Transient from crystallization to fractal growth observed in both boar bile and SnI sub 2 vapour
Zhang Ji Zhong; Xie An Jian
2003-01-01
A visual transient of the growth mechanism from crystallization to fractal growth was observed clearly in a drop of boar bile. The growing crystals were replaced by treelike fractal structures during solidification of the sample. It is fascinating to compare the transient with the result observed in SnI sub 2 vapour. They were completely identical, and revealed that under certain conditions a linear growth could be transferred spontaneously into nonlinear growth. It may be possible to consider the transient as a 'bridge' between linear and nonlinear growth, and to develop a quantitative expression of transient dynamics.
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....
Crossover from Nonequilibrium Fractal Growth to Equilibrium Compact Growth
DEFF Research Database (Denmark)
Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.
1988-01-01
Solidification controlled by vacancy diffusion is studied by Monte Carlo simulations of a two-dimensional Ising model defined by a Hamiltonian which models a thermally driven fluid-solid phase transition. The nonequilibrium morphology of the growing solid is studied as a function of time as the s...... as the system relaxes into equilibrium described by a temperature. At low temperatures the model exhibits fractal growth at early times and crossover to compact solidification as equilibrium is approached....
Focusing behavior of the fractal vector optical fields designed by fractal lattice growth model.
Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian
2018-01-22
We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.
An extended fractal growth regime in the diffusion limited aggregation including edge diffusion
Directory of Open Access Journals (Sweden)
Aritra Ghosh
2016-01-01
Full Text Available We have investigated on-lattice diffusion limited aggregation (DLA involving edge diffusion and compared the results with the standard DLA model. For both cases, we observe the existence of a crossover from the fractal to the compact regime as a function of sticking coefficient. However, our modified DLA model including edge diffusion shows an extended fractal growth regime like an earlier theoretical result using realistic growth models and physical parameters [Zhang et al., Phys. Rev. Lett. 73 (1994 1829]. While the results of Zhang et al. showed the existence of the extended fractal growth regime only on triangular but not on square lattices, we find its existence on the square lattice. There is experimental evidence of this growth regime on a square lattice. The standard DLA model cannot characterize fractal morphology as the fractal dimension (Hausdorff dimension, DH is insensitive to morphology. It also predicts DH = DP (the perimeter dimension. For the usual fractal structures, observed in growth experiments on surfaces, the perimeter dimension can differ significantly (DH ≠ DP depending on the morphology. Our modified DLA model shows minor sensitivity to this difference.
Fractal dimension evolution and spatial replacement dynamics of urban growth
International Nuclear Information System (INIS)
Chen Yanguang
2012-01-01
Highlights: ► The fractal dimension growth can be modeled by Boltzmann’s equation. ► Boltzmann’s model suggests urban spatial replacement dynamics. ► If the rate of urban growth is too high, periodic oscillations or chaos will arise. ► Chaos is associated with fractals by the fractal dimension evolution model. ► The fractal dimension of urban form implies the space-filling ratio of a city. - Abstract: This paper presents a new perspective of looking at the relation between fractals and chaos by means of cities. Especially, a principle of space filling and spatial replacement is proposed to interpret the fractal dimension of urban form. The fractal dimension evolution of urban growth can be empirically modeled with Boltzmann’s equation. For the normalized data, Boltzmann’s equation is just equivalent to the logistic function. The logistic equation can be transformed into the well-known 1-dimensional logistic map, which is based on a 2-dimensional map suggesting spatial replacement dynamics of city development. The 2-dimensional recurrence relations can be employed to generate the nonlinear dynamical behaviors such as bifurcation and chaos. A discovery is thus made in this article that, for the fractal dimension growth following the logistic curve, the normalized dimension value is the ratio of space filling. If the rate of spatial replacement (urban growth) is too high, the periodic oscillations and chaos will arise. The spatial replacement dynamics can be extended to general replacement dynamics, and bifurcation and chaos mirror a process of complex replacement.
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...
Theoretical study of fractal growth and stability on surface
DEFF Research Database (Denmark)
Dick, Veronika V.; Solov'yov, Ilia; Solov'yov, Andrey V.
2009-01-01
We perform a theoretical study of the fractal growing process on surface by using the deposition, diffusion, aggregation method. We present a detailed analysis of the post-growth processes occurring in a nanofractal on surface. For this study we developed a method which describes the internal...... dynamics of particles in a fractal and accounts for their diffusion and detachment. We demonstrate that these kinetic processes are responsible for the formation of the final shape of the islands on surface after the post-growth relaxation....
DEFF Research Database (Denmark)
Sørensen, Erik Schwartz; Fogedby, Hans C.; Mouritsen, Ole G.
1989-01-01
temperature are studied as functions of temperature, time, and concentration. At zero temperature and high dilution, the growing solid is found to have a fractal morphology and the effective fractal exponent D varies with concentration and ratio of time scales of the two dynamical processes. The mechanism...... responsible for forming the fractal solid is shown to be a buildup of a locally high vacancy concentration in the active growth zone. The growth-probability measure of the fractals is analyzed in terms of multifractality by calculating the f(α) spectrum. It is shown that the basic ideas of relating...... probability measures of static fractal objects to the growth-probability distribution during formation of the fractal apply to the present model. The f(α) spectrum is found to be in the universality class of diffusion-limited aggregation. At finite temperatures, the fractal solid domains become metastable...
Fractality and growth of He bubbles in metals
Kajita, Shin; Ito, Atsushi M.; Ohno, Noriyasu
2017-08-01
Pinholes are formed on surfaces of metals by the exposure to helium plasmas, and they are regarded as the initial process of the growth of fuzzy nanostructures. In this study, number density of the pinholes is investigated in detail from the scanning electron microscope (SEM) micrographs of tungsten and tantalum exposed to the helium plasmas. A power law relation was identified between the number density and the size of pinholes. From the slope and the region where the power law was satisfied, the fractal dimension D and smin, which characterize the SEM images, are deduced. Parametric dependences and material dependence of D and smin are revealed. To explain the fractality, simple Monte-Carlo simulations including random walks of He atoms and absorption on bubble was introduced. It is shown that the initial position of the random walk is one of the key factors to deduce the fractality. The results indicated that new nucleations of bubbles are necessary to reproduce the number-density distribution of bubbles.
International Nuclear Information System (INIS)
Dickau, Jonathan J.
2009-01-01
The use of fractals and fractal-like forms to describe or model the universe has had a long and varied history, which begins long before the word fractal was actually coined. Since the introduction of mathematical rigor to the subject of fractals, by Mandelbrot and others, there have been numerous cosmological theories and analyses of astronomical observations which suggest that the universe exhibits fractality or is by nature fractal. In recent years, the term fractal cosmology has come into usage, as a description for those theories and methods of analysis whereby a fractal nature of the cosmos is shown.
Fractal pattern growth simulation in electrodeposition and study of the shifting of center of mass
International Nuclear Information System (INIS)
Shaikh, Yusuf H.; Khan, A.R.; Pathan, J.M.; Patil, Aruna; Behere, S.H.
2009-01-01
We presented simulation of fractal pattern in electrodeposition (Diffusion limited aggregation) using concept of off lattice walk. It is seen that the growth patterns are based on a parameter called 'bias'. This parameter 'bias' controls the growth of patterns similar to that of electric field in electrodeposition technique. In present study the fractal patterns are grown for different values of 'bias'. Dendritic patterns grown at lower value of 'bias' comprises open structure and show limited branching. As the bias is increased the growth tends to be dense and show more crowded branching. Box counting was implemented to calculate fractal dimension. The structural and textural complexities and are compared with the experimental observations. It was also noted that in the evolution of DLA patterns, the center of mass of the growth is shifted slightly. We tracked the position of the center of mass of simulated electro deposits under different electric field conditions. The center of mass exhibit random walk like patterns and it wanders around the origin or the starting point of the growth.
Electric field driven fractal growth dynamics in polymeric medium
Energy Technology Data Exchange (ETDEWEB)
Dawar, Anit; Chandra, Amita, E-mail: achandra@physics.du.ac.in
2014-08-14
This paper reports the extension of earlier work (Dawar and Chandra, 2012) [27] by including the influence of low values of electric field on diffusion limited aggregation (DLA) patterns in polymer electrolyte composites. Subsequently, specified cut-off value of voltage has been determined. Below the cut-off voltage, the growth becomes direction independent (i.e., random) and gives rise to ramified DLA patterns while above the cut-off, growth is governed by diffusion, convection and migration. These three terms (i.e., diffusion, convection and migration) lead to structural transition that varies from dense branched morphology (DBM) to chain-like growth to dendritic growth, i.e., from high field region (A) to constant field region (B) to low field region (C), respectively. The paper further explores the growth under different kinds of electrode geometries (circular and square electrode geometry). A qualitative explanation for fractal growth phenomena at applied voltage based on Nernst–Planck equation has been proposed. - Highlights: • The paper is an extension of earlier work [Phys. Lett. A 376 (2012) 3604] on effect of electric field on DLA. • Threshold value of electric field has been determined. • Below the threshold, growth is random. • Above the threshold, the growth is governed by diffusion, migration and convection. • Different kinds of electrode geometries have been used to simulate the growth.
Electric field driven fractal growth dynamics in polymeric medium
International Nuclear Information System (INIS)
Dawar, Anit; Chandra, Amita
2014-01-01
This paper reports the extension of earlier work (Dawar and Chandra, 2012) [27] by including the influence of low values of electric field on diffusion limited aggregation (DLA) patterns in polymer electrolyte composites. Subsequently, specified cut-off value of voltage has been determined. Below the cut-off voltage, the growth becomes direction independent (i.e., random) and gives rise to ramified DLA patterns while above the cut-off, growth is governed by diffusion, convection and migration. These three terms (i.e., diffusion, convection and migration) lead to structural transition that varies from dense branched morphology (DBM) to chain-like growth to dendritic growth, i.e., from high field region (A) to constant field region (B) to low field region (C), respectively. The paper further explores the growth under different kinds of electrode geometries (circular and square electrode geometry). A qualitative explanation for fractal growth phenomena at applied voltage based on Nernst–Planck equation has been proposed. - Highlights: • The paper is an extension of earlier work [Phys. Lett. A 376 (2012) 3604] on effect of electric field on DLA. • Threshold value of electric field has been determined. • Below the threshold, growth is random. • Above the threshold, the growth is governed by diffusion, migration and convection. • Different kinds of electrode geometries have been used to simulate the growth
Fractal analysis of rainfall occurrence observed in the synoptic ...
African Journals Online (AJOL)
Fractal analysis is important for characterizing and modeling rainfall's space-time variations in hydrology. The purpose of this study consists on determining, in a mono-fractal framework, the scale invariance of rainfall series in Benin synopticstations located in two main geographical area: Cotonou, Bohicon , Savè in a sub ...
Formation of Non-symmetric Fractals During the First Stage of Pre-planetesimal Dust Growth
Kempf, S.; Blum, J.; Wurm, G.
It is a generally accepted view that the genesis of a planetary system coincide s with the formation of sun-like young stellar objects surrounded by gaseous disc s. The building blocks of the planetesimals are micron-sized solid particles (the so-called dust) embedded in the gas of the disc. The relevant process for formi ng larger aggregates is the growth due to collisional sticking. For particles to c ollide and stick, a relative velocity component between the grains must be present. In the onset of dust growth, Brownian motion dominates other relative-velocity sources . However, numerically determined time scales of the pure Brownian dust growth are much too large for explaining the formation of planets within the lifetime of a proto-planetary di sc. In order to verify the validity of the theoretical models, the Cosmic Dust Aggr egation Experiment CODAG was developed. It allows to observe the growth of micron-sized dust analogs under astrophysical realistic conditions. Surprisingly, the experi ments showed that at least in the onset of the dust growth needle-like fractal aggreg ates rather than symmetric fractals are formed. Here we discuss the implication of this experimental finding for the pre-planetesimal growth models.
Growth of fractal structures in flames with silicon admixture
Smirnov, B. M.; Dutka, M.; van Essen, V. M.; Gersen, S.; Visser, P.; Vainchtein, D.; De Hosson, J. Th. M.; Levinsky, H. B.; Mokhov, A. V.
Transmission electron microscopy (TEM) measurements and theoretical analysis are combined to construct the physical picture of formation of SiO2 fractal aggregates in a methane/hexamethyldisiloxane/air atmospheric pressure flame. The formation of SiO2 fractal aggregates is described as a multistage
Fractal based observables to probe jet substructure of quarks and gluons
Davighi, Joe; Harris, Philip
2018-04-01
New jet observables are defined which characterize both fractal and scale-dependent contributions to the distribution of hadrons in a jet. These infrared safe observables, named Extended Fractal Observables (EFOs), have been applied to quark-gluon discrimination to demonstrate their potential utility. The EFOs are found to be individually discriminating and only weakly correlated to variables used in existing discriminators. Consequently, their inclusion improves discriminator performance, as here demonstrated with particle level simulation from the parton shower.
Directory of Open Access Journals (Sweden)
Bogdanov Ana
2007-01-01
Full Text Available Urban forms and processes can be observed as fractal structures since in their seemingly chaotic development and complexity it can be noticed an internal order and regularity, which could be quantified and described by the methods of fractal analysis. With determination of fractal dimension it is possible to quantify the level of irregularity, the complexity and hierarchy of the urban structures, as well as the level of urban transformations in various time intersections. The fractal geometry method has been used in analyses of spatial distribution of population, networks and utilities because it corresponds more than deterministic methods to the nature of urban settlements as open, non-linear and dynamic systems. In that sense, fractal geometry becomes the means to grasp a complex morphological urban structure of urban settlements in general, the interrelationships between the inner spatial elements, and to predict future development possibilities. Moreover on the basis of urban pattern analysis by means of fractal geometry, it is possible to evaluate the growth and development process and to perform a comparative analysis of development in spatially and temporarily different settlement settings. Having in view that complex urban fabric presumes tight connections and diversity, which is in contrast to sprawl and monotony which increasingly characterize urban growth and development, this paper is a contribution to research of potential for modern urban settlements to regain the spirit of spontaneity and human dimension through application of development models that are fractal geometry based.
Invited Article: Plasmonic growth of patterned metamaterials with fractal geometry
Directory of Open Access Journals (Sweden)
Nobuyuki Takeyasu
2016-08-01
Full Text Available Large-scale metallic three-dimensional (3D structures composed of sub-wavelength fine details, called metamaterials, have attracted optical scientists and materials scientists because of their unconventional and extraordinary optical properties that are not seen in nature. However, existing nano-fabrication technologies including two-photon fabrication, e-beam, focused ion-beam, and probe microscopy are not necessarily suitable for fabricating such large-scale 3D metallic nanostructures. In this article, we propose a different method of fabricating metamaterials, which is based on a bottom-up approach. We mimicked the generation of wood forest under the sunlight and rain in nature. In our method, a silver nano-forest is grown from the silver seeds (nanoparticles placed on the glass substrate in silver-ion solution. The metallic nano-forest is formed only in the area where ultraviolet light is illuminated. The local temperature increases at nano-seeds and tips of nano-trees and their branches due to the plasmonic heating as a result of UV light excitation of localized mode of surface plasmon polaritons. We have made experiments of growth of metallic nano-forest patterned by the light distribution. The experimental results show a beautiful nano-forest made of silver with self-similarity. Fractal dimension and spectral response of the grown structure are discussed. The structures exhibit a broad spectral response from ultraviolet to infrared, which was used for surface-enhanced Raman detection of molecules.
International Nuclear Information System (INIS)
Huang, F.; Peng, R. D.; Liu, Y. H.; Chen, Z. Y.; Ye, M. F.; Wang, L.
2012-01-01
Fractal dust grains of different shapes are observed in a radially confined magnetized radio frequency plasma. The fractal dimensions of the dust structures in two-dimensional (2D) horizontal dust layers are calculated, and their evolution in the dust growth process is investigated. It is found that as the dust grains grow the fractal dimension of the dust structure decreases. In addition, the fractal dimension of the center region is larger than that of the entire region in the 2D dust layer. In the initial growth stage, the small dust particulates at a high number density in a 2D layer tend to fill space as a normal surface with fractal dimension D = 2. The mechanism of the formation of fractal dust grains is discussed.
International Nuclear Information System (INIS)
Jo, Junghyo; Periwal, Vipul; Hörnblad, Andreas; Ahlgren, Ulf; Kilimnik, German; Hara, Manami
2013-01-01
The islets of Langerhans, responsible for controlling blood glucose levels, are dispersed within the pancreas. A universal power law governing the fractal spatial distribution of islets in two-dimensional pancreatic sections has been reported. However, the fractal geometry in the actual three-dimensional pancreas volume, and the developmental process that gives rise to such a self-similar structure, has not been investigated. Here, we examined the three-dimensional spatial distribution of islets in intact mouse pancreata using optical projection tomography and found a power law with a fractal dimension of 2.1. Furthermore, based on two-dimensional pancreatic sections of human autopsies, we found that the distribution of human islets also follows a universal power law with a fractal dimension of 1.5 in adult pancreata, which agrees with the value previously reported in smaller mammalian pancreas sections. Finally, we developed a self-avoiding growth model for the development of the islet distribution and found that the fractal nature of the spatial islet distribution may be associated with the self-avoidance in the branching process of vascularization in the pancreas. (paper)
Self-affine fractal growth front of Aspergillus oryzae
Matsuura, Shu; Miyazima, Sasuke
1992-12-01
Aspergillus oryzae have been grown in various environmental conditions and analyzed from the viewpoint of self-affinity. The growth behavior can be described by the Eden model in favorable conditions, and by DLA in unfavorable conditions.
International Nuclear Information System (INIS)
Ul'yanov, A S; Lyapina, A M; Ulianova, O V; Fedorova, V A; Uianov, S S
2011-01-01
Specific statistical characteristics of biospeckles, emerging under the diffraction of coherent beams on the bacterial colonies, are studied. The dependence of the fractal dimensions of biospeckles on the conditions of both illumination and growth of the colonies is studied theoretically and experimentally. Particular attention is paid to the fractal properties of biospeckles, emerging under the scattering of light by the colonies of the vaccinal strain of the plague microbe. The possibility in principle to classify the colonies of Yersinia pestis EV NIIEG using the fractal dimension analysis is demonstrated. (optical technologies in biophysics and medicine)
A principle of fractal-stochastic dualism and Gompertzian dynamics of growth and self-organization.
Waliszewski, Przemyslaw
2005-10-01
The emergence of Gompertzian dynamics at the macroscopic, tissue level during growth and self-organization is determined by the existence of fractal-stochastic dualism at the microscopic level of supramolecular, cellular system. On one hand, Gompertzian dynamics results from the complex coupling of at least two antagonistic, stochastic processes at the molecular cellular level. It is shown that the Gompertz function is a probability function, its derivative is a probability density function, and the Gompertzian distribution of probability is of non-Gaussian type. On the other hand, the Gompertz function is a contraction mapping and defines fractal dynamics in time-space; a prerequisite condition for the coupling of processes. Furthermore, the Gompertz function is a solution of the operator differential equation with the Morse-like anharmonic potential. This relationship indicates that distribution of intrasystemic forces is both non-linear and asymmetric. The anharmonic potential is a measure of the intrasystemic interactions. It attains a point of the minimum (U(0), t(0)) along with a change of both complexity and connectivity during growth and self-organization. It can also be modified by certain factors, such as retinoids.
Fractal Structure and Entropy Production within the Central Nervous System
Directory of Open Access Journals (Sweden)
Andrew J. E. Seely
2014-08-01
Full Text Available Our goal is to explore the relationship between two traditionally unrelated concepts, fractal structure and entropy production, evaluating both within the central nervous system (CNS. Fractals are temporal or spatial structures with self-similarity across scales of measurement; whereas entropy production represents the necessary exportation of entropy to our environment that comes with metabolism and life. Fractals may be measured by their fractal dimension; and human entropy production may be estimated by oxygen and glucose metabolism. In this paper, we observe fractal structures ubiquitously present in the CNS, and explore a hypothetical and unexplored link between fractal structure and entropy production, as measured by oxygen and glucose metabolism. Rapid increase in both fractal structures and metabolism occur with childhood and adolescent growth, followed by slow decrease during aging. Concomitant increases and decreases in fractal structure and metabolism occur with cancer vs. Alzheimer’s and multiple sclerosis, respectively. In addition to fractals being related to entropy production, we hypothesize that the emergence of fractal structures spontaneously occurs because a fractal is more efficient at dissipating energy gradients, thus maximizing entropy production. Experimental evaluation and further understanding of limitations and necessary conditions are indicated to address broad scientific and clinical implications of this work.
Categorization of fractal plants
International Nuclear Information System (INIS)
Chandra, Munesh; Rani, Mamta
2009-01-01
Fractals in nature are always a result of some growth process. The language of fractals which has been created specifically for the description of natural growth process is called L-systems. Recently, superior iterations (essentially, investigated by Mann [Mann WR. Mean value methods in iteration. Proc Am Math Soc 1953;4:506-10 [MR0054846 (14,988f)
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)
Directory of Open Access Journals (Sweden)
Amato P
2008-01-01
Full Text Available Abstract Self-similar patterns are frequently observed in Nature. Their reproduction is possible on a length scale 102–105 nm with lithographic methods, but seems impossible on the nanometer length scale. It is shown that this goal may be achieved via a multiplicative variant of the multi-spacer patterning technology, in this way permitting the controlled preparation of fractal surfaces.
Mombrú, Dominique; Romero, Mariano; Faccio, Ricardo; Mombrú, Alvaro W.
2017-12-01
Here, we report a novel strategy for the preparation of TiO2 quantum dots fillers prepared from alkoxide precursor via in situ water vapor flow diffusion into poly(N-vinylcarbazole) host. A detailed characterization by means of infrared and Raman spectroscopy, X-ray powder diffraction, small angle X-ray scattering and differential scanning calorimetry is reported. The growth mechanism of both crystallites and particles was mostly governed by the classical coarsening reaction limited growth and the polymer host showed no detectable chemical modifications at the interface or active participation in the growing process. The main relevance of our strategy respect to the typical sol-gel growth in solution is the possibility of the interruption of the reaction by simple stopping the water vapor flow diffusion into the polymer host thus achieving good control in the nanoparticles size. The thermal stability and fractal behavior of our nanocomposites were also studied by differential scanning calorimetry and in situ small angle X-ray scattering versus temperature. Strong correlations between modifications in the fractal behavior and glass transition or fusion processes were observed for these nanocomposites.
Betancourt-Mar, J. A.; Llanos-Pérez, J. A.; Cocho, G.; Mansilla, R.; Martin, R. R.; Montero, S.; Nieto-Villar, J. M.
2017-05-01
By the use of thermodynamics formalism of irreversible processes, complex systems theory and systems biology, it is derived a relationship between the production of entropy per unit time, the fractal dimension and the tumor growth rate for human tumors cells. The thermodynamics framework developed demonstrates that, the dissipation function is a Landau potential and also the Lyapunov function of the dynamical behavior of tumor growth, which indicate the directional character, stability and robustness of the phenomenon. The entropy production rate may be used as a quantitative index of the metastatic potential of tumors. The current theoretical framework will hopefully provide a better understanding of cancer and contribute to improvements in cancer treatment.
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....
Esteban, Francisco J; Padilla, Nelly; Sanz-Cortés, Magdalena; de Miras, Juan Ruiz; Bargalló, Núria; Villoslada, Pablo; Gratacós, Eduard
2010-12-01
In the search for a useful parameter to detect and quantify subtle brain abnormalities in infants with intrauterine growth restriction (IUGR), we hypothesised that the analysis of the structural complexity of grey matter (GM) and white matter (WM) using the fractal dimension (FD), a measurement of the topological complexity of an object, could be established as a useful tool for quantitative studies of infant brain morphology. We studied a sample of 18 singleton IUGR premature infants, (12.72 months corrected age (CA), range: 12 months-14 months), 15 preterm infants matched one-to-one for gestational age (GA) at delivery (12.6 months; range: 12 months-14 months), and 15 neonates born at term (12.4 months; range: 11 months-14 months). The neurodevelopmental outcome was assessed in all subjects at 18 months CA according to the Bayley Scale for Infant and Toddler Development - Third edition (BSID-III). For MRI acquisition and processing, the infants were scanned at 12 months CA, in a TIM TRIO 3T scanner, sleeping naturally. Images were pre-processed using the SPM5 toolbox, the GM and WM segmented under the VBM5 toolbox, and the box-counting method was applied for FD calculation of normal and skeletonized segmented images. The results showed a significant decrease of the FD of the brain GM and WM in the IUGR group when compared to the preterm or at-term controls. We also identified a significant linear tendency of both GM and WM FD from IUGR to preterm and term groups. Finally, multiple linear analyses between the FD of the GM or WM and the neurodevelopmental scales showed a significant regression of the language and motor scales with the FD of the GM. In conclusion, a decreased FD of the GM and WM in IUGR infants could be a sensitive indicator for the investigation of structural brain abnormalities in the IUGR population at 12 months of age, which can also be related to functional disorders. Copyright © 2010 Elsevier Inc. All rights reserved.
Fractal characteristics of an asphaltene deposited heterogeneous surface
International Nuclear Information System (INIS)
Amin, J. Sayyad; Ayatollahi, Sh.; Alamdari, A.
2009-01-01
Several methods have been employed in recent years to investigate homogeneous surface topography based on image analysis, such as AFM (atomic force microscopy) and SEM (scanning electron microscopy). Fractal analysis of the images provides fractal dimension of the surface which is used as one of the most common surface indices. Surface topography has generally been considered to be mono-fractal. On the other hand, precipitation of organic materials on a rough surface and its irregular growth result in morphology alteration and converts a homogeneous surface to a heterogeneous one. In this case a mono-fractal description of the surface does not completely describe the nature of the altered surface. This work aims to investigate the topography alteration of a glass surface as a result of asphaltene precipitation and its growth at various pressures using a bi-fractal approach. The experimental results of the deposited surfaces were clearly indicating two regions of micro- and macro-asperities namely, surface types I and II, respectively. The fractal plots were indicative of bi-fractal behavior and for each surface type one fractal dimension was calculated. The topography information of the surfaces was obtained by two image analyses, AFM and SEM imaging techniques. Results of the bi-fractal analysis demonstrated that topography alteration in surface type II (macro-asperities) is more evident than that in surface type I (micro-asperities). Compared to surface type II, a better correlation was observed between the fractal dimensions inferred from the AFM images (D A ) and those of the SEM images (D S ) in surface type I.
Saw, Vee-Liem; Chew, Lock Yue
2013-01-01
We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line ...
Energy Technology Data Exchange (ETDEWEB)
Xu, Mengjia; Xu, Jijin, E-mail: xujijin_1979@sjtu.edu.cn; Lu, Hao; Chen, Jieshi; Chen, Junmei; Wei, Xiao
2015-12-30
Graphical abstract: - Highlights: • Statistical and fractal analysis is applied to study the creep fracture surface. • The tensile residual stresses promote the initiation of creep crack. • The fractal dimension of a mixed mode fracture surface shows a wavy variation. • The fractal dimension increases with increasing intergranular fracture percentage. • Height coordinates of intergranular fracture surface fit Gaussian distribution. - Abstract: In order to clarify creep crack growth behavior in 2.25Cr–1.6W steel incorporating residual stresses, creep crack tests were carried out on the tension creep specimens, in which the residual stresses were generated by local remelting and cooling. Residual stresses in the specimens were measured using Synchrotron X-ray diffraction techniques. The fracture surface of the creep specimen was analyzed using statistical methods and fractal analysis. The relation between fractal dimension of the fracture surface and fracture mode of the creep specimen was discussed. Due to different fracture mechanisms, the probability density functions of the height coordinates vary with the intergranular crack percentage. Good fitting was found between Gaussian distribution and the probability function of height coordinates of the high percentage intergranular crack surface.
International Nuclear Information System (INIS)
Xu, Mengjia; Xu, Jijin; Lu, Hao; Chen, Jieshi; Chen, Junmei; Wei, Xiao
2015-01-01
Graphical abstract: - Highlights: • Statistical and fractal analysis is applied to study the creep fracture surface. • The tensile residual stresses promote the initiation of creep crack. • The fractal dimension of a mixed mode fracture surface shows a wavy variation. • The fractal dimension increases with increasing intergranular fracture percentage. • Height coordinates of intergranular fracture surface fit Gaussian distribution. - Abstract: In order to clarify creep crack growth behavior in 2.25Cr–1.6W steel incorporating residual stresses, creep crack tests were carried out on the tension creep specimens, in which the residual stresses were generated by local remelting and cooling. Residual stresses in the specimens were measured using Synchrotron X-ray diffraction techniques. The fracture surface of the creep specimen was analyzed using statistical methods and fractal analysis. The relation between fractal dimension of the fracture surface and fracture mode of the creep specimen was discussed. Due to different fracture mechanisms, the probability density functions of the height coordinates vary with the intergranular crack percentage. Good fitting was found between Gaussian distribution and the probability function of height coordinates of the high percentage intergranular crack surface.
Dendritic design as an archetype for growth patterns in Nature: fractal and constructal views
Directory of Open Access Journals (Sweden)
Antonio F. Miguel
2014-02-01
Full Text Available The occurrence of configuration (design, shape, structure, rhythm is a universal phenomenon that occurs in every flow system. Dendritic configuration (or tree-shaped configurations is ubiquitous in nature and likely to arise in both animate and inanimate flow systems. Why is it so important? Is there a principle from which this configuration can be deduced? In this review paper we show that these systems own two of the most important properties of fractals that are self-similarity and scaling. Their configuration do not develop by chance. It´s occurrence is a universal phenomenon of physics covered by a principle. Here we also show that the emergence of dendritic configuration in flow systems constitutes a basic supportive flow path along which order need to persist is propagated.
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
Fractal analysis of Xylella fastidiosa biofilm formation
Moreau, A. L. D.; Lorite, G. S.; Rodrigues, C. M.; Souza, A. A.; Cotta, M. A.
2009-07-01
We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73±0.06 and 2.68±0.06, respectively, while in the maturation stage, Df=2.57±0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.
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
Contour fractal analysis of grains
Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB
2017-06-01
Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.
An enhanced fractal image denoising algorithm
International Nuclear Information System (INIS)
Lu Jian; Ye Zhongxing; Zou Yuru; Ye Ruisong
2008-01-01
In recent years, there has been a significant development in image denoising using fractal-based method. This paper presents an enhanced fractal predictive denoising algorithm for denoising the images corrupted by an additive white Gaussian noise (AWGN) by using quadratic gray-level function. Meanwhile, a quantization method for the fractal gray-level coefficients of the quadratic function is proposed to strictly guarantee the contractivity requirement of the enhanced fractal coding, and in terms of the quality of the fractal representation measured by PSNR, the enhanced fractal image coding using quadratic gray-level function generally performs better than the standard fractal coding using linear gray-level function. Based on this enhanced fractal coding, the enhanced fractal image denoising is implemented by estimating the fractal gray-level coefficients of the quadratic function of the noiseless image from its noisy observation. Experimental results show that, compared with other standard fractal-based image denoising schemes using linear gray-level function, the enhanced fractal denoising algorithm can improve the quality of the restored image efficiently
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
Study both films structure and fractal growth in the T-10 tokamak
International Nuclear Information System (INIS)
Khimchenko, L.N.; Budaev, V.P.; Guseva, M.I.; Kamneva, S.A.; Kolbasov, B.N.; Kuteev, B.V.; Martynenko, Yu.V.; Svechnikov, N.Yu.; Stankevich, V.G.; Loginov, B.A.; Romanov, P.B.
2005-01-01
In the paper results of films growth mechanism study, their internal structure are summarized. The mechanism leading to hydrogen capture effect on the first wall at over dusting stage is stated. Films internal structure have been studied with help of synchrotron radiation, electron paramagnetic resonance, IR reflection spectra, thermal gravimetric methods, spectroscopy in the vision spectrum range and UV vacuum range. Structure of the films surfaces have been examined with help of electron microscopy, probe scanning tunnel and atom-force microscopy, as well as miniature scanning tunnel microscope placed in the T-10 tokamak
Fractals: Giant impurity nonlinearities in optics of fractal clusters
International Nuclear Information System (INIS)
Butenko, A.V.; Shalaev, V.M.; Stockman, M.I.
1988-01-01
A theory of nonlinear optical properties of fractals is developed. Giant enhancement of optical susceptibilities is predicted for impurities bound to a fractal. This enhancement occurs if the exciting radiation frequency lies within the absorption band of the fractal. The giant optical nonlinearities are due to existence of high local electric fields in the sites of impurity locations. Such fields are due to the inhomogeneously broadened character of a fractal spectrum, i.e. partial conservation of individuality of fractal-forming particles (monomers). The field enhancement is proportional to the Q-factor of the resonance of a monomer. The effects of coherent anti-Stokes Raman scattering (CARS) and phase conjugation (PC) of light waves are enhanced to a much greater degree than generation of higher harmonics. In a general case the susceptibility of a higher-order is enhanced in the maximum way if the process includes ''subtraction'' of photons (at least one of the strong field frequencies enters the susceptibility with the minus sign). Alternatively, enhancement for the highest-order harmonic generation (when all the photons are ''accumulated'') is minimal. The predicted phenomena bear information on spectral properties of both impurity molecules and a fractal. In particular, in the CARS spectra a narrow (with the natural width) resonant structure, which is proper to an isolated monomer of a fractal, is predicted to be observed. (orig.)
Fractal analysis of sulphidic mineral
Directory of Open Access Journals (Sweden)
Miklúová Viera
2002-03-01
fractal dimensions of fine particles distribution were not observed.
Order-fractal transitions in abstract paintings
Energy Technology Data Exchange (ETDEWEB)
Calleja, E.M. de la, E-mail: elsama79@gmail.com [Instituto de Física, Universidade Federal do Rio Grande do Sul, Caixa Postal 15051, 91501-970, Porto Alegre, RS (Brazil); Cervantes, F. [Department of Applied Physics, CINVESTAV-IPN, Carr. Antigua a Progreso km.6, Cordemex, C.P.97310, Mérida, Yucatán (Mexico); Calleja, J. de la [Department of Informatics, Universidad Politécnica de Puebla, 72640 (Mexico)
2016-08-15
In this study, we determined the degree of order for 22 Jackson Pollock paintings using the Hausdorff–Besicovitch fractal dimension. Based on the maximum value of each multi-fractal spectrum, the artworks were classified according to the year in which they were painted. It has been reported that Pollock’s paintings are fractal and that this feature was more evident in his later works. However, our results show that the fractal dimension of these paintings ranges among values close to two. We characterize this behavior as a fractal-order transition. Based on the study of disorder-order transition in physical systems, we interpreted the fractal-order transition via the dark paint strokes in Pollock’s paintings as structured lines that follow a power law measured by the fractal dimension. We determined self-similarity in specific paintings, thereby demonstrating an important dependence on the scale of observations. We also characterized the fractal spectrum for the painting entitled Teri’s Find. We obtained similar spectra for Teri’s Find and Number 5, thereby suggesting that the fractal dimension cannot be rejected completely as a quantitative parameter for authenticating these artworks. -- Highlights: •We determined the degree of order in Jackson Pollock paintings using the Hausdorff–Besicovitch dimension. •We detected a fractal-order transition from Pollock’s paintings between 1947 and 1951. •We suggest that Jackson Pollock could have painted Teri’s Find.
Fractal vector optical fields.
Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian
2016-07-15
We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.
Direct observation of nanowire growth and decomposition
DEFF Research Database (Denmark)
Rackauskas, Simas; Shandakov, Sergey D; Jiang, Hua
2017-01-01
knowledge, so far this has been only postulated, but never observed at the atomic level. By means of in situ environmental transmission electron microscopy we monitored and examined the atomic layer transformation at the conditions of the crystal growth and its decomposition using CuO nanowires selected...
Comparison of two fractal interpolation methods
Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo
2017-03-01
As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has
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...
FELICIA RAMONA BIRAU
2012-01-01
In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and...
Fractal description of fractures
International Nuclear Information System (INIS)
Lung, C.W.
1991-06-01
Recent studies on the fractal description of fractures are reviewed. Some problems on this subject are discussed. It seems hopeful to use the fractal dimension as a parameter for quantitative fractography and to apply fractal structures to the development of high toughness materials. (author). 28 refs, 7 figs
Directory of Open Access Journals (Sweden)
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.
Transport properties of electrons in fractal magnetic-barrier structures
Sun, Lifeng; Fang, Chao; Guo, Yong
2010-09-01
Quantum transport properties in fractal magnetically modulated structures are studied by the transfer-matrix method. It is found that the transmission spectra depend sensitively not only on the incident energy and the direction of the wave vector but also on the stage of the fractal structures. Resonance splitting, enhancement, and position shift of the resonance peaks under different magnetic modulation are observed at four different fractal stages, and the relationship between the conductance in the fractal structure and magnetic modulation is also revealed. The results indicate the spectra of the transmission can be considered as fingerprints for the fractal structures, which show the subtle correspondence between magnetic structures and transport behaviors.
Optical diffraction from fractals with a structural transition
International Nuclear Information System (INIS)
Perez Rodriguez, F.; Canessa, E.
1994-04-01
A macroscopic characterization of fractals showing up a structural transition from dense to multibranched growth is made using optical diffraction theory. Such fractals are generated via the numerical solution of the 2D Poisson and biharmonic equations and are compared to more 'regular' irreversible clusters such as diffusion limited and Laplacian aggregates. The optical diffraction method enables to identify a decrease of the fractal dimension above the structural point. (author). 19 refs, 6 figs
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
Pulse regime in formation of fractal fibers
Energy Technology Data Exchange (ETDEWEB)
Smirnov, B. M., E-mail: bmsmirnov@gmail.com [Joint Institute for High Temperatures (Russian Federation)
2016-11-15
The pulse regime of vaporization of a bulk metal located in a buffer gas is analyzed as a method of generation of metal atoms under the action of a plasma torch or a laser beam. Subsequently these atoms are transformed into solid nanoclusters, fractal aggregates and then into fractal fibers if the growth process proceeds in an external electric field. We are guided by metals in which transitions between s and d-electrons of their atoms are possible, since these metals are used as catalysts and filters in interaction with gas flows. The resistance of metal fractal structures to a gas flow is evaluated that allows one to find optimal parameters of a fractal structure for gas flow propagation through it. The thermal regime of interaction between a plasma pulse or a laser beam and a metal surface is analyzed. It is shown that the basic energy from an external source is consumed on a bulk metal heating, and the efficiency of atom evaporation from the metal surface, that is the ratio of energy fluxes for vaporization and heating, is 10{sup –3}–10{sup –4} for transient metals under consideration. A typical energy flux (~10{sup 6} W/cm{sup 2}), a typical surface temperature (~3000 K), and a typical pulse duration (~1 μs) provide a sufficient amount of evaporated atoms to generate fractal fibers such that each molecule of a gas flow collides with the skeleton of fractal fibers many times.
International Nuclear Information System (INIS)
D'Onofrio, Alberto
2009-01-01
In this paper we study and extend the mechanistic mean field theory of growth of cellular populations proposed by Mombach et al. [Mombach JCM, Lemke N, Bodmann BEJ, Idiart MAP. A mean-field theory of cellular growth. Europhys Lett 2002;59:923-928] (MLBI model), and we demonstrate that the original model and our generalizations lead to inferences of biological interest. In the first part of this paper, we show that the model in study is widely general since it admits, as particular cases, the main phenomenological models of cellular growth. In the second part of this work, we generalize the MLBI model to a wider family of models by allowing the cells to have a generic unspecified biologically plausible interaction. Then, we derive a relationship between this generic microscopic interaction function and the growth rate of the corresponding macroscopic model. Finally, we propose to use this relationship in order to help the investigation of the biological plausibility of phenomenological models of cancer growth.
Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L.
1997-01-01
We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.
Thermodynamics for Fractal Statistics
da Cruz, Wellington
1998-01-01
We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.
Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM
1999-01-01
Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems
Enhancement of critical temperature in fractal metamaterial superconductors
Energy Technology Data Exchange (ETDEWEB)
Smolyaninov, Igor I., E-mail: smoly@umd.edu [Department of Electrical and Computer Engineering, University of Maryland, College Park, MD 20742 (United States); Smolyaninova, Vera N. [Department of Physics Astronomy and Geosciences, Towson University, 8000 York Road, Towson, MD 21252 (United States)
2017-04-15
Fractal metamaterial superconductor geometry has been suggested and analyzed based on the recently developed theoretical description of critical temperature increase in epsilon near zero (ENZ) metamaterial superconductors. Considerable enhancement of critical temperature has been predicted in such materials due to appearance of large number of additional poles in the inverse dielectric response function of the fractal. Our results agree with the recent observation (Fratini et al. Nature 466, 841 (2010)) that fractal defect structure promotes superconductivity.
Fractal analysis of fractures and microstructures in rocks
International Nuclear Information System (INIS)
Merceron, T.; Nakashima, S.; Velde, B.; Badri, A.
1991-01-01
Fractal geometry was used to characterize the distribution of fracture fields in rocks, which represent main pathways for material migration such as groundwater flow. Fractal investigations of fracture distribution were performed on granite along Auriat and Shikoku boreholes. Fractal dimensions range between 0.3 and 0.5 according to the different sets of fracture planes selected for the analyses. Shear, tension and compressional modes exhibit different fractal values while the composite fracture patterns are also fractal but with a different, median, fractal value. These observations indicate that the fractal method can be used to distinguish fracture types of different origins in a complex system. Fractal results for Shikoku borehole also correlate with geophysical parameters recorded along, drill-holes such as resistivity and possibly permeability. These results represent the first steps of the fractal investigation along drill-holes. Future studies will be conducted to verify relationships between fractal dimensions and permeability by using available geophysical data. Microstructures and microcracks were analysed in the Inada granite. Microcrack patterns are fractal but fractal dimensions values vary according to both mineral type and orientations of measurement within the mineral. Microcracks in quartz are characterized by more irregular distribution (average D = 0.40) than those in feldspars (D = 0.50) suggesting a different mode of rupture. Highest values of D are reported along main cleavage planes for feldspars or C axis for quartz. Further fractal investigations of microstructure in granite will be used to characterize the potential pathways for fluid migration and diffusion in the rock matrix. (author)
Electromagnetic fields in fractal continua
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Mena, Baltasar [Instituto de Ingeniería, Universidad Nacional Autónoma de México, México D.F. (Mexico); Patiño, Julián [Grupo “Mecánica Fractal”, Instituto Politécnico Nacional, México D.F., 07738 Mexico (Mexico); Morales, Daniel [Instituto Mexicano del Petróleo, México D.F., 07730 Mexico (Mexico)
2013-04-01
Fractal continuum electrodynamics is developed on the basis of a model of three-dimensional continuum Φ{sub D}{sup 3}⊂E{sup 3} with a fractal metric. The generalized forms of Maxwell equations are derived employing the local fractional vector calculus related to the Hausdorff derivative. The difference between the fractal continuum electrodynamics based on the fractal metric of continua with Euclidean topology and the electrodynamics in fractional space F{sup α} accounting the fractal topology of continuum with the Euclidean metric is outlined. Some electromagnetic phenomena in fractal media associated with their fractal time and space metrics are discussed.
The Impact of The Fractal Paradigm on Geography
De Cola, L.
2001-12-01
Being itself somewhat fractal, Benoit Mandelbrot's magnum opus THE FRACTAL GEOMETRY OF NATURE may be deconstructed in many ways, including geometrically, systematically, and epistemologically. Viewed as a work of geography it may be used to organize the major topics of interest to scientists preoccupied with the understanding of real-world space in astronomy, geology, meteorology, hydrology, and biology. We shall use it to highlight such recent geographic accomplishments as automated feature detection, understanding urban growth, and modeling the spread of disease in space and time. However, several key challenges remain unsolved, among them: 1. It is still not possible to move continuously from one map scale to another so that objects change their dimension smoothly. I.e. as a viewer zooms in on a map the zero-dimensional location of a city should gradually become a 2-dimensional polygon, then a network of 1-dimensional streets, then 3-dimensional buildings, etc. 2. Spatial autocorrelation continues to be regarded more as an econometric challenge than as a problem of scaling. Similarities of values among closely-spaced observation is not so much a problem to be overcome as a source of information about spatial structure. 3. Although the fractal paradigm is a powerful model for data analysis, its ideas and techniques need to be brought to bear on the problems of understanding such hierarchies as ecosystems (the flow networks of energy and matter), taxonomies (biological classification), and knowledge (hierarchies of bureaucratic information, networks of linked data, etc).
Fractal structures and fractal functions as disease indicators
Escos, J.M; Alados, C.L.; Emlen, J.M.
1995-01-01
Developmental instability is an early indicator of stress, and has been used to monitor the impacts of human disturbance on natural ecosystems. Here we investigate the use of different measures of developmental instability on two species, green peppers (Capsicum annuum), a plant, and Spanish ibex (Capra pyrenaica), an animal. For green peppers we compared the variance in allometric relationship between control plants, and a treatment group infected with the tomato spotted wilt virus. The results show that infected plants have a greater variance about the allometric regression line than the control plants. We also observed a reduction in complexity of branch structure in green pepper with a viral infection. Box-counting fractal dimension of branch architecture declined under stress infection. We also tested the reduction in complexity of behavioral patterns under stress situations in Spanish ibex (Capra pyrenaica). Fractal dimension of head-lift frequency distribution measures predator detection efficiency. This dimension decreased under stressful conditions, such as advanced pregnancy and parasitic infection. Feeding distribution activities reflect food searching efficiency. Power spectral analysis proves to be the most powerful tool for character- izing fractal behavior, revealing a reduction in complexity of time distribution activity under parasitic infection.
Willson, Stephen J.
1991-01-01
Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)
Peleg, M
1993-01-01
Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.
Incomplete information and fractal phase space
International Nuclear Information System (INIS)
Wang, Qiuping A.
2004-01-01
The incomplete statistics for complex systems is characterized by a so called incompleteness parameter ω which equals unity when information is completely accessible to our treatment. This paper is devoted to the discussion of the incompleteness of accessible information and of the physical signification of ω on the basis of fractal phase space. ω is shown to be proportional to the fractal dimension of the phase space and can be linked to the phase volume expansion and information growth during the scale refining process
FRACTAL IMAGE FEATURE VECTORS WITH APPLICATIONS IN FRACTOGRAPHY
Directory of Open Access Journals (Sweden)
Hynek Lauschmann
2011-05-01
Full Text Available The morphology of fatigue fracture surface (caused by constant cycle loading is strictly related to crack growth rate. This relation may be expressed, among other methods, by means of fractal analysis. Fractal dimension as a single numerical value is not sufficient. Two types of fractal feature vectors are discussed: multifractal and multiparametric. For analysis of images, the box-counting method for 3D is applied with respect to the non-homogeneity of dimensions (two in space, one in brightness. Examples of application are shown: images of several fracture surfaces are analyzed and related to crack growth rate.
