normal position and with variable density contrast. In this work, we apply FCEM to modelling magnetic anomalies and estimating SI of bodies with non-uniform magnetization having variable magnitude and direction. In magnetics as in gravity, FCEM allows us to study the spatial distribution of SI of the modelled bodies on contour maps and profiles. We believe that this will impact the forward and inverse modelling of potential field data, especially Euler deconvolution. As far as the author knows, this is the first time that gravity and magnetic anomalies, as well as SI, of self similar fractal bodies such as Menger sponges and Sierpinsky triangles are calculated using FCEM. The SI patterns derived from different order sponges and triangles are perfectly overlapped. This is true for bodies having variable property distributions (susceptibility or density contrast) under different field conditions (in case of magnetics) regardless of their orientation and depth of burial. We therefore propose SI as a new universal fractal-order-invariant measure which can be used in addition to the fractal dimensions for formulating potential field theory of fractal objects.
Pesticide bioconcentration modelling for fruit trees.
Paraíba, Lourival Costa
2007-01-01
The model presented allows simulating the pesticide concentration evolution in fruit trees and estimating the pesticide bioconcentration factor in fruits. Pesticides are non-ionic organic compounds that are degraded in soils cropped with woody species, fruit trees and other perennials. The model allows estimating the pesticide uptake by plants through the water transpiration stream and also the time in which maximum pesticide concentration occur in the fruits. The equation proposed presents the relationships between bioconcentration factor (BCF) and the following variables: plant water transpiration volume (Q), pesticide transpiration stream concentration factor (TSCF), pesticide stem-water partition coefficient (K(Wood,W)), stem dry biomass (M) and pesticide dissipation rate in the soil-plant system (k(EGS)). The modeling started and was developed from a previous model "Fruit Tree Model" (FTM), reported by Trapp and collaborators in 2003, to which was added the hypothesis that the pesticide degradation in the soil follows a first order kinetic equation. The FTM model for pesticides (FTM-p) was applied to a hypothetic mango plant cropping (Mangifera indica) treated with paclobutrazol (growth regulator) added to the soil. The model fitness was evaluated through the sensitivity analysis of the pesticide BCF values in fruits with respect to the model entry data variability.
Directory of Open Access Journals (Sweden)
Ries A.
2010-10-01
Full Text Available A numerical analysis of elementary particle masses on the logarithmic number line revealed systematic mass gaps of 2e, e, e/2, e/4, e/8 and e/16. Also in abundance data of the chemical elements, a repeated abundance gap of e/2 could be detected. This lead us to modify a fractal scaling model originally published by Müller in this journal, interpreting elementary particles as proton resonances. We express a set of 78 accurately determined particle masses on the logarithmic scale in a continued fraction form where all numerators are Euler’s number.
FUEL3-D: A Spatially Explicit Fractal Fuel Distribution Model
Russell A. Parsons
2006-01-01
Efforts to quantitatively evaluate the effectiveness of fuels treatments are hampered by inconsistencies between the spatial scale at which fuel treatments are implemented and the spatial scale, and detail, with which we model fire and fuel interactions. Central to this scale inconsistency is the resolution at which variability within the fuel bed is considered. Crown...
Multi-Dimensional Piece-Wise Self-Affine Fractal Interpolation Model
Institute of Scientific and Technical Information of China (English)
ZHANG Tong; ZHUANG Zhuo
2007-01-01
Iterated function system (IFS) models have been used to represent discrete sequences where the attractor of the IFS is piece-wise self-affine in R2 or R3 (R is the set of real numbers). In this paper, the piece-wise self-affine IFS model is extended from R3 to Rn (n is an integer greater than 3), which is called the multi-dimensional piece-wise self-affine fractal interpolation model. This model uses a "mapping partial derivative", and a constrained inverse algorithm to identify the model parameters. The model values depend continuously on all the model parameters, and represent most data which are not multi-dimensional self-affine in Rn. Therefore, the result is very general. The class of functions obtained is much more diverse because their values depend continuously on all of the variables, with all the coefficients of the possible multi-dimensional affine maps determining the functions.
Ju, Yang; Zhang, Qingang; Zheng, Jiangtao; Chang, Chun; Xie, Heping
2017-02-01
The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures.
Critical behavior of the Gaussian model on fractal lattices in external magnetic field
Institute of Scientific and Technical Information of China (English)
孔祥木; 林振权; 朱建阳
2000-01-01
For inhomogeneous lattices we generalize the classical Gaussian model, i. e. it is pro-posed that the Gaussian type distribution constant and the external magnetic field of site / in this model depend on the coordination number q, of site i, and that the relation bq1/bq1 = q1/q1 holds among bq1s, where bq1 is the Gaussian type distribution constant of site /. Using the decimation real-spacerenormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierar-chical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site i can be expressed in the form K’ = bq1/q1 and hq =0, respectively. it is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices,
Fractal model and Lattice Boltzmann Method for Characterization of Non-Darcy Flow in Rough Fractures
Ju, Yang; Zhang, Qingang; Zheng, Jiangtao; Chang, Chun; Xie, Heping
2017-02-01
The irregular morphology of single rock fracture significantly influences subsurface fluid flow and gives rise to a complex and unsteady flow state that typically cannot be appropriately described using simple laws. Yet the fluid flow in rough fractures of underground rock is poorly understood. Here we present a numerical method and experimental measurements to probe the effect of fracture roughness on the properties of fluid flow in fractured rock. We develop a series of fracture models with various degrees of roughness characterized by fractal dimensions that are based on the Weierstrass-Mandelbrot fractal function. The Lattice Boltzmann Method (LBM), a discrete numerical algorithm, is employed for characterizing the complex unsteady non-Darcy flow through the single rough fractures and validated by experimental observations under the same conditions. Comparison indicates that the LBM effectively characterizes the unsteady non-Darcy flow in single rough fractures. Our LBM model predicts experimental measurements of unsteady fluid flow through single rough fractures with great satisfactory, but significant deviation is obtained from the conventional cubic law, showing the superiority of LBM models of single rough fractures.
Relativistic Fractal Cosmologies
Ribeiro, Marcelo B
2009-01-01
This article reviews an approach for constructing a simple relativistic fractal cosmology whose main aim is to model the observed inhomogeneities of the distribution of galaxies by means of the Lemaitre-Tolman solution of Einstein's field equations for spherically symmetric dust in comoving coordinates. This model is based on earlier works developed by L. Pietronero and J.R. Wertz on Newtonian cosmology, whose main points are discussed. Observational relations in this spacetime are presented, together with a strategy for finding numerical solutions which approximate an averaged and smoothed out single fractal structure in the past light cone. Such fractal solutions are shown, with one of them being in agreement with some basic observational constraints, including the decay of the average density with the distance as a power law (the de Vaucouleurs' density power law) and the fractal dimension in the range 1 <= D <= 2. The spatially homogeneous Friedmann model is discussed as a special case of the Lemait...
McAteer, R. T. J.
2013-06-01
When Mandelbrot, the father of modern fractal geometry, made this seemingly obvious statement he was trying to show that we should move out of our comfortable Euclidean space and adopt a fractal approach to geometry. The concepts and mathematical tools of fractal geometry provides insight into natural physical systems that Euclidean tools cannot do. The benet from applying fractal geometry to studies of Self-Organized Criticality (SOC) are even greater. SOC and fractal geometry share concepts of dynamic n-body interactions, apparent non-predictability, self-similarity, and an approach to global statistics in space and time that make these two areas into naturally paired research techniques. Further, the iterative generation techniques used in both SOC models and in fractals mean they share common features and common problems. This chapter explores the strong historical connections between fractal geometry and SOC from both a mathematical and conceptual understanding, explores modern day interactions between these two topics, and discusses how this is likely to evolve into an even stronger link in the near future.
Simulation of ultrasonic scattering from a fractal model of the liver
Phillips, Daniel Brian
The liver has been particularly resistant to ultrasonic tissue characterization of diffuse pathological processes. This may be due, in part, to the difficulty in determining the scattering contribution of a complex structure comprised of components that span a size range from sub-resolveable to many times larger than the insonating wavelength. Due to the inherent random nature of scattering from such a complex structure, statistical evaluation of the backscattered signals has been pursued by a number of investigators in order to gain a better understanding of their relationship to the underlying scattering sources within a liver which contains an intricate network of vascular components with significant collagen content. This study maintains that the collagenous structures represented by the vessels associated with the portal vasculature, including how they are spatially organized, is a major source of the observed features of backscattered ultrasound signals from the liver. To that end, a three dimensional geometric computer model of the human portal vascular system has been constructed based on accepted anatomical and physiological information and utilizing a fractal generation algorithm. The fractal methodology is used to determine the branching characteristics of the model, such as vessel numbers, locations and dimensions. This complex, three dimensional data set is used as a source for producing simulated ultrasound B-scans which are subsequently subjected to statistical analysis and evaluation in order to (1) verify that the model produced data with characteristics similar to those from actual backscattered signals from human liver, and (2) attempt to understand the relationship between the characteristics of the modeled vasculature and the resulting backscattered signals. The fractal implementation of the vasculature model will be discussed and results will be presented which indicate that simple variations in the characteristics of the model can produce
Turcotte, Donald L.
Tectonic processes build landforms that are subsequently destroyed by erosional processes. Landforms exhibit fractal statistics in a variety of ways; examples include (1) lengths of coast lines; (2) number-size statistics of lakes and islands; (3) spectral behavior of topography and bathymetry both globally and locally; and (4) branching statistics of drainage networks. Erosional processes are dominant in the development of many landforms on this planet, but similar fractal statistics are also applicable to the surface of Venus where minimal erosion has occurred. A number of dynamical systems models for landforms have been proposed, including (1) cellular automata; (2) diffusion limited aggregation; (3) self-avoiding percolation; and (4) advective-diffusion equations. The fractal statistics and validity of these models will be discussed. Earthquakes also exhibit fractal statistics. The frequency-magnitude statistics of earthquakes satisfy the fractal Gutenberg-Richter relation both globally and locally. Earthquakes are believed to be a classic example of self-organized criticality. One model for earthquakes utilizes interacting slider-blocks. These slider block models have been shown to behave chaotically and to exhibit self-organized criticality. The applicability of these models will be discussed and alternative approaches will be presented. Fragmentation has been demonstrated to produce fractal statistics in many cases. Comminution is one model for fragmentation that yields fractal statistics. It has been proposed that comminution is also responsible for much of the deformation in the earth's crust. The brittle disruption of the crust and the resulting earthquakes present an integrated problem with many fractal aspects.
A hierarchical linear model for tree height prediction.
Vicente J. Monleon
2003-01-01
Measuring tree height is a time-consuming process. Often, tree diameter is measured and height is estimated from a published regression model. Trees used to develop these models are clustered into stands, but this structure is ignored and independence is assumed. In this study, hierarchical linear models that account explicitly for the clustered structure of the data...
Fractal analysis in digital cartographic modeling of Miroč mountain
Directory of Open Access Journals (Sweden)
Valjarević Aleksandar
2015-01-01
Full Text Available Miroc is a mountain in Eastern Serbia placed between Donji Milanovac and Tekija in Negotinska Krajina. The highest mountain summit is Veliki Strbac, 768 metres above sea level. Miroc is the most protruding part of Eastern Serbia and the most western part of the Djerdap Mountain Massive. The mountain is surrounded by the Danube from all the sides. Miroc Mountain, Veliki and Mali Srbac, the Danube River, the Djerdap Gorge, Veliki and Mali Kazan are the real place of world permeation both on land and in the water. This embraces the territory of nearly 500 km2. Fractal Geometry is a sort of new language used for describing, modeling or analyzing complex shapes in nature. A fractal is a diminished unity copy; the type that resembles itself. The work objective is to show the possibility of using computer analyses as well as the programme languages Python, C++, GIS software, Global Mapper 15.2 and QGIS/a in the example of Miroc Mountain morphometric features. [Projekat Ministarstva nauke Republike Srbije, br. 176008 i br. III44006
Energy Technology Data Exchange (ETDEWEB)
Bishnoi, L.R., E-mail: lrbishnoi@aerb.gov.in [Siting and Structural Engineering Division, Atomic Energy Regulatory Board, Mumbai 400 094 (India); Vedula, R.P., E-mail: rpv@iitb.ac.in [Mechanical Engineering Department, Indian Institute of Technology, Mumbai 400 076 (India)
2013-12-15
Highlights: • A fractal based numerical concrete crack morphology model is presented. • Computational studies conducted for airflow and aerosol transport through cracks. • Results are compared with experimental data and other empirical relations. • Comparative studies demonstrate model effectiveness and versatility of application. - Abstract: Cracks may appear in pressurized concrete containment of a nuclear power plant during a severe accident and provide leak paths for release of radioactive aerosols dispersed in the contained air. In this paper, a fractal based crack morphology model is presented for prediction of air leakage and aerosol transport through cracks in concrete. Airflow field generated in air leakage studies is used for aerosol transport studies with the Lagrangian discrete phase model using CFD code FLUENT. Computational studies conducted with the fractal based model are compared with the experimental data as well as the predictions from empirical relations available in open literature. The comparative studies demonstrate effectiveness of the proposed fractal based model and its versatility for practical applications.
Dewdney, A. K.
1991-01-01
Explores the subject of fractal geometry focusing on the occurrence of fractal-like shapes in the natural world. Topics include iterated functions, chaos theory, the Lorenz attractor, logistic maps, the Mandelbrot set, and mini-Mandelbrot sets. Provides appropriate computer algorithms, as well as further sources of information. (JJK)
Osler, Thomas J.
1999-01-01
Because fractal images are by nature very complex, it can be inspiring and instructive to create the code in the classroom and watch the fractal image evolve as the user slowly changes some important parameter or zooms in and out of the image. Uses programming language that permits the user to store and retrieve a graphics image as a disk file.…
Directory of Open Access Journals (Sweden)
Tatjana eStadnitski
2012-05-01
Full Text Available When investigating fractal phenomena, the following questions are fundamental for the applied researcher: (1 What are essential statistical properties of 1/f noise? (2 Which estimators are available for measuring fractality? (3 Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law and the related fractal parameters (the Hurst coefficient, the scaling exponent, the fractional differencing parameter d of the ARFIMA methodology, the power exponent of the spectral analysis are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short memory patterns are demonstrated with empirical time series.
Stadnitski, Tatjana
2012-01-01
WHEN INVESTIGATING FRACTAL PHENOMENA, THE FOLLOWING QUESTIONS ARE FUNDAMENTAL FOR THE APPLIED RESEARCHER: (1) What are essential statistical properties of 1/f noise? (2) Which estimators are available for measuring fractality? (3) Which measurement instruments are appropriate and how are they applied? The purpose of this article is to give clear and comprehensible answers to these questions. First, theoretical characteristics of a fractal pattern (self-similarity, long memory, power law) and the related fractal parameters (the Hurst coefficient, the scaling exponent α, the fractional differencing parameter d of the autoregressive fractionally integrated moving average methodology, the power exponent β of the spectral analysis) are discussed. Then, estimators of fractal parameters from different software packages commonly used by applied researchers (R, SAS, SPSS) are introduced and evaluated. Advantages, disadvantages, and constrains of the popular estimators ([Formula: see text] power spectral density, detrended fluctuation analysis, signal summation conversion) are illustrated by elaborate examples. Finally, crucial steps of fractal analysis (plotting time series data, autocorrelation, and spectral functions; performing stationarity tests; choosing an adequate estimator; estimating fractal parameters; distinguishing fractal processes from short-memory patterns) are demonstrated with empirical time series.
Multilayer adsorption on fractal surfaces.
Vajda, Péter; Felinger, Attila
2014-01-10
Multilayer adsorption is often observed in liquid chromatography. The most frequently employed model for multilayer adsorption is the BET isotherm equation. In this study we introduce an interpretation of multilayer adsorption measured on liquid chromatographic stationary phases based on the fractal theory. The fractal BET isotherm model was successfully used to determine the apparent fractal dimension of the adsorbent surface. The nonlinear fitting of the fractal BET equation gives us the estimation of the adsorption equilibrium constants and the monolayer saturation capacity of the adsorbent as well. In our experiments, aniline and proline were used as test molecules on reversed phase and normal phase columns, respectively. Our results suggest an apparent fractal dimension 2.88-2.99 in the case of reversed phase adsorbents, in the contrast with a bare silica column with a fractal dimension of 2.54.
Provata, A; Tsekouras, G A
2003-05-01
Dynamical patterns, in the form of consecutive moving stripes or rings, are shown to develop spontaneously in the cyclic lattice Lotka-Volterra model, when realized on square lattice, at the reaction limited regime. Each stripe consists of different particles (species) and the borderlines between consecutive stripes are fractal. The interface width w between the different species scales as w(L,t) approximately L(alpha)f(t/L(z)), where L is the linear size of the interface, t is the time, and alpha and z are the static and dynamical critical exponents, respectively. The critical exponents were computed as alpha=0.49+/-0.03 and z=1.53+/-0.13 and the propagating fronts show dynamical characteristics similar to those of the Eden growth models.
Semi-numerical solution for a fractal telegraphic dual-porosity fluid flow model
Herrera-Hernández, E C; Luis, D P; Hernández, D; Camacho-Velázquez, R G
2016-01-01
In this work, we present a semi-numerical solution of a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose numerical treatment outcomes in a tri-diagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions. Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor sem...
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Cheng Xu
2015-01-01
Full Text Available In this manuscript, the local fractional arbitrary Euler-Lagrange formula are utilized to address the diffusion model of fractal heat and mass transfer in a fluidized bed based on the Fick's law with local fractional vector calculus. This article has been corrected. Link to the correction 10.2298/TSCI150923149E
Fractal Theory and Contact Dynamics Modeling Vibration Characteristics of Damping Blade
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Ruishan Yuan
2014-01-01
Full Text Available The contact surface structure of dry friction damper is complicate, irregular, and self-similar. In this paper, contact surface structure is described with the fractal theory and damping blade is simplified as 2-DOF cantilever beam model with lumped masses. By changing the position of the damper, lacing and shroud structure are separately simulated to study vibration absorption effect of damping blade. The results show that both shroud structure and lacing could not only dissipate energy but also change stiffness of blade. Under the same condition of normal pressure and contact surface, the damping effect of lacing is stronger than that of shroud structure. Meanwhile, the effect on changing blade stiffness of shroud structure is stronger than that of lacing. This paper proposed that there is at least one position of the blade, at which the damper dissipates the most vibration energy during a vibration cycle.
Topological Vulnerability Evaluation Model Based on Fractal Dimension of Complex Networks.
Gou, Li; Wei, Bo; Sadiq, Rehan; Sadiq, Yong; Deng, Yong
2016-01-01
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.
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.
Derivations of fractal models of city hierarchies using entropy-maximization principle
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
A pair of models of fractal recursion on city hierarchy, fm=f1r1-mf and Pm=P1rm-1p, are derived using entropy-maximizing methods, and the relationship of inverse proportion between the number (fm) of cities at a given level of the urban hierarchy and the average population size (Pm) of the fm cities is established, i.e fm∝1/P. It is demonstrated that the underlying rationale of both the scale law of city rank-size distribution and the Zipf dimension value in standard state (dz=lnrp/lnrf=1) rests with maximization of information entropy of city hierarchies.
Stretched Exponential Relaxation in Disordered Complex Systems: Fractal Time Random Walk Model
Institute of Scientific and Technical Information of China (English)
Ekrem Aydmer
2007-01-01
We have analytically derived the relaxation function for one-dimensional disordered complex systems in terms of autocorrelation function of fractal time random walk by using operator formalism. We have shown that the relaxation function has stretched exponential, i.e. the Kohlrausch-Williams-Watts character for a fractal time random walk process.
Parsa, Mohammad; Maghsoudi, Abbas; Yousefi, Mahyar; Carranza, Emmanuel John M.
2017-04-01
The spectrum-area (S-A) fractal model is a powerful tool for decomposition of complex anomaly patterns of gridded geochemical data. Ordinary moving average interpolation techniques are commonly being used for gridding geochemical data; however, these methods suffer from two major drawbacks of (1) ignoring the locally high values and (2) smoothing the interpolated surface. Multifractal moving average interpolation methods have been developed to overcome the shortcomings of ordinary moving average methods. This study seeks to compare two sets of multifractal and ordinary gridded geochemical data using success rate curves and applies the S-A fractal model to decompose anomalous geochemical patterns. A set of stream sediment geochemical data in Ahar area, NW Iran, was used as a case study. Then, a mineralization-related multi-element geochemical signature was gridded by ordinary and multifractal approaches and considered for further analyses. The S-A fractal method was applied to decompose anomaly and background components of the resultant multi-element geochemical signature. Exploration targets were delimited and further evaluated using two bivariate statistical procedures of Student's t-value and normalized density index. The results revealed that (a) application of multifractal gridded data enhances the predicting ability of geochemical signatures, (b) application of S-A fractal model on multifractal gridded data allows for superior discrimination of geochemical anomalies, and (c) the multi-element geochemical anomalies in the Ahar area related to porphyry-Cu deposits were properly delineated through sequence application of multifractal interpolation and S-A fractal model.
Pruning Chinese trees : an experimental and modelling approach
Zeng, Bo
2002-01-01
Pruning of trees, in which some branches are removed from the lower crown of a tree, has been extensively used in China in silvicultural management for many purposes. With an experimental and modelling approach, the effects of pruning on tree growth and on the harvest of plant material were studied.
Fast Automatic Precision Tree Models from Terrestrial Laser Scanner Data
Directory of Open Access Journals (Sweden)
Mathias Disney
2013-01-01
Full Text Available This paper presents a new method for constructing quickly and automatically precision tree models from point clouds of the trunk and branches obtained by terrestrial laser scanning. The input of the method is a point cloud of a single tree scanned from multiple positions. The surface of the visible parts of the tree is robustly reconstructed by making a flexible cylinder model of the tree. The thorough quantitative model records also the topological branching structure. In this paper, every major step of the whole model reconstruction process, from the input to the finished model, is presented in detail. The model is constructed by a local approach in which the point cloud is covered with small sets corresponding to connected surface patches in the tree surface. The neighbor-relations and geometrical properties of these cover sets are used to reconstruct the details of the tree and, step by step, the whole tree. The point cloud and the sets are segmented into branches, after which the branches are modeled as collections of cylinders. From the model, the branching structure and size properties, such as volume and branch size distributions, for the whole tree or some of its parts, can be approximated. The approach is validated using both measured and modeled terrestrial laser scanner data from real trees and detailed 3D models. The results show that the method allows an easy extraction of various tree attributes from terrestrial or mobile laser scanning point clouds.
Statistical Decision-Tree Models for Parsing
Magerman, D M
1995-01-01
Syntactic natural language parsers have shown themselves to be inadequate for processing highly-ambiguous large-vocabulary text, as is evidenced by their poor performance on domains like the Wall Street Journal, and by the movement away from parsing-based approaches to text-processing in general. In this paper, I describe SPATTER, a statistical parser based on decision-tree learning techniques which constructs a complete parse for every sentence and achieves accuracy rates far better than any published result. This work is based on the following premises: (1) grammars are too complex and detailed to develop manually for most interesting domains; (2) parsing models must rely heavily on lexical and contextual information to analyze sentences accurately; and (3) existing {$n$}-gram modeling techniques are inadequate for parsing models. In experiments comparing SPATTER with IBM's computer manuals parser, SPATTER significantly outperforms the grammar-based parser. Evaluating SPATTER against the Penn Treebank Wall ...
Astaneh, Amin Faraji
2015-01-01
We use the Heat Kernel method to calculate the Entanglement Entropy for a given entangling region on a fractal. The leading divergent term of the entropy is obtained as a function of the fractal dimension as well as the walk dimension. The power of the UV cut-off parameter is (generally) a fractional number which indeed is a certain combination of these two indices. This exponent is known as the spectral dimension. We show that there is a novel log periodic oscillatory behavior in the entropy which has root in the complex dimension of a fractal. We finally indicate that the Holographic calculation in a certain Hyper-scaling violating bulk geometry yields the same leading term for the entanglement entropy, if one identifies the effective dimension of the hyper-scaling violating theory with the spectral dimension of the fractal. We provide more supports with comparing the behavior of the thermal entropy in terms of the temperature in these two cases.
一种基于分形结构的树生长微带天线设计%Design of a tree-growth microstrip antenna based on fractal structure
Institute of Scientific and Technical Information of China (English)
樊磊; 骆延; 黄卡玛; 杨阳
2014-01-01
基于分形理论和自然树竞争(TGCA)思想，提出了采用树枝结构在不同生长因子下进行迭代生长的方法，对分形天线多谐振频率点进行优化控制，克服常见分形天线难于调整多个谐振频率点位置关系的缺点。树生长分形天线通过生长因子和天线尺寸的线性调整，可以方便地实现高低谐振频率的优化设计，方法简单易行。基于该方法，采用时域有限差分(FDTD)算法优化设计了一种具有 GSM900/DCS1800双频谐振点的树生长微带分形天线。从实验和仿真结果可以看出，该微带分形天线在0.91 GHz,1.81 GHz谐振频率处带宽均大于100 MHz，水平方向为全向辐射，测量所得结果和仿真数据吻合较好，验证了采用生长因子调整分形天线谐振频率的方法。%Based on the fractal theory and the idea of the Tree Growth Competition Algorithm(TGCA), a method of optimizing the resonant frequencies by iterating the branch structure at different growth factors is proposed, which overcomes the inconvenience in adjusting the position relationships of multi-band frequencies for common fractal antennas. The lower and upper resonant frequencies of the tree-growth fractal antenna can be optimized conveniently by linearly changing its size and growth factors. Based on this method, a tree-growth fractal antenna is optimized in the GSM900/DCS1800 frequency band by using Finite-Difference Time-Domain(FDTD) algorithm. The measured and simulated results indicate that the bandwidths of microwave fractal antenna are both above 100 MHz at the resonant frequencies of 0.91 GHz and 1.81 GHz with good omni-directional radiation patterns in the horizontal direction. These good agreements of the measured and simulated results validate the feasibility of the proposed method.
Energy Technology Data Exchange (ETDEWEB)
Cruz G, H.S. [Instituto Nacional de Investigaciones Nucleares, A.P. 18-1027, 11801 Mexico D.F. (Mexico)
1997-07-01
The basic elements of the Fractals theory are developed. The physical basis of radon emission in solids are described briefly. It is obtained that the emanation power E{sub R} of mineral grains is scaled as r{sub 0} {sup D-3} (r{sub 0} : grain radius). From a logarithmic graph E{sub R} versus grain size is deduced the fractal dimension of the emanation surface. The experimental data of different materials give an interval in the fractal dimension D between 2.1 and 2.8 (Author)
Growth models for tree stems and vines
Bressan, Alberto; Palladino, Michele; Shen, Wen
2017-08-01
The paper introduces a PDE model for the growth of a tree stem or a vine. The equations describe the elongation due to cell growth, and the response to gravity and to external obstacles. An additional term accounts for the tendency of a vine to curl around branches of other plants. When obstacles are present, the model takes the form of a differential inclusion with state constraints. At each time t, a cone of admissible reactions is determined by the minimization of an elastic deformation energy. The main theorem shows that local solutions exist and can be prolonged globally in time, except when a specific ;breakdown configuration; is reached. Approximate solutions are constructed by an operator-splitting technique. Some numerical simulations are provided at the end of the paper.
Institute of Scientific and Technical Information of China (English)
PENG Yunfeng; GUO Yinbiao
2009-01-01
The strong stiction of adjacent surfaces with meniscus is a major design concern in the devices with a micro-sized interface.Today, more and more research works are devoted to understand the adhesion mechanism. This paper concerns the elastic-plastic adhesion of a fractal rough surface contacting with a perfectly wetted rigid plane. The topography of rough surface is modeled with a two-variable Weierstrass-Mandelbrot fractal function. The Laplace pressure is dealt with the Dugdale approximation. Then the adhesion model of the plastically deformed asperities with meniscus can be established with the fractal microcontact model. According to the plastic flow criterion, the elastic-plastic adhesion model of the contacting rough surfaces with meniscus can be solved by combining the Maugis-Dugdale (MD) model and its extension with the Morrow method. The necessity for considering the asperities' plastic deformation has been validated by comparing the simulation result of the presented model with that of the elastic adhesion model. The stiction mechanism of rough surfaces with meniscus is also discussed.
A spatial model of tree α-diversity and tree density for the Amazon
ter Steege, H.; Pitman, N.C.A.; Sabatier, D.; Castellanos, H.; van der Hout, P.; Daly, D.C.; Silveira, M.; Phillips, O.; Vasquez, R.; van Andel, T.; Duivenvoorden, J.; de Oliveira, A.A.; Ek, R.; Lilwah, R.; Thomas, R.; van Essen, J.; Baider, C.; Maas, P.; Mori, S.; Terborgh, J.; Nuñez-Vargas, P.; Mogollón, H.; Morawetz, W.
2003-01-01
Large-scale patterns of Amazonian biodiversity have until now been obscured by a sparse and scattered inventory record. Here we present the first comprehensive spatial model of tree α-diversity and tree density in Amazonian rainforests, based on the largest-yet compilation of forest inventories and
Modelling groundwater fractal flow with fractional differentiation via Mittag-Leffler law
Ahokposi, D. P.; Atangana, Abdon; Vermeulen, D. P.
2017-04-01
Modelling the flow of groundwater within a network of fractures is perhaps one of the most difficult exercises within the field of geohydrology. This physical problem has attracted the attention of several scientists across the globe. Already two different types of differentiations have been used to attempt modelling this problem including the classical and the fractional differentiation. In this paper, we employed the most recent concept of differentiation based on the non-local and non-singular kernel called the generalized Mittag-Leffler function, to reshape the model of groundwater fractal flow. We presented the existence of positive solution of the new model. Using the fixed-point approach, we established the uniqueness of the positive solution. We solve the new model with three different numerical schemes including implicit, explicit and Crank-Nicholson numerical methods. Experimental data collected from four constant discharge tests conducted in a typical fractured crystalline rock aquifer of the Northern Limb (Bushveld Complex) in the Limpopo Province (South Africa) are compared with the numerical solutions. It is worth noting that the four boreholes (BPAC1, BPAC2, BPAC3, and BPAC4) are located on Faults.
Kravet, Steven J; Bailey, Jennifer; Demski, Renee; Pronovost, Peter
2016-07-01
Academic health systems face challenges in the governance and oversight of quality and safety efforts across their organizations. Ambulatory practices, which are growing in number, size, and complexity, face particular challenges in these areas. In February 2014, leaders at Johns Hopkins Medicine (JHM) implemented a governance, oversight, and accountability structure for quality and safety efforts across JHM ambulatory practices. This model was based on the fractal approach, which balances independence and interdependence and provides horizontal and vertical support. It set expectations of accountability at all levels from the Board of Trustees to frontline staff and featured a cascading structure that reached all units and ambulatory practices. This model leveraged an Ambulatory Quality Council led by a physician and nurse dyad to provide the infrastructure to share best practices, continuously improve, and define accountable local leaders. This model was incorporated into the quality and safety infrastructure across JHM. Improved outcomes in the domains of patient safety/risk reduction, externally reported quality measures, patient care/experience, and value have been demonstrated. An additional benefit was an improvement in Medicaid value-based purchasing metrics, which are linked to several million dollars of revenue. As this model matures, it will serve as a mechanism to align quality standards and programs across regional, national, and international partners and to provide a clear quality structure as new practices join the health system. Future efforts will link this model to JHM's academic mission, enhancing education to address Accreditation Council for Graduate Medical Education core competencies.
Inferring gene regression networks with model trees
Directory of Open Access Journals (Sweden)
Aguilar-Ruiz Jesus S
2010-10-01
Full Text Available Abstract Background Novel strategies are required in order to handle the huge amount of data produced by microarray technologies. To infer gene regulatory networks, the first step is to find direct regulatory relationships between genes building the so-called gene co-expression networks. They are typically generated using correlation statistics as pairwise similarity measures. Correlation-based methods are very useful in order to determine whether two genes have a strong global similarity but do not detect local similarities. Results We propose model trees as a method to identify gene interaction networks. While correlation-based methods analyze each pair of genes, in our approach we generate a single regression tree for each gene from the remaining genes. Finally, a graph from all the relationships among output and input genes is built taking into account whether the pair of genes is statistically significant. For this reason we apply a statistical procedure to control the false discovery rate. The performance of our approach, named REGNET, is experimentally tested on two well-known data sets: Saccharomyces Cerevisiae and E.coli data set. First, the biological coherence of the results are tested. Second the E.coli transcriptional network (in the Regulon database is used as control to compare the results to that of a correlation-based method. This experiment shows that REGNET performs more accurately at detecting true gene associations than the Pearson and Spearman zeroth and first-order correlation-based methods. Conclusions REGNET generates gene association networks from gene expression data, and differs from correlation-based methods in that the relationship between one gene and others is calculated simultaneously. Model trees are very useful techniques to estimate the numerical values for the target genes by linear regression functions. They are very often more precise than linear regression models because they can add just different linear
Image-Based Modeling of Plants and Trees
Kang, Sing Bang
2009-01-01
Plants and trees are among the most complex natural objects. Much work has been done attempting to model them, with varying degrees of success. In this book, we review the various approaches in computer graphics, which we categorize as rule-based, image-based, and sketch-based methods. We describe our approaches for modeling plants and trees using images. Image-based approaches have the distinct advantage that the resulting model inherits the realistic shape and complexity of a real plant or tree. We use different techniques for modeling plants (with relatively large leaves) and trees (with re
Zuo, Xue; Zhu, Hua; Zhou, Yuankai; Ding, Cong; Sun, Guodong
2016-08-01
Relationships between material hardness, turning parameters (spindle speed and feed rate) and surface parameters (surface roughness Ra, fractal dimension D and characteristic roughness τ∗) are studied and modeled using response surface methodology (RSM). The experiments are carried out on a CNC lathe for six carbon steel material AISI 1010, AISI 1020, AISI 1030, AISI 1045, AISI 1050 and AISI 1060. The profile of turned surface and the surface roughness value are measured by a JB-5C profilometer. Based on the profile data, D and τ∗ are computed through the root-mean-square method. The analysis of variance (ANOVA) reveals that spindle speed is the most significant factors affecting Ra, while material hardness is the most dominant parameter affecting τ∗. Material hardness and spindle speed have the same influence on D. Feed rate has less effect on three surface parameters than spindle speed and material hardness. The second-order models of RSM are established for estimating Ra, D and τ∗. The validity of the developed models is approximately 80%. The response surfaces show that a surface with small Ra and large D and τ∗ can be obtained by selecting a high speed and a large hardness material. According to the established models, Ra, D and τ∗ of six carbon steels surfaces can be predicted under cutting conditions studied in this paper. The results have an instructive meaning to estimate the surface quality before turning.
