MEASURING THE FRACTAL STRUCTURE OF INTERSTELLAR CLOUDS

NARCIS (Netherlands)

VOGELAAR, MGR; WAKKER, BP

1994-01-01

To study the structure of interstellar matter we have applied the concept of fractal curves to the brightness contours of maps of interstellar clouds and from these estimated the fractal dimension for some of them. We used the so-called perimeter-area relation as the basis for these estimates. We

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.

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

Science.gov (United States)

Namazi, Hamidreza; Kulish, Vladimir V.; Akrami, Amin

2016-05-01

One of the major challenges in vision research is to analyze the effect of visual stimuli on human vision. However, no relationship has been yet discovered between the structure of the visual stimulus, and the structure of fixational eye movements. This study reveals the plasticity of human fixational eye movements in relation to the ‘complex’ visual stimulus. We demonstrated that the fractal temporal structure of visual dynamics shifts towards the fractal dynamics of the visual stimulus (image). The results showed that images with higher complexity (higher fractality) cause fixational eye movements with lower fractality. Considering the brain, as the main part of nervous system that is engaged in eye movements, we analyzed the governed Electroencephalogram (EEG) signal during fixation. We have found out that there is a coupling between fractality of image, EEG and fixational eye movements. The capability observed in this research can be further investigated and applied for treatment of different vision disorders.

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)

Reengineering through natural structures: the fractal factory

Science.gov (United States)

Sihn, Wilfried

1995-08-01

Many branches of European industry have had to recognize that their lead in the world market has been caught up with, particularly through Asian competition. In many cases a deficit of up to 30% in costs and productivity already exists. The reasons are rigid, Tayloristic company structures. The companies are not in a position to react flexibly to constantly changing environmental conditions. This article illustrates the methods of the `fractal company' which are necessary to solve the structure crisis. The fractal company distinguishes itself through its dynamics and its vitality, as well as its independent reaction to the changing circumstances. The developed methods, procedures, and framework conditions such as company structuring, human networking, hierarchy formation, and models for renumeration and working time are explained. They are based on practical examples from IPA's work with the automobile industry, their suppliers, and the engineering industry.

Fractal Bread.

Science.gov (United States)

Esbenshade, Donald H., Jr.

1991-01-01

Develops the idea of fractals through a laboratory activity that calculates the fractal dimension of ordinary white bread. Extends use of the fractal dimension to compare other complex structures as other breads and sponges. (MDH)

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

International Nuclear Information System (INIS)

Pyun, Su-Il; Rhee, Chang-Kyu

2004-01-01

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

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 patterns on the onset of coherent structures in a coupled map ...

Indian Academy of Sciences (India)

We report the formation of Cantor set-like fractals during the development of coherent structures in a coupled map lattice (CML). The dependence of these structures on the size of the lattice as well as the first three dimensions of the associated fractal patterns are analyzed numerically.

Analysis of a Model for the Morphological Structure of Renal Arterial Tree: Fractal Structure

Directory of Open Access Journals (Sweden)

Aurora Espinoza-Valdez

2013-01-01

experimental data measurements of the rat kidneys. The fractal dimension depends on the probability of sprouting angiogenesis in the development of the arterial vascular tree of the kidney, that is, of the distribution of blood vessels in the morphology generated by the analytical model. The fractal dimension might determine whether a suitable renal vascular structure is capable of performing physiological functions under appropriate conditions. The analysis can describe the complex structures of the development vasculature in kidney.

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

Stochastic Erosion of Fractal Structure in Nonlinear Dynamical Systems

Science.gov (United States)

Agarwal, S.; Wettlaufer, J. S.

2014-12-01

We analyze the effects of stochastic noise on the Lorenz-63 model in the chaotic regime to demonstrate a set of general issues arising in the interpretation of data from nonlinear dynamical systems typical in geophysics. The model is forced using both additive and multiplicative, white and colored noise and it is shown that, through a suitable choice of the noise intensity, both additive and multiplicative noise can produce similar dynamics. We use a recently developed measure, histogram distance, to show the similarity between the dynamics produced by additive and multiplicative forcing. This phenomenon, in a nonlinear fractal structure with chaotic dynamics can be explained by understanding how noise affects the Unstable Periodic Orbits (UPOs) of the system. For delta-correlated noise, the UPOs erode the fractal structure. In the presence of memory in the noise forcing, the time scale of the noise starts to interact with the period of some UPO and, depending on the noise intensity, stochastic resonance may be observed. This also explains the mixing in dissipative dynamical systems in presence of white noise; as the fractal structure is smoothed, the decay of correlations is enhanced, and hence the rate of mixing increases with noise intensity.

Fractal 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)

Modeling the self-affine structure and optimization conditions of city systems using the idea from fractals

International Nuclear Information System (INIS)

Chen Yanguang; Lin Jingyi

2009-01-01

This paper demonstrates self-affine fractal structure of city systems by means of theoretical and empirical analyses. A Cobb-Douglas-type function (C-D function) of city systems is derived from a general urban response equation, and the partial scaling exponent of the C-D function proved to be the fractal dimension reflecting the self-affine features of city systems. As a case, the self-affine fractal model is applied to the city of Zhengzhou, China, and the result is satisfying. A fractal parameter equation indicative of structural optimization conditions is then obtained from the C-D function. The equation suggests that priority should be given to the development of the urban element with a lower fractal dimension, or a higher partial scaling exponent, for utility maximization. Moreover, the fractal dimensions of different urban elements tend to become equivalent to each other in the long term. Accordingly, it is self-similar fractals rather than self-affine fractals that represent the optimal structure of city systems under ideal conditions.

The distribution function of a probability measure on a space with a fractal structure

Energy Technology Data Exchange (ETDEWEB)

Sanchez-Granero, M.A.; Galvez-Rodriguez, J.F.

2017-07-01

In this work we show how to define a probability measure with the help of a fractal structure. One of the keys of this approach is to use the completion of the fractal structure. Then we use the theory of a cumulative distribution function on a Polish ultrametric space and describe it in this context. Finally, with the help of fractal structures, we prove that a function satisfying the properties of a cumulative distribution function on a Polish ultrametric space is a cumulative distribution function with respect to some probability measure on the space. (Author)

Experimental modal analysis of fractal-inspired multi-frequency structures for piezoelectric energy converters

International Nuclear Information System (INIS)

Castagnetti, D

2012-01-01

An important issue in the field of energy harvesting through piezoelectric materials is the design of simple and efficient structures which are multi-frequency in the ambient vibration range. This paper deals with the experimental assessment of four fractal-inspired multi-frequency structures for piezoelectric energy harvesting. These structures, thin plates of square shape, were proposed in a previous work by the author and their modal response numerically analysed. The present work has two aims. First, to assess the modal response of these structures through an experimental investigation. Second, to evaluate, through computational simulation, the performance of a piezoelectric converter relying on one of these fractal-inspired structures. The four fractal-inspired structures are examined in the range between 0 and 100 Hz, with regard to both eigenfrequencies and eigenmodes. In the same frequency range, the modal response and power output of the piezoelectric converter are investigated. (paper)

Coder and decoder of fractal signals of comb-type structure

Directory of Open Access Journals (Sweden)

Politanskyi R. L.