Fractal-Based Image Analysis In Radiological Applications
Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.
1987-10-01
We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.
Nanoparticles dynamics on a surface: fractal pattern formation and fragmentation
DEFF Research Database (Denmark)
Dick, Veronika V.; Solov'yov, Ilia; Solov'yov, Andrey V.
2010-01-01
In this paper we review our recent results on the formation and the post-growth relaxation processes of nanofractals on surface. For this study we developed a method which describes the internal dynamics of particles in a fractal and accounts for their diffusion and detachment. We demonstrate...... that these kinetic processes determine the final shape of the islands on surface after post-growth relaxation. We consider different scenarios of fractal relaxation and analyze the time evolution of the island's morphology....
Preliminary observation of genital secretions, growth rate and ...
African Journals Online (AJOL)
Cane rats are large terrestial rodents which have the potential to increase animal protein intake. There is paucity of information on the genital secretions and growth rate of caged cane rats. This study observed the genital secretions, growth rate, feeds, feeding and the behaviour of caged cane rats. When animals adjusted to ...
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti
2017-08-17
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
Fractal Electrochemical Microsupercapacitors
Hota, Mrinal Kanti; Jiang, Qiu; Mashraei, Yousof; Salama, Khaled N.; Alshareef, Husam N.
2017-01-01
The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.
Random walk through fractal environments
Isliker, H.; Vlahos, L.
2002-01-01
We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...
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.
Positron annihilation near fractal surfaces
International Nuclear Information System (INIS)
Lung, C.W.; Deng, K.M.; Xiong, L.Y.
1991-07-01
A model for positron annihilation in the sub-surface region near a fractal surface is proposed. It is found that the power law relationship between the mean positron implantation depth and incident positron energy can be used to measure the fractal dimension of the fractal surface in materials. (author). 10 refs, 2 figs
DEFF Research Database (Denmark)
Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.
2010-01-01
applications. THz radiation can be employed for various purposes, among them the study of vibrations in biological molecules, motion of electrons in semiconductors and propagation of acoustic shock waves in crystals. We propose here a new THz fractal MTM design that shows very high transmission in the desired...... frequency range as well as a clear differentiation between one polarisation and another. Based on theoretical predictions we fabricated and measured a fractal based THz metamaterial that shows more than 60% field transmission at around 1THz for TE polarized light while the TM waves have almost 80% field...... transmission peak at 0.6THz. One of the main characteristics of this design is its tunability by design: by simply changing the length of the fractal elements one can choose the operating frequency window. The modelling, fabrication and characterisation results will be presented in this paper. Due to the long...
International Nuclear Information System (INIS)
Li, W.; Bak, P.
1986-01-01
At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D = 1 to the cantorus is governed by an exponent ν = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent
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....
Quantum waveguide theory of a fractal structure
International Nuclear Information System (INIS)
Lin Zhiping; Hou Zhilin; Liu Youyan
2007-01-01
The electronic transport properties of fractal quantum waveguide networks in the presence of a magnetic field are studied. A Generalized Eigen-function Method (GEM) is used to calculate the transmission and reflection coefficients of the studied systems unto the fourth generation Sierpinski fractal network with node number N=123. The relationship among the transmission coefficient T, magnetic flux Φ and wave vector k is investigated in detail. The numerical results are shown by the three-dimensional plots and contour maps. Some resonant-transmission features and the symmetry of the transmission coefficient T to flux Φ are observed and discussed, and compared with the results of the tight-binding model
The fractal nature of vacuum arc cathode spots
International Nuclear Information System (INIS)
Anders, Andre
2005-01-01
Cathode spot phenomena show many features of fractals, for example self-similar patterns in the emitted light and arc erosion traces. Although there have been hints on the fractal nature of cathode spots in the literature, the fractal approach to spot interpretation is underutilized. In this work, a brief review of spot properties is given, touching the differences between spot type 1 (on cathodes surfaces with dielectric layers) and spot type 2 (on metallic, clean surfaces) as well as the known spot fragment or cell structure. The basic properties of self-similarity, power laws, random colored noise, and fractals are introduced. Several points of evidence for the fractal nature of spots are provided. Specifically power laws are identified as signature of fractal properties, such as spectral power of noisy arc parameters (ion current, arc voltage, etc) obtained by fast Fourier transform. It is shown that fractal properties can be observed down to the cutoff by measurement resolution or occurrence of elementary steps in physical processes. Random walk models of cathode spot motion are well established: they go asymptotically to Brownian motion for infinitesimal step width. The power spectrum of the arc voltage noise falls as 1/f 2 , where f is frequency, supporting a fractal spot model associated with Brownian motion
Variability of fractal dimension of solar radio flux
Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om
2018-04-01
In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).
Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin
2016-05-01
One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.
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...
Observations concerning the COMPBRN III fire growth code
International Nuclear Information System (INIS)
Nicolette, V.F.; Nowlen, S.P.; Lambright, J.A.
1989-01-01
Nuclear power plant fire probabilistic risk assessments (PRAs) usually involve application of a fire growth model to calculate fire growth and the time required to damage critical safety equipment. Attempts to use the fire growth model COMPBRN III resulted in the observation of problems and nonphysical behavior in the code. In this paper the causes of these problems and nonphysical behavior are identified and possible modifications suggested. Incorporation of these modifications into COMPBRN III results in some significant differences in the calculated fire damage times, as well as making the code more physically realistic. 12 refs., 6 figs
Shower fractal dimension analysis in a highly-granular calorimeter
Ruan, M
2014-01-01
We report on an investigation of the self-similar structure of particle showers recorded at a highly-granular calorimeter. On both simulated and experimental data, a strong correlation between the number of hits and the spatial scale of the readout channels is observed, from which we define the shower fractal dimension. The measured fractal dimension turns out to be strongly dependent on particle type, which enables new approaches for particle identification. A logarithmic dependence of the particle energy on the fractal dimension is also observed.
Entrainment to a real time fractal visual stimulus modulates fractal gait dynamics.
Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K
2014-08-01
Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.
Transmission and reflection properties of terahertz fractal metamaterials
DEFF Research Database (Denmark)
Malureanu, Radu; Lavrinenko, Andrei; Cooke, David
2010-01-01
We use THz time-domain spectroscopy to investigate transmission and reflection properties of metallic fractal metamaterial structures. We observe loss of free-space energy at certain resonance frequencies, indicating excitation of surface modes of the metamaterial.......We use THz time-domain spectroscopy to investigate transmission and reflection properties of metallic fractal metamaterial structures. We observe loss of free-space energy at certain resonance frequencies, indicating excitation of surface modes of the metamaterial....
Shape characteristics of equilibrium and non-equilibrium fractal clusters.
Mansfield, Marc L; Douglas, Jack F
2013-07-28
It is often difficult in practice to discriminate between equilibrium and non-equilibrium nanoparticle or colloidal-particle clusters that form through aggregation in gas or solution phases. Scattering studies often permit the determination of an apparent fractal dimension, but both equilibrium and non-equilibrium clusters in three dimensions frequently have fractal dimensions near 2, so that it is often not possible to discriminate on the basis of this geometrical property. A survey of the anisotropy of a wide variety of polymeric structures (linear and ring random and self-avoiding random walks, percolation clusters, lattice animals, diffusion-limited aggregates, and Eden clusters) based on the principal components of both the radius of gyration and electric polarizability tensor indicates, perhaps counter-intuitively, that self-similar equilibrium clusters tend to be intrinsically anisotropic at all sizes, while non-equilibrium processes such as diffusion-limited aggregation or Eden growth tend to be isotropic in the large-mass limit, providing a potential means of discriminating these clusters experimentally if anisotropy could be determined along with the fractal dimension. Equilibrium polymer structures, such as flexible polymer chains, are normally self-similar due to the existence of only a single relevant length scale, and are thus anisotropic at all length scales, while non-equilibrium polymer structures that grow irreversibly in time eventually become isotropic if there is no difference in the average growth rates in different directions. There is apparently no proof of these general trends and little theoretical insight into what controls the universal anisotropy in equilibrium polymer structures of various kinds. This is an obvious topic of theoretical investigation, as well as a matter of practical interest. To address this general problem, we consider two experimentally accessible ratios, one between the hydrodynamic and gyration radii, the other
Fractals in several electrode materials
Energy Technology Data Exchange (ETDEWEB)
Zhang, Chunyong, E-mail: zhangchy@njau.edu.cn [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); Wu, Jingyu [Department of Chemistry, College of Science, Nanjing Agricultural University, Nanjing 210095 (China); Fu, Degang [Suzhou Key Laboratory of Environment and Biosafety, Suzhou Academy of Southeast University, Dushuhu lake higher education town, Suzhou 215123 (China); State Key Laboratory of Bioelectronics, Southeast University, Nanjing 210096 (China)
2014-09-15
Highlights: • Fractal geometry was employed to characterize three important electrode materials. • The surfaces of all studied electrodes were proved to be very rough. • The fractal dimensions of BDD and ACF were scale dependent. • MMO film was more uniform than BDD and ACF in terms of fractal structures. - Abstract: In the present paper, the fractal properties of boron-doped diamond (BDD), mixed metal oxide (MMO) and activated carbon fiber (ACF) electrode have been studied by SEM imaging at different scales. Three materials are self-similar with mean fractal dimension in the range of 2.6–2.8, confirming that they all exhibit very rough surfaces. Specifically, it is found that MMO film is more uniform in terms of fractal structure than BDD and ACF. As a result, the intriguing characteristics make these electrodes as ideal candidates for high-performance decontamination processes.
Fractal physiology and the fractional calculus: a perspective.
West, Bruce J
2010-01-01
This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a
Martin, Demetri
2015-03-01
Demetri Maritn prepared this palindromic poem as his project for Michael Frame's fractal geometry class at Yale. Notice the first, fourth, and seventh words in the second and next-to-second lines are palindromes, the first two and last two lines are palindromes, the middle line, "Be still if I fill its ebb" minus its last letter is a palindrome, and the entire poem is a palindrome...
Categorization of new fractal carpets
International Nuclear Information System (INIS)
Rani, Mamta; Goel, Saurabh
2009-01-01
Sierpinski carpet is one of the very beautiful fractals from the historic gallery of classical fractals. Carpet designing is not only a fascinating activity in computer graphics, but it has real applications in carpet industry as well. One may find illusionary delighted carpets designed here, which are useful in real designing of carpets. In this paper, we attempt to systematize their generation and put them into categories. Each next category leads to a more generalized form of the fractal carpet.
Bilipschitz embedding of homogeneous fractals
Lü, Fan; Lou, Man-Li; Wen, Zhi-Ying; Xi, Li-Feng
2014-01-01
In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.
ABC of multi-fractal spacetimes and fractional sea turtles
Energy Technology Data Exchange (ETDEWEB)
Calcagni, Gianluca [Instituto de Estructura de la Materia, CSIC, Madrid (Spain)
2016-04-15
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)
ABC of multi-fractal spacetimes and fractional sea turtles
International Nuclear Information System (INIS)
Calcagni, Gianluca
2016-01-01
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes. (orig.)
ABC of multi-fractal spacetimes and fractional sea turtles
Calcagni, Gianluca
2016-04-01
We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.
In Situ Observation of Antisite Defect Formation during Crystal Growth
International Nuclear Information System (INIS)
Kramer, M. J.; Napolitano, R. E.; Mendelev, M. I.
2010-01-01
In situ x-ray diffraction (XRD) coupled with molecular dynamics (MD) simulations have been used to quantify antisite defect trapping during crystallization. Rietveld refinement of the XRD data revealed a marked lattice distortion which involves an a axis expansion and a c axis contraction of the stable C11b phase. The observed lattice response is proportional in magnitude to the growth rate, suggesting that the behavior is associated with the kinetic trapping of lattice defects. MD simulations demonstrate that this lattice response is due to incorporation of 1% to 2% antisite defects during growth.
FONT DISCRIMINATIO USING FRACTAL DIMENSIONS
Directory of Open Access Journals (Sweden)
S. Mozaffari
2014-09-01
Full Text Available One of the related problems of OCR systems is discrimination of fonts in machine printed document images. This task improves performance of general OCR systems. Proposed methods in this paper are based on various fractal dimensions for font discrimination. First, some predefined fractal dimensions were combined with directional methods to enhance font differentiation. Then, a novel fractal dimension was introduced in this paper for the first time. Our feature extraction methods which consider font recognition as texture identification are independent of document content. Experimental results on different pages written by several font types show that fractal geometry can overcome the complexities of font recognition problem.
Two Dimensional Drug Diffusion Between Nanoparticles and Fractal Tumors
Samioti, S. E.; Karamanos, K.; Tsiantis, A.; Papathanasiou, A.; Sarris, I.
2017-11-01
Drug delivery methods based on nanoparticles are some of the most promising medical applications in nanotechnology to treat cancer. It is observed that drug released by nanoparticles to the cancer tumors may be driven by diffusion. A fractal tumor boundary of triangular Von Koch shape is considered here and the diffusion mechanism is studied for different drug concentrations and increased fractality. A high order Finite Elements method based on the Fenics library is incorporated in fine meshes to fully resolve these irregular boundaries. Drug concentration, its transfer rates and entropy production are calculated in an up to forth order fractal iteration boundaries. We observed that diffusion rate diminishes for successive prefractal generations. Also, the entropy production around the system changes greatly as the order of the fractal curve increases. Results indicate with precision where the active sites are, in which most of the diffusion takes place and thus drug arrives to the tumor.
Modeling of multibranched crosslike crack growth
International Nuclear Information System (INIS)
Canessa, E.; Tanatar, B.
1991-06-01
Multibranched crosslike crack patterns formed in concentrically loaded square plates are studied in terms of fractal geometry, where the associated fractal dimension d f is calculated for their characterization. We apply simplest deterministic and stochastic approaches at a phenomenological level in an attempt to find generic features as guidelines for future experimental and theoretical work. The deterministic model for fracture propagation we apply, which is a variant of the discretized Laplace approach for randomly ramified fractal cracks proposed by Takayasu, reproduces the basic ingredients of observed complex fracture patters. The stochastic model, although is not strictly a model for crack propagation, is based on diffusion-limited aggregation (DLA) for fractal growth and produces slightly more realistic assessment of the crosslike growth of the cracks in asymmetric multibranches. Nevertheless, this simple ad-hoc DLA-version for modeling the present phenomena as well as the deterministic approach for fracture propagation give fractal dimensionality for the fracture pattern in accord with our estimations made from recent experimental data. It is found that there is a crossover of two fractal dimensions, corresponding to the core (higher d f ) and multibranched crosslike (lower D f ) regions, that contains loops, that are interpreted as representing different symmetry regions within the square plates of finite size. (author). 26 refs, 5 figs
Fractal differential equations and fractal-time dynamical systems
Indian Academy of Sciences (India)
like fractal subsets of the real line may be termed as fractal-time dynamical systems. Formulation ... involving scaling and memory effects. But most of ..... begin by recalling the definition of the Riemann integral in ordinary calculus [33]. Let g: [a ...
Abnormal growth kinetics of h-BN epitaxial monolayer on Ru(0001) enhanced by subsurface Ar species
Wei, Wei; Meng, Jie; Meng, Caixia; Ning, Yanxiao; Li, Qunxiang; Fu, Qiang; Bao, Xinhe
2018-04-01
Growth kinetics of epitaxial films often follows the diffusion-limited aggregation mechanism, which shows a "fractal-to-compact" morphological transition with increasing growth temperature or decreasing deposition flux. Here, we observe an abnormal "compact-to-fractal" morphological transition with increasing growth temperature for hexagonal boron nitride growth on the Ru(0001) surface. The unusual growth process can be explained by a reaction-limited aggregation (RLA) mechanism. Moreover, introduction of the subsurface Ar atoms has enhanced this RLA growth behavior by decreasing both reaction and diffusion barriers. Our work may shed light on the epitaxial growth of two-dimensional atomic crystals and help to control their morphology.
Observation and simulation of crack growth in Zry-4
International Nuclear Information System (INIS)
Bertolino, Graciela; Meyer, Gabriel; Perez Ipina, J
2003-01-01
Security and life extension of components of nuclear reactors are the most motivating aspects that encourage to study embrittlement processes of zirconium alloys by reaction with hydrogen.Here, the use of fracture mechanics tests are suitable to monitor the material resistance of components under service.Because many times is difficult to obtain normalized probes from real size components, researchers look for alternative experimental techniques or crack growth simulation from the knowledge of particular material properties.In this work we present the results obtained after experimental observation and computer simulation of crack growth in Zry-4 probes.Experimental observation were obtained by performing flexion tests in three point probes SSEN(B) of 3 x 7 x 32 mm 3 located in the chamber of a scanning electron microscope, measuring in situ the crack length and opening when an external load is applied.Using the information obtained from stress-displacement measurements after tensile tests and the empiric relationship between crack opening and crack length, the crack growth process was simulated.Displacement field in the zone close to the crack tip was obtained by finite elements technique (Castem, DMT, CEA) assuming plain stress, a plastic bilinear homogeneous material and neglecting texture or directional anisotropy.To compare experimental observation and simulation, a grid (10 x 10 μm 2 each square) was drawn in the zone close to the crack tip by selective sputtering.Following the movement of two (three) points of the surface allows to compare uni (bi) dimensional deformation.A good agreement between observation and simulation was observed: after the crack opening grew 28 times (from 1.5 to 42 μm) the base-height relationship of a triangle involving the crack tip change 40% (35%) in the experimental observation (simulation)
Electromagnetism on anisotropic fractal media
Ostoja-Starzewski, Martin
2013-04-01
Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.
Fractals and multifractals in physics
International Nuclear Information System (INIS)
Arcangelis, L. de.
1987-01-01
We present a general introduction to the world of fractals. The attention is mainly devoted to stress how fractals do indeed appear in the real world and to find quantitative methods for characterizing their properties. The idea of multifractality is also introduced and it is presented in more details within the framework of the percolation problem
Simoson, Andrew J.
2009-01-01
This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)
Turbulent wakes of fractal objects
Staicu, A.D.; Mazzi, B.; Vassilicos, J.C.; Water, van de W.
2003-01-01
Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost dark energy model which was recently suggested to explain the present acceleration of the cosmic expansion. Next, we establish a connection between the quintessence scalar field and fractal ghost dark energy density.
Encounters with chaos and fractals
Gulick, Denny
2012-01-01
Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.
Energy Technology Data Exchange (ETDEWEB)
Guzman-Castaneda, J.I.; Garcia-Borquez, A. [Instituto Politecnico Nacional, ESFM, 07738 Mexico D.F. (Mexico); Arizabalo-Salas, R.D. [Instituto Mexicano del Petroleo, Direccion de Investigacion y Posgrado, 07730 Mexico D.F. (Mexico)
2012-06-15
Optical and scanning electron microscopy (OM and SEM) are techniques that are normally used for 2D-analysis of surface features. By fractal dimension analysis of the gray-scale OM and SEM images, it is possible to get quantitative topographical measurements. In this work, three different surface topographies (polished, eroded, and oxidized) were analyzed on FeCrAl alloy by OM and SEM. Clear surface topographical changes can be qualitatively observed. In order to quantify such changes, two steps were followed: (i) a gray-scale digitalization from each image was used to reproduce topographical features on the analyzed surface, and (ii) from this information, the fractal dimension (D) was determined using fractal3e software. The fractal dimension determined in this form follows coherently the topographical changes produced on the FeCrAl alloy after polishing, erosion, and oxidizing processes. The variations of fractal dimension values against the temperature of the oxidizing processes reflect well the oxide growth changes. Moreover, a minimum D-value is registered at 750 C, which corresponds to the {delta}-{theta} alumina phase transition temperature as determined by differential thermal analysis (DTA) on the same alloy. (Copyright copyright 2012 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim)
Fractal Analysis of Mobile Social Networks
International Nuclear Information System (INIS)
Zheng Wei; Pan Qian; Sun Chen; Deng Yu-Fan; Zhao Xiao-Kang; Kang Zhao
2016-01-01
Fractal and self similarity of complex networks have attracted much attention in recent years. The fractal dimension is a useful method to describe the fractal property of networks. However, the fractal features of mobile social networks (MSNs) are inadequately investigated. In this work, a box-covering method based on the ratio of excluded mass to closeness centrality is presented to investigate the fractal feature of MSNs. Using this method, we find that some MSNs are fractal at different time intervals. Our simulation results indicate that the proposed method is available for analyzing the fractal property of MSNs. (paper)
Fractal Dimension of Fracture Surface in Rock Material after High Temperature
Directory of Open Access Journals (Sweden)
Z. Z. Zhang
2015-01-01
Full Text Available Experiments on granite specimens after different high temperature under uniaxial compression were conducted and the fracture surfaces were observed by scanning electron microscope (SEM. The fractal dimensions of the fracture surfaces with increasing temperature were calculated, respectively. The fractal dimension of fracture surface is between 1.44 and 1.63. Its value approximately goes up exponentially with the increase of temperature. There is a quadratic polynomial relationship between the rockburst tendency and fractal dimension of fracture surface; namely, a fractal dimension threshold can be obtained. Below the threshold value, a positive correlativity shows between rockburst tendency and fractal dimension; when the fractal dimension is greater than the threshold value, it shows an inverse correlativity.
Static friction between rigid fractal surfaces.
Alonso-Marroquin, Fernando; Huang, Pengyu; Hanaor, Dorian A H; Flores-Johnson, E A; Proust, Gwénaëlle; Gan, Yixiang; Shen, Luming
2015-09-01
Using spheropolygon-based simulations and contact slope analysis, we investigate the effects of surface topography and atomic scale friction on the macroscopically observed friction between rigid blocks with fractal surface structures. From our mathematical derivation, the angle of macroscopic friction is the result of the sum of the angle of atomic friction and the slope angle between the contact surfaces. The latter is obtained from the determination of all possible contact slopes between the two surface profiles through an alternative signature function. Our theory is validated through numerical simulations of spheropolygons with fractal Koch surfaces and is applied to the description of frictional properties of Weierstrass-Mandelbrot surfaces. The agreement between simulations and theory suggests that for interpreting macroscopic frictional behavior, the descriptors of surface morphology should be defined from the signature function rather than from the slopes of the contacting surfaces.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fang, Jieran; Wang, Di; DeVault, Clayton T
2017-01-01
Graphene has been demonstrated to be a promising photodetection material because of its ultrabroadband optical absorption, compatibility with CMOS technology, and dynamic tunability in optical and electrical properties. However, being a single atomic layer thick, graphene has intrinsically small...... optical absorption, which hinders its incorporation with modern photodetecting systems. In this work, we propose a gold snowflake-like fractal metasurface design to realize broadband and polarization-insensitive plasmonic enhancement in graphene photodetector. We experimentally obtain an enhanced...... photovoltage from the fractal metasurface that is an order of magnitude greater than that generated at a plain gold-graphene edge and such an enhancement in the photovoltage sustains over the entire visible spectrum. We also observed a relatively constant photoresponse with respect to polarization angles...
Moghilevsky, Débora Estela
2011-01-01
A lo largo de los últimos años del siglo veinte se ha desarrollado la teoría de la complejidad. Este modelo relaciona las ciencias duras tales como la matemática, la teoría del caos, la física cuántica y la geometría fractal con las llamadas seudo ciencias. Dentro de este contexto podemos definir la Psicología Fractal como la ciencia que estudia los aspectos psíquicos como dinámicamente fractales.
Observations of the Growth of an Active Region Filament
Yang, Bo
2017-04-01
We present observations of the growth of an active region filament caused by magnetic interactions among the filament and its adjacent superpenumbral filament (SF) and dark thread-like structures (T). Multistep reconnections are identified during the whole growing process. Magnetic flux convergence and cancellation occurring at the positive footpoint region of the filament is the first step reconnection, which resulted in the filament bifurcating into two sets of intertwined threads. One set anchored in situ, while the other set moved toward and interacted with the SF and part of T. This indicates the second step reconnection, which gave rise to the disappearance of the SF and the formation of a long thread-like structure that connects the far ends of the filament and T. The long thread-like structure further interacted with the T and then separated into two parts, representing the third step reconnection. Finally, another similar long thread-like structure, which intertwined with the fixed filament threads, appeared. Hαobservations show that this twisted structure is a longer sinistral filament. Based on the observed photospheric vector magnetograms, we performed a non-linear force-free field extrapolation to reconstruct the magnetic fields above the photosphere and found that the coronal magnetic field lines associated with the filament consists of two twisted flux ropes winding around each other. These results suggest that magnetic interactions among filaments and their adjacent SFs and T could lead to the growth of the filaments, and the filament is probably supported in a flux rope.
Map of fluid flow in fractal porous medium into fractal continuum flow.
Balankin, Alexander S; Elizarraraz, Benjamin Espinoza
2012-05-01
This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.
Fractal geometry and computer graphics
Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele
1992-01-01
Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...
Thermal transport in fractal systems
DEFF Research Database (Denmark)
Kjems, Jørgen
1992-01-01
Recent experiments on the thermal transport in systems with partial fractal geometry, silica aerogels, are reviewed. The individual contributions from phonons, fractons and particle modes, respectively, have been identified and can be described by quantitative models consistent with heat capacity...
Fractal analysis in oral leukoplakia
Directory of Open Access Journals (Sweden)
Prashant Bhai Pandey
2015-01-01
Full Text Available Introduction: Fractal analysis (FA quantifies complex geometric structures by generating a fractal dimension (FD, which can measure the complexity of mucosa. FA is a quantitative tool used to measure the complexity of self-similar or semi-self-similar structures. Aim and Objective: The study was done to perform the FA of oral mucosa with keratotic changes, as it is also made up of self-similar tissues, and thus, its FD can be calculated. Results: In oral leukoplakia, keratinization increases the complexity of mucosa, which denotes fractal geometry. We evaluated and compared pretreated and post-treated oral leukoplakia in 50 patients with clinically proven oral leukoplakia and analyzed the normal oral mucosa and lesional or keratinized mucosa in oral leukoplakia patients through FA using box counting method. Conclusion: FA using the fractal geometry is an efficient, noninvasive prediction tool for early detection of oral leukoplakia and other premalignant conditions in patients.
Observation of Rayleigh - Taylor growth to short wavelengths on Nike
International Nuclear Information System (INIS)
Pawley, C.J.; Bodner, S.E.; Dahlburg, J.P.; Obenschain, S.P.; Schmitt, A.J.; Sethian, J.D.; Sullivan, C.A.; Gardner, J.H.; Aglitskiy, Y.; Chan, Y.; Lehecka, T.
1999-01-01
The uniform and smooth focal profile of the Nike KrF laser [S. Obenschain et al., Phys. Plasmas 3, 2098 (1996)] was used to ablatively accelerate 40 μm thick polystyrene planar targets with pulse shaping to minimize shock heating of the compressed material. The foils had imposed small-amplitude sinusoidal wave perturbations of 60, 30, 20, and 12.5 μm wavelength. The shortest wavelength is near the ablative stabilization cutoff for Rayleigh - Taylor growth. Modification of the saturated wave structure due to random laser imprint was observed. Excellent agreement was found between the two-dimensional simulations and experimental data for most cases where the laser imprint was not dominant. copyright 1999 American Institute of Physics
Fractals in Power Reactor Noise
International Nuclear Information System (INIS)
Aguilar Martinez, O.
1994-01-01
In this work the non- lineal dynamic problem of power reactor is analyzed using classic concepts of fractal analysis as: attractors, Hausdorff-Besikovics dimension, phase space, etc. A new non-linear problem is also analyzed: the discrimination of chaotic signals from random neutron noise signals and processing for diagnosis purposes. The advantages of a fractal analysis approach in the power reactor noise are commented in details
Random walk through fractal environments
International Nuclear Information System (INIS)
Isliker, H.; Vlahos, L.
2003-01-01
We analyze random walk through fractal environments, embedded in three-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e., of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D F of the fractal is less than 2, there is though, always a finite rate of unaffected escape. Random walks through fractal sets with D F ≤2 can thus be considered as defective Levy walks. The distribution of jump increments for D F >2 is decaying exponentially. The diffusive behavior of the random walk is analyzed in the frame of continuous time random walk, which we generalize to include the case of defective distributions of walk increments. It is shown that the particles undergo anomalous, enhanced diffusion for D F F >2 is normal for large times, enhanced though for small and intermediate times. In particular, it follows that fractals generated by a particular class of self-organized criticality models give rise to enhanced diffusion. The analytical results are illustrated by Monte Carlo simulations
The fractal nature materials microstructure influence on electrochemical energy sources
Directory of Open Access Journals (Sweden)
Mitić V.V.
2015-01-01
Full Text Available With increasing of the world energy crisis, research for new, renewable and alternative energy sources are in growth. The focus is on research areas, sometimes of minor importance and applications, where the different synthesis methods and microstructure properties optimization, performed significant improvement of output materials’ and components’ electro-physical properties, which is important for higher energy efficiency and in the electricity production (batteries and battery systems, fuel cells and hydrogen energy contribution. Also, the storage tanks capacity improvement, for the energy produced on such way, which is one of the most important development issues in the energy sphere, represents a very promising research and application area. Having in mind, the results achieved in the electrochemical energy sources field, especially electrolyte development, these energy sources, materials fractal nature optimization analysis contribution, have been investigated. Based on materials fractal structure research field, particularly electronic materials, we have performed microstructure influence parameters research in electrochemistry area. We have investigated the Ho2O3 concentration influence (from 0.01wt% to 1wt% and sintering temperature (from 1320°C to 1380°C, as consolidation parameters, and thus, also open the electrochemical function fractalization door and in the basic thermodynamic parameters the fractal correction introduced. The fractal dimension dependence on additive concentration is also investigated. [Projekat Ministarstva nauke Republike Srbije, br. 172057: Directed synthesis, structure and properties of multifunctional materials
Fractal Globule as a model of DNA folding in eukaryotes
Imakaev, Maksim; Mirny, Leonid
2012-02-01
A recent study (Lieberman-Aiden et al., Science, 2009) observed that the structure of the genome, on the scale of a few megabases, is consistent with a fractal globule. The fractal globule is a quasi-equilibrium state of a polymer after a rapid collapse. First proposed theoretically in 1988, this structure had never been simulated. Fractal globule was seen as a state, in which each subchain is compact, and doesn't mix with other subchains due to their mutual unentanglement (topological constraints). We use GPU-assisted dynamics to create fractal globules of different sizes and observe their dynamics. Our simulations confirm that a polymer after rapid collapse has compact subchains. We measure the scaling of looping probability of a subchain with it's length, and observe the remarkably robust inverse proportionality. Dynamic simulation of the equilibration of this state show that it exhibits Rose type subdiffusion. Due to diffusion, fractal globule quickly degrades to a quasi-equilibrium state, in which subchains of a polymer are mixed, but topologically unentangled. We propose that separation of spatial and topological equilibration of a polymer chain might have implications in different fields of physics.
Fractal geometry in an expanding, one-dimensional, Newtonian universe.
Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel
2007-09-01
Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-01-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape
A fractal-based image encryption system
Abd-El-Hafiz, S. K.; Radwan, Ahmed Gomaa; Abdel Haleem, Sherif H.; Barakat, Mohamed L.
2014-01-01
single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved
Effects of fractal pore on coal devolatilization
Energy Technology Data Exchange (ETDEWEB)
Chen, Yongli; He, Rong [Tsinghua Univ., Beijing (China). Dept. of Thermal Engineering; Wang, Xiaoliang; Cao, Liyong [Dongfang Electric Corporation, Chengdu (China). Centre New Energy Inst.
2013-07-01
Coal devolatilization is numerically investigated by drop tube furnace and a coal pyrolysis model (Fragmentation and Diffusion Model). The fractal characteristics of coal and char pores are investigated. Gas diffusion and secondary reactions in fractal pores are considered in the numerical simulations of coal devolatilization, and the results show that the fractal dimension is increased firstly and then decreased later with increased coal conversions during devolatilization. The mechanisms of effects of fractal pores on coal devolatilization are analyzed.
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.
2014-08-28
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
Enhanced Graphene Photodetector with Fractal Metasurface
DEFF Research Database (Denmark)
Fan, Jieran; Wang, Di; DeVault, Clayton
2016-01-01
We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure.......We designed and fabricated a broadband, polarization-independent photodetector by integrating graphene with a fractal Cayley tree metasurface. Our measurements show an almost uniform, tenfold enhancement in photocurrent generation due to the fractal metasurface structure....
Fractal Structures For Fixed Mems Capacitors
Elshurafa, Amro M.; Radwan, Ahmed Gomaa Ahmed; Emira, Ahmed A.; Salama, Khaled N.
2014-01-01
An embodiment of a fractal fixed capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure. The capacitor body has a first plate with a fractal shape separated by a horizontal distance from a second plate with a fractal shape. The first plate and the second plate are within the same plane. Such a fractal fixed capacitor further comprises a substrate above which the capacitor body is positioned.
Fractal Dimension and Maximum Sunspot Number in Solar Cycle
Directory of Open Access Journals (Sweden)
R.-S. Kim
2006-09-01
Full Text Available The fractal dimension is a quantitative parameter describing the characteristics of irregular time series. In this study, we use this parameter to analyze the irregular aspects of solar activity and to predict the maximum sunspot number in the following solar cycle by examining time series of the sunspot number. For this, we considered the daily sunspot number since 1850 from SIDC (Solar Influences Data analysis Center and then estimated cycle variation of the fractal dimension by using Higuchi's method. We examined the relationship between this fractal dimension and the maximum monthly sunspot number in each solar cycle. As a result, we found that there is a strong inverse relationship between the fractal dimension and the maximum monthly sunspot number. By using this relation we predicted the maximum sunspot number in the solar cycle from the fractal dimension of the sunspot numbers during the solar activity increasing phase. The successful prediction is proven by a good correlation (r=0.89 between the observed and predicted maximum sunspot numbers in the solar cycles.
Fractal Structures For Mems Variable Capacitors
Elshurafa, Amro M.
2014-08-28
In accordance with the present disclosure, one embodiment of a fractal variable capacitor comprises a capacitor body in a microelectromechanical system (MEMS) structure, wherein the capacitor body has an upper first metal plate with a fractal shape separated by a vertical distance from a lower first metal plate with a complementary fractal shape; and a substrate above which the capacitor body is suspended.
Steady laminar flow of fractal fluids
Energy Technology Data Exchange (ETDEWEB)
Balankin, Alexander S., E-mail: abalankin@ipn.mx [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico); Mena, Baltasar [Laboratorio de Ingeniería y Procesos Costeros, Instituto de Ingeniería, Universidad Nacional Autónoma de México, Sisal, Yucatán, 97355 (Mexico); Susarrey, Orlando; Samayoa, Didier [Grupo Mecánica Fractal, ESIME, Instituto Politécnico Nacional, México D.F., 07738 (Mexico)
2017-02-12
We study laminar flow of a fractal fluid in a cylindrical tube. A flow of the fractal fluid is mapped into a homogeneous flow in a fractional dimensional space with metric induced by the fractal topology. The equations of motion for an incompressible Stokes flow of the Newtonian fractal fluid are derived. It is found that the radial distribution for the velocity in a steady Poiseuille flow of a fractal fluid is governed by the fractal metric of the flow, whereas the pressure distribution along the flow direction depends on the fractal topology of flow, as well as on the fractal metric. The radial distribution of the fractal fluid velocity in a steady Couette flow between two concentric cylinders is also derived. - Highlights: • Equations of Stokes flow of Newtonian fractal fluid are derived. • Pressure distribution in the Newtonian fractal fluid is derived. • Velocity distribution in Poiseuille flow of fractal fluid is found. • Velocity distribution in a steady Couette flow is established.
Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...
African Journals Online (AJOL)
In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
Purpose: To determine the genetic contribution to the pattern of retinal vascular branching expressed by its fractal dimension. Methods: This was a cross-sectional study of 50 monozygotic and 49 dizygotic, same-sex twin pairs aged 20 to 46 years. In 50°, disc-centered fundus photographs, the reti...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0.......0002) in monozygotic twins than in dizygotic twins (0.108, P = 0.46), corresponding to a heritability h2 for the fractal dimension of 0.79. In quantitative genetic models, dominant genetic effects explained 54% of the variation and 46% was individually environmentally determined. Conclusions: In young adult twins...
Towards thermomechanics of fractal media
Ostoja-Starzewski, Martin
2007-11-01
Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.
Asymmetric multi-fractality in the U.S. stock indices using index-based model of A-MFDFA
International Nuclear Information System (INIS)
Lee, Minhyuk; Song, Jae Wook; Park, Ji Hwan; Chang, Woojin
2017-01-01
Highlights: • ‘Index-based A-MFDFA’ model is proposed to assess the asymmetric multi-fractality. • The asymmetric multi-fractality in the U.S. stock indices are investigated using ‘Index-based’ and ‘Return-based’ A-MFDFA. • The asymmetric feature is more significantly identified by ‘Index-based’ model than ‘return-based’ model. • Source of multi-fractality and time-varying features are analyzed. - Abstract: We detect the asymmetric multi-fractality in the U.S. stock indices based on the asymmetric multi-fractal detrended fluctuation analysis (A-MFDFA). Instead using the conventional return-based approach, we propose the index-based model of A-MFDFA where the trend based on the evolution of stock index rather than stock price return plays a role for evaluating the asymmetric scaling behaviors. The results show that the multi-fractal behaviors of the U.S. stock indices are asymmetric and the index-based model detects the asymmetric multi-fractality better than return-based model. We also discuss the source of multi-fractality and its asymmetry and observe that the multi-fractal asymmetry in the U.S. stock indices has a time-varying feature where the degree of multi-fractality and asymmetry increase during the financial crisis.
Fractal universe and quantum gravity.
Calcagni, Gianluca
2010-06-25
We propose a field theory which lives in fractal spacetime and is argued to be Lorentz invariant, power-counting renormalizable, ultraviolet finite, and causal. The system flows from an ultraviolet fixed point, where spacetime has Hausdorff dimension 2, to an infrared limit coinciding with a standard four-dimensional field theory. Classically, the fractal world where fields live exchanges energy momentum with the bulk with integer topological dimension. However, the total energy momentum is conserved. We consider the dynamics and the propagator of a scalar field. Implications for quantum gravity, cosmology, and the cosmological constant are discussed.
Fractals control in particle's velocity
International Nuclear Information System (INIS)
Zhang Yongping; Liu Shutang; Shen Shulan
2009-01-01
Julia set, a fractal set of the literature of nonlinear physics, has significance for the engineering applications. For example, the fractal structure characteristics of the generalized M-J set could visually reflect the change rule of particle's velocity. According to the real world requirement, the system need show various particle's velocity in some cases. Thus, the control of the nonlinear behavior, i.e., Julia set, has attracted broad attention. In this work, an auxiliary feedback control is introduced to effectively control the Julia set that visually reflects the change rule of particle's velocity. It satisfies the performance requirement of the real world problems.
Taylor dispersion on a fractal
International Nuclear Information System (INIS)
Mazo, R.M.
1998-01-01
Taylor dispersion is the greatly enhanced diffusion in the direction of a fluid flow caused by ordinary diffusion in directions orthogonal to the flow. It is essential that the system be bounded in space in the directions orthogonal to the flow. We investigate the situation where the medium through which the flow occurs has fractal properties so that diffusion in the orthogonal directions is anomalous and non-Fickian. The effective diffusion in the flow direction remains normal; its width grows proportionally with the time. However, the proportionality constant depends on the fractal dimension of the medium as well as its walk dimension. (author)
Applications of fractals in ecology.
Sugihara, G; M May, R
1990-03-01
Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.
Heritability of Retinal Vascular Fractals
DEFF Research Database (Denmark)
Vergmann, Anna Stage; Broe, Rebecca; Kessel, Line
2017-01-01
, the retinal vascular fractal dimension was measured using the box-counting method and compared within monozygotic and dizygotic twin pairs using Pearson correlation coefficients. Falconer's formula and quantitative genetic models were used to determine the genetic component of variation. Results: The mean...... fractal dimension did not differ statistically significantly between monozygotic and dizygotic twin pairs (1.505 vs. 1.495, P = 0.06), supporting that the study population was suitable for quantitative analysis of heritability. The intrapair correlation was markedly higher (0.505, P = 0...
Synergetics and fractals in tribology
Janahmadov, Ahad Kh
2016-01-01
This book examines the theoretical and practical aspects of tribological process using synergy, fractal and multifractal methods, and the fractal and multifractal models of self-similar tribosystems developed on their basis. It provides a comprehensive analysis of their effectiveness, and also considers the method of flicker noise spectroscopy with detailed parameterization of surface roughness friction. All models, problems and solutions are taken and tested on the set of real-life examples of oil-gas industry. The book is intended for researchers, graduate students and engineers specialising in the field of tribology, and also for senior students of technical colleges.
Multi-fractal analysis of highway traffic data
Institute of Scientific and Technical Information of China (English)
Shang Peng-Jian; Shen Jin-Sheng
2007-01-01
The purpose of the present study is to investigate the presence of multi-fractal behaviours in the traffic time series not only by statistical approaches but also by geometrical approaches. The pointwise H(o)lder exponent of a function is calculated by developing an algorithm for the numerical evaluation of H(o)lder exponent of time series. The traffic time series observed on the Beijing Yuquanying highway are analysed. The results from all these methods indicate that the traffic data exhibit the multi-fractal behaviour.
A fractal nature for polymerized laminin.
Directory of Open Access Journals (Sweden)
Camila Hochman-Mendez
Full Text Available Polylaminin (polyLM is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM, scanning electron microscopy (SEM and atomic force microscopy (AFM to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.
A fractal nature for polymerized laminin.
Hochman-Mendez, Camila; Cantini, Marco; Moratal, David; Salmeron-Sanchez, Manuel; Coelho-Sampaio, Tatiana
2014-01-01
Polylaminin (polyLM) is a non-covalent acid-induced nano- and micro-structured polymer of the protein laminin displaying distinguished biological properties. Polylaminin stimulates neuritogenesis beyond the levels achieved by ordinary laminin and has been shown to promote axonal regeneration in animal models of spinal cord injury. Here we used confocal fluorescence microscopy (CFM), scanning electron microscopy (SEM) and atomic force microscopy (AFM) to characterize its three-dimensional structure. Renderization of confocal optical slices of immunostained polyLM revealed the aspect of a loose flocculated meshwork, which was homogeneously stained by the antibody. On the other hand, an ordinary matrix obtained upon adsorption of laminin in neutral pH (LM) was constituted of bulky protein aggregates whose interior was not accessible to the same anti-laminin antibody. SEM and AFM analyses revealed that the seed unit of polyLM was a flat polygon formed in solution whereas the seed structure of LM was highly heterogeneous, intercalating rod-like, spherical and thin spread lamellar deposits. As polyLM was visualized at progressively increasing magnifications, we observed that the morphology of the polymer was alike independently of the magnification used for the observation. A search for the Hausdorff dimension in images of the two matrices showed that polyLM, but not LM, presented fractal dimensions of 1.55, 1.62 and 1.70 after 1, 8 and 12 hours of adsorption, respectively. Data in the present work suggest that the intrinsic fractal nature of polymerized laminin can be the structural basis for the fractal-like organization of basement membranes in the neurogenic niches of the central nervous system.
Fractal behaviour of flow of an inhomogeneous fluid over a smooth inclined surface
International Nuclear Information System (INIS)
Rouhani, S.; Maleki Jirsarani, N.; Ghane Motlagh, B.; Baradaran, S.; Shokrian, E.
2001-01-01
We have observed and analyzed fractal patterns made by the flow of an inhomogeneous fluid (a suspension) over an inclined smooth surface. We observed that if the angle of inclination is above a threshold (10 d eg C - 12 d eg C), the length of fractal clusters become infinity. We measured a fractal dimension of df=1.40 ± 0.05. This falls within the same general class of patterns of flow of water over an inhomogeneous surface. This observation is consistent with the results of theoretical modes for nonlinear fluid flow in random media
Fractals as macroscopic manifestation of squeezed coherent states and brain dynamics
International Nuclear Information System (INIS)
Vitiello, Giuseppe
2012-01-01
Recent results on the relation between self-similarity and squeezed coherent states are presented. I consider fractals which are generated iteratively according to a prescribed recipe, the so-called deterministic fractals. Fractal properties are incorporated in the framework of the theory of the entire analytical functions and deformed coherent states. Conversely, fractal properties of squeezed coherent states are recognized. This sheds some light on the understanding of the dynamical origin of fractals and their global nature emerging from local deformation processes. The self-similarity in brain background activity suggested by laboratory observations of power-law distributions of power spectral densities of electrocorticograms is also discussed and accounted in the frame of the dissipative many-body model of brain.
Energy Technology Data Exchange (ETDEWEB)
Das, Bipul; Bag, Swarup; Pal, Sukhomay [Indian Institute of Technology Guwahati, Assam (India)
2017-05-15
Providing solutions towards the improvisation of welding technologies is the recent trend in the Friction stir welding (FSW) process. We present a monitoring approach for ultimate tensile strength of the friction stir welded joints based on information extracted from process signals through implementing fractal theory. Higuchi and Katz algorithms were executed on current and tool rotational speed signals acquired during friction stir welding to estimate fractal dimensions. Estimated fractal dimensions when correlated with the ultimate tensile strength of the joints deliver an increasing trend with the increase in joint strength. It is observed that dynamicity of the system strengthens the weld joint, i.e., the greater the fractal dimension, the better will be the quality of the weld. Characterization of signals by fractal theory indicates that the single-valued indicator can be an alternative for effective monitoring of the friction stir welding process.
International Nuclear Information System (INIS)
Das, Bipul; Bag, Swarup; Pal, Sukhomay
2017-01-01
Providing solutions towards the improvisation of welding technologies is the recent trend in the Friction stir welding (FSW) process. We present a monitoring approach for ultimate tensile strength of the friction stir welded joints based on information extracted from process signals through implementing fractal theory. Higuchi and Katz algorithms were executed on current and tool rotational speed signals acquired during friction stir welding to estimate fractal dimensions. Estimated fractal dimensions when correlated with the ultimate tensile strength of the joints deliver an increasing trend with the increase in joint strength. It is observed that dynamicity of the system strengthens the weld joint, i.e., the greater the fractal dimension, the better will be the quality of the weld. Characterization of signals by fractal theory indicates that the single-valued indicator can be an alternative for effective monitoring of the friction stir welding process.