Relevance and limitations of crowding, fractal, and polymer models to describe nuclear architecture.
Huet, Sébastien; Lavelle, Christophe; Ranchon, Hubert; Carrivain, Pascal; Victor, Jean-Marc; Bancaud, Aurélien
2014-01-01
Chromosome architecture plays an essential role for all nuclear functions, and its physical description has attracted considerable interest over the last few years among the biophysics community. These researches at the frontiers of physics and biology have been stimulated by the demand for quantitative analysis of molecular biology experiments, which provide comprehensive data on chromosome folding, or of live cell imaging experiments that enable researchers to visualize selected chromosome loci in living or fixed cells. In this review our goal is to survey several nonmutually exclusive models that have emerged to describe the folding of DNA in the nucleus, the dynamics of proteins in the nucleoplasm, or the movements of chromosome loci. We focus on three classes of models, namely molecular crowding, fractal, and polymer models, draw comparisons, and discuss their merits and limitations in the context of chromosome structure and dynamics, or nuclear protein navigation in the nucleoplasm. Finally, we identify future challenges in the roadmap to a unified model of the nuclear environment.
Modelling a Coupled Thermoelectromechanical Behaviour of Contact Elements via Fractal Surfaces
Directory of Open Access Journals (Sweden)
G. Mazzucco
2016-01-01
Full Text Available A three-dimensional coupled thermoelectromechanical model for electrical connectors is here proposed to evaluate local stress and temperature distributions around the contact area of electric connectors under different applied loads. A micromechanical numerical model has been developed by merging together the contact theory approach, which makes use of the so-called roughness parameters obtained from experimental measurements on real contact surfaces, with the topology description of the rough surface via the theory of fractal geometry. Particularly, the variation of asperities has been evaluated via the Weierstrass-Mandelbrot function. In this way the micromechanical model allowed for an upgraded contact algorithm in terms of effective contact area and thermal and electrical contact conductivities. Such an algorithm is subsequently implemented to construct a global model for performing transient thermoelectromechanical analyses without the need of simulating roughness asperities of contact surfaces, so reducing the computational cost. A comparison between numerical and analytical results shows that the adopted procedure is suitable to simulate the transient thermoelectromechanical response of electric connectors.
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
Stochastic Models for Phylogenetic Trees on Higher-order Taxa
Aldous, David; Popovic, Lea
2007-01-01
Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of higher-order taxa. A coherent model for trees on (say) genera should involve both a species-level model and a model for the classification scheme by which species are assigned to genera. We present a general framework for such models, and describe three alternate classification schemes. Combining with the species-level model of Aldous-Popovic (2005), one gets models for higher-order trees, and we initiate analytic study of such models. In particular we derive formulas for the lifetime of genera, for the distribution of number of species per genus, and for the offspring structure of the tree on genera.
A spatial model for sporadic tree species distribution in support of tree oriented silviculture
Directory of Open Access Journals (Sweden)
Davide Melini
2013-12-01
Full Text Available This technical note describes how a spatial model for sporadic tree species distribution in the territory of the Unione di Comuni Montana Colline Metallifere (UCMCM was built using the Random Forest (RF algorithm and 48 predictors, including reflectance values from ground cover - provided by satellite sensors - and ecological factors. The P.Pro.SPO.T. project - Policy and Protection of Sporadic tree species in Tuscany forest (LIFE 09 ENV/IT/000087 is currently carried out in this area with the purpose of initiating the implementation of tree oriented silviculture in the Tuscany forests. Tree oriented silviculture aims at obtaining both forest biodiversity protection and local production of valuable timber. After creating a map showing the probability of presence of sporadic tree species, it was possible to identify the most suitable areas for sporadic tree species which are under protection according to the regulation of the Tuscany Region.Using data and software provided free of charge, and applying the RF algorithm, distribution models could be developed in order to identify the most suitable areas for the application of tree oriented silviculture. This can provide a support to forestry planning that includes tree oriented silviculture, thus reducing its implementation cost.
一种使用四叉树分割的分形信息隐藏算法%A FRACTAL INFORMATION HIDING ALGORITHM BASED ON QUAD-TREE PARTITION
Institute of Scientific and Technical Information of China (English)
聂道聪; 郑洪源
2015-01-01
Existing information hiding algorithms of orthogonal fractal always divide original image into average partition when carrying out orthogonal fractal coding,which are not image-adaptive and are time consuming.What’s more,they fail to consider the correlation among components and the collage error in colour image processing,therefore the robustness is poor.We propose an improved orthogonal fractal information hiding algorithm which uses quad-tree partition.The algorithm can realise quad-tree partition on original image according image feature,and takes into account the correlation of three components (R,G,B)of colour image,as well as extracts the luminance component for fractal coding.Moreover,the algorithm uses collage error characteristics to dynamically regulate the modifying value of fractal parameters for embedding secret image.Experiments and applications show that the improved algorithm has short encoding time,good transparency and is robust to JPEG image compression,noise,filtering and geometric distortion.%目前的正交分形信息隐藏算法在进行正交分形编码时都是等分割原始图像，这样无法自适应图像内容且耗时，并且在处理彩色图像时没能考虑分量之间的相关性以及拼贴误差，因此鲁棒性较差。提出一种采用四叉树分割的正交分形信息隐藏算法。该算法能够根据图像特征实现原始图像的四叉树分割，同时考虑彩色图像 R、G、B 三个分量的相关性，提取亮度分量进行分形编码，并利用拼贴误差特性，动态调整分型参数的修改量来嵌入秘密图像。实验及应用表明，该算法编码时间短、具有很好的透明性以及对 JPEG 压缩、加噪、滤波、几何形变等具有较好的鲁棒性。
Fractal Representation of Exergy
Directory of Open Access Journals (Sweden)
Yvain Canivet
2016-02-01
Full Text Available We developed a geometrical model to represent the thermodynamic concepts of exergy and anergy. The model leads to multi-scale energy lines (correlons that we characterised by fractal dimension and entropy analyses. A specific attention will be paid to overlapping points, rising interesting remarks about trans-scale dynamics of heat flows.
Marks-Tarlow, Terry
Linear concepts of time plus the modern capacity to track history emerged out of circular conceptions characteristic of ancient and traditional cultures. A fractal concept of time lies implicitly within the analog clock, where each moment is treated as unique. With fractal geometry the best descriptor of nature, qualities of self-similarity and scale invariance easily model her endless variety and recursive patterning, both in time and across space. To better manage temporal aspects of our lives, a fractal concept of time is non-reductive, based more on the fullness of being than on fragments of doing. By using a fractal concept of time, each activity or dimension of life is multiply and vertically nested. Each nested cycle remains simultaneously present, operating according to intrinsic dynamics and time scales. By adding the vertical axis of simultaneity to the horizontal axis of length, time is already full and never needs to be filled. To attend to time's vertical dimension is to tap into the imaginary potential for infinite depth. To switch from linear to fractal time allows us to relax into each moment while keeping in mind the whole.
The reality model of the plum tree based on SpeedTree
Bai, Zhi-yong; Huang, Xin-yuan
2010-02-01
Plum Blossom as the Chinese traditional flowers may be unique all over the world and has the first right of access to international registry of flower. In this paper, the SpeedTree software is used to quickly build reality model of the plum tree. The graphics texture mapping techniques is used, and the plum tree image maps express the geometric model of the surface material, which constitutes a visual image of the graphic objects. It is significant for non-destructive study of plum and virtual garden.
Boosted Regression Tree Models to Explain Watershed ...
Boosted regression tree (BRT) models were developed to quantify the nonlinear relationships between landscape variables and nutrient concentrations in a mesoscale mixed land cover watershed during base-flow conditions. Factors that affect instream biological components, based on the Index of Biotic Integrity (IBI), were also analyzed. Seasonal BRT models at two spatial scales (watershed and riparian buffered area [RBA]) for nitrite-nitrate (NO2-NO3), total Kjeldahl nitrogen, and total phosphorus (TP) and annual models for the IBI score were developed. Two primary factors — location within the watershed (i.e., geographic position, stream order, and distance to a downstream confluence) and percentage of urban land cover (both scales) — emerged as important predictor variables. Latitude and longitude interacted with other factors to explain the variability in summer NO2-NO3 concentrations and IBI scores. BRT results also suggested that location might be associated with indicators of sources (e.g., land cover), runoff potential (e.g., soil and topographic factors), and processes not easily represented by spatial data indicators. Runoff indicators (e.g., Hydrological Soil Group D and Topographic Wetness Indices) explained a substantial portion of the variability in nutrient concentrations as did point sources for TP in the summer months. The results from our BRT approach can help prioritize areas for nutrient management in mixed-use and heavily impacted watershed
Fractal Dimension Invariant Filtering and Its CNN-based Implementation
Xu, Hongteng; Yan, Junchi; Persson, Nils; Lin, Weiyao; Zha, Hongyuan
2016-01-01
Fractal analysis has been widely used in computer vision, especially in texture image processing and texture analysis. The key concept of fractal-based image model is the fractal dimension, which is invariant to bi-Lipschitz transformation of image, and thus capable of representing intrinsic structural information of image robustly. However, the invariance of fractal dimension generally does not hold after filtering, which limits the application of fractal-based image model. In this paper, we...
Institute of Scientific and Technical Information of China (English)
ZhinhongLi; DongWu; Yuhansun; JunWang; YiLiu; BaozhongDong; Zhinhong
2001-01-01
Silica aggregates were prepared by base-catalyzed hydrolysis and condensation of alkoxides in alcohol.Polyethylene glycol(PEG) was used as organic modifier.The sols were characterized using Small Angle X-ray Scattering (SAXS) with synchrotron radiation as X-ray source.The structure evolution during the sol-gel process was determined and described in terms of the fractal geometry.As-produced silica aggregates were found to be mass fractals.The fractl dimensions spanned the regime 2.1-2.6 corresponding to more branched and compact structures.Both RLCA and Eden models dominated the kinetic growth under base-catalyzed condition.
Lin, Guoxing
2016-01-01
Pulsed field gradient (PFG) has been increasingly employed to study anomalous diffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, the analysis of PFG anomalous diffusion is complicated. In this paper, a fractal derivative model based modified Gaussian phase distribution method is proposed to describe PFG anomalous diffusion. By using the phase distribution obtained from the effective phase shift diffusion method based on fractal derivatives, and employing some of the traditional Gaussian phase distribution approximation techniques, a general signal attenuation expression for free fractional diffusion is derived. This expression describes a stretched exponential function based attenuation, which is distinct from both the exponential attenuation for normal diffusion obtained from conventional Gaussian phase distribution approximation, and the Mittag-Leffler function based attenuation for anomalous diffusion obtained from fractional derivative. The obtained signal attenu...
A generalized item response tree model for psychological assessments.
Jeon, Minjeong; De Boeck, Paul
2016-09-01
A new item response theory (IRT) model with a tree structure has been introduced for modeling item response processes with a tree structure. In this paper, we present a generalized item response tree model with a flexible parametric form, dimensionality, and choice of covariates. The utilities of the model are demonstrated with two applications in psychological assessments for investigating Likert scale item responses and for modeling omitted item responses. The proposed model is estimated with the freely available R package flirt (Jeon et al., 2014b).
Study on Impeller Fracture Model Based on Vibration Characteristics and Fractal Theory
Directory of Open Access Journals (Sweden)
Xiaolong Zhang
2015-01-01
Full Text Available During the operation of centrifugal compressor, failure easily occurs in the presence of complicated external forces. The failure process characterizes with strong nonlinearity, and hence it is difficult to be described by conventional methods. In this paper, firstly, the cracks in different positions are described using crack fractal theory. The basic failure modes of the impeller are summarized. Secondly, a three-dimensional finite element model of the impeller is constructed. Then the von Mises stress under the centrifugal force is calculated, and the corresponding impeller failure process is simulated by “element life and death technology” in ANSYS. Finally, the impeller failure mechanism is analyzed. It can be found that the static stress is not the main cause of the impeller failure, and the dynamic characteristics of the impeller are not perfect because of the pitch vibration modes which appeared in the investigated frequency range. Meanwhile, the natural frequency of the impeller also cannot avoid the frequency of the excitation force.
Amir, S.; Hashim Ali, S. A.; Mohamed, N. S.
2011-10-01
We initially prepared films of poly(vinylidene fluoride-co-hexafluoropropylene)/poly(ethyl methacrylate)-ammonium trifluorome-thanesulfonate dispersed with various wt.% of chromium oxide to study their properties and potential application in electrochemical devices. However, a few months later the nanocomposite polymer electrolyte membranes were found to become a sort of medium for fractal growth. This discovery led to a simulation of the fractals observed in these polymer electrolyte films using a diffusion-limited aggregation model that is based on Brownian motion theory (random walk). The fractal dimensions, D, of the fractal patterns obtained from experimental and simulation work were calculated using the box-counting method. The fractal patterns and dimensions of the simulated fractal patterns were comparable with those obtained from the original fractals observed in the polymer electrolyte films.
A Knowledge Tree Model for Managing Organizational Knowledge
Institute of Scientific and Technical Information of China (English)
BAO Zhen-qiang; WANG Ning-sheng
2002-01-01
According to the relation of organizational knowledge, this paper analyzes the structure of organizational knowledge at first. A concept of knowledge tree is introduced and a process model of knowledge management is described by a knowledge tree. In this paper a definition of value of knowledge is given and the life cycle of a knowledge tree is analyzed. Finally, some principles for knowledge management are presented.
Impacts of Tree Height-Dbh Allometry on Lidar-Based Tree Aboveground Biomass Modeling
Fang, R.
2016-06-01
Lidar has been widely used in tree aboveground biomass (AGB) estimation at plot or stand levels. Lidar-based AGB models are usually constructed with the ground AGB reference as the response variable and lidar canopy indices as predictor variables. Tree diameter at breast height (dbh) is the major variable of most allometric models for estimating reference AGB. However, lidar measurements are mainly related to tree vertical structure. Therefore, tree height-dbh allometric model residuals are expected to have a large impact on lidar-based AGB model performance. This study attempts to investigate sensitivity of lidar-based AGB model to the decreasing strength of height-dbh relationship using a Monte Carlo simulation approach. Striking decrease in R2 and increase in relative RMSE were found in lidar-based AGB model, as the variance of height-dbh model residuals grew. I, therefore, concluded that individual tree height-dbh model residuals fundamentally introduce errors to lidar-AGB models.
Motif Yggdrasil: sampling sequence motifs from a tree mixture model.
Andersson, Samuel A; Lagergren, Jens
2007-06-01
In phylogenetic foot-printing, putative regulatory elements are found in upstream regions of orthologous genes by searching for common motifs. Motifs in different upstream sequences are subject to mutations along the edges of the corresponding phylogenetic tree, consequently taking advantage of the tree in the motif search is an appealing idea. We describe the Motif Yggdrasil sampler; the first Gibbs sampler based on a general tree that uses unaligned sequences. Previous tree-based Gibbs samplers have assumed a star-shaped tree or partially aligned upstream regions. We give a probabilistic model (MY model) describing upstream sequences with regulatory elements and build a Gibbs sampler with respect to this model. The model allows toggling, i.e., the restriction of a position to a subset of nucleotides, but does not require aligned sequences nor edge lengths, which may be difficult to come by. We apply the collapsing technique to eliminate the need to sample nuisance parameters, and give a derivation of the predictive update formula. We show that the MY model improves the modeling of difficult motif instances and that the use of the tree achieves a substantial increase in nucleotide level correlation coefficient both for synthetic data and 37 bacterial lexA genes. We investigate the sensitivity to errors in the tree and show that using random trees MY sampler still has a performance similar to the original version.
Curie-point Depths Estimated from Fractal Magnetization Models in the Indian-Himalayan Region
Wang, J.; Li, C. F.; Lei, J., Sr.; Zhang, G.; Sun, C., Sr.
2016-12-01
The convergence between the Indian and Eurasian plates has developed the world's extreme topography and has also resulted in the occurrence of large earthquakes in the region. The April 25, 2015 (Mw 7.8) earthquake in central Nepal is the largest earthquake that has been recorded in the Nepal Himalaya since 1934. The earthquake caused thousands of people to die and massive destruction of famous heritage-structures in and around kathmandu and was attributed to the interations between the Indian and Eurasian plates. The crustal thermal structure which can be inferred from the Curie-point depths is critial to understand the seismotectonics and subduction in the Indian-Himalayan region. We present our inversion of Curie-point depths of the Indian-Himalayan region based on fractal spectral analyses both from aeromagnetic and satellite data. The first magnetic anomaly model used for estimatiion of Curie-point depths is the EMAG2 model, which has a resolution of 2-arc minute and an altitude of 4 km above the geoid. The second magnetic anomaly model is the CHAMP lithospheric model MF6. The third and the last magnetic anomaly model is the NGDC-720 lithospheric model, which is based on both the EMAG2 and MF6 models, has the smallest wavelength of 56 km. We first test variable windows sizes of 100.8×100.8 km2, 201.6×201.6 km2 and 302.4×302.4 km2 to estimate the Curie-point depths and then take the average of the results from these three different window sizes as the final Curie depths for the EMAG2 and MF6 models, respectively. The differences between the two Curie depths estimations from the EMAG2 and MF6 models mostly range within about ±4 km except for that in the Central Tibetan Plateau and Northeast India. This result shows that the NGDC-720 lithospheric model which contains both the EMAG2 and MF6 models is valid for the Curie-point estimation in the Indian-Himalayan region. The average Curie depths estimated from the NGDC-720 lithospheric model show small values in
Darwinian Evolution and Fractals
Carr, Paul H.
2009-05-01
Did nature's beauty emerge by chance or was it intelligently designed? Richard Dawkins asserts that evolution is blind aimless chance. Michael Behe believes, on the contrary, that the first cell was intelligently designed. The scientific evidence is that nature's creativity arises from the interplay between chance AND design (laws). Darwin's ``Origin of the Species,'' published 150 years ago in 1859, characterized evolution as the interplay between variations (symbolized by dice) and the natural selection law (design). This is evident in recent discoveries in DNA, Madelbrot's Fractal Geometry of Nature, and the success of the genetic design algorithm. Algorithms for generating fractals have the same interplay between randomness and law as evolution. Fractal statistics, which are not completely random, characterize such phenomena such as fluctuations in the stock market, the Nile River, rainfall, and tree rings. As chaos theorist Joseph Ford put it: God plays dice, but the dice are loaded. Thus Darwin, in discovering the evolutionary interplay between variations and natural selection, was throwing God's dice!
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
Berejnov, Viatcheslav; Sinton, David; Djilali, Ned
2009-01-01
Experimental two-phase invasion percolation flow patterns were observed in hydrophobic micro-porous networks designed to model fuel cell specific porous media. In order to mimic the operational conditions encountered in the porous electrodes of polymer electrolyte membrane fuel cells (PEMFCs), micro-porous networks were fabricated with corresponding microchannel size distributions. The inlet channels were invaded homogeneously with flow rates corresponding to fuel cell current densities of 1.0 to 0.1 A/cm2 (Ca 10e-7-10e-8). A variety of fractal breakthrough patterns were observed and analyzed to quantify flooding density and geometrical diversity in terms of the total saturation, St, local saturations, s, and fractal dimension, D. It was found that St increases monotonically during the invasion process until the breakthrough point is reached, and s profiles indicate the dynamic distribution of the liquid phase during the process. Fractal analysis confirmed that the experiments fall within the flow regime of i...
Decision tree modeling with relational views
Bentayeb, Fadila
2002-01-01
Data mining is a useful decision support technique that can be used to discover production rules in warehouses or corporate data. Data mining research has made much effort to apply various mining algorithms efficiently on large databases. However, a serious problem in their practical application is the long processing time of such algorithms. Nowadays, one of the key challenges is to integrate data mining methods within the framework of traditional database systems. Indeed, such implementations can take advantage of the efficiency provided by SQL engines. In this paper, we propose an integrating approach for decision trees within a classical database system. In other words, we try to discover knowledge from relational databases, in the form of production rules, via a procedure embedding SQL queries. The obtained decision tree is defined by successive, related relational views. Each view corresponds to a given population in the underlying decision tree. We selected the classical Induction Decision Tree (ID3) a...
Band structure characteristics of T-square fractal phononic crystals
Institute of Scientific and Technical Information of China (English)
Liu Xiao-Jian; Fan You-Hua
2013-01-01
The T-square fractal two-dimensional phononic crystal model is presented in this article.A comprehensive study is performed for the Bragg scattering and locally resonant fractal phononic crystal.We find that the band structures of the fractal and non-fractal phononic crystals at the same filling ratio are quite different through using the finite element method.The fractal design has an important impact on the band structures of the two-dimensional phononic crystals.
Al-Khaja, Nawal
2007-01-01
This is a thematic lesson plan for young learners about palm trees and the importance of taking care of them. The two part lesson teaches listening, reading and speaking skills. The lesson includes parts of a tree; the modal auxiliary, can; dialogues and a role play activity.
Massive-scale tree modelling from TLS data
Raumonen, P.; Casella, E.; Calders, K.; Murphy, S.; Åkerblom, M.; Kaasalainen, M.
2015-01-01
This paper presents a method for reconstructing automatically the quantitative structure model of every tree in a forest plot from terrestrial laser scanner data. A new feature is the automatic extraction of individual trees from the point cloud. The method is tested with a 30-m diameter English oak
Ising model on the generalized Bruhat-Tits tree
Zinoviev, Yu. M.
1991-08-01
The partition function and the correlation functions of the Ising model on the generalized Bruhat-Tits tree are calculated. We computed also the averages of these correlation functions when the corresponding vertices are attached to the boundary of the generalized Bruhat-Tits tree.
Configuration entropy of fractal landscapes
National Research Council Canada - National Science Library
Rodríguez‐Iturbe, Ignacio; D'Odorico, Paolo; Rinaldo, Andrea
1998-01-01
.... The spatial arrangement of two‐dimensional images is found to be an effective way to characterize fractal landscapes and the configurational entropy of these arrangements imposes demanding conditions for models attempting to represent these fields.
Weighted Hybrid Decision Tree Model for Random Forest Classifier
Kulkarni, Vrushali Y.; Sinha, Pradeep K.; Petare, Manisha C.
2016-06-01
Random Forest is an ensemble, supervised machine learning algorithm. An ensemble generates many classifiers and combines their results by majority voting. Random forest uses decision tree as base classifier. In decision tree induction, an attribute split/evaluation measure is used to decide the best split at each node of the decision tree. The generalization error of a forest of tree classifiers depends on the strength of the individual trees in the forest and the correlation among them. The work presented in this paper is related to attribute split measures and is a two step process: first theoretical study of the five selected split measures is done and a comparison matrix is generated to understand pros and cons of each measure. These theoretical results are verified by performing empirical analysis. For empirical analysis, random forest is generated using each of the five selected split measures, chosen one at a time. i.e. random forest using information gain, random forest using gain ratio, etc. The next step is, based on this theoretical and empirical analysis, a new approach of hybrid decision tree model for random forest classifier is proposed. In this model, individual decision tree in Random Forest is generated using different split measures. This model is augmented by weighted voting based on the strength of individual tree. The new approach has shown notable increase in the accuracy of random forest.
Maximum Leaf Spanning Trees of Growing Sierpinski Networks Models
Yao, Bing; Xu, Jin
2016-01-01
The dynamical phenomena of complex networks are very difficult to predict from local information due to the rich microstructures and corresponding complex dynamics. On the other hands, it is a horrible job to compute some stochastic parameters of a large network having thousand and thousand nodes. We design several recursive algorithms for finding spanning trees having maximal leaves (MLS-trees) in investigation of topological structures of Sierpinski growing network models, and use MLS-trees to determine the kernels, dominating and balanced sets of the models. We propose a new stochastic method for the models, called the edge-cumulative distribution, and show that it obeys a power law distribution.
Simulation and fabrication of the atmospheric turbulence phase screen based on a fractal model
Institute of Scientific and Technical Information of China (English)
Peng Jia; Sijiong Zhang
2012-01-01
An atmospheric turbulence phase screen generated using a fractal method is introduced.It is etched onto fused silica and tested in the laboratory.The etched screen has relatively low cost,high resolution,and can be used in the broad waveband under severe temperature conditions.Our results are shown to agree well with the theory.
Fractal and Multifractal Time Series
Kantelhardt, Jan W
2008-01-01
Data series generated by complex systems exhibit fluctuations on many time scales and/or broad distributions of the values. In both equilibrium and non-equilibrium situations, the natural fluctuations are often found to follow a scaling relation over several orders of magnitude, allowing for a characterisation of the data and the generating complex system by fractal (or multifractal) scaling exponents. In addition, fractal and multifractal approaches can be used for modelling time series and deriving predictions regarding extreme events. This review article describes and exemplifies several methods originating from Statistical Physics and Applied Mathematics, which have been used for fractal and multifractal time series analysis.
Thermal collapse of snowflake fractals
Gallo, T.; Jurjiu, A.; Biscarini, F.; Volta, A.; Zerbetto, F.
2012-08-01
Snowflakes are thermodynamically unstable structures that would ultimately become ice balls. To investigate their dynamics, we mapped atomistic molecular dynamics simulations of small ice crystals - built as filled von Koch fractals - onto a discrete-time random walk model. Then the walkers explored the thermal evolution of high fractal generations. The in silico experiments showed that the evolution is not entirely random. The flakes step down one fractal generation before forfeiting their architecture. The effect may be used to trace the thermal history of snow.
On the fractal properties microaccelerations
Sedelnikov, A V
2012-01-01
In this paper the fractal property of the internal environment of space laboratory microaccelerations that occur. Changing the size of the space lab leads to the fact that the dependence of microaccelerations from time to time has the property similar to the self-affinity of fractal functions. With the help of microaccelerations, based on the model of the real part of the fractal Weierstrass-Mandelbrot function is proposed to form the inertial-mass characteristics of laboratory space with a given level of microaccelerations.
Modeling fractal structure of city-size distributions using correlation functions.
Directory of Open Access Journals (Sweden)
Yanguang Chen
Full Text Available Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2. Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity, and the other the Zipf effect indicating city size growth (internal complexity. Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.
Modeling fractal structure of city-size distributions using correlation functions.
Chen, Yanguang
2011-01-01
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Using the idea from general fractals and scaling, I propose a dual competition hypothesis of city development to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another, but represent different processes of urban evolution, respectively. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is the Pareto effect indicating city number increase (external complexity), and the other the Zipf effect indicating city size growth (internal complexity). Because of struggle of the two effects, the scaling exponent varies from 0.5 to 2; but if the two effects reach equilibrium with each other, the scaling exponent approaches 1. A series of mathematical experiments on hierarchical correlation are employed to verify the models and a conclusion can be drawn that if cities in a given region follow Zipf's law, the frequency and size correlations will follow the scaling law. This theory can be generalized to interpret the inverse power-law distributions in various fields of physical and social sciences.
Generalized fragmentation functions for fractal jet observables
Elder, Benjamin T.; Procura, Massimiliano; Thaler, Jesse; Waalewijn, Wouter J.; Zhou, Kevin
2017-06-01
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phenomenological implications. As an application, we present examples of fractal jet observables that are useful in discriminating quark jets from gluon jets.
Fractal properties of forest fires in Amazonia as a basis for modelling pan-tropical burnt area
Fletcher, I. N.; Aragão, L. E. O. C.; Lima, A.; Shimabukuro, Y.; Friedlingstein, P.
2014-03-01
Current methods for modelling burnt area in dynamic global vegetation models (DGVMs) involve complex fire spread calculations, which rely on many inputs, including fuel characteristics, wind speed and countless parameters. They are therefore susceptible to large uncertainties through error propagation, but undeniably useful for modelling specific, small-scale burns. Using observed fractal distributions of fire scars in Brazilian Amazonia in 2005, we propose an alternative burnt area model for tropical forests, with fire counts as sole input and few parameters. This model is intended for predicting large-scale burnt area rather than looking at individual fire events. A simple parameterization of a tapered fractal distribution is calibrated at multiple spatial resolutions using a satellite-derived burnt area map. The model is capable of accurately reproducing the total area burnt (16 387 km2) and its spatial distribution. When tested pan-tropically using the MODIS MCD14ML active fire product, the model accurately predicts temporal and spatial fire trends, but the magnitude of the differences between these estimates and the GFED3.1 burnt area products varies per continent.
Pestana, Dinis D.; Aleixo, Sandra M.; Rocha, J. Leonel
Classical central limit theorems, culminating in the theory of infinite divisibility, accurately describe the behaviour of stochastic phenomena with asymptotically negligible components. The classical theory fails when a single component may assume an extreme protagonism. The early developments of the speculation theory didn't incorporate the pioneer work of Pareto on heavy tailed models, and the proper setup to conciliate regularity and abrupt changes, in a wide range of natural phenomena, is Karamata's concept of regular variation and the role it plays in the theory of domains of attraction, [8], and Resnick's tail equivalence leading to the importance of generalized Pareto distribution is the scope of extreme value theory, [13]. Waliszewski and Konarski discussed the applicability of the Gompertz curve and its fractal behaviour for instance in modeling healthy and neoplasic cells tissue growth, [15]. Gompertz function is the Gumbel extreme value model, whose broad domain of attraction contains intermediate tail weight laws with a wide range of behaviour. Aleixo et al. investigated fractality associated with Beta (p,q) models, [1], [2], [10] and [11]. In this work, we introduce a new family of probability density functions tied to the classical beta family, the Beta*(p,q) models, some of which are generalized Pareto, that span the possible regular variation of tails. We extend the investigation to other extreme stable models, namely Fréchet's and Weibull's types in the General Extreme Value (GEV) model.
A generalized model for stability of trees under impact conditions
Dattola, Giuseppe; Crosta, Giovanni; Castellanza, Riccardo; di Prisco, Claudio; Canepa, Davide
2016-04-01
Stability of trees to external actions involve the combined effects of stem and tree root systems. A block impacting on the stem or an applied force pulling the stem can cause a tree instability involving stem bending or failure and tree root rotation. So different contributions are involved in the stability of the system. The rockfalls are common natural phenomena that can be unpredictable in terms of frequency and magnitude characteristics, and this makes difficult the estimate of potential hazard and risk for human lives and activities. In mountain areas a natural form of protection from rockfalls is provided by forest growing. The difficulties in the assessment of the real capability of this natural barrier by means of models is an open problem. Nevertheless, a large amount of experimental data are now available which provides support for the development of advanced theoretical framework and corresponding models. The aim of this contribution consists in presenting a model developed to predict the behavior of trees during a block impact. This model describes the tree stem by means of a linear elastic beam system consisting of two beams connected in series and with an equivalent geometry. The tree root system is described via an equivalent foundation, whose behavior is modelled through an elasto-plastic macro-element model. In order to calibrate the model parameters, simulations reproducing a series of winching tests, are performed. These numerical simulations confirm the capability of the model to predict the mechanical behavior of the stem-root system in terms of displacement vs force curves. Finally, numerical simulations of the impact of a boulder with a tree stem are carried out. These simulations, done under dynamic regime and with the model parameters obtained from the previous set of simulations, confirm the capability of the model to reproduce the effects on the stem-roots system generated by impulsive loads.
A new approach to modeling tree rainfall interception
Xiao, Qingfu; McPherson, E. Gregory; Ustin, Susan L.; Grismer, Mark E.
2000-12-01
A three-dimensional physically based stochastic model was developed to describe canopy rainfall interception processes at desired spatial and temporal resolutions. Such model development is important to understand these processes because forest canopy interception may exceed 59% of annual precipitation in old growth trees. The model describes the interception process from a single leaf, to a branch segment, and then up to the individual tree level. It takes into account rainfall, meteorology, and canopy architecture factors as explicit variables. Leaf and stem surface roughness, architecture, and geometric shape control both leaf drip and stemflow. Model predictions were evaluated using actual interception data collected for two mature open grown trees, a 9-year-old broadleaf deciduous pear tree (Pyrus calleryana "Bradford" or Callery pear) and an 8-year-old broadleaf evergreen oak tree (Quercus suber or cork oak). When simulating 18 rainfall events for the oak tree and 16 rainfall events for the pear tree, the model over estimated interception loss by 4.5% and 3.0%, respectively, while stemflow was under estimated by 0.8% and 3.3%, and throughfall was under estimated by 3.7% for the oak tree and over estimated by 0.3% for the pear tree. A model sensitivity analysis indicates that canopy surface storage capacity had the greatest influence on interception, and interception losses were sensitive to leaf and stem surface area indices. Among rainfall factors, interception losses relative to gross precipitation were most sensitive to rainfall amount. Rainfall incident angle had a significant effect on total precipitation intercepting the projected surface area. Stemflow was sensitive to stem segment and leaf zenith angle distributions. Enhanced understanding of interception loss dynamics should lead to improved urban forest ecosystem management.
A tree-based model for homogeneous groupings of multinomials.
Yang, Tae Young
2005-11-30
The motivation of this paper is to provide a tree-based method for grouping multinomial data according to their classification probability vectors. We produce an initial tree by binary recursive partitioning whereby multinomials are successively split into two subsets and the splits are determined by maximizing the likelihood function. If the number of multinomials k is too large, we propose to order the multinomials, and then build the initial tree based on a dramatically smaller number k-1 of possible splits. The tree is then pruned from the bottom up. The pruning process involves a sequence of hypothesis tests of a single homogeneous group against the alternative that there are two distinct, internally homogeneous groups. As pruning criteria, the Bayesian information criterion and the Wilcoxon rank-sum test are proposed. The tree-based model is illustrated on genetic sequence data. Homogeneous groupings of genetic sequences present new opportunities to understand and align these sequences.