2014-08-01

Full Text Available The article presents a coder and decoder of fractal signals of comb-type structure (FSCS based on microcontrollers (MC. The coder and decoder consist of identical control modules, while their managed modules have different schematic constructions. The control module performs forming or recognition of signals, and also carries out the function of information exchange with a computer. The basic element of the control module is a PIC18F2550 microcontroller from MicroChip. The coder of the system forms fractal signals of a given order according to the information bits coming from the computer. Samples of the calculated values of the amplitudes of elementary rectangular pulses that constitute the structure of fractal pulses are stored in the memory of the microcontroller as a table. Minimum bit capacity of the DAC necessary for the generation of FSCS of fourth order is four bits. The operation algorithm, "wired" into the controller of the program, provides for encoding of the transmitted information by two-bit symbols. Recognition of the start of transmission of each byte in communication channel is performed by the transmission of the timing signal. In a decoder the microcontroller carries out reception and decoding of the received fractal signals which are then transmitted to the computer. The developed algorithm of the program for the microcontroller of the decoder is carried out by determination of order of fractal impulse after the value of sum of amplitudes of elementary impulses, constituents fractal signal. The programs for coder and decoder are written in "C". In the most critical places of the program influencing on the fast-acting of chart “assembler” insertions are done. The blocks of the coder and decoder were connected with a coaxial 10 meters long cable with an impendance of 75 Ohm. The signals generated by the developed coder of FSCS, were studied using a digital oscillograph. On the basis of the obtained spectrums, it is possible

Chlordecone retention in the fractal structure of volcanic clay

International Nuclear Information System (INIS)

Woignier, Thierry; Clostre, Florence; Macarie, Hervé; Jannoyer, Magalie

2012-01-01

Highlights: ► Allophanic soils are highly polluted but less contaminant for cultivated vegetables. ► SAXS and TEM show the fractal structure of allophane aggregates at the nanoscale. ► Allophane aggregates play the role of a labyrinth which fixes and traps chlordecone. ► Allophane physical properties contribute to chlordecone retention in andosols. - Abstract: Chlordecone (CHLD), a soil and foodstuff pollutant, as well as an environmentally persistent organochlorine insecticide, was used intensively in banana fields. The chlordecone uptake of three crops was measured for two types of polluted soils: allophanic and non-allophanic. The uptake is lower for allophanic soils even if their chlordecone content is higher than with non-allophanic soils. The fractal structure of the allophane aggregates was characterized at the nanoscale by small angle X-rays scattering, pore size distribution and transmission electron microscopy. We showed that clay microstructures should be an important physico-chemical factor governing the fate of chlordecone in the environment. Allophanic clays result in two counterintuitive findings: higher contaminant trappings yet lower contaminant availability. We propose that this specific, tortuous structure, along with its associated low accessibility, partly explains the low availability of chlordecone confined in allophanic soils. Capsule The fractal and tortuous microstructure of allophane clay favours the chlordecone retention in soils and disfavours the crop uptake.

Ag nanoparticles formed by femtosecond pulse laser ablation in water: self-assembled fractal structures

Energy Technology Data Exchange (ETDEWEB)

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.

Evolution of atomic-scale surface structures during ion bombardment: A fractal simulation

International Nuclear Information System (INIS)

Shaheen, M.A.; Ruzic, D.N.

1993-01-01

Surfaces of interest in microelectronics have been shown to exhibit fractal topographies on the atomic scale. A model utilizing self-similar fractals to simulate surface roughness has been added to the ion bombardment code TRIM. The model has successfully predicted experimental sputtering yields of low energy (less then 1000 eV) Ar on Si and D on C using experimentally determined fractal dimensions. Under ion bombardment the fractal surface structures evolve as the atoms in the collision cascade are displaced or sputtered. These atoms have been tracked and the evolution of the surface in steps of one monolayer of flux has been determined. The Ar--Si system has been studied for incidence energies of 100 and 500 eV, and incidence angles of 0 degree, 30 degree, and 60 degree. As expected, normally incident ion bombardment tends to reduce the roughness of the surface, whereas large angle ion bombardment increases the degree of surface roughness. Of particular interest though, the surfaces are still locally self-similar fractals after ion bombardment and a steady state fractal dimension is reached, except at large angles of incidence

Irreducible fractal structures for Moran's theorems

Energy Technology Data Exchange (ETDEWEB)

Fernandez-Martinez, M.; Sanchez-Granero, M.A.

2017-07-01

Along this talk, we shall deal with a classical problem in Fractal Geometry consisting of the calculation of the similarity dimension of self-similar sets. Clasically, the open set condition has been understood as the right separation condition for IFS-attractors since it becomes a sufficient (though not necessary) condition allowing to easily calculate their similarity dimensions. However, it depends on an external open set. Our contribution consists of a novel separation condition for self-similar sets we shall characterize in terms of the natural fractal structure which any IFS-attractor can be endowed with. We justify that such a separation condition is weaker than the strong open set condition and allows to prove some Moran's type theorems. (Author)

Fractal dust grains in plasma

International Nuclear Information System (INIS)

Huang, F.; Peng, R. D.; Liu, Y. H.; Chen, Z. Y.; Ye, M. F.; Wang, L.

2012-01-01

Fractal dust grains of different shapes are observed in a radially confined magnetized radio frequency plasma. The fractal dimensions of the dust structures in two-dimensional (2D) horizontal dust layers are calculated, and their evolution in the dust growth process is investigated. It is found that as the dust grains grow the fractal dimension of the dust structure decreases. In addition, the fractal dimension of the center region is larger than that of the entire region in the 2D dust layer. In the initial growth stage, the small dust particulates at a high number density in a 2D layer tend to fill space as a normal surface with fractal dimension D = 2. The mechanism of the formation of fractal dust grains is discussed.

The crack energy absorptive capacity of composites with fractal structure

International Nuclear Information System (INIS)

Lung, C.W.

1990-11-01

This paper discusses the energy absorptive capacity of composites with fibers of fractal structures. It is found that this kind of structure may increase the absorption energy during the crack propagation and hence the fracture toughness of composites. (author). 10 refs, 6 figs, 2 tabs

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

The correlation of fractal structures in the photospheric and the coronal magnetic field

Science.gov (United States)

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

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 structure formation on the surfaces of solids subjected to high intensity electron and ion treatment

International Nuclear Information System (INIS)

Altajskij, M.V.; Ivanov, V.V.; Korenev, S.A.; Orelovich, O.L.; Puzynin, I.V.; Chernik, V.V.

1997-01-01

We discuss the results of scanning electron microscopy of surfaces of the solids subjected to high intensity electron and ion beam treatment. The appearance of fractal structures on the modified surfaces is shown. The fractal dimensions of these structures were estimated by box-counting algorithm

Quantum Fractal Eigenstates

OpenAIRE

Casati, Giulio; Maspero, Giulio; Shepelyansky, Dima L.

1997-01-01

We study quantum chaos in open dynamical systems and show that it is characterized by quantum fractal eigenstates located on the underlying classical strange repeller. The states with longest life times typically reveal a scars structure on the classical fractal set.