Plot-slope soil erosion using 7Be measurement and rill fractal dimension
International Nuclear Information System (INIS)
Zhang Fengbao; Yang Mingyi
2010-01-01
In this study, we intended to use 7 Be measurement and fractal theory to quantify soil erosion process on slope. The results showed that contribution rate of inter rill erosion was more than that of rill erosion during early stage of rainfall. When it rained, contribution rate of rill erosion began to be higher than inter rill erosion and become the main part of erosion during medium stage of rainfall. The trend of contribution rate of inter rill erosion was growing and the rill erosion was lowering during late stage of rainfall. Rill fractal dimension on the plot slope was almost growing larger during rainfall,growing quickly during early stage of rainfall and slowly during the late stage. Correlations was positive between rill fractal dimension and total erosion amount, also positive between rill fractal dimension and rill erosion. The correlations was positive between rill fractal dimension variation and total erosion amount, also was positive between rill fractal dimension variation and rill erosion amount. The best correlation was observed between rill fractal dimension and rill erosion amount. These results indicated that the rill fractal dimension on the plot slope could represent the development process of rill,the complex degree of rill and the variation of soil erosion intensity on the entire slope. (authors)
The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction.
Najafi, Elham; Darooneh, Amir H
2015-01-01
A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction.
The Fractal Patterns of Words in a Text: A Method for Automatic Keyword Extraction
Najafi, Elham; Darooneh, Amir H.
2015-01-01
A text can be considered as a one dimensional array of words. The locations of each word type in this array form a fractal pattern with certain fractal dimension. We observe that important words responsible for conveying the meaning of a text have dimensions considerably different from one, while the fractal dimensions of unimportant words are close to one. We introduce an index quantifying the importance of the words in a given text using their fractal dimensions and then ranking them according to their importance. This index measures the difference between the fractal pattern of a word in the original text relative to a shuffled version. Because the shuffled text is meaningless (i.e., words have no importance), the difference between the original and shuffled text can be used to ascertain degree of fractality. The degree of fractality may be used for automatic keyword detection. Words with the degree of fractality higher than a threshold value are assumed to be the retrieved keywords of the text. We measure the efficiency of our method for keywords extraction, making a comparison between our proposed method and two other well-known methods of automatic keyword extraction. PMID:26091207
From quantum fields to fractal structures: intermittency in particle physics
International Nuclear Information System (INIS)
Peschanski, R.
1991-01-01
Some features and theoretical interpretations of the intermittency phenomenon observed in high-energy multi-particle production are recalled. One develops on the various connections found with fractal structuration of fluctuations in turbulence, spin-glass physics and aggregation phenomena described by the non-linear Smoluchowski equation. This may lead to a new approach to quantum field properties
Mycelial growth observation of Pleurotus eryngii (Higher Basidiomycota In Vitro
Directory of Open Access Journals (Sweden)
Mustafa Nadhim Owaid
2016-09-01
Full Text Available Five agro-substrates including date palm fibers (fibrillum, wheat straw, white sawdust and their combinations were investigated to grow Pleurotus eryngii. The longer mycelium complete time within bags was 20 days on sawdust (S4, in contrast, the shorter time for mycelium overgrew was completed after 15 days on date palm fiber (S5. In significant (p<0.05, S5 showed the higher growth intensity level (vigorous growth than other substrates. Thus use of date palm wastes (S5 medium may be useful for successfully cultivation king oyster mushroom in farm.International Journal of Environment Vol.5(3 2016, pp.1-10
Ghost quintessence in fractal gravity
Indian Academy of Sciences (India)
In this study, using the time-like fractal theory of gravity, we mainly focus on the ghost ... Here a(t) is the cosmic scale factor and it measures the expansion of the Universe. ..... effectively appear as self-conserved dark energy, with a non-trivial ...
Fractals in DNA sequence analysis
Institute of Scientific and Technical Information of China (English)
Yu Zu-Guo(喻祖国); Vo Anh; Gong Zhi-Min(龚志民); Long Shun-Chao(龙顺潮)
2002-01-01
Fractal methods have been successfully used to study many problems in physics, mathematics, engineering, finance,and even in biology. There has been an increasing interest in unravelling the mysteries of DNA; for example, how can we distinguish coding and noncoding sequences, and the problems of classification and evolution relationship of organisms are key problems in bioinformatics. Although much research has been carried out by taking into consideration the long-range correlations in DNA sequences, and the global fractal dimension has been used in these works by other people, the models and methods are somewhat rough and the results are not satisfactory. In recent years, our group has introduced a time series model (statistical point of view) and a visual representation (geometrical point of view)to DNA sequence analysis. We have also used fractal dimension, correlation dimension, the Hurst exponent and the dimension spectrum (multifractal analysis) to discuss problems in this field. In this paper, we introduce these fractal models and methods and the results of DNA sequence analysis.
Fractal nature of humic materials
International Nuclear Information System (INIS)
Rice, J.A.
1992-01-01
Fractals are geometric representatives of strongly disordered systems whose structure is described by nonintegral dimensions. A fundamental tenet of fractal geometry is that disorder persists at any characterization scale-length used to describe the system. The nonintegral nature of these fractal dimensions is the result of the realization that a disordered system must possess more structural detail than an ordered system with classical dimensions of 1, 2, or 3 in order to accommodate this ''disorder within disorder.'' Thus from a fractal perspective, disorder is seen as an inherent characteristic of the system rather than as a perturbative phenomena forced upon it. Humic materials are organic substances that are formed by the profound alteration of organic matter in a natural environment. They can be operationally divided into 3 fractions; humic acid (soluble in base), fulvic acid (soluble in acid or base), and humin (insoluble in acid or base). Each of these fraction has been shown to be an extremely heterogeneous mixture. These mixtures have proven so intractable that they may represent the ultimate in molecular disorder. In fact, based on the characteristics that humic materials must possess in order to perform their functions in natural systems, it has been proposed that the fundamental chemical characteristic of a humic material is not a discrete chemical structure but a pronounced lack of order on a molecular level. If the fundamental chemical characteristic of a humic material is a strongly disordered nature, as has been proposed, then humic materials should be amenable to characterization by fractal geometry. The purpose of this paper is to test this hypothesis
Fractal characterization of acupuncture-induced spike trains of rat WDR neurons
International Nuclear Information System (INIS)
Chen, Yingyuan; Guo, Yi; Wang, Jiang; Hong, Shouhai; Wei, Xile; Yu, Haitao; Deng, Bin
2015-01-01
Highlights: •Fractal analysis is a valuable tool for measuring MA-induced neural activities. •In course of the experiments, the spike trains display different fractal properties. •The fractal properties reflect the long-term modulation of MA on WDR neurons. •The results may explain the long-lasting effects induced by acupuncture. -- Abstract: The experimental and the clinical studies have showed manual acupuncture (MA) could evoke multiple responses in various neural regions. Characterising the neuronal activities in these regions may provide more deep insights into acupuncture mechanisms. This paper used fractal analysis to investigate MA-induced spike trains of Wide Dynamic Range (WDR) neurons in rat spinal dorsal horn, an important relay station and integral component in processing acupuncture information. Allan factor and Fano factor were utilized to test whether the spike trains were fractal, and Allan factor were used to evaluate the scaling exponents and Hurst exponents. It was found that these two fractal exponents before and during MA were different significantly. During MA, the scaling exponents of WDR neurons were regulated in a small range, indicating a special fractal pattern. The neuronal activities were long-range correlated over multiple time scales. The scaling exponents during and after MA were similar, suggesting that the long-range correlations not only displayed during MA, but also extended to after withdrawing the needle. Our results showed that fractal analysis is a useful tool for measuring acupuncture effects. MA could modulate neuronal activities of which the fractal properties change as time proceeding. This evolution of fractal dynamics in course of MA experiments may explain at the level of neuron why the effect of MA observed in experiment and in clinic are complex, time-evolutionary, long-range even lasting for some time after stimulation
Development and application of 3-D fractal reservoir model based on collage theorem
Energy Technology Data Exchange (ETDEWEB)
Kim, I.K.; Kim, K.S.; Sung, W.M. [Hanyang Univ., Seoul (Korea, Republic of)
1995-04-30
Reservoir characterization is the essential process to accurately evaluate the reservoir and has been conducted by geostatistical method, SRA algorithm, and etc. The characterized distribution of heterogeneous property by these methods shows randomly distributed phenomena, and does not present anomalous shape of property variation at discontinued space as compared with the observed shape in nature. This study proposed a new algorithm of fractal concept based on collage theorem, which can virtually present not only geometric shape of irregular and anomalous pore structures or coastlines, but also property variation for discontinuously observed data. With a basis of fractal concept, three dimensional fractal reservoir model was developed to more accurately characterize the heterogeneous reservoir. We performed analysis of pre-predictable hypothetically observed permeability data by using the fractal reservoir model. From the results, we can recognize that permeability distributions in the areal view or the cross-sectional view were consistent with the observed data. (author). 8 refs., 1 tab., 6 figs.
Boundary Fractal Analysis of Two Cube-oriented Grains in Partly Recrystallized Copper
DEFF Research Database (Denmark)
Sun, Jun; Zhang, Yubin; Dahl, Anders Bjorholm
2015-01-01
The protrusions and retrusions observed on the recrystallizing boundaries affect the migration kinetics during recrystallization. Characterization of the boundary roughness is necessary in order to evaluate their effects. This roughness has a structure that can be characterized by fractal analysis...
Formation of fractals by the self-assembly of interpolymer adducts of ...
Indian Academy of Sciences (India)
Polycarboxylic acids form self-organized poly- ... observation of the formation of fractal patterns in self- organizing polyacrylic acid systems in films driven by hydrogen bonding .... various positions, the SEM and EDX studies are car- ried out.
Growth and optical microscopy observation of the lysozyme crystals
R.Vlokh; L.Marsel; I.Teslyuk; O.G.Vlokh
2001-01-01
The little single lysozyme crystals in the capillary after 15 days of growth process with average size 0.1´0.1´0.16mm3 were obtained. It was shown that lysozyme crystals are optically anisotropical and birefringence along a axis is Dn=(2.2±0.5)´10-3 in visible spectrum region. From the measurements of crystallographic angles follows that on the {001} faces angles equal a=81o, b=99o. On the sexangle faces angles equal e=100o, f=140o and g=120o. On the base of obtained results the lysozyme crys...
From Fractal Trees to Deltaic Networks
Cazanacli, D.; Wolinsky, M. A.; Sylvester, Z.; Cantelli, A.; Paola, C.
2013-12-01
Geometric networks that capture many aspects of natural deltas can be constructed from simple concepts from graph theory and normal probability distributions. Fractal trees with symmetrical geometries are the result of replicating two simple geometric elements, line segments whose lengths decrease and bifurcation angles that are commonly held constant. Branches could also have a thickness, which in the case of natural distributary systems is the equivalent of channel width. In river- or wave-dominated natural deltas, the channel width is a function of discharge. When normal variations around the mean values for length, bifurcating angles, and discharge are applied, along with either pruning of 'clashing' branches or merging (equivalent to channel confluence), fractal trees start resembling natural deltaic networks, except that the resulting channels are unnaturally straight. Introducing a bifurcation probability fewer, naturally curved channels are obtained. If there is no bifurcation, the direction of each new segment depends on the direction the previous segment upstream (correlated random walk) and, to a lesser extent, on a general direction of growth (directional bias). When bifurcation occurs, the resulting two directions also depend on the bifurcation angle and the discharge split proportions, with the dominant branch following the direction of the upstream parent channel closely. The bifurcation probability controls the channel density and, in conjunction with the variability of the directional angles, the overall curvature of the channels. The growth of the network in effect is associated with net delta progradation. The overall shape and shape evolution of the delta depend mainly on the bifurcation angle average size and angle variability coupled with the degree of dominant direction dependency (bias). The proposed algorithm demonstrates how, based on only a few simple rules, a wide variety of channel networks resembling natural deltas, can be replicated
Gao, Wei; Zakharov, Valery P.; Myakinin, Oleg O.; Bratchenko, Ivan A.; Artemyev, Dmitry N.; Kornilin, Dmitry V.
2015-07-01
Optical coherence tomography (OCT) is usually employed for the measurement of retinal thickness characterizing the structural changes of tissue. However, fractal dimension (FD) could also character the structural changes of tissue. Therefore, fractal dimension changes may provide further information regarding cellular layers and early damage in ocular diseases. We investigated the possibility of OCT in detecting changes in fractal dimension from layered retinal structures. OCT images were obtained from diabetic patients without retinopathy (DM, n = 38 eyes) or mild diabetic retinopathy (MDR, n = 43 eyes) and normal healthy subjects (Controls, n = 74 eyes). Fractal dimension was calculated using the differentiate box counting methodology. We evaluated the usefulness of quantifying fractal dimension of layered structures in the detection of retinal damage. Generalized estimating equations considering within-subject intereye relations were used to test for differences between the groups. A modified p value of <0.001 was considered statistically significant. Receiver operating characteristic (ROC) curves were constructed to describe the ability of fractal dimension to discriminate between the eyes of DM, MDR and healthy eyes. Significant decreases of fractal dimension were observed in all layers in the MDR eyes compared with controls except in the inner nuclear layer (INL). Significant decreases of fractal dimension were also observed in all layers in the MDR eyes compared with DM eyes. The highest area under receiver operating characteristic curve (AUROC) values estimated for fractal dimension were observed for the outer plexiform layer (OPL) and outer segment photoreceptors (OS) when comparing MDR eyes with controls. The highest AUROC value estimated for fractal dimension were also observed for the retinal nerve fiber layer (RNFL) and OS when comparing MDR eyes with DM eyes. Our results suggest that fractal dimension of the intraretinal layers may provide useful
Emergence of fractal scale-free networks from stochastic evolution on the Cayley tree
Energy Technology Data Exchange (ETDEWEB)
Chełminiak, Przemysław, E-mail: geronimo@amu.edu.pl
2013-11-29
An unexpected recognition of fractal topology in some real-world scale-free networks has evoked again an interest in the mechanisms stimulating their evolution. To explain this phenomenon a few models of a deterministic construction as well as a probabilistic growth controlled by a tunable parameter have been proposed so far. A quite different approach based on the fully stochastic evolution of the fractal scale-free networks presented in this Letter counterpoises these former ideas. It is argued that the diffusive evolution of the network on the Cayley tree shapes its fractality, self-similarity and the branching number criticality without any control parameter. The last attribute of the scale-free network is an intrinsic property of the skeleton, a special type of spanning tree which determines its fractality.
Brief communication: age and fractal dimensions of human sagittal and coronal sutures
DEFF Research Database (Denmark)
Lynnerup, Niels; Jacobsen, Jens Christian Brings
2003-01-01
The fractal dimensions of human sagittal and coronal sutures were calculated on 31 complete skulls from the Terry Collection. The aim was to investigate whether the fractal dimension, relying on the whole sutural length, might yield a better description of age-related changes in sutural morphology......, as opposed to other methods of quantification, which generally rely on more arbitrary scoring systems. However, the fractal dimension did not yield better age correlations than other previously described methods. At best, the results reflected the general observation that young adults below age 40 years...
Conference on Fractals and Related Fields III
Seuret, Stéphane
2017-01-01
This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.
Chaos, Fractals and Their Applications
Thompson, J. Michael T.
2016-12-01
This paper gives an up-to-date account of chaos and fractals, in a popular pictorial style for the general scientific reader. A brief historical account covers the development of the subject from Newton’s laws of motion to the astronomy of Poincaré and the weather forecasting of Lorenz. Emphasis is given to the important underlying concepts, embracing the fractal properties of coastlines and the logistics of population dynamics. A wide variety of applications include: NASA’s discovery and use of zero-fuel chaotic “superhighways” between the planets; erratic chaotic solutions generated by Euler’s method in mathematics; atomic force microscopy; spontaneous pattern formation in chemical and biological systems; impact mechanics in offshore engineering and the chatter of cutting tools; controlling chaotic heartbeats. Reference is made to a number of interactive simulations and movies accessible on the web.
Fractals, malware, and data models
Jaenisch, Holger M.; Potter, Andrew N.; Williams, Deborah; Handley, James W.
2012-06-01
We examine the hypothesis that the decision boundary between malware and non-malware is fractal. We introduce a novel encoding method derived from text mining for converting disassembled programs first into opstrings and then filter these into a reduced opcode alphabet. These opcodes are enumerated and encoded into real floating point number format and used for characterizing frequency of occurrence and distribution properties of malware functions to compare with non-malware functions. We use the concept of invariant moments to characterize the highly non-Gaussian structure of the opcode distributions. We then derive Data Model based classifiers from identified features and interpolate and extrapolate the parameter sample space for the derived Data Models. This is done to examine the nature of the parameter space classification boundary between families of malware and the general non-malware category. Preliminary results strongly support the fractal boundary hypothesis, and a summary of our methods and results are presented here.
The fractal dimension of architecture
Ostwald, Michael J
2016-01-01
Fractal analysis is a method for measuring, analysing and comparing the formal or geometric properties of complex objects. In this book it is used to investigate eighty-five buildings that have been designed by some of the twentieth-century’s most respected and celebrated architects. Including designs by Le Corbusier, Eileen Gray, Frank Lloyd Wright, Robert Venturi, Frank Gehry, Peter Eisenman, Richard Meier and Kazuyo Sejima amongst others, this book uses mathematics to analyse arguments and theories about some of the world’s most famous designs. Starting with 625 reconstructed architectural plans and elevations, and including more than 200 specially prepared views of famous buildings, this book presents the results of the largest mathematical study ever undertaken into architectural design and the largest single application of fractal analysis presented in any field. The data derived from this study is used to test three overarching hypotheses about social, stylistic and personal trends in design, along...
Dimensional analysis, scaling and fractals
International Nuclear Information System (INIS)
Timm, L.C.; Reichardt, K.; Oliveira Santos Bacchi, O.
2004-01-01
Dimensional analysis refers to the study of the dimensions that characterize physical entities, like mass, force and energy. Classical mechanics is based on three fundamental entities, with dimensions MLT, the mass M, the length L and the time T. The combination of these entities gives rise to derived entities, like volume, speed and force, of dimensions L 3 , LT -1 , MLT -2 , respectively. In other areas of physics, four other fundamental entities are defined, among them the temperature θ and the electrical current I. The parameters that characterize physical phenomena are related among themselves by laws, in general of quantitative nature, in which they appear as measures of the considered physical entities. The measure of an entity is the result of its comparison with another one, of the same type, called unit. Maps are also drawn in scale, for example, in a scale of 1:10,000, 1 cm 2 of paper can represent 10,000 m 2 in the field. Entities that differ in scale cannot be compared in a simple way. Fractal geometry, in contrast to the Euclidean geometry, admits fractional dimensions. The term fractal is defined in Mandelbrot (1982) as coming from the Latin fractus, derived from frangere which signifies to break, to form irregular fragments. The term fractal is opposite to the term algebra (from the Arabic: jabara) which means to join, to put together the parts. For Mandelbrot, fractals are non topologic objects, that is, objects which have as their dimension a real, non integer number, which exceeds the topologic dimension. For the topologic objects, or Euclidean forms, the dimension is an integer (0 for the point, 1 for a line, 2 for a surface, and 3 for a volume). The fractal dimension of Mandelbrot is a measure of the degree of irregularity of the object under consideration. It is related to the speed by which the estimate of the measure of an object increases as the measurement scale decreases. An object normally taken as uni-dimensional, like a piece of a
Fuzzy fractals, chaos, and noise
Energy Technology Data Exchange (ETDEWEB)
Zardecki, A.
1997-05-01
To distinguish between chaotic and noisy processes, the authors analyze one- and two-dimensional chaotic mappings, supplemented by the additive noise terms. The predictive power of a fuzzy rule-based system allows one to distinguish ergodic and chaotic time series: in an ergodic series the likelihood of finding large numbers is small compared to the likelihood of finding them in a chaotic series. In the case of two dimensions, they consider the fractal fuzzy sets whose {alpha}-cuts are fractals, arising in the context of a quadratic mapping in the extended complex plane. In an example provided by the Julia set, the concept of Hausdorff dimension enables one to decide in favor of chaotic or noisy evolution.
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-01-01
reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics
Fractals via iterated functions and multifunctions
International Nuclear Information System (INIS)
Singh, S.L.; Prasad, Bhagwati; Kumar, Ashish
2009-01-01
Fractals have wide applications in biology, computer graphics, quantum physics and several other areas of applied sciences (see, for instance [Daya Sagar BS, Rangarajan Govindan, Veneziano Daniele. Preface - fractals in geophysics. Chaos, Solitons and Fractals 2004;19:237-39; El Naschie MS. Young double-split experiment Heisenberg uncertainty principles and cantorian space-time. Chaos, Solitons and Fractals 1994;4(3):403-09; El Naschie MS. Quantum measurement, information, diffusion and cantorian geodesics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 191-205; El Naschie MS. Iterated function systems, information and the two-slit experiment of quantum mechanics. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995. p. 185-9; El Naschie MS, Rossler OE, Prigogine I. Forward. In: El Naschie MS, Rossler OE, Prigogine I, editors. Quantum mechanics, diffusion and Chaotic fractals. Oxford: Elsevier Science Ltd; 1995; El Naschie MS. A review of E-infinity theory and the mass spectrum of high energy particle physics. Chaos, Solitons and Fractals 2004;19:209-36; El Naschie MS. Fractal black holes and information. Chaos, Solitons and Fractals 2006;29:23-35; El Naschie MS. Superstring theory: what it cannot do but E-infinity could. Chaos, Solitons and Fractals 2006;29:65-8). Especially, the study of iterated functions has been found very useful in the theory of black holes, two-slit experiment in quantum mechanics (cf. El Naschie, as mentioned above). The intent of this paper is to give a brief account of recent developments of fractals arising from IFS. We also discuss iterated multifunctions.
Node insertion in Coalescence Fractal Interpolation Function
International Nuclear Information System (INIS)
Prasad, Srijanani Anurag
2013-01-01
The Iterated Function System (IFS) used in the construction of Coalescence Hidden-variable Fractal Interpolation Function (CHFIF) depends on the interpolation data. The insertion of a new point in a given set of interpolation data is called the problem of node insertion. In this paper, the effect of insertion of new point on the related IFS and the Coalescence Fractal Interpolation Function is studied. Smoothness and Fractal Dimension of a CHFIF obtained with a node are also discussed
Fractional hydrodynamic equations for fractal media
International Nuclear Information System (INIS)
Tarasov, Vasily E.
2005-01-01
We use the fractional integrals in order to describe dynamical processes in the fractal medium. We consider the 'fractional' continuous medium model for the fractal media and derive the fractional generalization of the equations of balance of mass density, momentum density, and internal energy. The fractional generalization of Navier-Stokes and Euler equations are considered. We derive the equilibrium equation for fractal media. The sound waves in the continuous medium model for fractional media are considered
Power Load Prediction Based on Fractal Theory
Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song
2015-01-01
The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...
Fractal Metrology for biogeosystems analysis
Directory of Open Access Journals (Sweden)
V. Torres-Argüelles
2010-11-01
Full Text Available The solid-pore distribution pattern plays an important role in soil functioning being related with the main physical, chemical and biological multiscale and multitemporal processes of this complex system. In the present research, we studied the aggregation process as self-organizing and operating near a critical point. The structural pattern is extracted from the digital images of three soils (Chernozem, Solonetz and "Chocolate" Clay and compared in terms of roughness of the gray-intensity distribution quantified by several measurement techniques. Special attention was paid to the uncertainty of each of them measured in terms of standard deviation. Some of the applied methods are known as classical in the fractal context (box-counting, rescaling-range and wavelets analyses, etc. while the others have been recently developed by our Group. The combination of these techniques, coming from Fractal Geometry, Metrology, Informatics, Probability Theory and Statistics is termed in this paper Fractal Metrology (FM. We show the usefulness of FM for complex systems analysis through a case study of the soil's physical and chemical degradation applying the selected toolbox to describe and compare the structural attributes of three porous media with contrasting structure but similar clay mineralogy dominated by montmorillonites.
Fractal Geometry and Stochastics V
Falconer, Kenneth; Zähle, Martina
2015-01-01
This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott, Michał Rams, Pablo Shmerkin, and András Te...
Fractal systems of central places based on intermittency of space-filling
International Nuclear Information System (INIS)
Chen Yanguang
2011-01-01
Highlights: → The idea of intermittency is introduced into central place model. → The revised central place model suggests incomplete space filling. → New central place fractals are presented for urban analysis. → The average nearest distance is proposed to estimate the fractal dimension. → The concept of distance-based space is replaced by that of dimension-based space. - Abstract: The central place models are fundamentally important in theoretical geography and city planning theory. The texture and structure of central place networks have been demonstrated to be self-similar in both theoretical and empirical studies. However, the underlying rationale of central place fractals in the real world has not yet been revealed so far. This paper is devoted to illustrating the mechanisms by which the fractal patterns can be generated from central place systems. The structural dimension of the traditional central place models is d = 2 indicating no intermittency in the spatial distribution of human settlements. This dimension value is inconsistent with empirical observations. Substituting the complete space filling with the incomplete space filling, we can obtain central place models with fractional dimension D < d = 2 indicative of spatial intermittency. Thus the conventional central place models are converted into fractal central place models. If we further integrate the chance factors into the improved central place fractals, the theory will be able to explain the real patterns of urban places very well. As empirical analyses, the US cities and towns are employed to verify the fractal-based models of central places.
Laboratory observation of magnetic field growth driven by shear flow
Energy Technology Data Exchange (ETDEWEB)
Intrator, T. P., E-mail: intrator@lanl.gov; Feng, Y.; Sears, J.; Weber, T. [Los Alamos National Laboratory, M.S. E526, Los Alamos, New Mexico 87545 (United States); Dorf, L. [Applied Materials, Inc., Santa Clara, CA 95054 (United States); Sun, X. [University of Science and Technology, Hefei (China)
2014-04-15
Two magnetic flux ropes that collide and bounce have been characterized in the laboratory. We find screw pinch profiles that include ion flow v{sub i}, magnetic field B, current density J, and plasma pressure. The electron flow v{sub e} can be inferred, allowing the evaluation of the Hall J×B term in a two fluid magnetohydrodynamic Ohm's Law. Flux ropes that are initially cylindrical are mutually attracted and compress each other, which distorts the cylindrical symmetry. Magnetic field is created via the ∇×v{sub e}×B induction term in Ohm's Law where in-plane (perpendicular) shear of parallel flow (along the flux rope) is the dominant feature, along with some dissipation and magnetic reconnection. We predict and measure the growth of a quadrupole out-of-plane magnetic field δB{sub z}. This is a simple and coherent example of a shear flow driven dynamo. There is some similarity with two dimensional reconnection scenarios, which induce a current sheet and thus out-of-plane flow in the third dimension, despite the customary picture that considers flows only in the reconnection plane. These data illustrate a general and deterministic mechanism for large scale sheared flows to acquire smaller scale magnetic features, disordered structure, and possibly turbulence.
Observation of carbon growth and interface structures in methanol solution
Okuno, Kimio
2015-11-01
In the deposition of carbon on the surface of a tungsten tip in methanol solution by electrolysis, the growth structure of the carbon films, the interface state, and the dissolution of carbon atoms into the tungsten matrix of the substrate have been investigated with the atomic events by field ion microscopy (FIM). The carbon films preferentially condense on the W{111} plane. The interfacial reaction at the carbon atom-tungsten substrate interface is vigorous and the carbon atoms also readily dissolve into the substrate matrix to form a tungsten-carbon complex. The reaction depth of the deposited carbon depends on the magnitude of electrolytic current and the treatment duration in the methanol solution. In this work, the resolution depth of carbon was found to be approximately 270 atomic layers below the top layer of the tungsten substrate by a field evaporation technique. In the case of a low electrolytic current, the tungsten substrate surface is entirely covered with carbon atoms having a pseudomorphic structure. The field-electron emission characteristics were also evaluated for various coverages of the carbon film formed on the substrate.
Fractal geometry mathematical foundations and applications
Falconer, Kenneth
2013-01-01
The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals. The book introduces and develops the general theory and applica
A variational principle for the Hausdorff dimension of fractal sets
DEFF Research Database (Denmark)
Olsen, Lars; Cutler, Colleen D.
1994-01-01
Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)......Matematik, fraktal (fractal), Hausdorff dimension, Renyi dimension, pakke dimension (packing dimension)...
Inkjet-Printed Ultra Wide Band Fractal Antennas
Maza, Armando Rodriguez
2012-05-01
In this work, Paper-based inkjet-printed Ultra-wide band (UWB) fractal antennas are presented. Three new designs, a combined UWB fractal monopole based on the fourth order Koch Snowflake fractal which utilizes a Sierpinski Gasket fractal for ink reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics. It is shown that fractals prove to be a successful method of reducing fabrication cost in inkjet printed antennas while retaining or enhancing printed antenna performance.
Fractal approach to computer-analytical modelling of tree crown
International Nuclear Information System (INIS)
Berezovskaya, F.S.; Karev, G.P.; Kisliuk, O.F.; Khlebopros, R.G.; Tcelniker, Yu.L.
1993-09-01
In this paper we discuss three approaches to the modeling of a tree crown development. These approaches are experimental (i.e. regressive), theoretical (i.e. analytical) and simulation (i.e. computer) modeling. The common assumption of these is that a tree can be regarded as one of the fractal objects which is the collection of semi-similar objects and combines the properties of two- and three-dimensional bodies. We show that a fractal measure of crown can be used as the link between the mathematical models of crown growth and light propagation through canopy. The computer approach gives the possibility to visualize a crown development and to calibrate the model on experimental data. In the paper different stages of the above-mentioned approaches are described. The experimental data for spruce, the description of computer system for modeling and the variant of computer model are presented. (author). 9 refs, 4 figs
Fractal diffusion coefficient from dynamical zeta functions
Energy Technology Data Exchange (ETDEWEB)
Cristadoro, Giampaolo [Max Planck Institute for the Physics of Complex Systems, Noethnitzer Str. 38, D 01187 Dresden (Germany)
2006-03-10
Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero. (letter to the editor)
Fractal diffusion coefficient from dynamical zeta functions
International Nuclear Information System (INIS)
Cristadoro, Giampaolo
2006-01-01
Dynamical zeta functions provide a powerful method to analyse low-dimensional dynamical systems when the underlying symbolic dynamics is under control. On the other hand, even simple one-dimensional maps can show an intricate structure of the grammar rules that may lead to a non-smooth dependence of global observables on parameters changes. A paradigmatic example is the fractal diffusion coefficient arising in a simple piecewise linear one-dimensional map of the real line. Using the Baladi-Ruelle generalization of the Milnor-Thurnston kneading determinant, we provide the exact dynamical zeta function for such a map and compute the diffusion coefficient from its smallest zero. (letter to the editor)
Ciro, D'Orazio; Padoan, Rita; Blau, Hannah; Marostica, Anna; Fuoti, Maurizio; Volpi, Sonia; Pilotta, Alba; Meyerovitch, Joseph; Sher, Daniel; Assael, Baroukh M
2013-03-01
Growth delay in cystic fibrosis is frequent and is usually the result of several interacting causes. It most often derives from severe respiratory impairment and severe malabsorption. There are however patients whose clinical condition is not severe enough to be held accountable for this phenomenon. We aimed at describing patients who showed growth delay, who were not affected by severe pulmonary disease or malabsorption and who, when tested, showed a reduced GH secretion after stimulation with conventional agents. We noticed a disproportionately large prevalence of growth hormone (GH) release deficit (GHRD) in pediatric cystic fibrosis (CF) patients. We examined all patients under our care in the period 2006-11, who were older than 5 and younger than 16 years old. We focussed on those who fell below the 3rd height percentile, or whose growth during the previous 18 months faltered by >2SD, and who did not present clinical conditions that could reasonably explain their failure to thrive. These patients were subjected to standard GH provocative tests. Out of 285 who matched the age criterion, 33 patients also matched the height percentile criterion. While 15/33 suffered clinical conditions that could reasonably explain their failure to thrive, 18/33 underwent GH release provocative tests and 12/18 showed a release deficit. We conclude that impaired GH secretion is more frequent among CF patients compared to the prevalence of GH deficiency in the general population and that GH release impairment may be an independent cause of growth delay in CF. Our findings are in agreement with recent studies that have described low GH levels in CF piglets and in neonates with CF [1]. Copyright © 2012 European Cystic Fibrosis Society. Published by Elsevier B.V. All rights reserved.
Fractal analysis of polar bear hairs
Directory of Open Access Journals (Sweden)
Wang Qing-Li
2015-01-01
Full Text Available Hairs of a polar bear (Ursus maritimus are of superior properties such as the excellent thermal protection. Why do polar bears can resist such cold environment? The paper concludes that its fractal porosity plays an important role, and its fractal dimensions are very close to the golden mean, 1.618, revealing the possible optimal structure of polar bear hair.
Design of LTCC Based Fractal Antenna
AdbulGhaffar, Farhan
2010-09-01
The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP; SCHWARZ, UJ
1991-01-01
To study the structure of interstellar clouds we used the so-called perimeter-area relation to estimate fractal dimensions. We studied the reliability of the method by applying it to artificial fractals and discuss some of the problems and pitfalls. Results for two different cloud types
Fractal Image Coding with Digital Watermarks
Directory of Open Access Journals (Sweden)
Z. Klenovicova
2000-12-01
Full Text Available In this paper are presented some results of implementation of digitalwatermarking methods into image coding based on fractal principles. Thepaper focuses on two possible approaches of embedding digitalwatermarks into fractal code of images - embedding digital watermarksinto parameters for position of similar blocks and coefficients ofblock similarity. Both algorithms were analyzed and verified on grayscale static images.
Chaos and fractals an elementary introduction
Feldman, David P
2012-01-01
For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.
MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS
VOGELAAR, MGR; WAKKER, BP
1994-01-01
To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We
Undergraduate Experiment with Fractal Diffraction Gratings
Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.
2011-01-01
We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…
Chaos and fractals. Applications to nuclear engineering
International Nuclear Information System (INIS)
Clausse, A.; Delmastro, D.F.
1990-01-01
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author) [es
Fractal Analysis of Rock Joint Profiles
Audy, Ondřej; Ficker, Tomáš
2017-10-01
Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.
A random walk through fractal dimensions
Kaye, Brian H
2008-01-01
Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science.From reviews of the first edition:''...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.'' MRS Bulletin
Excitation gap of fractal quantum hall states in graphene
International Nuclear Information System (INIS)
Luo, Wenchen; Chakraborty, Tapash
2016-01-01
In the presence of a magnetic field and an external periodic potential the Landau level spectrum of a two-dimensional electron gas exhibits a fractal pattern in the energy spectrum which is described as the Hofstadter’s butterfly. In this work, we develop a Hartree–Fock theory to deal with the electron-electron interaction in the Hofstadter’s butterfly state in a finite-size graphene with periodic boundary conditions, where we include both spin and valley degrees of freedom. We then treat the butterfly state as an electron crystal so that we could obtain the order parameters of the crystal in the momentum space and also in an infinite sample. A phase transition between the liquid phase and the fractal crystal phase can be observed. The excitation gaps obtained in the infinite sample is comparable to those in the finite-size study, and agree with a recent experimental observation. (paper)
Scaling-up vaccine production: implementation aspects of a biomass growth observer and controller
Soons, Z.I.T.A.; IJssel, van den, J.; Pol, van der, L.A.; Straten, van, G.; Boxtel, van, A.J.B.
2009-01-01
Abstract This study considers two aspects of the implementation of a biomass growth observer and specific growth rate controller in scale-up from small- to pilot-scale bioreactors towards a feasible bulk production process for whole-cell vaccine against whooping cough. The first is the calculation of the oxygen uptake rate, the starting point for online monitoring and control of biomass growth, taking into account the dynamics in the gas-phase. Mixing effects and delays are caused by amongst ...
International Nuclear Information System (INIS)
Rodriguez V, Javier O; Prieto, Signed E; Ortiz, Liliana
2010-01-01
Geometry allows the objective mathematical characterization of forms. Fractal geometry characterizes irregular objects. The left ventricle dynamical states form observed through echocardiography can be objectively evaluated through fractal dimension measures. Methods: A measurement of fractal dimension was performed using the Box-counting method of three defined objects in 28 echocardiographic images, 16 from normal children (group A) and 12 ill children (group B), in order to establish differences between health and illness from its comparison with the fractal dimensions of 2 normality prototypes and 2 disease prototypes. Results: A new diagnostic, clinical application methodology was developed based in the intrinsic mathematical harmony (IMH) concept, and it was observed that the fractal dimensions of the defined objects for an abnormal echocardiogram show similarity to its fourth significant number, thus demonstrating the possibility of following up the evolution from normality towards disease. According to the performed calculations, 68.75% of the cases in group A could be better evaluated with the developed diagnostic methodology, and the ill ones could be diagnosed more effectively. Conclusions: The pediatric echocardiography images can be objectively characterized with fractal dimension measurements, thus enabling the development of a clinical diagnostic methodology of echocardiography in children from the IMH concept.
On fractal space-time and fractional calculus
Directory of Open Access Journals (Sweden)
Hu Yue
2016-01-01
Full Text Available This paper gives an explanation of fractional calculus in fractal space-time. On observable scales, continuum models can be used, however, when the scale tends to a smaller threshold, a fractional model has to be adopted to describe phenomena in micro/nano structure. A time-fractional Fornberg-Whitham equation is used as an example to elucidate the physical meaning of the fractional order, and its solution process is given by the fractional complex transform.
Fractal dimension and turbulence in Giant HII Regions
International Nuclear Information System (INIS)
Caicedo-Ortiz, H E; Santiago-Cortes, E; López-Bonilla, J; er piso, CP 07738, México D.F (Mexico))" data-affiliation=" (ESFM, Instituto Politécnico Nacional, Edif. 9, 1er piso, CP 07738, México D.F (Mexico))" >Castañeda, H O
2015-01-01
We have measured the fractal dimensions of the Giant HII Regions Hubble X and Hubble V in NGC6822 using images obtained with the Hubble's Wide Field Planetary Camera 2 (WFPC2). These measures are associated with the turbulence observed in these regions, which is quantified through the velocity dispersion of emission lines in the visible. Our results suggest low turbulence behaviour
Random fractal structures in North American energy markets
Energy Technology Data Exchange (ETDEWEB)
Serletis, Apostolos [Calgary Univ., Dept. of Economics, Calgary, AB (Canada); Andreadis, Ioannis [European Univ. of the Hague, Center of Management Studies, The Hague (Netherlands)
2004-05-01
This paper uses daily observations on West Texas Intermediate (WTI) crude oil prices at Chicago and Henry Hub natural gas prices at LA (over the deregulated period of the 1990s) and various tests from statistics and dynamical systems theory to support a random fractal structure for North American energy markets. In particular, this evidence is supported by the Vassilicos et al. (1993) multifractal structure test and the Ghashghaie et al. [Nature 381 (1996) 767] turbulent behavior test. (Author)
Scaling-up vaccine production: implementation aspects of a biomass growth observer and controller
Soons, Z.I.T.A.; IJssel, van den J.; Pol, van der L.A.; Straten, van G.; Boxtel, van A.J.B.
2009-01-01
Abstract This study considers two aspects of the implementation of a biomass growth observer and specific growth rate controller in scale-up from small- to pilot-scale bioreactors towards a feasible bulk production process for whole-cell vaccine against whooping cough. The first is the calculation
Pre-Service Teachers' Concept Images on Fractal Dimension
Karakus, Fatih
2016-01-01
The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…
Diagnosis of Lung Cancer by Fractal Analysis of Damaged DNA
Directory of Open Access Journals (Sweden)
Hamidreza Namazi
2015-01-01
Full Text Available Cancer starts when cells in a part of the body start to grow out of control. In fact cells become cancer cells because of DNA damage. A DNA walk of a genome represents how the frequency of each nucleotide of a pairing nucleotide couple changes locally. In this research in order to study the cancer genes, DNA walk plots of genomes of patients with lung cancer were generated using a program written in MATLAB language. The data so obtained was checked for fractal property by computing the fractal dimension using a program written in MATLAB. Also, the correlation of damaged DNA was studied using the Hurst exponent measure. We have found that the damaged DNA sequences are exhibiting higher degree of fractality and less correlation compared with normal DNA sequences. So we confirmed this method can be used for early detection of lung cancer. The method introduced in this research not only is useful for diagnosis of lung cancer but also can be applied for detection and growth analysis of different types of cancers.
Morphometric relations of fractal-skeletal based channel network model
Directory of Open Access Journals (Sweden)
B. S. Daya Sagar
1998-01-01
Full Text Available A fractal-skeletal based channel network (F-SCN model is proposed. Four regular sided initiator-basins are transformed as second order fractal basins by following a specific generating mechanism with non-random rule. The morphological skeletons, hereafter referred to as channel networks, are extracted from these fractal basins. The morphometric and fractal relationships of these F-SCNs are shown. The fractal dimensions of these fractal basins, channel networks, and main channel lengths (computed through box counting method are compared with those of estimated length–area measures. Certain morphometric order ratios to show fractal relations are also highlighted.
Fractal dimension of turbulent black holes
Westernacher-Schneider, John Ryan
2017-11-01
We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.
Classification of radar echoes using fractal geometry
International Nuclear Information System (INIS)
Azzaz, Nafissa; Haddad, Boualem
2017-01-01
Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.
The Role of Resolution in the Estimation of Fractal Dimension Maps From SAR Data
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Gerardo Di Martino
2017-12-01
Full Text Available This work is aimed at investigating the role of resolution in fractal dimension map estimation, analyzing the role of the different surface spatial scales involved in the considered estimation process. The study is performed using a data set of actual Cosmo/SkyMed Synthetic Aperture Radar (SAR images relevant to two different areas, the region of Bidi in Burkina Faso and the city of Naples in Italy, acquired in stripmap and enhanced spotlight modes. The behavior of fractal dimension maps in the presence of areas with distinctive characteristics from the viewpoint of land-cover and surface features is discussed. Significant differences among the estimated maps are obtained in the presence of fine textural details, which significantly affect the fractal dimension estimation for the higher resolution spotlight images. The obtained results show that if we are interested in obtaining a reliable estimate of the fractal dimension of the observed natural scene, stripmap images should be chosen in view of both economic and computational considerations. In turn, the combination of fractal dimension maps obtained from stripmap and spotlight images can be used to identify areas on the scene presenting non-fractal behavior (e.g., urban areas. Along this guideline, a simple example of stripmap-spotlight data fusion is also presented.
Predicting beauty: fractal dimension and visual complexity in art.
Forsythe, A; Nadal, M; Sheehy, N; Cela-Conde, C J; Sawey, M
2011-02-01
Visual complexity has been known to be a significant predictor of preference for artistic works for some time. The first study reported here examines the extent to which perceived visual complexity in art can be successfully predicted using automated measures of complexity. Contrary to previous findings the most successful predictor of visual complexity was Gif compression. The second study examined the extent to which fractal dimension could account for judgments of perceived beauty. The fractal dimension measure accounts for more of the variance in judgments of perceived beauty in visual art than measures of visual complexity alone, particularly for abstract and natural images. Results also suggest that when colour is removed from an artistic image observers are unable to make meaningful judgments as to its beauty. ©2010 The British Psychological Society.
Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael
2016-02-01
One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.
Undergraduate experiment with fractal diffraction gratings
International Nuclear Information System (INIS)
Monsoriu, Juan A; Furlan, Walter D; Pons, Amparo; Barreiro, Juan C; Gimenez, Marcos H
2011-01-01
We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics laboratories and compared with those obtained with conventional periodic gratings. It is shown that fractal gratings produce self-similar diffraction patterns which can be evaluated analytically. Good agreement is obtained between experimental and numerical results.
Zipf’s law, 1/f noise, and fractal hierarchy
International Nuclear Information System (INIS)
Chen Yanguang
2012-01-01
Highlights: ► I developed a general scaling method based on hierarchies of cites. ► Hierarchy is classified into three types based on monofractal and multifractals. ► Zipf’s law can be used to estimate the capacity dimension of a multifractal set. ► I derive the self-similar hierarchy from the rank-size distribution. ► The hierarchical scaling method can be applied to the 1/f spectra. - Abstract: Fractals, 1/f noise, and Zipf’s laws are frequently observed within the natural living world as well as in social institutions, representing three signatures of complex systems. All these observations are associated with scaling laws and therefore have created much research interest in many diverse scientific circles. However, the inherent relationships between these scaling phenomena are not yet clear. In this paper, theoretical demonstration and mathematical experiments based on urban studies are employed to reveal the analogy between fractal patterns, 1/f spectra, and the Zipf distribution. First, the multifractal process empirically suggests the Zipf distribution. Second, a 1/f spectrum is mathematically identical to Zipf’s law. Third, both 1/f spectra and Zipf’s law can be converted into a self-similar hierarchy. Fourth, fractals, 1/f spectra, Zipf’s law can be rescaled with similar exponential laws and power laws. The self-similar hierarchy is a more general scaling method which can be used to unify different scaling phenomena and rules in both physical and social systems such as cities, rivers, earthquakes, fractals, 1/f noise, and rank-size distributions. The mathematical laws of this hierarchical structure can provide us with a holistic perspective of looking at complexity and complex systems.
Directory of Open Access Journals (Sweden)
María Eugenia Torres
2007-01-01
Full Text Available En este trabajo comparamos tres métodos diferentes utilizados para estimar el exponente de Hurst, y analizamos su eficiencia cuando son aplicados a series de datos de diferentes longitudes. Se analizan series temporales de fBm sintetizada pura y con tendencias sinusoidales superpuestas. Mostraremos que los tres métodos aquí discutidos, DFA, basado en wavelets y de variaciones discretas, no sólo son altamente dependientes de la longitud de la señal, sino también del orden o número de los momentos (polinómico, regularidad wavelet o variaciones discretas. Para longitudes de datos suficientemente grandes (superiores a 212, los métodos basados en wavelets y de variaciones discretas mostraron ser menos sesgados y más estables para señales fBm simuladas. Mostraremos que el método de DFA, más utilizado en el ambiente biomédico, es el que proporciona peores estimaciones, arrojando resultados ambiguos cuando son aplicados a señales biológicas de diferentes longitudes o con diferentes parámetros de estimación, sin que pueda considerarse a ninguno de los otros dos como métodos confiables en el momento de desear obtener resultados de relevancia física o fisiológica. Los resultados obtenidos indican que debería procederse con más cautela cuando se trata de obtener conclusiones fisiológicas a partir de estimaciones realizadas a partir de señales reales.
Fractal statistics of brittle fragmentation
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M. Davydova
2013-04-01
Full Text Available The study of fragmentation statistics of brittle materials that includes four types of experiments is presented. Data processing of the fragmentation of glass plates under quasi-static loading and the fragmentation of quartz cylindrical rods under dynamic loading shows that the size distribution of fragments (spatial quantity is fractal and can be described by a power law. The original experimental technique allows us to measure, apart from the spatial quantity, the temporal quantity - the size of time interval between the impulses of the light reflected from the newly created surfaces. The analysis of distributions of spatial (fragment size and temporal (time interval quantities provides evidence of obeying scaling laws, which suggests the possibility of self-organized criticality in fragmentation.
Model of fractal aggregates induced by shear
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Wan Zhanhong
2013-01-01
Full Text Available It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.