Anomalous diffusion in fractal globules.
Tamm, M V; Nazarov, L I; Gavrilov, A A; Chertovich, A V
2015-05-01
The fractal globule state is a popular model for describing chromatin packing in eukaryotic nuclei. Here we provide a scaling theory and dissipative particle dynamics computer simulation for the thermal motion of monomers in the fractal globule state. Simulations starting from different entanglement-free initial states show good convergence which provides evidence supporting the existence of a unique metastable fractal globule state. We show monomer motion in this state to be subdiffusive described by ⟨X(2)(t)⟩∼t(αF) with αF close to 0.4. This result is in good agreement with existing experimental data on the chromatin dynamics, which makes an additional argument in support of the fractal globule model of chromatin packing.
Discrete Discriminant analysis based on tree-structured graphical models
DEFF Research Database (Denmark)
Perez de la Cruz, Gonzalo; Eslava, Guillermina
The purpose of this paper is to illustrate the potential use of discriminant analysis based on tree{structured graphical models for discrete variables. This is done by comparing its empirical performance using estimated error rates for real and simulated data. The results show that discriminant...... analysis based on tree{structured graphical models is a simple nonlinear method competitive with, and sometimes superior to, other well{known linear methods like those assuming mutual independence between variables and linear logistic regression....
Discrete Discriminant analysis based on tree-structured graphical models
DEFF Research Database (Denmark)
Perez de la Cruz, Gonzalo; Eslava, Guillermina
The purpose of this paper is to illustrate the potential use of discriminant analysis based on tree{structured graphical models for discrete variables. This is done by comparing its empirical performance using estimated error rates for real and simulated data. The results show that discriminant a...... analysis based on tree{structured graphical models is a simple nonlinear method competitive with, and sometimes superior to, other well{known linear methods like those assuming mutual independence between variables and linear logistic regression....
Institute of Scientific and Technical Information of China (English)
ZHANG Di; ZHANG Min; YE Pei-da
2006-01-01
This article explores the short-range dependence (SRD) and the long-range dependence (LRD) of self-similar traffic generated by the fractal-binomial-noise-driven Poisson process (FBNDP) model and lays emphasis on the former. By simulation, the SRD decaying trends with the increase of Hurst value and peak rate are obtained, respectively. After a comprehensive analysis of accuracy of self-similarity intensity,the optimal range of peak rate is determined by taking into account the time cost, the accuracy of self-similarity intensity,and the effect of SRD.
Modeling EEG fractal dimension changes in wake and drowsy states in humans--a preliminary study.
Bojić, Tijana; Vuckovic, Aleksandra; Kalauzi, Aleksandar
2010-01-21
Aim of this preliminary study was to examine and compare topographic distribution of Higuchi's fractal dimension (FD, measure of signal complexity) of EEG signals between states of relaxed wakefulness and drowsiness, as well as their FD differences. The experiments were performed on 10 healthy individuals using a fourteen-channel montage. An explanation is offered on the causes of the detected FD changes. FD values of 60s records belonging to wake (Hori's stage 1) and drowsy (Hori's stages 2-4) states were calculated for each channel and each subject. In 136 out of 140 epochs an increase in FD was obtained. Relationship between signal FD and its relative alpha amplitude was mathematically modeled and we quantitatively demonstrated that the increase in FD was predominantly due to a reduction in alpha activity. The model was generalized to include other EEG oscillations. By averaging FD values for each channel across 10 subjects, four clusters (O2O1; T6P4T5P3; C3F3F4C4F8F7; T4T3) for the wake and two clusters (O2O1P3T6P4T5; C3C4F4F3F8T4T3F7) for the drowsy state were statistically verified. Topographic distribution of FD values in wakefulness showed a lateral symmetry and a partial fronto-occipital gradient. In drowsiness, a reduction in the number of clusters was detected, due to regrouping of channels T3, T4, O1 and O2. Topographic distribution of absolute FD differences revealed largest values at F7, O1 and F3. Reorganization of channel clusters showed that regionalized brain activity, specific for wakefulness, became more global by entering into drowsiness. Since the global increase in FD during wake-to-drowsy transition correlated with the decrease of alpha power, we inferred that increase of EEG complexity may not necessarily be an index of brain activation.
SMOOTH TRANSITION LOGISTIC REGRESSION MODEL TREE
RODRIGO PINTO MOREIRA
2008-01-01
Este trabalho tem como objetivo principal adaptar o modelo STR-Tree, o qual é a combinação de um modelo Smooth Transition Regression com Classification and Regression Tree (CART), a fim de utilizá-lo em Classificação. Para isto algumas alterações foram realizadas em sua forma estrutural e na estimação. Devido ao fato de estarmos fazendo classificação de variáveis dependentes binárias, se faz necessária a utilização das técnicas empregadas em Regressão Logística, dessa forma a estimação dos pa...
Renormalization and small-world model of fractal quantum repeater networks
Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu
2013-01-01
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks. PMID:23386977
Renormalization and small-world model of fractal quantum repeater networks.
Wei, Zong-Wen; Wang, Bing-Hong; Han, Xiao-Pu
2013-01-01
Quantum networks provide access to exchange of quantum information. The primary task of quantum networks is to distribute entanglement between remote nodes. Although quantum repeater protocol enables long distance entanglement distribution, it has been restricted to one-dimensional linear network. Here we develop a general framework that allows application of quantum repeater protocol to arbitrary quantum repeater networks with fractal structure. Entanglement distribution across such networks is mapped to renormalization. Furthermore, we demonstrate that logarithmical times of recursive such renormalization transformations can trigger fractal to small-world transition, where a scalable quantum small-world network is achieved. Our result provides new insight into quantum repeater theory towards realistic construction of large-scale quantum networks.
Realistic Representation of Trees in an Urban Canopy Model
Ryu, Young-Hee; Bou-Zeid, Elie; Wang, Zhi-Hua; Smith, James A.
2016-05-01
A single-layer urban canopy model that captures sub-facet heterogeneity and various hydrological processes is further developed to explicitly incorporate trees within the urban canyon. The physical processes associated with trees are shortwave/longwave radiation exchange, including mutual interception and shading by trees and buildings and multiple reflections, sensible heat and latent heat (through transpiration) exchange, and root water uptake. A computationally-efficient geometric approach is applied to the radiation exchanges, requiring a priori knowledge of view factors. These view factors are first obtained from independent Monte Carlo ray-tracing simulations, and subsequently simple relations, which are functions of canyon aspect ratio and tree-crown ratio, are proposed to estimate them. The developed model is evaluated against field observations at two urban sites and one suburban site, showing improved performance for latent heat flux compared to the previous version that only includes ground vegetation. The trees in the urban canopy act to considerably decrease sensible heat flux and increase latent heat flux, and these effects are found to be more significant in the more dense urban site. Sensitivity tests are then performed to examine the effects of tree geometry relative to canyon geometry. The results indicate that the tree-crown size relative to canyon width is the most influential parameter to decrease sensible heat flux and increase latent heat flux, resulting in cooling of the urban area.
The fractal globule as a model of chromatin architecture in the cell
Mirny, Leonid A.
2011-01-01
The fractal globule is a compact polymer state that emerges during polymer condensation as a result of topological constraints which prevent one region of the chain from passing across another one. This long-lived intermediate state was introduced in 1988 (Grosberg et al. 1988) and has not been observed in experiments or simulations until recently (Lieberman-Aiden et al. 2009). Recent characterization of human chromatin using a novel chromosome conformational capture technique brought the fra...
AIRWAY LABELING USING A HIDDEN MARKOV TREE MODEL
Ross, James C.; Díaz, Alejandro A.; Okajima, Yuka; Wassermann, Demian; Washko, George R.; Dy, Jennifer; San José Estépar, Raúl
2014-01-01
We present a novel airway labeling algorithm based on a Hidden Markov Tree Model (HMTM). We obtain a collection of discrete points along the segmented airway tree using particles sampling [1] and establish topology using Kruskal’s minimum spanning tree algorithm. Following this, our HMTM algorithm probabilistically assigns labels to each point. While alternative methods label airway branches out to the segmental level, we describe a general method and demonstrate its performance out to the subsubsegmental level (two generations further than previously published approaches). We present results on a collection of 25 computed tomography (CT) datasets taken from a Chronic Obstructive Pulmonary Disease (COPD) study. PMID:25436039
Modeling and Testing Landslide Hazard Using Decision Tree
Directory of Open Access Journals (Sweden)
Mutasem Sh. Alkhasawneh
2014-01-01
Full Text Available This paper proposes a decision tree model for specifying the importance of 21 factors causing the landslides in a wide area of Penang Island, Malaysia. These factors are vegetation cover, distance from the fault line, slope angle, cross curvature, slope aspect, distance from road, geology, diagonal length, longitude curvature, rugosity, plan curvature, elevation, rain perception, soil texture, surface area, distance from drainage, roughness, land cover, general curvature, tangent curvature, and profile curvature. Decision tree models are used for prediction, classification, and factors importance and are usually represented by an easy to interpret tree like structure. Four models were created using Chi-square Automatic Interaction Detector (CHAID, Exhaustive CHAID, Classification and Regression Tree (CRT, and Quick-Unbiased-Efficient Statistical Tree (QUEST. Twenty-one factors were extracted using digital elevation models (DEMs and then used as input variables for the models. A data set of 137570 samples was selected for each variable in the analysis, where 68786 samples represent landslides and 68786 samples represent no landslides. 10-fold cross-validation was employed for testing the models. The highest accuracy was achieved using Exhaustive CHAID (82.0% compared to CHAID (81.9%, CRT (75.6%, and QUEST (74.0% model. Across the four models, five factors were identified as most important factors which are slope angle, distance from drainage, surface area, slope aspect, and cross curvature.
Choosing appropriate subpopulations for modeling tree canopy cover nationwide
Gretchen G. Moisen; John W. Coulston; Barry T. Wilson; Warren B. Cohen; Mark V. Finco
2012-01-01
In prior national mapping efforts, the country has been divided into numerous ecologically similar mapping zones, and individual models have been constructed for each zone. Additionally, a hierarchical approach has been taken within zones to first mask out areas of nonforest, then target models of tree attributes within forested areas only. This results in many models...
Modeling Dynamic Height and Crown Growth in Trees
Franklin, O.; Fransson, P.; Brännström, Å.
2015-12-01
Previously we have shown how principles based on productivity maximization (e.g. maximization of net primary production, net growth maximization, or functional balance) can explain allocation responses to resources, such as nutrients and light (Franklin et al., 2012). However, the success of these approaches depend on how well they align with the ultimate driver of plant behavior, fitness, or life time reproductive success. Consequently, they may not fully explain how allocation changes during the life cycle of trees where not only growth but also survival and reproduction are important. In addition, maximizing instantaneous productivity does not account for path dependence of tree growth. For example, maximizing productivity during early growth in shade may delay emergence in the forest canopy and reduce lifetime fitness compared to a more height oriented strategy. Here we present an approach to model how growth of stem diameter and leaf area in relation to stem height dynamically responds to light conditions in a way that maximizes life-time fitness (rather than instantaneous growth). The model is able to predict growth of trees growing in different types of forests, including trees emerging under a closed canopy and seedlings planted in a clear-cut area. It can also predict the response to sudden changes in the light environment, due to disturbances or harvesting. We envisage two main applications of the model, (i) Modeling effects of forest management, including thinning and planting (ii) Elucidating height growth strategies in trees and how they can be represented in vegetation models. ReferenceFranklin O, Johansson J, Dewar RC, Dieckmann U, McMurtrie RE, Brännström Å, Dybzinski R. 2012. Modeling carbon allocation in trees: a search for principles. Tree Physiology 32(6): 648-666.
Letort, Veronique; Mathieu, Amélie; De Reffye, Philippe; Constant, Thiéry
2010-01-01
Functional-structural models provide detailed representations of tree growth and their application to forestry seems full of prospects. However, owing to the complexity of tree architecture, parametric identification of such models remains a critical issue. We present the GreenLab approach for modelling tree growth. It simulates tree growth plasticity in response to changes of their internal level of trophic competition, especially topological development and cambial growth. The model includes a simplified representation of tree architecture, based on a species-specific description of branching patterns. We study whether those simplifications allow enough flexibility to reproduce with the same set of parameters the growth of two observed understorey beech trees (Fagus sylvatica L.) of different ages in different environmental conditions. The parametric identification of the model is global, i.e. all parameters are estimated simultaneously, potentially providing a better description of interactions between sub...
Biomass models to estimate carbon stocks for hardwood tree species
Energy Technology Data Exchange (ETDEWEB)
Ruiz-Peinado, R.; Montero, G.; Rio, M. del
2012-11-01
To estimate forest carbon pools from forest inventories it is necessary to have biomass models or biomass expansion factors. In this study, tree biomass models were developed for the main hardwood forest species in Spain: Alnus glutinosa, Castanea sativa, Ceratonia siliqua, Eucalyptus globulus, Fagus sylvatica, Fraxinus angustifolia, Olea europaea var. sylvestris, Populus x euramericana, Quercus canariensis, Quercus faginea, Quercus ilex, Quercus pyrenaica and Quercus suber. Different tree biomass components were considered: stem with bark, branches of different sizes, above and belowground biomass. For each species, a system of equations was fitted using seemingly unrelated regression, fulfilling the additivity property between biomass components. Diameter and total height were explored as independent variables. All models included tree diameter whereas for the majority of species, total height was only considered in the stem biomass models and in some of the branch models. The comparison of the new biomass models with previous models fitted separately for each tree component indicated an improvement in the accuracy of the models. A mean reduction of 20% in the root mean square error and a mean increase in the model efficiency of 7% in comparison with recently published models. So, the fitted models allow estimating more accurately the biomass stock in hardwood species from the Spanish National Forest Inventory data. (Author) 45 refs.
Flocculation control study based on fractal theory
Institute of Scientific and Technical Information of China (English)
无
2005-01-01
A study on flocculation control based on fractal theory was carried out. Optimization test of chemical coagulant dosage confirmed that the fractal dimension could reflect the flocculation degree and settling characteristics of aggregates and the good correlation with the turbidity of settled effluent. So that the fractal dimension can be used as the major parameter for flocculation system control and achieve self-acting adjustment of chemical coagulant dosage. The fractal dimension flocculation control system was used for further study carried out on the effects of various flocculation parameters, among which are the dependency relationship among aggregates fractal dimension, chemical coagulant dosage, and turbidity of settled effluent under the conditions of variable water quality and quantity. And basic experimental data were obtained for establishing the chemical coagulant dosage control model mainly based on aggregates fractal dimension.
Henri Epstein
2016-01-01
An algebraic formalism, developed with V. Glaser and R. Stora for the study of the generalized retarded functions of quantum field theory, is used to prove a factorization theorem which provides a complete description of the generalized retarded functions associated with any tree graph. Integrating over the variables associated to internal vertices to obtain the perturbative generalized retarded functions for interacting fields arising from such graphs is shown to be possible for a large cate...
Epstein, Henri
2016-01-01
An algebraic formalism, developped with V. Glaser and R. Stora for the study of the generalized retarded functions of quantum field theory, is used to prove a factorization theorem which provides a complete description of the generalized retarded functions associated with any tree graph. Integrating over the variables associated to internal vertices to obtain the perturbative generalized retarded functions for interacting fields arising from such graphs is shown to be possible for a large cat...
Epstein, Henri
2016-01-01
An algebraic formalism, developped with V.~Glaser and R.~Stora for the study of the generalized retarded functions of quantum field theory, is used to prove a factorization theorem which provides a complete description of the generalized retarded functions associated with any tree graph. Integrating over the variables associated to internal vertices to obtain the perturbative generalized retarded functions for interacting fields arising from such graphs is shown to be possible for a large category of space-times.
Amezquita-Sanchez, Juan P.; Adeli, Hojjat
2015-06-01
A new methodology is presented for (a) detecting, (b) locating, and (c) quantifying the damage severity in a smart highrise building structure. The methodology consists of three steps: In step 1, the synchrosqueezed wavelet transform is used to eliminate the noise in the signals. In step 2, a nonlinear dynamics measure based on the chaos theory, fractality dimension (FD), is employed to detect features to be used for damage detection. In step 3, a new structural damage index, based on the estimated FD values, is proposed as a measure of the condition of the structure. Further, the damage location is obtained using the changes of the estimated FD values. Three different FD algorithms for computing the fractality of time series signals are investigated. They are Katz’s FD, Higuchi’s FD, and box dimension. The usefulness and effectiveness of the proposed methodology are validated using the sensed data obtained experimentally for the 1:20 scaled model of a 38-storey concrete building structure.
Okie, Jordan G
2013-03-01
Surface areas and volumes of biological systems-from molecules to organelles, cells, and organisms-affect their biological rates and kinetics. Therefore, surface area-to-volume ratios and the scaling of surface area with volume profoundly influence ecology, physiology, and evolution. The zeroth-order geometric expectation is that surface area scales with body mass or volume as a power law with an exponent of two-thirds, with consequences for surface area-to-volume (SA : V) ratios and constraints on size; however, organisms have adaptations for altering the surface area scaling and SA : V ratios of their bodies and structures. The strategies fall into three groups: (1) fractal-like surface convolutions and crinkles; (2) classic geometric dissimilitude through elongating, flattening, fattening, and hollowing; and (3) internalization of surfaces. Here I develop general quantitative theory to model the spectra of effects of these strategies on SA : V ratios and surface area scaling, from exponents of less than two-thirds to superlinear scaling and mixed-power laws. Applying the theory to cells helps quantitatively evaluate the effects of membrane fractality, shape-shifting, vacuoles, vesicles, and mitochondria on surface area scaling, informing understanding of cell allometry, morphology, and evolution. Analysis of compiled data indicates that through hollowness and surface internalization, eukaryotic phytoplankton increase their effective surface area scaling, attaining near-linear scaling in larger cells. This unifying theory highlights the fundamental role of biological surfaces in metabolism and morphological evolution.
Lin, Guoxing
2017-02-01
Pulsed field gradient (PFG) technique is a noninvasive tool, and has been increasingly employed to study anomalous diffusions in Nuclear Magnetic Resonance (NMR) and Magnetic Resonance Imaging (MRI). However, the analysis of PFG anomalous diffusion is much more complicated than normal diffusion. In this paper, a fractal derivative model based modified Gaussian phase distribution method is proposed to describe PFG anomalous diffusion. By using the phase distribution obtained from the effective phase shift diffusion method based on fractal derivatives, and employing some of the traditional Gaussian phase distribution approximation techniques, a general signal attenuation expression for free fractional diffusion is derived. This expression describes a stretched exponential function based attenuation, which is distinct from both the exponential attenuation for normal diffusion obtained from conventional Gaussian phase distribution approximation, and the Mittag-Leffler function based attenuation for anomalous diffusion obtained from fractional derivative. The obtained signal attenuation expression can analyze the finite gradient pulse width (FGPW) effect. Additionally, it can generally be applied to all three types of PFG fractional diffusions classified based on time derivative order α and space derivative order β. These three types of fractional diffusions include time-fractional diffusion with { 0 reported results based on effective phase shift diffusion equation method and instantaneous signal attenuation method. This method provides a new, convenient approximation formalism for analyzing PFG anomalous diffusion experiments. The expression that can simultaneously interpret general fractional diffusion and FGPW effect could be especially important in PFG MRI, where the narrow gradient pulse limit cannot be satisfied.
Mineral resource analysis by parabolic fractals
Institute of Scientific and Technical Information of China (English)
XIE Shu-yun; YANG Yong-guo; BAO Zheng-yu; KE Xian-zhong; LIU Xiao-long
2009-01-01
Elemental concentration distributions in space have been analyzed using different approaches. These analyses are of great significance for the quantitative characterization of various kinds of distribution patterns. Fractal and multi-fiactal methods have been extensively applied to this topic. Traditionally, approximately linear-fractal laws have been regarded as useful tools for characterizing the self-similarities of element concentrations. But, in nature, it is not always easy to fred perfect linear fractal laws. In this paper the parabolic fractal model is used. First a two dimensional multiplicative multi-fractal cascade model is used to study the concentration patterns. The results show the parabolic fractal (PF) properties of the concentrations and the validity of non-linear fractal analysis. By dividing the studied area into four sub-areas it was possible to show that each part follows a non-linear para-bolic fractal law and that the dispersion within each part varies. The ratio of the polynomial coefficients of the fitted parabolic curves can reflect, to some degree, the relative concentration and dispersal distribution patterns. This can provide new insight into the ore-forming potential in space. The parabolic fractal evaluations of ore-forming potential for the four subareas are in good agreement with field investigation work and geochemical mapping results based on analysis of the original data.
Using fractal analysis in modeling the dynamics of forest areas and economic impact assessment
DEFF Research Database (Denmark)
Pintilii, Radu Daniel; Andronache, Ion; Diaconu, Daniel Constantin
2017-01-01
This study uses fractal analysis to quantify the spatial changes of forest resources caused by an increase of deforested areas. The method introduced contributes to the evaluation of forest resources being under significant pressure from anthropogenic activities. The pressure on the forest resour......-2014 containing economic activities (turnover) related to woody recourses, important indicators of forest exploitation. Taken together, the results obtained indicate a dramatic increase in deforested areas (over 19,122 ha in total for the period of analysis), in Maramures, County....
Runtime Optimizations for Tree-Based Machine Learning Models
N. Asadi; J.J.P. Lin (Jimmy); A.P. de Vries (Arjen)
2014-01-01
htmlabstractTree-based models have proven to be an effective solution for web ranking as well as other machine learning problems in diverse domains. This paper focuses on optimizing the runtime performance of applying such models to make predictions, specifically using gradient-boosted regression
Fruit tree model for uptake of organic compounds from soil
DEFF Research Database (Denmark)
Trapp, Stefan; Rasmussen, D.; Samsoe-Petersen, L.
2003-01-01
soils, regressions or models are in use, which were not intended to be used for tree fruits. A simple model for uptake of neutral organic contaminants into fruits is developed. It considers xylem and phloem transport to fruits through the stem. The mass balance is solved for the steady...
Directory of Open Access Journals (Sweden)
Stefanie M. Herrmann
2013-10-01
Full Text Available Field trees are an integral part of the farmed parkland landscape in West Africa and provide multiple benefits to the local environment and livelihoods. While field trees have received increasing interest in the context of strengthening resilience to climate variability and change, the actual extent of farmed parkland and spatial patterns of tree cover are largely unknown. We used the rule-based predictive modeling tool Cubist® to estimate field tree cover in the west-central agricultural region of Senegal. A collection of rules and associated multiple linear regression models was constructed from (1 a reference dataset of percent tree cover derived from very high spatial resolution data (2 m Orbview as the dependent variable, and (2 ten years of 10-day 250 m Moderate Resolution Imaging Spectrometer (MODIS Normalized Difference Vegetation Index (NDVI composites and derived phenological metrics as independent variables. Correlation coefficients between modeled and reference percent tree cover of 0.88 and 0.77 were achieved for training and validation data respectively, with absolute mean errors of 1.07 and 1.03 percent tree cover. The resulting map shows a west-east gradient from high tree cover in the peri-urban areas of horticulture and arboriculture to low tree cover in the more sparsely populated eastern part of the study area. A comparison of current (2000s tree cover along this gradient with historic cover as seen on Corona images reveals dynamics of change but also areas of remarkable stability of field tree cover since 1968. The proposed modeling approach can help to identify locations of high and low tree cover in dryland environments and guide ground studies and management interventions aimed at promoting the integration of field trees in agricultural systems.
Fractal Pattern Growth in Ti-Implanted Steel with High Ion Flux
Institute of Scientific and Technical Information of China (English)
张通和; 吴瑜光; 刘安东
2002-01-01
We report on the formation of metal nanometre phase and fractal patterns in steel using metal vapour vacuum arc source ion implantation with high ion flux. The dense nanometre phases are cylindrical and well dispersed in the Ti-implanted layer with an ion flux up to 50μA/cm2. The collision fractal pattern is formed in Ti-implanted steel with an ion flux of 25μA/cm2 and the disconnected fractal pattern is observed with an ion flux of 50μA/cm2.The average density ofnanometre phases decreases from 1.2 × 1011/cm2 to 6.5 × 1010/cm2 as the ion flux increases from 25 μA/cm2 to 50 μA/cm2. Fractal pattern growth is in remarkable agreement with Sander's diffusion-limited aggregation model. The alloy clusters have diffused and aggregated in chains forming branches to grow a beautiful tree during Ti implantation with an ion flux ranging from 75μA/cm2 to 85μA/cm2. We discuss the model of fractal pattern growth during ion implantation with high ion flux.
Fractal model of lightning channel for simulating lightning strikes to transmission lines
Institute of Scientific and Technical Information of China (English)
HE JinLiang; ZHANG XueWei; DONG Lin; ZENG Rong; LIU ZeHong
2009-01-01
How to accurately evaluate the direct-strike lightning protection is one of the key issues in the design of transmission lines.In this paper, three important issues in applying the fractal simulation to the lightning protection of transmission lines were discussed, including the criteria and implementation of upward leader inception, the connection with the magnitude of lightning current, and the calculation and control of fractal dimensions.Then we conducted the simulation iterately, leading to statistical results, which indicate that even if the transmission line satisfies the perfect shielding condition, shielding failure fault remains possible.Furthermore, we calculated the shielding failure fault rates of an EHV line with different ground obliquities and distribution of strike points over the interval between two neighboring towers along a UHV-DC line to find out the weak point of transmission-line lightning protection.This work provides a promising approach for improving the lightning protection property of transmission lines by optimizing the configuration of shielding wires and phase or pole conductors.
Fractal model of lightning channel for simulating lightning strikes to transmission lines
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
How to accurately evaluate the direct-strike lightning protection is one of the key issues in the design of transmission lines. In this paper, three important issues in applying the fractal simulation to the lightning protection of transmission lines were discussed, including the criteria and implementation of upward leader inception, the connection with the magnitude of lightning current, and the calculation and control of fractal dimensions. Then we conducted the simulation iterately, leading to statistical results, which indicate that even if the transmission line satisfies the perfect shielding condition, shielding failure fault remains possible. Furthermore, we calculated the shielding failure fault rates of an EHV line with different ground obliquities and distribution of strike points over the interval between two neighboring towers along a UHV-DC line to find out the weak point of transmission-line lightning protection. This work provides a promising approach for improving the lightning protection property of transmission lines by optimizing the configuration of shielding wires and phase or pole conductors.
Monceau, P.; Hsiao, P.-Y.
2003-02-01
We study the cluster size distributions generated by the Wolff algorithm in the framework of the Ising model on Sierpinski fractals with Hausdorff dimension Df between 1 and 2. We show that these distributions exhibit a scaling property involving the magnetic exponent yh associated with one of the eigen-direction of the renormalization flows. We suggest that a single cluster tends to invade the whole lattice as Df tends towards the lower critical dimension of the Ising model, namely 1. The autocorrelation times associated with the Wolff and Swendsen-Wang algorithms enable us to calculate dynamical exponents; the cluster algorithms are shown to be more efficient in reducing the critical slowing down when Df is lowered.
Bojare, Inara; Skrinda, Astrida
2016-01-01
The present study is aimed at creating a holistic fractal model (HFM) of autonomous learning for English acquisition in a blended environment of e-studies in adult non-formal education on the basis of the theories and paradigms of philosophy, psychology and education for sustainable development to promote the development of adult learners'…
Fractals and finite scales; Fractales et echelles finies
Energy Technology Data Exchange (ETDEWEB)
Aubry, J.M
1997-08-01
Fractal description is used in various scientific domains and in particular in the modeling of particle aggregates and in the modeling of the Rayleigh-Taylor instabilities in turbulent two-phase flows. In particular, the interface geometry between fluids in a turbulent mixing is a crucial parameter for the modeling of mixtures in inertial confinement fusion devices. In this paper, a review of the various fractal dimensions is given first. Then, for a more rigorous use, a probabilistic description of the dimension of an ensemble which is known only up to a finite scale is proposed. This description is based on a probabilistic measurement of the overall fractals. (J.S.) 22 refs.
Modeling tree crown dynamics with 3D partial differential equations.
Beyer, Robert; Letort, Véronique; Cournède, Paul-Henry
2014-01-01
We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth toward light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.
Modeling Tree Crown Dynamics with 3D Partial Differential Equations
Directory of Open Access Journals (Sweden)
Robert eBeyer
2014-07-01
Full Text Available We characterize a tree's spatial foliage distribution by the local leaf area density. Considering this spatially continuous variable allows to describe the spatiotemporal evolution of the tree crown by means of 3D partial differential equations. These offer a framework to rigorously take locally and adaptively acting effects into account, notably the growth towards light. Biomass production through photosynthesis and the allocation to foliage and wood are readily included in this model framework. The system of equations stands out due to its inherent dynamic property of self-organization and spontaneous adaptation, generating complex behavior from even only a few parameters. The density-based approach yields spatially structured tree crowns without relying on detailed geometry. We present the methodological fundamentals of such a modeling approach and discuss further prospects and applications.
Fractal Image Filters for Specialized Image Recognition Tasks
2010-02-11
The Fractal Geometry of Nature, [24], Mandelbrot argues that random frac- tals provide geometrical models for naturally occurring shapes and forms...Fractal Properties of Number Systems, Period. Math. Hungar 42 (2001) 51-68. [24] Benoit Mandelbrot , The Fractal Geometry of Nature, W. H. Freeman, San
A fast and efficient hybrid fractal-wavelet image coder.
Iano, Yuzo; da Silva, Fernando Silvestre; Cruz, Ana Lúcia Mendes
2006-01-01
The excellent visual quality and compression rate of fractal image coding have limited applications due to exhaustive inherent encoding time. This paper presents a new fast and efficient image coder that applies the speed of the wavelet transform to the image quality of the fractal compression. Fast fractal encoding using Fisher's domain classification is applied to the lowpass subband of wavelet transformed image and a modified set partitioning in hierarchical trees (SPIHT) coding, on the remaining coefficients. Furthermore, image details and wavelet progressive transmission characteristics are maintained, no blocking effects from fractal techniques are introduced, and the encoding fidelity problem common in fractal-wavelet hybrid coders is solved. The proposed scheme promotes an average of 94% reduction in encoding-decoding time comparing to the pure accelerated Fractal coding results. The simulations also compare the results to the SPIHT wavelet coding. In both cases, the new scheme improves the subjective quality of pictures for high-medium-low bitrates.
Modeling fractal structure of city-size distributions using correlation function
Chen, Yanguang
2011-01-01
Zipf's law is one the most conspicuous empirical facts for cities, however, there is no convincing explanation for the scaling relation between rank and size and its scaling exponent. Based on the idea from general fractals and scaling, this paper proposes a dual competition hypothesis of city develop to explain the value intervals and the special value, 1, of the power exponent. Zipf's law and Pareto's law can be mathematically transformed into one another. Based on the Pareto distribution, a frequency correlation function can be constructed. By scaling analysis and multifractals spectrum, the parameter interval of Pareto exponent is derived as (0.5, 1]; Based on the Zipf distribution, a size correlation function can be built, and it is opposite to the first one. By the second correlation function and multifractals notion, the Pareto exponent interval is derived as [1, 2). Thus the process of urban evolution falls into two effects: one is Pareto effect indicating city number increase (external complexity), a...
Directory of Open Access Journals (Sweden)
Pierre Philippe
1998-12-01
Full Text Available An approach is suggested in this paper that has successfully been applied in physics, ecology, and the biomedical sciences. This is called fractal-complex-adaptive-system (FCAS modeling. The objective of this type of analysis is to reconstruct the dynamics of the pathological process that has been leading to the disease. Diabetes, a complexdisease, has been used to test the methodology. Biometrical analyses were undertaken on subjects diagnosed with overt diabetes (hereafter called IDDM, chemical diabetes (NIDDM, and a group of normal subjects. The studied variables were plasma glucose, insulin concentration, and insulin sensitivity. FCAS modeling consists in fitting a power-law function to the bivariate lognormal distribution of the variables. The power-law exponent is estimated by principal component analysis (PCA. Analyses have shown that glucose disposal can be considered a fractal process, thereby implying a complex hierarchy of interacting scales and mechanisms in glucose handling. The first principal component represents quantitative glucose disposal, and the second component is compatible with insulin efficiency. PCA further retrieved distinct ongoing pathological processes within clinical groups of subjects. The IDDM insulin production defect had a high (absolute value exponent of -3.5 that confirms a crude defect scanning the whole fractal hierarchy. Definite insulin resistance has been detected in clinically normal subjects with a low exponent of -0.5, thus suggesting a subtle and complex problem possibly due to aging or reduced physical activity. Insulin sensitivity was definitely impaired in the NIDDM clinical group with an exponent of -2.2, thereby suggesting poorly scheduled insulin feedback, possibly due to peripheral insensitivity. NIDDM appeared to result from aggravation of the subtle insensitivity seen in normal subjects. On the whole, the fractal model seemed to be capable of assessing the degree of complexity of a disease
Free energies of the Potts model on a Cayley tree
Rozikov, U. A.; Rakhmatullaev, M. M.
2017-01-01
For the Potts model on the Cayley tree, we obtain some explicit formulas for the free energies and entropies in the case of vector-valued boundary conditions. These formulas include translation-invariant, periodic, and Dobrushin-like boundary conditions and also those corresponding to weakly periodic Gibbs measures.
Towards Effective Elicitation of NIN-AND Tree Causal Models
Xiang, Yang; Li, Yu; Zhu, Zoe Jingyu
To specify a Bayes net (BN), a conditional probability table (CPT), often of an effect conditioned on its n causes, needs assessed for each node. It generally has the complexity exponential on n. Noisy-OR reduces the complexity to linear, but can only represent reinforcing causal interactions. The non-impeding noisy-AND (NIN-AND) tree is the first causal model that explicitly expresses reinforcement, undermining, and their mixture. It has linear complexity, but requires elicitation of a tree topology for types of causal interactions. We study their topology space and develop two novel techniques for more effective elicitation.