Fractals and the Large-Scale Structure in the Universe

Indian Academy of Sciences (India)

Home; Journals; Resonance – Journal of Science Education; Volume 7; Issue 4. Fractals and the Large-Scale Structure in the Universe - Is the Cosmological Principle Valid? A K Mittal T R Seshadri. General Article Volume 7 Issue 4 April 2002 pp 39-47 ...

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)

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.

Spatiotemporal Diffusive Evolution and Fractal Structure of Ground Motion

Science.gov (United States)

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.

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 in radiological and nuclear medicine perfusion imaging: a systematic review

Energy Technology Data Exchange (ETDEWEB)

Michallek, Florian; Dewey, Marc [Humboldt-Universitaet zu Berlin, Freie Universitaet Berlin, Charite - Universitaetsmedizin Berlin, Medical School, Department of Radiology, Berlin (Germany)

2014-01-15

To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)

Fractal analysis in radiological and nuclear medicine perfusion imaging: a systematic review

International Nuclear Information System (INIS)

Michallek, Florian; Dewey, Marc

2014-01-01

To provide an overview of recent research in fractal analysis of tissue perfusion imaging, using standard radiological and nuclear medicine imaging techniques including computed tomography (CT), magnetic resonance imaging (MRI), ultrasound, positron emission tomography (PET) and single-photon emission computed tomography (SPECT) and to discuss implications for different fields of application. A systematic review of fractal analysis for tissue perfusion imaging was performed by searching the databases MEDLINE (via PubMed), EMBASE (via Ovid) and ISI Web of Science. Thirty-seven eligible studies were identified. Fractal analysis was performed on perfusion imaging of tumours, lung, myocardium, kidney, skeletal muscle and cerebral diseases. Clinically, different aspects of tumour perfusion and cerebral diseases were successfully evaluated including detection and classification. In physiological settings, it was shown that perfusion under different conditions and in various organs can be properly described using fractal analysis. Fractal analysis is a suitable method for quantifying heterogeneity from radiological and nuclear medicine perfusion images under a variety of conditions and in different organs. Further research is required to exploit physiologically proven fractal behaviour in the clinical setting. (orig.)

New fractal structures for frequencies close to the visible range

DEFF Research Database (Denmark)

Malureanu, Radu; Sandru, A.; Andryieuski, Andrei

2011-01-01

In this paper we present a new type of fractal resonator to be used in the red/NIR region of the spectra. The structure presents high-transmission band in 795-825nm range. The stop band is in the 683-731 nm range. Due to the huge difference in the spectra within such a short range, the structure...

Fractal Electrochemical Microsupercapacitors

KAUST Repository

Hota, Mrinal Kanti

2017-08-17

The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.

Fractal Electrochemical Microsupercapacitors

KAUST Repository

Hota, Mrinal Kanti; Jiang, Qiu; Mashraei, Yousof; Salama, Khaled N.; Alshareef, Husam N.

2017-01-01

The first successful fabrication of microsupercapacitors (μ-SCs) using fractal electrode designs is reported. Using sputtered anhydrous RuO thin-film electrodes as prototypes, μ-SCs are fabricated using Hilbert, Peano, and Moore fractal designs, and their performance is compared to conventional interdigital electrode structures. Microsupercapacitor performance, including energy density, areal and volumetric capacitances, changes with fractal electrode geometry. Specifically, the μ-SCs based on the Moore design show a 32% enhancement in energy density compared to conventional interdigital structures, when compared at the same power density and using the same thin-film RuO electrodes. The energy density of the Moore design is 23.2 mWh cm at a volumetric power density of 769 mW cm. In contrast, the interdigital design shows an energy density of only 17.5 mWh cm at the same power density. We show that active electrode surface area cannot alone explain the increase in capacitance and energy density. We propose that the increase in electrical lines of force, due to edging effects in the fractal electrodes, also contribute to the higher capacitance. This study shows that electrode fractal design is a viable strategy for improving the performance of integrated μ-SCs that use thin-film electrodes at no extra processing or fabrication cost.

Discovery of cosmic fractals

CERN Document Server

Baryshev, Yuri

2002-01-01

This is the first book to present the fascinating new results on the largest fractal structures in the universe. It guides the reader, in a simple way, to the frontiers of astronomy, explaining how fractals appear in cosmic physics, from our solar system to the megafractals in deep space. It also offers a personal view of the history of the idea of self-similarity and of cosmological principles, from Plato's ideal architecture of the heavens to Mandelbrot's fractals in the modern physical cosmos. In addition, this invaluable book presents the great fractal debate in astronomy (after Luciano Pi

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...

Investigation of changes in fractal dimension from layered retinal structures of healthy and diabetic eyes with optical coherence tomography

Science.gov (United States)

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

Pore-Fractal Structure in Porous Carbons Made from Corn and Wheat

Science.gov (United States)

Kapoor, Y. M.; Schmidt, P. W.; Rice, Randall D.; Shulse, Laural; Voss, D. J.; Venkatraman, A.; Fan, L. T.; Walawender, W. P.; Rieker, T. P.

1998-03-01

Small-angle X-ray scattering has been used in a study of the pore structure of some porous and activated carbons on length scales between about 5 and 10^4 ÅThe carbons were obtained by pyrolysis and activation of wheat and American corn (maize). The scattering data showed that in each carbon there are at least two of the following four types of pores: (1) pores with diameters of at least 10^4 Åpores with smooth or fractal surfaces and diameters of at least 5 x 10^3 Åpore-fractals with diameters of no more than about 10^3 Åand (4) pores with diameters no larger than 100 ÅThe relation between the pore structure and the procedure used to obtain the carbon and will be discussed.

Synthesis of gold nanostars with fractal structure: application in surface-enhanced Raman scattering

Science.gov (United States)

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.

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

DEFF Research Database (Denmark)

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

2017-01-01

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

Efficient RF energy harvesting by using a fractal structured rectenna system

Science.gov (United States)

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

2014-04-01

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

An improved model for estimating fractal structure of silica nano-agglomerates in a vibro-fluidized bed

OpenAIRE

A Esmailpour; N Mostoufi; R Zarghami

2016-01-01

A study has been conducted to determine the effects of operating conditions such as vibration frequency, vibration amplitude on the fractal structure of silica (SiO2) nanoparticle agglomerate in a vibro-fluidized bed. An improved model was proposed by assimilation of fractal theory, Richardson-Zaki equation and mass balance. This model has been developed to predict the properties of nanoparticle agglomerate, such as fractal dimension and its size. It has been found out the vibration intensity...

Fractal properties and small-scale structure of cosmic string networks

International Nuclear Information System (INIS)

Martins, C.J.A.P.; Shellard, E.P.S.

2006-01-01

We present results from a detailed numerical study of the small-scale and loop production properties of cosmic string networks, based on the largest and highest resolution string simulations to date. We investigate the nontrivial fractal properties of cosmic strings, in particular, the fractal dimension and renormalized string mass per unit length, and we also study velocity correlations. We demonstrate important differences between string networks in flat (Minkowski) spacetime and the two very similar expanding cases. For high resolution matter era network simulations, we provide strong evidence that small-scale structure has converged to 'scaling' on all dynamical length scales, without the need for other radiative damping mechanisms. We also discuss preliminary evidence that the dominant loop production size is also approaching scaling

Fractal structure in the volumetric contrast enhancement of malignant gliomas as a marker of oxidative metabolic pathway gene expression

NARCIS (Netherlands)

Miller, Kai J.; Berendsen, Sharon; Seute, Tatjana; Yeom, Kristen; Gephardt, Melanie H.; Grant, Gerald A.; Robe, Pierre A.