A Parallel Approach to Fractal Image Compression
Lubomir Dedera
2004-01-01
The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
Random walks of oriented particles on fractals
International Nuclear Information System (INIS)
Haber, René; Prehl, Janett; Hoffmann, Karl Heinz; Herrmann, Heiko
2014-01-01
Random walks of point particles on fractals exhibit subdiffusive behavior, where the anomalous diffusion exponent is smaller than one, and the corresponding random walk dimension is larger than two. This is due to the limited space available in fractal structures. Here, we endow the particles with an orientation and analyze their dynamics on fractal structures. In particular, we focus on the dynamical consequences of the interactions between the local surrounding fractal structure and the particle orientation, which are modeled using an appropriate move class. These interactions can lead to particles becoming temporarily or permanently stuck in parts of the structure. A surprising finding is that the random walk dimension is not affected by the orientation while the diffusion constant shows a variety of interesting and surprising features. (paper)
Lévy processes on a generalized fractal comb
Sandev, Trifce; Iomin, Alexander; Méndez, Vicenç
2016-09-01
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial kernels. In particular, the fractal structure of the fingers, which is controlled by the spatial kernel in both the real and the Fourier spaces, leads to the Lévy processes (Lévy flights) and superdiffusion. This generalization of the fractional diffusion is described by the Riesz space fractional derivative. In the framework of this generalized fractal comb model, Lévy processes are considered, and exact solutions for the probability distribution functions are obtained in terms of the Fox H-function for a variety of the memory kernels, and the rate of the superdiffusive spreading is studied by calculating the fractional moments. For a special form of the memory kernels, we also observed a competition between long rests and long jumps. Finally, we considered the fractal structure of the fingers controlled by a Weierstrass function, which leads to the power-law kernel in the Fourier space. This is a special case, when the second moment exists for superdiffusion in this competition between long rests and long jumps.
Lévy processes on a generalized fractal comb
International Nuclear Information System (INIS)
Sandev, Trifce; Iomin, Alexander; Méndez, Vicenç
2016-01-01
Comb geometry, constituted of a backbone and fingers, is one of the most simple paradigm of a two-dimensional structure, where anomalous diffusion can be realized in the framework of Markov processes. However, the intrinsic properties of the structure can destroy this Markovian transport. These effects can be described by the memory and spatial kernels. In particular, the fractal structure of the fingers, which is controlled by the spatial kernel in both the real and the Fourier spaces, leads to the Lévy processes (Lévy flights) and superdiffusion. This generalization of the fractional diffusion is described by the Riesz space fractional derivative. In the framework of this generalized fractal comb model, Lévy processes are considered, and exact solutions for the probability distribution functions are obtained in terms of the Fox H -function for a variety of the memory kernels, and the rate of the superdiffusive spreading is studied by calculating the fractional moments. For a special form of the memory kernels, we also observed a competition between long rests and long jumps. Finally, we considered the fractal structure of the fingers controlled by a Weierstrass function, which leads to the power-law kernel in the Fourier space. This is a special case, when the second moment exists for superdiffusion in this competition between long rests and long jumps. (paper)
Feature extraction algorithm for space targets based on fractal theory
Tian, Balin; Yuan, Jianping; Yue, Xiaokui; Ning, Xin
2007-11-01
In order to offer a potential for extending the life of satellites and reducing the launch and operating costs, satellite servicing including conducting repairs, upgrading and refueling spacecraft on-orbit become much more frequently. Future space operations can be more economically and reliably executed using machine vision systems, which can meet real time and tracking reliability requirements for image tracking of space surveillance system. Machine vision was applied to the research of relative pose for spacecrafts, the feature extraction algorithm was the basis of relative pose. In this paper fractal geometry based edge extraction algorithm which can be used in determining and tracking the relative pose of an observed satellite during proximity operations in machine vision system was presented. The method gets the gray-level image distributed by fractal dimension used the Differential Box-Counting (DBC) approach of the fractal theory to restrain the noise. After this, we detect the consecutive edge using Mathematical Morphology. The validity of the proposed method is examined by processing and analyzing images of space targets. The edge extraction method not only extracts the outline of the target, but also keeps the inner details. Meanwhile, edge extraction is only processed in moving area to reduce computation greatly. Simulation results compared edge detection using the method which presented by us with other detection methods. The results indicate that the presented algorithm is a valid method to solve the problems of relative pose for spacecrafts.
Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems
Agarwal, S.; Wettlaufer, J. S.
2014-12-01
We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.
Designing a fractal antenna of 2400 MHz
International Nuclear Information System (INIS)
Miranda Hamburger, Fabio
2012-01-01
The design of a fractal antenna with 2400 MHz of frequency has been studied. The fractal used is described by Waclaw Spierpi.ski. The initial figure, also known as seed, is divided using equilateral triangles with the aim of obtaining a perimeter similar to a meaningful portion of wave length. The use of λ to establish an ideal perimeter has reduced the radiation resistance. The adequate number of iterations needed to design the antenna is calculated based on λ. (author) [es
Fractal effects on excitations in diluted ferromagnets
International Nuclear Information System (INIS)
Kumar, D.
1981-08-01
The low energy spin-wave like excitations in diluted ferromagnets near percolation threshold are studied. For this purpose an explicit use of the fractal model for the backbone of the infinite percolating cluster due to Kirkpatrick is made. Three physical effects are identified, which cause the softening of spin-waves as the percolation point is approached. The importance of fractal effects in the calculation of density of states and the low temperature thermodynamics is pointed out. (author)
A fractal-like resistive network
International Nuclear Information System (INIS)
Saggese, A; De Luca, R
2014-01-01
The equivalent resistance of a fractal-like network is calculated by means of approaches similar to those employed in defining the equivalent resistance of an infinite ladder. Starting from an elementary triangular circuit, a fractal-like network, named after Saggese, is developed. The equivalent resistance of finite approximations of this network is measured, and the didactical implications of the model are highlighted. (paper)
Heat kernels and zeta functions on fractals
International Nuclear Information System (INIS)
Dunne, Gerald V
2012-01-01
On fractals, spectral functions such as heat kernels and zeta functions exhibit novel features, very different from their behaviour on regular smooth manifolds, and these can have important physical consequences for both classical and quantum physics in systems having fractal properties. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical in honour of Stuart Dowker's 75th birthday devoted to ‘Applications of zeta functions and other spectral functions in mathematics and physics’. (paper)
In situ TEM observation of the growth and decomposition of monoclinic W18O49 nanowires
International Nuclear Information System (INIS)
Chen, C L; Mori, H
2009-01-01
The growth of monoclinic W 18 O 49 nanowires by heat treatment of a tungsten filament at ∼873 K and the decomposition of these nanowires under 200 keV electron irradiation at ∼1023 K have been investigated using in situ transmission electron microscopy (TEM). In situ TEM observation of the growth confirmed the vapor-solid growth mechanism of the monoclinic W 18 O 49 nanowires. In situ irradiation experiments revealed the formation of metallic bcc tungsten from monoclinic W 18 O 49 nanowires under 200 keV electron irradiation.
Fractal formation of a Y-Ba-Cu-O thin film on SrTiO3
International Nuclear Information System (INIS)
Chow, L.; Chen, J.; Desai, V.; Sundaram, K.; Arora, S.
1989-01-01
Fractal formation has been observed after thermal annealing of the rf-sputtered Y-Ba-Cu-O thin film on SrTiO 3 substrate. Through energy-dispersive x-ray analysis, it was found that the composition of the fractal was YBa 2 Cu 3 O x and the surrounding film composition wasY 2 Ba 2 Cu 3 O x . The fractal dimensions D ranging from 1.26 to 1.65 were obtained using the standard sandbox method with different thresholds
Surface structures of equilibrium restricted curvature model on two fractal substrates
International Nuclear Information System (INIS)
Song Li-Jian; Tang Gang; Zhang Yong-Wei; Han Kui; Xun Zhi-Peng; Xia Hui; Hao Da-Peng; Li Yan
2014-01-01
With the aim to probe the effects of the microscopic details of fractal substrates on the scaling of discrete growth models, the surface structures of the equilibrium restricted curvature (ERC) model on Sierpinski arrowhead and crab substrates are analyzed by means of Monte Carlo simulations. These two fractal substrates have the same fractal dimension d f , but possess different dynamic exponents of random walk z rw . The results show that the surface structure of the ERC model on fractal substrates are related to not only the fractal dimension d f , but also to the microscopic structures of the substrates expressed by the dynamic exponent of random walk z rw . The ERC model growing on the two substrates follows the well-known Family—Vicsek scaling law and satisfies the scaling relations 2α + d f ≍ z ≍ 2z rw . In addition, the values of the scaling exponents are in good agreement with the analytical prediction of the fractional Mullins—Herring equation. (general)
Sharma, Vijay
2009-09-10
Physiological systems such as the cardiovascular system are capable of five kinds of behavior: equilibrium, periodicity, quasi-periodicity, deterministic chaos and random behavior. Systems adopt one or more these behaviors depending on the function they have evolved to perform. The emerging mathematical concepts of fractal mathematics and chaos theory are extending our ability to study physiological behavior. Fractal geometry is observed in the physical structure of pathways, networks and macroscopic structures such the vasculature and the His-Purkinje network of the heart. Fractal structure is also observed in processes in time, such as heart rate variability. Chaos theory describes the underlying dynamics of the system, and chaotic behavior is also observed at many levels, from effector molecules in the cell to heart function and blood pressure. This review discusses the role of fractal structure and chaos in the cardiovascular system at the level of the heart and blood vessels, and at the cellular level. Key functional consequences of these phenomena are highlighted, and a perspective provided on the possible evolutionary origins of chaotic behavior and fractal structure. The discussion is non-mathematical with an emphasis on the key underlying concepts.
Fractal patterns of fracture in sandwich composite materials under biaxial tension
Fang, Jing; Yao, Xuefeng; Qi, Jia
1996-04-01
The paper presents a successful experiment to generate a fractal pattern of branching cracks in a brittle material sandwiched in ductile plates. A glass sheet bonded between two polycarbonate plates was heated at different levels of temperatures and the stress field due to the difference of thermal coefficients of the materials was solved by combining the results from isochromatic fringes and thermal stress analysis. At a critical degree of temperature, a crack was initiated at a point and soon produced crack branches to release the stored energy. A tree—like fractal patterns of the branch cracks was then developed with the growth of the branches that subsequently produced more branches on their ways of propagation. The fractal dimension of the fracture pattern was evaluated and the mechanism of the fragmentation was analyzed with the help of the residual stress field of isochromatic and isoclinic patterns.
On the Lipschitz condition in the fractal calculus
International Nuclear Information System (INIS)
Golmankhaneh, Alireza K.; Tunc, Cemil
2017-01-01
In this paper, the existence and uniqueness theorems are proved for the linear and non-linear fractal differential equations. The fractal Lipschitz condition is given on the F"α-calculus which applies for the non-differentiable function in the sense of the standard calculus. More, the metric spaces associated with fractal sets and about functions with fractal supports are defined to build fractal Cauchy sequence. Furthermore, Picard iterative process in the F"α-calculus which have important role in the numerical and approximate solution of fractal differential equations is explored. We clarify the results using the illustrative examples.
Band structures in fractal grading porous phononic crystals
Wang, Kai; Liu, Ying; Liang, Tianshu; Wang, Bin
2018-05-01
In this paper, a new grading porous structure is introduced based on a Sierpinski triangle routine, and wave propagation in this fractal grading porous phononic crystal is investigated. The influences of fractal hierarchy and porosity on the band structures in fractal graidng porous phononic crystals are clarified. Vibration modes of unit cell at absolute band gap edges are given to manifest formation mechanism of absolute band gaps. The results show that absolute band gaps are easy to form in fractal structures comparatively to the normal ones with the same porosity. Structures with higher fractal hierarchies benefit multiple wider absolute band gaps. This work provides useful guidance in design of fractal porous phononic crystals.
Fractal geometry and number theory complex dimensions of fractal strings and zeros of zeta functions
Lapidus, Michael L
1999-01-01
A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...
A New Strategy in Observer Modeling for Greenhouse Cucumber Seedling Growth
Qiu, Quan; Zheng, Chenfei; Wang, Wenping; Qiao, Xiaojun; Bai, He; Yu, Jingquan; Shi, Kai
2017-01-01
State observer is an essential component in computerized control loops for greenhouse-crop systems. However, the current accomplishments of observer modeling for greenhouse-crop systems mainly focus on mass/energy balance, ignoring physiological responses of crops. As a result, state observers for crop physiological responses are rarely developed, and control operations are typically made based on experience rather than actual crop requirements. In addition, existing observer models require a large number of parameters, leading to heavy computational load and poor application feasibility. To address these problems, we present a new state observer modeling strategy that takes both environmental information and crop physiological responses into consideration during the observer modeling process. Using greenhouse cucumber seedlings as an instance, we sample 10 physiological parameters of cucumber seedlings at different time point during the exponential growth stage, and employ them to build growth state observers together with 8 environmental parameters. Support vector machine (SVM) acts as the mathematical tool for observer modeling. Canonical correlation analysis (CCA) is used to select the dominant environmental and physiological parameters in the modeling process. With the dominant parameters, simplified observer models are built and tested. We conduct contrast experiments with different input parameter combinations on simplified and un-simplified observers. Experimental results indicate that physiological information can improve the prediction accuracies of the growth state observers. Furthermore, the simplified observer models can give equivalent or even better performance than the un-simplified ones, which verifies the feasibility of CCA. The current study can enable state observers to reflect crop requirements and make them feasible for applications with simplified shapes, which is significant for developing intelligent greenhouse control systems for modern
A New Strategy in Observer Modeling for Greenhouse Cucumber Seedling Growth
Directory of Open Access Journals (Sweden)
Quan Qiu
2017-08-01
Full Text Available State observer is an essential component in computerized control loops for greenhouse-crop systems. However, the current accomplishments of observer modeling for greenhouse-crop systems mainly focus on mass/energy balance, ignoring physiological responses of crops. As a result, state observers for crop physiological responses are rarely developed, and control operations are typically made based on experience rather than actual crop requirements. In addition, existing observer models require a large number of parameters, leading to heavy computational load and poor application feasibility. To address these problems, we present a new state observer modeling strategy that takes both environmental information and crop physiological responses into consideration during the observer modeling process. Using greenhouse cucumber seedlings as an instance, we sample 10 physiological parameters of cucumber seedlings at different time point during the exponential growth stage, and employ them to build growth state observers together with 8 environmental parameters. Support vector machine (SVM acts as the mathematical tool for observer modeling. Canonical correlation analysis (CCA is used to select the dominant environmental and physiological parameters in the modeling process. With the dominant parameters, simplified observer models are built and tested. We conduct contrast experiments with different input parameter combinations on simplified and un-simplified observers. Experimental results indicate that physiological information can improve the prediction accuracies of the growth state observers. Furthermore, the simplified observer models can give equivalent or even better performance than the un-simplified ones, which verifies the feasibility of CCA. The current study can enable state observers to reflect crop requirements and make them feasible for applications with simplified shapes, which is significant for developing intelligent greenhouse control
A New Strategy in Observer Modeling for Greenhouse Cucumber Seedling Growth.
Qiu, Quan; Zheng, Chenfei; Wang, Wenping; Qiao, Xiaojun; Bai, He; Yu, Jingquan; Shi, Kai
2017-01-01
State observer is an essential component in computerized control loops for greenhouse-crop systems. However, the current accomplishments of observer modeling for greenhouse-crop systems mainly focus on mass/energy balance, ignoring physiological responses of crops. As a result, state observers for crop physiological responses are rarely developed, and control operations are typically made based on experience rather than actual crop requirements. In addition, existing observer models require a large number of parameters, leading to heavy computational load and poor application feasibility. To address these problems, we present a new state observer modeling strategy that takes both environmental information and crop physiological responses into consideration during the observer modeling process. Using greenhouse cucumber seedlings as an instance, we sample 10 physiological parameters of cucumber seedlings at different time point during the exponential growth stage, and employ them to build growth state observers together with 8 environmental parameters. Support vector machine (SVM) acts as the mathematical tool for observer modeling. Canonical correlation analysis (CCA) is used to select the dominant environmental and physiological parameters in the modeling process. With the dominant parameters, simplified observer models are built and tested. We conduct contrast experiments with different input parameter combinations on simplified and un-simplified observers. Experimental results indicate that physiological information can improve the prediction accuracies of the growth state observers. Furthermore, the simplified observer models can give equivalent or even better performance than the un-simplified ones, which verifies the feasibility of CCA. The current study can enable state observers to reflect crop requirements and make them feasible for applications with simplified shapes, which is significant for developing intelligent greenhouse control systems for modern
New observational constraints on the growth of the first supermassive black holes
International Nuclear Information System (INIS)
Treister, E.; Schawinski, K.; Volonteri, M.; Natarajan, P.
2013-01-01
We constrain the total accreted mass density in supermassive black holes at z > 6, inferred via the upper limit derived from the integrated X-ray emission from a sample of photometrically selected galaxy candidates. Studying galaxies obtained from the deepest Hubble Space Telescope images combined with the Chandra 4 Ms observations of the Chandra Deep Field-South, we achieve the most restrictive constraints on total black hole growth in the early universe. We estimate an accreted mass density <1000 M ☉ Mpc –3 at z ∼ 6, significantly lower than the previous predictions from some existing models of early black hole growth and earlier prior observations. These results place interesting constraints on early black hole growth and mass assembly by accretion and imply one or more of the following: (1) only a fraction of the luminous galaxies at this epoch contain active black holes; (2) most black hole growth at early epochs happens in dusty and/or less massive—as yet undetected—host galaxies; (3) there is a significant fraction of low-z interlopers in the galaxy sample; (4) early black hole growth is radiatively inefficient, heavily obscured, and/or due to black hole mergers as opposed to accretion; or (5) the bulk of the black hole growth occurs at late times. All of these possibilities have important implications for our understanding of high-redshift seed formation models.
Direct observation of densification and grain growth in a W--Ni alloy
International Nuclear Information System (INIS)
Riegger, H.; Pask, J.A.; Exner, H.E.
1979-04-01
Densification and grain growth in a tungsten--nickel alloy containing 32 vol % of liquid at 1550 0 C were studied by conventional methods aided by hot stage scanning electron microscopy and cinematography. This technique yields important additional qualitative information on the mechanisms. Two stages can be discerned. In stage 1, essentially complete pore elimination, rapid grain growth and adjustment of microstructural geometry take place. In the second stage, microstructure coarsening occurs which is characterized by geometric similarity. Columnar grain growth at the surface is observed due to squeezing out of Ni--W liquid, flooding of surface grains and fast evaporation of the Ni. The driving forces for these processes are discussed showing that a high ratio of grain boundary energy to liquid surface energy is essential. A W--Cu alloy with 32 vol % liquid at 1100 0 C did not show any grain growth due to essentially no solubility of W in Cu at this temperature
Directory of Open Access Journals (Sweden)
Renkuan Liao
2014-01-01
Full Text Available The water absorption capacity of superabsorbent polymers (SAPs is important for agricultural drought resistance. However, herbicides may leach into the soil and affect water absorption by damaging the SAP three-dimensional membrane structures. We used 100-mesh sieves, electron microscopy, and fractal theory to study swelling and water absorption in SAPs in the presence of three common herbicides (atrazine, alachlor, and tribenuron-methyl at concentrations of 0.5, 1.0, and 2.0 mg/L. In the sieve experiments it was found that 2.0 mg/L atrazine reduces the capacity by 9.64–23.3% at different swelling points; no significant diminution was observed for the other herbicides or for lower atrazine concentrations. We found that the hydrogel membrane pore distributions have fractal characteristics in both deionized water and atrazine solution. The 2.0 mg/L atrazine destroyed the water-retaining polymer membrane pores and reduced the water-absorbing mass by modifying its three-dimensional membrane structure. A linear correlation was observed between the fractal analysis and the water-absorbing mass. Multifractal analysis characterized the membrane pore distribution by using the range of singularity indexes Δα (relative distinguishing range of 16.54–23.44%, which is superior to single-fractal analysis that uses the fractal dimension D (relative distinguishing range of 2.5–4.0%.
Fractals as objects with nontrivial structures at all scales
International Nuclear Information System (INIS)
Lacan, Francis; Tresser, Charles
2015-01-01
Toward the middle of 2001, the authors started arguing that fractals are important when discussing the operational resilience of information systems and related computer sciences issues such as artificial intelligence. But in order to argue along these lines it turned out to be indispensable to define fractals so as to let one recognize as fractals some sets that are very far from being self similar in the (usual) metric sense. This paper is devoted to define (in a loose sense at least) fractals in ways that allow for instance all the Cantor sets to be fractals and that permit to recognize fractality (the property of being fractal) in the context of the information technology issues that we had tried to comprehend. Starting from the meta-definition of a fractal as an “object with non-trivial structure at all scales” that we had used for long, we ended up taking these words seriously. Accordingly we define fractals in manners that depend both on the structures that the fractals are endowed with and the chosen sets of structure compatible maps, i.e., we approach fractals in a category-dependent manner. We expect that this new approach to fractals will contribute to the understanding of more of the fractals that appear in exact and other sciences than what can be handled presently
Self-stabilized Fractality of Sea-coasts Through Damped Erosion
Sapoval, B.; Baldassari, A.; Gabrielli, A.
2004-05-01
Coastline morphology is of current interest in geophysical research and coastline erosion has important economic consequences. At the same time, although the geometry of seacoasts is often used as an introductory archetype of fractal morphology in nature there has been no explanation about which physical mechanism could justify that empirical observation. The present work propose a minimal, but robust, model of evolution of rocky coasts towards fractality. The model describes how a stationary fractal geometry arises spontaneously from the mutual self-stabilization of a rocky coast morphology and sea eroding power. If, on one hand, erosion generally increases the geometrical irregularity of the coast, on the other hand this increase creates a stronger damping of the sea and a consequent diminution of its eroding power. The increased damping argument relies on the studies of fractal acoustical cavities, which have shown that viscous damping is augmented on a longer, irregular, surface. A minimal two-dimensional model of erosion is introduced which leads to the through a complex dynamics of the earth-sea interface, to the appearance of a stationary fractal seacoast with dimension close to 4/3. Fractal geometry plays here the role of a morphological attractor directly related to percolation geometry. The model reproduces at least qualitatively some of the features of real coasts using only simple ingredients: the randomness of the lithology and the decrease of the erosion power of the sea. B. Sapoval, Fractals (Aditech, Paris, 1989). B. Sapoval, O. Haeberlé, and S.Russ, J. Acoust. Soc. Am., 2014 (1997). B. Hébert B., B. Sapoval, and S.Russ, J. Acoust. Soc. Am., 1567 (1999).
Fractal Property in the Light Curve of BL Lac Object S5 0716+714 ...
Indian Academy of Sciences (India)
tal method and then simulate the data with the Weierstrass–Mandelbrot. (W–M) function. It is considered that the ... The infrared observation indicated that the interstellar clouds have a fractal structure with dimension ... The observational data of the R-band (top panel) and simulation data with W–M function (bottom panel).
Bisht, Konark; Klumpp, Stefan; Banerjee, Varsha; Marathe, Rahul
2017-11-01
A human pathogen, Neisseria gonorrhoeae (NG), moves on surfaces by attaching and retracting polymeric structures called Type IV pili. The tug-of-war between the pili results in a two-dimensional stochastic motion called twitching motility. In this paper, with the help of real-time NG trajectories, we develop coarse-grained models for their description. The fractal properties of these trajectories are determined and their influence on first passage time and formation of bacterial microcolonies is studied. Our main observations are as follows: (i) NG performs a fast ballistic walk on small time scales and a slow diffusive walk over long time scales with a long crossover region; (ii) there exists a characteristic persistent length lp*, which yields the fastest growth of bacterial aggregates or biofilms. Our simulations reveal that lp*˜L0.6 , where L ×L is the surface on which the bacteria move; (iii) the morphologies have distinct fractal characteristics as a consequence of the ballistic and diffusive motion of the constituting bacteria.
Continuous observation of cavity growth and coalescence by creep-fatigue tests in SEM
International Nuclear Information System (INIS)
Arai, Masayuki; Ogata, Takashi; Nitta, Akito
1995-01-01
Structural components operating at high temperatures in power plants are subjected to interaction of thermal fatigue and creep which results in creep-fatigue damage. In evaluating the life of those components, it is important to understand microscopic damage evolution under creep-fatigue conditions. In this study, static creep and creep-fatigue tests with tensile holdtime were conducted on SUS304 stainless steel by using a high-temperature fatigue machine combined with a scanning electron microscope (SEM), and cavity growth and coalescence behaviors on surface grain boundaries were observed continuously by the SEM. Quantitative analysis of creep cavity growth based on the observation was made for comparison with theoretical growth models. As a result, it was found that grain boundary cavities nucleate at random and grow preferentially on grain boundaries in a direction almost normal to the stress axis. Under the creep condition, the cavities grow monotonously on grain boundaries while they remain the elliptical shape. On the other hand, under the creep-fatigue condition the cavities grow with an effect of local strain distribution around the grain boundary due to cyclic loading and the micro cracks of one grain-boundary length were formed by coalescence of the cavities. Also, cavity nucleation and growth rates for creep-fatigue were more rapid than those for static creep and the constrained cavity growth model coincided well with the experimental data for creep. (author)
Fractal analysis of cervical intraepithelial neoplasia.
Directory of Open Access Journals (Sweden)
Markus Fabrizii
Full Text Available INTRODUCTION: Cervical intraepithelial neoplasias (CIN represent precursor lesions of cervical cancer. These neoplastic lesions are traditionally subdivided into three categories CIN 1, CIN 2, and CIN 3, using microscopical criteria. The relation between grades of cervical intraepithelial neoplasia (CIN and its fractal dimension was investigated to establish a basis for an objective diagnosis using the method proposed. METHODS: Classical evaluation of the tissue samples was performed by an experienced gynecologic pathologist. Tissue samples were scanned and saved as digital images using Aperio scanner and software. After image segmentation the box counting method as well as multifractal methods were applied to determine the relation between fractal dimension and grades of CIN. A total of 46 images were used to compare the pathologist's neoplasia grades with the predicted groups obtained by fractal methods. RESULTS: Significant or highly significant differences between all grades of CIN could be found. The confusion matrix, comparing between pathologist's grading and predicted group by fractal methods showed a match of 87.1%. Multifractal spectra were able to differentiate between normal epithelium and low grade as well as high grade neoplasia. CONCLUSION: Fractal dimension can be considered to be an objective parameter to grade cervical intraepithelial neoplasia.
From dendrimers to fractal polymers and beyond
Directory of Open Access Journals (Sweden)
Charles N. Moorefield
2013-01-01
Full Text Available The advent of dendritic chemistry has facilitated materials research by allowing precise control of functional component placement in macromolecular architecture. The iterative synthetic protocols used for dendrimer construction were developed based on the desire to craft highly branched, high molecular weight, molecules with exact mass and tailored functionality. Arborols, inspired by trees and precursors of the utilitarian macromolecules known as dendrimers today, were the first examples to employ predesigned, 1 → 3 C-branched, building blocks; physical characteristics of the arborols, including their globular shapes, excellent solubilities, and demonstrated aggregation, combined to reveal the inherent supramolecular potential (e.g., the unimolecular micelle of these unique species. The architecture that is a characteristic of dendritic materials also exhibits fractal qualities based on self-similar, repetitive, branched frameworks. Thus, the fractal design and supramolecular aspects of these constructs are suggestive of a larger field of fractal materials that incorporates repeating geometries and are derived by complementary building block recognition and assembly. Use of terpyridine-M2+-terpyridine (where, M = Ru, Zn, Fe, etc connectivity in concert with mathematical algorithms, such as forms the basis for the Seirpinski gasket, has allowed the beginning exploration of fractal materials construction. The propensity of the fractal molecules to self-assemble into higher order architectures adds another dimension to this new arena of materials and composite construction.
Multirate diversity strategy of fractal modulation
International Nuclear Information System (INIS)
Yuan Yong; Shi Si-Hong; Luo Mao-Kang
2011-01-01
Previous analyses of fractal modulation were carried out mostly from a signle perspective or a subband, but the analyses from the perspective of multiscale synthesis have not been found yet; while multiscale synthesis is just the essence of the mutlirate diversity which is the most important characteristic of fractal modulation. As for the mutlirate diversity of fractal modulation, previous studies only dealt with the general outspread of its concept, lacked the thorough and intensive quantitative comparison and analysis. In light of the above fact, from the perspective of multiscale synthesis, in this paper we provide a comprehensive analysis of the multirate diversity of fractal modulation and corresponding quantitative analysis. The results show that mutlirate diversity, which is a fusion of frequency diversity and time diversity, pays an acceptable price in spectral efficiency in exchange for a significant improvement in bit error rate. It makes fractal modulation particularly suitable for the channels whose bandwidth and duration parameters are unknown or cannot be predicted to the transmitter. Surely it is clearly of great significance for reliable communications. Moreover, we also attain the ability to flexibly make various rate-bandwidth tradeoffs between the transmitter and the receiver, to freely select the reception time and to expediently control the total bandwidth. Furthermore, the acquisitions or improvements of these fine features could provide support of the technical feasibility for the electromagnetic spectrum control technology in a complex electromagnetic environment. (general)
Charney, Noah D; Babst, Flurin; Poulter, Benjamin; Record, Sydne; Trouet, Valerie M; Frank, David; Enquist, Brian J; Evans, Margaret E K
2016-09-01
Predicting long-term trends in forest growth requires accurate characterisation of how the relationship between forest productivity and climatic stress varies across climatic regimes. Using a network of over two million tree-ring observations spanning North America and a space-for-time substitution methodology, we forecast climate impacts on future forest growth. We explored differing scenarios of increased water-use efficiency (WUE) due to CO2 -fertilisation, which we simulated as increased effective precipitation. In our forecasts: (1) climate change negatively impacted forest growth rates in the interior west and positively impacted forest growth along the western, southeastern and northeastern coasts; (2) shifting climate sensitivities offset positive effects of warming on high-latitude forests, leaving no evidence for continued 'boreal greening'; and (3) it took a 72% WUE enhancement to compensate for continentally averaged growth declines under RCP 8.5. Our results highlight the importance of locally adapted forest management strategies to handle regional differences in growth responses to climate change. © 2016 John Wiley & Sons Ltd/CNRS.
Directory of Open Access Journals (Sweden)
Lesley A. Judd
2015-07-01
Full Text Available The study, characterization, observation, and quantification of plant root growth and root systems (Rhizometrics has been and remains an important area of research in all disciplines of plant science. In the horticultural industry, a large portion of the crops grown annually are grown in pot culture. Root growth is a critical component in overall plant performance during production in containers, and therefore it is important to understand the factors that influence and/or possible enhance it. Quantifying root growth has varied over the last several decades with each method of quantification changing in its reliability of measurement and variation among the results. Methods such as root drawings, pin boards, rhizotrons, and minirhizotrons initiated the aptitude to measure roots with field crops, and have been expanded to container-grown plants. However, many of the published research methods are monotonous and time-consuming. More recently, computer programs have increased in use as technology advances and measuring characteristics of root growth becomes easier. These programs are instrumental in analyzing various root growth characteristics, from root diameter and length of individual roots to branching angle and topological depth of the root architecture. This review delves into the expanding technologies involved with expertly measuring root growth of plants in containers, and the advantages and disadvantages that remain.
Judd, Lesley A; Jackson, Brian E; Fonteno, William C
2015-07-03
The study, characterization, observation, and quantification of plant root growth and root systems (Rhizometrics) has been and remains an important area of research in all disciplines of plant science. In the horticultural industry, a large portion of the crops grown annually are grown in pot culture. Root growth is a critical component in overall plant performance during production in containers, and therefore it is important to understand the factors that influence and/or possible enhance it. Quantifying root growth has varied over the last several decades with each method of quantification changing in its reliability of measurement and variation among the results. Methods such as root drawings, pin boards, rhizotrons, and minirhizotrons initiated the aptitude to measure roots with field crops, and have been expanded to container-grown plants. However, many of the published research methods are monotonous and time-consuming. More recently, computer programs have increased in use as technology advances and measuring characteristics of root growth becomes easier. These programs are instrumental in analyzing various root growth characteristics, from root diameter and length of individual roots to branching angle and topological depth of the root architecture. This review delves into the expanding technologies involved with expertly measuring root growth of plants in containers, and the advantages and disadvantages that remain.
Multiple new-particle growth pathways observed at the US DOE Southern Great Plains field site
Directory of Open Access Journals (Sweden)
A. L. Hodshire
2016-07-01
observed differing growth pathways, while also predicting that ELVOCs contribute more to growth than organic salt formation. However, most MABNAG model simulations tend to underpredict the observed growth rates between 10 and 20 nm in diameter; this underprediction may come from neglecting the contributions to growth from semi-to-low-volatility species or accretion reactions. Our results suggest that in addition to sulfuric acid, ELVOCs are also very important for growth in this rural setting. We discuss the limitations of our study that arise from not accounting for semi- and low-volatility organics, as well as nitrogen-containing species beyond ammonia and amines in the model. Quantitatively understanding the overall budget, evolution, and thermodynamic properties of lower-volatility organics in the atmosphere will be essential for improving global aerosol models.
On the arithmetic of fractal dimension using hyperhelices
International Nuclear Information System (INIS)
Toledo-Suarez, Carlos D.
2009-01-01
A hyperhelix is a fractal curve generated by coiling a helix around a rect line, then another helix around the first one, a third around the second... an infinite number of times. A way to generate hyperhelices with any desired fractal dimension is presented, leading to the result that they have embedded an algebraic structure that allows making arithmetic with fractal dimensions and to the idea of an infinitesimal of fractal dimension
Poiseuille equation for steady flow of fractal fluid
Tarasov, Vasily E.
2016-07-01
Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.
Fractal Structures on Silica Aerogels Containing Titanium: A Small Angle Neutron Scattering Study
International Nuclear Information System (INIS)
Widya Sari; Dian Fitriyani; Abdul Aziz Mohamed; Noordin Ibrahim
2009-01-01
Full text: The fractal structure of silica aerogels containing titanium has been investigated by means of small-angle neutron scattering (SANS) technique. The SANS experiments were conducted using a 36 meter SANS BATAN spectrometer (SMARTer) in Serpong, Indonesia in the range of momentum transfer Q, 0.006 -1 ) < 0.3. The power-law for a fractal object scattering Q-D observed from all measured samples. The Fourier transform of pattern I(Q) a pair correlation model function was implemented in analyzing the structure factor from the power-law scattering profiles. The results are showing that the silica aerogels containing titanium has a mass fractal where its dimension DM is larger than the pure silica aerogels. The mass fractal dimension of silica aerogels containing titanium is relatively constant between 2.23 to 2.40 with the decrease of acid concentrations during a sol-gel process and formed a nanometer size of aggregate. Those fractal structures were simulated using a Delphi language and the results are presented in this paper. (author)
2-D Fractal Carpet Antenna Design and Performance
Barton, C. C.; Tebbens, S. F.; Ewing, J. J.; Peterman, D. J.; Rizki, M. M.
2017-12-01
A 2-D fractal carpet antenna uses a fractal (self-similar) pattern to increase its perimeter by iteration and can receive or transmit electromagnetic radiation within its perimeter-bounded surface area. 2-D fractals are shapes that, at their mathematical limit (infinite iterations) have an infinite perimeter bounding a finite surface area. The fractal dimension describes the degree of space filling and lacunarity which quantifies the size and spatial distribution of open space bounded by a fractal shape. A key aspect of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that are very compact, wideband and multiband. As the number of iterations increases, the antenna operates at higher and higher frequencies. Manifestly different from traditional antenna designs, a fractal antenna can operate at multiple frequencies simultaneously. We have created a MATLAB code to generate deterministic and stochastic modes of Sierpinski carpet fractal antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, number of iterations, and lacunarities have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance
Investigation into How 8th Grade Students Define Fractals
Karakus, Fatih
2015-01-01
The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…
Generalized Warburg impedance on realistic self-affine fractals ...
Indian Academy of Sciences (India)
2016-08-26
Aug 26, 2016 ... We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals.
Fractal tomography and its application in 3D vision
Trubochkina, N.
2018-01-01
A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.
Constructing and applying the fractal pied de poule (houndstooth)
Feijs, L.M.G.; Toeters, M.J.; Hart, G.; Sarhangi, R.
2013-01-01
Time is ready for a fractal version of pied de poule; it is almost "in the air". Taking inspiration from the Cantor set, and using the analysis of the classical pattern, we obtain a family of elegant new fractal Pied de Poules. We calculate the fractal dimension and develop an attractive fashion
Monitoring of dry sliding wear using fractal analysis
Zhang, Jindang; Regtien, Paulus P.L.; Korsten, Maarten J.
2005-01-01
Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power
Fractal characterization of the compaction and sintering of ferrites
Glass, H.J.; With, de G.
2001-01-01
A novel parameter, the fractal exponent DE, is derived using the concept of fractal scaling. The fractal exponent DE relates the development of a feature within a material to the development of the size of the material. As an application, structural changes during the compaction and sintering of
Generalized Warburg impedance on realistic self-affine fractals
Indian Academy of Sciences (India)
We analyse the problem of impedance for a diffusion controlled charge transfer process across an irregular interface. These interfacial irregularities are characterized as two class of random fractals: (i) a statistically isotropic self-affine fractals and (ii) a statistically corrugated self-affine fractals. The information about the ...
Lectures on fractal geometry and dynamical systems
Pesin, Yakov
2009-01-01
Both fractal geometry and dynamical systems have a long history of development and have provided fertile ground for many great mathematicians and much deep and important mathematics. These two areas interact with each other and with the theory of chaos in a fundamental way: many dynamical systems (even some very simple ones) produce fractal sets, which are in turn a source of irregular "chaotic" motions in the system. This book is an introduction to these two fields, with an emphasis on the relationship between them. The first half of the book introduces some of the key ideas in fractal geometry and dimension theory--Cantor sets, Hausdorff dimension, box dimension--using dynamical notions whenever possible, particularly one-dimensional Markov maps and symbolic dynamics. Various techniques for computing Hausdorff dimension are shown, leading to a discussion of Bernoulli and Markov measures and of the relationship between dimension, entropy, and Lyapunov exponents. In the second half of the book some examples o...
Computer Security: The dilemma of fractal defence
Stefan Lueders, Computer Security Team
2015-01-01
Aren’t mathematical fractals just beautiful? The Mandelbrot set and the Julia set, the Sierpinski gasket, the Menger sponge, the Koch curve (see here)… Based on very simple mathematical rules, they quickly develop into a mosaic of facets slightly different from each other. More and more features appear the closer you zoom into a fractal and expose similar but not identical features of the overall picture. Computer security is like these fractals, only much less pretty: simple at first glance, but increasingly complex and complicated when you look more closely at the details. The deeper you dig, the more and more possibilities open up for malicious people as the attack surface grows, just like that of “Koch’s snowflakes”, where the border length grows exponentially. Consequently, the defensive perimeter also increases when we follow the bits and bytes layer by layer from their processing in the CPU, trickling up the software stack thro...
Fractal design concepts for stretchable electronics.
Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A
2014-01-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
On Nonextensive Statistics, Chaos and Fractal Strings
Castro, C
2004-01-01
Motivated by the growing evidence of universality and chaos in QFT and string theory, we study the Tsallis non-extensive statistics ( with a non-additive $ q$-entropy ) of an ensemble of fractal strings and branes of different dimensionalities. Non-equilibrium systems with complex dynamics in stationary states may exhibit large fluctuations of intensive quantities which are described in terms of generalized statistics. Tsallis statistics is a particular representative of such class. The non-extensive entropy and probability distribution of a canonical ensemble of fractal strings and branes is studied in terms of their dimensional spectrum which leads to a natural upper cutoff in energy and establishes a direct correlation among dimensions, energy and temperature. The absolute zero temperature ( Kelvin ) corresponds to zero dimensions (energy ) and an infinite temperature corresponds to infinite dimensions. In the concluding remarks some applications of fractal statistics, quasi-particles, knot theory, quantum...
A fractal-based image encryption system
Abd-El-Hafiz, S. K.
2014-12-01
This study introduces a novel image encryption system based on diffusion and confusion processes in which the image information is hidden inside the complex details of fractal images. A simplified encryption technique is, first, presented using a single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved through several parameters: feedback delay, multiplexing and independent horizontal or vertical shifts. The effect of each parameter is studied separately and, then, they are combined to illustrate their influence on the encryption quality. The encryption quality is evaluated using different analysis techniques such as correlation coefficients, differential attack measures, histogram distributions, key sensitivity analysis and the National Institute of Standards and Technology (NIST) statistical test suite. The obtained results show great potential compared to other techniques.
Fractal design concepts for stretchable electronics
Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.
2014-02-01
Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.
The relationship of fractals in geophysics to 'the new science'
International Nuclear Information System (INIS)
Turcotte, Donald L.
2004-01-01
Many phenomena in geophysics satisfy fractal statistics, examples range from the frequency-area statistics of earthquakes to the time series of the earth's magnetic field. Solutions to classical differential equations cannot give this type of behavior. Several 'cellular automata' models have successfully reproduced the observed statistics. For example, the slider-block model for earthquakes. Stephen Wolfram's recent book A New Kind of Science sets forth a 'new science' based on cellular automata. This paper discusses the role of cellular automata in geophysics
Fractal properties of percolation clusters in Euclidian neural networks
International Nuclear Information System (INIS)
Franovic, Igor; Miljkovic, Vladimir
2009-01-01
The process of spike packet propagation is observed in two-dimensional recurrent networks, consisting of locally coupled neuron pools. Local population dynamics is characterized by three key parameters - probability for pool connectedness, synaptic strength and neuron refractoriness. The formation of dynamic attractors in our model, synfire chains, exhibits critical behavior, corresponding to percolation phase transition, with probability for non-zero synaptic strength values representing the critical parameter. Applying the finite-size scaling method, we infer a family of critical lines for various synaptic strengths and refractoriness values, and determine the Hausdorff-Besicovitch fractal dimension of the percolation clusters.
Scaling-up vaccine production: implementation aspects of a biomass growth observer and controller.
Soons, Zita I T A; van den IJssel, Jan; van der Pol, Leo A; van Straten, Gerrit; van Boxtel, Anton J B
2009-04-01
This study considers two aspects of the implementation of a biomass growth observer and specific growth rate controller in scale-up from small- to pilot-scale bioreactors towards a feasible bulk production process for whole-cell vaccine against whooping cough. The first is the calculation of the oxygen uptake rate, the starting point for online monitoring and control of biomass growth, taking into account the dynamics in the gas-phase. Mixing effects and delays are caused by amongst others the headspace and tubing to the analyzer. These gas phase dynamics are modelled using knowledge of the system in order to reconstruct oxygen consumption. The second aspect is to evaluate performance of the monitoring and control system with the required modifications of the oxygen consumption calculation on pilot-scale. In pilot-scale fed-batch cultivation good monitoring and control performance is obtained enabling a doubled concentration of bulk vaccine compared to standard batch production.
In-situ observations of bubble growth in basaltic, andesitic and rhyodacitic melts
Masotta, M.; Ni, H.; Keppler, H.
2013-12-01
Bubble growth strongly affects the physical properties of degassing magmas and their eruption dynamics. Natural samples and products from quench experiments provide only a snapshot of the final state of volatile exsolution, leaving the processes occurring during its early stages unconstrained. In order to fill this gap, we present in-situ high-temperature observations of bubble growth in magmas of different compositions (basalt, andesite and rhyodacite) at 1100 to 1240 °C and 1 bar, obtained using a moissanite cell apparatus. The data show that nucleation occurs at very small degrees of supersaturaturation (bubbles occurring simultaneously with the nucleation of crystals. During the early stages of exsolution, melt degassing is the driving mechanism of bubble growth, with coalescence becoming increasingly important as exsolution progresses. Ostwald ripening occurs only at the end of the process and only in basaltic melt. The average bubble growth rate (GR) ranges from 3.4*10-6 to 5.2*10-7 mm/s, with basalt and andesite showing faster growth rates than rhyodacite. The bubble number density (NB) at nucleation ranges from 1.8*108 to 7.9*107 cm-3 and decreases exponentially over time. While the rhyodacite melt maintained a well-sorted bubble-size distribution (BSD) through time, the BSD's of basalt and andesite are much more inhomogeneous. Our experimental observations demonstrate that bubble growth cannot be ascribed to a single mechanism but is rather a combination of many processes, which depend on the physical properties of the melt. Depending on coalescence rate, annealing of bubbles following a single nucleation event can produce complex bubble size distributions. In natural samples, such BSD's may be misinterpreted as resulting from several separate nucleation events. Incipient crystallization upon cooling of a magma may allow bubble nucleation already at very small degrees of supersaturation and could therefore be an important trigger for volatile release and
On the Boundedness and Symmetry Properties of the Fractal Sets Generated from Alternated Complex Map
Directory of Open Access Journals (Sweden)
Da Wang
2016-01-01
Full Text Available A complex map can give rise to two kinds of fractal sets: the Julia sets and the parameters sets (or the connectivity loci which represent different connectivity properties of the corresponding Julia sets. In the significative results of (Int. J. Bifurc. Chaos, 2009, 19:2123–2129 and (Nonlinear. Dyn. 2013, 73:1155–1163, the authors presented the two kinds of fractal sets of a class of alternated complex map and left some visually observations to be proved about the boundedness and symmetry properties of these fractal sets. In this paper, we improve the previous results by giving the strictly mathematical proofs of the two properties. Some simulations that verify the theoretical proofs are also included.
The virtual education fractality: nature and organization
Directory of Open Access Journals (Sweden)
Osbaldo Turpo Gebera
2013-04-01
Full Text Available The potential generated by ICT in education raises reflect on the underlying frameworks. In this sense, the fractal is an opportunity to explain how it organizes and manages virtual education.This approach recognizes that educational dynamics are recursive and iterative processes instituted as progressive sequences, by way of fractals. This understanding enables becoming as mediated and articulated successive levels. In each dimension are embodied own activities and in turn, involves the recurrence of subsequent levels as possible solving of problem situations. Thus, the knowledge built in response to a collaborative action, participation in networks, ranging from autonomous to the cultural level or conversely.
Chen, Bin
2018-04-01
Understanding the spatiotemporal change trend of global crop growth and multiple cropping system under climate change scenarios is a critical requirement for supporting the food security issue that maintains the function of human society. Many studies have predicted the effects of climate changes on crop production using a combination of filed studies and models, but there has been limited evidence relating decadal-scale climate change to global crop growth and the spatiotemporal distribution of multiple cropping system. Using long-term satellite-derived Normalized Difference Vegetation Index (NDVI) and observed climate data from 1982 to 2012, we investigated the crop growth trend, spatiotemporal pattern trend of agricultural cropping intensity, and their potential correlations with respect to the climate change drivers at a global scale. Results show that 82.97 % of global cropland maximum NDVI witnesses an increased trend while 17.03 % of that shows a decreased trend over the past three decades. The spatial distribution of multiple cropping system is observed to expand from lower latitude to higher latitude, and the increased cropping intensity is also witnessed globally. In terms of regional major crop zones, results show that all nine selected zones have an obvious upward trend of crop maximum NDVI (p impact on the crop growth trend.