An Introduction to Fractals and Chaos
1989-06-01
Maridelbrst ioct lines, pllmcs _id cubes oft Euclid, Mindelbrot. fie is to fractal geometry Frttals h.:e corni po~pulzrc he corn - %liuh ha)’v ben part of our...shape, such ing could never reproduce it without a .)F a tree !r , hill, could require hun- computer. More important, the moun- JreJs of 9 h tusa -nds cr
Neutron scattering from fractals
DEFF Research Database (Denmark)
Kjems, Jørgen; Freltoft, T.; Richter, D.
1986-01-01
The scattering formalism for fractal structures is presented. Volume fractals are exemplified by silica particle clusters formed either from colloidal suspensions or by flame hydrolysis. The determination of the fractional dimensionality through scattering experiments is reviewed, and recent small...
Thamrin, Cindy; Stern, Georgette; Frey, Urs
2010-06-01
There is increasing interest in the study of fractals in medicine. In this review, we provide an overview of fractals, of techniques available to describe fractals in physiological data, and we propose some reasons why a physician might benefit from an understanding of fractals and fractal analysis, with an emphasis on paediatric respiratory medicine where possible. Among these reasons are the ubiquity of fractal organisation in nature and in the body, and how changes in this organisation over the lifespan provide insight into development and senescence. Fractal properties have also been shown to be altered in disease and even to predict the risk of worsening of disease. Finally, implications of a fractal organisation include robustness to errors during development, ability to adapt to surroundings, and the restoration of such organisation as targets for intervention and treatment.
Ji-Huan He
2011-01-01
A new fractal derive is defined, which is very easy for engineering applications to discontinuous problems, two simple examples are given to elucidate to establish governing equations with fractal derive and how to solve such equations, respectively.
Synergetics and fractals in tribology
Janahmadov, Ahad Kh
2016-01-01
This book examines the theoretical and practical aspects of tribological process using synergy, fractal and multifractal methods, and the fractal and multifractal models of self-similar tribosystems developed on their basis. It provides a comprehensive analysis of their effectiveness, and also considers the method of flicker noise spectroscopy with detailed parameterization of surface roughness friction. All models, problems and solutions are taken and tested on the set of real-life examples of oil-gas industry. The book is intended for researchers, graduate students and engineers specialising in the field of tribology, and also for senior students of technical colleges.
Empirical genome evolution models root the tree of life.
Harish, Ajith; Kurland, Charles G
2017-07-01
A reliable phylogenetic reconstruction of the evolutionary history of contemporary species depends on a robust identification of the universal common ancestor (UCA) at the root of the Tree of Life (ToL). That root polarizes the tree so that the evolutionary succession of ancestors to descendants is discernable. In effect, the root determines the branching order and the direction of character evolution. Typically, conventional phylogenetic analyses implement time-reversible models of evolution for which character evolution is un-polarized. Such practices leave the root and the direction of character evolution undefined by the data used to construct such trees. In such cases, rooting relies on theoretic assumptions and/or the use of external data to interpret unrooted trees. The most common rooting method, the outgroup method is clearly inapplicable to the ToL, which has no outgroup. Both here and in the accompanying paper (Harish and Kurland, 2017) we have explored the theoretical and technical issues related to several rooting methods. We demonstrate (1) that Genome-level characters and evolution models are necessary for species phylogeny reconstructions. By the same token, standard practices exploiting sequence-based methods that implement gene-scale substitution models do not root species trees; (2) Modeling evolution of complex genomic characters and processes that are non-reversible and non-stationary is required to reconstruct the polarized evolution of the ToL; (3) Rooting experiments and Bayesian model selection tests overwhelmingly support the earlier finding that akaryotes and eukaryotes are sister clades that descend independently from UCA (Harish and Kurland, 2013); (4) Consistent ancestral state reconstructions from independent genome samplings confirm the previous finding that UCA features three fourths of the unique protein domain-superfamilies encoded by extant genomes. Copyright © 2017 Elsevier B.V. and Société Française de Biochimie et Biologie
Price, B; Gomez, A; Mathys, L; Gardi, O; Schellenberger, A; Ginzler, C; Thürig, E
2017-03-01
Trees outside forest (TOF) can perform a variety of social, economic and ecological functions including carbon sequestration. However, detailed quantification of tree biomass is usually limited to forest areas. Taking advantage of structural information available from stereo aerial imagery and airborne laser scanning (ALS), this research models tree biomass using national forest inventory data and linear least-square regression and applies the model both inside and outside of forest to create a nationwide model for tree biomass (above ground and below ground). Validation of the tree biomass model against TOF data within settlement areas shows relatively low model performance (R (2) of 0.44) but still a considerable improvement on current biomass estimates used for greenhouse gas inventory and carbon accounting. We demonstrate an efficient and easily implementable approach to modelling tree biomass across a large heterogeneous nationwide area. The model offers significant opportunity for improved estimates on land use combination categories (CC) where tree biomass has either not been included or only roughly estimated until now. The ALS biomass model also offers the advantage of providing greater spatial resolution and greater within CC spatial variability compared to the current nationwide estimates.
Institute of Scientific and Technical Information of China (English)
吴则焰; 刘金福; 洪伟; 郑世群; 何中声
2012-01-01
The average increment of diameter at breast height ( DBH) and tree height of Glyptostrobus pensilis from different provenances were studied by combining geostatistical methods with fractal theory. The fractal dimensions of DBH and tree height growth of G. pensilis were calculated in order to reveal the rule of spatial distribution variation. Results showed that the fractal dimensions of DBH and tree height were 1.635 and 1. 824, respectively. DBH can be used as an index for evaluating different provenances of G. pensilis to reflect the spatial variability.%以珍稀濒危植物水松(Glyptostrobus pensilis)不同种源树高和胸径平均生长量为研究对象,将分形理论与地统计学原理相结合,计算水松种源树高和胸径生长的分形维数,揭示其空间分布变异规律和分形特征.结果表明:水松种源胸径、树高生长特性的分维值分别为1.635和1.824,胸径的分维值小于树高的分维值.为反映水松种源的空间差异性,在评价水松种源时应选取胸径生长指标.
The fractal aggregation of asphaltenes.
Hoepfner, Michael P; Fávero, Cláudio Vilas Bôas; Haji-Akbari, Nasim; Fogler, H Scott
2013-07-16
This paper discusses time-resolved small-angle neutron scattering results that were used to investigate asphaltene structure and stability with and without a precipitant added in both crude oil and model oil. A novel approach was used to isolate the scattering from asphaltenes that are insoluble and in the process of aggregating from those that are soluble. It was found that both soluble and insoluble asphaltenes form fractal clusters in crude oil and the fractal dimension of the insoluble asphaltene clusters is higher than that of the soluble clusters. Adding heptane also increases the size of soluble asphaltene clusters without modifying the fractal dimension. Understanding the process of insoluble asphaltenes forming fractals with higher fractal dimensions will potentially reveal the microscopic asphaltene destabilization mechanism (i.e., how a precipitant modifies asphaltene-asphaltene interactions). It was concluded that because of the polydisperse nature of asphaltenes, no well-defined asphaltene phase stability envelope exists and small amounts of asphaltenes precipitated even at dilute precipitant concentrations. Asphaltenes that are stable in a crude oil-precipitant mixture are dispersed on the nanometer length scale. An asphaltene precipitation mechanism is proposed that is consistent with the experimental findings. Additionally, it was found that the heptane-insoluble asphaltene fraction is the dominant source of small-angle scattering in crude oil and the previously unobtainable asphaltene solubility at low heptane concentrations was measured.
Fraboni, Michael; Moller, Trisha
2008-01-01
Fractal geometry offers teachers great flexibility: It can be adapted to the level of the audience or to time constraints. Although easily explained, fractal geometry leads to rich and interesting mathematical complexities. In this article, the authors describe fractal geometry, explain the process of iteration, and provide a sample exercise.…
Decision Tree Model for Non-Fatal Road Accident Injury
Directory of Open Access Journals (Sweden)
Fatin Ellisya Sapri
2017-02-01
Full Text Available Non-fatal road accident injury has become a great concern as it is associated with injury and sometimes leads to the disability of the victims. Hence, this study aims to develop a model that explains the factors that contribute to non-fatal road accident injury severity. A sample data of 350 non-fatal road accident cases of the year 2016 were obtained from Kota Bharu District Police Headquarters, Kelantan. The explanatory variables include road geometry, collision type, accident time, accident causes, vehicle type, age, airbag, and gender. The predictive data mining techniques of decision tree model and multinomial logistic regression were used to model non-fatal road accident injury severity. Based on accuracy rate, decision tree with CART algorithm was found to be more accurate as compared to the logistic regression model. The factors that significantly contribute to non-fatal traffic crashes injury severity are accident cause, road geometry, vehicle type, age and collision type.
Multitask Efficiencies in the Decision Tree Model
Drucker, Andrew
2008-01-01
In Direct Sum problems [KRW], one tries to show that for a given computational model, the complexity of computing a collection $F = \\{f_i\\}$ of functions on independent inputs is approximately the sum of their individual complexities. In this paper, by contrast, we study the diversity of ways in which the joint computational complexity can behave when all the $f_i$ are evaluated on a \\textit{common} input. Fixing some model of computational cost, let $C_F(X): \\{0, 1\\}^l \\to \\mathbf{R}$ give the cost of computing the subcollection $\\{f_i(x): X_i = 1\\}$, on common input $x$. What constraints do the functions $C_F(X)$ obey, when $F$ is chosen freely? $C_F(X)$ will, for reasonable models, obey nonnegativity, monotonicity, and subadditivity. We show that, in the deterministic, adaptive query model, these are `essentially' the only constraints: for any function $C(X)$ obeying these properties and any $\\epsilon > 0$, there exists a family $F$ of boolean functions and a $T > 0$ such that for all $X \\in \\{0, 1\\}^l$, \\...
Definition of fractal topography to essential understanding of scale-invariance
Jin, Yi; Wu, Ying; Li, Hui; Zhao, Mengyu; Pan, Jienan
2017-04-01
Fractal behavior is scale-invariant and widely characterized by fractal dimension. However, the cor-respondence between them is that fractal behavior uniquely determines a fractal dimension while a fractal dimension can be related to many possible fractal behaviors. Therefore, fractal behavior is independent of the fractal generator and its geometries, spatial pattern, and statistical properties in addition to scale. To mathematically describe fractal behavior, we propose a novel concept of fractal topography defined by two scale-invariant parameters, scaling lacunarity (P) and scaling coverage (F). The scaling lacunarity is defined as the scale ratio between two successive fractal generators, whereas the scaling coverage is defined as the number ratio between them. Consequently, a strictly scale-invariant definition for self-similar fractals can be derived as D = log F /log P. To reflect the direction-dependence of fractal behaviors, we introduce another parameter Hxy, a general Hurst exponent, which is analytically expressed by Hxy = log Px/log Py where Px and Py are the scaling lacunarities in the x and y directions, respectively. Thus, a unified definition of fractal dimension is proposed for arbitrary self-similar and self-affine fractals by averaging the fractal dimensions of all directions in a d-dimensional space, which . Our definitions provide a theoretical, mechanistic basis for understanding the essentials of the scale-invariant property that reduces the complexity of modeling fractals.
Spherical Model on a Cayley Tree: Large Deviations
Patrick, A. E.
2017-01-01
We study the spherical model of a ferromagnet on a Cayley tree and show that in the case of empty boundary conditions a ferromagnetic phase transition takes place at the critical temperature T_c =6√{2}/5J, where J is the interaction strength. For any temperature the equilibrium magnetization, m_n, tends to zero in the thermodynamic limit, and the true order parameter is the renormalized magnetization r_n=n^{3/2}m_n, where n is the number of generations in the Cayley tree. Below T_c, the equilibrium values of the order parameter are given by ± ρ ^*, where ρ ^*=2π /(√{2-1)^2}√{1-T/T_c}. One more notable temperature in the model is the penetration temperature T_p=J/W_Cayley(3/2)( 1-1/√{2}( h/2J) ^2) . Below T_p the influence of homogeneous boundary field of magnitude h penetrates throughout the tree. The main new technical result of the paper is a complete set of orthonormal eigenvectors for the discrete Laplace operator on a Cayley tree.
Regional Mapping, Modelling, and Monitoring of Tree Aboveground Biomass Carbon
Hudak, Andrew
2016-04-01
Airborne lidar collections are preferred for mapping aboveground biomass carbon (AGBC), while historical Landsat imagery are preferred for monitoring decadal scale forest cover change. Our modelling approach tracks AGBC change regionally using Landsat time series metrics; training areas are defined by airborne lidar extents within which AGBC is accurately mapped with high confidence. Geospatial topographic and climate layers are also included in the predictive model. Validation is accomplished using systematically sampled Forest Inventory and Analysis (FIA) plot data that have been independently collected, processed and summarized at the county level. Our goal is to demonstrate that spatially and temporally aggregated annual AGBC map predictions show no bias when compared to annual county-level summaries across the Northwest USA. A prominent source of bias is trees outside forest; much of the more arid portions of our study area meet the FIA definition of non-forest because the tree cover does not exceed their minimum tree cover threshold. We employ detailed tree cover maps derived from high-resolution aerial imagery to extend our AGBC predictions into non-forest areas. We also employ Landsat-derived annual disturbance maps into our mapped AGBC predictions prior to aggregation and validation.
Modeling synchronized calling behavior of Japanese tree frogs
Aihara, Ikkyu
2009-07-01
We experimentally observed synchronized calling behavior of male Japanese tree frogs Hyla japonica; namely, while isolated single frogs called nearly periodically, a pair of interacting frogs called synchronously almost in antiphase or inphase. In this study, we propose two types of phase-oscillator models on different degrees of approximations, which can quantitatively explain the phase and frequency properties in the experiment. Moreover, it should be noted that, although the second model is obtained by fitting to the experimental data of the two synchronized states, the model can also explain the transitory dynamics in the interactive calling behavior, namely, the shift from a transient inphase state to a stable antiphase state. We also discuss the biological relevance of the estimated parameter values to calling behavior of Japanese tree frogs and the possible biological meanings of the synchronized calling behavior.
Dimensional Reduction for the General Markov Model on Phylogenetic Trees.
Sumner, Jeremy G
2017-03-01
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the dimensionality of the model from exponential in the number of extant taxa, to quadratic in the number of taxa, while retaining the ability to statistically identify phylogenetic divergence events. A key feature is the identification of an invariant subspace which depends only bilinearly on the model parameters, in contrast to the usual multi-linear dependence in the full space. We discuss potential applications including the computation of split (edge) weights on phylogenetic trees from observed sequence data.
Directory of Open Access Journals (Sweden)
Carlos Fuentes
2005-02-01
Full Text Available Baseado nos conceitos da geometria fractal e nas leis de Laplace e de Poiseuille, foi criado um modelo geral para estimar a condutividade hidráulica de solos não saturados, utilizando a curva de retenção da água no solo, conforme representada por um modelo em potência. Considerando o fato de que este novo modelo da condutividade hidráulica introduz um parâmetro de interpolação ainda desconhecido, e que, por sua vez, depende das propriedades dos solos, a validação do modelo foi realizada, utilizando dois valores-limite fisicamente representativos. Para a aplicação do modelo, os parâmetros de forma da curva de retenção da água no solo foram escolhidos de maneira a se obter o modelo de van Genuchten. Com a finalidade de obter fórmulas algébricas da condutividade hidráulica, foram impostas relações entre seus parâmetros de forma. A comparação dos resultados obtidos com o modelo da condutividade e a curva experimental da condutividade dos dois solos, Latossolo Vermelho-Amarelo e Argissolo Amarelo, permitiu concluir que o modelo proposto é simples em sua utilização e é capaz de predizer satisfatoriamente a condutividade hidráulica dos solos não saturados.From a conceptual model based on fractal geometry and Laplace's and Poiseuille's laws, a versatile and general fractal model for the hydraulic conductivity to be used in the soils was developed. The soil-moisture retention curve is derived from a power model. Due to the fact that the proposed model of hydraulic conductivity introduces a still unknown interpolation parameter, which in turn is a function of soil properties, its limiting values were considered for the analysis. To apply the model in the soil, the form parameters of the soil-moisture retention curve were chosen so as to reproduce van Genuchten's equation. In order to obtain a closed-form equation for the hydraulic conductivity, relationships between the form parameters were imposed. The comparison between
Fractal properties of forest fires in Amazonia as a basis for modelling pan-tropical burned area
Fletcher, I. N.; Aragão, L. E. O. C.; Lima, A.; Shimabukuro, Y.; Friedlingstein, P.
2013-08-01
Current methods for modelling burnt area in Dynamic Global Vegetation Models involve complex fire spread calculations, which rely on many inputs, including fuel characteristics, wind speed and countless parameters. They are therefore susceptible to large uncertainties through error propagation. Using observed fractal distributions of fire scars in Brazilian Amazonia, we propose an alternative burnt area model for tropical forests, with fire counts as sole input and few parameters. Several parameterizations of two possible distributions are calibrated at multiple spatial resolutions using a satellite-derived burned area map, and compared. The tapered Pareto model most accurately simulates the total area burnt (only 3.5 km2 larger than the recorded 16 387 km2) and its spatial distribution. When tested pan-tropically using MODIS MCD14ML fire counts, the model accurately predicts temporal and spatial fire trends, but produces generally higher estimates than the GFED3.1 burnt area product, suggesting higher pan-tropical carbon emissions from fires than previously estimated.
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.
Ripe Fuji Apple Detection Model Analysis in Natural Tree Canopy
Directory of Open Access Journals (Sweden)
Dongjian He
2012-11-01
Full Text Available In this work we develop a novel approach for the automatic recognition of red Fuji apples within a tree canopy using three distinguishable color models in order to achieve automated harvesting. How to select the recognition model is important for the certain intelligent harvester employed to perform in real orchards. The L*a*b color model, HSI (Hue, Saturation and Intensity color model and LCD color difference model, which are insensitive to light conditions, are analyzed and applied to detect the fruit under the different lighting conditions because the fruit has the highest red color among the objects in the image. The fuzzy 2-partition entropy, which could discriminate the object and the background in grayscale images and is obtained from the histogram, is applied to the segment the Fuji apples under complex backgrounds. A series of mathematical morphological operations are used to eliminate segmental fragments after segmentation. Finally, the proposed approach is validated on apple images taken in natural tree canopies. A contribution reported in this work, is the voting scheme added to the natural tree canopy which recognizes apples under different light influences.
Fat fractal percolation and k-fractal percolation
Broman, Erik; Camia, Federico; Joosten, Matthijs; Meester, Ronald
2011-01-01
We consider two variations on the Mandelbrot fractal percolation model. In the k-fractal percolation model, the d-dimensional unit cube is divided in N^d equal subcubes, k of which are retained while the others are discarded. The procedure is then iterated inside the retained cubes at all smaller scales. We show that the (properly rescaled) percolation critical value of this model converges to the critical value of site percolation in L^d as N tends to infinity. This is analogous to the result of Falconer and Grimmett that the critical value for Mandelbrot fractal percolation converges to the critical value of site percolation in L^d. In the fat fractal percolation model, subcubes are retained with probability p_n at step n of the construction, where (p_n) is a non-decreasing sequence with \\prod p_n > 0. The Lebesgue measure of the limit set is positive a.s. given non-extinction. We show that with probability 1 either the set of "dust" points or the set of connected components larger than one point has positi...
Directory of Open Access Journals (Sweden)
Jörgen Wallerman
2013-04-01
Full Text Available Individual tree crowns may be delineated from airborne laser scanning (ALS data by segmentation of surface models or by 3D analysis. Segmentation of surface models benefits from using a priori knowledge about the proportions of tree crowns, which has not yet been utilized for 3D analysis to any great extent. In this study, an existing surface segmentation method was used as a basis for a new tree model 3D clustering method applied to ALS returns in 104 circular field plots with 12 m radius in pine-dominated boreal forest (64°14'N, 19°50'E. For each cluster below the tallest canopy layer, a parabolic surface was fitted to model a tree crown. The tree model clustering identified more trees than segmentation of the surface model, especially smaller trees below the tallest canopy layer. Stem attributes were estimated with k-Most Similar Neighbours (k-MSN imputation of the clusters based on field-measured trees. The accuracy at plot level from the k-MSN imputation (stem density root mean square error or RMSE 32.7%; stem volume RMSE 28.3% was similar to the corresponding results from the surface model (stem density RMSE 33.6%; stem volume RMSE 26.1% with leave-one-out cross-validation for one field plot at a time. Three-dimensional analysis of ALS data should also be evaluated in multi-layered forests since it identified a larger number of small trees below the tallest canopy layer.
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
Abhay Parvate; A D Gangal
2005-03-01
Differential equations and maps are the most frequently studied examples of dynamical systems and may be considered as continuous and discrete time-evolution processes respectively. The processes in which time evolution takes place on Cantor- like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation of these systems requires an appropriate framework. A new calculus called -calculus, is a natural calculus on subsets ⊂ R of dimension , 0 < ≤ 1. It involves integral and derivative of order , called -integral and -derivative respectively. The -integral is suitable for integrating functions with fractal support of dimension , while the -derivative enables us to differentiate functions like the Cantor staircase. The functions like the Cantor staircase function occur naturally as solutions of -differential equations. Hence the latter can be used to model fractal-time processes or sublinear dynamical systems. We discuss construction and solutions of some fractal differential equations of the form $$D^{}_{F,t} x = h(x, t),$$ where ℎ is a vector field and $D^{}_{F,t}$ is a fractal differential operator of order in time . We also consider some equations of the form $$D^{}_{F,t} W(x, t) = L[W(x, t)],$$ where is an ordinary differential operator in the real variable , and $(t, x) F × \\mathbf{R}^{n}$ where is a Cantor-like set of dimension . Further, we discuss a method of finding solutions to -differential equations: They can be mapped to ordinary differential equations, and the solutions of the latter can be transformed back to get those of the former. This is illustrated with a couple of examples.
Fractal characterization of pore microstructure evolution in carbon/carbon composites
Institute of Scientific and Technical Information of China (English)
LI MiaoLing; QI LeHua; LI HeJun; XU GuoZhong
2009-01-01
A fractal characterization approach was proposed to research pore microstructure evolution in carbon/carbon (C/C) composites during the chemical vapor infiltration process. The data obtained from mercury porosimetry determinations were analyzed using the sponge fractal model and the thermodynamics relation fractal model, respectively. The fractal dimensions of C/C composites at different densification stages were evaluated. The pore microstructure evolution with densification time was studied by fractal dimension analysis. The results showed that ClC composites belong to porous fractal structure. The fractal dimensions increase on the whole with decreasing porosity as the densification proceeds. The fractal dimensions are influenced by the texture of pyrocarbon and decrease with increasing anisotropy from isotropic pyrocarbon to high textural one. Both the complicacy of pore structure and the textural morphology of pyrocarbon can be represented simultaneously by the fractal dimension. The pore evolution of C/C composites in the densification process can be monitored using fractal dimension.
[A depression model of social defeat etiology using tree shrews].
Wang, Jing; Zhou, Qi-Xin; Lv, Long-Bao; Xu, Lin; Yang, Yue-Xiong
2012-02-01
Depression is a common neuropsychiatric disorder, marked by depressed mood for at least two weeks. The World Health Organization predicts that depression will be the number one leading cause of disease and injury burden by 2030. Clinical treatment faces at least three serious obstacles. First, the disease mechanism is not fully understood and thus there are no effective ways to predict and prevent depression and no biological method of diagnosis. Second, available antidepressants are based on monoamine mechanisms that commonly have a long delay of action and possibly cause a higher risk of suicide. Third, no other antidepressant mechanisms are available, with fast action and few side effects. Unfortunately, several decades of research based on rodent models of depression have not been successful in resolving these problems, at least partially due to the huge differences in brain function between rodents and people. Tree shrews are the closest sister to primates, and brain functions in these species are closer to those of humans. In this review, we discuss a tree shrew model of depression with social defeat etiology and aspects of construct, face and predicted validity of an animal model. Although a tree shrew model of depression has long been ignored and not fully established, its similarities to those aspects of depression in humans may open a new avenue to address this human condition.
Individual Tree Biomass Models for Plantation Grown American Sycamore
Regan B. Willson; Bryce E. Schlaegel; Harvey E. Kennedy
1982-01-01
Individual tree volume and green and dry weight equations are derived for American sycamore from a 5-year-old plantation in southeast Arkansas. Two trees have been destructively sampled each year from each of 20 plots. Observations from 168 trees are used to predict tree weight and volume as a function of dbh, total height, age, and initial number of trees. Separate...
The Fractal Simulation Of Biological Shapes
Pickover, Clifford A.
1989-04-01
This paper provides a light introduction to simple graphics techniques for visualizing a large class of biological shapes generated from recursive algorithms. In order to capture some of the structural richness inherent in organisms, the algorithms produce not only extreme variability but also a high level of organization. The material primarily comes from previous published works of the author. For a general background on fractal methods in mathematics and science, see Mandelbrot's famous book. For research on the fractal characterization of other biological structures, such as the lung's bronchial tree and the surfaces of protein molecules.
Modeling of Earth's Gravity Fields Visualization Based on Quad Tree
Institute of Scientific and Technical Information of China (English)
LUO Zhicai; LI Zhenhai; ZHONG Bo
2010-01-01
The problems of the earth's gravity fields' visualization are both focus and puzzle currently. Aiming at multiresolution rendering, modeling of the Earth's gravity fields' data is discussed in the paper by using LOD algorithm based on Quad Tree. First,this paper employed the method of LOD based on Quad Tree to divide up the regional gravity anomaly data, introduced the combined node evaluation system that was composed of viewpoint related and roughness related systems, and then eliminated the T-cracks that appeared among the gravity anomaly data grids with different resolutions. The test results demonstrated that the gravity anomaly data grids' rendering effects were living, and the computational power was low. Therefore, the proposed algorithm was a suitable method for modeling the gravity anomaly data and has potential applications in visualization of the earth's gravity fields.
Thermal transport in fractal systems
DEFF Research Database (Denmark)
Kjems, Jørgen
1992-01-01
Recent experiments on the thermal transport in systems with partial fractal geometry, silica aerogels, are reviewed. The individual contributions from phonons, fractons and particle modes, respectively, have been identified and can be described by quantitative models consistent with heat capacity...... data. The interpretation in the particle mode regime sheds light on the mechanisms for thermal conductivity in normal vitreous silica....
Wu, Yu; Cheng, Tianhai; Zheng, Lijuan; Chen, Hao
2016-10-01
Light absorption enhancement of aged soot aerosols is highly sensitive to the morphologies and mixing states of soot aggregates and their non-absorbing coatings, such as organic materials. The quantification of these effects on the optical properties of thinly coated soot aerosols is simulated using an effective model with fixed volume fractions. Fractal aggregated soot was simulated using the diffusion limited aggregation (DLA) algorithm and discretized into soot dipoles. The dipoles of non-absorbing aerosols, whose number was fixed by the volume fraction, were further generated from the neighboring random edge dipoles. Their optical properties were calculated using the discrete dipole approximation (DDA) method and were compared with other commonly used models. The optical properties of thinly coated soot calculated using the fixed volume fraction model are close to (less than ~10% difference) the results of the fixed coating thickness model, except their asymmetry parameters (up to ~25% difference). In the optical simulations of thinly coated soot aerosols, this relative difference of asymmetry parameters and phase functions between these realistic models may be notable. The realizations of the fixed volume fraction model may introduce smaller variation of optical results than those of the fixed coating thickness model. Moreover, the core-shell monomers model and homogeneous aggregated spheres model with the Maxwell-Garnett (MG) theory may underestimate (up to ~20%) the cross sections of thinly coated soot aggregates. The single core-shell sphere model may largely overestimate (up to ~150%) the cross sections and single scattering albedo of thinly coated soot aggregates, and it underestimated (up to ~60%) their asymmetry parameters. It is suggested that the widely used single core-shell sphere approximation may not be suitable for the single scattering calculations of thinly coated soot aerosols.
Alcobendas, Rosalía; Alarcón, Juan José; VALSESIA, Pierre; Génard, Michel; Nicolás, Emilio
2013-01-01
Low water availability has increased the use of regulated deficit irrigation strategies in fruit orchards.However, these water restrictions may have implications on fruit growth and quality. The current paperassesses the suitability of an existing fruit tree model (QualiTree) for describing the effects of water stresson peach fruit growth and quality. The model was parameterised and calibrated for a mid-late maturingpeach cultivar (‘Catherine’). Mean and variability over time of fruit and veg...
Spasic, Sladjana; Kalauzi, Aleksandar; Kesic, Srdjan; Obradovic, Milica; Saponjic, Jasna
2011-11-21
We used spectral analysis and Higuchi fractal dimension (FD) to correlate the EEG spectral characteristics of the sensorimotor cortex, hippocampus, and pons with their corresponding EEG signal complexities in anesthetized rats. We have explored the quantitative relationship between the mean FDs and EEG wide range high frequency (8-50 Hz) activity during ketamine/xylazine versus nembutal anesthesia at surgical plane. Using FD we detected distinct inter-structure complexity pattern and uncovered for the first time that the polygraphically and behaviorally defined anesthetized state at surgical plane as equal during experiment in two anesthetic regimens, is not the same with respect to the degree of neuronal activity (degree of generalized neuronal inhibition achieved) at different brain levels. Using the correlation of certain brain structure EEG spectral characteristics with their corresponding FDs, and the surrogate data modeling, we determined what particular frequency band contributes to EEG complexities in ketamine/xylazine versus nembutal anesthesia. In this study we have shown that the quantitative relationship between higher frequency EEG amplitude and EEG complexity is the best-modeled by surrogate data as a 3rd order polynomial. On the base of our EEG amplitude/EEG complexity relationship model, and the evidenced spectral differences in ketamine versus nembutal anesthesia we have proved that higher amplitudes of sigma, beta, and gamma frequency in ketamine anesthesia yields to higher FDs.
Asfahani, Jamal
2017-05-01
Fractal theory modeling technique is newly proposed in this research for interpreting the combination of nuclear well logging, including natural gamma ray, density and neutron-porosity, and the electrical well logging of long and short normal, for establishing the lithological cross section in basaltic environments. The logging data of Kodana well, localized in Southern Syria are used for testing and applying the proposed technique. The established cross section clearly shows the distribution and the identification of four kinds of basalt which are hard massive basalt, hard basalt, pyroclastic basalt and the alteration basalt products, clay. The concentration- Number (C-N) fractal modeling technique is successfully applied on the Kodana well logging data in southern Syria, and can be used efficiently when several wells with much well logging data with a high number of variables are required to be interpreted.
Shedding light on fractals: exploration of the Sierpinski carpet optical antenna
Chen, Ting Lee
2015-01-01
We describe experimental and theoretical investigations of the properties of a fractal optical antenna-the Sierpinski carpet optical antenna. Fractal optical antennas are inspired by fractal antennas designed in radio frequency (RF) region. Shrinking the size of fractal optical antennas from fractal antennas in RF regions by a factor of lE-5 arises challenges of fabrication, characterization and modelling their response to incident light. The comparison between optical antennas with the Sierp...
Fractal electrodynamics via non-integer dimensional space approach
Energy Technology Data Exchange (ETDEWEB)
Tarasov, Vasily E., E-mail: tarasov@theory.sinp.msu.ru
2015-09-25
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. - Highlights: • Electrodynamics of fractal media is described by non-integer dimensional spaces. • Applications of the fractal Gauss's and Ampere's laws are suggested. • Fractal Poisson equation, equation for fractal stream of charges are considered.
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.
Han, H. H.; Wang, Y. L.; Ren, G. L.; LI, J. Q.; Gao, T.; Yang, M.; Yang, J. L.
2016-11-01
Remote sensing plays an important role in mineral exploration of “One Belt One Road” plan. One of its applications is extracting and locating hydrothermal alteration zones that are related to mines. At present, the extracting method for alteration anomalies from principal component image mainly relies on the data's normal distribution, without considering the nonlinear characteristics of geological anomaly. In this study, a Fractal Dimension Change Point Model (FDCPM), calculated by the self-similarity and mutability of alteration anomalies, is employed to quantitatively acquire the critical threshold of alteration anomalies. The realization theory and access mechanism of the model are elaborated by an experiment with ASTER data in Beishan mineralization belt, also the results are compared with traditional method (De-Interfered Anomalous Principal Component Thresholding Technique, DIAPCTT). The results show that the findings produced by FDCPM are agree with well with a mounting body of evidence from different perspectives, with the extracting accuracy over 80%, indicating that FDCPM is an effective extracting method for remote sensing alteration anomalies, and could be used as an useful tool for mineral exploration in similar areas in Silk Road Economic Belt.
Model-Based Design of Tree WSNs for Decentralized Detection.
Tantawy, Ashraf; Koutsoukos, Xenofon; Biswas, Gautam
2015-08-20
The classical decentralized detection problem of finding the optimal decision rules at the sensor and fusion center, as well as variants that introduce physical channel impairments have been studied extensively in the literature. The deployment of WSNs in decentralized detection applications brings new challenges to the field. Protocols for different communication layers have to be co-designed to optimize the detection performance. In this paper, we consider the communication network design problem for a tree WSN. We pursue a system-level approach where a complete model for the system is developed that captures the interactions between different layers, as well as different sensor quality measures. For network optimization, we propose a hierarchical optimization algorithm that lends itself to the tree structure, requiring only local network information. The proposed design approach shows superior performance over several contentionless and contention-based network design approaches.
Model-Based Design of Tree WSNs for Decentralized Detection
Directory of Open Access Journals (Sweden)
Ashraf Tantawy
2015-08-01
Full Text Available The classical decentralized detection problem of finding the optimal decision rules at the sensor and fusion center, as well as variants that introduce physical channel impairments have been studied extensively in the literature. The deployment of WSNs in decentralized detection applications brings new challenges to the field. Protocols for different communication layers have to be co-designed to optimize the detection performance. In this paper, we consider the communication network design problem for a tree WSN. We pursue a system-level approach where a complete model for the system is developed that captures the interactions between different layers, as well as different sensor quality measures. For network optimization, we propose a hierarchical optimization algorithm that lends itself to the tree structure, requiring only local network information. The proposed design approach shows superior performance over several contentionless and contention-based network design approaches.