2017-01-01

Background: Fractal structure is found throughout many processes in nature, and often arises from sets of simple rules. We examined MRI contrast enhancement patterns from glioblastoma patients for evidence of fractal structure and correlated these with gene expression patterns. Methods: For 39

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

Science.gov (United States)

Bellido, Edson P; Bernasconi, Gabriel D; Rossouw, David; Butet, Jérémy; Martin, Olivier J F; Botton, Gianluigi A

2017-11-28

We investigate the plasmonic behavior of Koch snowflake fractal geometries and their possible application as broadband optical antennas. Lithographically defined planar silver Koch fractal antennas were fabricated and characterized with high spatial and spectral resolution using electron energy loss spectroscopy. The experimental data are supported by numerical calculations carried out with a surface integral equation method. Multiple surface plasmon edge modes supported by the fractal structures have been imaged and analyzed. Furthermore, by isolating and reproducing self-similar features in long silver strip antennas, the edge modes present in the Koch snowflake fractals are identified. We demonstrate that the fractal response can be obtained by the sum of basic self-similar segments called characteristic edge units. Interestingly, the plasmon edge modes follow a fractal-scaling rule that depends on these self-similar segments formed in the structure after a fractal iteration. As the size of a fractal structure is reduced, coupling of the modes in the characteristic edge units becomes relevant, and the symmetry of the fractal affects the formation of hybrid modes. This analysis can be utilized not only to understand the edge modes in other planar structures but also in the design and fabrication of fractal structures for nanophotonic applications.

Comparison of two fractal interpolation methods

Science.gov (United States)

Fu, Yang; Zheng, Zeyu; Xiao, Rui; Shi, Haibo

2017-03-01

As a tool for studying complex shapes and structures in nature, fractal theory plays a critical role in revealing the organizational structure of the complex phenomenon. Numerous fractal interpolation methods have been proposed over the past few decades, but they differ substantially in the form features and statistical properties. In this study, we simulated one- and two-dimensional fractal surfaces by using the midpoint displacement method and the Weierstrass-Mandelbrot fractal function method, and observed great differences between the two methods in the statistical characteristics and autocorrelation features. From the aspect of form features, the simulations of the midpoint displacement method showed a relatively flat surface which appears to have peaks with different height as the fractal dimension increases. While the simulations of the Weierstrass-Mandelbrot fractal function method showed a rough surface which appears to have dense and highly similar peaks as the fractal dimension increases. From the aspect of statistical properties, the peak heights from the Weierstrass-Mandelbrot simulations are greater than those of the middle point displacement method with the same fractal dimension, and the variances are approximately two times larger. When the fractal dimension equals to 1.2, 1.4, 1.6, and 1.8, the skewness is positive with the midpoint displacement method and the peaks are all convex, but for the Weierstrass-Mandelbrot fractal function method the skewness is both positive and negative with values fluctuating in the vicinity of zero. The kurtosis is less than one with the midpoint displacement method, and generally less than that of the Weierstrass-Mandelbrot fractal function method. The autocorrelation analysis indicated that the simulation of the midpoint displacement method is not periodic with prominent randomness, which is suitable for simulating aperiodic surface. While the simulation of the Weierstrass-Mandelbrot fractal function method has

Effect of preparation conditions on fractal structure and phase transformations in the synthesis of nanoscale M-type barium hexaferrite

Energy Technology Data Exchange (ETDEWEB)

Pashkova, E.V. [V.I. Vernadskii Institute of General and Inorganic Chemistry, 32/34 Prospect Palladina, Kyiv-142, 03680 (Ukraine); Solovyova, E.D., E-mail: solovyovak@mail.ru [V.I. Vernadskii Institute of General and Inorganic Chemistry, 32/34 Prospect Palladina, Kyiv-142, 03680 (Ukraine); Kotenko, I.E., E-mail: Hab2420@yahoo.com [National Technical University of Ukraine ' KPI' , Pr. Pobedy, 37, Kyiv-57 (Ukraine); Kolodiazhnyi, T.V., E-mail: kolodiazhnyi.taras@nims.go.jp [National Institute for Materials Science, 1-1 Namiki, Tsukuba, Ibaraki 305-0044 (Japan); Belous, A.G., E-mail: belous@ionc.kar.net [V.I. Vernadskii Institute of General and Inorganic Chemistry, 32/34 Prospect Palladina, Kyiv-142, 03680 (Ukraine)

2011-10-15

The conditions of the synthesis of carbonate-hydroxide precursors (pH of FeOOH precipitation and heat treatment regimes) were studied in terms of their effect on the fractal structure and physical-chemical properties of precursors. Phase transformations which occur during the synthesis of nanosize M-type barium hexaferrite (BHF) were studied as well. The first structural level of precursors' aggregation for mass fractals, the correlation between fractal dimension and precursors' activity during the synthesis of BHF were determined. Synthesis parameters for the precursors with the optimal fractal structure were determined. These data permit an enhancement of the filtration coefficient of the precipitates by a factor of 4-5, obtaining substantial decrease in the temperature required for synthesis of a single-phase BHF, and monodispersed plate-like nanoparticles (60 nm diameter) with the shape anisotropy and good magnetic characteristics (saturation magnetization (M{sub s})=68,7 emu/g and coercitivity (H{sub c})=5440 Oe). - Highlights: > The nanosize M-type BHF obtained by precipitation of hydroxicarbonates technique. > Optimal fractal structure of a precursor for nanosize M-type BHF has been determined. > The precursor precipitated at pH 4.3 allows getting monodisperse particles of BHF.

Completion of a fractal structure | Gálvez-Rodríguez | Quaestiones ...

African Journals Online (AJOL)

metrization, and there is a strong relationship between these two concepts. In this paper we give a construction of a completion of a fractal structure by using inverse limits of a sequence of partially ordered sets. This completion extents nicely all the ...

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)

An improved model for estimating fractal structure of silica nano-agglomerates in a vibro-fluidized bed

Directory of Open Access Journals (Sweden)

A Esmailpour

2016-10-01

Full Text Available A study has been conducted to determine the effects of operating conditions such as vibration frequency, vibration amplitude on the fractal structure of silica (SiO2 nanoparticle agglomerate in a vibro-fluidized bed. An improved model was proposed by assimilation of fractal theory, Richardson-Zaki equation and mass balance. This model has been developed to predict the properties of nanoparticle agglomerate, such as fractal dimension and its size. It has been found out the vibration intensity increase leads to a slight reduction in fractal dimension of agglomerate. This Paper is also indicated that the size of agglomerate has the same behavior as fractal dimension with respect to vibration intensity changes. This study demonstrated that the fractal dimension of Silica nanoparticle agglomerate is in the range of 2.61 to 2.69 and the number of primary particles in the agglomerate is in the order of 1010. The vibration frequency is more impressive than its amplitude on agglomerate size reduction. Calculated Minimum fluidization velocity by applying predicted agglomerate sizes and experimental data are acceptable fitted.