Directory of Open Access Journals (Sweden)
B. Chen
2018-04-01
Full Text Available Understanding the spatiotemporal change trend of global crop growth and multiple cropping system under climate change scenarios is a critical requirement for supporting the food security issue that maintains the function of human society. Many studies have predicted the effects of climate changes on crop production using a combination of filed studies and models, but there has been limited evidence relating decadal-scale climate change to global crop growth and the spatiotemporal distribution of multiple cropping system. Using long-term satellite-derived Normalized Difference Vegetation Index (NDVI and observed climate data from 1982 to 2012, we investigated the crop growth trend, spatiotemporal pattern trend of agricultural cropping intensity, and their potential correlations with respect to the climate change drivers at a global scale. Results show that 82.97 % of global cropland maximum NDVI witnesses an increased trend while 17.03 % of that shows a decreased trend over the past three decades. The spatial distribution of multiple cropping system is observed to expand from lower latitude to higher latitude, and the increased cropping intensity is also witnessed globally. In terms of regional major crop zones, results show that all nine selected zones have an obvious upward trend of crop maximum NDVI (p < 0.001, and as for climatic drivers, the gradual temperature and precipitation changes have had a measurable impact on the crop growth trend.
Fractal geometry of cosmic strings and correlations among galaxies and Abell clusters
International Nuclear Information System (INIS)
Pagels, H.R.
1987-01-01
In the context of the cosmic-string picture of galaxy and cluster formation we develop a model for the loop correlation function. Assuming that parent loops have dimension 1 and that the production of child loops cut off from the parent with a peculiar velocity v is described by a Brownian random walk we estimate for the fractal dimension of the correlations D = 1+3.28v 2 . For v≅0.24 this gives the observed fractal D≅1.2
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volume 1 of Eric Hammel's Fractal Dimensions, Volume 2 is filled wit
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1, 2, and 3 of Eric Hammel's Fractal Dimensions, Volume 4 is
Fractal dimensions the digital art of Eric Hammel
Hammel, Eric
2014-01-01
The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1 and 2 of Eric Hammel's Fractal Dimensions, Volume 3 is fil
Energy Technology Data Exchange (ETDEWEB)
Clausse, A; Delmastro, D F
1991-12-31
This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author). [Espanol] En este trabajo se presenta una descripcion de las lineas de investigacion que los autores estan llevando a cabo en teoria de caos y fractales orientadas al campo nuclear. Es de especial importancia las posibilidades que se abren en el area de la seguridad nuclear, en donde la informacion proveniente de las tecnicas de caos y fractales pueden ayudar al desarrollo de mejores criterios y disenos mas confiables. (Autor).
The correlation of fractal structures in the photospheric and the coronal magnetic field
Dimitropoulou, M.; Georgoulis, M.; Isliker, H.; Vlahos, L.; Anastasiadis, A.; Strintzi, D.; Moussas, X.
2009-10-01
Context: This work examines the relation between the fractal properties of the photospheric magnetic patterns and those of the coronal magnetic fields in solar active regions. Aims: We investigate whether there is any correlation between the fractal dimensions of the photospheric structures and the magnetic discontinuities formed in the corona. Methods: To investigate the connection between the photospheric and coronal complexity, we used a nonlinear force-free extrapolation method that reconstructs the 3d magnetic fields using 2d observed vector magnetograms as boundary conditions. We then located the magnetic discontinuities, which are considered as spatial proxies of reconnection-related instabilities. These discontinuities form well-defined volumes, called here unstable volumes. We calculated the fractal dimensions of these unstable volumes and compared them to the fractal dimensions of the boundary vector magnetograms. Results: Our results show no correlation between the fractal dimensions of the observed 2d photospheric structures and the extrapolated unstable volumes in the corona, when nonlinear force-free extrapolation is used. This result is independent of efforts to (1) bring the photospheric magnetic fields closer to a nonlinear force-free equilibrium and (2) omit the lower part of the modeled magnetic field volume that is almost completely filled by unstable volumes. A significant correlation between the fractal dimensions of the photospheric and coronal magnetic features is only observed at the zero level (lower limit) of approximation of a current-free (potential) magnetic field extrapolation. Conclusions: We conclude that the complicated transition from photospheric non-force-free fields to coronal force-free ones hampers any direct correlation between the fractal dimensions of the 2d photospheric patterns and their 3d counterparts in the corona at the nonlinear force-free limit, which can be considered as a second level of approximation in this
Spatiotemporal Diffusive Evolution and Fractal Structure of Ground Motion
Suwada, Tsuyoshi
2018-02-01
The spatiotemporal diffusive evolution and fractal structure of ground motion have been investigated at the in-ground tunnel of the KEK B-Factory (KEKB) injector linear accelerator (linac). The slow dynamic fluctuating displacements of the tunnel floor are measured in real time with a new remote-controllable sensing system based on a laser-based alignment system. Based on spatiotemporal analyses with linear-regression models, which were applied in both the time and frequency domains to time-series data recorded over a period of approximately 8 months, both coherent and stochastic components in the displacements of the tunnel floor were clearly observed along the entire length of the linac. In particular, it was clearly observed that the stochastic components exhibited characteristic spatiotemporal diffusive evolution with the fractal structure and fractional dimension. This report describes in detail the experimental techniques and analyses of the spatiotemporal diffusive evolution of ground motion observed at the in-ground tunnel of the injector linac using a real-time remote-controllable sensing system.
2-D Fractal Wire Antenna Design and Performance
Tebbens, S. F.; Barton, C. C.; Peterman, D. J.; Ewing, J. J.; Abbott, C. S.; Rizki, M. M.
2017-12-01
A 2-D fractal wire antenna uses a fractal (self-similar) pattern to increase its length by iteration and can receive or transmit electromagnetic radiation. 2-D fractals are shapes that, at their mathematical limit (of infinite iterations) have an infinite length. The fractal dimension describes the degree of space filling. A fundamental property of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that can be very compact, wideband and multiband. As the number of iterations increases, the antenna tends to have additional frequencies that minimize far field return loss. This differs from traditional antenna designs in that a single fractal antenna can operate well at multiple frequencies. We have created a MATLAB code to generate deterministic and stochastic modes of fractal wire antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, and number of iterations have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance.
Fractal characteristic in the wearing of cutting tool
Mei, Anhua; Wang, Jinghui
1995-11-01
This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.
Fractal electrodynamics via non-integer dimensional space approach
Tarasov, Vasily E.
2015-09-01
Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.
Fractals and spectra related to fourier analysis and function spaces
Triebel, Hans
1997-01-01
Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...
Fractal analysis of lateral movement in biomembranes.
Gmachowski, Lech
2018-04-01
Lateral movement of a molecule in a biomembrane containing small compartments (0.23-μm diameter) and large ones (0.75 μm) is analyzed using a fractal description of its walk. The early time dependence of the mean square displacement varies from linear due to the contribution of ballistic motion. In small compartments, walking molecules do not have sufficient time or space to develop an asymptotic relation and the diffusion coefficient deduced from the experimental records is lower than that measured without restrictions. The model makes it possible to deduce the molecule step parameters, namely the step length and time, from data concerning confined and unrestricted diffusion coefficients. This is also possible using experimental results for sub-diffusive transport. The transition from normal to anomalous diffusion does not affect the molecule step parameters. The experimental literature data on molecular trajectories recorded at a high time resolution appear to confirm the modeled value of the mean free path length of DOPE for Brownian and anomalous diffusion. Although the step length and time give the proper values of diffusion coefficient, the DOPE speed calculated as their quotient is several orders of magnitude lower than the thermal speed. This is interpreted as a result of intermolecular interactions, as confirmed by lateral diffusion of other molecules in different membranes. The molecule step parameters are then utilized to analyze the problem of multiple visits in small compartments. The modeling of the diffusion exponent results in a smooth transition to normal diffusion on entering a large compartment, as observed in experiments.
Stochastic self-similar and fractal universe
International Nuclear Information System (INIS)
Iovane, G.; Laserra, E.; Tortoriello, F.S.
2004-01-01
The structures formation of the Universe appears as if it were a classically self-similar random process at all astrophysical scales. An agreement is demonstrated for the present hypotheses of segregation with a size of astrophysical structures by using a comparison between quantum quantities and astrophysical ones. We present the observed segregated Universe as the result of a fundamental self-similar law, which generalizes the Compton wavelength relation. It appears that the Universe has a memory of its quantum origin as suggested by R. Penrose with respect to quasi-crystal. A more accurate analysis shows that the present theory can be extended from the astrophysical to the nuclear scale by using generalized (stochastically) self-similar random process. This transition is connected to the relevant presence of the electromagnetic and nuclear interactions inside the matter. In this sense, the presented rule is correct from a subatomic scale to an astrophysical one. We discuss the near full agreement at organic cell scale and human scale too. Consequently the Universe, with its structures at all scales (atomic nucleus, organic cell, human, planet, solar system, galaxy, clusters of galaxy, super clusters of galaxy), could have a fundamental quantum reason. In conclusion, we analyze the spatial dimensions of the objects in the Universe as well as space-time dimensions. The result is that it seems we live in an El Naschie's E-infinity Cantorian space-time; so we must seriously start considering fractal geometry as the geometry of nature, a type of arena where the laws of physics appear at each scale in a self-similar way as advocated long ago by the Swedish school of astrophysics
Turbulence Enhancement by Fractal Square Grids: Effects of the Number of Fractal Scales
Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei
2017-11-01
Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.
A Parallel Approach to Fractal Image Compression
Directory of Open Access Journals (Sweden)
Lubomir Dedera
2004-01-01
Full Text Available The paper deals with a parallel approach to coding and decoding algorithms in fractal image compressionand presents experimental results comparing sequential and parallel algorithms from the point of view of achieved bothcoding and decoding time and effectiveness of parallelization.
Fractal structures and intermittency in QCD
International Nuclear Information System (INIS)
Gustafson, Goesta.
1990-04-01
New results are presented for fractal structures and intermittency in QCD parton showers. A geometrical interpretation of the anomalous dimension in QCD is given. It is shown that model predications for factorial moments in the PEP-PETRA energy range are increased. if the properties of directly produced pions are more carefully taken into account
Flames in fractal grid generated turbulence
Energy Technology Data Exchange (ETDEWEB)
Goh, K H H; Hampp, F; Lindstedt, R P [Department of Mechanical Engineering, Imperial College, London SW7 2AZ (United Kingdom); Geipel, P, E-mail: p.lindstedt@imperial.ac.uk [Siemens Industrial Turbomachinery AB, SE-612 83 Finspong (Sweden)
2013-12-15
Twin premixed turbulent opposed jet flames were stabilized for lean mixtures of air with methane and propane in fractal grid generated turbulence. A density segregation method was applied alongside particle image velocimetry to obtain velocity and scalar statistics. It is shown that the current fractal grids increase the turbulence levels by around a factor of 2. Proper orthogonal decomposition (POD) was applied to show that the fractal grids produce slightly larger turbulent structures that decay at a slower rate as compared to conventional perforated plates. Conditional POD (CPOD) was also implemented using the density segregation technique and the results show that CPOD is essential to segregate the relative structures and turbulent kinetic energy distributions in each stream. The Kolmogorov length scales were also estimated providing values {approx}0.1 and {approx}0.5 mm in the reactants and products, respectively. Resolved profiles of flame surface density indicate that a thin flame assumption leading to bimodal statistics is not perfectly valid under the current conditions and it is expected that the data obtained will be of significant value to the development of computational methods that can provide information on the conditional structure of turbulence. It is concluded that the increase in the turbulent Reynolds number is without any negative impact on other parameters and that fractal grids provide a route towards removing the classical problem of a relatively low ratio of turbulent to bulk strain associated with the opposed jet configuration. (paper)
Design of silicon-based fractal antennas
Ghaffar, Farhan A.
2012-11-20
This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.
Effect of noise on fractal structure
Energy Technology Data Exchange (ETDEWEB)
Serletis, Demitre [Division of Neurosurgery, Hospital for Sick Children, 1504-555 University Avenue, Toronto, Ont., M5G 1X8 (Canada)], E-mail: demitre.serletis@utoronto.ca
2008-11-15
In this paper, I investigate the effect of dynamical noise on the estimation of the Hurst exponent and the fractal dimension of time series. Recently, Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on estimation of Lyapunov exponents from a time series. Chaos, Solitons and Fractals, forthcoming] have shown that dynamical noise can make the detection of chaotic dynamics very difficult, and Serletis et al. [Serletis, Apostolos, Asghar Shahmoradi, Demitre Serletis. Effect of noise on the bifurcation behavior of dynamical systems. Chaos, Solitons and Fractals, forthcoming] have shown that dynamical noise can also shift bifurcation points and produce noise-induced transitions, making the determination of bifurcation boundaries difficult. Here I apply the detrending moving average (DMA) method, recently developed by Alessio et al. [Alessio E, Carbone A, Castelli G, Frappietro V. Second-order moving average and scaling of stochastic time series. The Eur Phys J B 2002;27:197-200] and Carbone et al. [Carbone A, Castelli G, Stanley HE. Time-dependent Hurst exponent in financial time series. Physica A 2004;344:267-71; Carbone A, Castelli G, Stanley HE. Analysis of clusters formed by the moving average of a long-range correlated time series. Phys Rev E 2004;69:026105], to estimate the Hurst exponent of a Brownian walk with a Hurst exponent of 0.5, coupled with low and high intensity noise, and show that dynamical noise has no effect on fractal structure.
Fractal geometry of high temperature superconductors
International Nuclear Information System (INIS)
Mosolov, A.B.
1989-01-01
Microstructural geometry of superconducting structural composites of Ag-Yba 2 Cu 3 O x system with a volumetric shave of silver from 0 to 60% is investigated by light and electron microscopy methods. It is ascertained that the structure of cermets investigated is characterized by fractal geometry which is sufficient for describing the electrical and mechanical properties of these materials
Fractality and the law of the wall
Xu, Haosen H. A.; Yang, X. I. A.
2018-05-01
Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.
Design of silicon-based fractal antennas
Ghaffar, Farhan A.; Shamim, Atif
2012-01-01
This article presents Sierpinski carpet fractal antennas implemented in conventional low resistivity (Ï =10 Ω cm) as well as high resistivity (Ï =1500 Ω cm) silicon mediums. The fractal antenna is 36% smaller as compared with a typical patch antenna at 24 GHz and provides 13% bandwidth on high resistivity silicon, suitable for high data rate applications. For the first time, an on-chip fractal antenna array is demonstrated in this work which provides double the gain of a single fractal element as well as enhanced bandwidth. A custom test fixture is utilized to measure the radiation pattern and gain of these probe-fed antennas. In addition to gain and impedance characterization, measurements have also been made to study intrachip communication through these antennas. The comparison between the low resistivity and high resistivity antennas indicate that the former is not a suitable medium for array implementation and is only suitable for short range communication whereas the latter is appropriate for short and medium range wireless communication. The design is well-suited for compact, high data rate System-on-Chip (SoC) applications as well as for intrachip communication such as wireless global clock distribution in synchronous systems. © 2012 Wiley Periodicals, Inc. Microwave Opt Technol Lett 55:180-186, 2013; View this article online at wileyonlinelibrary.com. DOI 10.1002/mop.27245 Copyright © 2012 Wiley Periodicals, Inc.
Mitered fractal trees: constructions and properties
Verhoeff, T.; Verhoeff, K.; Bosch, R.; McKenna, D.; Sarhangi, R.
2012-01-01
Tree-like structures, that is, branching structures without cycles, are attractive for artful expression. Especially interesting are fractal trees, where each subtree is a scaled and possibly otherwise transformed version of the entire tree. Such trees can be rendered in 3D by using beams with a
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
In this work the use of fractal scaling exponents for geological mapping was first investigated using theoretical models, and results from the analysis showed that the scaling exponents mapped isolated bodies but did not properly resolve bodies close to each other. However application on real data (the Mamfe basin, the ...
Geological mapping using fractal technique | Lawal | Nigerian ...
African Journals Online (AJOL)
... in Nigeria) showed good correlation with the geological maps of the areas. The results also indicated that basement rocks can generally be represented by scaling exponents with values ranging between -3.0 and -2.0. Keywords: Fractal, dimension, susceptibility, spectra, scaling exponent. Nigerian Journal of Physics Vol.
Fractal nature of hydrocarbon deposits. 2. Spatial distribution
International Nuclear Information System (INIS)
Barton, C.C.; Schutter, T.A; Herring, P.R.; Thomas, W.J.; Scholz, C.H.
1991-01-01
Hydrocarbons are unevenly distributed within reservoirs and are found in patches whose size distribution is a fractal over a wide range of scales. The spatial distribution of the patches is also fractal and this can be used to constrain the design of drilling strategies also defined by a fractal dimension. Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. The authors have performed fractal analyses on the spatial distribution of producing and showing wells combined and of dry wells in 1,600-mi 2 portions of the Denver and Powder River basins that were nearly completely drilled on quarter-mile square-grid spacings. They have limited their analyses to wells drilled to single stratigraphic intervals so that the map pattern revealed by drilling is representative of the spatial patchiness of hydrocarbons at depth. The fractal dimensions for the spatial patchiness of hydrocarbons in the two basins are 1.5 and 1.4, respectively. The fractal dimension for the pattern of all wells drilled is 1.8 for both basins, which suggests a drilling strategy with a fractal dimension significantly higher than the dimensions 1.5 and 1.4 sufficient to efficiently and economically explore these reservoirs. In fact, the fractal analysis reveals that the drilling strategy used in these basins approaches a fractal dimension of 2.0, which is equivalent to random drilling with no geologic input. Knowledge of the fractal dimension of a reservoir prior to drilling would provide a basis for selecting and a criterion for halting a drilling strategy for exploration whose fractal dimension closely matches that of the spatial fractal dimension of the reservoir, such a strategy should prove more efficient and economical than current practice
Visual observation of gas hydrates nucleation and growth at a water - organic liquid interface
Stoporev, Andrey S.; Semenov, Anton P.; Medvedev, Vladimir I.; Sizikov, Artem A.; Gushchin, Pavel A.; Vinokurov, Vladimir A.; Manakov, Andrey Yu.
2018-03-01
Visual observation of nucleation sites of methane and methane-ethane-propane hydrates and their further growth in water - organic liquid - gas systems with/without surfactants was carried out. Sapphire Rocking Cell RCS6 with transparent sapphire cells was used. The experiments were conducted at the supercooling ΔTsub = 20.2 °C. Decane, toluene and crude oils were used as organics. Gas hydrate nucleation occurred on water - metal - gas and water - sapphire - organic liquid three-phase contact lines. At the initial stage of growth hydrate crystals rapidly covered the water - gas or water - organics interfaces (depending on the nucleation site). Further hydrate phase accrete on cell walls (sapphire surface) and into the organics volume. At this stage, growth was accompanied by water «drawing out» from under initial hydrate film formed at water - organic interface. Apparently, it takes place due to water capillary inflow in the reaction zone. It was shown that the hydrate crystal morphology depends on the organic phase composition. In the case of water-in-decane emulsion relay hydrate crystallization was observed in the whole sample, originating most likely due to the hydrate crystal intergrowth through decane. Contacts of such crystals with adjacent water droplets result in rapid hydrate crystallization on this droplet.
Electron spin-lattice relaxation in fractals
International Nuclear Information System (INIS)
Shrivastava, K.N.
1986-08-01
We have developed the theory of the spin-fracton interaction for paramagnetic ions in fractal structures. The interaction is exponentially damped by the self-similarity length of the fractal and by the range dimensionality d Φ . The relaxation time of the spin due to the absorption and emission of the fracton has been calculated for a general dimensionality called the Raman dimensionality d R , which for the fractons differs from the Hausdorff (fractal) dimensionality, D, as well as from the Euclidean dimensionality, d. The exponent of the energy level separation in the relaxation rate varies with d R d Φ /D. We have calculated the spin relaxation rate due to a new type of Raman process in which one fracton is absorbed to affect a spin transition from one electronic level to another and later another fracton is emitted along with a spin transition such that the difference in the energies of the two fractons is equal to the electronic energy level separation. The temperature and the dimensionality dependence of such a process has been found in several approximations. In one of the approximations where the van Vleck relaxation rate for a spin in a crystal is known to vary with temperature as T 9 , our calculated variation for fractals turns out to be T 6.6 , whereas the experimental value for Fe 3+ in frozen solutions of myoglobin azide is T 6.3 . Since we used d R =4/3 and the fracton range dimensionality d Φ =D/1.8, we expect to measure the dimensionalities of the problem by measuring the temperature dependence of the relaxation times. We have also calculated the shift of the paramagnetic resonance transition for a spin in a fractal for general dimensionalities. (author)
International Nuclear Information System (INIS)
Meng Ping; Zhang Jingsong
2005-01-01
The characteristics correlation between solar total radiations(Q) and net radiation(R n) on the apple tree canopy at mainly growth stage in the hilly of Taihang Mountain are analyzed with fractal theory based on regression analysis. The results showed that:1)Q and R n had good liner correlation. The regression function was as the following:R n=0.740 8Q-32.436, which coefficient r is 0.981 1(n=26 279), F cal= 343 665.2 F 0.01 36 277=6.63; 2)The fractal dimension curves of Q and R n both had two no s caling regions, which circumscription time value of the inflexion was 453 and 441 minutes respectively.In the first region, fractal dimensions of Q and R n was 1.112 6, 1.131 9 respectively,and 1.913 6@@@ 1.883 4 in the second region.Those information showed that fractal characteristics of Q and R n is similar. So R n can be calculated with Q on the apple tree canopy
In situ observations of bubble growth in basaltic, andesitic and rhyodacitic melts
Masotta, M.; Ni, H.; Keppler, H.
2014-02-01
Bubble growth strongly affects the physical properties of degassing magmas and their eruption dynamics. Natural samples and products from quench experiments provide only a snapshot of the final state of volatile exsolution, leaving the processes occurring during its early stages unconstrained. In order to fill this gap, we present in situ high-temperature observations of bubble growth in magmas of different compositions (basalt, andesite and rhyodacite) at 1,100 to 1,240 °C and 0.1 MPa (1 bar), obtained using a moissanite cell apparatus. The data show that nucleation occurs at very small degrees of supersaturaturation (bubbles occurring simultaneously with the nucleation of crystals. During the early stages of exsolution, melt degassing is the driving mechanism of bubble growth, with coalescence becoming increasingly important as exsolution progresses. Ostwald ripening occurs only at the end of the process and only in basaltic melt. The average bubble growth rate ( G R) ranges from 3.4 × 10-6 to 5.2 × 10-7 mm/s, with basalt and andesite showing faster growth rates than rhyodacite. The bubble number density ( N B) at nucleation ranges from 7.9 × 104 mm-3 to 1.8 × 105 mm-3 and decreases exponentially over time. While the rhyodacite melt maintained a well-sorted bubble size distribution (BSD) through time, the BSDs of basalt and andesite are much more inhomogeneous. Our experimental observations demonstrate that bubble growth cannot be ascribed to a single mechanism but is rather a combination of many processes, which depend on the physical properties of the melt. Depending on coalescence rate, annealing of bubbles following a single nucleation event can produce complex bubble size distributions. In natural samples, such BSDs may be misinterpreted as resulting from several separate nucleation events. Incipient crystallization upon cooling of a magma may allow bubble nucleation already at very small degrees of supersaturation and could therefore be an important
Shantz, N. C.; Chang, R. Y.-W.; Slowik, J. G.; Vlasenko, A.; Abbatt, J. P. D.; Leaitch, W. R.
2010-01-01
Growth rates of water droplets were measured with a static diffusion cloud condensation chamber in May-June 2007 at a rural field site in Southern Ontario, Canada, 70 km north of Toronto. The observations include periods when the winds were from the south and the site was impacted by anthropogenic air from the U.S. and Southern Ontario as well as during a 5-day period of northerly wind flow when the aerosol was dominated by biogenic sources. The growth of droplets on anthropogenic size-selected particles centred at 0.1 μm diameter and composed of approximately 40% organic and 60% ammonium sulphate (AS) by mass, was delayed by on the order of 1 s compared to a pure AS aerosol. Simulations of the growth rate on monodisperse particles indicate that a lowering of the water mass accommodation coefficient from αc=1 to an average of αc=0.04 is needed (assuming an insoluble organic with hygroscopicity parameter, κorg, of zero). Simulations of the initial growth rate on polydisperse anthropogenic particles agree best with observations for αc=0.07. In contrast, the growth rate of droplets on size-selected aerosol of biogenic character, consisting of >80% organic, was similar to that of pure AS. Simulations of the predominantly biogenic polydisperse aerosol show agreement between the observations and simulations when κorg=0.2 (with upper and lower limits of 0.5 and 0.07, respectively) and αc=1. Inhibition of water uptake by the anthropogenic organic applied to an adiabatic cloud parcel model in the form of a constant low αc increases the number of droplets in a cloud compared to pure AS. If the αc is assumed to increase with increasing liquid water on the droplets, then the number of droplets decreases which could diminish the indirect climate forcing effect. The slightly lower κorg in the biogenic case decreases the number of droplets in a cloud compared to pure AS.
Cassini CAPS-ELS observations of carbon-based anions and aerosol growth in Titan's ionosphere
Desai, Ravindra; Coates, Andrew; Wellbrock, Anne; Kataria, Dhiren; Jones, Geraint; Lewis, Gethyn; Waite, J.
2016-06-01
Cassini observations of Titans ionosphere revealed an atmosphere rich in positively charged ions with masses up to > 350 amu and negatively charged ions and aerosols with mass over charge ratios as high as 13,800 amu/q. The detection of negatively charged molecules by the Cassini CAPS Electron Spectrometer (CAPS-ELS) was particularly surprising and showed how the synthesis of large aerosol-size particles takes place at altitudes much greater than previously thought. Here, we present further analysis into this CAPS-ELS dataset, through an enhanced understanding of the instrument's response function. In previous studies the intrinsic E/E energy resolution of the instrument did not allow specific species to be identified and the detections were classified into broad mass ranges. In this study we use an updated fitting procedure to show how the ELS mass spectrum can be resolved into specific peaks at multiples of carbon-based anions up to > 100 amu/q. The negatively charged ions and aerosols in Titans ionosphere increase in mass with decreasing altitude, the lightest species being observed close to Titan's exobase of ˜1,450km and heaviest species observed at altitudes < 950km. We identify key stages in this apparent growth process and report on key intermediaries which appear to trigger the rapid growth of the larger aerosol-size particles.
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Santillán, Jesica M. J. [CONICET La Plata-CIC, Centro de Investigaciones Ópticas (CIOp) (Argentina); Fernández van Raap, Marcela B., E-mail: raap@fisica.unlp.edu.ar; Mendoza Zélis, Pedro; Coral, Diego [CONICET, Instituto de Física La Plata (IFLP) (Argentina); Muraca, Diego [Universidade Estadual de Campinas, Instituto de Física “Gleb Wataghin” (IFGW) (Brazil); Schinca, Daniel C.; Scaffardi, Lucía B., E-mail: lucias@ciop.unlp.edu.ar [CONICET La Plata-CIC, Centro de Investigaciones Ópticas (CIOp) (Argentina)
2015-02-15
We report for the first time on the formation of self-assembled fractals of spherical Ag nanoparticles (Nps) fabricated by femtosecond pulse laser ablation of a solid silver target in water. Fractal structures grew both in two and three Euclidean dimensions (d). Ramified-fractal assemblies of 2 nm height and 5–14 μm large, decorated with Ag Nps of 3 nm size, were obtained in a 2d geometry when highly diluted drops of colloidal suspension were dried at a fast heating rate over a mica substrate. When less-diluted drops were dried at slow heating rate, isolated single Nps or rosette-like structures were formed. Fractal aggregates about 31 nm size in 3d geometry were observed in the as-prepared colloidal suspension. Electron diffraction and optical extinction spectroscopy (OES) analyses performed on the samples confirmed the presence of Ag and Ag{sub 2}O. The analysis of the optical extinction spectrum, using the electrostatic approximation of Mie theory for small spheres, showed the existence of Ag bare core, Ag–Ag{sub 2}O and air–Ag core–shell Nps, Ag–Ag{sub 2}O being the most frequent type [69 % relative abundance (r.a.)]. Core-size and shell-thickness distribution was derived from OES. In situ scattering measurements of the Ag colloidal suspension, carried out by small-angle X-ray scattering, indicate a mass fractal composed of packaged 〈D{sub SAXS}〉 = (5 ± 1) nm particles and fractal dimension d{sub f} = 2.5. Ex situ atomic force microscopy imaging displayed well-ramified structures, which, analyzed with box-counting method, yield a fractal dimension d{sub f} = 1.67. The growing behavior of these 2d and 3d self-assembled fractals is consistent with the diffusion-limited aggregation model.
Direct atomic force microscopy observation of DNA tile crystal growth at the single-molecule level.
Evans, Constantine G; Hariadi, Rizal F; Winfree, Erik
2012-06-27
While the theoretical implications of models of DNA tile self-assembly have been extensively researched and such models have been used to design DNA tile systems for use in experiments, there has been little research testing the fundamental assumptions of those models. In this paper, we use direct observation of individual tile attachments and detachments of two DNA tile systems on a mica surface imaged with an atomic force microscope (AFM) to compile statistics of tile attachments and detachments. We show that these statistics fit the widely used kinetic Tile Assembly Model and demonstrate AFM movies as a viable technique for directly investigating DNA tile systems during growth rather than after assembly.
FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY
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Ian Parkinson
2011-05-01
Full Text Available A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge. The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals, with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.
Closed contour fractal dimension estimation by the Fourier transform
International Nuclear Information System (INIS)
Florindo, J.B.; Bruno, O.M.
2011-01-01
Highlights: → A novel fractal dimension concept, based on Fourier spectrum, is proposed. → Computationally simple. Computational time smaller than conventional fractal methods. → Results are closer to Hausdorff-Besicovitch than conventional methods. → The method is more accurate and robustness to geometric operations and noise addition. - Abstract: This work proposes a novel technique for the numerical calculus of the fractal dimension of fractal objects which can be represented as a closed contour. The proposed method maps the fractal contour onto a complex signal and calculates its fractal dimension using the Fourier transform. The Fourier power spectrum is obtained and an exponential relation is verified between the power and the frequency. From the parameter (exponent) of the relation, is obtained the fractal dimension. The method is compared to other classical fractal dimension estimation methods in the literature, e.g., Bouligand-Minkowski, box-counting and classical Fourier. The comparison is achieved by the calculus of the fractal dimension of fractal contours whose dimensions are well-known analytically. The results showed the high precision and robustness of the proposed technique.
International Nuclear Information System (INIS)
Ogura, Tatsuo; Miyamoto, Masanori; Budiyono, Agung; Nakamura, Katsuhiro
2007-01-01
Fractal magnetoconductance fluctuations are often observed in experiments on ballistic quantum dots. Although the analysis of the exact self-affine fractal has been given by the semiclassical theory using self-similar periodic orbits in systems with a soft-walled potential with a saddle, there has been no corresponding quantum mechanical investigation. We numerically calculate the quantum conductance with use of the recursive Green's function method applied to open cavities characterized by a Henon-Heiles type potential. The conductance fluctuations show exact self-affinity just as in some of the experimental observations. The enlargement factor for the horizontal axis can be explained by the scaling factor of the area of self-similar periodic orbits, and therefore be attributed to the curvature of the saddle in the cavity potential. The fractal dimension obtained through the box counting method agrees with those evaluated with use of the Hurst exponent, and coincides with the semiclassical prediction. We further investigate the variation of the fractal dimension by changing the control parameters between the classical and quantum domains. (fast track communication)
FRACTAL DIMENSION OF URBAN EXPANSION BASED ON REMOTE SENSING IMAGES
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IACOB I. CIPRIAN
2012-11-01
Full Text Available Fractal Dimension of Urban Expansion Based on Remote Sensing Images: In Cluj-Napoca city the process of urbanization has been accelerated during the years and implication of local authorities reflects a relevant planning policy. A good urban planning framework should take into account the society demands and also it should satisfy the natural conditions of local environment. The expansion of antropic areas it can be approached by implication of 5D variables (time as a sequence of stages, space: with x, y, z and magnitude of phenomena into the process, which will allow us to analyse and extract the roughness of city shape. Thus, to improve the decision factor we take a different approach in this paper, looking at geometry and scale composition. Using the remote sensing (RS and GIS techniques we manage to extract a sequence of built-up areas (from 1980 to 2012 and used the result as an input for modelling the spatialtemporal changes of urban expansion and fractal theory to analysed the geometric features. Taking the time as a parameter we can observe behaviour and changes in urban landscape, this condition have been known as self-organized – a condition which in first stage the system was without any turbulence (before the antropic factor and during the time tend to approach chaotic behaviour (entropy state without causing an disequilibrium in the main system.
Fractal analysis of striatal dopamine re-uptake sites
International Nuclear Information System (INIS)
Kuikka, J.T.; Bergstroem, K.A.; Tiihonen, J.; Raesaenen, P.; Karhu, J.
1997-01-01
Spatial variation in regional blood flow, metabolism and receptor density within the brain and in other organs is measurable even with a low spatial resolution technique such as emission tomography. It has been previously shown that the observed variance increases with increasing number of subregions in the organ/tissue studied. This resolution-dependent variance can be described by fractal analysis. We studied striatal dopamine re-uptake sites in 39 healthy volunteers with high-resolution single-photon emission tomography using iodine-123 labelled 2β-carbomethoxy-3β-(4-iodophenyl)tropane ([ 123 I]β-CIT). The mean fractal dimension was 1.15±0.07. The results indicate that regional striatal dopamine re-uptake sites involve considerable spatial heterogeneity which is higher than the uniform density (dimension=1.00) but much lower than complete randomness (dimension=1.50). There was a gender difference, with females having a higher heterogeneity in both the left and the right striatum. In addition, we found striatal asymmetry (left-to-right heterogeneity ratio of 1.19±0.15; P<0.001), suggesting functional hemispheric lateralization consistent with the control of motor behaviour and integrative functions. (orig.). With 5 figs., 1 tab
Fractal analysis of striatal dopamine re-uptake sites
Energy Technology Data Exchange (ETDEWEB)
Kuikka, J.T.; Bergstroem, K.A. [Department of Clinical Physiology, Kuopio University Hospital, Kuopio (Finland); Tiihonen, J.; Raesaenen, P. [Department of Forensic Psychiatry, University of Kuopio and Niuvanniemi Hospital, Kuopio (Finland); Karhu, J. [Department of Clinical Neurophysiology, Kuopio University Hospital, Kuopio (Finland)
1997-09-01
Spatial variation in regional blood flow, metabolism and receptor density within the brain and in other organs is measurable even with a low spatial resolution technique such as emission tomography. It has been previously shown that the observed variance increases with increasing number of subregions in the organ/tissue studied. This resolution-dependent variance can be described by fractal analysis. We studied striatal dopamine re-uptake sites in 39 healthy volunteers with high-resolution single-photon emission tomography using iodine-123 labelled 2{beta}-carbomethoxy-3{beta}-(4-iodophenyl)tropane ([{sup 123}I]{beta}-CIT). The mean fractal dimension was 1.15{+-}0.07. The results indicate that regional striatal dopamine re-uptake sites involve considerable spatial heterogeneity which is higher than the uniform density (dimension=1.00) but much lower than complete randomness (dimension=1.50). There was a gender difference, with females having a higher heterogeneity in both the left and the right striatum. In addition, we found striatal asymmetry (left-to-right heterogeneity ratio of 1.19{+-}0.15; P<0.001), suggesting functional hemispheric lateralization consistent with the control of motor behaviour and integrative functions. (orig.). With 5 figs., 1 tab.
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Huang, K. Q.; Cao, C. R.; Sun, Y. T.; Li, J.; Bai, H. Y.; Zheng, D. N., E-mail: l.gu@iphy.ac.cn, E-mail: dzheng@iphy.ac.cn, E-mail: whw@iphy.ac.cn; Wang, W. H., E-mail: l.gu@iphy.ac.cn, E-mail: dzheng@iphy.ac.cn, E-mail: whw@iphy.ac.cn [Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Gu, L., E-mail: l.gu@iphy.ac.cn, E-mail: dzheng@iphy.ac.cn, E-mail: whw@iphy.ac.cn [Institute of Physics, Chinese Academy of Sciences, Beijing 100190 (China); Collaborative Innovation Center of Quantum Matter, Beijing 100190 (China)
2016-01-07
Till date, there have been no direct atomic-level experimental observations of the earliest stages of the nucleation and growth processes of nanocrystals formed by thermally induced crystallization in ultrathin metallic glasses (MGs). Here, we present a study of the crystallization process in atomically thin and highly stable MG films using double spherical aberration-corrected scanning transmission electron microscopy (Cs-TEM). Taking advantage of the stability of MG films with a slow crystallization process and the atomic-level high resolution of Cs-TEM, we observe the formation of the nucleus precursor of nanocrystals formed by atom aggregation followed by concomitant coalescence and stepwise evolution of the shape of the nanocrystals with a monodispersed and separated bimodal size distribution. Molecular dynamics simulation of the atomic motion in the glass film on a rigid amorphous substrate confirms the stepwise evolution processes of atom aggregation, cluster formation, cluster movement on the substrate, and cluster coalescence into larger crystalline particles. Our results might provide a better fundamental understanding of the nucleation and growth processes of nanocrystals in thin MG films.
Song, Hyon-Min
2015-06-17
A series of magnetically active ferrite nanoparticles (NPs) are prepared by using Mn oxide NPs as seeds. Verwey transition is identified in Fe3O4 NPs with an average diameter of 14.5 nm at 96 K, where a sharp drop of magnetic susceptibility occurs. In MnFe2O4 NPs, spin glass-like state is observed with the decrease of magnetization below the blocking temperature due to the disordered spins during the freezing process. From these MnFe2O4 NPs, MnFe2O4@MnxFe1-xO core-shell NPs are prepared by seeded growth. The structure of core is cubic spinels (Fd-3m), and shell is composed of iron-manganese oxide (MnxFe1-xO) with a rock salt structure (Fm-3m). Moiré fringes appear perpendicular to <110> directions on the cubic shape NPs through the plane-matched epitaxial growth. These fringes are due to the difference in their lattice spacings between MnFe2O4 and MnxFe1-xO. Exchange bias is observed in these MnFe2O4@MnxFe1-xO core-shell NPs with an enhanced coercivity as well as the shift of hysteresis along the field direction.
International Nuclear Information System (INIS)
Grizzi, Fabio; Russo, Carlo; Colombo, Piergiuseppe; Franceschini, Barbara; Frezza, Eldo E; Cobos, Everardo; Chiriva-Internati, Maurizio
2005-01-01
Modeling the complex development and growth of tumor angiogenesis using mathematics and biological data is a burgeoning area of cancer research. Architectural complexity is the main feature of every anatomical system, including organs, tissues, cells and sub-cellular entities. The vascular system is a complex network whose geometrical characteristics cannot be properly defined using the principles of Euclidean geometry, which is only capable of interpreting regular and smooth objects that are almost impossible to find in Nature. However, fractal geometry is a more powerful means of quantifying the spatial complexity of real objects. This paper introduces the surface fractal dimension (D s ) as a numerical index of the two-dimensional (2-D) geometrical complexity of tumor vascular networks, and their behavior during computer-simulated changes in vessel density and distribution. We show that D s significantly depends on the number of vessels and their pattern of distribution. This demonstrates that the quantitative evaluation of the 2-D geometrical complexity of tumor vascular systems can be useful not only to measure its complex architecture, but also to model its development and growth. Studying the fractal properties of neovascularity induces reflections upon the real significance of the complex form of branched anatomical structures, in an attempt to define more appropriate methods of describing them quantitatively. This knowledge can be used to predict the aggressiveness of malignant tumors and design compounds that can halt the process of angiogenesis and influence tumor growth
Fractal zeta functions and fractal drums higher-dimensional theory of complex dimensions
Lapidus, Michel L; Žubrinić, Darko
2017-01-01
This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the f...
International Nuclear Information System (INIS)
Micic, Miodrag; Klymyshyn, Nicholas A.; Lu, H Peter
2004-01-01
Near-field optical enhancement at metal surfaces and methods such as surface plasmon resonance (SPR), surface-enhanced Raman scattering (SERS), fluorescent quenching and enhancement, and various near-field scanning microscopies (NSOM) all depend on a metals surface properties, mainly on its morphology and SPR resonant frequency. We report on simulations of the influence of different surface morphologies on electromagnetic field enhancements at the rough surfaces of noble metals and also evaluate the optimal conditions for the generation of a surface-enhanced Raman signal of absorbed species on a metallic substrate. All simulations were performed with a classical electrodynamics approach using the full set of Maxwells equations, which were solved with the three-dimensional finite element method (FEM). Two different classes of surfaces where modeled using fractals, representing diffusion limited aggregation growth dendritic structures, such as one on the surface of electrodes, and second one representing the sponge-like structure used to model surfaces of particles with high porosity, such as metal coated catalyst supports. The simulations depict the high inhomogeneity of an enhanced electromagnetic field as both a field enhancement and field attenuation near the surface. While the diffusion limited aggregation dendritical fractals enhanced the near-field electromagnetic field, the sponge fractals significantly reduced the local electromagnetic field intensity. Moreover, the fractal orders of the fractal objects did not significantly alter the total enhancement, and the distribution of a near-field enhancement was essentially invariant to the changes in the angle of an incoming laser beam
Fractal dimension analysis of complexity in Ligeti piano pieces
Bader, Rolf
2005-04-01
Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.
A new numerical approximation of the fractal ordinary differential equation
Atangana, Abdon; Jain, Sonal
2018-02-01
The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.
Evaluation of 3D Printer Accuracy in Producing Fractal Structure.
Kikegawa, Kana; Takamatsu, Kyuuichirou; Kawakami, Masaru; Furukawa, Hidemitsu; Mayama, Hiroyuki; Nonomura, Yoshimune
2017-01-01
Hierarchical structures, also known as fractal structures, exhibit advantageous material properties, such as water- and oil-repellency as well as other useful optical characteristics, owing to its self-similarity. Various methods have been developed for producing hierarchical geometrical structures. Recently, fractal structures have been manufactured using a 3D printing technique that involves computer-aided design data. In this study, we confirmed the accuracy of geometrical structures when Koch curve-like fractal structures with zero to three generations were printed using a 3D printer. The fractal dimension was analyzed using a box-counting method. This analysis indicated that the fractal dimension of the third generation hierarchical structure was approximately the same as that of the ideal Koch curve. These findings demonstrate that the design and production of fractal structures can be controlled using a 3D printer. Although the interior angle deviated from the ideal value, the side length could be precisely controlled.
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Parent, Lucas R. [Department; amp, Biochemistry, University of California, San Diego, La Jolla, California 92093, United States; Bakalis, Evangelos [Dipartimento; Ramírez-Hernández, Abelardo [Materials; Institute; Kammeyer, Jacquelin K. [Department; amp, Biochemistry, University of California, San Diego, La Jolla, California 92093, United States; Park, Chiwoo [Department; de Pablo, Juan [Materials; Institute; Zerbetto, Francesco [Dipartimento; Patterson, Joseph P. [Department; amp, Biochemistry, University of California, San Diego, La Jolla, California 92093, United States; Laboratory; Gianneschi, Nathan C. [Department; amp, Biochemistry, University of California, San Diego, La Jolla, California 92093, United States
2017-11-16
Amphiphilic small molecules and polymers form commonplace nanoscale macromolecular compartments and bilayers, and as such are truly essential components in all cells and in many cellular processes. The nature of these architectures, including their formation, phase changes, and stimuli-response behaviors, is necessary for the most basic functions of life, and over the past half-century, these natural micellar structures have inspired a vast diversity of industrial products, from biomedicines to detergents, lubricants, and coatings. The importance of these materials and their ubiquity have made them the subject of intense investigation regarding their nanoscale dynamics with increasing interest in obtaining sufficient temporal and spatial resolution to directly observe nanoscale processes. However, the vast majority of experimental methods involve either bulk-averaging techniques including light, neutron, and X-ray scattering, or are static in nature including even the most advanced cryogenic transmission electron microscopy techniques. Here, we employ in situ liquid-cell transmission electron microscopy (LCTEM) to directly observe the evolution of individual amphiphilic block copolymer micellar nanoparticles in solution, in real time with nanometer spatial resolution. These observations, made on a proof-of-concept bioconjugate polymer amphiphile, revealed growth and evolution occurring by unimer addition processes and by particle-particle collision-and-fusion events. The experimental approach, combining direct LCTEM observation, quantitative analysis of LCTEM data, and correlated in silico simulations, provides a unique view of solvated soft matter nanoassemblies as they morph and evolve in time and space, enabling us to capture these phenomena in solution.
Bruner, Emiliano; Mantini, Simone; Perna, Agostino; Maffei, Carlotta; Manzi, Giorgio
2005-01-01
The middle meningeal vascular network leaves its traces on the endocranial surface because of the tight relationship between neurocranial development and brain growth. Analysing the endocast of fossil specimens, it is therefore possible to describe the morphology of these structures, leading inferences on the cerebral physiology and metabolism in extinct human groups. In this paper, general features of the meningeal vascular traces are described for specimens included in the Homo erectus, Homo neanderthalensis, and Homo sapiens hypodigms. The complexity of the arterial network is quantified by its fractal dimension, calculated through the box-counting method. Modern humans show significant differences from the other two taxa because of the anterior vascular dominance and the larger fractal dimension. Neither the fractal dimension nor the anterior development are merely associated with cranial size increase. Considering the differences between Neanderthals and modern humans, these results may be interpreted in terms of phylogeny, cerebral functions, or cranial structural network.
Generation of fractals from complex logistic map
Energy Technology Data Exchange (ETDEWEB)
Rani, Mamta [Galgotias College of Engg. and Technology, Greater Noida (India)], E-mail: mamtarsingh@rediffmail.com; Agarwal, Rashi [IEC College of Engg. and Tech., Greater Noida (India)], E-mail: agarwal_rashi@yahoo.com
2009-10-15
Remarkably benign looking logistic transformations x{sub n+1} = r x{sub n}(1 - x{sub n}) for choosing x{sub 0} between 0 and 1 and 0 < r {<=} 4 have found a celebrated place in chaos, fractals and discrete dynamics. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck [Beck C. Physical meaning for Mandelbrot and Julia sets. Physica D 1999;125(3-4):171-182. Zbl0988.37060] to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter case. The purpose of this paper is to study the bounded behavior of the complex logistic map using superior iterates and generate fractals from the same. The analysis in this paper shows that many beautiful properties of the logistic map are extendable for a larger value of r.