Directory of Open Access Journals (Sweden)
Mirko Ahmadfaraj
2016-06-01
Full Text Available The aim of this study is determination and separation of alteration zones using Concentration-Area (C-A fractal model based on remote sensing data which has been extracted from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER images. The studied area is on the SW part of Saveh, 1:250,000 geological map, which is located in Urumieh-Dokhtar magmatic belt, Central Iran. The pixel values were computed by Principal Component Analysis (PCA method used to determine phyllic, argillic, and propylitic alteration zones. The C-A fractal model is utilized for separation of different parts of alteration zones due to their intensity. The log-log C-A plots reveal multifractal nature for phyllic, argillic, and propylitic alteration zones. The obtained results based on fractal model show that the main trend of the alteration zones is in NW-SE direction. Compared to the geological map of the study area and copper mineralizations, the alteration zones have been detected properly and correlate with the mineral occurrences, intrusive rock, and faults.
Data acquisition in modeling using neural networks and decision trees
Directory of Open Access Journals (Sweden)
R. Sika
2011-04-01
Full Text Available The paper presents a comparison of selected models from area of artificial neural networks and decision trees in relation with actualconditions of foundry processes. The work contains short descriptions of used algorithms, their destination and method of data preparation,which is a domain of work of Data Mining systems. First part concerns data acquisition realized in selected iron foundry, indicating problems to solve in aspect of casting process modeling. Second part is a comparison of selected algorithms: a decision tree and artificial neural network, that is CART (Classification And Regression Trees and BP (Backpropagation in MLP (Multilayer Perceptron networks algorithms.Aim of the paper is to show an aspect of selecting data for modeling, cleaning it and reducing, for example due to too strong correlationbetween some of recorded process parameters. Also, it has been shown what results can be obtained using two different approaches:first when modeling using available commercial software, for example Statistica, second when modeling step by step using Excel spreadsheetbasing on the same algorithm, like BP-MLP. Discrepancy of results obtained from these two approaches originates from a priorimade assumptions. Mentioned earlier Statistica universal software package, when used without awareness of relations of technologicalparameters, i.e. without user having experience in foundry and without scheduling ranks of particular parameters basing on acquisition, can not give credible basis to predict the quality of the castings. Also, a decisive influence of data acquisition method has been clearly indicated, the acquisition should be conducted according to repetitive measurement and control procedures. This paper is based on about 250 records of actual data, for one assortment for 6 month period, where only 12 data sets were complete (including two that were used for validation of neural network and useful for creating a model. It is definitely too
Patricio, Pedro; Duarte, Jorge; Januario, Cristina
2015-01-01
We investigate the rheology of a fractal network, in the framework of the linear theory of viscoelasticity. We identify each segment of the network with a simple Kelvin-Voigt element, with a well defined equilibrium length. The final structure retains the elastic characteristics of a solid or a gel. By considering a very simple regular self-similar structure of segments in series and in parallel, in 1, 2 or 3 dimensions, we are able to express the viscoelasticity of the network as an effective generalised Kelvin-Voigt model with a power law spectrum of retardation times, $\\phi\\sim\\tau^{\\alpha-1}$. We relate the parameter $\\alpha$ with the fractal dimension of the gel. In some regimes ($0<\\alpha<1$), we recover the weak power law behaviours of the elastic and viscous moduli with the angular frequencies, $G'\\sim G''\\sim w^\\alpha$, that occur in a variety of soft materials, including living cells. In other regimes, we find different and interesting power laws for $G'$ and $G''$.
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.
An Optical Demonstration of Fractal Geometry
Scannel, Billy; Taylor, Richard
2012-01-01
We have built a Sinai cube to illustrate and investigate the scaling properties that result by iterating chaotic trajectories into a well ordered system. We allow red, green and blue light to reflect off a mirrored sphere, which is contained in an otherwise, closed mirrored cube. The resulting images are modeled by ray tracing procedures and both sets of images undergo fractal analysis. We offer this as a novel demonstration of fractal geometry, utilizing the aesthetic appeal of these images to motivate an intuitive understanding of the resulting scaling plots and associated fractal dimensions.
Gou, Xiaofan; Schwartz, Justin
2013-10-01
Bi2Sr2CaCu2Ox/AgMg (Bi2212) multi filamentary superconducting round wires (RWs) can be only potential candidate for constructing the superconducting magnet with higher magnetic field (>25T). Very complicated microstructure of Bi2212 RWs has been found by recent SEM studies, and then the vital problems of Characterization of this unique microstructure and further exploration of the correlation of macro electromechanical properties with this microstructure arise. In this paper, it is firstly found that the rough surface of individual filaments can be well characterized by fractals. On the geometrical model with the fractal simulation of the rough surface, stress-strain relation of Bi2212 RWs has been investigated. The modelling result with considering the rough surface has a better agreement to the experimental data. At the request of the authors, and with the agreement of the Proceedings Editor, the above paper in AIP Proceedings has been retracted (as of 26 November 2013) due to a prior publication by the authors which reports similar data/results. That paper was first published in volume 26 (issue 5) of the journal Superconductor Science and Technology and was published on 4 April 2013: Fractal analysis of the role of the rough interface between Bi2Sr2CaCu2Ox filaments and the Ag matrix in the mechanical behavior of composite round wires The authors wish to apologize for any inconvenience caused by publication of their AIP Proceedings article.
Discrimination of surface tracking patterns of gamma irradiated polymers using fractals
Indian Academy of Sciences (India)
V Rajini; K Udaya Kumar
2006-06-01
The purpose of this paper is to evaluate the radiation resistance of gamma irradiated ethylene propylene diene monomer (EPDM) and to identify the pattern discriminating abilities of the surface tracking patterns. Simple objects can be described by the ideal shape primitives such as cubes, cones and cylinders. But most of the natural objects are so complex that cannot be described in terms of simple primitives. Fractals have been very successfully used to address the problem of modeling and to provide a description of naturally occurring phenomena and shapes, wherein conventional and existing mathematical models were found to be inadequate. The geometrical patterns of dielectric breakdown like electrical trees, surface discharges, and lightning are known to be of fractal in nature. These fractal patterns can be analysed numerically using fractal dimensions and lacunarity. Surface tracking occurring in HV insulation systems is a very complex phenomenon and more so are the shapes of tracking patterns. It has been fairly well established that the shapes and the underlying parameters causing tracking have a 1 : 1 correspondence and therefore, methods to describe and quantify these patterns must be explored. This paper reports preliminary results of such a study wherein 2- tracking patterns of gamma irradiated ethylene propylene diene monomer were analysed and found to possess fairly reasonable pattern discriminating abilities. This approach appears promising and further research is essential before any long-term predictions can be made.
Köhler, Peter; Huth, A.
1998-01-01
Due to high biodiversity in tropical rainforests, tree species are aggregatedinto functional groups for modelling purposes. In this article the influencesof two different classifications of tropical tree species into functionalgroups on the output of a rainforest model are analysed. The FORMIND modelis documented. FORMIND simulates the tree growth of tropical rainforests.The model is individual-based and developed from the FORMIX3 model. In themodel, trees compete for light and space in plots...
Baker, Robert G. V.
2017-02-01
Self-similar matrices of the fine structure constant of solar electromagnetic force and its inverse, multiplied by the Carrington synodic rotation, have been previously shown to account for at least 98% of the top one hundred significant frequencies and periodicities observed in the ACRIM composite irradiance satellite measurement and the terrestrial 10.7cm Penticton Adjusted Daily Flux data sets. This self-similarity allows for the development of a time-space differential equation (DE) where the solutions define a solar model for transmissions through the core, radiative, tachocline, convective and coronal zones with some encouraging empirical and theoretical results. The DE assumes a fundamental complex oscillation in the solar core and that time at the tachocline is smeared with real and imaginary constructs. The resulting solutions simulate for tachocline transmission, the solar cycle where time-line trajectories either 'loop' as Hermite polynomials for an active Sun or 'tail' as complementary error functions for a passive Sun. Further, a mechanism that allows for the stable energy transmission through the tachocline is explored and the model predicts the initial exponential coronal heating from nanoflare supercharging. The twisting of the field at the tachocline is then described as a quaternion within which neutrinos can oscillate. The resulting fractal bubbles are simulated as a Julia Set which can then aggregate from nanoflares into solar flares and prominences. Empirical examples demonstrate that time and space fractals are important constructs in understanding the behaviour of the Sun, from the impact on climate and biological histories on Earth, to the fractal influence on the spatial distributions of the solar system. The research suggests that there is a fractal clock underpinning solar frequencies in packages defined by the fine structure constant, where magnetic flipping and irradiance fluctuations at phase changes, have periodically impacted on the
Applications of Fractal Signals
Directory of Open Access Journals (Sweden)
Ion TUTĂNESCU
2008-05-01
Full Text Available "Fractal" term - which in Latin languagedefines something fragmented anomalous - wasintroduced in mathematics by B. B. Mandelbrot in1975. He avoided to define it rigorously and used it todesignate some "rugged" and "self-similar"geometrical forms. Fractals were involved in the theoryof chaotic dynamic systems and used to designatecertain specific sets; finally, they were “captured” bygeometry and remarked in tackling of the boundaryproblems. It proved that the fractals can be of interesteven in the signal’s theory.
Saenko, Viacheslav V
2016-01-01
The task of cosmic rays transport with finite speed in framework of fractal Galaxy model have considered. The moment method have been used for analysis of space characteristics of process. The asymptotic moments (at $t\\to\\infty$) have been obtained in the task of random walk with finite speed and with power law distributions of free path races $p_{\\xi}(x)=\\alpha x_0^\\alpha x^{-\\alpha-1}$, $x\\to\\infty$, $0<\\alpha<2$. Accounting a finite speed led to necessity divide the original task into two separate tasks. The former consist in propagation of cosmic rays with finite mathematical expectation of free path races ($1<\\alpha<2$), and the latter consist in the propagation of cosmic rays with infinite mathematical expectation of free path races ($0<\\alpha<1$). In the former case the asymptotic distribution is described by stable law and influence of finite speed reduced to decrease of diffusivity. In the latter case a situation cardinally is changing. The asymptotic distribution has U-shape or W-s...
Li, Jia-Sheng; Tang, Yong; Li, Zong-Tao; Ding, Xin-Rui; Li, Zhi
2017-07-01
Although LEDs have been widely studied using optical simulations, there is no optical model considering the effect of micro-roughness surface (MRS) on the optical performance for packaged LEDs. In this work, we employ the finite-difference time-domain method and the direction-sensitive bidirectional scattering distribution function to characterize the optical properties of the MRS upon the n-GaN layer. The MRS is generated by the Weierstrass-Mandelbrot fractal function. Furthermore, thin-film LEDs (TFLEDs), blue TFLED devices, and white TFLED devices considering the MRS are investigated using the ray-tracing (RT) method. The results show that the MRS has different optical properties when the light propagates out and in the n-GaN layer. In turn, the difference in the scattering ability of various MRS causes a significant effect on the optical performance of packaged TFLEDs, including radiant efficacy, luminous efficacy, intensity pattern and spectrum, as well as the correlated color temperature.
Energy Technology Data Exchange (ETDEWEB)
Amir, S; Mohamed, N S [Center for Foundation Studies in Science, University of Malaya, 50603 Kuala Lumpur (Malaysia); Hashim Ali, S A, E-mail: shahizat@um.edu.my [Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur (Malaysia)
2011-10-15
We initially prepared films of poly(vinylidene fluoride-co-hexafluoropropylene)/poly(ethyl methacrylate)-ammonium trifluorome-thanesulfonate dispersed with various wt.% of chromium oxide to study their properties and potential application in electrochemical devices. However, a few months later the nanocomposite polymer electrolyte membranes were found to become a sort of medium for fractal growth. This discovery led to a simulation of the fractals observed in these polymer electrolyte films using a diffusion-limited aggregation model that is based on Brownian motion theory (random walk). The fractal dimensions, D, of the fractal patterns obtained from experimental and simulation work were calculated using the box-counting method. The fractal patterns and dimensions of the simulated fractal patterns were comparable with those obtained from the original fractals observed in the polymer electrolyte films.
pHMM-tree: phylogeny of profile hidden Markov models.
Huo, Luyang; Zhang, Han; Huo, Xueting; Yang, Yasong; Li, Xueqiong; Yin, Yanbin
2017-04-01
Protein families are often represented by profile hidden Markov models (pHMMs). Homology between two distant protein families can be determined by comparing the pHMMs. Here we explored the idea of building a phylogeny of protein families using the distance matrix of their pHMMs. We developed a new software and web server (pHMM-tree) to allow four major types of inputs: (i) multiple pHMM files, (ii) multiple aligned protein sequence files, (iii) mixture of pHMM and aligned sequence files and (iv) unaligned protein sequences in a single file. The output will be a pHMM phylogeny of different protein families delineating their relationships. We have applied pHMM-tree to build phylogenies for CAZyme (carbohydrate active enzyme) classes and Pfam clans, which attested its usefulness in the phylogenetic representation of the evolutionary relationship among distant protein families. This software is implemented in C/C ++ and is available at http://cys.bios.niu.edu/pHMM-Tree/source/. zhanghan@nankai.edu.cn or yyin@niu.edu. Supplementary data are available at Bioinformatics online.
Pre-growth mortality of Abies cilicica trees and mortality models performance.
Carus, Serdar
2010-05-01
In this study, we compared tree-growth rates (basal area increment) from recently dead and living Taurus fir (Abies cilicica Carr.) trees in the Kovada lake Forest of Isparta, Turkey. For each dead tree, tree-growth rates were analyzed for the presence of pre-death growth depressions in the study area (number of sample plots = 11) in 2006. However, we compared both the magnitude and rate of growth prior to death to a control (living) group of trees. Basal area increment (BAI) averaged substantially less during the last 10 years before death than for control trees. Trees that died started diverging in growth, on average, 50-60 years before death. About 18% of trees that died had chronically slow growth, 46% had pronounced declines in growth, whereas 36% had good growth up to death. However, tree-ring-based growth patterns of dead and living Taurus fir trees were compared and used 12 mortality models that were derived using logistic regression from growth patterns of tree-ring series as predictor variables. The four models with the highest overall performance correctly classified 43.8-56.3% of all dead trees and 75.0-87.5% of all living trees, and they predicted 25.0-43.8% of all dead trees to die within 0-15 years prior to the actual year of death.
Directory of Open Access Journals (Sweden)
Gao Guang-Lei
2016-02-01
Full Text Available We constructed an aeolian soil database across arid, semi-arid, and dry sub-humid regions, China. Soil particle size distribution was measured with a laser diffraction technique, and fractal dimensions were calculated. The results showed that: (i the predominant soil particle size distributed in fine and medium sand classifications, and fractal dimensions covered a wide range from 2.0810 to 2.6351; (ii through logarithmic transformations, fractal dimensions were significantly positive correlated with clay and silt contents (R2 = 0.81 and 0.59, P < 0.01, and significantly negative correlated with sand content (R2 = 0.50, P < 0.01; (3 hierarchical cluster analysis divided the plots into three types which were similar to sand dune types indicating desertification degree. In a large spatial scale, fractal dimensions are still sensitive to wind-induced desertification. Therefore, we highly recommend that fractal dimension be used as a reliable and quantitative parameter to monitor soil environment changes in desertified regions. This improved information provides a firm basis for better understanding of desertification processes.
Fractal Geometry of Architecture
Lorenz, Wolfgang E.
In Fractals smaller parts and the whole are linked together. Fractals are self-similar, as those parts are, at least approximately, scaled-down copies of the rough whole. In architecture, such a concept has also been known for a long time. Not only architects of the twentieth century called for an overall idea that is mirrored in every single detail, but also Gothic cathedrals and Indian temples offer self-similarity. This study mainly focuses upon the question whether this concept of self-similarity makes architecture with fractal properties more diverse and interesting than Euclidean Modern architecture. The first part gives an introduction and explains Fractal properties in various natural and architectural objects, presenting the underlying structure by computer programmed renderings. In this connection, differences between the fractal, architectural concept and true, mathematical Fractals are worked out to become aware of limits. This is the basis for dealing with the problem whether fractal-like architecture, particularly facades, can be measured so that different designs can be compared with each other under the aspect of fractal properties. Finally the usability of the Box-Counting Method, an easy-to-use measurement method of Fractal Dimension is analyzed with regard to architecture.
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
A Cayley Tree Immune Network Model with Antibody Dynamics
Anderson, R W; Perelson, A S; Anderson, Russell W.; Neumann, Avidan U.; Perelson, Alan S.
1993-01-01
Abstract: A Cayley tree model of idiotypic networks that includes both B cell and antibody dynamics is formulated and analyzed. As in models with B cells only, localized states exist in the network with limited numbers of activated clones surrounded by virgin or near-virgin clones. The existence and stability of these localized network states are explored as a function of model parameters. As in previous models that have included antibody, the stability of immune and tolerant localized states are shown to depend on the ratio of antibody to B cell lifetimes as well as the rate of antibody complex removal. As model parameters are varied, localized steady-states can break down via two routes: dynamically, into chaotic attractors, or structurally into percolation attractors. For a given set of parameters, percolation and chaotic attractors can coexist with localized attractors, and thus there do not exist clear cut boundaries in parameter space that separate regions of localized attractors from regions of percola...
Fractal black holes and information
Energy Technology Data Exchange (ETDEWEB)
El Naschie, M.S. [Department of Physics, University of Alexandria, Alexandria (Egypt); Department of Astrophysics, Cairo University (Egypt); Department of Physics, Mansura University (Egypt)
2006-07-15
If nature is fractal as it evidently is, at classical resolution and if it is suspected to also be fractal at the quantum resolution as it is now a days generally believed to be, then we must have over looked at least two points or so in our physical model building of mini black holes. To start with at such ultra high resolution, the mini black hole geometry must be a fractal. Consequently we have zero volume and only a fractal surface area. Second because we cannot take the differential limit for the -bar {sub p}{sup 2} covering the transfinite surface area, there will be many gaps between the (-bar {sub p}){sup 2} tilings. In other words we must introduce transfinite corrections to the final result. Proceeding this way the information entropy unit of a black hole should be a=I=(7+{phi}{sup 3})(10){sup -66}cm{sup 2}=7.23606799(10){sup -66}cm{sup 2}The nearest classical result to the above is that obtained by Gerard 't Hoofta=I=(0.724)(10){sup -65}cm{sup 2}The paper ends with a general discussion of E-infinity theory and its possible relation with 't Hooft's holographic principle and his gluons-quark strings.
Fractal Characterization of Hyperspectral Imagery
Qiu, Hon-Iie; Lam, Nina Siu-Ngan; Quattrochi, Dale A.; Gamon, John A.
1999-01-01
Two Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) hyperspectral images selected from the Los Angeles area, one representing urban and the other, rural, were used to examine their spatial complexity across their entire spectrum of the remote sensing data. Using the ICAMS (Image Characterization And Modeling System) software, we computed the fractal dimension values via the isarithm and triangular prism methods for all 224 bands in the two AVIRIS scenes. The resultant fractal dimensions reflect changes in image complexity across the spectral range of the hyperspectral images. Both the isarithm and triangular prism methods detect unusually high D values on the spectral bands that fall within the atmospheric absorption and scattering zones where signature to noise ratios are low. Fractal dimensions for the urban area resulted in higher values than for the rural landscape, and the differences between the resulting D values are more distinct in the visible bands. The triangular prism method is sensitive to a few random speckles in the images, leading to a lower dimensionality. On the contrary, the isarithm method will ignore the speckles and focus on the major variation dominating the surface, thus resulting in a higher dimension. It is seen where the fractal curves plotted for the entire bandwidth range of the hyperspectral images could be used to distinguish landscape types as well as for screening noisy bands.
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti......Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs......, the retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficients. Falconer's formula and quantitative genetic models were used to determine the genetic component of variation. Results: The mean......, the branching pattern of the retinal vessels demonstrated a higher structural similarity in monozygotic than in dizygotic twin pairs. The retinal vascular fractal dimension was mainly determined by genetic factors, which accounted for 54% of the variation. The genetically predetermination of the retinal...
A deterministic model for the growth of non-conducting electrical tree structures
Dodd, S J
2003-01-01
Electrical treeing is of interest to the electrical generation, transmission and distribution industries as it is one of the causes of insulation failure in electrical machines, switchgear and transformer bushings. In this paper a deterministic electrical tree growth model is described. The model is based on electrostatics and local electron avalanches to model partial discharge activity within the growing tree structure. Damage to the resin surrounding the tree structure is dependent on the local electrostatic energy dissipation by partial discharges within the tree structure and weighted by the magnitudes of the local electric fields in the resin surrounding the tree structure. The model is successful in simulating the formation of branched structures without the need of a random variable, a requirement of previous stochastic models. Instability in the spatial development of partial discharges within the tree structure takes the role of the stochastic element as used in previous models to produce branched t...
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.
Wind tunnel experiment of drag of isolated tree models in surface boundary layer
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
For very sparse tree land individual tree was the basic element of interaction between atmosphere and the surface. Drag of isolated tree was preliminary aerodynamic index for analyzing the atmospheric boundary layer of this kind of surface. A simple pendulum method was designed and carried out in wind tunnel to measure drag of isolated tree models according to balance law of moment of force. The method was easy to conduct and with small error. The results showed that the drag and drag coefficient of isolated tree increased with decreasing of its permeability or porosity. Relationship between drag coefficient and permeability of isolated tree empirically was expressed by quadric curve.
Optimum Binary Search Trees on the Hierarchical Memory Model
Thite, Shripad
2008-01-01
The Hierarchical Memory Model (HMM) of computation is similar to the standard Random Access Machine (RAM) model except that the HMM has a non-uniform memory organized in a hierarchy of levels numbered 1 through h. The cost of accessing a memory location increases with the level number, and accesses to memory locations belonging to the same level cost the same. Formally, the cost of a single access to the memory location at address a is given by m(a), where m: N -> N is the memory cost function, and the h distinct values of m model the different levels of the memory hierarchy. We study the problem of constructing and storing a binary search tree (BST) of minimum cost, over a set of keys, with probabilities for successful and unsuccessful searches, on the HMM with an arbitrary number of memory levels, and for the special case h=2. While the problem of constructing optimum binary search trees has been well studied for the standard RAM model, the additional parameter m for the HMM increases the combinatorial comp...
DEFF Research Database (Denmark)
Rasmussen, Mads Olander; Goettsche, Frank-M.; Diop, Doudou
2011-01-01
radius, and diameter at breast height (DBH), for which allometric models were determined. An object-based classification method was used to determine tree crown cover (TCC) from Quickbird data. The average TCC from the tree survey and the respective TCC from remote sensing were both about 3.0 For areas...... beyond the surveyed areas TCC varied between 3.0% and 4.5 Furthermore, an empirical correction factor for tree clumping was obtained, which considerably improved the estimated number of trees and the estimated average tree crown area and radius. An allometric model linking TCC to tree stem crosssectional...
Energy Absorption in a Load-Unload Cycle of Knee Implant Using Fractal Model of Rough Surfaces
Hodaei, Mohammad; Farhang, Kambiz
2016-05-01
Roughness measurement of knee implant surfaces is investigated. The study of roughness measurement show that the topography of knee implant surface is multi-scale and surface spectra follows a power law behavior. A magnification of rough surface topography implies that there is no difference between original and magnified profile of implant surface. For implant surface, statistical parameters such as variance of height, curvature, and slope are found to be scale-dependent. Fractal representation of implant surface shows that the size-distribution of the multi-scale contacts spots follows a power law and is characterized by the fractal dimension of implant surface. Fractal surface description of the rough surfaces of knee implant is used to obtain force-displacement relationship of the contact force. Using an approximate function through the fusion of two piecewise functions, energy absorption of a knee implant in a single cycle of load-unload is obtained.
Engineering of Algorithms for Hidden Markov models and Tree Distances
DEFF Research Database (Denmark)
Sand, Andreas
grown exponentially because of drastic improvements in the technology behind DNA and RNA sequencing, and focus on the research field has increased due to its potential to expand our knowledge about biological mechanisms and to improve public health. There has therefore been a continuously growing demand...... of the algorithms to exploit the parallel architecture of modern computers. In this PhD dissertation, I present my work with algorithmic optimizations and parallelizations in primarily two areas in algorithmic bioinformatics: algorithms for analyzing hidden Markov models and algorithms for computing distance...... measures between phylogenetic trees. Hidden Markov models is a class of probabilistic models that is used in a number of core applications in bioinformatics such as modeling of proteins, gene finding and reconstruction of species and population histories. I show how a relatively simple parallelization can...
Allowed Parameter Regions for a Tree-Level Inflation Model
Institute of Scientific and Technical Information of China (English)
MENG Xin-He
2001-01-01
The early universe inflation is well known as a promising theory to explain the origin of large-scale structure of universe and to solve the early universe pressing problems. For a reasonable inflation model, the potential during inflation must be very flat, at least, in the direction of the inflaton. To construct the inflaton potential all the known related astrophysics observations should be included. For a general tree-level hybrid inflation potential, which is notdiscussed fully so far, the parameters in it are shown how to be constrained via the astrophysics data observed and to be obtained to the expected accuracy, and to be consistent with cosmology requirements.``
Paradigms of Complexity: Fractals and Structures in the Sciences
Novak, Miroslav M.
The Table of Contents for the book is as follows: * Preface * The Origin of Complexity (invited talk) * On the Existence of Spatially Uniform Scaling Laws in the Climate System * Multispectral Backscattering: A Fractal-Structure Probe * Small-Angle Multiple Scattering on a Fractal System of Point Scatterers * Symmetric Fractals Generated by Cellular Automata * Bispectra and Phase Correlations for Chaotic Dynamical Systems * Self-Organized Criticality Models of Neural Development * Altered Fractal and Irregular Heart Rate Behavior in Sick Fetuses * Extract Multiple Scaling in Long-Term Heart Rate Variability * A Semi-Continous Box Counting Method for Fractal Dimension Measurement of Short Single Dimension Temporal Signals - Preliminary Study * A Fractional Brownian Motion Model of Cracking * Self-Affine Scaling Studies on Fractography * Coarsening of Fractal Interfaces * A Fractal Model of Ocean Surface Superdiffusion * Stochastic Subsurface Flow and Transport in Fractal Fractal Conductivity Fields * Rendering Through Iterated Function Systems * The σ-Hull - The Hull Where Fractals Live - Calculating a Hull Bounded by Log Spirals to Solve the Inverse IFS-Problem by the Detected Orbits * On the Multifractal Properties of Passively Convected Scalar Fields * New Statistical Textural Transforms for Non-Stationary Signals: Application to Generalized Mutlifractal Analysis * Laplacian Growth of Parallel Needles: Their Mullins-Sekerka Instability * Entropy Dynamics Associated with Self-Organization * Fractal Properties in Economics (invited talk) * Fractal Approach to the Regional Seismic Event Discrimination Problem * Fractal and Topological Complexity of Radioactive Contamination * Pattern Selection: Nonsingular Saffman-Taylor Finger and Its Dynamic Evolution with Zero Surface Tension * A Family of Complex Wavelets for the Characterization of Singularities * Stabilization of Chaotic Amplitude Fluctuations in Multimode, Intracavity-Doubled Solid-State Lasers * Chaotic
Monceau, Pascal; Hsiao, Pai-Yi
2002-09-01
We study the Wolff cluster size distributions obtained from Monte Carlo simulations of the Ising phase transition on Sierpinski fractals with Hausdorff dimensions Df between 2 and 3. These distributions are shown to be invariant when going from an iteration step of the fractal to the next under a scaling of the cluster sizes involving the exponent (β/ν)+(γ/ν). Moreover, the decay of the autocorrelation functions at the critical points enables us to calculate the Wolff dynamical critical exponents z for three different values of Df. The Wolff algorithm is more efficient in reducing the critical slowing down when Df is lowered.
Inferring tree causal models of cancer progression with probability raising.
Directory of Open Access Journals (Sweden)
Loes Olde Loohuis
Full Text Available Existing techniques to reconstruct tree models of progression for accumulative processes, such as cancer, seek to estimate causation by combining correlation and a frequentist notion of temporal priority. In this paper, we define a novel theoretical framework called CAPRESE (CAncer PRogression Extraction with Single Edges to reconstruct such models based on the notion of probabilistic causation defined by Suppes. We consider a general reconstruction setting complicated by the presence of noise in the data due to biological variation, as well as experimental or measurement errors. To improve tolerance to noise we define and use a shrinkage-like estimator. We prove the correctness of our algorithm by showing asymptotic convergence to the correct tree under mild constraints on the level of noise. Moreover, on synthetic data, we show that our approach outperforms the state-of-the-art, that it is efficient even with a relatively small number of samples and that its performance quickly converges to its asymptote as the number of samples increases. For real cancer datasets obtained with different technologies, we highlight biologically significant differences in the progressions inferred with respect to other competing techniques and we also show how to validate conjectured biological relations with progression models.
Spatially dependent polya tree modeling for survival data.
Zhao, Luping; Hanson, Timothy E
2011-06-01
With the proliferation of spatially oriented time-to-event data, spatial modeling in the survival context has received increased recent attention. A traditional way to capture a spatial pattern is to introduce frailty terms in the linear predictor of a semiparametric model, such as proportional hazards or accelerated failure time. We propose a new methodology to capture the spatial pattern by assuming a prior based on a mixture of spatially dependent Polya trees for the baseline survival in the proportional hazards model. Thanks to modern Markov chain Monte Carlo (MCMC) methods, this approach remains computationally feasible in a fully hierarchical Bayesian framework. We compare the spatially dependent mixture of Polya trees (MPT) approach to the traditional spatial frailty approach, and illustrate the usefulness of this method with an analysis of Iowan breast cancer survival data from the Surveillance, Epidemiology, and End Results (SEER) program of the National Cancer Institute. Our method provides better goodness of fit over the traditional alternatives as measured by log pseudo marginal likelihood (LPML), the deviance information criterion (DIC), and full sample score (FSS) statistics. © 2010, The International Biometric Society.
Forward modelling of tree-ring width and comparison with a global network of tree-ring chronologies
Directory of Open Access Journals (Sweden)
P. Breitenmoser
2013-07-01
Full Text Available We investigate the relationship between climate and tree-ring data on a global scale using the process-based Vaganov–Shashkin–Lite (VSL forward model of tree-ring width formation. The VSL model requires as inputs only latitude, monthly mean temperature, and monthly accumulated precipitation. Hence, this simple, process-based model enables ring-width simulation at any location where monthly climate records exist. In this study, we analyse the growth response of simulated tree-rings to monthly climate conditions obtained from the CRU TS3.1 data set back to 1901. Our key aims are (a to examine the relations between simulated and observed growth at 2287 globally distributed sites and (b to evaluate the potential of the VSL model to reconstruct past climate. The assessment of the growth-onset threshold temperature of approximately 4–6 °C for most sites and species using a Bayesian estimation approach complements other studies on the lower temperature limits where plant growth may be sustained. Our results suggest that the VSL model skilfully simulates site level tree-ring series in response to climate forcing for a wide range of environmental conditions and species. Spatial aggregation of the tree-ring chronologies to reduce non-climatic noise at the site level yields notable improvements in the coherence between modelled and actual growth. The resulting distinct and coherent patterns of significant relationships between the aggregated and simulated series further demonstrate the VSL model's ability to skilfully capture the climatic signal contained in tree-series. Finally, we propose that the VSL model can be used as an observation operator in data assimilation approaches to reconstruct past climate.
Fractals and Spatial Statistics of Point Patterns
Institute of Scientific and Technical Information of China (English)
Frederik P Agterberg
2013-01-01
The relationship between fractal point pattern modeling and statistical methods of parameter estimation in point-process modeling is reviewed.Statistical estimation of the cluster fractal dimension by using Ripley's K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects,not only for rectangular study areas but also for study areas with curved boundaries determined by regional geology.Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that,in general,it is subject to relatively strong "roll-off" effects for smaller boxes.Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield.Additionally,it is proposed that,worldwide,the local point patterns of podiform Cr,volcanogenic massive sulphide and porphyry copper deposits,which are spatially distributed within irregularly shaped favorable tracts,satisfy the fractal clustering model with similar fractal dimensions.The problem of deposit size (metal tonnage) is also considered.Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.
Susan L. King
2003-01-01
The performance of two classifiers, logistic regression and neural networks, are compared for modeling noncatastrophic individual tree mortality for 21 species of trees in West Virginia. The output of the classifier is usually a continuous number between 0 and 1. A threshold is selected between 0 and 1 and all of the trees below the threshold are classified as...
Brown, Molly E.; McGroddy, Megan; Spence, Caitlin; Flake, Leah; Sarfraz, Amna; Nowak, David J.; Milesi, Cristina
2012-01-01
As the world becomes increasingly urban, the need to quantify the effect of trees in urban environments on energy usage, air pollution, local climate and nutrient run-off has increased. By identifying, quantifying and valuing the ecological activity that provides services in urban areas, stronger policies and improved quality of life for urban residents can be obtained. Here we focus on two radically different models that can be used to characterize urban forests. The i-Tree Eco model (formerly UFORE model) quantifies ecosystem services (e.g., air pollution removal, carbon storage) and values derived from urban trees based on field measurements of trees and local ancillary data sets. Biome-BGC (Biome BioGeoChemistry) is used to simulate the fluxes and storage of carbon, water, and nitrogen in natural environments. This paper compares i-Tree Eco's methods to those of Biome-BGC, which estimates the fluxes and storage of energy, carbon, water and nitrogen for vegetation and soil components of the ecosystem. We describe the two models and their differences in the way they calculate similar properties, with a focus on carbon and nitrogen. Finally, we discuss the implications of further integration of these two communities for land managers such as those in Maryland.
Combining an additive and tree-based regression model simultaneously: STIMA
Dusseldorp, E.; Conversano, C.; Os, B.J. van
2010-01-01
Additive models and tree-based regression models are two main classes of statistical models used to predict the scores on a continuous response variable. It is known that additive models become very complex in the presence of higher order interaction effects, whereas some tree-based models, such as
A Novel Fractal Wavelet Image Compression Approach
Institute of Scientific and Technical Information of China (English)
SONG Chun-lin; FENG Rui; LIU Fu-qiang; CHEN Xi
2007-01-01
By investigating the limitation of existing wavelet tree based image compression methods, we propose a novel wavelet fractal image compression method in this paper. Briefly, the initial errors are appointed given the different levels of importance accorded the frequency sublevel band wavelet coefficients. Higher frequency sublevel bands would lead to larger initial errors. As a result, the sizes of sublevel blocks and super blocks would be changed according to the initial errors. The matching sizes between sublevel blocks and super blocks would be changed according to the permitted errors and compression rates. Systematic analyses are performed and the experimental results demonstrate that the proposed method provides a satisfactory performance with a clearly increasing rate of compression and speed of encoding without reducing SNR and the quality of decoded images. Simulation results show that our method is superior to the traditional wavelet tree based methods of fractal image compression.