Turbulent wakes of fractal objects

NARCIS (Netherlands)

Staicu, A.D.; Mazzi, B.; Vassilicos, J.C.; Water, van de W.

2003-01-01

Turbulence of a windtunnel flow is stirred using objects that have a fractal structure. The strong turbulent wakes resulting from three such objects which have different fractal dimensions are probed using multiprobe hot-wire anemometry in various configurations. Statistical turbulent quantities are

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

Fractal cosmology

International Nuclear Information System (INIS)

Dickau, Jonathan J.

2009-01-01

The use of fractals and fractal-like forms to describe or model the universe has had a long and varied history, which begins long before the word fractal was actually coined. Since the introduction of mathematical rigor to the subject of fractals, by Mandelbrot and others, there have been numerous cosmological theories and analyses of astronomical observations which suggest that the universe exhibits fractality or is by nature fractal. In recent years, the term fractal cosmology has come into usage, as a description for those theories and methods of analysis whereby a fractal nature of the cosmos is shown.

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.

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.

L-system fractals

CERN Document Server

Mishra, Jibitesh

2007-01-01

The book covers all the fundamental aspects of generating fractals through L-system. Also it provides insight to various researches in this area for generating fractals through L-system approach & estimating dimensions. Also it discusses various applications of L-system fractals. Key Features: - Fractals generated from L-System including hybrid fractals - Dimension calculation for L-system fractals - Images & codes for L-system fractals - Research directions in the area of L-system fractals - Usage of various freely downloadable tools in this area - Fractals generated from L-System including hybrid fractals- Dimension calculation for L-system fractals- Images & codes for L-system fractals- Research directions in the area of L-system fractals- Usage of various freely downloadable tools in this area

Growth of fractal structures in flames with silicon admixture

NARCIS (Netherlands)

Smirnov, B. M.; Dutka, M.; van Essen, V. M.; Gersen, S.; Visser, P.; Vainchtein, D.; De Hosson, J. Th. M.; Levinsky, H. B.; Mokhov, A. V.

Transmission electron microscopy (TEM) measurements and theoretical analysis are combined to construct the physical picture of formation of SiO2 fractal aggregates in a methane/hexamethyldisiloxane/air atmospheric pressure flame. The formation of SiO2 fractal aggregates is described as a multistage

FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY

Directory of Open Access Journals (Sweden)

Ian Parkinson

2011-05-01

Full Text Available A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge. The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals, with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.

Characteristics of Pore Structure and Fractal Dimension of Isometamorphic Anthracite

Directory of Open Access Journals (Sweden)

Di Gao

2017-11-01

Full Text Available The geologic conditions of No. 3 coal seams are similar to Sihe and Zhaozhuang Collieries, however, the gas production is significantly different. To better understand the effect of pores, by means of experimental measurements and quantitative analysis, the pore properties of high-rank isometamorphic anthracite were thoroughly studied. Our study showed that the pore structures were predominantly adsorptive, accounting for more than 88% of the specific surface area. The coal pores showed typical three-stage fractal characteristics at boundary points of 1 nm and 9 nm (7 nm of coal samples from Zhaozhuang Colliery, and the fractal dimension with 1–9 nm (or 1–7 nm, as being significantly larger than those measured outside the given ranges. Pores in samples from Sihe Colliery were mainly open spherical or ellipsoidal pores in shape; conversely, those from Zhaozhuang Colliery were mainly Y-shaped, V-shaped, or ‘ink-bottle’ type.

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

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

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

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.

Labelling Of Coolant Flow Anomaly Using Fractal Structure

International Nuclear Information System (INIS)

Djainal, Djen Djen

1996-01-01

This research deals with the instrumentation of the detection and characterization of vertical two-phase flow coolant. This type of work is particularly intended to find alternative method for the detection and identification of noise in vertical two-phase flow in a nuclear reactor environment. Various new methods have been introduced in the past few years, an attempt to developed an objective indicator off low patterns. One of new method is Fractal analysis which can complement conventional methods in the description of highly irregular fluctuations. In the present work, Fractal analysis was applied to analyze simulated boiling coolant signal. This simulated signals were built by sum random elements in small subchannels of the coolant channel. Two modes are defined and both are characterized by their void fractions. In the case of uni modal -PDF signals, the difference between these modes is relatively small. On other hand, bimodal -PDF signals have relative large range. In this research, Fractal dimension can indicate the characters of that signals simulation

Biophysical Chemistry of Fractal Structures and Processes in Environmental Systems

NARCIS (Netherlands)

Buffle, J.; Leeuwen, van H.P.

2008-01-01

This book aims to provide the scientific community with a novel and valuable approach based on fractal geometry concepts on the important properties and processes of diverse environmental systems. The interpretation of complex environmental systems using modern fractal approaches is compared and

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

Science.gov (United States)

Balankin, Alexander S; Elizarraraz, Benjamin Espinoza

2012-05-01

This paper is devoted to fractal continuum hydrodynamics and its application to model fluid flows in fractally permeable reservoirs. Hydrodynamics of fractal continuum flow is developed on the basis of a self-consistent model of fractal continuum employing vector local fractional differential operators allied with the Hausdorff derivative. The generalized forms of Green-Gauss and Kelvin-Stokes theorems for fractional calculus are proved. The Hausdorff material derivative is defined and the form of Reynolds transport theorem for fractal continuum flow is obtained. The fundamental conservation laws for a fractal continuum flow are established. The Stokes law and the analog of Darcy's law for fractal continuum flow are suggested. The pressure-transient equation accounting the fractal metric of fractal continuum flow is derived. The generalization of the pressure-transient equation accounting the fractal topology of fractal continuum flow is proposed. The mapping of fluid flow in a fractally permeable medium into a fractal continuum flow is discussed. It is stated that the spectral dimension of the fractal continuum flow d(s) is equal to its mass fractal dimension D, even when the spectral dimension of the fractally porous or fissured medium is less than D. A comparison of the fractal continuum flow approach with other models of fluid flow in fractally permeable media and the experimental field data for reservoir tests are provided.

Multi-branched gold nanostars with fractal structure for SERS detection of the pesticide thiram

Science.gov (United States)

Zhu, Jian; Liu, Mei-Jin; Li, Jian-Jun; Li, Xin; Zhao, Jun-Wu

2018-01-01

The surface-enhanced Raman scattering (SERS) activity of multi-branched gold nanostars with fractal structure has been investigated for trace detection of pesticide thiram. Raman spectrum results show that the gold nanostars substrate can produce about 102 fold stronger signal than the thiram alone with the thiram concentration increase of 103 times and 1.4 fold stronger signal than the gold nanostars without fractal feature. In the detection procedure, the most prominent SERS peak at 1376 cm- 1 has been chosen to characterize and quantify the concentration of thiram. Experimental results indicate this Raman substrate based on fractal gold nanostars exhibits excellent selective probing performance for thiram with a detection limit as low as 10- 10 M in solution and 0.24 ng/cm2 in apple peels. Interference experiment results show that the effects from the interfering pesticides could be neglected in the detection procedure. Therefore, the gold nanostars as a SERS substrate have excellent sensitivity and selectivity.