Fractal Adaptive Web Service for Mobile Learning
Directory of Open Access Journals (Sweden)
Ichraf Tirellil
2006-06-01
Full Text Available This paper describes our proposition for adaptive web services which is based on configurable, re-usable adaptive/personalized services. To realize our ideas, we have developed an approach for designing, implementing and maintaining personal service. This approach enables the user to accomplish an activity with a set of services answering to his preferences, his profiles and to a personalized context. In this paper, we describe the principle of our approach that we call fractal adaptation approach, and we discuss the implementation of personalization services in the context of mobile and collaborative scenario of learning. We have realized a platform in this context -a platform for mobile and collaborative learning- based on fractal adaptable web services. The platform is tested with a population of students and tutors, in order to release the gaps and the advantages of the approach suggested.
Fractal Analysis of Stealthy Pathfinding Aesthetics
Directory of Open Access Journals (Sweden)
Ron Coleman
2009-01-01
Full Text Available This paper uses a fractal model to analyze aesthetic values of a new class of obstacle-prone or “stealthy” pathfinding which seeks to avoid detection, exposure, openness, and so forth in videogames. This study is important since in general the artificial intelligence literature has given relatively little attention to aesthetic outcomes in pathfinding. The data we report, according to the fractal model, suggests that stealthy paths are statistically significantly unique in relative aesthetic value when compared to control paths. We show furthermore that paths generated with different stealth regimes are also statistically significantly unique. These conclusions are supported by statistical analysis of model results on experimental trials involving pathfinding in randomly generated, multiroom virtual worlds.
A TUTORIAL INTRODUCTION TO ADAPTIVE FRACTAL ANALYSIS
Directory of Open Access Journals (Sweden)
Michael A Riley
2012-09-01
Full Text Available The authors present a tutorial description of adaptive fractal analysis (AFA. AFA utilizes an adaptive detrending algorithm to extract globally smooth trend signals from the data and then analyzes the scaling of the residuals to the fit as a function of the time scale at which the fit is computed. The authors present applications to synthetic mathematical signals to verify the accuracy of AFA and demonstrate the basic steps of the analysis. The authors then present results from applying AFA to time series from a cognitive psychology experiment on repeated estimation of durations of time to illustrate some of the complexities of real-world data. AFA shows promise in dealing with many types of signals, but like any fractal analysis method there are special challenges and considerations to take into account, such as determining the presence of linear scaling regions.
Reengineering through natural structures: the fractal factory
Sihn, Wilfried
1995-08-01
Many branches of European industry have had to recognize that their lead in the world market has been caught up with, particularly through Asian competition. In many cases a deficit of up to 30% in costs and productivity already exists. The reasons are rigid, Tayloristic company structures. The companies are not in a position to react flexibly to constantly changing environmental conditions. This article illustrates the methods of the `fractal company' which are necessary to solve the structure crisis. The fractal company distinguishes itself through its dynamics and its vitality, as well as its independent reaction to the changing circumstances. The developed methods, procedures, and framework conditions such as company structuring, human networking, hierarchy formation, and models for renumeration and working time are explained. They are based on practical examples from IPA's work with the automobile industry, their suppliers, and the engineering industry.
Generation of fractals from complex logistic map
International Nuclear Information System (INIS)
Rani, Mamta; Agarwal, Rashi
2009-01-01
Remarkably benign looking logistic transformations x n+1 = r x n (1 - x n ) for choosing x 0 between 0 and 1 and 0 < r ≤ 4 have found a celebrated place in chaos, fractals and discrete dynamics. The strong physical meaning of Mandelbrot and Julia sets is broadly accepted and nicely connected by Christian Beck [Beck C. Physical meaning for Mandelbrot and Julia sets. Physica D 1999;125(3-4):171-182. Zbl0988.37060] to the complex logistic maps, in the former case, and to the inverse complex logistic map, in the latter case. The purpose of this paper is to study the bounded behavior of the complex logistic map using superior iterates and generate fractals from the same. The analysis in this paper shows that many beautiful properties of the logistic map are extendable for a larger value of r.
Tumor cells diagnostic through fractal dimensions
International Nuclear Information System (INIS)
Timbo, Christiano dos Santos
2004-01-01
This method relies on the application of an algorithm for the quantitative and statistic differentiation of a sample of cells stricken by a certain kind of pathology and a sample of healthy cells. This differentiation is made by applying the principles of fractal dimension to digital images of the cells. The algorithm was developed using the the concepts of Object- Oriented Programming, resulting in a simple code, divided in 5 distinct procedures, and a user-friendly interface. To obtain the fractal dimension of the images of the cells, the program processes the image, extracting its border, and uses it to characterize the complexity of the form of the cell in a quantitative way. In order to validate the code, it was used a digitalized image found in an article by W. Bauer, developer of an analog method. The result showed a difference of 6% between the value obtained by Bauer and the value obtained the algorithm developed in this work. (author)
a New Method for Calculating Fractal Dimensions of Porous Media Based on Pore Size Distribution
Xia, Yuxuan; Cai, Jianchao; Wei, Wei; Hu, Xiangyun; Wang, Xin; Ge, Xinmin
Fractal theory has been widely used in petrophysical properties of porous rocks over several decades and determination of fractal dimensions is always the focus of researches and applications by means of fractal-based methods. In this work, a new method for calculating pore space fractal dimension and tortuosity fractal dimension of porous media is derived based on fractal capillary model assumption. The presented work establishes relationship between fractal dimensions and pore size distribution, which can be directly used to calculate the fractal dimensions. The published pore size distribution data for eight sandstone samples are used to calculate the fractal dimensions and simultaneously compared with prediction results from analytical expression. In addition, the proposed fractal dimension method is also tested through Micro-CT images of three sandstone cores, and are compared with fractal dimensions by box-counting algorithm. The test results also prove a self-similar fractal range in sandstone when excluding smaller pores.
Engagement as a Driver of Growth of Online Health Forums: Observational Study.
Gopalsamy, Rahul; Semenov, Alexander; Pasiliao, Eduardo; McIntosh, Scott; Nikolaev, Alexander
2017-08-29
The emerging research on nurturing the growth of online communities posits that it is in part attributed to network effects, wherein every increase in the volume of user-generated content increases the value of the community in the eyes of its potential new members. The recently introduced metric engagement capacity offers a means of quantitatively assessing the ability of online platform users to engage each other into generating content; meanwhile, the quantity engagement value is useful for quantifying communication-based platform use. If the claim that higher engagement leads to accelerated growth holds true for online health forums (OHFs), then engagement tracking should become an important tool in the arsenal of OHF managers. Indeed, it might allow for quantifying the ability of an OHF to exploit network effects, thus predicting the OHF's future success. This study aimed to empirically analyze the relationship between internal OHF use (quantified using engagement measurement), and external growth. We collected data from 7 OHFs posted between the years 1999 and 2016. Longitudinal analyses were conducted by evaluating engagement in the OHFs over time. We analyzed 2-way causality effects between the engagement value and metrics evaluating OHF growth using Granger causality tests. User activity metrics per week were correlated with engagement metrics, followed by linear regression analyses. Observational data showed a 1-way causal relationship between the OHF engagement value and reach (P=.02). We detected a 2-way causal relationship between the engagement value and delurking, with further analysis indicating that the engagement value was more likely to cause delurking (PUsers who engaged each other more were more likely (up to 14 times, depending on how much one user engaged another) to develop personal connections. Finally, we found that the more engaging an OHF user was in a given week, the more likely (up to 2 times, depending on their ability to engage
Engagement as a Driver of Growth of Online Health Forums: Observational Study
Gopalsamy, Rahul; Semenov, Alexander; Pasiliao, Eduardo; McIntosh, Scott
2017-01-01
Background The emerging research on nurturing the growth of online communities posits that it is in part attributed to network effects, wherein every increase in the volume of user-generated content increases the value of the community in the eyes of its potential new members. The recently introduced metric engagement capacity offers a means of quantitatively assessing the ability of online platform users to engage each other into generating content; meanwhile, the quantity engagement value is useful for quantifying communication-based platform use. If the claim that higher engagement leads to accelerated growth holds true for online health forums (OHFs), then engagement tracking should become an important tool in the arsenal of OHF managers. Indeed, it might allow for quantifying the ability of an OHF to exploit network effects, thus predicting the OHF’s future success. Objective This study aimed to empirically analyze the relationship between internal OHF use (quantified using engagement measurement), and external growth. Methods We collected data from 7 OHFs posted between the years 1999 and 2016. Longitudinal analyses were conducted by evaluating engagement in the OHFs over time. We analyzed 2-way causality effects between the engagement value and metrics evaluating OHF growth using Granger causality tests. User activity metrics per week were correlated with engagement metrics, followed by linear regression analyses. Results Observational data showed a 1-way causal relationship between the OHF engagement value and reach (P=.02). We detected a 2-way causal relationship between the engagement value and delurking, with further analysis indicating that the engagement value was more likely to cause delurking (Pdepending on how much one user engaged another) to develop personal connections. Finally, we found that the more engaging an OHF user was in a given week, the more likely (up to 2 times, depending on their ability to engage others) they were to remain active
A Fractal Perspective on Scale in Geography
Directory of Open Access Journals (Sweden)
Bin Jiang
2016-06-01
Full Text Available Scale is a fundamental concept that has attracted persistent attention in geography literature over the past several decades. However, it creates enormous confusion and frustration, particularly in the context of geographic information science, because of scale-related issues such as image resolution and the modifiable areal unit problem (MAUP. This paper argues that the confusion and frustration arise from traditional Euclidean geometric thinking, in which locations, directions, and sizes are considered absolute, and it is now time to revise this conventional thinking. Hence, we review fractal geometry, together with its underlying way of thinking, and compare it to Euclidean geometry. Under the paradigm of Euclidean geometry, everything is measurable, no matter how big or small. However, most geographic features, due to their fractal nature, are essentially unmeasurable or their sizes depend on scale. For example, the length of a coastline, the area of a lake, and the slope of a topographic surface are all scale-dependent. Seen from the perspective of fractal geometry, many scale issues, such as the MAUP, are inevitable. They appear unsolvable, but can be dealt with. To effectively deal with scale-related issues, we present topological and scaling analyses illustrated by street-related concepts such as natural streets, street blocks, and natural cities. We further contend that one of the two spatial properties, spatial heterogeneity, is de facto the fractal nature of geographic features, and it should be considered the first effect among the two, because it is global and universal across all scales, which should receive more attention from practitioners of geography.
FRACTAL DIMENSIONALITY ANALYSIS OF MAMMARY GLAND THERMOGRAMS
Directory of Open Access Journals (Sweden)
Yu. E. Lyah
2016-06-01
Full Text Available Thermography may enable early detection of a cancer tumour within a mammary gland at an early, treatable stage of the illness, but thermogram analysis methods must be developed to achieve this goal. This study analyses the feasibility of applying the Hurst exponent readings algorithm for evaluation of the high dimensionality fractals to reveal any possible difference between normal thermograms (NT and malignant thermograms (MT.
Fractal characterization of brain lesions in CT images
International Nuclear Information System (INIS)
Jauhari, Rajnish K.; Trivedi, Rashmi; Munshi, Prabhat; Sahni, Kamal
2005-01-01
Fractal Dimension (FD) is a parameter used widely for classification, analysis, and pattern recognition of images. In this work we explore the quantification of CT (computed tomography) lesions of the brain by using fractal theory. Five brain lesions, which are portions of CT images of diseased brains, are used for the study. These lesions exhibit self-similarity over a chosen range of scales, and are broadly characterized by their fractal dimensions
A short history of fractal-Cantorian space-time
International Nuclear Information System (INIS)
Marek-Crnjac, L.
2009-01-01
The article attempts to give a short historical overview of the discovery of fractal-Cantorian space-time starting from the 17th century up to the present. In the last 25 years a great number of scientists worked on fractal space-time notably Garnet Ord in Canada, Laurent Nottale in France and Mohamed El Naschie in England who gave an exact mathematical procedure for the derivation of the dimensionality and curvature of fractal space-time fuzzy manifold.
Hybrid 3D Fractal Coding with Neighbourhood Vector Quantisation
Directory of Open Access Journals (Sweden)
Zhen Yao
2004-12-01
Full Text Available A hybrid 3D compression scheme which combines fractal coding with neighbourhood vector quantisation for video and volume data is reported. While fractal coding exploits the redundancy present in different scales, neighbourhood vector quantisation, as a generalisation of translational motion compensation, is a useful method for removing both intra- and inter-frame coherences. The hybrid coder outperforms most of the fractal coders published to date while the algorithm complexity is kept relatively low.
Password Authentication Based on Fractal Coding Scheme
Directory of Open Access Journals (Sweden)
Nadia M. G. Al-Saidi
2012-01-01
Full Text Available Password authentication is a mechanism used to authenticate user identity over insecure communication channel. In this paper, a new method to improve the security of password authentication is proposed. It is based on the compression capability of the fractal image coding to provide an authorized user a secure access to registration and login process. In the proposed scheme, a hashed password string is generated and encrypted to be captured together with the user identity using text to image mechanisms. The advantage of fractal image coding is to be used to securely send the compressed image data through a nonsecured communication channel to the server. The verification of client information with the database system is achieved in the server to authenticate the legal user. The encrypted hashed password in the decoded fractal image is recognized using optical character recognition. The authentication process is performed after a successful verification of the client identity by comparing the decrypted hashed password with those which was stored in the database system. The system is analyzed and discussed from the attacker’s viewpoint. A security comparison is performed to show that the proposed scheme provides an essential security requirement, while their efficiency makes it easier to be applied alone or in hybrid with other security methods. Computer simulation and statistical analysis are presented.
Fractal theory of radon emanation from solids
International Nuclear Information System (INIS)
Semkow, T.M.
1991-01-01
The author developed a fractal theory of Rn emanation from solids, based on α recoil from the α decay of Ra. Range straggling of the recoiling Rn atoms in the solid state is included and the fractal geometry is used to describe the roughness of the emanating surface. A fractal dimension D of the surface and the median projected range become important parameters in calculating the radon emanating power E R from solids. A relation between E R and the specific surface area measured by the gas adsorption is derived for the first time, assuming a uniform distribution of the precursor Ra throughout the samples. It is suggested that the E R measurements can be used to determine D of the surfaces on the scale from tens to hundreds of nm. One obtains, for instance, D = 2.17 ± 0.06 for Lipari volcanic glass and D = 2.83 ± 0.03 for pitchblende. In addition, the author suggests a new process of penetrating recoil and modify the role of indirect recoil. The penetrating recoil may be important for rough surfaces, in which case Rn loses its kinetic energy by penetrating a large number of small surface irregularities. The indirect recoil may be important at the very last stage of energy-loss process, for kinetic energies below ∼ 5 keV
Aero-acoustic performance of Fractal Spoilers
Nedic, J.; Ganapathisubramani, B.; Vassilicos, C.; Boree, J.; Brizzi, L.; Spohn, A.
2010-11-01
One of the major environmental problems facing the aviation industry is that of aircraft noise. The work presented in this paper, done as part of the OPENAIR Project, looks at reducing spoiler noise through means of large-scale fractal porosity. It is hypothesised that the highly turbulent flow generated by these grids, which have multi-length-scales, would remove the re-circulation region and with it, the low frequency noise it generates. In its place, a higher frequency noise is introduced which is susceptible to atmospheric attenuation, and would be deemed less offensive to the human ear. A total of nine laboratory scaled spoilers were looked at, seven of which had a fractal design, one conventionally porous and one solid for reference. All of the spoilers were mounted on a flat plate and inclined at 30^o to the horizontal. Far-field, microphone array and PIV measurements were taken in an anechoic chamber to determine the acoustic performance and to study the flow coming through the spoilers. A significant reduction in sound pressure level is recorded and is found to be very sensitive to small changes in fractal grid parameters. Wake and drag force measurements indicated that the spoilers increase the drag whilst having minimal effect on the lift.
Fractal analysis of visual search activity for mass detection during mammographic screening.
Alamudun, Folami; Yoon, Hong-Jun; Hudson, Kathleen B; Morin-Ducote, Garnetta; Hammond, Tracy; Tourassi, Georgia D
2017-03-01
The objective of this study was to assess the complexity of human visual search activity during mammographic screening using fractal analysis and to investigate its relationship with case and reader characteristics. The study was performed for the task of mammographic screening with simultaneous viewing of four coordinated breast views as typically done in clinical practice. Eye-tracking data and diagnostic decisions collected for 100 mammographic cases (25 normal, 25 benign, 50 malignant) from 10 readers (three board certified radiologists and seven Radiology residents), formed the corpus for this study. The fractal dimension of the readers' visual scanning pattern was computed with the Minkowski-Bouligand box-counting method and used as a measure of gaze complexity. Individual factor and group-based interaction ANOVA analysis was performed to study the association between fractal dimension, case pathology, breast density, and reader experience level. The consistency of the observed trends depending on gaze data representation was also examined. Case pathology, breast density, reader experience level, and individual reader differences are all independent predictors of the complexity of visual scanning pattern when screening for breast cancer. No higher order effects were found to be significant. Fractal characterization of visual search behavior during mammographic screening is dependent on case properties and image reader characteristics. © 2017 American Association of Physicists in Medicine.
International Nuclear Information System (INIS)
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-01-01
Highlights: • Fractal theory is introduced into the prediction of VOC diffusion coefficient. • MSFC model of the diffusion coefficient is developed for porous building materials. • The MSFC model contains detailed pore structure parameters. • The accuracy of the MSFC model is verified by independent experiments. - Abstract: Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber.
Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale
Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian
2018-06-01
Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.
A study of radiative properties of fractal soot aggregates using the superposition T-matrix method
International Nuclear Information System (INIS)
Li Liu; Mishchenko, Michael I.; Patrick Arnott, W.
2008-01-01
We employ the numerically exact superposition T-matrix method to perform extensive computations of scattering and absorption properties of soot aggregates with varying state of compactness and size. The fractal dimension, D f , is used to quantify the geometrical mass dispersion of the clusters. The optical properties of soot aggregates for a given fractal dimension are complex functions of the refractive index of the material m, the number of monomers N S , and the monomer radius a. It is shown that for smaller values of a, the absorption cross section tends to be relatively constant when D f f >2. However, a systematic reduction in light absorption with D f is observed for clusters with sufficiently large N S , m, and a. The scattering cross section and single-scattering albedo increase monotonically as fractals evolve from chain-like to more densely packed morphologies, which is a strong manifestation of the increasing importance of scattering interaction among spherules. Overall, the results for soot fractals differ profoundly from those calculated for the respective volume-equivalent soot spheres as well as for the respective external mixtures of soot monomers under the assumption that there are no electromagnetic interactions between the monomers. The climate-research implications of our results are discussed
International Conference on Advances of Fractals and Related Topics
Lau, Ka-Sing
2014-01-01
This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
FAST TRACK COMMUNICATION: Weyl law for fat fractals
Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos
2010-10-01
It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.
Electro-chemical manifestation of nanoplasmonics in fractal media
Baskin, Emmanuel; Iomin, Alexander
2013-06-01
Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.
Fractal characteristic study of shearer cutter cutting resistance curves
Energy Technology Data Exchange (ETDEWEB)
Liu, C. [Heilongjiang Scientific and Technical Institute, Haerbin (China). Dept of Mechanical Engineering
2004-02-01
The cutting resistance curve is the most useful tool for reflecting the overall cutting performance of a cutting machine. The cutting resistance curve is influenced by many factors such as the pick structure and arrangement, the cutter operation parameters, coal quality and geologic conditions. This paper discusses the use of fractal geometry to study the properties of the cutting resistance curve, and the use of fractal dimensions to evaluate cutting performance. On the basis of fractal theory, the general form and calculation method of fractal characteristics are given. 4 refs., 3 figs., 1 tab.
Mechanical test and fractal analysis on anisotropic fracture of cortical bone
Energy Technology Data Exchange (ETDEWEB)
Yin, Dagang [State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044 (China); College of Aerospace Engineering, Chongqing University, Chongqing 400044 (China); Chen, Bin, E-mail: bchen@cqu.edu.cn [State Key Laboratory of Coal Mine Disaster Dynamics and Control, Chongqing University, Chongqing 400044 (China); College of Aerospace Engineering, Chongqing University, Chongqing 400044 (China); Ye, Wei [College of Aerospace Engineering, Chongqing University, Chongqing 400044 (China); Gou, Jihua [Department of Mechanical and Aerospace Engineering, University of Central Florida, Orlando, FL 32816 (United States); Fan, Jinghong [Division of Mechanical Engineering, Alfred University, Alfred, NY 14802 (United States)
2015-12-01
Highlights: • The mechanical properties of the cortical bone of fresh bovine femora along three different directions are tested through four-point bending experiments. • SEM observation shows that the roughness of the fracture surfaces of the three different directions of the bone are remarkably different. • The fractal dimensions of the different fracture surfaces of the bone are calculated by box-counting method in MATLAB. • The fracture energies of the different fracture directions are calculated based on their fractal models. - Abstract: The mechanical properties of the cortical bone of fresh bovine femora along three different directions are tested through four-point bending experiments. It is indicated that the fracture energy along the transversal direction of the bone is distinctly larger than those of the longitudinal and radial directions. The fracture surfaces of the three different directions are observed by scanning electron microscope (SEM). It is shown that the roughness of the fracture surface of the transversal direction is obviously larger than those of the fracture surfaces of the longitudinal and radial directions. It is also revealed that the osteons in the bone are perpendicular to the fracture surface of the transversal direction and parallel to the fracture surfaces of the longitudinal and radial directions. Based on these experimental results, the fractal dimensions of the fracture surfaces of different directions are calculated by box-counting method in MATLAB. The calculated results show that the fractal dimension of the fracture surface of the transversal direction is remarkably larger than those of the fracture surfaces of the longitudinal and radial directions. The fracture energies of different directions are also calculated based on their fractal models. It is denoted that the fracture energy of the transversal direction is remarkably larger than those of the longitudinal and radial directions. The calculated results are in
Mechanical test and fractal analysis on anisotropic fracture of cortical bone
International Nuclear Information System (INIS)
Yin, Dagang; Chen, Bin; Ye, Wei; Gou, Jihua; Fan, Jinghong
2015-01-01
Highlights: • The mechanical properties of the cortical bone of fresh bovine femora along three different directions are tested through four-point bending experiments. • SEM observation shows that the roughness of the fracture surfaces of the three different directions of the bone are remarkably different. • The fractal dimensions of the different fracture surfaces of the bone are calculated by box-counting method in MATLAB. • The fracture energies of the different fracture directions are calculated based on their fractal models. - Abstract: The mechanical properties of the cortical bone of fresh bovine femora along three different directions are tested through four-point bending experiments. It is indicated that the fracture energy along the transversal direction of the bone is distinctly larger than those of the longitudinal and radial directions. The fracture surfaces of the three different directions are observed by scanning electron microscope (SEM). It is shown that the roughness of the fracture surface of the transversal direction is obviously larger than those of the fracture surfaces of the longitudinal and radial directions. It is also revealed that the osteons in the bone are perpendicular to the fracture surface of the transversal direction and parallel to the fracture surfaces of the longitudinal and radial directions. Based on these experimental results, the fractal dimensions of the fracture surfaces of different directions are calculated by box-counting method in MATLAB. The calculated results show that the fractal dimension of the fracture surface of the transversal direction is remarkably larger than those of the fracture surfaces of the longitudinal and radial directions. The fracture energies of different directions are also calculated based on their fractal models. It is denoted that the fracture energy of the transversal direction is remarkably larger than those of the longitudinal and radial directions. The calculated results are in
Fractal-based exponential distribution of urban density and self-affine fractal forms of cities
International Nuclear Information System (INIS)
Chen Yanguang; Feng Jian
2012-01-01
Highlights: ► The model of urban population density differs from the common exponential function. ► Fractal landscape influences the exponential distribution of urban density. ► The exponential distribution of urban population suggests a self-affine fractal. ► Urban space can be divided into three layers with scaling and non-scaling regions. ► The dimension of urban form with characteristic scale can be treated as 2. - Abstract: Urban population density always follows the exponential distribution and can be described with Clark’s model. Because of this, the spatial distribution of urban population used to be regarded as non-fractal pattern. However, Clark’s model differs from the exponential function in mathematics because that urban population is distributed on the fractal support of landform and land-use form. By using mathematical transform and empirical evidence, we argue that there are self-affine scaling relations and local power laws behind the exponential distribution of urban density. The scale parameter of Clark’s model indicating the characteristic radius of cities is not a real constant, but depends on the urban field we defined. So the exponential model suggests local fractal structure with two kinds of fractal parameters. The parameters can be used to characterize urban space filling, spatial correlation, self-affine properties, and self-organized evolution. The case study of the city of Hangzhou, China, is employed to verify the theoretical inference. Based on the empirical analysis, a three-ring model of cities is presented and a city is conceptually divided into three layers from core to periphery. The scaling region and non-scaling region appear alternately in the city. This model may be helpful for future urban studies and city planning.
International Nuclear Information System (INIS)
Ren Xincheng; Guo Lixin
2008-01-01
A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)
Growth laws for delta crevasses in the Mississippi River Delta: observations and modeling
Yocum, T. A.; Georgiou, I. Y.
2016-02-01
River deltas are accumulations of sedimentary deposits delivered by rivers via a network of distributary channels. Worldwide they are threatened by environmental changes, including subsidence, global sea level rise and a suite of other local factors. In the Mississippi River Delta (MRD) these impacts are exemplified, and have led to proposed solutions to build land that include sediment diversions, thereby reinitiating the delta cycle. While economically efficient, there are too few analogs of small deltas aside from laboratory studies, numerical modeling studies, theoretical approaches, and limited field driven observations. Anthropogenic crevasses in the modern delta are large enough to overcome limitations of laboratory deltas, and small enough to allow for "rapid" channel and wetland development, providing an ideal setting to investigate delta development mechanics. Crevasse metrics were obtained using a combination of geospatial tools, extracting key parameters (bifurcation length and width, channel order and depth) that were non-dimensionalized and compared to river-dominated delta networks previously studied. Analysis showed that most crevasses in the MRD appear to obey delta growth laws and delta allometry relationships, suggesting that crevasses do exhibit similar planform metrics to larger Deltas; the distance to mouth bar versus bifurcation order demonstrated to be a very reasonable first order estimate of delta-top footprint. However, some crevasses exhibited different growth metrics. To better understand the hydrodynamic and geomorphic controls governing crevasse evolution in the MRD, we assess delta dynamics via a suite of field observations and numerical modeling in both well-established and newly constructed crevasses. Our analysis suggests that delta development is affected by the relative influence of external (upstream and downstream) and internal controls on the hydrodynamic and sediment transport patterns in these systems.
Arshinov, Mikhail Yu.; Belan, Boris D.; Davydov, Denis K.; Kozlov, Artem V.; Arshinova, Victoria
2015-04-01
In spite of fact that the first report on the new particle formation (NPF) itself was done by John Aitken more than one century ago (Aitken, 1898), a phenomenon of NPF bursts taken place in the atmosphere was discovered not very long ago. Nevertheless, to date it is known that they may occur quite often in a variety of environments (Kulmala et al., 2004; Hirsikko et al., 2011). Siberia occupies a vast area covered by forests, but the comprehensive data on burst frequency, as well as on formation and growth rates of freshly nucleated particles in this key region are still lacking. Continuous measurements of aerosol size distribution carried out in recent years at two West Siberian stations (TOR-station - 56o28'41"N, 85o03'15"E; Fonovaya Observatory - 56o25'07"N, 84o04'27"E) allowed this gap in data to be filled up. Analysis of the size spectra classified in accordance with criteria proposed by Dal Maso et al. (2005) and Hammed et al. (2007) enabled a conclusion to be drawn that NPF events in Wets Siberia are more often observed during spring (from March to May) and early autumn (secondary frequency peak in September). On average, particle formation bursts took place on 23-28 % of all days. Such a seasonal pattern of the NPF occurrence is very similar to one observed at SMEAR II Station (Hyytiälä, Finland; Dal Maso et al. 2005, 2007). Formation rates (FR) of particles with diameters below 25 nm varied in a wide range from 0.1 to 10 cm-3 s-1. Mean values of FR for the entire period of observations were 1.7 cm-3s-1 (median = 1.13 cm-3 s-1) at TOR-station and 0.88 cm-3 s-1 (median = 0.69 cm-3 s-1) at Fonovaya Observatory. Enhanced values of FR are usually observed from spring to autumn. Mean growth rates of observed at TOR-station and Fonovaya Observatory were 6.5 nm h-1 (median = 5.0 nm h-1) and 8.3 nm h-1 (median = 6.4 nm h-1), respectively. This work was supported by the Branch of Geology, Geophysics and Mining Sciences of RAS (Program No. 5); State contracts of
Synthesis of gold nanostars with fractal structure: application in surface-enhanced Raman scattering
Zhu, Jian; Liu, Mei-Jin; Li, Jian-Jun; Zhao, Jun-Wu
2017-11-01
Multi-branched gold nanostars with fractal feature were synthesized using the Triton X-100 participant seed-growth method. By increasing the amount of ascorbic acid, the branch length of gold nanostars could be greatly increased. It has been interesting to find that the secondary growth of new branches takes place from the elementary structure when the aspect ratio of the branches is greater than 8.0 and the corresponding plasmon absorption wavelength is greater than 900 nm. Raman activity of the gold nanostar films has been investigated by using the 4-mercaptobenzoic acid (4-MBA) as Raman active probe. Experimental results show that the surface-enhanced Raman scattering (SERS) ability of the gold nanostars could be efficiently improved when the fractal structure appears. The physical mechanism has been attributed to the intense increased secondary branch number and the increased "hot spots". These unique multi-branched gold nanostars with fractal feature and great SERS activity should have great potential in sensing applications.
Geometrical study of astrocytomas through fractals and scaling analysis
International Nuclear Information System (INIS)
Torres H, F.; Baena N, R.; Vergara V, J.; Guerrero M, M.
2017-10-01
The tumor growth is a complex process characterized by the proliferation of uncontrollable cells which invade neighbor tissues. The understanding process of this type of phenomena is very relevant in order to establish diagnosis and proper therapy strategies and to start the valorization of its complexity with proper descriptors produced by the scaling analysis, which define the tumor growth geometry. In this work, obtained results through the scaling analysis for pilocytic astrocytomas, anaplastic and diffuse, are shown, which tumors of primary origin are. On them, it is calculated the fractal dimension and critic exponents of local roughness to characterize in vivo three-dimensional tumor growth. The acquisition of the images for this type of injuries was carried out according to the standard protocol used for brain radiotherapy and radiosurgery, i.e., axial, coronal and sagittal magnetic resonance T1 weighted images and comprising the brain volume for image registration. Image segmentation was performed by the application the K-means procedure upon contrasted images. The results show significant variations of the parameters depending on the tumor stage and its histological origin. (Author)
Pore Structure and Fractal Characteristics of Niutitang Shale from China
Directory of Open Access Journals (Sweden)
Zhaodong Xi
2018-04-01
Full Text Available A suite of shale samples from the Lower Cambrian Niutitang Formation in northwestern Hunan Province, China, were investigated to better understand the pore structure and fractal characteristics of marine shale. Organic geochemistry, mineralogy by X-ray diffraction, porosity, permeability, mercury intrusion and nitrogen adsorption and methane adsorption experiments were conducted for each sample. Fractal dimension D was obtained from the nitrogen adsorption data using the fractal Frenkel-Halsey-Hill (FHH model. The relationships between total organic carbon (TOC content, mineral compositions, pore structure parameters and fractal dimension are discussed, along with the contributions of fractal dimension to shale gas reservoir evaluation. Analysis of the results showed that Niutitang shale samples featured high TOC content (2.51% on average, high thermal maturity (3.0% on average, low permeability and complex pore structures, which are highly fractal. TOC content and mineral compositions are two major factors affecting pore structure but they have different impacts on the fractal dimension. Shale samples with higher TOC content had a larger specific surface area (SSA, pore volume (PV and fractal dimension, which enhanced the heterogeneity of the pore structure. Quartz content had a relatively weak influence on shale pore structure, whereas SSA, PV and fractal dimension decreased with increasing clay mineral content. Shale with a higher clay content weakened pore structure heterogeneity. The permeability and Langmuir volume of methane adsorption were affected by fractal dimension. Shale samples with higher fractal dimension had higher adsorption capacity but lower permeability, which is favorable for shale gas adsorption but adverse to shale gas seepage and diffusion.
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
Kraus, Virginia Byers; Feng, Sheng; Wang, ShengChu; White, Scott; Ainslie, Maureen; Brett, Alan; Holmes, Anthony; Charles, H Cecil
2009-12-01
To evaluate the effectiveness of using subchondral bone texture observed on a radiograph taken at baseline to predict progression of knee osteoarthritis (OA) over a 3-year period. A total of 138 participants in the Prediction of Osteoarthritis Progression study were evaluated at baseline and after 3 years. Fractal signature analysis (FSA) of the medial subchondral tibial plateau was performed on fixed flexion radiographs of 248 nonreplaced knees, using a commercially available software tool. OA progression was defined as a change in joint space narrowing (JSN) or osteophyte formation of 1 grade according to a standardized knee atlas. Statistical analysis of fractal signatures was performed using a new model based on correlating the overall shape of a fractal dimension curve with radius. Fractal signature of the medial tibial plateau at baseline was predictive of medial knee JSN progression (area under the curve [AUC] 0.75, of a receiver operating characteristic curve) but was not predictive of osteophyte formation or progression of JSN in the lateral compartment. Traditional covariates (age, sex, body mass index, knee pain), general bone mineral content, and joint space width at baseline were no more effective than random variables for predicting OA progression (AUC 0.52-0.58). The predictive model with maximum effectiveness combined fractal signature at baseline, knee alignment, traditional covariates, and bone mineral content (AUC 0.79). We identified a prognostic marker of OA that is readily extracted from a plain radiograph using FSA. Although the method needs to be validated in a second cohort, our results indicate that the global shape approach to analyzing these data is a potentially efficient means of identifying individuals at risk of knee OA progression.
On the oscillatory dynamical behaviour of epidemic spreading in fractal media
International Nuclear Information System (INIS)
Bab, M A; Albano, E V
2008-01-01
We present numerical evidence that dynamical physical processes that develop a time-dependent characteristic length, and take place in fractal media exhibiting spatial discrete scale invariance (DSI) with fundamental scaling ratio b, may become coupled to the topology of the fractal leading to the observation of time DSI. The hallmark of time DSI is the observation of a log-periodic modulation of the dynamic or kinetic observables, which is characterized by a well-defined fundamental time scaling ratio (τ). Both fundamental scaling ratios are linked according to b = τ 1/z , where z is the dynamic exponent characteristic of the physical process. Specifically, we have studied the epidemic behaviour of the contact process (CP) in Sierpinski Carpets. The CP exhibits second-order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility. We observed that relevant dynamic observables, such as the number of active sites, the survival probability of the epidemics and the mean square displacement of the epidemic from the origin (R 2 (t)), exhibit log-periodic modulations. By fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents. Since, at criticality, one has that R 2 (t) ∼ t 2/z , an independent estimation of the dynamic exponent can be performed, in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and τ
On the oscillatory dynamical behaviour of epidemic spreading in fractal media
Energy Technology Data Exchange (ETDEWEB)
Bab, M A; Albano, E V [Instituto de Investigaciones FisicoquImicas Teoricas y Aplicadas (INIFTA), Facultad de Ciencias Exactas, UNLP, CONICET, Casilla de Correo 16, Sucursal 4 (1900) La Plata (Argentina)
2008-02-01
We present numerical evidence that dynamical physical processes that develop a time-dependent characteristic length, and take place in fractal media exhibiting spatial discrete scale invariance (DSI) with fundamental scaling ratio b, may become coupled to the topology of the fractal leading to the observation of time DSI. The hallmark of time DSI is the observation of a log-periodic modulation of the dynamic or kinetic observables, which is characterized by a well-defined fundamental time scaling ratio ({tau}). Both fundamental scaling ratios are linked according to b = {tau}{sup 1/z}, where z is the dynamic exponent characteristic of the physical process. Specifically, we have studied the epidemic behaviour of the contact process (CP) in Sierpinski Carpets. The CP exhibits second-order irreversible phase transitions between an active regime and an absorbing state where the system is trapped without any escape possibility. We observed that relevant dynamic observables, such as the number of active sites, the survival probability of the epidemics and the mean square displacement of the epidemic from the origin (R{sup 2}(t)), exhibit log-periodic modulations. By fitting the data we evaluate the fundamental time scaling ratio for various fractals and the corresponding dynamic exponents. Since, at criticality, one has that R{sup 2}(t) {approx} t{sup 2/z}, an independent estimation of the dynamic exponent can be performed, in excellent agreement with results obtained by using the conjectured relationship for the fundamental scaling ratios b and {tau}.
Directory of Open Access Journals (Sweden)
Gut Robert
2010-09-01
Full Text Available To assess gender-, pubertal-, age-related differences in change from baseline height standard deviation score (, data from 5,797 growth hormone (GH naïve pediatric patients ( at year 1 was significantly greater for males versus females (, but no other gender differences were observed. For patients with GHD, was greater in prepubertal than in pubertal patients. Younger patients for both genders ( ( for GHD, MPHD, and ISS. Overall, positive were observed in all patients, with greater growth responses in younger prepubertal children, emphasizing the importance of starting GH treatment early.
International Nuclear Information System (INIS)
Imai, Kuniharu; Ikeda, Mitsuru; Enchi, Yukihiro; Niimi, Takanaga
2008-01-01
Purpose: To confirm whether or not the influence of anatomic noise on the detection of nodules in digital chest radiography can be evaluated by the fractal-feature distance. Materials and methods: We used the square images with and without a simulated nodule which were generated in our previous observer performance study; the simulated nodule was located on the upper margin of a rib, the inside of a rib, the lower margin of a rib, or the central region between two adjoining ribs. For the square chest images, fractal analysis was conducted using the virtual volume method. The fractal-feature distances between the considered and the reference images were calculated using the pseudo-fractal dimension and complexity, and the square images without the simulated nodule were employed as the reference images. We compared the fractal-feature distances with the observer's confidence level regarding the presence of a nodule in plain chest radiograph. Results: For all square chest images, the relationships between the length of the square boxes and the mean of the virtual volumes were linear on a log-log scale. For all types of the simulated nodules, the fractal-feature distance was the highest for the simulated nodules located on the central region between two adjoining ribs and was the lowest for those located in the inside of a rib. The fractal-feature distance showed a linear relation to an observer's confidence level. Conclusion: The fractal-feature distance would be useful for evaluating the influence of anatomic noise on the detection of nodules in digital chest radiography
Fractal dimension of the fractured surface of materials
International Nuclear Information System (INIS)
Lung, C.W.; Zhang, S.Z.
1989-05-01
Fractal dimension of the fractured surface of materials is discussed to show that the origin of the negative correlation between D F and toughness lies in the method of fractal dimension measurement with perimeter-area relation and also in the physical mechanism of crack propagation. (author). 8 refs, 4 figs, 1 tab
Three-dimensional fractal geometry for gas permeation in microchannels
Malankowska, Magdalena; Schlautmann, Stefan; Berenschot, Erwin J.W.; Tiggelaar, Roald M.; Pina, Maria Pilar; Mallada, Reyes; Tas, Niels R.; Gardeniers, Han
2018-01-01
The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The
Fractal sets generated by chemical reactions discrete chaotic dynamics
International Nuclear Information System (INIS)
Gontar, V.; Grechko, O.
2007-01-01
Fractal sets composed by the parameters values of difference equations derived from chemical reactions discrete chaotic dynamics (DCD) and corresponding to the sequences of symmetrical patterns were obtained in this work. Examples of fractal sets with the corresponding symmetrical patterns have been presented
Fractal Dimension analysis for seismicity spatial and temporal ...
Indian Academy of Sciences (India)
23
The research can further promote the application of fractal theory in the study ... spatial-temporal propagation characteristics of seismic activities, fractal theory is not ... provide a theoretical basis for the prevention and control of earthquakes. 2. ... random self-similar structure of the earthquake in the time series and the spatial.
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.
Experiencia en el aula de secundaria con fractales
Gallardo, Sandra; Martínez-Santaolalla, Manuel José; Molina, Marta; Peñas, María; Cañadas, María C.; Crisóstomo, Edson
2006-01-01
Presentamos una experiencia docente en un aula de 2º ESO en la que trabajamos los fractales mediante el uso de material de carácter manipulativo. La metodología seguida se basa en la construcción de casos particulares con el fin de llegar al concepto de fractal.
Evaluation of surface quality by Fractal Dimension and Volume ...
African Journals Online (AJOL)
Experimental and simulation results have enabled to show than the large diameter ball under low loads and medium feed speeds, favors the elimination of peaks and reduction of fractal dimension whence quality improvement of surface. Keywords: burnishing, volume parameters, fractal dimension, experimental designs ...
Bouguer correction density determination from fractal analysis using ...
African Journals Online (AJOL)
In this work, Bouguer density is determined using the fractal approach. This technique was applied to the gravity data of the Kwello area of the Basement Complex, north-western Nigeria. The density obtained using the fractal approach is 2500 kgm which is lower than the conventional value of 2670 kgm used for average ...
Usefulness of fractal analysis for the diagnosis of periodontitis
Energy Technology Data Exchange (ETDEWEB)
Cha, Sang Yun; Han, Won Jeong; Kim, Eun Kyung [Dankook Univ. School of Dentistry, Seoul (Korea, Republic of)
2001-03-15
To evaluate the usefulness of fractal analysis for diagnosis of periodontitis. Each 30 cases of periapical films of male mandibular molar were selected in normal group and patient group which had complete furcation involvement. They were digitized at 300 dpi, 256 gray levels and saved with gif format. Rectangular ROIs (10 X 20 pixel) were selected at furcation, interdental crest, and interdental middle 1/3 area. Fractal dimensions were calculated three times at each area by mass radius method and were determined using a mean of three measurements. We computed fractal dimensions at furcation and interdental crest area of normal group with those of patient group. And then we compared ratio of fractal dimensions at furcation area, interdental crest area to interdental middle 1/3 area. Fractal dimension at interdental crest area of normal group was 1.979{+-}0.018 (p<0.05). The radio of fractal dimension at furcation area to interdental middle 1/3 of normal group was 1.006{+-}0.018 and that of patient group 0.9940.018 (p<0.05). The radio of fractal dimension at interdental crest and furcation area to interdental middle 1/3 area showed a statistically significant difference between normal and patient group. In conclusion, it is thought that fractal analysis might be useful for the diagnosis of periodontitis.
Separation in Data Mining Based on Fractal Nature of Data
Czech Academy of Sciences Publication Activity Database
Jiřina, Marcel; Jiřina jr., M.
2013-01-01
Roč. 3, č. 1 (2013), s. 44-60 ISSN 2225-658X Institutional support: RVO:67985807 Keywords : nearest neighbor * fractal set * multifractal * IINC method * correlation dimension Subject RIV: JC - Computer Hardware ; Software http://sdiwc.net/digital-library/separation-in-data-mining-based-on-fractal-nature-of-data.html
Fractal Dimension Of CT Images Of Normal Parotid Glands
International Nuclear Information System (INIS)
Lee, Sang Jin; Heo, Min Suk; You, Dong Soo
1999-01-01
This study was to investigate the age and sex differences of the fractal dimension of the normal parotid glands in the digitized CT images. The six groups, which were composed of 42 men and women from 20's, 40's and 60's and over were picked. Each group contained seven people of the same sex. The normal parotid CT images were digitized, and their fractal dimensions were calculated using Scion Image PC program. The mean of fractal dimensions in males was 1.7292 (+/-0.0588) and 1.6329 (+/-0.0425) in females. The mean of fractal dimensions in young males was 1.7617, 1.7328 in middle males, and 1.6933 in old males. The mean of fractal dimensions in young females was 1.6318, 1.6365 in middle females, and 1.6303 in old females. There was no statistical difference in fractal dimension between left and right parotid gland of the same subject (p>0.05). Fractal dimensions in male were decreased in older group (p 0.05). The fractal dimension of parotid glands in the digitized CT images will be useful to evaluate the age and sex differences.
Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems
Buffle, J.; Leeuwen, van H.P.
2008-01-01
This book aims to provide the scientific community with a novel and valuable approach based on fractal geometry concepts on the important properties and processes of diverse environmental systems. The interpretation of complex environmental systems using modern fractal approaches is compared and
Fractal ventilation enhances respiratory sinus arrhythmia
Directory of Open Access Journals (Sweden)
Girling Linda G
2005-05-01
Full Text Available Abstract Background Programming a mechanical ventilator with a biologically variable or fractal breathing pattern (an example of 1/f noise improves gas exchange and respiratory mechanics. Here we show that fractal ventilation increases respiratory sinus arrhythmia (RSA – a mechanism known to improve ventilation/perfusion matching. Methods Pigs were anaesthetised with propofol/ketamine, paralysed with doxacurium, and ventilated in either control mode (CV or in fractal mode (FV at baseline and then following infusion of oleic acid to result in lung injury. Results Mean RSA and mean positive RSA were nearly double with FV, both at baseline and following oleic acid. At baseline, mean RSA = 18.6 msec with CV and 36.8 msec with FV (n = 10; p = 0.043; post oleic acid, mean RSA = 11.1 msec with CV and 21.8 msec with FV (n = 9, p = 0.028; at baseline, mean positive RSA = 20.8 msec with CV and 38.1 msec with FV (p = 0.047; post oleic acid, mean positive RSA = 13.2 msec with CV and 24.4 msec with FV (p = 0.026. Heart rate variability was also greater with FV. At baseline the coefficient of variation for heart rate was 2.2% during CV and 4.0% during FV. Following oleic acid the variation was 2.1 vs. 5.6% respectively. Conclusion These findings suggest FV enhances physiological entrainment between respiratory, brain stem and cardiac nonlinear oscillators, further supporting the concept that RSA itself reflects cardiorespiratory interaction. In addition, these results provide another mechanism whereby FV may be superior to conventional CV.
Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method
Zhu, Fanglong; Li, Kejing
2010-03-01
In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.
Fractal analysis for heat extraction in geothermal system
Directory of Open Access Journals (Sweden)
Shang Xiaoji
2017-01-01
Full Text Available Heat conduction and convection play a key role in geothermal development. These two processes are coupled and influenced by fluid seepage in hot porous rock. A number of integer dimension thermal fluid models have been proposed to describe this coupling mechanism. However, fluid flow, heat conduction and convection in porous rock are usually non-linear, tortuous and fractal, thus the integer dimension thermal fluid flow models can not well describe these phenomena. In this study, a fractal thermal fluid coupling model is proposed to describe the heat conduction and flow behaviors in fractal hot porous rock in terms of local fractional time and space derivatives. This coupling equation is analytically solved through the fractal travelling wave transformation method. Analytical solutions of Darcy’s velocity, fluid temperature with fractal time and space are obtained. The solutions show that the introduction of fractional parameters is essential to describe the mechanism of heat conduction and convection.