Warchalowski, Wiktor; Krawczyk, Malgorzata J.
2017-03-01
We found the Lindenmayer systems for line graphs built on selected fractals. We show that the fractal dimension of such obtained graphs in all analysed cases is the same as for their original graphs. Both for the original graphs and for their line graphs we identified classes of nodes which reflect symmetry of the graph.
Groundwater Level Prediction using M5 Model Trees
Nalarajan, Nitha Ayinippully; Mohandas, C.
2015-01-01
Groundwater is an important resource, readily available and having high economic value and social benefit. Recently, it had been considered a dependable source of uncontaminated water. During the past two decades, increased rate of extraction and other greedy human actions have resulted in the groundwater crisis, both qualitatively and quantitatively. Under prevailing circumstances, the availability of predicted groundwater levels increase the importance of this valuable resource, as an aid in the planning of groundwater resources. For this purpose, data-driven prediction models are widely used in the present day world. M5 model tree (MT) is a popular soft computing method emerging as a promising method for numeric prediction, producing understandable models. The present study discusses the groundwater level predictions using MT employing only the historical groundwater levels from a groundwater monitoring well. The results showed that MT can be successively used for forecasting groundwater levels.
An invisible axion model with controlled FCNCs at tree level
Directory of Open Access Journals (Sweden)
Alejandro Celis
2015-02-01
Full Text Available We derive the necessary conditions to build a class of invisible axion models with Flavor Changing Neutral Currents at tree-level controlled by the fermion mixing matrices and present an explicit model implementation. A horizontal Peccei–Quinn symmetry provides a solution to the strong CP problem via the Peccei–Quinn mechanism and predicts a cold dark mater candidate, the invisible axion or familon. The smallness of active neutrino masses can be explained via a type I seesaw mechanism, providing a dynamical origin for the heavy seesaw scale. The possibility to avoid the domain wall problem stands as one of the most interesting features of the type of models considered. Experimental limits relying on the axion–photon coupling, astrophysical considerations and familon searches in rare kaon and muon decays are discussed.
An invisible axion model with controlled FCNCs at tree level
Energy Technology Data Exchange (ETDEWEB)
Celis, Alejandro, E-mail: alejandro.celis@ific.uv.es [Departament de Física Teòrica and IFIC, Universitat de València-CSIC, E-46100, Burjassot (Spain); Fuentes-Martín, Javier, E-mail: javier.fuentes@ific.uv.es [Departament de Física Teòrica and IFIC, Universitat de València-CSIC, E-46100, Burjassot (Spain); Department of Physics, National Tsing Hua University, Hsinchu 300, Taiwan (China); Serôdio, Hugo, E-mail: hserodio@kaist.ac.kr [Departament de Física Teòrica and IFIC, Universitat de València-CSIC, E-46100, Burjassot (Spain); Department of Physics, Korea Advanced Institute of Science and Technology, 335 Gwahak-ro, Yuseong-gu, Daejeon 305-701 (Korea, Republic of)
2015-02-04
We derive the necessary conditions to build a class of invisible axion models with Flavor Changing Neutral Currents at tree-level controlled by the fermion mixing matrices and present an explicit model implementation. A horizontal Peccei–Quinn symmetry provides a solution to the strong CP problem via the Peccei–Quinn mechanism and predicts a cold dark mater candidate, the invisible axion or familon. The smallness of active neutrino masses can be explained via a type I seesaw mechanism, providing a dynamical origin for the heavy seesaw scale. The possibility to avoid the domain wall problem stands as one of the most interesting features of the type of models considered. Experimental limits relying on the axion–photon coupling, astrophysical considerations and familon searches in rare kaon and muon decays are discussed.
Spatially-explicit models of global tree density
Glick, Henry B.; Bettigole, Charlie; Maynard, Daniel S.; Covey, Kristofer R.; Smith, Jeffrey R.; Crowther, Thomas W.
2016-08-01
Remote sensing and geographic analysis of woody vegetation provide means of evaluating the distribution of natural resources, patterns of biodiversity and ecosystem structure, and socio-economic drivers of resource utilization. While these methods bring geographic datasets with global coverage into our day-to-day analytic spheres, many of the studies that rely on these strategies do not capitalize on the extensive collection of existing field data. We present the methods and maps associated with the first spatially-explicit models of global tree density, which relied on over 420,000 forest inventory field plots from around the world. This research is the result of a collaborative effort engaging over 20 scientists and institutions, and capitalizes on an array of analytical strategies. Our spatial data products offer precise estimates of the number of trees at global and biome scales, but should not be used for local-level estimation. At larger scales, these datasets can contribute valuable insight into resource management, ecological modelling efforts, and the quantification of ecosystem services.
Macroscopic Models of Clique Tree Growth for Bayesian Networks
National Aeronautics and Space Administration — In clique tree clustering, inference consists of propagation in a clique tree compiled from a Bayesian network. In this paper, we develop an analytical approach to...
Fractal Reconnection in Solar and Stellar Environments
Shibata, Kazunari
2016-01-01
Recent space based observations of the Sun revealed that magnetic reconnection is ubiquitous in the solar atmosphere, ranging from small scale reconnection (observed as nanoflares) to large scale one (observed as long duration flares or giant arcades). Often the magnetic reconnection events are associated with mass ejections or jets, which seem to be closely related to multiple plasmoid ejections from fractal current sheet. The bursty radio and hard X-ray emissions from flares also suggest the fractal reconnection and associated particle acceleration. We shall discuss recent observations and theories related to the plasmoid-induced-reconnection and the fractal reconnection in solar flares, and their implication to reconnection physics and particle acceleration. Recent findings of many superflares on solar type stars that has extended the applicability of the fractal reconnection model of solar flares to much a wider parameter space suitable for stellar flares are also discussed.
Fractal Fluctuations and Statistical Normal Distribution
Selvam, A M
2008-01-01
Dynamical systems in nature exhibit selfsimilar fractal fluctuations and the corresponding power spectra follow inverse power law form signifying long-range space-time correlations identified as self-organized criticality. The physics of self-organized criticality is not yet identified. The Gaussian probability distribution used widely for analysis and description of large data sets underestimates the probabilities of occurrence of extreme events such as stock market crashes, earthquakes, heavy rainfall, etc. The assumptions underlying the normal distribution such as fixed mean and standard deviation, independence of data, are not valid for real world fractal data sets exhibiting a scale-free power law distribution with fat tails. A general systems theory for fractals visualizes the emergence of successively larger scale fluctuations to result from the space-time integration of enclosed smaller scale fluctuations. The model predicts a universal inverse power law incorporating the golden mean for fractal fluct...
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.
Fractal images induce fractal pupil dilations and constrictions.
Moon, P; Muday, J; Raynor, S; Schirillo, J; Boydston, C; Fairbanks, M S; Taylor, R P
2014-09-01
Fractals are self-similar structures or patterns that repeat at increasingly fine magnifications. Research has revealed fractal patterns in many natural and physiological processes. This article investigates pupillary size over time to determine if their oscillations demonstrate a fractal pattern. We predict that pupil size over time will fluctuate in a fractal manner and this may be due to either the fractal neuronal structure or fractal properties of the image viewed. We present evidence that low complexity fractal patterns underlie pupillary oscillations as subjects view spatial fractal patterns. We also present evidence implicating the autonomic nervous system's importance in these patterns. Using the variational method of the box-counting procedure we demonstrate that low complexity fractal patterns are found in changes within pupil size over time in millimeters (mm) and our data suggest that these pupillary oscillation patterns do not depend on the fractal properties of the image viewed.
Tree cover bistability in the MPI Earth system model due to fire-vegetation feedback
Lasslop, Gitta; Brovkin, Victor; Kloster, Silvia; Reick, Christian
2015-04-01
The global distribution of tree cover is mainly limited by precipitation and temperature. Within tropical ecosystems different tree cover values have been observed in regions with similar climate. Satellite data even revealed a lack of ecosystems with tree coverage around 60% and dominant tree covers of 20% and 80%. Conceptual models have been used to explain this tree cover distribution and base it on a bistability in tree cover caused by fire-vegetation interactions or competition between trees and grasses. Some ecological models also show this property of multiple stable tree covers, but it remains unclear which mechanism is the cause for this behaviour. Vegetation models used in climate simulations usually use simple approaches and were criticised to neglect such ecological theories and misrepresent tropical tree cover distribution and dynamics. Here we show that including the process based fire model SPITFIRE generated a bistability in tree cover in the land surface model JSBACH. Previous model versions showed only one stable tree cover state. Using a conceptual model we can show that a bistability can occur due to a feedback between grasses and fire. Grasses and trees are represented in the model based on plant functional types. With respect to fire the main difference between grasses and trees is the fuel characteristics. Grass fuels are smaller in size, and have a higher surface area to volume ratio. These grass fuels dry faster increasing their flammability which leads to a higher fire rate of spread. Trees are characterized by coarse fuels, which are less likely to ignite and rather suppress fire. Therefore a higher fraction of grasses promotes fire, fire kills trees and following a fire, grasses establish faster. This feedback can stabilize ecosystems with low tree cover in a low tree cover state and systems with high tree cover in a high tree cover state. In previous model versions this feedback was absent. Based on the new JSBACH model driven with
[Tree shrews under the spot light: emerging model of human diseases].
Xu, Lin; Zhang, Yun; Liang, Bin; Lü, Long-Bao; Chen, Ce-Shi; Chen, Yong-Bin; Zhou, Ju-Min; Yao, Yong-Gang
2013-04-01
Animal models are indispensible in biomedical research and have made tremendous contributions to answer fundamental questions on human biology, disease mechanisms, and to the development of new drugs and diagnostic tools. Due to the limitations of rodent models in translational medicine, tree shrews (Tupaia belangeri chinensis), the closest relative of primates, have attracted increasing attention in modeling human diseases and therapeutic responses. Here we discuss the recent progress in tree shrew biology and the development of tree shrews as human disease models including infectious diseases, metabolic diseases, neurological and psychiatric diseases, and cancers. Meanwhile, the current problems and future perspectives of the tree shrew model are explored.
Construction of Fractal Surfaces by Recurrent Fractal Interpolation Curves
Yun, Chol-Hui; O., Hyong-chol; Choi, Hui-chol
2013-01-01
A method to construct fractal surfaces by recurrent fractal curves is provided. First we construct fractal interpolation curves using a recurrent iterated functions system(RIFS) with function scaling factors and estimate their box-counting dimension. Then we present a method of construction of wider class of fractal surfaces by fractal curves and Lipschitz functions and calculate the box-counting dimension of the constructed surfaces. Finally, we combine both methods to have more flexible con...
Prediction model based on decision tree analysis for laccase mediators.
Medina, Fabiola; Aguila, Sergio; Baratto, Maria Camilla; Martorana, Andrea; Basosi, Riccardo; Alderete, Joel B; Vazquez-Duhalt, Rafael
2013-01-10
A Structure Activity Relationship (SAR) study for laccase mediator systems was performed in order to correctly classify different natural phenolic mediators. Decision tree (DT) classification models with a set of five quantum-chemical calculated molecular descriptors were used. These descriptors included redox potential (ɛ°), ionization energy (E(i)), pK(a), enthalpy of formation of radical (Δ(f)H), and OH bond dissociation energy (D(O-H)). The rationale for selecting these descriptors is derived from the laccase-mediator mechanism. To validate the DT predictions, the kinetic constants of different compounds as laccase substrates, their ability for pesticide transformation as laccase-mediators, and radical stability were experimentally determined using Coriolopsis gallica laccase and the pesticide dichlorophen. The prediction capability of the DT model based on three proposed descriptors showed a complete agreement with the obtained experimental results. Copyright © 2012 Elsevier Inc. All rights reserved.
Mixtures of Polya trees for flexible spatial frailty survival modelling.
Zhao, Luping; Hanson, Timothy E; Carlin, Bradley P
2009-06-01
Mixtures of Polya trees offer a very flexible nonparametric approach for modelling time-to-event data. Many such settings also feature spatial association that requires further sophistication, either at the point level or at the lattice level. In this paper, we combine these two aspects within three competing survival models, obtaining a data analytic approach that remains computationally feasible in a fully hierarchical Bayesian framework using Markov chain Monte Carlo methods. We illustrate our proposed methods with an analysis of spatially oriented breast cancer survival data from the Surveillance, Epidemiology and End Results program of the National Cancer Institute. Our results indicate appreciable advantages for our approach over competing methods that impose unrealistic parametric assumptions, ignore spatial association or both.
New Fractal Localized Structures in Boiti-Leon-Pempinelli System
Institute of Scientific and Technical Information of China (English)
MAZheng-Yi; ZHUJia-Min; ZHENGChun-Long
2004-01-01
A novel phenomenon that the localized coherent structures of a (2+1)-dimensional physical model possess fractal behaviors is revealed. To clarify the interesting phenomenon, we take the (2+1)-dimensional Boiti Leon-Pempinelli system as a concrete example. Starting from an extended homogeneous balance approach, a general solution of the system is derived. From which some special localized excitations with fractal behaviors are obtained by introducin gsome types of lower-dimensional fractal patterns.
Lorenz, HW; Nusse, HE
Goodwin's nonlinear accelerator model with periodic investment outlays is reconsidered and used as an economic example of the emergence of complex motion in nonlinear dynamical systems. In addition to chaotic attractors, the model can possess coexisting attracting periodic orbits or simple
DEFF Research Database (Denmark)
Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.
1989-01-01
A version of the two-dimensional site-diluted spin-(1/2 Ising model is proposed as a microscopic interaction model which governs solidification and growth processes controlled by vacancy diffusion. The Ising Hamiltonian describes a solid-fluid phase transition and it permits a thermodynamic......-water interfaces....
Drolet, Jean-Philippe; Giroux, Bernard; Bouligand, Claire
2017-04-01
New technologies that allow geothermal energy production in colder conditions result in interest for geothermal exploration in low heat flux regions that were previously overlooked. The Province of Québec, eastern Canada, is such a case. It is a large and cold area with a low amount of heat flux measurements, and mapping the Curie point depth is appealing as an exploration tool due to the scarcity of the direct data. For that purpose, we have revisited a methodology to estimate the Curie point depth using a fractal source distribution model and aeromagnetic data. Our methodology relies on a statistical model of crustal magnetization having a constant magnetization direction and random magnetization amplitude. The shape of the radial average of the logarithm of the power spectrum of magnetic anomalies is predicted using this model. The model parameters (thickness and depth to the top of the magnetic layer, the fractal exponent β and the constant C') are obtained by calculating the best fit between the theoretical and observed radial power spectra using a non-linear least-square algorithm. Rather than using a constant value for the fractal exponent β over the whole study area, which would overcorrect the shape of the radially averaged power spectra in some zones, we propose a new calibration workflow based on heat flux measurements and lithology. This workflow includes the use of sequential Gaussian simulations (SGS) of heat flux data to enlarge the limited available dataset. The use of SGS also allows quantifying the uncertainty and the range of the predicted Curie point depths. This work contributes to mapping the Curie point depth at large scale and help identifying potential areas for further detailed exploration programs and potential geothermal energy production in the Province of Québec.
Bayesian nonparametric meta-analysis using Polya tree mixture models.
Branscum, Adam J; Hanson, Timothy E
2008-09-01
Summary. A common goal in meta-analysis is estimation of a single effect measure using data from several studies that are each designed to address the same scientific inquiry. Because studies are typically conducted in geographically disperse locations, recent developments in the statistical analysis of meta-analytic data involve the use of random effects models that account for study-to-study variability attributable to differences in environments, demographics, genetics, and other sources that lead to heterogeneity in populations. Stemming from asymptotic theory, study-specific summary statistics are modeled according to normal distributions with means representing latent true effect measures. A parametric approach subsequently models these latent measures using a normal distribution, which is strictly a convenient modeling assumption absent of theoretical justification. To eliminate the influence of overly restrictive parametric models on inferences, we consider a broader class of random effects distributions. We develop a novel hierarchical Bayesian nonparametric Polya tree mixture (PTM) model. We present methodology for testing the PTM versus a normal random effects model. These methods provide researchers a straightforward approach for conducting a sensitivity analysis of the normality assumption for random effects. An application involving meta-analysis of epidemiologic studies designed to characterize the association between alcohol consumption and breast cancer is presented, which together with results from simulated data highlight the performance of PTMs in the presence of nonnormality of effect measures in the source population.
Modeling Answer Change Behavior: An Application of a Generalized Item Response Tree Model
Jeon, Minjeong; De Boeck, Paul; van der Linden, Wim
2017-01-01
We present a novel application of a generalized item response tree model to investigate test takers' answer change behavior. The model allows us to simultaneously model the observed patterns of the initial and final responses after an answer change as a function of a set of latent traits and item parameters. The proposed application is illustrated…
Fractal-Based Exponential Distribution of Urban Density and Self-Affine Fractal Forms of Cities
Chen, Yanguang
2016-01-01
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 ...
U.S. Environmental Protection Agency — Spreadsheets are included here to support the manuscript "Boosted Regression Tree Models to Explain Watershed Nutrient Concentrations and Biological Condition". This...
Yield curve event tree construction for multi stage stochastic programming models
DEFF Research Database (Denmark)
Rasmussen, Kourosh Marjani; Poulsen, Rolf
by the quality and size of the event trees representing the underlying uncertainty. Most often the DSP literature assumes existence of ``appropriate'' event trees without defining and examining qualities that must be met (ex--ante) in such an event tree in order for the results of the DSP model to be reliable....... Indeed defining a universal and tractable framework for fully ``appropriate'' event trees is in our opinion an impossible task. A problem specific approach to designing such event trees is the way ahead. In this paper we propose a number of desirable properties which should be present in an event tree...... of yield curves. Such trees may then be used to represent the underlying uncertainty in DSP models of fixed income risk and portfolio management....
Directory of Open Access Journals (Sweden)
Søren Ventegodt
2006-01-01
Full Text Available In this paper we have made a draft of a physical fractal essence of the universe, a sketch of a new cosmology, which we believe to lay at the root of our new holistic biological paradigm. We present the fractal roomy spiraled structures and the energy-rich dancing infinite strings or lines of the universe that our hypothesis is based upon. The geometric language of this cosmology is symbolic and both pre-mathematical and pre-philosophical. The symbols are both text and figures, and using these we step by step explain the new model that at least to some extent is able to explain the complex informational system behind morphogenesis, ontogenesis, regeneration and healing. We suggest that it is from this highly dynamic spiraled structure that organization of cells, organs, and the wholeness of the human being including consciousness emerge. The model of “dancing fractal spirals” carries many similarities to premodern cultures descriptions of the energy of the life and universe. Examples are the Native American shamanistic descriptions of their perception of energy and the old Indian Yogis descriptions of the life-energy within the body and outside. Similar ideas of energy and matter are found in the modern superstring theories. The model of the informational system of the organism gives new meaning to Batesons definition of information: A difference that makes a difference, and indicates how information-directed self-organization can exist on high structural levels in living organisms, giving birth to their subjectivity and consciousness.
Fractal parameters and vascular networks: facts & artifacts
Directory of Open Access Journals (Sweden)
Maniero Fabrizio
2008-07-01
Full Text Available Abstract Background Several fractal and non-fractal parameters have been considered for the quantitative assessment of the vascular architecture, using a variety of test specimens and of computational tools. The fractal parameters have the advantage of being scale invariant, i.e. to be independent of the magnification and resolution of the images to be investigated, making easier the comparison among different setups and experiments. Results The success of several commercial and/or free codes in computing the fractal parameters has been tested on well known exact models. Based on such a preliminary study, we selected the code Frac-lac in order to analyze images obtained by visualizing the angiogenetic process occurring in chick Chorio Allontoic Membranes (CAM, assumed to be paradigmatic of a realistic 2D vascular network. Among the parameters investigated, the fractal dimension Df proved to be the most robust estimator for CAM vascular networks. Moreover, only Df was able to discriminate between effective and elusive increases in vascularization after drug-induced angiogenic stimulations on CAMs. Conclusion The fractal dimension Df is likely to be the most promising tool for monitoring the effectiveness of anti-angiogenic therapies in various clinical contexts.
Fractal Structure in Galactic Star Fields
Elmegreen, B G; Elmegreen, Bruce G.; Elmegreen, Debra Meloy
2001-01-01
The fractal structure of star formation on large scales in disk galaxies is studied using the size distribution function of stellar aggregates in kpc-scale star fields. Achival HST images of 10 galaxies are Gaussian smoothed to define the aggregates, and a count of these aggregates versus smoothing scale gives the fractal dimension. Fractal and Poisson models confirm the procedure. The fractal dimension of star formation in all of the galaxies is ~2.3. This is the same as the fractal dimension of interstellar gas in the Milky Way and nearby galaxies, suggesting that star formation is a passive tracer of gas structure defined by self-gravity and turbulence. Dense clusters like the Pleiades form at the bottom of the hierarchy of structures, where the protostellar gas is densest. If most stars form in such clusters, then the fractal arises from the spatial distribution of their positions, giving dispersed star fields from continuous cluster disruption. Dense clusters should have an upper mass limit that increase...
Nicolleau, FCGA; Redondo, J-M
2012-01-01
This book contains a collection of the main contributions from the first five workshops held by Ercoftac Special Interest Group on Synthetic Turbulence Models (SIG42. It is intended as an illustration of the sig's activities and of the latest developments in the field. This volume investigates the use of Kinematic Simulation (KS) and other synthetic turbulence models for the particular application to environmental flows. This volume offers the best syntheses on the research status in KS, which is widely used in various domains, including Lagrangian aspects in turbulence mixing/stirring, partic
Objetos fractales y arquitectura
MARTÍNEZ REQUENA, CELIA ANA
2015-01-01
Este trabajo final de grado versa acerca de la fractalidad y su posible aplicación arquitectónica. Se parte del concepto de fractal quedándose con la idea de que “un fractal es un diseño que se repite indefinidamente hacia el infinito cada vez a escala menor” y se presentan los diferentes conjuntos haciendo especial hincapié en los fractales clásicos. La fractalidad se puede apreciar en la naturaleza (p.e: un árbol tiene un tronco, este se divide en ramas, cada una de ellas en ...
Directory of Open Access Journals (Sweden)
M. A. Navascués
2013-01-01
Full Text Available This paper tackles the construction of fractal maps on the unit sphere. The functions defined are a generalization of the classical spherical harmonics. The methodology used involves an iterated function system and a linear and bounded operator of functions on the sphere. For a suitable choice of the coefficients of the system, one obtains classical maps on the sphere. The different values of the system parameters provide Bessel sequences, frames, and Riesz fractal bases for the Lebesgue space of the square integrable functions on the sphere. The Laplace series expansion is generalized to a sum in terms of the new fractal mappings.
Objetos fractales y arquitectura
MARTÍNEZ REQUENA, CELIA ANA
2015-01-01
Este trabajo final de grado versa acerca de la fractalidad y su posible aplicación arquitectónica. Se parte del concepto de fractal quedándose con la idea de que “un fractal es un diseño que se repite indefinidamente hacia el infinito cada vez a escala menor” y se presentan los diferentes conjuntos haciendo especial hincapié en los fractales clásicos. La fractalidad se puede apreciar en la naturaleza (p.e: un árbol tiene un tronco, este se divide en ramas, cada una de ellas en ...
USAHA PENINGKATAN PRODUKTIVITAS DENGAN PRODUCTIVITY EVALUATION TREE (PET MODELS
Directory of Open Access Journals (Sweden)
Muchlison Anis
2007-04-01
Full Text Available Usaha peningkatan produktivitas merupakan suatu langkah menuju perbaikan perusahaan dimasa yang akan datang. Model perencanaan produktivitas Productivity Evaluation Tree (PET memberikan kemudahan bagi perusahaan dalam mengembangkan dan menilai seluruh alternatif yang mungkin dilakukan dalam menetapkan target peningkatan produktivitas dan usaha peningkatan produktivitas. Dalam penelitian ini alternatif perencanaan ada tiga. Pertama, meningkatkan standart penggunaan bahan baku dari 20% menjadi 30%. Kedua, pengeluaran bahan baku diusulkan sama dengan bulan lalu dengan menerapkan peningkatan standart penggunaan bahan baku sama seperti dengan alternatif pertama, Ketiga, menstimulasi alternatif 2 dengan melakukan manajemen motivasi terhadap tenaga kerja. Dari hasil evaluasi pohon produktivitas maka dapat diketahui estimasi peningkatan produktivitas yang tertinggi adalah alternatif ke tiga dengan perubahan tingkat produktivitas sebesar 0,39.
Factor models on locally tree-like graphs
Dembo, Amir; Sun, Nike
2011-01-01
We consider homogeneous factor models on uniformly sparse graph sequences converging locally to a (unimodular) random tree T, and study the existence of the free energy density phi, the limit of the log-partition function divided by the number of vertices n as n tends to infinity. We provide a new interpolation scheme and use it to prove existence of, and to explicitly compute, the quantity phi subject to uniqueness of a relevant Gibbs measure for the factor model on T. By way of example we compute phi for the independent set (or hard-core) model at low fugacity, for the ferromagnetic Ising model at all parameter values, and for the ferromagnetic Potts model with both weak enough and strong enough interactions. Even beyond uniqueness our interpolation provides useful explicit bounds on phi. In the regimes in which we establish existence of the limit, we show that it coincides with the Bethe free energy functional evaluated at a suitable fixed point of the belief propagation recursions on T. In the special cas...
Institute of Scientific and Technical Information of China (English)
KESHAN－ZHE; QIANJUN－LONG; 等
1994-01-01
The chemical element contents in tree rings are correlated with those in the soils near the tree roots,The results in the present study showed that the correlation between them could be described using the following logarithmic linear correlation model:lgC'(Z)=a(Z)+b(Z)lgC(Z).Therefor,by determining the chrono-sequence C(Z,t),where Z is the atomic number and t the year,of elemental contents in the annual growth rings of trees,we could get the chrono-sequence C'(Z,t) of elemental contents in the soil,thus inferring the dynaminc variations of relevant elemental contents in the soil.
Fractal analysis of scatter imaging signatures to distinguish breast pathologies
Eguizabal, Alma; Laughney, Ashley M.; Krishnaswamy, Venkataramanan; Wells, Wendy A.; Paulsen, Keith D.; Pogue, Brian W.; López-Higuera, José M.; Conde, Olga M.
2013-02-01
Fractal analysis combined with a label-free scattering technique is proposed for describing the pathological architecture of tumors. Clinicians and pathologists are conventionally trained to classify abnormal features such as structural irregularities or high indices of mitosis. The potential of fractal analysis lies in the fact of being a morphometric measure of the irregular structures providing a measure of the object's complexity and self-similarity. As cancer is characterized by disorder and irregularity in tissues, this measure could be related to tumor growth. Fractal analysis has been probed in the understanding of the tumor vasculature network. This work addresses the feasibility of applying fractal analysis to the scattering power map (as a physical modeling) and principal components (as a statistical modeling) provided by a localized reflectance spectroscopic system. Disorder, irregularity and cell size variation in tissue samples is translated into the scattering power and principal components magnitude and its fractal dimension is correlated with the pathologist assessment of the samples. The fractal dimension is computed applying the box-counting technique. Results show that fractal analysis of ex-vivo fresh tissue samples exhibits separated ranges of fractal dimension that could help classifier combining the fractal results with other morphological features. This contrast trend would help in the discrimination of tissues in the intraoperative context and may serve as a useful adjunct to surgeons.
Linking individual-tree and whole-stand models for forest growth and yield prediction
Directory of Open Access Journals (Sweden)
Quang V Cao
2014-10-01
Full Text Available Background Different types of growth and yield models provide essential information for making informed decisions on how to manage forests. Whole-stand models often provide well-behaved outputs at the stand level, but lack information on stand structures. Detailed information from individual-tree models and size-class models typically suffers from accumulation of errors. The disaggregation method, in assuming that predictions from a whole-stand model are reliable, partitions these outputs to individual trees. On the other hand, the combination method seeks to improve stand-level predictions from both whole-stand and individual-tree models by combining them. Methods Data from 100 plots randomly selected from the Southwide Seed Source Study of loblolly pine (Pinus taeda L. were used to evaluate the unadjusted individual-tree model against the disaggregation and combination methods. Results Compared to the whole-stand model, the combination method did not show improvements in predicting stand attributes in this study. The combination method also did not perform as well as the disaggregation method in tree-level predictions. The disaggregation method provided the best predictions of tree- and stand-level survival and growth. Conclusions The disaggregation approach provides a link between individual-tree models and whole-stand models, and should be considered as a better alternative to the unadjusted tree model.
Thomas C. Edwards; D. Richard Cutler; Niklaus E. Zimmermann; Linda Geiser; Gretchen G. Moisen
2006-01-01
We evaluated the effects of probabilistic (hereafter DESIGN) and non-probabilistic (PURPOSIVE) sample surveys on resultant classification tree models for predicting the presence of four lichen species in the Pacific Northwest, USA. Models derived from both survey forms were assessed using an independent data set (EVALUATION). Measures of accuracy as gauged by...
Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method
Zhu, Fanglong; Li, Kejing
2010-03-01
In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.
Eloy, Christophe
2015-11-01
In general, trees have self-similar architectures with longer and thicker branches near the roots. Yet, branch segments grown each year always have approximately the same length. This hierarchy of branch lengths and the whole self-similar characteristics results in fact from a continuous process of growth of new branches and shedding of old ones. To assess how such a process affects tree architecture, a functional-structural mechanically-based model of virtual trees is developed. In this model, trees grow into fractal structures to promote efficient photosynthesis in a competing environment. In addition, branch diameters increase in response to wind-induced loads. The results of this model suggest that most self-similar characteristics of trees can be explained by considering that tree are growing structure able to resist mechanical loads due to wind efficiently.
Trabajando fractales con Winlogo
Sabogal, Sonia; Arenas, Gilberto
2007-01-01
Después de una breve introducción en la cual se establecerán algunos conceptos teóricos básicos de la geometría fractal, se realizarán talleres en los cuales, con ayuda de las herramientas que trabaja el software WinLogo, se construirán diversos fractales, analizando sus principales características (autosimilitud, dimensión, etc.)
Dynamics models and modeling of tree stand development
Directory of Open Access Journals (Sweden)
M. V. Rogozin
2015-04-01
Full Text Available Brief analysis of scientific works in Russia and in the CIS over the past 100 years. Logical and mathematical models consider the conceptual and show some of the results of their verification. It was found that the models include different laws and the parameters, the sum of which allows you to divide them into four categories: models of static states, development models, models of care for the natural forest and models of cultivation. Each category has fulfilled and fulfills its tasks in economic management. Thus, the model states in statics (table traverse growth played a prominent role in figuring out what may be the most productive (full stands in different regions of the country. However, they do not answer the question of what the initial states lead to the production of complete stands. In a study of the growth of stands used system analysis, and it is observed dominance of works studying static state, snatched from the biological time. Therefore, the real drama of the growth of stands remained almost unexplored. It is no accident there were «chrono-forestry» «plantation forestry» and even «non-traditional forestry», where there is a strong case of a number of new concepts of development stands. That is quite in keeping with Kuhn (Kuhn, 2009 in the forestry crisis began – there were alternative theories and coexist conflicting scientific schools. To develop models of stand development, it is proposed to use a well-known method of repeated observations within 10–20 years, in conjunction with the explanation of the history of the initial density. It mounted on the basis of studying the dynamics of its indicators: the trunk, crown overlap coefficient, the sum of volumes of all crowns and the relative length of the crown. According to these indicators, the researcher selects natural series of development stands with the same initial density. As a theoretical basis for the models it is possible to postulate the general properties of
Statistical modeling and design in forestry : The case of single tree models
2008-01-01
Forest quantification methods have evolved from a simple graphical approach to complex regression models with stochastic structural components. Currently, mixed effects models methodology is receiving attention in the forestry literature. However, the review work (Paper I) indicates a tendency to overlook appropriate covariance structures in the NLME modeling process. A nonlinear mixed effects modeling process is demonstrated in Paper II using Cupressus lustanica tree merchantable volume data...
Modeling the effectiveness of tree planting to mitigate habitat loss in blue oak woodlands
Richard B. Standiford; Douglas McCreary; William Frost
2002-01-01
Many local conservation policies have attempted to mitigate the loss of oak woodland habitat resulting from conversion to urban or intensive agricultural land uses through tree planting. This paper models the development of blue oak (Quercus douglasii) stand structure attributes over 50 years after planting. The model uses a single tree, distance...
A Model of Desired Performance in Phylogenetic Tree Construction for Teaching Evolution.
Brewer, Steven D.
This research paper examines phylogenetic tree construction-a form of problem solving in biology-by studying the strategies and heuristics used by experts. One result of the research is the development of a model of desired performance for phylogenetic tree construction. A detailed description of the model and the sample problems which illustrate…
A modeling study of the impact of urban trees on ozone
David J. Nowak; Kevin L. Civerolo; S. Trivikrama Rao; Gopal Sistla; Christopher J. Luley; Daniel E. Crane
2000-01-01
Modeling the effects of increased urban tree cover on ozone concentrations (July 13-15, 1995) from Washington, DC, to central Massachusetts reveals that urban trees generally reduce ozone concentrations in cities, but tend to increase average ozone concentrations in the overall modeling domain. During the daytime, average ozone reductions in urban areas (1 ppb) were...
Decision-Tree Models of Categorization Response Times, Choice Proportions, and Typicality Judgments
Lafond, Daniel; Lacouture, Yves; Cohen, Andrew L.