Determining Effective Thermal Conductivity of Fabrics by Using Fractal Method

Science.gov (United States)

Zhu, Fanglong; Li, Kejing

2010-03-01

In this article, a fractal effective thermal conductivity model for woven fabrics with multiple layers is developed. Structural models of yarn and plain woven fabric are derived based on the fractal characteristics of macro-pores (gap or channel) between the yarns and micro-pores inside the yarns. The fractal effective thermal conductivity model can be expressed as a function of the pore structure (fractal dimension) and architectural parameters of the woven fabric. Good agreement is found between the fractal model and the thermal conductivity measurements in the general porosity ranges. It is expected that the model will be helpful in the evaluation of thermal comfort for woven fabric in the whole range of porosity.

Fractal characterization of the compaction and sintering of ferrites

NARCIS (Netherlands)

Glass, H.J.; With, de G.

2001-01-01

A novel parameter, the fractal exponent DE, is derived using the concept of fractal scaling. The fractal exponent DE relates the development of a feature within a material to the development of the size of the material. As an application, structural changes during the compaction and sintering of

A contact angle hysteresis model based on the fractal structure of contact line.

Science.gov (United States)

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.

Model of fractal aggregates induced by shear

Directory of Open Access Journals (Sweden)

Wan Zhanhong

2013-01-01

Full Text Available It is an undoubted fact that particle aggregates from marine, aerosol, and engineering systems have fractal structures. In this study, fractal geometry is used to describe the morphology of irregular aggregates. The mean-field theory is employed to solve coagulation kinetic equation of aggregates. The Taylor-expansion method of moments in conjunction with the self-similar fractal characteristics is used to represent the particulate field. The effect of the target fractal dimensions on zeroth-order moment, second-order moment, and geometric standard deviation of the aggregates is explored. Results show that the developed moment method is an efficient and powerful approach to solving such evolution equations.

Electro-chemical manifestation of nanoplasmonics in fractal media

Science.gov (United States)

Baskin, Emmanuel; Iomin, Alexander

2013-06-01

Electrodynamics of composite materials with fractal geometry is studied in the framework of fractional calculus. This consideration establishes a link between fractal geometry of the media and fractional integrodifferentiation. The photoconductivity in the vicinity of the electrode-electrolyte fractal interface is studied. The methods of fractional calculus are employed to obtain an analytical expression for the giant local enhancement of the optical electric field inside the fractal composite structure at the condition of the surface plasmon excitation. This approach makes it possible to explain experimental data on photoconductivity in the nano-electrochemistry.

FAST TRACK COMMUNICATION: Weyl law for fat fractals

Science.gov (United States)

Spina, María E.; García-Mata, Ignacio; Saraceno, Marcos

2010-10-01

It has been conjectured that for a class of piecewise linear maps the closure of the set of images of the discontinuity has the structure of a fat fractal, that is, a fractal with positive measure. An example of such maps is the sawtooth map in the elliptic regime. In this work we analyze this problem quantum mechanically in the semiclassical regime. We find that the fraction of states localized on the unstable set satisfies a modified fractal Weyl law, where the exponent is given by the exterior dimension of the fat fractal.

Fractal markets: Liquidity and investors on different time horizons

Science.gov (United States)

Li, Da-Ye; Nishimura, Yusaku; Men, Ming

2014-08-01

In this paper, we propose a new agent-based model to study the source of liquidity and the “emergent” phenomenon in financial market with fractal structure. The model rests on fractal market hypothesis and agents with different time horizons of investments. What is interesting is that though the agent-based model reveals that the interaction between these heterogeneous agents affects the stability and liquidity of the financial market the real world market lacks detailed data to bring it to light since it is difficult to identify and distinguish the investors with different time horizons in the empirical approach. results show that in a relatively short period of time fractal market provides liquidity from investors with different horizons and the market gains stability when the market structure changes from uniformity to diversification. In the real world the fractal structure with the finite of horizons can only stabilize the market within limits. With the finite maximum horizons, the greater diversity of the investors and the fractal structure will not necessarily bring more stability to the market which might come with greater fluctuation in large time scale.

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

Directory of Open Access Journals (Sweden)

Bogdanov Ana

2007-01-01

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

Fractal characteristic in the wearing of cutting tool

Science.gov (United States)

Mei, Anhua; Wang, Jinghui

1995-11-01

This paper studies the cutting tool wear with fractal geometry. The wearing image of the flank has been collected by machine vision which consists of CCD camera and personal computer. After being processed by means of preserving smoothing, binary making and edge extracting, the clear boundary enclosing the worn area has been obtained. The fractal dimension of the worn surface is calculated by the methods called `Slit Island' and `Profile'. The experiments and calciating give the conclusion that the worn surface is enclosed by a irregular boundary curve with some fractal dimension and characteristics of self-similarity. Furthermore, the relation between the cutting velocity and the fractal dimension of the worn region has been submitted. This paper presents a series of methods for processing and analyzing the fractal information in the blank wear, which can be applied to research the projective relation between the fractal structure and the wear state, and establish the fractal model of the cutting tool wear.

Facile fabrication of superhydrophobic films with fractal structures using epoxy resin microspheres

Energy Technology Data Exchange (ETDEWEB)

Quan, Yun-Yun; Zhang, Li-Zhi, E-mail: lzzhang@scut.edu.cn

2014-02-15

A simple method has been developed to fabricate superhydrophobic surfaces with fractal structures with epoxy resin microspheres (ERMs). The ERMs is produced by phase separation in an epoxy-amine curing system with a silica sol (SS) dispersant. The transparent epoxy solution becomes cloudy and turns into epoxy suspension (ES) in this process. The fractal structure (two tier structure) generated by synthetic epoxy resin microspheres (ERMs) and deposited nanoincrutations on the surfaces of these ERMs, which have been observed by scanning electron microscope (SEM). The curing time of ES is an important condition to obtain films with good comprehensive performances. Superhydrophobic films can be prepared by adding extra SS into ES with a curing time longer than 5 h. The optimal curing time is 10 h to fabricate a film with good mechanical stability and high superhydrophobicity. In addition, a surface with anti-wetting property of impacting microdroplets can be fabricated by prolonging the curing time of ES to 24 h. The gradually decreased hydrophilic groups resulted from a longer curing time enable the surface to have smaller surface adhesions to water droplets, which is the main reason to keep its superhydrophobicity under impacting conditions. The coated surface is highly hydrophobic and the impacting water droplets are bounced off from the surface.

Facile fabrication of superhydrophobic films with fractal structures using epoxy resin microspheres

Science.gov (United States)

Quan, Yun-Yun; Zhang, Li-Zhi

2014-02-01

A simple method has been developed to fabricate superhydrophobic surfaces with fractal structures with epoxy resin microspheres (ERMs). The ERMs is produced by phase separation in an epoxy-amine curing system with a silica sol (SS) dispersant. The transparent epoxy solution becomes cloudy and turns into epoxy suspension (ES) in this process. The fractal structure (two tier structure) generated by synthetic epoxy resin microspheres (ERMs) and deposited nanoincrutations on the surfaces of these ERMs, which have been observed by scanning electron microscope (SEM). The curing time of ES is an important condition to obtain films with good comprehensive performances. Superhydrophobic films can be prepared by adding extra SS into ES with a curing time longer than 5 h. The optimal curing time is 10 h to fabricate a film with good mechanical stability and high superhydrophobicity. In addition, a surface with anti-wetting property of impacting microdroplets can be fabricated by prolonging the curing time of ES to 24 h. The gradually decreased hydrophilic groups resulted from a longer curing time enable the surface to have smaller surface adhesions to water droplets, which is the main reason to keep its superhydrophobicity under impacting conditions. The coated surface is highly hydrophobic and the impacting water droplets are bounced off from the surface.