International Conference and Workshop on Fractals and Wavelets
Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod
2014-01-01
Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.
Vibration modes of 3n-gaskets and other fractals
Energy Technology Data Exchange (ETDEWEB)
Bajorin, N; Chen, T; Dagan, A; Emmons, C; Hussein, M; Khalil, M; Mody, P; Steinhurst, B; Teplyaev, A [Department of Mathematics, University of Connecticut, Storrs CT 06269 (United States)
2008-01-11
We rigorously study eigenvalues and eigenfunctions (vibration modes) on the class of self-similar symmetric finitely ramified fractals, which include the Sierpinski gasket and other 3n-gaskets. We consider the classical Laplacian on fractals which generalizes the usual one-dimensional second derivative, is the generator of the self-similar diffusion process, and has possible applications as the quantum Hamiltonian. We develop a theoretical matrix analysis, including analysis of singularities, which allows us to compute eigenvalues, eigenfunctions and their multiplicities exactly. We support our theoretical analysis by symbolic and numerical computations. Our analysis, in particular, allows the computation of the spectral zeta function on fractals and the limiting distribution of eigenvalues (i.e., integrated density of states). We consider such examples as the level-3 Sierpinski gasket, a fractal 3-tree, and the diamond fractal.
Band structures in Sierpinski triangle fractal porous phononic crystals
International Nuclear Information System (INIS)
Wang, Kai; Liu, Ying; Liang, Tianshu
2016-01-01
In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.
Determination of fish gender using fractal analysis of ultrasound images
DEFF Research Database (Denmark)
McEvoy, Fintan J.; Tomkiewicz, Jonna; Støttrup, Josianne
2009-01-01
The gender of cod Gadus morhua can be determined by considering the complexity in their gonadal ultrasonographic appearance. The fractal dimension (DB) can be used to describe this feature in images. B-mode gonadal ultrasound images in 32 cod, where gender was known, were collected. Fractal...... by subjective analysis alone. The mean (and standard deviation) of the fractal dimension DB for male fish was 1.554 (0.073) while for female fish it was 1.468 (0.061); the difference was statistically significant (P=0.001). The area under the ROC curve was 0.84 indicating the value of fractal analysis in gender...... result. Fractal analysis is useful for gender determination in cod. This or a similar form of analysis may have wide application in veterinary imaging as a tool for quantification of complexity in images...
Band structures in Sierpinski triangle fractal porous phononic crystals
Energy Technology Data Exchange (ETDEWEB)
Wang, Kai; Liu, Ying, E-mail: yliu5@bjtu.edu.cn; Liang, Tianshu
2016-10-01
In this paper, the band structures in Sierpinski triangle fractal porous phononic crystals (FPPCs) are studied with the aim to clarify the effect of fractal hierarchy on the band structures. Firstly, one kind of FPPCs based on Sierpinski triangle routine is proposed. Then the influence of the porosity on the elastic wave dispersion in Sierpinski triangle FPPCs is investigated. The sensitivity of the band structures to the fractal hierarchy is discussed in detail. The results show that the increase of the hierarchy increases the sensitivity of ABG (Absolute band gap) central frequency to the porosity. But further increase of the fractal hierarchy weakens this sensitivity. On the same hierarchy, wider ABGs could be opened in Sierpinski equilateral triangle FPPC; whilst, a lower ABG could be opened at lower porosity in Sierpinski right-angled isosceles FPPCs. These results will provide a meaningful guidance in tuning band structures in porous phononic crystals by fractal design.
A Tutorial Review on Fractal Spacetime and Fractional Calculus
He, Ji-Huan
2014-11-01
This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.
Using Peano Curves to Construct Laplacians on Fractals
Molitor, Denali; Ott, Nadia; Strichartz, Robert
2015-12-01
We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.
Insulator Contamination Forecasting Based on Fractal Analysis of Leakage Current
Directory of Open Access Journals (Sweden)
Bing Luo
2012-07-01
Full Text Available In this paper, an artificial pollution test is carried out to study the leakage current of porcelain insulators. Fractal theory is adopted to extract the characteristics hidden in leakage current waveforms. Fractal dimensions of the leakage current for the security, forecast and danger zones are analyzed under four types of degrees of contamination. The mean value and the standard deviation of the fractal dimension in the forecast zone are calculated to characterize the differences. The analysis reveals large differences in the fractal dimension of leakage current under different contamination discharge stages and degrees. The experimental and calculation results suggest that the fractal dimension of a leakage current waveform can be used as a new indicator of the discharge process and contamination degree of insulators. The results provide new methods and valid indicators for forecasting contamination flashovers.
Pepe, S.; Di Martino, G.; Iodice, A.; Manzo, M.; Pepe, A.; Riccio, D.; Ruello, G.; Sansosti, E.; Tizzani, P.; Zinno, I.
2012-04-01
In the last two decades several aspects relevant to volcanic activity have been analyzed in terms of fractal parameters that effectively describe natural objects geometry. More specifically, these researches have been aimed at the identification of (1) the power laws that governed the magma fragmentation processes, (2) the energy of explosive eruptions, and (3) the distribution of the associated earthquakes. In this paper, the study of volcano morphology via satellite images is dealt with; in particular, we use the complete forward model developed by some of the authors (Di Martino et al., 2012) that links the stochastic characterization of amplitude Synthetic Aperture Radar (SAR) images to the fractal dimension of the imaged surfaces, modelled via fractional Brownian motion (fBm) processes. Based on the inversion of such a model, a SAR image post-processing has been implemented (Di Martino et al., 2010), that allows retrieving the fractal dimension of the observed surfaces, dictating the distribution of the roughness over different spatial scales. The fractal dimension of volcanic structures has been related to the specific nature of materials and to the effects of active geodynamic processes. Hence, the possibility to estimate the fractal dimension from a single amplitude-only SAR image is of fundamental importance for the characterization of volcano structures and, moreover, can be very helpful for monitoring and crisis management activities in case of eruptions and other similar natural hazards. The implemented SAR image processing performs the extraction of the point-by-point fractal dimension of the scene observed by the sensor, providing - as an output product - the map of the fractal dimension of the area of interest. In this work, such an analysis is performed on Cosmo-SkyMed, ERS-1/2 and ENVISAT images relevant to active stratovolcanoes in different geodynamic contexts, such as Mt. Somma-Vesuvio, Mt. Etna, Vulcano and Stromboli in Southern Italy, Shinmoe
Fractal solutions of recirculation tubular chemical reactors
International Nuclear Information System (INIS)
Berezowski, Marek
2003-01-01
Three kinds of fractal solutions of model of recirculation non-adiabatic tubular chemical reactors are presented. The first kind concerns the structure of Feigenbaum's diagram on the limit of chaos. The second kind and the third one concern the effect of initial conditions on the dynamic solutions of models. In the course of computations two types of recirculation were considered, viz. the recirculation of mass (return of a part of products' stream) and recirculation of heat (heat exchange in the external heat exchanger)
A contact angle hysteresis model based on the fractal structure of contact line.
Wu, Shuai; Ma, Ming
2017-11-01
Contact angle is one of the most popular concept used in fields such as wetting, transport and microfludics. In practice, different contact angles such as equilibrium, receding and advancing contact angles are observed due to hysteresis. The connection among these contact angles is important in revealing the chemical and physical properties of surfaces related to wetting. Inspired by the fractal structure of contact line, we propose a single parameter model depicting the connection of the three angles. This parameter is decided by the fractal structure of the contact line. The results of this model agree with experimental observations. In certain cases, it can be reduced to other existing models. It also provides a new point of view in understanding the physical nature of the contact angle hysteresis. Interestingly, some counter-intuitive phenomena, such as the binary receding angles, are indicated in this model, which are waited to be validated by experiments. Copyright © 2017 Elsevier Inc. All rights reserved.
Litvak, Leonid M; Spahr, Anthony J; Emadi, Gulam
2007-08-01
Most cochlear implant strategies utilize monopolar stimulation, likely inducing relatively broad activation of the auditory neurons. The spread of activity may be narrowed with a tripolar stimulation scheme, wherein compensating current of opposite polarity is simultaneously delivered to two adjacent electrodes. In this study, a model and cochlear implant subjects were used to examine loudness growth for varying amounts of tripolar compensation, parameterized by a coefficient sigma, ranging from 0 (monopolar) to 1 (full tripolar). In both the model and the subjects, current required for threshold activation could be approximated by I(sigma)=Ithr(0)(1-sigmaK), with fitted constants Ithr(0) and K. Three of the subjects had a "positioner," intended to place their electrode arrays closer to their neural tissue. The values of K were smaller for the positioner users and for a "close" electrode-to-tissue distance in the model. Above threshold, equal-loudness contours for some subjects deviated significantly from a linear scale-up of the threshold approximations. The patterns of deviation were similar to those observed in the model for conditions in which most of the neurons near the center electrode were excited.
Ryu, Won-Hee; Gittleson, Forrest S; Li, Jinyang; Tong, Xiao; Taylor, André D
2016-08-10
Understanding the catalyzed formation and evolution of lithium-oxide products in Li-O2 batteries is central to the development of next-generation energy storage technology. Catalytic sites, while effective in lowering reaction barriers, often become deactivated when placed on the surface of an oxygen electrode due to passivation by solid products. Here we investigate a mechanism for alleviating catalyst deactivation by dispersing Pd catalytic sites away from the oxygen electrode surface in a well-structured anodic aluminum oxide (AAO) porous membrane interlayer. We observe the cross-sectional product growth and evolution in Li-O2 cells by characterizing products that grow from the electrode surface. Morphological and structural details of the products in both catalyzed and uncatalyzed cells are investigated independently from the influence of the oxygen electrode. We find that the geometric decoration of catalysts far from the conductive electrode surface significantly improves the reaction reversibility by chemically facilitating the oxidation reaction through local coordination with PdO surfaces. The influence of the catalyst position on product composition is further verified by ex situ X-ray photoelectron spectroscopy and Raman spectroscopy in addition to morphological studies.
International Nuclear Information System (INIS)
Kubo, Y.; Asano, H.
1987-01-01
To clarify the growth feature and the structure of hard tissue, we studied the vertebral centrum of rainbow trout Salmo gairdneri, using three specimens (BL: 21.0, 29.0 and 40.0cm). We examined the ratio of centrum length to centrum diameter in each vertebral centrum and obtained the value of 0.8-1.0 in most centra. This indicates that the vertebral centra of rainbow trout belong to the so-called equivalent type. The hard tissue was observed by microradiography, with the longitudinal and cross sections (about 100 μm)cut through the center of notochordal pore. The microradiograph of thin section of centrurn differentiated serially and changed in pattern, but it is clear to sustain the specific characteristics. In longitudinal sections, the V-shaped part of bone was composed of structure like compact bone through the length of vertebral column. In cross sections, the notochordal pore was enclosed by the radial trabecular bones, the arrangement gradually turning toward the posterior centra like paired fans set opposite each other laterally
Fractal analysis of power spectra
International Nuclear Information System (INIS)
Johnston, S.
1982-01-01
A general argument is presented concerning the Hausdorff dimension D of the power spectrum curve for a system of N weakly-coupled oscillators. Explicit upper and lower bounds for D are derived in terms of the number N of interacting modes. The mathematical reasoning relies upon the celebrated KAM theorem concerning the perturbation of Hamiltonian systems and the finite measure of the set of destroyed tori in phase space; this set can be related to Hausdorff dimension by certain mathematical theorems. An important consequence of these results is a simple empirical test for the applicability of Hamiltonian perturbation theory in the analysis of an experimentally observed spectrum. As an illustration, the theory is applied to the interpretation of a recent numerical analysis of both the power spectrum of the Sun and certain laboratory spectra of hydrodynamic turbulence. (Auth.)
Directory of Open Access Journals (Sweden)
Silvester Tursiloadi
2010-06-01
Full Text Available A technique to determine the surface fractal dimension of mesoporous TiO2 using a dynamic flow adsorption instrument is described. Fractal dimension is an additional technique to characterize surface morphology. Surface fractal dimension, a quantitative measurement of surface ruggedness, can be determined by adsorbing a homologous series of adsorbates onto an adsorbent sample of mesoporous TiO2. Titania wet gel prepared by hydrolysis of Ti-alkoxide was immersed in the flow of supercritical CO2 at 60 °C and the solvent was extracted. Mesoporous TiO2 consists of anatase nano-particles, about 5nm in diameter, have been obtained. After calcination at 600 °C, the average pore size of the extracted gel, about 20nm in diameter, and the pore volume, about 0.35cm3g-1, and the specific surface area, about 58 m2g-1. Using the N2 adsorption isotherm, the surface fractal dimension, DS, has been estimated according to the Frenkel-Halsey-Hill (FHH theory. The N2 adsorption isotherm for the as-extracted aerogel indicates the mesoporous structure. Two linear regions are found for the FHH plot of the as-extracted aerogel. The estimated surface fractal dimensions are about 2.49 and 2.68. Both of the DS values indicate rather complex surface morphology. The TEM observation shows that there are amorphous and crystalline particles. Two values of DS may be attributed to these two kinds of particles. The two regions are in near length scales, and the smaller DS, DS =2.49, for the smaller region. This result indicates that there are two kinds of particles, probably amorphous and anatase particles as shown by the TEM observation. Keywords: surface fractal dimensions, CO2 supercritically extraction, sol-gel, aerogel, titania
Directory of Open Access Journals (Sweden)
Xiaxiang Li
2017-05-01
Full Text Available The effect of vegetation on temperature is an emerging topic in the climate science community. Existing studies have mostly examined the effects of vegetation on daytime temperature (Tmax, whereas this study investigates the effects on nighttime temperature (Tmin. Ground measurements from 53 sites across northeastern China (NEC from 1982 to 2006 show that early summer (June Tmax and Tmin increased at mean rates of approximately 0.61 °C/10 year and 0.67 °C/10 year, respectively. Over the same period, the satellite-based Normalized Difference Vegetation Index (NDVI decreased by approximately 0.10 (accounting for 18% of the climatological NDVI for 1982–1991. It is highlighted that a larger increase in Tmax (Tmin co-occurred spatially with a larger (smaller decrease in NDVI. Deriving from such spatial co-occurrences, we found that the spatial variability of changes in Tmax (i.e., ΔTmax is negatively correlated with the spatial variability of changes in NDVI (i.e., ΔNDVI, while the spatial variability of changes in Tmin (i.e., ΔTmin is positively correlated (r2 = 0.10; p < 0.05 with that of ΔNDVI. Similarly, we detected significant positive correlations between the spatial variability of ΔNDVI and the change in surface latent heat flux (r2 = 0.16; p < 0.01 and in surface air specific humidity (r2 = 0.28; p < 0.001. These findings on the spatial co-occurrences suggest that the vegetation growth intensifies the atmospheric water vapor through evapotranspiration, which enhances the atmospheric downward longwave radiation and strengthens the greenhouse warming effects at night. Thereby, the positive correlation between ΔNDVI and ΔTmin is better understood. These results indicate that vegetation growth may not only exert effects on daytime temperature but also exert warming effects on nighttime temperature by increasing atmospheric water vapor and thus intensifying the local greenhouse effect. This study presents new observation evidence of the
John R. Jones; George A. Schier
1985-01-01
This chapter considers aspen growth as a process, and discusses some characteristics of the growth and development of trees and stands. For the most part, factors affecting growth are discussed elsewhere, particularly in the GENETICS AND VARIATION chapter and in chapters in PART 11. ECOLOGY. Aspen growth as it relates to wood production is examined in the WOOD RESOURCE...
Rheological and fractal characteristics of unconditioned and conditioned water treatment residuals.
Dong, Y J; Wang, Y L; Feng, J
2011-07-01
The rheological and fractal characteristics of raw (unconditioned) and conditioned water treatment residuals (WTRs) were investigated in this study. Variations in morphology, size, and image fractal dimensions of the flocs/aggregates in these WTR systems with increasing polymer doses were analyzed. The results showed that when the raw WTRs were conditioned with the polymer CZ8688, the optimum polymer dosage was observed at 24 kg/ton dry sludge. The average diameter of irregularly shaped flocs/aggregates in the WTR suspensions increased from 42.54 μm to several hundred micrometers with increasing polymer doses. Furthermore, the aggregates in the conditioned WTR system displayed boundary/surface and mass fractals. At the optimum polymer dosage, the aggregates formed had a volumetric average diameter of about 820.7 μm, with a one-dimensional fractal dimension of 1.01 and a mass fractal dimension of 2.74 on the basis of the image analysis. Rheological tests indicated that the conditioned WTRs at the optimum polymer dosage showed higher levels of shear-thinning behavior than the raw WTRs. Variations in the limiting viscosity (η(∞)) of conditioned WTRs with sludge content could be described by a linear equation, which were different from the often-observed empirical exponential relationship for most municipal sludge. With increasing temperature, the η(∞) of the raw WTRs decreased more rapidly than that of the raw WTRs. Good fitting results for the relationships between lgη(∞)∼T using the Arrhenius equation indicate that the WTRs had a much higher activation energy for viscosity of about 17.86-26.91 J/mol compared with that of anaerobic granular sludge (2.51 J/mol) (Mu and Yu, 2006). In addition, the Bingham plastic model adequately described the rheological behavior of the conditioned WTRs, whereas the rheology of the raw WTRs fit the Herschel-Bulkley model well at only certain sludge contents. Considering the good power-law relationships between the
Fractal profit landscape of the stock market.
Grönlund, Andreas; Yi, Il Gu; Kim, Beom Jun
2012-01-01
We investigate the structure of the profit landscape obtained from the most basic, fluctuation based, trading strategy applied for the daily stock price data. The strategy is parameterized by only two variables, p and q Stocks are sold and bought if the log return is bigger than p and less than -q, respectively. Repetition of this simple strategy for a long time gives the profit defined in the underlying two-dimensional parameter space of p and q. It is revealed that the local maxima in the profit landscape are spread in the form of a fractal structure. The fractal structure implies that successful strategies are not localized to any region of the profit landscape and are neither spaced evenly throughout the profit landscape, which makes the optimization notoriously hard and hypersensitive for partial or limited information. The concrete implication of this property is demonstrated by showing that optimization of one stock for future values or other stocks renders worse profit than a strategy that ignores fluctuations, i.e., a long-term buy-and-hold strategy.
Fractal analysis of agricultural nozzles spray
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Francisco Agüera
2012-02-01
Full Text Available Fractal scaling of the exponential type is used to establish the cumulative volume (V distribution applied through agricultural spray nozzles in size x droplets, smaller than the characteristic size X. From exponent d, we deduced the fractal dimension (Df which measures the degree of irregularity of the medium. This property is known as 'self-similarity'. Assuming that the droplet set from a spray nozzle is self-similar, the objectives of this study were to develop a methodology for calculating a Df factor associated with a given nozzle and to determine regression coefficients in order to predict droplet spectra factors from a nozzle, taking into account its own Df and pressure operating. Based on the iterated function system, we developed an algorithm to relate nozzle types to a particular value of Df. Four nozzles and five operating pressure droplet size characteristics were measured using a Phase Doppler Particle Analyser (PDPA. The data input consisted of droplet size spectra factors derived from these measurements. Estimated Df values showed dependence on nozzle type and independence of operating pressure. We developed an exponential model based on the Df to enable us to predict droplet size spectra factors. Significant coefficients of determination were found for the fitted model. This model could prove useful as a means of comparing the behavior of nozzles which only differ in not measurable geometric parameters and it can predict droplet spectra factors of a nozzle operating under different pressures from data measured only in extreme work pressures.
Elasticity of fractal materials using the continuum model with non-integer dimensional space
Tarasov, Vasily E.
2015-01-01
Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.
International Nuclear Information System (INIS)
Farkas, J.; Andrassy, E.; Meszaros, L.; Beczner, J.; Polyak-Feher, K.; Gaal, O.; Lebovics, V.K.; Lugasi, A.
2009-01-01
As a result of intensive predictive microbiological modelling activities, several computer programs and softwares became available recently for facilitating microbiological risk assessment. Among these tools, the establishment of the ComBase, an international database and its predictive modelling softwares of the Pathogen Modelling Program (PMP) set up by the USDA Eastern Regional Research Center, Wyndmore, PA, and the Food Micromodel/Growth Predictor by the United Kingdom's Institute of Food Research, Norwich, are most important. The authors have used the PMP 6.1 software version of ComBase as a preliminary trial to compare observed growth of selected test organisms in relation to their food irradiation work during recent years within the FAO/IAEA Coordinated Food Irradiation Research Projects (D6.10.23 and D6.20.07) with the predicted growth on the basis of growth models available in ComBase for the same species as those of the authors' test organisms. The results of challenge tests with Listeria monocytogenes inoculum in untreated or irradiated experimental batches of semi-prepared breaded turkey meat steaks (cordon bleu), sliced tomato, sliced watermelon, sliced cantaloupe and sous vide processed mixed vegetables, as well as Staphylococcus aureus inoculum of a pasta product, tortellini, were compared with their respective growth models under relevant environmental conditions. This comparison showed good fits in the case of non-irradiated and high moisture food samples, but growth of radiation survivors lagged behind the predicted values. (author)
Effective degrees of freedom of a random walk on a fractal
Balankin, Alexander S.
2015-12-01
We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.
The increase in fatigue crack growth rates observed for Zircaloy-4 in a PWR environment
Cockeram, B. V.; Kammenzind, B. F.
2018-02-01
Cyclic stresses produced during the operation of nuclear reactors can result in the extension of cracks by processes of fatigue. Although fatigue crack growth rate (FCGR) data for Zircaloy-4 in air are available, little testing has been performed in a PWR primary water environment. Test programs have been performed by Gee et al., in 1989 and Picker and Pickles in 1984 by the UK Atomic Energy Authority, and by Wisner et al., in 1994, that have shown an enhancement in FCGR for Zircaloy-2 and Zircaloy-4 in high-temperature water. In this work, FCGR testing is performed on Zircaloy-4 in a PWR environment in the hydrided and non-hydrided condition over a range of stress-intensity. Measurements of crack extension are performed using a direct current potential drop (DCPD) method. The cyclic rate in the PWR primary water environment is varied between 1 cycle per minute to 0.1 cycle per minute. Faster FCGR rates are observed in water in comparison to FCGR testing performed in air for the hydrided material. Hydrided and non-hydrided materials had similar FCGR values in air, but the non-hydrided material exhibited much lower rates of FCGR in a PWR primary water environment than for hydrided material. Hydrides are shown to exhibit an increased tendency for cracking or decohesion in a PWR primary water environment that results in an enhancement in FCGR values. The FCGR in the PWR primary water only increased slightly with decreasing cycle frequency in the range of 1 cycle per minute to 0.1 cycle per minute. Comparisons between the FCGR in water and air show the enhancement from the PWR environment is affected by the applied stress intensity.
Sierpinski triangles as a tool to introduce fractal geometry to children and their parents
Gires, Auguste; Schertzer, Daniel
2017-04-01
There are currently two somehow contradictory trends in the public debates involving scientific issues. On the one hand there is a need to address topics of increasing complexity, while on the other hand simple(istic) solutions are suggested by numerous people (including high level ones). Meanwhile there seems to be growing defiance towards science findings. Such problems are faced in numerous fields including geosciences where famous examples are the debates dealing with climate change, or water / air contamination. Such unfortunate trends means that the input of scientists in the society and public debates is strongly required. Although it not actually their job, scientists should get involved as a citizens. They should try to explain the complexity of the issues at stake, and take the necessary time to achieve this; not all problems can be explained with the help of a 140 characters tweet! Rather than hiding the uncertainties, they should try to explain this notion often not well understood, and admit the current limitations of knowledge. In the meantime it would be positive if this dialogue could help children and their parents to get familiarized with science and scientists, show that science is not obscure and actually present in everyday life. Scientists obviously also have the hope of fostering a desire for understanding, enhancing scientific culture and even promoting careers in this field. Fractals and fractal geometry are actually a rather good tool to achieve this. Indeed through numerous iterations of a simple process, one can easily obtain a rather complex shape, exhibiting some of the features observed in the nature. Fractal shapes are scale invariant, i.e. the more you zoom in, the more details you see; a portion of the shape is similar to the full one. This paper aims at presenting a series of activities presenting fractals to young people developed primarily around the famous Sierpinski triangles. Two types of activities were carefully designed
Semiflexible crossing-avoiding trails on plane-filling fractals
International Nuclear Information System (INIS)
Živić, I.; Elezović-Hadžić, S.; Milošević, S.
2015-01-01
We have studied the statistics of semiflexible polymer chains modeled by crossing-avoiding trails (CAT) situated on the family of plane-filling (PF) fractals. The fractals are compact, that is, their fractal dimension d_f is equal to 2 for all members of the fractal family. By applying the exact and Monte Carlo real-space renormalization group method we have calculated the critical exponent ν, which governs the scaling behavior of the end-to-end distance of the polymer, as well as the entropic critical exponent γ, for a large set of fractals, and various values of polymer flexibility. Our results, obtained for CAT model on PF fractals, show that both critical exponents depend on the polymer flexibility, in such a way that less flexible polymer chains display enlarged values of ν, and diminished values of γ. We have compared the obtained results for CAT model with the known results for the self-avoiding walk and self-avoiding trail models and discussed the influence of excluded volume effect on the values of semiflexible polymer critical exponents, for a large set of studied compact fractals.
Convergence of trajectories in fractal interpolation of stochastic processes
International Nuclear Information System (INIS)
MaIysz, Robert
2006-01-01
The notion of fractal interpolation functions (FIFs) can be applied to stochastic processes. Such construction is especially useful for the class of α-self-similar processes with stationary increments and for the class of α-fractional Brownian motions. For these classes, convergence of the Minkowski dimension of the graphs in fractal interpolation of the Hausdorff dimension of the graph of original process was studied in [Herburt I, MaIysz R. On convergence of box dimensions of fractal interpolation stochastic processes. Demonstratio Math 2000;4:873-88.], [MaIysz R. A generalization of fractal interpolation stochastic processes to higher dimension. Fractals 2001;9:415-28.], and [Herburt I. Box dimension of interpolations of self-similar processes with stationary increments. Probab Math Statist 2001;21:171-8.]. We prove that trajectories of fractal interpolation stochastic processes converge to the trajectory of the original process. We also show that convergence of the trajectories in fractal interpolation of stochastic processes is equivalent to the convergence of trajectories in linear interpolation
Quantitative assessment of early diabetic retinopathy using fractal analysis.
Cheung, Ning; Donaghue, Kim C; Liew, Gerald; Rogers, Sophie L; Wang, Jie Jin; Lim, Shueh-Wen; Jenkins, Alicia J; Hsu, Wynne; Li Lee, Mong; Wong, Tien Y
2009-01-01
Fractal analysis can quantify the geometric complexity of the retinal vascular branching pattern and may therefore offer a new method to quantify early diabetic microvascular damage. In this study, we examined the relationship between retinal fractal dimension and retinopathy in young individuals with type 1 diabetes. We conducted a cross-sectional study of 729 patients with type 1 diabetes (aged 12-20 years) who had seven-field stereoscopic retinal photographs taken of both eyes. From these photographs, retinopathy was graded according to the modified Airlie House classification, and fractal dimension was quantified using a computer-based program following a standardized protocol. In this study, 137 patients (18.8%) had diabetic retinopathy signs; of these, 105 had mild retinopathy. Median (interquartile range) retinal fractal dimension was 1.46214 (1.45023-1.47217). After adjustment for age, sex, diabetes duration, A1C, blood pressure, and total cholesterol, increasing retinal vascular fractal dimension was significantly associated with increasing odds of retinopathy (odds ratio 3.92 [95% CI 2.02-7.61] for fourth versus first quartile of fractal dimension). In multivariate analysis, each 0.01 increase in retinal vascular fractal dimension was associated with a nearly 40% increased odds of retinopathy (1.37 [1.21-1.56]). This association remained after additional adjustment for retinal vascular caliber. Greater retinal fractal dimension, representing increased geometric complexity of the retinal vasculature, is independently associated with early diabetic retinopathy signs in type 1 diabetes. Fractal analysis of fundus photographs may allow quantitative measurement of early diabetic microvascular damage.
Fractal physiology and the fractional calculus: a perspective
Directory of Open Access Journals (Sweden)
Bruce J West
2010-10-01
Full Text Available This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. We review the allometric aggregation approach to the processing of physiologic time series as a way of determining the fractal character of the underlying phenomena. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. Fractional operators acting on fractal functions yield fractal functions, allowing us to construct a fractional Langevin equation to describe the evolution of a fractal statistical process. Control of physiologic complexity is one of the goals of medicine. Allometric control incorporates long-time memory, inverse power-law (IPL correlations, and long-range interactions in complex phenomena as manifest by IPL distributions. We hypothesize that allometric control, rather than homeostatic control, maintains the fractal character of erratic physiologic time series to enhance the robustness of physiological networks. Moreover, allometric control can be described using the fractional calculus to capture the dynamics of complex physiologic networks. This hypothesis is supported by a number of physiologic time series data.
Extremal dynamics: A unifying physical explanation of fractals, 1/f noise, and activated processes
International Nuclear Information System (INIS)
Miller, S.L.; Miller, W.M.; McWhorter, P.J.
1993-01-01
The properties of physical systems whose observable properties depend upon random exceedances of critical parameters are quantitatively examined. Using extreme value theory, the dynamical behavior of this broad class of systems is derived. This class of systems can exhibit two characteristic signatures: generalized activation when far from equilibrium and noise with a characteristic power spectrum (including 1/f ) when in quasiequilibrium. Fractal structures can also arise from these systems. It is thus demonstrated that generalized activation, noise, and fractals, in some cases, are simply different manifestations of a single common dynamical principle, which is termed ''extremal dynamics.'' Examples of physical processes governed by extremal dynamics are discussed, including data loss of nonvolatile memories and dielectric breakdown
Circulating persistent current and induced magnetic field in a fractal network
Energy Technology Data Exchange (ETDEWEB)
Saha, Srilekha [Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata 700 064 (India); Maiti, Santanu K., E-mail: santanu.maiti@isical.ac.in [Physics and Applied Mathematics Unit, Indian Statistical Institute, 203 Barrackpore Trunk Road, Kolkata 700 108 (India); Karmakar, S.N. [Condensed Matter Physics Division, Saha Institute of Nuclear Physics, Sector-I, Block-AF, Bidhannagar, Kolkata 700 064 (India)
2016-04-29
We present the overall conductance as well as the circulating currents in individual loops of a Sierpinski gasket (SPG) as we apply bias voltage via the side attached electrodes. SPG being a self-similar structure, its manifestation on loop currents and magnetic fields is examined in various generations of this fractal and it has been observed that for a given configuration of the electrodes, the physical quantities exhibit certain regularity as we go from one generation to another. Also a notable feature is the introduction of anisotropy in hopping causes an increase in magnitude of overall transport current. These features are a subject of interest in this article. - Highlights: • Voltage driven circular current is analyzed in a fractal network. • Current induced magnetic field is strong enough to flip a spin. • Anisotropy in hopping enhances overall transport current.
An Explanation for the Arctic Sea Ice Melt Pond Fractal Transition
Popovic, P.; Abbot, D. S.
2016-12-01
As Arctic sea ice melts during the summer, pools of melt water form on its surface. This decreases the ice's albedo, which signifcantly impacts its subsequent evolution. Understanding this process is essential for buiding accurate sea ice models in GCMs and using them to forecast future changes in sea ice. A feature of melt ponds that helps determine their impact on ice albedo is that they often form complex geometric shapes. One characteristic of their shape, the fractal dimension of the pond boundaries, D, has been shown to transition between the two fundamental limits of D = 1 and D = 2 at some critical pond size. Here, we provide an explanation for this behavior. First, using aerial photographs taken during the SHEBA mission, we show how this fractal transition curve changes with time, and show that there is a qualitative difference in the pond shape as ice transitions from impermeable to permeable. While ice is impermeable, the maximum fractal dimension is less than 2, whereas after it becomes permeable, the maximum fractal dimension becomes very close to 2. We then show how the fractal dimension of the boundary of a collection of overlapping circles placed randomly on a plane also transitions from D = 1 to D = 2 at a size equal to the average size of a single circle. We, therefore, conclude that this transition is a simple geometric consequence of regular shapes connecting. The one physical parameter that can be extracted from the fractal transition curve is the length scale at which transition occurs. Previously, this length scale has been associated with the typical size of snow dunes created on the ice surface during winter. We provide an alternative explanation by noting that the flexural wavelength of the ice poses a fundamental limit on the size of melt ponds on permeable ice. If this is true, melt ponds could be used as a proxy for ice thickness. Finally, we provide some remarks on how to observationally distinguish between the two ideas for what
International Nuclear Information System (INIS)
Sasaki, Takuo; Shimomura, Kenichi; Kamiya, Itaru; Ohshita, Yoshio; Yamaguchi, Masafumi; Suzuki, Hidetoshi; Takahasi, Masamitu
2012-01-01
In-plane asymmetric strain relaxation in lattice-mismatched InGaAs/GaAs(001) heteroepitaxy is studied by in situ three-dimensional X-ray reciprocal space mapping. Repeating crystal growth and growth interruptions during measurements allows us to investigate whether the strain relaxation is limited at a certain thickness or saturated. We find that the degree of relaxation during growth interruption depends on both the film thickness and the in-plane directions. Significant lattice relaxation is observed in rapid relaxation regimes during interruption. This is a clear indication that relaxation is kinetically limited. In addition, relaxation along the [110] direction can saturate more readily than that along the [1-bar10] direction. We discuss this result in terms of the interaction between orthogonally aligned dislocations. (author)
Fractality of profit landscapes and validation of time series models for stock prices
Yi, Il Gu; Oh, Gabjin; Kim, Beom Jun
2013-08-01
We apply a simple trading strategy for various time series of real and artificial stock prices to understand the origin of fractality observed in the resulting profit landscapes. The strategy contains only two parameters p and q, and the sell (buy) decision is made when the log return is larger (smaller) than p (-q). We discretize the unit square (p,q) ∈ [0,1] × [0,1] into the N × N square grid and the profit Π(p,q) is calculated at the center of each cell. We confirm the previous finding that local maxima in profit landscapes are scattered in a fractal-like fashion: the number M of local maxima follows the power-law form M ˜ Na, but the scaling exponent a is found to differ for different time series. From comparisons of real and artificial stock prices, we find that the fat-tailed return distribution is closely related to the exponent a ≈ 1.6 observed for real stock markets. We suggest that the fractality of profit landscape characterized by a ≈ 1.6 can be a useful measure to validate time series model for stock prices.
Moisture diffusivity in structure of random fractal fiber bed
Energy Technology Data Exchange (ETDEWEB)
Zhu, Fanglong, E-mail: zhufanglong_168@163.com [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); The Chinese People' s Armed Police Forces Academy, Langfan City (China); Zhou, Yu; Feng, Qianqian [College of Textile, Zhongyuan University of Technology, Zhengzhou City (China); Xia, Dehong [School of Mechanical Engineering, University of Science and Technology, Beijing (China)
2013-11-08
A theoretical expression related to effective moisture diffusivity to random fiber bed is derived by using fractal theory and considering both parallel and perpendicular channels to diffusion flow direction. In this Letter, macroporous structure of hydrophobic nonwoven material is investigated, and Knudsen diffusion and surface diffusion are neglected. The effective moisture diffusivity predicted by the present fractal model are compared with water vapor transfer rate (WVTR) experiment data and calculated values obtained from other theoretical models. This verifies the validity of the present fractal diffusivity of fibrous structural beds.
A fractal analysis of the public transportation system of Paris
L Benguigui
1995-01-01
An analysis of the railway networks of the public transportation system of Paris, based on the notion of fractals, is presented. The two basic networks, (metropolitan and suburban) which have different functions, have also a different fractal dimension: 1.8 for the metropolitan network, and 1.5 for the suburban network. By means of computer simulation, it is concluded that the true dimension of the metro network is probably 2.0. A fractal model of the suburban network, with the same features ...
Fractal studies on the positron annihilation in metals
International Nuclear Information System (INIS)
Lung, C.W.
1994-06-01
Traditionally, the Euclidean lines, circles and spheres have served as the basis of the intuitive understanding of the geometry of nature. Recently, the concept of fractals has caught the imagination of scientists in many fields. This paper is to continue our previous work on position annihilation near fractal surfaces to demonstrate that the concept of fractals provides a powerful tool for understanding the structure and properties of defects and rough surfaces in relation to positron annihilation studies. Some problems on Berry geometrical phase have also been discussed. (author). 15 refs, fig., 1 tab
Some fractal properties of the percolating backbone in two dimensions
International Nuclear Information System (INIS)
Laidlaw, D.; MacKay, G.; Jan, N.
1987-01-01
A new algorithm is presented, based on elements of artificial intelligence theory, to determine the fractal properties of the backbone of the incipient infinite cluster. It is found that fractal dimensionality of the backbone is d/sub f//sup BB/ = 1.61 +/- 0.01, the chemical dimensionality is d/sub t/ = 1.40 +/- 0.01, and the fractal dimension of the minimum path d/sub min/ = 1.15 +/- 0.02 for the two-dimensional triangular lattice
Delay Bound: Fractal Traffic Passes through Network Servers
Directory of Open Access Journals (Sweden)
Ming Li
2013-01-01
Full Text Available Delay analysis plays a role in real-time systems in computer communication networks. This paper gives our results in the aspect of delay analysis of fractal traffic passing through servers. There are three contributions presented in this paper. First, we will explain the reasons why conventional theory of queuing systems ceases in the general sense when arrival traffic is fractal. Then, we will propose a concise method of delay computation for hard real-time systems as shown in this paper. Finally, the delay computation of fractal traffic passing through severs is presented.
An Efficient Computational Technique for Fractal Vehicular Traffic Flow
Directory of Open Access Journals (Sweden)
Devendra Kumar
2018-04-01
Full Text Available In this work, we examine a fractal vehicular traffic flow problem. The partial differential equations describing a fractal vehicular traffic flow are solved with the aid of the local fractional homotopy perturbation Sumudu transform scheme and the local fractional reduced differential transform method. Some illustrative examples are taken to describe the success of the suggested techniques. The results derived with the aid of the suggested schemes reveal that the present schemes are very efficient for obtaining the non-differentiable solution to fractal vehicular traffic flow problem.
Fractal aspects and convergence of Newton`s method
Energy Technology Data Exchange (ETDEWEB)
Drexler, M. [Oxford Univ. Computing Lab. (United Kingdom)
1996-12-31
Newton`s Method is a widely established iterative algorithm for solving non-linear systems. Its appeal lies in its great simplicity, easy generalization to multiple dimensions and a quadratic local convergence rate. Despite these features, little is known about its global behavior. In this paper, we will explain a seemingly random global convergence pattern using fractal concepts and show that the behavior of the residual is entirely explicable. We will also establish quantitative results for the convergence rates. Knowing the mechanism of fractal generation, we present a stabilization to the orthodox Newton method that remedies the fractal behavior and improves convergence.
Weerdt, de, Wallie H.
1981-01-01
The historical background of the taxonomic problems in the fire-coral, Millepora, is reviewed. The growth forms of the Caribbean species: Millepora alcicornis Linnaeus, M. complanata Lamarck and M. squarrosa Lamarck are investigated in relation with environmental factors: water movement, current, light and turbidity. Several sites on Curaçao and Bonaire were visited and all forms of Millepora collected. The localities have been divided in biotopes and the relative frequencies of the growth fo...
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
International Nuclear Information System (INIS)
Kawamura, Tomoaki; Bhunia, Satyaban; Watanabe, Yoshio; Fujikawa, Seiji
2008-01-01
We made the x-ray diffractometer combined with the MOCVD growth system for the real-time observation of epitaxial growth in gaseous environment, and investigated the growth mechanism of InP crystals. Changes of the (-5/2 O) Bragg diffraction during the growth revealed that the growth starts immediately after the In source has been supplied and gradually stopped, owing to the migrating In atoms on the surface. Additionally, one can easily determine the growth modes, including 3-dimensional mode, layer-by-layer mode, and step-flow mode, by observing the change of x-ray reflectivity with various growth conditions. (author)
International Nuclear Information System (INIS)
Marsh, D.; Green, D.; Parker, R.
1984-01-01
This paper reports the results of an experiment in which a severe thermal cycle comprising of alternate upshocks and downshocks has been applied to an axisymmetric feature with an internal, partial penetration weld and crevice. The direction of cracking and crack growth rate were observed experimentally and detailed records made of the thermal cycle. A second part to the paper, reported separately, compares a linear elastic fracture mechanics assessment of the cracking to the experimental observations
Transient effects in friction fractal asperity creep
Goedecke, Andreas
2013-01-01
Transient friction effects determine the behavior of a wide class of mechatronic systems. Classic examples are squealing brakes, stiction in robotic arms, or stick-slip in linear drives. To properly design and understand mechatronic systems of this type, good quantitative models of transient friction effects are of primary interest. The theory developed in this book approaches this problem bottom-up, by deriving the behavior of macroscopic friction surfaces from the microscopic surface physics. The model is based on two assumptions: First, rough surfaces are inherently fractal, exhibiting roughness on a wide range of scales. Second, transient friction effects are caused by creep enlargement of the real area of contact between two bodies. This work demonstrates the results of extensive Finite Element analyses of the creep behavior of surface asperities, and proposes a generalized multi-scale area iteration for calculating the time-dependent real contact between two bodies. The toolset is then demonstrated both...
Stochastic and fractal analysis of fracture trajectories
Bessendorf, Michael H.
1987-01-01
Analyses of fracture trajectories are used to investigate structures that fall between 'micro' and 'macro' scales. It was shown that fracture trajectories belong to the class of nonstationary processes. It was also found that correlation distance, which may be related to a characteristic size of a fracture process, increases with crack length. An assemblage of crack trajectory processes may be considered as a diffusive process. Chudnovsky (1981-1985) introduced a 'crack diffusion coefficient' d which reflects the ability of the material to deviate the crack trajectory from the most energetically efficient path and thus links the material toughness to its structure. For the set of fracture trajectories in AISI 304 steel, d was found to be equal to 1.04 microns. The fractal dimension D for the same set of trajectories was found to be 1.133.
Fractal like charge transport in polyaniline nanostructures
International Nuclear Information System (INIS)
Nath, Chandrani; Kumar, A.
2013-01-01
The structural and electrical properties of camphorsulfonic acid (CSA) doped nanotubes, and hydrochloric acid (HCl) doped nanofibers and nanoparticles of polyaniline have been studied as a function of doping level. The crystallinity increases with doping for all the nanostructures. Electrical transport measurements in the temperature range of 5–300 K show an increase in conductivity with doping for the nanostructures. All the nanostructures exhibit metal to insulator (MIT) transition below 40 K. The metallic behavior is ascribed to the electron–electron interaction effects. In the insulating regime of the nanotubes conduction follows the Mott quasi-1D variable range hopping model, whereas the conduction in the nanofibers and nanoparticles occur by variable range hopping of charge carriers among superlocalized states without and with Coulomb interaction, respectively. The smaller dopant size in case of HCl makes the polymer fractal resulting in superlocalization of electronic wave-functions. The confined morphology of the nanoparticles results in effective Coulomb interaction dominating the intersite hopping
Proteins in solution: Fractal surfaces in solutions
Directory of Open Access Journals (Sweden)
R. Tscheliessnig
2016-02-01
Full Text Available The concept of the surface of a protein in solution, as well of the interface between protein and 'bulk solution', is introduced. The experimental technique of small angle X-ray and neutron scattering is introduced and described briefly. Molecular dynamics simulation, as an appropriate computational tool for studying the hydration shell of proteins, is also discussed. The concept of protein surfaces with fractal dimensions is elaborated. We finish by exposing an experimental (using small angle X-ray scattering and a computer simulation case study, which are meant as demonstrations of the possibilities we have at hand for investigating the delicate interfaces that connect (and divide protein molecules and the neighboring electrolyte solution.
Iterons, fractals and computations of automata
Siwak, Paweł
1999-03-01
Processing of strings by some automata, when viewed on space-time (ST) diagrams, reveals characteristic soliton-like coherent periodic objects. They are inherently associated with iterations of automata mappings thus we call them the iterons. In the paper we present two classes of one-dimensional iterons: particles and filtrons. The particles are typical for parallel (cellular) processing, while filtrons, introduced in (32) are specific for serial processing of strings. In general, the images of iterated automata mappings exhibit not only coherent entities but also the fractals, and quasi-periodic and chaotic dynamics. We show typical images of such computations: fractals, multiplication by a number, and addition of binary numbers defined by a Turing machine. Then, the particles are presented as iterons generated by cellular automata in three computations: B/U code conversion (13, 29), majority classification (9), and in discrete version of the FPU (Fermi-Pasta-Ulam) dynamics (7, 23). We disclose particles by a technique of combinational recoding of ST diagrams (as opposed to sequential recoding). Subsequently, we recall the recursive filters based on FCA (filter cellular automata) window operators, and considered by Park (26), Ablowitz (1), Fokas (11), Fuchssteiner (12), Bruschi (5) and Jiang (20). We present the automata equivalents to these filters (33). Some of them belong to the class of filter automata introduced in (30). We also define and illustrate some properties of filtrons. Contrary to particles, the filtrons interact nonlocally in the sense that distant symbols may influence one another. Thus their interactions are very unusual. Some examples have been given in (32). Here we show new examples of filtron phenomena: multifiltron solitonic collisions, attracting and repelling filtrons, trapped bouncing filtrons (which behave like a resonance cavity) and quasi filtrons.
Fractals and Forecasting in Earthquakes and Finance
Rundle, J. B.; Holliday, J. R.; Turcotte, D. L.