2009-01-01
The authors present 3 decision-tree models of categorization adapted from T. Trabasso, H. Rollins, and E. Shaughnessy (1971) and use them to provide a quantitative account of categorization response times, choice proportions, and typicality judgments at the individual-participant level. In Experiment 1, the decision-tree models were fit to…
Decision-Tree Models of Categorization Response Times, Choice Proportions, and Typicality Judgments
Lafond, Daniel; Lacouture, Yves; Cohen, Andrew L.
2009-01-01
The authors present 3 decision-tree models of categorization adapted from T. Trabasso, H. Rollins, and E. Shaughnessy (1971) and use them to provide a quantitative account of categorization response times, choice proportions, and typicality judgments at the individual-participant level. In Experiment 1, the decision-tree models were fit to…
Vásquez, A.; Tolson, G.
2012-12-01
The quantification of fracture systems is important to understand the phenomenon of fluid flow in naturally fractured petroleum reservoirs. In this work, we present a case of detailed analysis of filled fracture networks (veins) covering four orders of magnitude of scale. For our analysis we selected rocks of the El Doctor platform in the state of Querétaro, Central Mexico, which is an exposed analog of naturally fractured carbonate reservoir rocks common in the near-offshore oil fields in southeast Mexico. The fractal properties of one and two dimensional natural fracture patterns mapped on limestone outcrops, are present and compared to the results obtained in other studies at different scales. The fractal dimension of different fracture properties, such as spacing, thickness, spatial distribution, density, connectivity and length are investigated and measured using different methods. The principal fractal parameters obtained in this study include the cumulative-frequency exponent of spacing and thickness, box-counting dimension, correlation dimension and Lyapunov exponent in 1D analysis; whereas the 2D analysis included the cumulative-length exponent (fragmentation dimension), box-counting dimension, mass dimension (mid and intersection points of fractures), lacunarity and connectivity. In addition, we analyzed the orientation, density and intensity of the fracture arrays. The results of the 1D analysis indicate that the fracture spacing can be characterised using the parameters mentioned before, but the best fractal parameter to characterize the distribution and array of fractures is the Lyapunov exponent, because it's value (1.06-1.42) can differentiate between different types of array. The fractal dimension obtained for cumulative-frequency of the spacing, shows a power law with a negative exponent between -1.08 and -0.70. In the case of box-counting and correlation dimensions, the values of dimension were 0.30-0.68 and 0.40-0.63 respectively. With respect
A carbon balance model of peach tree growth and development for studying the pruning response.
Génard, Michel; Pagès, Loïc; Kervella, Jocelyne
1998-06-01
We modeled tree responses to pruning on the basis of growth rules established on unpruned trees and a simple principle governing root-shoot interactions. The model, which integrates architectural and ecophysiological approaches, distinguishes four types of anatomical organs in a tree: rootstock, main axis, secondary axes and new roots. Tree structure is described by the position of secondary axes on the main axis. The main processes considered are plastochronal activity, branching, assimilate production, respiration and assimilate partitioning. Growth and development rules were based on measurements of two unpruned trees. The model was used to simulate growth of peach trees (Prunus persica (L.) Batsch) in their first growing season. Assuming that the equilibrium between roots and shoots tends to be restored after pruning, the response to removal of the main axis above the twentieth internode in mid-July was simulated and compared to the response measured in three pruned trees. The model fit the unpruned tree data reasonably well and predicted the main traits of tree behavior after pruning. Dry matter growth of the secondary axes of pruned trees was increased so that shoot seasonal carbon balance was hardly modified by pruning. Rhythmicity of growth was enhanced by pruning, and might result from variations induced in the root:shoot ratio. Variation in pruning severity had greater effects than variation in pruning date. A sensitivity analysis indicated that: (1) root-shoot partitioning was a critical process of the model; (2) tree growth was mainly dependent on assimilate availability; and (3) tree shape was highly dependent on the branching process.
Fractal Dimension in Epileptic EEG Signal Analysis
Uthayakumar, R.
Fractal Analysis is the well developed theory in the data analysis of non-linear time series. Especially Fractal Dimension is a powerful mathematical tool for modeling many physical and biological time signals with high complexity and irregularity. Fractal dimension is a suitable tool for analyzing the nonlinear behaviour and state of the many chaotic systems. Particularly in analysis of chaotic time series such as electroencephalograms (EEG), this feature has been used to identify and distinguish specific states of physiological function.Epilepsy is the main fatal neurological disorder in our brain, which is analyzed by the biomedical signal called Electroencephalogram (EEG). The detection of Epileptic seizures in the EEG Signals is an important tool in the diagnosis of epilepsy. So we made an attempt to analyze the EEG in depth for knowing the mystery of human consciousness. EEG has more fluctuations recorded from the human brain due to the spontaneous electrical activity. Hence EEG Signals are represented as Fractal Time Series.The algorithms of fractal dimension methods have weak ability to the estimation of complexity in the irregular graphs. Divider method is widely used to obtain the fractal dimension of curves embedded into a 2-dimensional space. The major problem is choosing initial and final step length of dividers. We propose a new algorithm based on the size measure relationship (SMR) method, quantifying the dimensional behaviour of irregular rectifiable graphs with minimum time complexity. The evidence for the suitability (equality with the nature of dimension) of the algorithm is illustrated graphically.We would like to demonstrate the criterion for the selection of dividers (minimum and maximum value) in the calculation of fractal dimension of the irregular curves with minimum time complexity. For that we design a new method of computing fractal dimension (FD) of biomedical waveforms. Compared to Higuchi's algorithm, advantages of this method include
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.
Menger sponge-like fractal body created by a novel template method.
Mayama, H; Tsujii, K
2006-09-28
We have established experimental strategies on how to create a Menger sponge-like fractal body and how to control its fractal dimension. The essence was to utilize alkylketene dimer (AKD), which spontaneously forms super-water-repellent fractal surface. We prepared "fractal AKD particles" with fractal surface structure as templates of pores in fractal body. The fractal body was synthesized by filling the remained space between the packed template particles with a tetramethyl orthosilicate solution, solidifying it by the sol-gel process, and removing the template by calcinations. We have succeeded in systematically creating fractal bodies of silica with different cross-sectional fractal dimensions D(cs)=1.87, 1.84, and 1.80 using "fractal template particles" compressed under the ratio=1.0, 2.0, and 3.0, respectively. We also discussed the possibilities of their fractal geometries in comparison with mathematical models. We concluded that the created fractal bodies were close to a Menger sponge and its modified one. Our experimental strategy allows us to design fractality of porous materials.
Achieving Convergence in Galaxy Formation Models by Augmenting N-body Merger Trees
Benson, Andrew J; Cole, Shaun
2016-01-01
Accurate modeling of galaxy formation in a hierarchical, cold dark matter universe requires the use of sufficiently high-resolution merger trees to obtain convergence in the predicted properties of galaxies. When semi-analytic galaxy formation models are applied to cosmological N-body simulation merger trees, it is often the case that those trees have insufficient resolution to give converged galaxy properties. We demonstrate a method to augment the resolution of N-body merger trees by grafting in branches of Monte Carlo merger trees with higher resolution, but which are consistent with the pre-existing branches in the N-body tree. We show that this approach leads to converged galaxy properties.
On the value of the critical point in fractal percolation
White, D.G.
1999-01-01
We derive a new lower bound pc > 0:8107 for the critical value of Mandelbrot's dyadic fractal percolation model. This is achieved by taking the random fractal set (to be denoted A 1) and adding to it a countable number of straight line segments, chosen in a certain (non-random) way as to simplify
Parallel family trees for transfer matrices in the Potts model
Navarro, Cristobal A; Kahler, Nancy Hitschfeld; Navarro, Gonzalo
2013-01-01
The computational cost of transfer matrix methods for the Potts model is directly related to the problem of \\textit{into how many ways can two adjacent blocks of a lattice be connected}. Answering this question leads to the generation of a combinatorial set of lattice configurations. This set defines the \\textit{configuration space} of the problem, and the smaller it is, the faster the transfer matrix method can be. The configuration space of generic transfer matrix methods for strip lattices in the Potts model is in the order of the Catalan numbers, leading to an asymptotic cost of $O(4^m)$ with $m$ being the width of the strip. Transfer matrix methods with a smaller configuration space indeed exist but they make assumptions on the temperature, number of spin states, or restrict the topology of the lattice in order to work. In this paper we propose a general and parallel transfer matrix method, based on family trees, that uses a sub-Catalan configuration space of size $O(3^m)$. The improvement is achieved by...
Invasion percolation on a tree and queueing models.
Gabrielli, A; Caldarelli, G
2009-04-01
We study the properties of the Barabási model of queuing [A.-L. Barabási, Nature (London) 435, 207 (2005); J. G. Oliveira and A.-L. Barabási, Nature (London) 437, 1251 (2005)] in the hypothesis that the number of tasks grows with time steadily. Our analytical approach is based on two ingredients. First we map exactly this model into an invasion percolation dynamics on a Cayley tree. Second we use the theory of biased random walks. In this way we obtain the following results: the stationary-state dynamics is a sequence of causally and geometrically connected bursts of execution activities with scale-invariant size distribution. We recover the correct waiting-time distribution PW(tau) approximately tau(-3/2) at the stationary state (as observed in different realistic data). Finally we describe quantitatively the dynamics out of the stationary state quantifying the power-law slow approach to stability both in single dynamical realization and in average. These results can be generalized to the case of a stochastic increase in the queue length in time with limited fluctuations. As a limit case we recover the situation in which the queue length fluctuates around a constant average value.
Fractal Weyl law for quantum fractal eigenstates.
Shepelyansky, D L
2008-01-01
The properties of the resonant Gamow states are studied numerically in the semiclassical limit for the quantum Chirikov standard map with absorption. It is shown that the number of such states is described by the fractal Weyl law, and their Husimi distributions closely follow the strange repeller set formed by classical orbits nonescaping in future times. For large matrices the distribution of escape rates converges to a fixed shape profile characterized by a spectral gap related to the classical escape rate.
arXiv Generalized Fragmentation Functions for Fractal Jet Observables
Elder, Benjamin T.; Thaler, Jesse; Waalewijn, Wouter J.; Zhou, Kevin
2017-06-15
We introduce a broad class of fractal jet observables that recursively probe the collective properties of hadrons produced in jet fragmentation. To describe these collinear-unsafe observables, we generalize the formalism of fragmentation functions, which are important objects in QCD for calculating cross sections involving identified final-state hadrons. Fragmentation functions are fundamentally nonperturbative, but have a calculable renormalization group evolution. Unlike ordinary fragmentation functions, generalized fragmentation functions exhibit nonlinear evolution, since fractal observables involve correlated subsets of hadrons within a jet. Some special cases of generalized fragmentation functions are reviewed, including jet charge and track functions. We then consider fractal jet observables that are based on hierarchical clustering trees, where the nonlinear evolution equations also exhibit tree-like structure at leading order. We develop a numeric code for performing this evolution and study its phen...
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
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...... tomographic pulmonary angiograms findings, dogs were divided in three groups: diseased with pulmonary thromboembolism (n = 7), diseased but without pulmonary thromboembolism (n = 21), and healthy (n = 6). An observer who was aware of group status created three-dimensional pulmonary artery vascular trees...... 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...
Analytical Model and Algorithm of Fuzzy Fault Tree
Institute of Scientific and Technical Information of China (English)
杨艺; 何学秋; 王恩元; 刘贞堂
2002-01-01
In the past, the probabilities of basic events were described as triangular or trapezoidal fuzzy number that cannot characterize the common distribution of the primary events in engineering, and the fault tree analyzed by fuzzy set theory did not include repeated basic events. This paper presents a new method to a nalyze the fault tree by using normal fuzzy number to describe the fuzzy probability of each basic event which is more suitably used to analyze the reliability in safety systems, and then the formulae of computing the fuzzy probability of the top event of the fault tree which includes repeated events are derived. Finally, an example is given.
Models for Predicting the Biomass of Cunninghamialanceolata Trees and Stands in Southeastern China.
Guangyi, Mei; Yujun, Sun; Saeed, Sajjad
2017-01-01
Using existing equations to estimate the biomass of a single tree or a forest stand still involves large uncertainties. In this study, we developed individual-tree biomass models for Chinese Fir (Cunninghamia lanceolata.) stands in Fujian Province, southeast China, by using 74 previously established models that have been most commonly used to estimate tree biomass. We selected the best fit models and modified them. The results showed that the published model ln(B(Biomass)) = a + b * ln(D) + c * (ln(H))2 + d * (ln(H))3 + e * ln(WD) had the best fit for estimating the tree biomass of Chinese Fir stands. Furthermore, we observed that variables D(diameter at breast height), H (height), and WD(wood density)were significantly correlated with the total tree biomass estimation model. As a result, a natural logarithm structure gave the best estimates for the tree biomass structure. Finally, when a multi-step improvement on tree biomass model was performed, the tree biomass model with Tree volume(TV), WD and biomass wood density conversion factor (BECF),achieved the highest simulation accuracy, expressed as ln(TB) = -0.0703 + 0.9780 * ln(TV) + 0.0213 * ln(WD) + 1.0166 * ln(BECF). Therefore, when TV, WD and BECF were combined with tree biomass volume coefficient bi for Chinese Fir, the stand biomass (SB)model included both volume(SV) and coefficient bi variables of the stand as follows: bi = Exp(-0.0703+0.9780*ln(TV)+0.0213 * ln(WD)+1.0166*ln(BECF)). The stand biomass model is SB = SV/TV * bi.
DEFF Research Database (Denmark)
Kheir, Rania Bou; Greve, Mogens Humlekrog; Bøcher, Peder Klith
2010-01-01
the geographic distribution of SOC across Denmark using remote sensing (RS), geographic information systems (GISs) and decision-tree modeling (un-pruned and pruned classification trees). Seventeen parameters, i.e. parent material, soil type, landscape type, elevation, slope gradient, slope aspect, mean curvature...... field measurements in the area of interest (Denmark). A large number of tree-based classification models (588) were developed using (i) all of the parameters, (ii) all Digital Elevation Model (DEM) parameters only, (iii) the primary DEM parameters only, (iv), the remote sensing (RS) indices only, (v......) selected pairs of parameters, (vi) soil type, parent material and landscape type only, and (vii) the parameters having a high impact on SOC distribution in built pruned trees. The best constructed classification tree models (in the number of three) with the lowest misclassification error (ME...
Fractal and multifractal analyses of bipartite networks.
Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua
2017-03-31
Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.
Fractal and multifractal analyses of bipartite networks
Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua
2017-01-01
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. PMID:28361962
Fractal and multifractal analyses of bipartite networks
Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua
2017-03-01
Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.
Fractal structures in centrifugal flywheel governor system
Rao, Xiao-Bo; Chu, Yan-Dong; Lu-Xu; Chang, Ying-Xiang; Zhang, Jian-Gang
2017-09-01
The global structure of nonlinear response of mechanical centrifugal governor, forming in two-dimensional parameter space, is studied in this paper. By using three kinds of phases, we describe how responses of periodicity, quasi-periodicity and chaos organize some self-similarity structures with parameters varying. For several parameter combinations, the regular vibration shows fractal characteristic, that is, the comb-shaped self-similarity structure is generated by alternating periodic response with intermittent chaos, and Arnold's tongues embedded in quasi-periodic response are organized according to Stern-Brocot tree. In particular, a new type of mixed-mode oscillations (MMOs) is found in the periodic response. These unique structures reveal the natural connection of various responses between part and part, part and the whole in parameter space based on self-similarity of fractal. Meanwhile, the remarkable and unexpected results are to contribute a valid dynamic reference for practical applications with respect to mechanical centrifugal governor.
Di Ieva, A; Grizzi, F; Ceva-Grimaldi, G; Aimar, E; Serra, S; Pisano, P; Lorenzetti, M; Tancioni, F; Gaetani, P; Crotti, F; Tschabitscher, M; Matula, C; Rodriguez Y Baena, R
2010-06-01
In geometrical terms, tumor vascularity is an exemplary anatomical system that irregularly fills a three-dimensional Euclidean space. This physical characteristic, together with the highly variable vessel shapes and surfaces, leads to considerable spatial and temporal heterogeneity in the delivery of oxygen, nutrients and drugs, and the removal of metabolites. Although these biological features have now been well established, quantitative analyses of neovascularity in two-dimensional histological sections still fail to view tumor architecture in non-Euclidean terms, and this leads to errors in visually interpreting the same tumor, and discordant results from different laboratories. A review of the literature concerning the application of microvessel density (MVD) estimates, an Euclidean-based approach used to quantify vascularity in normal and neoplastic pituitary tissues, revealed some disagreements in the results and led us to discuss the limitations of the Euclidean quantification of vascularity. Consequently, we introduced fractal geometry as a better means of quantifying the microvasculature of normal pituitary glands and pituitary adenomas, and found that the use of the surface fractal dimension is more appropriate than MVD for analysing the vascular network of both. We propose extending the application of this model to the analysis of the angiogenesis and angioarchitecture of brain tumors.
The fractal forest: fractal geometry and applications in forest science.
Nancy D. Lorimer; Robert G. Haight; Rolfe A. Leary
1994-01-01
Fractal geometry is a tool for describing and analyzing irregularity. Because most of what we measure in the forest is discontinuous, jagged, and fragmented, fractal geometry has potential for improving the precision of measurement and description. This study reviews the literature on fractal geometry and its applications to forest measurements.
An image retrieval system based on fractal dimension
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
This paper presents a new kind of image retrieval system which obtains the feature vectors of images by estimating their fractal dimension; and at the same time establishes a tree-structure image database. After preprocessing and feature extracting, a given image is matched with the standard images in the image database using a hierarchical method of image indexing.
An image retrieval system based on fractal dimension.
Yao, Min; Yi, Wen-Sheng; Shen, Bin; Dai, Hong-Hua
2003-01-01
This paper presents a new kind of image retrieval system which obtains the feature vectors of images by estimating their fractal dimension; and at the same time establishes a tree-structure image database. After preprocessing and feature extracting, a given image is matched with the standard images in the image database using a hierarchical method of image indexing.
Realization of Fractal Affine Transformation
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
This paper gives the definition of fractal affine transformation and presents a specific method for its realization and its cor responding mathematical equations which are essential in fractal image construction.
Fractal Patterns and Chaos Games
Devaney, Robert L.
2004-01-01
Teachers incorporate the chaos game and the concept of a fractal into various areas of the algebra and geometry curriculum. The chaos game approach to fractals provides teachers with an opportunity to help students comprehend the geometry of affine transformations.
Biomechanics of Growing Trees: Mathematical Model, Numerical Resolution and Perspectives
Fourcaud, Thierry; Guillon, Thomas; Dumont, Yves
2011-09-01
The growth of trees is characterized by the elongation and thickening of its axes. New cells are formed at the periphery of the existing body, the properties of the older inner material being unchanged. The calculation of the progressive deflection of a growing stem is not a classical problem in mechanics for three main reasons: 1- the hypothesis of mass conservation is not valid; 2- the new material added at the periphery of the existing and deformed structure does not participate retroactively to the total equilibrium and tends to "fix" the actual shape; 3- an initial reference configuration corresponding to the unloaded structure cannot be classically defined to formulate the equilibrium equations. This paper proposes a theoretical framework that allows bypassing these difficulties. Equations adapted from the beam theory and considering the strong dependencies between space and time are given. A numerical scheme based on the finite element method is proposed to solve these equations. The model opens new research perspectives both in mathematics and plant biology.
Interaction of tea tree oil with model and cellular membranes.
Giordani, Cristiano; Molinari, Agnese; Toccacieli, Laura; Calcabrini, Annarica; Stringaro, Annarita; Chistolini, Pietro; Arancia, Giuseppe; Diociaiuti, Marco
2006-07-27
Tea tree oil (TTO) is the essential oil steam-distilled from Melaleuca alternifolia, a species of northern New South Wales, Australia. It exhibits a broad-spectrum antimicrobial activity and an antifungal activity. Only recently has TTO been shown to inhibit the in vitro growth of multidrug resistant (MDR) human melanoma cells. It has been suggested that the effect of TTO on tumor cells could be mediated by its interaction with the plasma membrane, most likely by inducing a reorganization of lipid architecture. In this paper we report biophysical and structural results obtained using simplified planar model membranes (Langmuir films) mimicking lipid "rafts". We also used flow cytometry analysis (FCA) and freeze-fracturing transmission electron microscopy to investigate the effects of TTO on actual MDR melanoma cell membranes. Thermodynamic (compression isotherms and adsorption kinetics) and structural (Brewster angle microscopy) investigation of the lipid monolayers clearly indicates that TTO interacts preferentially with the less ordered DPPC "sea" and that it does not alter the more ordered lipid "rafts". Structural observations, performed by freeze fracturing, confirm that TTO interacts with the MDR melanoma cell plasma membrane. Moreover, experiments performed by FCA demonstrate that TTO does not interfere with the function of the MDR drug transporter P-gp. We therefore propose that the effect exerted on MDR melanoma cells is mediated by the interaction with the fluid DPPC phase, rather than with the more organized "rafts" and that this interaction preferentially influences the ATP-independent antiapoptotic activity of P-gp likely localized outside "rafts".
Exotic topological order from quantum fractal code
Yoshida, Beni
2014-03-01
We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a formal level, may be viewed as condensation of string-like extended objects with discrete gauge symmetries, being at fixed points with continuous scale symmetries. In contrast, ground states of fractal spin liquids are condensation of highly-fluctuating fractal objects with certain algebraic symmetries, corresponding to limit cycles under real-space renormalization group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries. A particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems.
Exotic topological order in fractal spin liquids
Yoshida, Beni
2013-09-01
We present a large class of three-dimensional spin models that possess topological order with stability against local perturbations, but are beyond description of topological quantum field theory. Conventional topological spin liquids, on a formal level, may be viewed as condensation of stringlike extended objects with discrete gauge symmetries, being at fixed points with continuous scale symmetries. In contrast, ground states of fractal spin liquids are condensation of highly fluctuating fractal objects with certain algebraic symmetries, corresponding to limit cycles under real-space renormalization group transformations which naturally arise from discrete scale symmetries of underlying fractal geometries. A particular class of three-dimensional models proposed in this paper may potentially saturate quantum information storage capacity for local spin systems.
Reconstructing 3D Tree Models Using Motion Capture and Particle Flow
Directory of Open Access Journals (Sweden)
Jie Long
2013-01-01
Full Text Available Recovering tree shape from motion capture data is a first step toward efficient and accurate animation of trees in wind using motion capture data. Existing algorithms for generating models of tree branching structures for image synthesis in computer graphics are not adapted to the unique data set provided by motion capture. We present a method for tree shape reconstruction using particle flow on input data obtained from a passive optical motion capture system. Initial branch tip positions are estimated from averaged and smoothed motion capture data. Branch tips, as particles, are also generated within a bounding space defined by a stack of bounding boxes or a convex hull. The particle flow, starting at branch tips within the bounding volume under forces, creates tree branches. The forces are composed of gravity, internal force, and external force. The resulting shapes are realistic and similar to the original tree crown shape. Several tunable parameters provide control over branch shape and arrangement.
Thermodynamics of Fractal Universe
Sheykhi, Ahmad; Wang, Bin
2012-01-01
We investigate the thermodynamical properties of the apparent horizon in a fractal universe. We find that one can always rewrite the Friedmann equation of the fractal universe in the form of the entropy balance relation $ \\delta Q=TdS+Td\\tilde{S}$, where $ \\delta Q $ and $ T $ are the energy flux and Unruh temperature seen by an accelerated observer just inside the apparent horizon, and $d\\tilde{S}$ is the entropy production term due to nonequilibrium thermodynamics of fractal universe. This shows that in a fractal universe, a treatment with nonequilibrium thermodynamics of spacetime may be needed. We also study the generalized second law of thermodynamics in the framework of fractal universe. When the temperature of the apparent horizon and the matter fields inside the horizon are equal, i.e. $T=T_h$, the generalized second law of thermodynamics can be fulfilled provided the deceleration and the equation of state parameters ranges either as $-1 \\leq q < 0 $, $- 1 \\leq w < - 1/3$ or as $q<-1$, $w<...
Using New Approaches to obtain Gibbs Measures of Vannimenus model on a Cayley tree
2015-01-01
In this paper, we consider Vannimenus model with competing nearest-neighbors and prolonged next-nearest-neighbors interactions on a Cayley tree. For this model we define Markov random fields with memory of length 2. By using a new approach, we obtain new sets of Gibbs measures of Ising-Vannimenus model on Cayley tree of order 2. We construct the recurrence equations corresponding Ising-Vannimenus model. We prove the Kolmogorov consistency condition. We investigate the translation-invariant an...
The fractal nature of vacuum arc cathode spots
Energy Technology Data Exchange (ETDEWEB)
Anders, Andre
2005-05-27
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 {sup 2}, where f is frequency, supporting a fractal spot model associated with Brownian motion.
Gibbs Properties of the Fuzzy Potts Model on Trees and in Mean Field
Häggström, O.; Külske, C.
2004-01-01
We study Gibbs properties of the fuzzy Potts model in the mean field case (i.e. on a complete graph) and on trees. For the mean field case, a complete characterization of the set of temperatures for which non-Gibbsianness happens is given. The results for trees are somewhat less explicit, but we do
Fractal geometry and stochastics IV
Bandt, Christoph
2010-01-01
Over the years fractal geometry has established itself as a substantial mathematical theory in its own right. This book collects survey articles covering many of the developments, like Schramm-Loewner evolution, fractal scaling limits, exceptional sets for percolation, and heat kernels on fractals.
Fabian C.C. Uzoh; William W. Oliver
2008-01-01
A diameter increment model is developed and evaluated for individual trees of ponderosa pine throughout the species range in the United States using a multilevel linear mixed model. Stochastic variability is broken down among period, locale, plot, tree and within-tree components. Covariates acting at tree and stand level, as breast height diameter, density, site index...
Mirfenderesgi, Golnazalsadat; Bohrer, Gil; Matheny, Ashley M.; Fatichi, Simone; Moraes Frasson, Renato Prata; Schäfer, Karina V. R.
2016-07-01
The finite difference ecosystem-scale tree crown hydrodynamics model version 2 (FETCH2) is a tree-scale hydrodynamic model of transpiration. The FETCH2 model employs a finite difference numerical methodology and a simplified single-beam conduit system to explicitly resolve xylem water potentials throughout the vertical extent of a tree. Empirical equations relate water potential within the stem to stomatal conductance of the leaves at each height throughout the crown. While highly simplified, this approach brings additional realism to the simulation of transpiration by linking stomatal responses to stem water potential rather than directly to soil moisture, as is currently the case in the majority of land surface models. FETCH2 accounts for plant hydraulic traits, such as the degree of anisohydric/isohydric response of stomata, maximal xylem conductivity, vertical distribution of leaf area, and maximal and minimal xylem water content. We used FETCH2 along with sap flow and eddy covariance data sets collected from a mixed plot of two genera (oak/pine) in Silas Little Experimental Forest, NJ, USA, to conduct an analysis of the intergeneric variation of hydraulic strategies and their effects on diurnal and seasonal transpiration dynamics. We define these strategies through the parameters that describe the genus level transpiration and xylem conductivity responses to changes in stem water potential. Our evaluation revealed that FETCH2 considerably improved the simulation of ecosystem transpiration and latent heat flux in comparison to more conventional models. A virtual experiment showed that the model was able to capture the effect of hydraulic strategies such as isohydric/anisohydric behavior on stomatal conductance under different soil-water availability conditions.
Assessing the predictive capability of randomized tree-based ensembles in streamflow modelling
Directory of Open Access Journals (Sweden)
S. Galelli
2013-02-01
Full Text Available Combining randomization methods with ensemble prediction is emerging as an effective option to balance accuracy and computational efficiency in data-driven modeling. In this paper we investigate the prediction capability of extremely randomized trees (Extra-Trees, in terms of accuracy, explanation ability and computational efficiency, in a streamflow modeling exercise. Extra-Trees are a totally randomized tree-based ensemble method that (i alleviates the poor generalization property and tendency to overfitting of traditional standalone decision trees (e.g. CART; (ii is computationally very efficient; and, (iii allows to infer the relative importance of the input variables, which might help in the ex-post physical interpretation of the model. The Extra-Trees potential is analyzed on two real-world case studies (Marina catchment (Singapore and Canning River (Western Australia representing two different morphoclimatic contexts comparatively with other tree-based methods (CART and M5 and parametric data-driven approaches (ANNs and multiple linear regression. Results show that Extra-Trees perform comparatively well to the best of the benchmarks (i.e. M5 in both the watersheds, while outperforming the other approaches in terms of computational requirement when adopted on large datasets. In addition, the ranking of the input variable provided can be given a physically meaningful interpretation.
Assessing the predictive capability of randomized tree-based ensembles in streamflow modelling
Galelli, S.; Castelletti, A.
2013-07-01
Combining randomization methods with ensemble prediction is emerging as an effective option to balance accuracy and computational efficiency in data-driven modelling. In this paper, we investigate the prediction capability of extremely randomized trees (Extra-Trees), in terms of accuracy, explanation ability and computational efficiency, in a streamflow modelling exercise. Extra-Trees are a totally randomized tree-based ensemble method that (i) alleviates the poor generalisation property and tendency to overfitting of traditional standalone decision trees (e.g. CART); (ii) is computationally efficient; and, (iii) allows to infer the relative importance of the input variables, which might help in the ex-post physical interpretation of the model. The Extra-Trees potential is analysed on two real-world case studies - Marina catchment (Singapore) and Canning River (Western Australia) - representing two different morphoclimatic contexts. The evaluation is performed against other tree-based methods (CART and M5) and parametric data-driven approaches (ANNs and multiple linear regression). Results show that Extra-Trees perform comparatively well to the best of the benchmarks (i.e. M5) in both the watersheds, while outperforming the other approaches in terms of computational requirement when adopted on large datasets. In addition, the ranking of the input variable provided can be given a physically meaningful interpretation.
Directory of Open Access Journals (Sweden)
Howard A Crystal
Full Text Available The fractal dimension of retinal arteries and veins is a measure of the complexity of the vascular tree. We hypothesized that retinal fractal dimension would be associated with brain volume and white matter integrity in HIV-infected women.Nested case-control within longitudinal cohort study.Women were recruited from the Brooklyn site of the Women's Interagency HIV study (WIHS; 34 HIV-infected and 21 HIV-uninfected women with analyzable MRIs and retinal photographs were included. Fractal dimension was determined using the SIVA software program on skeletonized retinal images. The relationship between predictors (retinal vascular measures and outcomes (quantitative MRI measures were analyzed with linear regression models. All models included age, intracranial volume, and both arterial and venous fractal dimension. Some models were adjusted for blood pressure, race/ethnicity, and HIV-infection.The women were 45.6 ± 7.3 years of age. Higher arterial dimension was associated with larger cortical volumes, but higher venous dimension was associated with smaller cortical volumes. In fully adjusted models, venous dimension was significantly associated with fractional anisotropy (standardized β = -0.41, p = 0.009 and total gray matter volume (β = -0.24, p = 0.03, and arterial dimension with mean diffusivity (β = -0.33,.p = 0.04 and fractional anisotropy (β = 0.34, p = 0.03. HIV-infection was not associated with any retinal or MRI measure.Higher venous fractal dimension was associated with smaller cortical volumes and lower fractional anisotropy, whereas higher arterial fractal dimension was associated with the opposite patterns. Longitudinal studies are needed to validate this finding.
Directory of Open Access Journals (Sweden)
Jinmo Kim
2016-09-01
Full Text Available This study proposes a modeling method that can effectively generate multiple diverse digital trees for creating immersive virtual landscape based on virtual reality and an optimization method for real-time rendering. The proposed method simplifies a process of procedures from growth of tree models to the generation of the three-dimensional branch geometric model. Here, the procedural branch graph (PBG algorithm is proposed, which simultaneously and effectively generates diverse trees that have a similar branch pattern. Moreover, the optimization method is designed in a polygon-based branch model which controls the resolution of tree models according to the distance from the camera to generate a tree model structure that is appropriate for an immersive system based on virtual reality. Finally, a virtual reality system is established based on the Oculus SDK (Software Development Kit and Unity3D engine. In this process, the image processing-based pixel to tree (PTT method is proposed as a technique for easily and efficiently generating a virtual landscape by allocating multiple trees on terrain. An immersive virtual landscape that has a stereoscopic perception and spatial impression is created through the proposed method and whether it can deliver experience of nature in virtual reality to the users was checked through an experiment.
Energy Technology Data Exchange (ETDEWEB)
Benenti, Giuliano; Casati, Giulio; Guarneri, Italo; Terraneo, Marcello
2001-07-02
We numerically analyze quantum survival probability fluctuations in an open, classically chaotic system. In a quasiclassical regime and in the presence of classical mixed phase space, such fluctuations are believed to exhibit a fractal pattern, on the grounds of semiclassical arguments. In contrast, we work in a classical regime of complete chaoticity and in a deep quantum regime of strong localization. We provide evidence that fluctuations are still fractal, due to the slow, purely quantum algebraic decay in time produced by dynamical localization. Such findings considerably enlarge the scope of the existing theory.
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....
Deppman, Airton
2016-01-01
The non extensive aspects of $p_T$ distributions obtained in high energy collisions are discussed in relation to possible fractal structure in hadrons, in the sense of the thermofractal structure recently introduced. The evidences of self-similarity in both theoretical and experimental works in High Energy and in Hadron Physics are discussed, to show that the idea of fractal structure of hadrons and fireballs have being under discussion for decades. The non extensive self-consistent thermodynamics and the thermofractal structure allow one to connect non extensivity to intermittence and possibly to parton distribution functions in a single theoretical framework.
Three-dimensional tumor perfusion reconstruction using fractal interpolation functions.