Fractal and chaotic laws on seismic dissipated energy in an energy system of engineering structures

Science.gov (United States)

Cui, Yu-Hong; Nie, Yong-An; Yan, Zong-Da; Wu, Guo-You

1998-09-01

Fractal and chaotic laws of engineering structures are discussed in this paper, it means that the intrinsic essences and laws on dynamic systems which are made from seismic dissipated energy intensity E d and intensity of seismic dissipated energy moment I e are analyzed. Based on the intrinsic characters of chaotic and fractal dynamic system of E d and I e, three kinds of approximate dynamic models are rebuilt one by one: index autoregressive model, threshold autoregressive model and local-approximate autoregressive model. The innate laws, essences and systematic error of evolutional behavior I e are explained over all, the short-term behavior predictability and long-term behavior probability of which are analyzed in the end. That may be valuable for earthquake-resistant theory and analysis method in practical engineering structures.

Classification of radar echoes using fractal geometry

International Nuclear Information System (INIS)

Azzaz, Nafissa; Haddad, Boualem

2017-01-01

Highlights: • Implementation of two concepts of fractal geometry to classify two types of meteorological radar echoes. • A new approach, called a multi-scale fractal dimension is used for classification between fixed echoes and rain echoes. • An Automatic identification system of meteorological radar echoes was proposed using fractal geometry. - Abstract: This paper deals with the discrimination between the precipitation echoes and the ground echoes in meteorological radar images using fractal geometry. This study aims to improve the measurement of precipitations by weather radars. For this, we considered three radar sites: Bordeaux (France), Dakar (Senegal) and Me lbourne (USA). We showed that the fractal dimension based on contourlet and the fractal lacunarity are pertinent to discriminate between ground and precipitation echoes. We also demonstrated that the ground echoes have a multifractal structure but the precipitations are more homogeneous than ground echoes whatever the prevailing climate. Thereby, we developed an automatic classification system of radar using a graphic interface. This interface, based on the fractal geometry makes possible the identification of radar echoes type in real time. This system can be inserted in weather radar for the improvement of precipitation estimations.

Fractal analysis of 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.

Fractal structure of hadrons in processes with polarized protons at SPD NICA (proposal for experiment)

International Nuclear Information System (INIS)

Tokarev, M.V.; Aparin, A.A.; Zborovsky, I.

2014-01-01

The concept of z-scaling previously developed for analysis of inclusive reactions in proton-proton collisions is applied for description of processes with polarized protons at the planned Spin Physics Detector NICA in Dubna. A hypothesis of self-similarity and fractality of the proton spin structure is discussed. The possibilities to extract information on spin-dependent fractal dimensions of hadrons and fragmentation process from asymmetries and coefficients of polarization transfer are justified. The double longitudinal spin asymmetry A LL of π 0 -meson production and the coefficient of the polarization transfer D LL of Λ hyperon production in proton-proton collisions measured at RHIC are analyzed in the framework of z-scaling. The spin-dependent fractal dimensions of proton and fragmentation process with polarized Λ hyperon are estimated. A study of the spin-dependent constituent energy loss as a function of transverse momentum of the inclusive hadron and collision energy is suggested.

Infrastructural Fractals

DEFF Research Database (Denmark)

Bruun Jensen, Casper

2007-01-01

. Instead, I outline a fractal approach to the study of space, society, and infrastructure. A fractal orientation requires a number of related conceptual reorientations. It has implications for thinking about scale and perspective, and (sociotechnical) relations, and for considering the role of the social...... and a fractal social theory....

An integral time series on simulated labeling using fractal structure

International Nuclear Information System (INIS)

Djainal, D.D.

1997-01-01

This research deals with the detection of time series of vertical two-phase flow, in attempt to developed an objective indicator of time series flow patterns. One of new method is fractal analysis which can complement conventional methods in the description of highly irregular fluctuations. in the present work, fractal analysis applied to analyze simulated boiling coolant signal. this simulated signals built by sum random elements in small subchannels of the coolant channel. Two modes are defined and both modes are characterized by their void fractions. in the case of unimodal-PDF signals, the difference between these modes is relative small. on other hand, bimodal-PDF signals have relative large range. in this research, fractal dimension can indicate the characters of that signals simulation

Medial/skeletal linking structures for multi-region configurations

CERN Document Server

Damon, James

2018-01-01

The authors consider a generic configuration of regions, consisting of a collection of distinct compact regions \\{ \\Omega_i\\} in \\mathbb{R}^{n+1} which may be either regions with smooth boundaries disjoint from the others or regions which meet on their piecewise smooth boundaries \\mathcal{B}_i in a generic way. They introduce a skeletal linking structure for the collection of regions which simultaneously captures the regions' individual shapes and geometric properties as well as the "positional geometry" of the collection. The linking structure extends in a minimal way the individual "skeletal structures" on each of the regions. This allows the authors to significantly extend the mathematical methods introduced for single regions to the configuration of regions.

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.

Fractal dimensions of silica gels generated using reactive molecular dynamics simulations

International Nuclear Information System (INIS)

Bhattacharya, Sudin; Kieffer, John

2005-01-01

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

Converting skeletal structures to quad dominant meshes

DEFF Research Database (Denmark)

Bærentzen, Jakob Andreas; Misztal, Marek Krzysztof; Welnicka, Katarzyna

2012-01-01

We propose the Skeleton to Quad-dominant polygonal Mesh algorithm (SQM), which converts skeletal structures to meshes composed entirely of polar and annular regions. Both types of regions have a regular structure where all faces are quads except for a single ring of triangles at the center of each...

How the mach phenomenon and shape affect the radiographic appearance of skeletal structures

International Nuclear Information System (INIS)

Papageorges, M.

1991-01-01

The shape of skeletal structures and their position relative to the x-ray beam have a considerable effect on their radiographic appearance. Depending on the thickness of the cortical or subchondral bone, skeletal structures display the characteristics of either homogeneous or compound lamellar structures. Convex homogeneous structures are associated with a negative Mach line, and concave homogeneous structures are associated with a positive Mach line. Convex compound lamellar structures are associated with a negative Mach band and visualization of the lamina (subchondral or cortical bone) is reduced. Concave compound lamellar structures are associated with a positive Mach band and visualization of the lamina is enhanced. The combined effect of Mach phenomenon, shape, and thickness enhances visualization of some skeletal surfaces and make others imperceptible. These principles are very useful to correctly identify complex skeletal structures and avoid misinterpretations

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.

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 vector optical fields.