2011-12-01
It is now recognized that Benoit Mandelbrot's fractals play a critical role in describing a vast range of physical and social phenomena. Here we focus on two systems, earthquakes and finance. Since 1942, earthquakes have been characterized by the Gutenberg-Richter magnitude-frequency relation, which in more recent times is often written as a moment-frequency power law. A similar relation can be shown to hold for financial markets. Moreover, a recent New York Times article, titled "A Richter Scale for the Markets" [1] summarized the emerging viewpoint that stock market crashes can be described with similar ideas as large and great earthquakes. The idea that stock market crashes can be related in any way to earthquake phenomena has its roots in Mandelbrot's 1963 work on speculative prices in commodities markets such as cotton [2]. He pointed out that Gaussian statistics did not account for the excessive number of booms and busts that characterize such markets. Here we show that both earthquakes and financial crashes can both be described by a common Landau-Ginzburg-type free energy model, involving the presence of a classical limit of stability, or spinodal. These metastable systems are characterized by fractal statistics near the spinodal. For earthquakes, the independent ("order") parameter is the slip deficit along a fault, whereas for the financial markets, it is financial leverage in place. For financial markets, asset values play the role of a free energy. In both systems, a common set of techniques can be used to compute the probabilities of future earthquakes or crashes. In the case of financial models, the probabilities are closely related to implied volatility, an important component of Black-Scholes models for stock valuations. [2] B. Mandelbrot, The variation of certain speculative prices, J. Business, 36, 294 (1963)
Engineering flat electronic bands in quasiperiodic and fractal loop geometries
Energy Technology Data Exchange (ETDEWEB)
Nandy, Atanu, E-mail: atanunandy1989@gmail.com; Chakrabarti, Arunava, E-mail: arunava_chakrabarti@yahoo.co.in
2015-11-06
Exact construction of one electron eigenstates with flat, non-dispersive bands, and localized over clusters of various sizes is reported for a class of quasi-one-dimensional looped networks. Quasiperiodic Fibonacci and Berker fractal geometries are embedded in the arms of the loop threaded by a uniform magnetic flux. We work out an analytical scheme to unravel the localized single particle states pinned at various atomic sites or over clusters of them. The magnetic field is varied to control, in a subtle way, the extent of localization and the location of the flat band states in energy space. In addition to this we show that an appropriate tuning of the field can lead to a re-entrant behavior of the effective mass of the electron in a band, with a periodic flip in its sign. - Highlights: • Exact construction of eigenstates with flat and dispersive bands is reported. • Competition between translational order and growth of aperiodicity is discussed. • The effect of magnetic field on the location of flat band states is shown. • Flux tunable re-entrant behavior of the effective mass of electron is studied.
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.
Integration of Fractal Biosensor in a Digital Microfluidic Platform
Mashraei, Yousof; Sivashankar, Shilpa; Buttner, Ulrich; Salama, Khaled N.
2016-01-01
fractal electrode biosensor that is used for both droplet actuation and sensing C-reactive protein (CRP) concentration levels to assess cardiac disease risk. Our proposed electrode is the first two-terminal electrode design to be integrated into DMF
Vortex-ring-fractal Structure of Atom and Molecule
International Nuclear Information System (INIS)
Osmera, Pavel
2010-01-01
This chapter is an attempt to attain a new and profound model of the nature's structure using a vortex-ring-fractal theory (VRFT). Scientists have been trying to explain some phenomena in Nature that have not been explained so far. The aim of this paper is the vortex-ring-fractal modeling of elements in the Mendeleev's periodic table, which is not in contradiction to the known laws of nature. We would like to find some acceptable structure model of the hydrogen as a vortex-fractal-coil structure of the proton and a vortex-fractal-ring structure of the electron. It is known that planetary model of the hydrogen atom is not right, the classical quantum model is too abstract. Our imagination is that the hydrogen is a levitation system of the proton and the electron. Structures of helium, oxygen, and carbon atoms and a hydrogen molecule are presented too.
Biometric feature extraction using local fractal auto-correlation
International Nuclear Information System (INIS)
Chen Xi; Zhang Jia-Shu
2014-01-01
Image texture feature extraction is a classical means for biometric recognition. To extract effective texture feature for matching, we utilize local fractal auto-correlation to construct an effective image texture descriptor. Three main steps are involved in the proposed scheme: (i) using two-dimensional Gabor filter to extract the texture features of biometric images; (ii) calculating the local fractal dimension of Gabor feature under different orientations and scales using fractal auto-correlation algorithm; and (iii) linking the local fractal dimension of Gabor feature under different orientations and scales into a big vector for matching. Experiments and analyses show our proposed scheme is an efficient biometric feature extraction approach. (condensed matter: structural, mechanical, and thermal properties)
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 sh...
The colours of infinity the beauty and power of fractals
Lesmoir-Gordon, Nigel
2010-01-01
The groundbreaking documentary (accompanying this book) has been shown in over 50 countries around the world. The contributors to the film are joined in this comprehensive survey of fractal theory and practice by leading experts in the field.
RF MEMS Fractal Capacitors With High Self-Resonant Frequencies
Elshurafa, Amro M.; Emira, Ahmed; Radwan, Ahmed Gomaa; Salama, Khaled N.
2012-01-01
This letter demonstrates RF microelectromechanical systems (MEMS) fractal capacitors possessing the highest reported self-resonant frequencies (SRFs) in PolyMUMPS to date. Explicitly, measurement results show SRFs beyond 20 GHz. Furthermore, quality
Solar Cycle Phase Dependence of Supergranular Fractal Dimension
Indian Academy of Sciences (India)
Solar Cycle Phase Dependence of Supergranular Fractal Dimension ... NIE Institute of Technology, Mysore, India. ... This means that each accepted article is being published immediately online with DOI and article citation ID with starting page ...
Wetting characteristics of 3-dimensional nanostructured fractal surfaces
Davis, Ethan; Liu, Ying; Jiang, Lijia; Lu, Yongfeng; Ndao, Sidy
2017-01-01
This article reports the fabrication and wetting characteristics of 3-dimensional nanostructured fractal surfaces (3DNFS). Three distinct 3DNFS surfaces, namely cubic, Romanesco broccoli, and sphereflake were fabricated using two-photon direct laser writing. Contact angle measurements were performed on the multiscale fractal surfaces to characterize their wetting properties. Average contact angles ranged from 66.8° for the smooth control surface to 0° for one of the fractal surfaces. The change in wetting behavior was attributed to modification of the interfacial surface properties due to the inclusion of 3-dimensional hierarchical fractal nanostructures. However, this behavior does not exactly obey existing surface wetting models in the literature. Potential applications for these types of surfaces in physical and biological sciences are also discussed.
Fractal based curves in musical creativity: A critical annotation
Georgaki, Anastasia; Tsolakis, Christos
In this article we examine fractal curves and synthesis algorithms in musical composition and research. First we trace the evolution of different approaches for the use of fractals in music since the 80's by a literature review. Furthermore, we review representative fractal algorithms and platforms that implement them. Properties such as self-similarity (pink noise), correlation, memory (related to the notion of Brownian motion) or non correlation at multiple levels (white noise), can be used to develop hierarchy of criteria for analyzing different layers of musical structure. L-systems can be applied in the modelling of melody in different musical cultures as well as in the investigation of musical perception principles. Finally, we propose a critical investigation approach for the use of artificial or natural fractal curves in systematic musicology.
Hyper-Fractal Analysis: A visual tool for estimating the fractal dimension of 4D objects
Grossu, I. V.; Grossu, I.; Felea, D.; Besliu, C.; Jipa, Al.; Esanu, T.; Bordeianu, C. C.; Stan, E.
2013-04-01
This work presents a new version of a Visual Basic 6.0 application for estimating the fractal dimension of images and 3D objects (Grossu et al. (2010) [1]). The program was extended for working with four-dimensional objects stored in comma separated values files. This might be of interest in biomedicine, for analyzing the evolution in time of three-dimensional images. New version program summaryProgram title: Hyper-Fractal Analysis (Fractal Analysis v03) Catalogue identifier: AEEG_v3_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEEG_v3_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Standard CPC license, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 745761 No. of bytes in distributed program, including test data, etc.: 12544491 Distribution format: tar.gz Programming language: MS Visual Basic 6.0 Computer: PC Operating system: MS Windows 98 or later RAM: 100M Classification: 14 Catalogue identifier of previous version: AEEG_v2_0 Journal reference of previous version: Comput. Phys. Comm. 181 (2010) 831-832 Does the new version supersede the previous version? Yes Nature of problem: Estimating the fractal dimension of 4D images. Solution method: Optimized implementation of the 4D box-counting algorithm. Reasons for new version: Inspired by existing applications of 3D fractals in biomedicine [3], we extended the optimized version of the box-counting algorithm [1, 2] to the four-dimensional case. This might be of interest in analyzing the evolution in time of 3D images. The box-counting algorithm was extended in order to support 4D objects, stored in comma separated values files. A new form was added for generating 2D, 3D, and 4D test data. The application was tested on 4D objects with known dimension, e.g. the Sierpinski hypertetrahedron gasket, Df=ln(5)/ln(2) (Fig. 1). The algorithm could be extended, with minimum effort, to
International Nuclear Information System (INIS)
Knaap, A.G.A.C.; Simons, J.W.I.M.
1983-01-01
As it is not known to what extent differential growth rates of induced mutants lead to over- and under-representation of mutants in treated populations and thereby affect the determination of mutant frequencies, the mutation induction in X-irradiated L5178Y mouse lymphoma cells was determined via two methods. The first method involves the standard protocol which may suffer from the effect of differential growth rates, while the second method is based upon the fluctuation test in which the differential growth rates can be actually measured. It appeared that the standard protocol led to a mutant frequency that was similar to the mutant frequency determined in the fluctuation test. Therefore, the standard protocol appears to lead to only a minor under-estimation if any. Substantial heterogeneity in growth rates of induced mutants was observed, but the mutants with a selective advantage appear largely to compensate for the mutants that are lost because of selective disadvantage. It was calculated that the chance for isolating the same mutant twice from a treated population had been increased 2.2-fold because of the observed differential growth rates. (orig./AJ)
Fractal dimension algorithms and their application to time series associated with natural phenomena
International Nuclear Information System (INIS)
La Torre, F Cervantes-De; González-Trejo, J I; Real-Ramírez, C A; Hoyos-Reyes, L F
2013-01-01
Chaotic invariants like the fractal dimensions are used to characterize non-linear time series. The fractal dimension is an important characteristic of systems, because it contains information about their geometrical structure at multiple scales. In this work, three algorithms are applied to non-linear time series: spectral analysis, rescaled range analysis and Higuchi's algorithm. The analyzed time series are associated with natural phenomena. The disturbance storm time (Dst) is a global indicator of the state of the Earth's geomagnetic activity. The time series used in this work show a self-similar behavior, which depends on the time scale of measurements. It is also observed that fractal dimensions, D, calculated with Higuchi's method may not be constant over-all time scales. This work shows that during 2001, D reaches its lowest values in March and November. The possibility that D recovers a change pattern arising from self-organized critical phenomena is also discussed
Liu, Yanfeng; Zhou, Xiaojun; Wang, Dengjia; Song, Cong; Liu, Jiaping
2015-12-15
Most building materials are porous media, and the internal diffusion coefficients of such materials have an important influences on the emission characteristics of volatile organic compounds (VOCs). The pore structure of porous building materials has a significant impact on the diffusion coefficient. However, the complex structural characteristics bring great difficulties to the model development. The existing prediction models of the diffusion coefficient are flawed and need to be improved. Using scanning electron microscope (SEM) observations and mercury intrusion porosimetry (MIP) tests of typical porous building materials, this study developed a new diffusivity model: the multistage series-connection fractal capillary-bundle (MSFC) model. The model considers the variable-diameter capillaries formed by macropores connected in series as the main mass transfer paths, and the diameter distribution of the capillary bundles obeys a fractal power law in the cross section. In addition, the tortuosity of the macrocapillary segments with different diameters is obtained by the fractal theory. Mesopores serve as the connections between the macrocapillary segments rather than as the main mass transfer paths. The theoretical results obtained using the MSFC model yielded a highly accurate prediction of the diffusion coefficients and were in a good agreement with the VOC concentration measurements in the environmental test chamber. Copyright © 2015 Elsevier B.V. All rights reserved.
Detecting abrupt dynamic change based on changes in the fractal properties of spatial images
Liu, Qunqun; He, Wenping; Gu, Bin; Jiang, Yundi
2017-10-01
Many abrupt climate change events often cannot be detected timely by conventional abrupt detection methods until a few years after these events have occurred. The reason for this lag in detection is that abundant and long-term observational data are required for accurate abrupt change detection by these methods, especially for the detection of a regime shift. So, these methods cannot help us understand and forecast the evolution of the climate system in a timely manner. Obviously, spatial images, generated by a coupled spatiotemporal dynamical model, contain more information about a dynamic system than a single time series, and we find that spatial images show the fractal properties. The fractal properties of spatial images can be quantitatively characterized by the Hurst exponent, which can be estimated by two-dimensional detrended fluctuation analysis (TD-DFA). Based on this, TD-DFA is used to detect an abrupt dynamic change of a coupled spatiotemporal model. The results show that the TD-DFA method can effectively detect abrupt parameter changes in the coupled model by monitoring the changing in the fractal properties of spatial images. The present method provides a new way for abrupt dynamic change detection, which can achieve timely and efficient abrupt change detection results.
Fractal structures in two-metal electrodeposition systems I: Pb and Zn
International Nuclear Information System (INIS)
Nakouzi, Elias; Sultan, Rabih
2011-01-01
Pattern formation in two-metal electrochemical deposition has been scarcely explored in the chemical literature. In this paper, we report new experiments on zinc-lead fractal co-deposition. Electrodeposits are grown in special cells at a fixed large value of the zinc ion concentration, while that of the lead ion is increased gradually. A very wide diversity of morphologies are obtained and classified. Most of the deposited domains are almost exclusively Pb or Zn. But certain regions originating at the base cathode, ranging from a short grass alley to dense, grown-up bushes or shrubs, manifest a combined Pb-Zn composition. Composition is determined using scanning electron microscopy/energy dispersive x ray measurements as well atomic absorption spectroscopy. Pb domains are characterized by shiny leaf-like and dense deposits as well as flowers with round, balloon-like corollas. The Zn zones display a greater variety of morphologies such as thick trunks and thin and fine branching, in addition to minute ''cigar flower'' structures. The various morphologies are analyzed and classified from the viewpoint of fractal nature, characterized by the box-count fractal dimension. Finally, macroscopic spatial alternation between two different characteristic morphologies is observed under certain conditions.
Long-Range Order and Fractality in the Structure and Organization of Eukaryotic Genomes
Polychronopoulos, Dimitris; Tsiagkas, Giannis; Athanasopoulou, Labrini; Sellis, Diamantis; Almirantis, Yannis
2014-12-01
The late Professor J.S. Nicolis always emphasized, both in his writings and in presentations and discussions with students and friends, the relevance of a dynamical systems approach to biology. In particular, viewing the genome as a "biological text" captures the dynamical character of both the evolution and function of the organisms in the form of correlations indicating the presence of a long-range order. This genomic structure can be expressed in forms reminiscent of natural languages and several temporal and spatial traces l by the functioning of dynamical systems: Zipf laws, self-similarity and fractality. Here we review several works of our group and recent unpublished results, focusing on the chromosomal distribution of biologically active genomic components: Genes and protein-coding segments, CpG islands, transposable elements belonging to all major classes and several types of conserved non-coding genomic elements. We report the systematic appearance of power-laws in the size distribution of the distances between elements belonging to each of these types of functional genomic elements. Moreover, fractality is also found in several cases, using box-counting and entropic scaling.We present here, for the first time in a unified way, an aggregative model of the genomic dynamics which can explain the observed patterns on the grounds of known phenomena accompanying genome evolution. Our results comply with recent findings about a "fractal globule" geometry of chromatin in the eukaryotic nucleus.
Fast hybrid fractal image compression using an image feature and neural network
International Nuclear Information System (INIS)
Zhou Yiming; Zhang Chao; Zhang Zengke
2008-01-01
Since fractal image compression could maintain high-resolution reconstructed images at very high compression ratio, it has great potential to improve the efficiency of image storage and image transmission. On the other hand, fractal image encoding is time consuming for the best matching search between range blocks and domain blocks, which limits the algorithm to practical application greatly. In order to solve this problem, two strategies are adopted to improve the fractal image encoding algorithm in this paper. Firstly, based on the definition of an image feature, a necessary condition of the best matching search and FFC algorithm are proposed, and it could reduce the search space observably and exclude most inappropriate domain blocks according to each range block before the best matching search. Secondly, on the basis of FFC algorithm, in order to reduce the mapping error during the best matching search, a special neural network is constructed to modify the mapping scheme for the subblocks, in which the pixel values fluctuate greatly (FNFC algorithm). Experimental results show that the proposed algorithms could obtain good quality of the reconstructed images and need much less time than the baseline encoding algorithm
Spectral Analysis and Dirichlet Forms on Barlow-Evans Fractals
Steinhurst, Benjamin; Teplyaev, Alexander
2012-01-01
We show that if a Barlow-Evans Markov process on a vermiculated space is symmetric, then one can study the spectral properties of the corresponding Laplacian using projective limits. For some examples, such as the Laakso spaces and a Spierpinski P\\^ate \\`a Choux, one can develop a complete spectral theory, including the eigenfunction expansions that are analogous to Fourier series. Also, one can construct connected fractal spaces isospectral to the fractal strings of Lapidus and van Frankenhu...
The Validity of Dimensional Regularization Method on Fractal Spacetime
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Yong Tao
2013-01-01
Full Text Available Svozil developed a regularization method for quantum field theory on fractal spacetime (1987. Such a method can be applied to the low-order perturbative renormalization of quantum electrodynamics but will depend on a conjectural integral formula on non-integer-dimensional topological spaces. The main purpose of this paper is to construct a fractal measure so as to guarantee the validity of the conjectural integral formula.
Gap sequence, Lipschitz equivalence and box dimension of fractal sets
International Nuclear Information System (INIS)
Rao Hui; Yang Yamin; Ruan Huojun
2008-01-01
We introduce a notion of gap sequences for compact sets E subset of R d , which is a generalization of the gap sequences of compact sets on the real line. We show that if the gap sequences of two fractal sets are not equivalent, then these two sets cannot be Lipschitz equivalent, where the latter fact is usually very hard to verify. Finally, we show that for some typical fractal sets, the gap sequences characterize the upper box dimension
Factorial moment and fractal analysis of γ families
International Nuclear Information System (INIS)
Kalmakhelidze, M.Eh.; Roinishvili, N.N.; Svanidze, M.S.; Khizanishvili, L.A.; Chadranyan, L.Kh.
1997-01-01
Factorial and fractal methods were applied to nuclear-electromagnetic cascades in the atmosphere (γ families) to find sensitivity of these methods to multiparticle fluctuations in γ families. Averaged parameters of factorial and fractal methods of the real families were compared with the same quantities for the statistical set of random families. The correlations between the same parameters for families divided into sectors and into rings are studied. The correlations between different parameters for the same families divided into sectors are investigated
Random a-adic groups and random net fractals
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Li Yin [Department of Mathematics, Nanjing University, Nanjing 210093 (China)], E-mail: Lyjerry7788@hotmail.com; Su Weiyi [Department of Mathematics, Nanjing University, Nanjing 210093 (China)], E-mail: suqiu@nju.edu.cn
2008-08-15
Based on random a-adic groups, this paper investigates the relationship between the existence conditions of a positive flow in a random network and the estimation of the Hausdorff dimension of a proper random net fractal. Subsequently we describe some particular random fractals for which our results can be applied. Finally the Mauldin and Williams theorem is shown to be very important example for a random Cantor set with application in physics as shown in E-infinity theory.
Nonlinear internal friction, chaos, fractal and musical instruments
International Nuclear Information System (INIS)
Sun, Z.Q.; Lung, C.W.
1995-08-01
Nonlinear and structure sensitive internal friction phenomena in materials are used for characterizing musical instruments. It may be one of the most important factors influencing timbre of instruments. As a nonlinear dissipated system, chaos and fractals are fundamental peculiarities of sound spectra. It is shown that the concept of multi range fractals can be used to decompose the frequency spectra of melody. New approaches are suggested to improve the fabrication, property characterization and physical understanding of instruments. (author). 18 refs, 4 figs
Institute of Scientific and Technical Information of China (English)
Yili Wang; Emilie Dieude-Fauvel; Steven K Dentel
2011-01-01
The changes in the physical characteristics of unconditioned and conditioned anaerobic digested sludge (ADS) biosolids,such as capillary suction time (CST),yield stress,average size and fractal dimensions,were investigated through a CST test,transient and dynamic rheological test and image analysis.The results showed that the optimum polymer dose range was observed when CST or its reciprocal value was employed as an indicator.There were good correlations between the yield stresses determined from both a controlled shear stress test and a strain amplitude sweep test.The yield stress and storage modulus (G') increased as the polymer dose increased in most cases.A frequency sweep test revealed that polymer conditioning could extend the frequency sweep ranges for their elastic behaviors over viscous behaviors as well as the gel-like structure in the linear viscoelastic range.These results implied that more deformation energy was stored in this rigid structure,and that elastic behavior became increasingly dominant with the addition of the polymer in most cases.In addition,both the average sizes and two-dimensional fractal dimensions for conditioned ADS biosolids presented a similar up-climax-down variation trend as the polymer doses increased,whereas the critical polymer doses at the highest average sizes or two-dimensional fractal dimensions,were different.Correlation analysis revealed that the conditioned ADS dewaterability was not correlated with the yield stresses,while the average sizes or the two-dimensional fractal dimensions for conditioned ADS biosolids could be taken as the indication parameters for ADS dewaterability.
Texture segmentation of non-cooperative spacecrafts images based on wavelet and fractal dimension
Wu, Kanzhi; Yue, Xiaokui
2011-06-01
With the increase of on-orbit manipulations and space conflictions, missions such as tracking and capturing the target spacecrafts are aroused. Unlike cooperative spacecrafts, fixing beacons or any other marks on the targets is impossible. Due to the unknown shape and geometry features of non-cooperative spacecraft, in order to localize the target and obtain the latitude, we need to segment the target image and recognize the target from the background. The data and errors during the following procedures such as feature extraction and matching can also be reduced. Multi-resolution analysis of wavelet theory reflects human beings' recognition towards images from low resolution to high resolution. In addition, spacecraft is the only man-made object in the image compared to the natural background and the differences will be certainly observed between the fractal dimensions of target and background. Combined wavelet transform and fractal dimension, in this paper, we proposed a new segmentation algorithm for the images which contains complicated background such as the universe and planet surfaces. At first, Daubechies wavelet basis is applied to decompose the image in both x axis and y axis, thus obtain four sub-images. Then, calculate the fractal dimensions in four sub-images using different methods; after analyzed the results of fractal dimensions in sub-images, we choose Differential Box Counting in low resolution image as the principle to segment the texture which has the greatest divergences between different sub-images. This paper also presents the results of experiments by using the algorithm above. It is demonstrated that an accurate texture segmentation result can be obtained using the proposed technique.
Experimental study of circle grid fractal pattern on turbulent intensity in pipe flow
International Nuclear Information System (INIS)
Manshoor, B; Zaman, I; Othman, M F; Khalid, Amir
2013-01-01
Fractal turbulence is deemed much more efficient than grid turbulence in terms of a turbulence generation. In this paper, the hotwire experimental results for the circle grids fractal pattern as a turbulent generator will be presented. The self-similar edge characteristic of the circle grid fractal pattern is thought to play a vital role in the enhancement of turbulent intensity. Three different beta ratios of perforated plates based on circle grids fractal pattern were used in the experimental work and each paired with standard circle grids with similar porosity. The objectives were to study the fractal scaling influence on the flow and also to explore the potential of the circle grids fractal pattern in enhancing the turbulent intensity. The results provided an excellent insight of the fractal generated turbulence and the fractal flow physics. Across the circle grids fractal pattern, the pressure drop was lower but the turbulent intensity was higher than those across the paired standard circle grids
Weerdt, de Wallie H.
1981-01-01
The historical background of the taxonomic problems in the fire-coral, Millepora, is reviewed. The growth forms of the Caribbean species: Millepora alcicornis Linnaeus, M. complanata Lamarck and M. squarrosa Lamarck are investigated in relation with environmental factors: water movement, current,
Growth of the human lens in the Indian adult population: Preliminary observations
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Ashik Mohamed
2012-01-01
Full Text Available Context: The eye lens grows throughout life by the addition of new cells inside the surrounding capsule. How this growth affects the properties of the lens is essential for understanding disorders such as cataract and presbyopia. Aims: To examine growth of the human lens in the Indian population and compare this with the growth in Western populations by measuring in vitro dimensions together with wet and dry weights. Settings and Design: The study was conducted at the research wing of a tertiary eye care center in South India and the study design was prospective. Materials and Methods: Lenses were removed from eye bank eyes and their dimensions measured with a digital caliper. They were then carefully blotted dry and weighed before being placed in 5% buffered formalin. After 1 week fixation, the lenses were dried at 80 °C until constant weight was achieved. The constant weight was noted as the dry weight of the lens. Statistical Analysis Used: Lens parameters were analyzed as a function of age using linear and logarithmic regression methods. Results: Data were obtained for 251 lenses, aged 16-93 years, within a median postmortem time of 22 h. Both wet and dry weights increased linearly at 1.24 and 0.44 mg/year, respectively, throughout adult life. The dimensions also increased continuously throughout this time. Conclusions: Over the age range examined, lens growth in the Indian population is very similar to that in Western populations.
Pivovarova, Margarita; Amrein-Beardsley, Audrey
2018-01-01
While states are no longer required to set up teacher evaluation systems based in significant part on student test scores, quite a few continue to use value-added (VAMs) or student growth percentile (SGP) models for that purpose. In this study, we analyzed three years of teacher data to illustrate the performance of teachers' median growth…
Exploring the relationship between fractal features and bacterial essential genes
International Nuclear Information System (INIS)
Yu Yong-Ming; Yang Li-Cai; Zhao Lu-Lu; Liu Zhi-Ping; Zhou Qian
2016-01-01
Essential genes are indispensable for the survival of an organism in optimal conditions. Rapid and accurate identifications of new essential genes are of great theoretical and practical significance. Exploring features with predictive power is fundamental for this. Here, we calculate six fractal features from primary gene and protein sequences and then explore their relationship with gene essentiality by statistical analysis and machine learning-based methods. The models are applied to all the currently available identified genes in 27 bacteria from the database of essential genes (DEG). It is found that the fractal features of essential genes generally differ from those of non-essential genes. The fractal features are used to ascertain the parameters of two machine learning classifiers: Naïve Bayes and Random Forest. The area under the curve (AUC) of both classifiers show that each fractal feature is satisfactorily discriminative between essential genes and non-essential genes individually. And, although significant correlations exist among fractal features, gene essentiality can also be reliably predicted by various combinations of them. Thus, the fractal features analyzed in our study can be used not only to construct a good essentiality classifier alone, but also to be significant contributors for computational tools identifying essential genes. (paper)
Heterogeneity of cerebral blood flow: a fractal approach
International Nuclear Information System (INIS)
Kuikka, J.T.; Hartikainen, P.
2000-01-01
Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and single-photon emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (=coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17±0.05 (mean±SD) for the left hemisphere and 1.15±0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04±0.03 than in healthy controls. (orig.) [de
Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.
2010-01-01
The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103
Statistical properties and fractals of nucleotide clusters in DNA sequences
International Nuclear Information System (INIS)
Sun Tingting; Zhang Linxi; Chen Jin; Jiang Zhouting
2004-01-01
Statistical properties of nucleotide clusters in DNA sequences and their fractals are investigated in this paper. The average size of nucleotide clusters in non-coding sequence is larger than that in coding sequence. We investigate the cluster-size distribution P(S) for human chromosomes 21 and 22, and the results are different from previous works. The cluster-size distribution P(S 1 +S 2 ) with the total size of sequential Pu-cluster and Py-cluster S 1 +S 2 is studied. We observe that P(S 1 +S 2 ) follows an exponential decay both in coding and non-coding sequences. However, we get different results for human chromosomes 21 and 22. The probability distribution P(S 1 ,S 2 ) of nucleotide clusters with the size of sequential Pu-cluster and Py-cluster S 1 and S 2 respectively, is also examined. In the meantime, some of the linear correlations are obtained in the double logarithmic plots of the fluctuation F(l) versus nucleotide cluster distance l along the DNA chain. The power spectrums of nucleotide clusters are also discussed, and it is concluded that the curves are flat and hardly changed and the 1/3 frequency is neither observed in coding sequence nor in non-coding sequence. These investigations can provide some insights into the nucleotide clusters of DNA sequences
Observations of the severity of notch-root radius in initiation of subcritical crack growth
International Nuclear Information System (INIS)
Reuter, W.G.; Eiholzer, C.R.; Tupper, M.A.
1981-01-01
Slow bend tests were conducted on Charpy specimens containing precracks or machined notches of 0.10 or 0.25 mm radius. The test specimens were fabricated from three heats of annealed Type 304 stainless steel. The purpose of these tests was to examine the effects of notch root radius, in very ductile materials, on initiation of subcritical crack growth. In addition, it was intended to establish the critical values of J, COD, etc. for the single-edge notch specimen for comparison with results obtained from specimens containing surface flaws. This paper will briefly describe only those results of the calculation for J. The tests were monitored by acoustic emission to identify the load corresponding to initiation of subcritical crack growth, by a crack-opening displacement gage (COD), by cross-head displacement, and by stop-action photography
Observation of propane cluster size distributions during nucleation and growth in a Laval expansion
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Ferreiro, Jorge J.; Chakrabarty, Satrajit; Schläppi, Bernhard; Signorell, Ruth [Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog Weg 2, CH-8093 Zürich (Switzerland)
2016-12-07
We report on molecular-level studies of the condensation of propane gas and propane/ethane gas mixtures in the uniform (constant pressure and temperature) postnozzle flow of Laval expansions using soft single-photon ionization by vacuum ultraviolet light and mass spectrometric detection. The whole process, from the nucleation to the growth to molecular aggregates of sizes of several nanometers (∼5 nm), can be monitored at the molecular level with high time-resolution (∼3 μs) for a broad range of pressures and temperatures. For each time, pressure, and temperature, a whole mass spectrum is recorded, which allows one to determine the critical cluster size range for nucleation as well as the kinetics and mechanisms of cluster-size specific growth. The detailed information about the size, composition, and population of individual molecular clusters upon condensation provides unique experimental data for comparison with future molecular-level simulations.
2013-01-01
Complementary in situ X-ray photoelectron spectroscopy (XPS), X-ray diffractometry, and environmental scanning electron microscopy are used to fingerprint the entire graphene chemical vapor deposition process on technologically important polycrystalline Cu catalysts to address the current lack of understanding of the underlying fundamental growth mechanisms and catalyst interactions. Graphene forms directly on metallic Cu during the high-temperature hydrocarbon exposure, whereby an upshift in the binding energies of the corresponding C1s XPS core level signatures is indicative of coupling between the Cu catalyst and the growing graphene. Minor carbon uptake into Cu can under certain conditions manifest itself as carbon precipitation upon cooling. Postgrowth, ambient air exposure even at room temperature decouples the graphene from Cu by (reversible) oxygen intercalation. The importance of these dynamic interactions is discussed for graphene growth, processing, and device integration. PMID:24041311
Shih, Po-Hsun; Wu, Sheng Yun
2017-07-21
Plenty of studies have been performed to probe the diverse properties of ZnO nanowires, but only a few have focused on the physical properties of a single nanowire since analyzing the growth mechanism along a single nanowire is difficult. In this study, a single ZnO nanowire was synthesized using a Ti-assisted chemical vapor deposition (CVD) method to avoid the appearance of catalytic contamination. Two-dimensional energy dispersive spectroscopy (EDS) mapping with a diffusion model was used to obtain the diffusion length and the activation energy ratio. The ratio value is close to 0.3, revealing that the growth of ZnO nanowires was attributed to the short-circuit diffusion.
Svatoš, Vojtěch; Gablech, Imrich; Ilic, B. Robert; Pekárek, Jan; Neužil, Pavel
2018-03-01
Carbon nanotubes (CNTs) have near unity infrared (IR) absorption efficiency, making them extremely attractive for IR imaging devices. Since CNT growth occurs at elevated temperatures, the integration of CNTs with IR imaging devices is challenging and has not yet been achieved. Here, we show a strategy for implementing CNTs as IR absorbers using differential heating of thermally isolated microbolometer membranes in a C2H2 environment. During the process, CNTs were catalytically grown on the surface of a locally heated membrane, while the substrate was maintained at an ambient temperature. CNT growth was monitored in situ in real time using optical microscopy. During growth, we measured the intensity of light emission and the reflected light from the heated microbolometer. Our measurements of bolometer performance show that the CNT layer on the surface of the microbolometer membrane increases the IR response by a factor of (2.3 ± 0.1) (mean ± one standard deviation of the least-squares fit parameters). This work opens the door to integrating near unity IR absorption, CNT-based, IR absorbers with hybrid complementary metal-oxide-semiconductor focal plane array architectures.
In situ observations of the atomistic mechanisms of Ni catalyzed low temperature graphene growth.
Patera, Laerte L; Africh, Cristina; Weatherup, Robert S; Blume, Raoul; Bhardwaj, Sunil; Castellarin-Cudia, Carla; Knop-Gericke, Axel; Schloegl, Robert; Comelli, Giovanni; Hofmann, Stephan; Cepek, Cinzia
2013-09-24
The key atomistic mechanisms of graphene formation on Ni for technologically relevant hydrocarbon exposures below 600 °C are directly revealed via complementary in situ scanning tunneling microscopy and X-ray photoelectron spectroscopy. For clean Ni(111) below 500 °C, two different surface carbide (Ni2C) conversion mechanisms are dominant which both yield epitaxial graphene, whereas above 500 °C, graphene predominantly grows directly on Ni(111) via replacement mechanisms leading to embedded epitaxial and/or rotated graphene domains. Upon cooling, additional carbon structures form exclusively underneath rotated graphene domains. The dominant graphene growth mechanism also critically depends on the near-surface carbon concentration and hence is intimately linked to the full history of the catalyst and all possible sources of contamination. The detailed XPS fingerprinting of these processes allows a direct link to high pressure XPS measurements of a wide range of growth conditions, including polycrystalline Ni catalysts and recipes commonly used in industrial reactors for graphene and carbon nanotube CVD. This enables an unambiguous and consistent interpretation of prior literature and an assessment of how the quality/structure of as-grown carbon nanostructures relates to the growth modes.
Naturaleza fractal en redes de cristales de grasas
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Gómez Herrera, C.
2004-06-01
Full Text Available The determination of the mechanical and rheological characterisÂtics of several plastic fats requires a detailed understanding of the microstructure of the fat crystal network aggregates. The (or A fractal approach is useful for the characterization of this microsÂtructure. This review begins with information on fractality and statistical self-similar structure. Estimations for fractal dimension by means of equations relating the volume fraction of solid fat to shear elastic modulus G' in linear region are described. The influence of interesterification on fractal dimension decrease (from 2, 46 to 2 ,15 for butterfat-canola oil blends is notable . This influence is not significant for fat blends without butterfat. The need for an increase in research concerning the relationship between fractality and rheology in plastic fats is emphasized.La determinación de las características mecánicas y reológicas de ciertas grasas plásticas requiere conocimientos detallados sobre las microestructuras de los agregados que forman la red de cristales grasos. El estudio de la naturaleza fractal de estas microestructuras resulta útil para su caracÂterización. Este artículo de información se inicia con descripciones de la dimensión fractal y de la "autosimilitud estadística". A continuación se describe el cálculo de la dimensión fractal mediante ecuaciones que relacionan la fracción en volumen de grasa sólida con el módulo de recuperación (G' dentro de un comportamiento viscoelástico lineal. Se destaca la influencia que la interesterificación ejerce sobre la dimensión fractal de una mezcla de grasa láctea y aceite de canola (que pasa de 2,64 a 2,15. Esta influencia no se presenta en mezclas sin grasa láctea. Se insiste sobre la necesidad de incrementar las investiÂgaciones sobre la relación entre reología y estructura fractal en grasas plásticas.
Fu, Yanshu; Qiu, Yaohui; Li, Yulong
2018-05-01
The mechanical anisotropy of an explosive welding composite plate made of 304 stainless steel/245 steel was studied through shear experiments performed on explosively welded wavy interfaces along several orientation angles. The results indicated that the strength and the fracture energy of samples significantly varied with the orientation angles. The fracture surfaces of all samples were observed using a scanning electron microscope and through three-dimensional structure microscopy. The periodic features of all the fracture surfaces were clearly shown in different fracture modes. The fractal dimension of the fracture surfaces was calculated based on the fractal geometry by the box-counting method in MATLAB. The cohesive element model was used to analyze the fracture energy according to the physical dependence of the fractal dimension on thermodynamic entropy and interface separation energy. The fracture energy was an exponential function of the fractal dimension value, which was in good agreement with the experimental results. All results were validated for effective use in the application of anisotropy analysis to the welded interface and structural optimization of explosively welded composite plates.
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Fajar Perdhana
2016-09-01
Full Text Available Ventilator-associated pneumonia (VAP remains a problem with the highest cos, morbidity and mortalityt in the Intensive Care Unit (ICU. The correlation between mechanical ventilation and pneumonia is considered as common sense, yet scientific evidence to support this statement is still needed. This research aims to analyze the bacterial colony grows in mechanical ventilation circuit and those grew in the patient’s sputum culture. We performed an observational study. Samples for bacterial culture were taken from ventilator circuit and patient sputum on Day-0, Day-3 and Day-7. Sputum samplings are collected using double catheter tracheal aspiration technique; Results are then analyzed with Chi-square test. While the similarity of bacteria species in ventilator circuit to patient’s sputum is analyzed with Binomial test. Two samples are dropped out immediately due to the rate of bacterial growth on Day-0. Bacterial colony growth in ventilator circuit shows a significant difference on Day-3 and Day-7 at 50% and 92% respectively (p = 0.05. A comparison for the bacterial similarity of the ventilator circuit and patient’s sputum shows that the bacterial growth on Day-3 is 7 out of 14 (50% and 3 with more than 105 CFU/ml colony; while on Day-7, there are 13 out of 14 positive bacterial growth, both in the circuit and the patient’s sputum. Among them, 5 out of 14 (35% of the bacterial colony which grow in the circuit have the same species as those grow in patient’s sputum. The recent study shows that there is bacteria colony growth in the ventilator circuit after Day-3 and a significant increase on Day-7. Almost half of the colony illustrates similar species from both ventilator circuit and patient’s sputum. This suggests that the bacterial growth on Day-7 in the ventilator circuit might be related to those growth in patient’s sputum.
Yu, Huan; Dai, Liang; Zhao, Yi; Kanawade, Vijay P.; Tripathi, Sachchida N.; Ge, Xinlei; Chen, Mindong; Lee, Shan-Hu
2017-02-01
Temperature and relative humidity (RH) are the most important thermodynamic parameters in aerosol formation, yet laboratory studies of nucleation and growth dependencies on temperature and RH are lacking. Here we report the experimentally observed temperature and RH dependences of sulfuric acid aerosol nucleation and growth. Experiments were performed in a flow tube in the temperature range from 248 to 313 K, RH from 0.8% to 79%, and relative acidity (RA) of sulfuric acid from 6 × 10-5 to 0.38 (2 × 107-109 cm-3). The impurity levels of base compounds were determined to be NH3 nucleation at fixed sulfuric acid concentration but impede nucleation when RA is fixed. It is also shown that binary nucleation of sulfuric acid and water is negligible in planetary boundary layer temperature and sulfuric acid ranges. An empirical algorithm was derived to correlate the nucleation rate with RA, RH, and temperature together. Collision-limited condensation of free-sulfuric acid molecules fails to predict the observed growth rate in the sub-3 nm size range, as well as its dependence on temperature and RH. This suggests that evaporation, sulfuric acid hydration, and possible involvement of other ternary molecules should be considered for the sub-3 nm particle growth.
Multi-fractal analysis and lacunarity spectrum of the dark matter haloes in the SDSS-DR7
International Nuclear Information System (INIS)
Chacón-Cardona, C.A.; Casas-Miranda, R.A.; Muñoz-Cuartas, J.C.
2016-01-01
Highlights: • We analysed the dark matter in Seventh Data Release of the Sloan Digital Sky Survey. • From the initial sample with 412,468 galaxies, 339,505 dark matter haloes were used. • We found the multifractal and the lacunarity spectrum as radial distance function. • The dark matter set did not achieve at the physical dimension of the space. - Abstract: The dark matter halo distribution of the nearby universe is used to study the fractal behaviour in the proximate universe. The data, which is based on four volume-limited galaxy samples was obtained by Muñoz-Cuartas and Mueller (2012) from the Seventh Data Release of the Sloan Digital Sky Survey (SDSS-DR7). In order to know the fractal behaviour of the observed universe, from the initial sample which contains 412,468 galaxies and 339,505 dark matter haloes were used as input for the fractal calculations. Using this data we use the sliding-window technique for the dark matter distribution and compute the multi-fractal dimension and the lacunarity spectrum and use it to study its dependence on radial distance in every sample. The transition to homogeneity is not observed in the dark matter halo distribution obtained from the SDSS-DR7 volume-limited galaxy samples; in its place the dark matter halo distribution exhibits a persistent multi-fractal behaviour where the measured dimension does not arrive at the value of the physical dimension of the space, for all structure parameter values of the analysed set, at least up to radial distances of the ordered from 165 Mpc/h from the available centres of each sample. Our results and their implications are discussed in the context of the formation of large-scale structures in the universe.
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Jian Xiong
2015-01-01
Full Text Available We mainly focus on the Permian, Lower Cambrian, Lower Silurian, and Upper Ordovician Formation; the fractal dimensions of marine shales in southern China were calculated using the FHH fractal model based on the low-pressure nitrogen adsorption analysis. The results show that the marine shales in southern China have the dual fractal characteristics. The fractal dimension D1 at low relative pressure represents the pore surface fractal characteristics, whereas the fractal dimension D2 at higher relative pressure describes the pore structure fractal characteristics. The fractal dimensions D1 range from 2.0918 to 2.718 with a mean value of 2.4762, and the fractal dimensions D2 range from 2.5842 to 2.9399 with a mean value of 2.8015. There are positive relationships between fractal dimension D1 and specific surface area and total pore volume, whereas the fractal dimensions D2 have negative correlation with average pore size. The larger the value of the fractal dimension D1 is, the rougher the pore surface is, which could provide more adsorption sites, leading to higher adsorption capacity for gas. The larger the value of the fractal dimension D2 is, the more complicated the pore structure is, resulting in the lower flow capacity for gas.
Meseguer-Ruiz, Oliver; Osborn, Timothy J.; Sarricolea, Pablo; Jones, Philip D.; Cantos, Jorge Olcina; Serrano-Notivoli, Roberto; Martin-Vide, Javier
2018-03-01
Precipitation on the Spanish mainland and in the Balearic archipelago exhibits a high degree of spatial and temporal variability, regardless of the temporal resolution of the data considered. The fractal dimension indicates the property of self-similarity, and in the case of this study, wherein it is applied to the temporal behaviour of rainfall at a fine (10-min) resolution from a total of 48 observatories, it provides insights into its more or less convective nature. The methodology of Jenkinson & Collison which automatically classifies synoptic situations at the surface, as well as an adaptation of this methodology at 500 hPa, was applied in order to gain insights into the synoptic implications of extreme values of the fractal dimension. The highest fractal dimension values in the study area were observed in places with precipitation that has a more random behaviour over time with generally high totals. Four different regions in which the atmospheric mechanisms giving rise to precipitation at the surface differ from the corresponding above-ground mechanisms have been identified in the study area based on the fractal dimension. In the north of the Iberian Peninsula, high fractal dimension values are linked to a lower frequency of anticyclonic situations, whereas the opposite occurs in the central region. In the Mediterranean, higher fractal dimension values are associated with a higher frequency of the anticyclonic type and a lower frequency of the advective type from the east. In the south, lower fractal dimension values indicate higher frequency with respect to the anticyclonic type from the east and lower frequency with respect to the cyclonic type.
Persistent fluctuations in stride intervals under fractal auditory stimulation.
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Vivien Marmelat
Full Text Available Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.
Persistent fluctuations in stride intervals under fractal auditory stimulation.
Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J; Daffertshofer, Andreas
2014-01-01
Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.
Bony change of apical lesion healing process using fractal analysis
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Lee, Ji Min; Park, Hyok; Jeong, Ho Gul; Kim, Kee Deog; Park, Chang Seo [Yonsei University College of Medicine, Seoul (Korea, Republic of)
2005-06-15
To investigate the change of bone healing process after endodontic treatment of the tooth with an apical lesion by fractal analysis. Radiographic images of 35 teeth from 33 patients taken on first diagnosis, 6 months, and 1 year after endodontic treatment were selected. Radiographic images were taken by JUPITER computerized Dental X-ray System. Fractal dimensions were calculated three times at each area by Scion Image PC program. Rectangular region of interest (30 x 30) were selected at apical lesion and normal apex of each image. The fractal dimension at apical lesion of first diagnosis (L{sub 0}) is 0.940 {+-} 0.361 and that of normal area (N{sub 0}) is 1.186 {+-} 0.727 (p<0.05). Fractal dimension at apical lesion of 6 months after endodontic treatment (L{sub 1}) is 1.076 {+-} 0.069 and that of normal area (N{sub 1}) is 1.192 {+-} 0.055 (p<0.05). Fractal dimension at apical lesion of 1 year after endodontic treatment (L{sub 2}) is 1.163 {+-} 0.074 and that of normal area (N{sub 2}) is 1.225 {+-} 0.079 (p<0.05). After endodontic treatment, the fractal dimensions at each apical lesions depending on time showed statistically significant difference. And there are statistically significant different between normal area and apical lesion on first diagnosis, 6 months after, 1 year after. But the differences were grow smaller as time flows. The evaluation of the prognosis after the endodontic treatment of the apical lesion was estimated by bone regeneration in apical region. Fractal analysis was attempted to overcome the limit of subjective reading, and as a result the change of the bone during the healing process was able to be detected objectively and quantitatively.
Electronic confining effects in Sierpiński triangle fractals
Wang, Hao; Zhang, Xue; Jiang, Zhuoling; Wang, Yongfeng; Hou, Shimin
2018-03-01
Electron confinement in fractal Sierpiński triangles (STs) on Ag(111) is investigated using scanning tunneling spectroscopy and theoretically simulated by employing an improved two-dimensional (2D) multiple scattering theory in which the energy-dependent phase shifts are explicitly calculated from the electrostatic potentials of the molecular building block of STs. Well-defined bound surface states are observed in three kinds of triangular cavities with their sides changing at a scale factor of 2. The decrease in length of the cavities results in an upshift of the resonances that deviates from an expected inverse quadratic dependence on the cavity length due to the less efficient confinement of smaller triangular cavities. Differential conductance maps at some specific biases present a series of alternative bright and dark rounded triangles preserving the symmetry of the boundary. Our improved 2D multiple scattering model reproduces the characteristics of the standing wave patterns and all features in the differential conductance spectra measured in experiments, illustrating that the elastic loss boundary scattering dominates the resonance broadening in these ST quantum corrals. Moreover, the self-similar structure of STs, that a larger central cavity is surrounded by three smaller ones with a half side length, gives rise to interactions of surface states confined in neighboring cavities, which are helpful for the suppression of the linewidth in differential conductance spectra.