Craciunescu, O I; Das, S K; Poulson, J M; Samulski, T V
2001-04-01
It has been shown that the perfusion of blood in tumor tissue can be approximated using the relative perfusion index determined from dynamic contrast-enhanced magnetic resonance imaging (DE-MRI) of the tumor blood pool. Also, it was concluded in a previous report that the blood perfusion in a two-dimensional (2-D) tumor vessel network has a fractal structure and that the evolution of the perfusion front can be characterized using invasion percolation. In this paper, the three-dimensional (3-D) tumor perfusion is reconstructed from the 2-D slices using the method of fractal interpolation functions (FIF), i.e., the piecewise self-affine fractal interpolation model (PSAFIM) and the piecewise hidden variable fractal interpolation model (PHVFIM). The fractal models are compared to classical interpolation techniques (linear, spline, polynomial) by means of determining the 2-D fractal dimension of the reconstructed slices. Using FIFs instead of classical interpolation techniques better conserves the fractal-like structure of the perfusion data. Among the two FIF methods, PHVFIM conserves the 3-D fractality better due to the cross correlation that exists between the data in the 2-D slices and the data along the reconstructed direction. The 3-D structures resulting from PHVFIM have a fractal dimension within 3%-5% of the one reported in literature for 3-D percolation. It is, thus, concluded that the reconstructed 3-D perfusion has a percolation-like scaling. As the perfusion term from bio-heat equation is possibly better described by reconstruction via fractal interpolation, a more suitable computation of the temperature field induced during hyperthermia treatments is expected.
Fractal Cosmology in an Open Universe
Joyce, M; Montuori, M; Pietronero, L; Sylos-Labini, F
2000-01-01
The clustering of galaxies is well characterized by fractal properties, withthe presence of an eventual cross-over to homogeneity still a matter ofconsiderable debate. In this letter we discuss the cosmological implications ofa fractal distribution of matter, with a possible cross-over to homogeneity atan undetermined scale R_{homo}. Contrary to what is generally assumed, we showthat, even when R_{homo} -> \\infty, this possibility can be treatedconsistently within the framework of the expanding universe solutions ofFriedmann. The fractal is a perturbation to an open cosmology in which theleading homogeneous component is the cosmic background radiation (CBR). Thiscosmology, inspired by the observed galaxy distributions, provides a simpleexplanation for the recent data which indicate the absence of deceleration inthe expansion (q_o \\approx 0). Correspondingly the `age problem' is alsoresolved. Further we show that the model can be extended back from thecurvature dominated arbitrarily deep into the radiation dom...
Fractal dynamics in chaotic quantum transport.
Kotimäki, V; Räsänen, E; Hennig, H; Heller, E J
2013-08-01
Despite several experiments on chaotic quantum transport in two-dimensional systems such as semiconductor quantum dots, corresponding quantum simulations within a real-space model have been out of reach so far. Here we carry out quantum transport calculations in real space and real time for a two-dimensional stadium cavity that shows chaotic dynamics. By applying a large set of magnetic fields we obtain a complete picture of magnetoconductance that indicates fractal scaling. In the calculations of the fractality we use detrended fluctuation analysis-a widely used method in time-series analysis-and show its usefulness in the interpretation of the conductance curves. Comparison with a standard method to extract the fractal dimension leads to consistent results that in turn qualitatively agree with the previous experimental data.
Mechanisms and models which govern bending and reconfiguring of trees under water flow action
Wilson, Catherine; Whittaker, Peter; Hydroenvironmental Research Centre Team
2015-11-01
A model for predicting the drag and reconfiguration of flexible vegetation under hydrodynamic loading is presented. The model is based on a refined ``vegetative'' Cauchy number to incorporate the magnitude and rate of a tree's reconfiguration. In addition, analysis of data from a tree drag force study conducted at the Canal de Experiencias Hidrodinamicas de El Pardo, Madrid, is also presented. This data enables the analysis of the frontal projected and the side-view areas as well as the bending angle of the main tree stems over a full range of velocities. New physical mechanisms which link tree posture, permeability, and the Reconfiguration number-Cauchy number relationship for various key stages of reconfiguration are proposed. These mechanisms are mainly developed for multi-stem trees in their foliated state. In addition direct comparisons of mechanisms for foliated and defoliated states are also presented.
ORPOM model for optimum distribution of tree ring sampling based on the climate observation network
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
Tree ring dating plays an important role in obtaining past climate information.The fundamental study of obtaining tree ring samples in typical climate regions is particularly essential.The optimum distribution of tree ring sampling sites based on climate information from the Climate Observation Network(ORPOM model) is presented in this article.In this setup,the tree rings in a typical region are used for surface representation,by applying excellent correlation with the climate information as the main principle.Taking the Horqin Sandy Land in the cold and arid region of China as an example,the optimum distribution range of the tree ring sampling sites was obtained through the application of the ORPOM model,which is considered a reasonably practical scheme.
Topology of correlation-based minimal spanning trees in real and model markets.
Bonanno, Giovanni; Caldarelli, Guido; Lillo, Fabrizio; Mantegna, Rosario N
2003-10-01
We compare the topological properties of the minimal spanning tree obtained from a large group of stocks traded at the New York Stock Exchange during a 12-year trading period with the one obtained from surrogated data simulated by using simple market models. We find that the empirical tree has features of a complex network that cannot be reproduced, even as a first approximation, by a random market model and by the widespread one-factor model.
A simple method to estimate fractal dimension of mountain surfaces
Kolwankar, Kiran M
2014-01-01
Fractal surfaces are ubiquitous in nature as well as in the sciences. The examples range from the cloud boundaries to the corroded surfaces. Fractal dimension gives a measure of the irregularity in the object under study. We present a simple method to estimate the fractal dimension of mountain surface. We propose to use easily available satellite images of lakes for this purpose. The fractal dimension of the boundary of a lake, which can be extracted using image analysis softwares, can be determined easily which gives the estimate of the fractal dimension of the mountain surface and hence a quantitative characterization of the irregularity of the topography of the mountain surface. This value will be useful in validating models of mountain formation
Spatial Analysis of Cities Using Renyi Entropy and Fractal Parameters
Chen, Yanguang
2016-01-01
Spatial distributions of cities fall into groups: one is the simple distribution with characteristic scale (e.g. exponential distribution), and the other is the complex distribution without characteristic scale (e.g. power-law distribution). The latter belongs to scale-free distributions, which can be modeled with fractal geometry. However, fractal dimension is suitable for the former distribution. In contrast, spatial entropy can be used to measure any types of urban distributions. This paper is devoted to developing multifractal parameters by means of the relation between entropy and fractal dimension. A new discovery is that normalized fractal dimension is equal to normalized entropy. Based on this finding, we can define a set of spatial indexes, which bears an analogy with the multifractal parameters. These indexes can be employed to describe both the simple distributions and complex distributions. The generalized fractal parameters are applied to the spatial density of population density of Hangzhou city...
Relaxation Dynamics of Semiflexible Fractal Macromolecules
Directory of Open Access Journals (Sweden)
Jonas Mielke
2016-07-01
Full Text Available We study the dynamics of semiflexible hyperbranched macromolecules having only dendritic units and no linear spacers, while the structure of these macromolecules is modeled through T-fractals. We construct a full set of eigenmodes of the dynamical matrix, which couples the set of Langevin equations. Based on the ensuing relaxation spectra, we analyze the mechanical relaxation moduli. The fractal character of the macromolecules reveals itself in the storage and loss moduli in the intermediate region of frequencies through scaling, whereas at higher frequencies, we observe the locally-dendritic structure that is more pronounced for higher stiffness.
Fractal Symmetries: Ungauging the Cubic Code
Williamson, Dominic J
2016-01-01
Gauging is a ubiquitous tool in many-body physics. It allows one to construct highly entangled topological phases of matter from relatively simple phases and to relate certain characteristics of the two. Here we develop a gauging procedure for general submanifold symmetries of Pauli Hamiltonians, including symmetries of fractal type. We show a relation between the pre- and post- gauging models and use this to construct short range entangled phases with fractal like symmetries, one of which is mapped to the cubic code by the gauging.
Modelling Mediterranean agro-ecosystems by including agricultural trees in the LPJmL model
Fader, M.; von Bloh, W.; Shi, S.; Bondeau, A.; Cramer, W.
2015-11-01
In the Mediterranean region, climate and land use change are expected to impact on natural and agricultural ecosystems by warming, reduced rainfall, direct degradation of ecosystems and biodiversity loss. Human population growth and socioeconomic changes, notably on the eastern and southern shores, will require increases in food production and put additional pressure on agro-ecosystems and water resources. Coping with these challenges requires informed decisions that, in turn, require assessments by means of a comprehensive agro-ecosystem and hydrological model. This study presents the inclusion of 10 Mediterranean agricultural plants, mainly perennial crops, in an agro-ecosystem model (Lund-Potsdam-Jena managed Land - LPJmL): nut trees, date palms, citrus trees, orchards, olive trees, grapes, cotton, potatoes, vegetables and fodder grasses. The model was successfully tested in three model outputs: agricultural yields, irrigation requirements and soil carbon density. With the development presented in this study, LPJmL is now able to simulate in good detail and mechanistically the functioning of Mediterranean agriculture with a comprehensive representation of ecophysiological processes for all vegetation types (natural and agricultural) and in a consistent framework that produces estimates of carbon, agricultural and hydrological variables for the entire Mediterranean basin. This development paves the way for further model extensions aiming at the representation of alternative agro-ecosystems (e.g. agroforestry), and opens the door for a large number of applications in the Mediterranean region, for example assessments of the consequences of land use transitions, the influence of management practices and climate change impacts.
Modelling Mediterranean agro-ecosystems by including agricultural trees in the LPJmL model
Directory of Open Access Journals (Sweden)
M. Fader
2015-06-01
Full Text Available Climate and land use change in the Mediterranean region is expected to affect natural and agricultural ecosystems by decreases in precipitation, increases in temperature as well as biodiversity loss and anthropogenic degradation of natural resources. Demographic growth in the Eastern and Southern shores will require increases in food production and put additional pressure on agro-ecosystems and water resources. Coping with these challenges requires informed decisions that, in turn, require assessments by means of a comprehensive agro-ecosystem and hydrological model. This study presents the inclusion of 10 Mediterranean agricultural plants, mainly perennial crops, in an agro-ecosystem model (LPJmL: nut trees, date palms, citrus trees, orchards, olive trees, grapes, cotton, potatoes, vegetables and fodder grasses. The model was successfully tested in three model outputs: agricultural yields, irrigation requirements and soil carbon density. With the development presented in this study, LPJmL is now able to simulate in good detail and mechanistically the functioning of Mediterranean agriculture with a comprehensive representation of ecophysiological processes for all vegetation types (natural and agricultural and in a consistent framework that produces estimates of carbon, agricultural and hydrological variables for the entire Mediterranean basin. This development pave the way for further model extensions aiming at the representation of alternative agro-ecosystems (e.g. agroforestry, and opens the door for a large number of applications in the Mediterranean region, for example assessments on the consequences of land use transitions, the influence of management practices and climate change impacts.
Fractal elements and their applications
Gil’mutdinov, Anis Kharisovich; El-Khazali, Reyad
2017-01-01
This book describes a new type of passive electronic components, called fractal elements, from a theoretical and practical point of view. The authors discuss in detail the physical implementation and design of fractal devices for application in fractional-order signal processing and systems. The concepts of fractals and fractal signals are explained, as well as the fundamentals of fractional calculus. Several implementations of fractional impedances are discussed, along with comparison of their performance characteristics. Details of design, schematics, fundamental techniques and implementation of RC-based fractal elements are provided. .
Mulder, Willem H; Crawford, Forrest W
2015-01-01
Efforts to reconstruct phylogenetic trees and understand evolutionary processes depend fundamentally on stochastic models of speciation and mutation. The simplest continuous-time model for speciation in phylogenetic trees is the Yule process, in which new species are "born" from existing lineages at a constant rate. Recent work has illuminated some of the structural properties of Yule trees, but it remains mostly unknown how these properties affect sequence and trait patterns observed at the tips of the phylogenetic tree. Understanding the interplay between speciation and mutation under simple models of evolution is essential for deriving valid phylogenetic inference methods and gives insight into the optimal design of phylogenetic studies. In this work, we derive the probability distribution of interspecies covariance under Brownian motion and Ornstein-Uhlenbeck models of phenotypic change on a Yule tree. We compute the probability distribution of the number of mutations shared between two randomly chosen taxa in a Yule tree under discrete Markov mutation models. Our results suggest summary measures of phylogenetic information content, illuminate the correlation between site patterns in sequences or traits of related organisms, and provide heuristics for experimental design and reconstruction of phylogenetic trees.
Alejandro Martínez; Alejandro Díaz; Mónico Linares; Javier Vega
2006-01-01
En este trabajo se presenta una arquitectura simple y rápida para compresión fractal de imágenes basada en un método para compresión fractal multi-resolución de imagen, utilizando particionamiento en árbol cuádruple piramidal y un esquema de clasificación de bloques de acuerdo a su tamaño y a su contraste. El uso de bloques rangos expandidos, bloques dominios no contraídos, y decimación de bloques tipo tablero de ajedrez compensa pérdidas en la calidad de imagen y permite obtener los parámetr...
Fractal Analysis of Stress Sensitivity of Permeability in Porous Media
Tan, Xiao-Hua; Li, Xiao-Ping; Liu, Jian-Yi; Zhang, Lie-Hui; Cai, Jianchao
2015-12-01
A permeability model for porous media considering the stress sensitivity is derived based on mechanics of materials and the fractal characteristics of solid cluster size distribution. The permeability of porous media considering the stress sensitivity is related to solid cluster fractal dimension, solid cluster fractal tortuosity dimension, solid cluster minimum diameter and solid cluster maximum diameter, Young's modulus, Poisson's ratio, as well as power index. Every parameter has clear physical meaning without the use of empirical constants. The model predictions of permeability show good agreement with those obtained by the available experimental expression. The proposed model may be conducible to a better understanding of the mechanism for flow in elastic porous media.
Maximizing Adaptivity in Hierarchical Topological Models Using Cancellation Trees
Energy Technology Data Exchange (ETDEWEB)
Bremer, P; Pascucci, V; Hamann, B
2008-12-08
We present a highly adaptive hierarchical representation of the topology of functions defined over two-manifold domains. Guided by the theory of Morse-Smale complexes, we encode dependencies between cancellations of critical points using two independent structures: a traditional mesh hierarchy to store connectivity information and a new structure called cancellation trees to encode the configuration of critical points. Cancellation trees provide a powerful method to increase adaptivity while using a simple, easy-to-implement data structure. The resulting hierarchy is significantly more flexible than the one previously reported. In particular, the resulting hierarchy is guaranteed to be of logarithmic height.
Empereur-Mot, Luc; Villemin, Thierry
A numerical rock fragmentation model was elaborated, producing a 3D puzzle of convex polyhedra, geometrically described in a database. In the first scenario, a constant proportion of blocks are fragmented at each step of the process and leads to fractal distribution. In the second scenario, division affects one random block at each stage of the process, and produces a Weibull volume distribution law. Imposing a minimal distance between the fractures, the third scenario reveals a power law. The inhibition of new fractures in the neighbourhood of existing discontinuities could be responsible for fractal properties in rock mass fragmentation. To cite this article: L. Empereur-Mot, T. Villemin, C. R. Geoscience 334 (2002) 127-133.
Institute of Scientific and Technical Information of China (English)
XU Jian-hua; AI Nan-shan; CHEN Yong; MEI An-xin; LIAO Hong-juan
2003-01-01
The mosaic structure of landscape of the central area of Shanghai Metropolis is studied by quantitative methods of landscape ecology based on Remote Sensing (RS) and Geographic Information System (GIS) in this pa-per. Firstly, landscapes are classified into eight categories: residential quarter, industrial quarter, road, other urban landscape, farmland, village and small town, on-building area, river and other water bodies (such as lake, etc.). Sec-ondly, a GIS is designed and set up based on the remote sensing data and field investigation, and a digital map of landscape mosaic is made. Then the indexes of diversity, dominance, fragmentation and isolation, and fractal dimen-sion of each type of landscape in different periods are calculated by using spatial analysis method of GIS. With refer-ence to the calculated results, a series of relative issues are discussed.
Propagation of action potentials along complex axonal trees. Model and implementation.
Manor, Y; Gonczarowski, J; Segev, I
1991-01-01
Axonal trees are typically morphologically and physiologically complicated structures. Because of this complexity, axonal trees show a large repertoire of behavior: from transmission lines with delay, to frequency filtering devices in both temporal and spatial domains. Detailed theoretical exploration of the electrical behavior of realistically complex axonal trees is notably lacking, mainly because of the absence of a simple modeling tool. AXONTREE is an attempt to provide such a simulator. It is written in C for the SUN workstation and implements both a detailed compartmental modeling of Hodgkin and Huxley-like kinetics, and a more abstract, event-driven, modeling approach. The computing module of AXONTREE is introduced together with its input/output features. These features allow graphical construction of arbitrary trees directly on the computer screen, and superimposition of the results on the simulated structure. Several numerical improvements that increase the computational efficiency by a factor of 5-10 are presented; most notable is a novel method of dynamic lumping of the modeled tree into simpler representations ("equivalent cables"). AXONTREE's performance is examined using a reconstructed terminal of an axon from a Y cell in cat visual cortex. It is demonstrated that realistically complicated axonal trees can be handled efficiently. The application of AXONTREE for the study of propagation delays along axonal trees is presented in the companion paper (Manor et al., 1991). Images FIGURE 4 PMID:1777566
Kumral, Mustafa; Abdelnasser, Amr; Karaman, Muhittin; Budakoglu, Murat
2016-04-01
The Tepeoba porphyry Cu-Mo-Au mineralization that located at the Biga peninsula (W Turkey) developed around the Eybek pluton concentrated at its southern contact. This mineralization that hosted in the hornfels rocks of Karakaya Complex is associated with three main alteration zones; potassic, phyllic and propylitic alterations along the fault controlled margins of the Eybek pluton and quartz stockwork veining as well as brecciation zones. As well as two mineralized zones were occurred in the mine area; hypogene and oxidation/supergene zone. The hypogene zone has differentiated alteration types; high potassic and low phyllic alteration, while the oxidation/supergene zone has high phyllic and propylitic alterations. This work deals with the delineation of gold mineralized zone within this porphyry deposit using the concentration-volume (C-V) fractal model. Five zones of gold were calculated using its power-law C-V relationship that revealed that the main phase of gold mineralization stated at 5.3083 ppm Au concentration. In addition, the C-V log-log plot shows that the highly and moderately Au mineralization zone developed in western part of deposit correlated with oxidation zone related to propylitic alteration. On the other hand, its weakly mineralization zone has a widespread in the hypogene zone related to potassic alteration. This refers to the enrichment of gold and depletion of copper at the oxidation/supergene zone is due to the oxidation/supergene alteration processes that enrich the deposits by the meteoric water. Keywords: Concentration-volume (C-V) fractal model; gold mineralized zone; Tepeoba porphyry Cu-Mo-Au; Balikesir; NW Turkey.
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...
Translation-invariant and periodic Gibbs measures for the Potts model on a Cayley tree
Khakimov, R. M.; Khaydarov, F. Kh.
2016-11-01
We study translation-invariant Gibbs measures on a Cayley tree of order k = 3 for the ferromagnetic three-state Potts model. We obtain explicit formulas for translation-invariant Gibbs measures. We also consider periodic Gibbs measures on a Cayley tree of order k for the antiferromagnetic q-state Potts model. Moreover, we improve previously obtained results: we find the exact number of periodic Gibbs measures with the period two on a Cayley tree of order k ≥ 3 that are defined on some invariant sets.
Mechanical properties of tree roots for soil reinforcement models
Cofie, P.
2001-01-01
Evidence from forestry has shown that part of the forest floor bearing capacity is delivered by tree roots. The beneficial effect however varies and diminishes with increasing number of vehicle passes. Roots potential for reinforcing the soil is known to depend among others on root mechanical proper
Mechanical properties of tree roots for soil reinforcement models
Cofie, P.
2001-01-01
Evidence from forestry has shown that part of the forest floor bearing capacity is delivered by tree roots. The beneficial effect however varies and diminishes with increasing number of vehicle passes. Roots potential for reinforcing the soil is known to depend among others on root
Soil Organic Matter Mapping by Decision Tree Modeling
Institute of Scientific and Technical Information of China (English)
ZHOU Bin; ZHANG Xing-Gang; WANG Fan; WANG Ren-Chao
2005-01-01
Based on a case study of Longyou County, Zhejiang Province, the decision tree, a data mining method, was used to analyze the relationships between soil organic matter (SOM) and other environmental and satellite sensing spatial data.The decision tree associated SOM content with some extensive easily observable landscape attributes, such as landform,geology, land use, and remote sensing images, thus transforming the SOM-related information into a clear, quantitative,landscape factor-associated regular system. This system could be used to predict continuous SOM spatial distribution.By analyzing factors such as elevation, geological unit, soil type, land use, remotely sensed data, upslope contributing area, slope, aspect, planform curvature, and profile curvature, the decision tree could predict distribution of soil organic matter levels. Among these factors, elevation, land use, aspect, soil type, the first principle component of bitemporal Landsat TM, and upslope contributing area were considered the most important variables for predicting SOM. Results of the prediction between SOM content and landscape types sorted by the decision tree showed a close relationship with an accuracy of 81.1%.
Boosted Regression Tree Models to Explain Watershed Nutrient Concentrations and Biological Condition
Boosted regression tree (BRT) models were developed to quantify the nonlinear relationships between landscape variables and nutrient concentrations in a mesoscale mixed land cover watershed during base-flow conditions. Factors that affect instream biological components, based on ...
Boosted Regression Tree Models to Explain Watershed Nutrient Concentrations and Biological Condition
Boosted regression tree (BRT) models were developed to quantify the nonlinear relationships between landscape variables and nutrient concentrations in a mesoscale mixed land cover watershed during base-flow conditions. Factors that affect instream biological components, based on ...
Do-It-Yourself Fractal Functions
Shriver, Janet; Willard, Teri; McDaniel, Mandy
2017-01-01
In the set of fractal activities described in this article, students will accomplish much more than just creating a fun set of cards that simply resemble an art project. Goals of this activity, designed for an algebra 1 class, are to encourage students to generate data, look for and analyze patterns, and create their own models--all from a set of…
Highly Accurate Tree Models Derived from Terrestrial Laser Scan Data: A Method Description
Directory of Open Access Journals (Sweden)
Jan Hackenberg
2014-05-01
Full Text Available This paper presents a method for fitting cylinders into a point cloud, derived from a terrestrial laser-scanned tree. Utilizing high scan quality data as the input, the resulting models describe the branching structure of the tree, capable of detecting branches with a diameter smaller than a centimeter. The cylinders are stored as a hierarchical tree-like data structure encapsulating parent-child neighbor relations and incorporating the tree’s direction of growth. This structure enables the efficient extraction of tree components, such as the stem or a single branch. The method was validated both by applying a comparison of the resulting cylinder models with ground truth data and by an analysis between the input point clouds and the models. Tree models were accomplished representing more than 99% of the input point cloud, with an average distance from the cylinder model to the point cloud within sub-millimeter accuracy. After validation, the method was applied to build two allometric models based on 24 tree point clouds as an example of the application. Computation terminated successfully within less than 30 min. For the model predicting the total above ground volume, the coefficient of determination was 0.965, showing the high potential of terrestrial laser-scanning for forest inventories.
CT-based geometry analysis and finite element models of the human and ovine bronchial tree.
Tawhai, Merryn H; Hunter, Peter; Tschirren, Juerg; Reinhardt, Joseph; McLennan, Geoffrey; Hoffman, Eric A
2004-12-01
The interpretation of experimental results from functional medical imaging is complicated by intersubject and interspecies differences in airway geometry. The application of computational models in understanding the significance of these differences requires methods for generation of subject-specific geometric models of the bronchial airway tree. In the current study, curvilinear airway centerline and diameter models have been fitted to human and ovine bronchial trees using detailed data segmented from multidetector row X-ray-computed tomography scans. The trees have been extended to model the entire conducting airway system by using a volume-filling algorithm to generate airway centerline locations within detailed volume descriptions of the lungs or lobes. Analysis of the geometry of the scan-based and model-based airways has verified their consistency with measures from previous anatomic studies and has provided new anatomic data for the ovine bronchial tree. With the use of an identical parameter set, the volume-filling algorithm has produced airway trees with branching asymmetry appropriate for the human and ovine lung, demonstrating the dependence of the method on the shape of the lung or lobe volume. The modeling approach that has been developed can be applied to any level of detail of the airway tree and into any volume shape for the lung; hence it can be used directly for different individuals or animals and for any number of scan-based airways. The resulting models are subject-specific computational meshes with anatomically consistent geometry, suitable for application in simulation studies.
Baudena, Mara; D'Andrea, Fabio; Provenzale, A.
2010-01-01
1. We discuss a simple implicit-space model for the competition of trees and grasses in an idealized savanna environment. The model represents patch occupancy dynamics within the habitat and introduces life stage structure in the tree population, namely adults and seedlings. A tree can be out-compet
iTree-Hydro: Snow hydrology update for the urban forest hydrology model
Yang Yang; Theodore A. Endreny; David J. Nowak
2011-01-01
This article presents snow hydrology updates made to iTree-Hydro, previously called the Urban Forest EffectsâHydrology model. iTree-Hydro Version 1 was a warm climate model developed by the USDA Forest Service to provide a process-based planning tool with robust water quantity and quality predictions given data limitations common to most urban areas. Cold climate...
Parametric Generation of Polygonal Tree Models for Rendering on Tessellation-Enabled Hardware
Nystad, Jørgen
2010-01-01
The main contribution of this thesis is a parametric method for generation of single-mesh polygonal tree models that follow natural rules as indicated by da Vinci in his notebooks. Following these rules allow for a relatively simple scheme of connecting branches to parent branches. Proper branch connection is a requirement for gaining the benefits of subdivision. Techniques for proper texture coordinate generation and subdivision are also explored.The result is a tree model generation scheme ...
A Tree-based Approach for Modelling Interception Loss From Evergreen Oak Mediterranean Savannas
Pereira, Fernando L.; Gash, John H. C.; David, Jorge S.; David, Teresa S.; Monteiro, Paulo R.; Valente, Fernanda
2010-05-01
Evaporation of rainfall intercepted by tree canopies is usually an important part of the overall water balance of forested catchments and there have been many studies dedicated to measuring and modelling rainfall interception loss. These studies have mainly been conducted in dense forests; there have been few studies on the very sparse forests which are common in dry and semi-arid areas. Water resources are scarce in these areas making sparse forests particularly important. Methods for modelling interception loss are thus required to support sustainable water management in those areas. In very sparse forests, trees occur as widely spaced individuals rather than as a continuous forest canopy. We therefore suggest that interception loss for this vegetation type can be more adequately modelled if the overall forest evaporation is derived by scaling up the evaporation from individual trees. The evaporation rate for a single tree can be estimated using a simple Dalton-type diffusion equation for water vapour as long as its surface temperature is known. From theory, this temperature is shown to be dependent upon the available energy and windspeed. However, the surface temperature of a fully saturated tree crown, under rainy conditions, should approach the wet bulb temperature as the radiative energy input to the tree reduces to zero. This was experimentally confirmed from measurements of the radiation balance and surface temperature of an isolated tree crown. Thus, evaporation of intercepted rainfall can be estimated using an equation which only requires knowledge of the air dry and wet bulb temperatures and of the bulk tree-crown aerodynamic conductance. This was taken as the basis of a new approach for modelling interception loss from savanna-type woodland, i.e. by combining the Dalton-type equation with the Gash's analytical model to estimate interception loss from isolated trees. This modelling approach was tested using data from two Mediterranean savanna-type oak
Accounting for Epistemic Uncertainty in PSHA: Logic Tree and Ensemble Model
Taroni, M.; Marzocchi, W.; Selva, J.
2014-12-01
The logic tree scheme is the probabilistic framework that has been widely used in the last decades to take into account epistemic uncertainties in probabilistic seismic hazard analysis (PSHA). Notwithstanding the vital importance for PSHA to incorporate properly the epistemic uncertainties, we argue that the use of the logic tree in a PSHA context has conceptual and practical drawbacks. Despite some of these drawbacks have been reported in the past, a careful evaluation of their impact on PSHA is still lacking. This is the goal of the present work. In brief, we show that i) PSHA practice does not meet the assumptions that stand behind the logic tree scheme; ii) the output of a logic tree is often misinterpreted and/or misleading, e.g., the use of percentiles (median included) in a logic tree scheme raises theoretical difficulties from a probabilistic point of view; iii) in case the assumptions that stand behind a logic tree are actually met, this leads to several problems in testing any PSHA model. We suggest a different strategy - based on ensemble modeling - to account for epistemic uncertainties in a more proper probabilistic framework. Finally, we show that in many PSHA practical applications, the logic tree is de facto loosely applied to build sound ensemble models.
Comparing M5 Model Trees and Neural Networks for River Level Forecasting
Khan, S.; See, L.
2005-12-01
Artificial neural networks (ANNs) have been the subject of much research activity in hydrological modelling over the last decade yet this represents only one data-driven modelling approach from among a very rich set. M5 model trees are an example of a technique that has had little application in the hydrological domain yet the results are promising (Solomatine and Xue, 2004). They are a machine learning approach that combines regression trees and classification. The input space is partitioned into subsets based on entropy measures, and regression equations are then fit to these subsets. The advantages over ANNs are (a) their ability to provide knowledge in the form of a decision tree and (b) much faster training times. This has important implications for operational use as they are not black box models. In this study ANNs, M5 model trees and time series analysis have been used to develop models to predict river levels at a gauging station in the River Ouse catchment in Northern England. Two lead times have been used: t+6 and t+24 hours. The input data consisted of historical levels at the gauging stations, upstream level data and rainfall from five rain gauges across the catchment, determined by correlation with the output. The results of the study showed that the ANNs outperformed both the M5 model trees and time series approaches when considering global goodness-of-fit measures such as root mean squared error and coefficient of efficiency. However, the difference in performance between the ANNs and M5 model trees was not large, e.g. 1 percent difference in coefficient of efficiency for t+6 hours. When considering the longer lead time of t+24 hours, the performance of the ANNs and M5 model trees almost converged. The M5 model tree, however, also provides the rules of operation. The first partition for both the t+6 and t+24 hour models was determined by the value of the river level at one of the upstream stations. The individual regression equations associated with
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....
Yu, Kailiang; Foster, Adrianna
2016-04-01
Past studies have largely focused on hydraulic redistribution (HR) in trees, shrubs, and grasses, and recognized its role in interspecies interactions. HR in plants that conduct crassulacean acid metabolism (CAM), however, remains poorly investigated, as does the effect of HR on transpiration in different vegetation associations (i.e., tree-grass, CAM-grass, and tree-CAM associations). We have developed a mechanistic model to investigate the net direction and magnitude of HR at the patch scale for tree-grass, CAM-grass, and tree-CAM associations at the growing season to yearly timescale. The modeling results show that deep-rooted CAM plants in CAM-grass associations could perform hydraulic lift at a higher rate than trees in tree-grass associations in a relatively wet environment, as explained by a significant increase in grass transpiration rate in the shallow soil layer, balancing a lower transpiration rate by CAM plants. By comparison, trees in tree-CAM associations may perform hydraulic descent at a higher rate than those in tree-grass associations in a dry environment. Model simulations also show that hydraulic lift increases the transpiration of shallow-rooted plants, while hydraulic descent increases that of deep-rooted plants. CAM plants transpire during the night and thus perform HR during the day. Based on these model simulations, we suggest that the ability of CAM plants to perform HR at a higher rate may have different effects on the surrounding plant community than those of plants with C3 or C4 photosynthetic pathways (i.e., diurnal transpiration).
A simple model of trees for unicellular maps
Chapuy, Guillaume; Fusy, Eric
2012-01-01
We consider unicellular maps, or polygon gluings, of fixed genus. A few years ago the first author gave a recursive bijection transforming unicellular maps into trees, explaining the presence of Catalan numbers in counting formulas for these objects. In this paper, we give another bijection that explicitly describes the "recursive part" of the first bijection. As a result we obtain a very simple description of unicellular maps as pairs made by a plane tree and a permutation-like structure. All the previously known formulas follow as an immediate corollary or easy exercise, thus giving a bijective proof for each of them, in a unified way. For some of these formulas, this is the first bijective proof, e.g. the Harer-Zagier recurrence formula, or the Lehman-Walsh/Goupil-Schaeffer formulas. Thanks to previous work of the second author this also leads us to a new expression for Stanley character polynomials, which evaluate irreducible characters of the symmetric group.
Besselink, R.; Stawski, T. M.; Van Driessche, A. E. S.; Benning, L. G.
2016-12-01
Densely packed surface fractal aggregates form in systems with high local volume fractions of particles with very short diffusion lengths, which effectively means that particles have little space to move. However, there are no prior mathematical models, which would describe scattering from such surface fractal aggregates and which would allow the subdivision between inter- and intraparticle interferences of such aggregates. Here, we show that by including a form factor function of the primary particles building the aggregate, a finite size of the surface fractal interfacial sub-surfaces can be derived from a structure factor term. This formalism allows us to define both a finite specific surface area for fractal aggregates and the fraction of particle interfacial sub-surfaces at the perimeter of an aggregate. The derived surface fractal model is validated by comparing it with an ab initio approach that involves the generation of a "brick-in-a-wall" von Koch type contour fractals. Moreover, we show that this approach explains observed scattering intensities from in situ experiments that followed gypsum (CaSO4 ṡ 2H2O) precipitation from highly supersaturated solutions. Our model of densely packed "brick-in-a-wall" surface fractal aggregates may well be the key precursor step in the formation of several types of mosaic- and meso-crystals.
Fractal Characteristics and Prediction of Ti-15-3 Alloy Recrystallized Microstructure
Institute of Scientific and Technical Information of China (English)
Ping LI; Qing ZHANG; Kemin XUE
2008-01-01
Grain shape of the hot deforming alloy is an important index to character the microstructure and performance of material.The fractal theory was applied to analyze the recrystallized microstructure of Ti-15-3 alloy after hot deformation and solution treatment.The fractal dimensions of recrystallized grains were calculated by slit island method.The influence of processing parameters on fractal dimension and grain size was studied.It has been shown that the shapes of recrystallized grain boundaries are self-similar,and the fractal dimension varies from 1 to 2.With increasing deformation degree and strain rate or decreasing deformation temperature,the fractal dimension of grain boundaries increased and the grain size decreased.So the fractal dimension could characterize the grain shape and size.A neural network model was trained to predict the fractal dimension of recrystallized microstructure and the result is in excellent agreement with the experimental data.