Science.gov (United States)

Pan, Yue; Gao, Xu-Zhen; Cai, Meng-Qiang; Zhang, Guan-Lin; Li, Yongnan; Tu, Chenghou; Wang, Hui-Tian

2016-07-15

We introduce the concept of a fractal, which provides an alternative approach for flexibly engineering the optical fields and their focal fields. We propose, design, and create a new family of optical fields-fractal vector optical fields, which build a bridge between the fractal and vector optical fields. The fractal vector optical fields have polarization states exhibiting fractal geometry, and may also involve the phase and/or amplitude simultaneously. The results reveal that the focal fields exhibit self-similarity, and the hierarchy of the fractal has the "weeding" role. The fractal can be used to engineer the focal field.

Wetting characteristics of 3-dimensional nanostructured fractal surfaces

Energy Technology Data Exchange (ETDEWEB)

Davis, Ethan, E-mail: ethan.davis4@huskers.unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States); Liu, Ying; Jiang, Lijia; Lu, Yongfeng [Laser Assisted Nano Engineering Lab, Department of Electrical and Computer Engineering, University of Nebraska-Lincoln, 209N Scott Engineering Center, Lincoln, NE 68588-0511 (United States); Ndao, Sidy, E-mail: sndao2@unl.edu [Nano & Microsystems Research Laboratory, Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, W342 Nebraska Hall, Lincoln, NE 68588-0526 (United States)

2017-01-15

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

Wetting characteristics of 3-dimensional nanostructured fractal surfaces

International Nuclear Information System (INIS)

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

2017-01-01

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

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

Damage Effects and Fractal Characteristics of Coal Pore Structure during Liquid CO2 Injection into a Coal Bed for E-CBM

Directory of Open Access Journals (Sweden)

Li Ma

2018-05-01

Full Text Available Pore structure has a significant influence on coal-bed methane (CBM enhancement. Injecting liquid CO2 into coal seams is an effective way to increase CBM recovery. However, there has been insufficient research regarding the damage effects and fractal characteristics of pore structure at low temperature induced by injecting liquid CO2 into coal samples. Therefore, the methods of low-pressure nitrogen adsorption-desorption (LP-N2-Ad and mercury intrusion porosimetry (MIP were used to investigate the damage effects and fractal characteristics of pore structure with full aperture as the specimens were frozen by liquid CO2. The adsorption isotherms revealed that the tested coal samples belonged to type B, indicating that they contained many bottle and narrow-slit shaped pores. The average pore diameter (APD; average growth rate of 18.20%, specific surface area (SSA; average growth rate of 7.38%, and total pore volume (TPV; average growth rate of 18.26% increased after the specimens were infiltrated by liquid CO2, which indicated the generation of new pores and the transformation of original pores. Fractal dimensions D1 (average of 2.58 and D2 (average of 2.90 of treated coal samples were both larger the raw coal (D1, average of 2.55 and D2, average of 2.87, which indicated that the treated specimens had more rough pore surfaces and complex internal pore structures than the raw coal samples. The seepage capacity was increased because D4 (average of 2.91 of the treated specimens was also higher than the raw specimens (D4, average of 2.86. The grey relational coefficient between the fractal dimension and pore structure parameters demonstrated that the SSA, APD, and porosity positively influenced the fractal features of the coal samples, whereas the TPV and permeability exerted negative influences.

Near-Field Optical Microscopy of Fractal Structures

DEFF Research Database (Denmark)

Coello, Victor; Bozhevolnyi, Sergey I.

1999-01-01

Using a photon scanning tunnelling microscope combined with a shear-force feedback system, we image both topographical and near-field optical images (at the wavelengths of 633 and 594 nm) of silver colloid fractals. Near-field optical imaging is calibrated with a standing evanescent wave pattern...

Structural, biochemical, cellular, and functional changes in skeletal muscle extracellular matrix with aging

DEFF Research Database (Denmark)

Kragstrup, T W; Kjaer, M; Mackey, A L

2011-01-01

The extracellular matrix (ECM) of skeletal muscle is critical for force transmission and for the passive elastic response of skeletal muscle. Structural, biochemical, cellular, and functional changes in skeletal muscle ECM contribute to the deterioration in muscle mechanical properties with aging....... Structural changes include an increase in the collagen concentration, a change in the elastic fiber system, and an increase in fat infiltration of skeletal muscle. Biochemical changes include a decreased turnover of collagen with potential accumulation of enzymatically mediated collagen cross...

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)

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.

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)

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....

Structural hierarchy of chromatin in chicken erythrocyte nuclei based on small-angle neutron scattering: Fractal nature of the large-scale chromatin organization

International Nuclear Information System (INIS)

Lebedev, D. V.; Filatov, M. V.; Kuklin, A. I.; Islamov, A. Kh.; Stellbrink, J.; Pantina, R. A.; Denisov, Yu. Yu.; Toperverg, B. P.; Isaev-Ivanov, V. V.

2008-01-01

The chromatin organization in chicken erythrocyte nuclei was studied by small-angle neutron scattering in the scattering-vector range from 1.5 x 10 -1 to 10 -4 A -1 with the use of the contrast-variation technique. This scattering-vector range corresponds to linear dimensions from 4 nm to 6 μm and covers the whole hierarchy of chromatin structures, from the nucleosomal structure to the entire nucleus. The results of the present study allowed the following conclusions to be drawn: (1) both the chromatin-protein structure and the structure of the nucleic acid component in chicken erythrocyte nuclei have mass-fractal properties, (2) the structure of the protein component of chromatin exhibits a fractal behavior on scales extending over two orders of magnitude, from the nucleosomal size to the size of an entire nucleus, and (3) the structure of the nucleic acid component of chromatin in chicken erythrocyte nuclei is likewise of a fractal nature and has two levels of organization or two phases with the crossover point at about 300-400 nm

Stochastic dislocation kinetics and fractal structures in deforming metals probed by acoustic emission and surface topography measurements

Energy Technology Data Exchange (ETDEWEB)

Vinogradov, A. [Laboratory for the Physics of Strength of Materials and Intelligent Diagnostic Systems, Togliatti State University, Togliatti 445667 (Russian Federation); Laboratory of Hybrid Nanostructured Materials, NITU MISiS, Moscow 119490 (Russian Federation); Yasnikov, I. S. [Laboratory for the Physics of Strength of Materials and Intelligent Diagnostic Systems, Togliatti State University, Togliatti 445667 (Russian Federation); Estrin, Y. [Laboratory of Hybrid Nanostructured Materials, NITU MISiS, Moscow 119490 (Russian Federation); Centre for Advanced Hybrid Materials, Department of Materials Engineering, Monash University, Clayton, VIC 3800 (Australia)

2014-06-21

We demonstrate that the fractal dimension (FD) of the dislocation population in a deforming material is an important quantitative characteristic of the evolution of the dislocation structure. Thus, we show that peaking of FD signifies a nearing loss of uniformity of plastic flow and the onset of strain localization. Two techniques were employed to determine FD: (i) inspection of surface morphology of the deforming crystal by white light interferometry and (ii) monitoring of acoustic emission (AE) during uniaxial tensile deformation. A connection between the AE characteristics and the fractal dimension determined from surface topography measurements was established. As a common platform for the two methods, the dislocation density evolution in the bulk was used. The relations found made it possible to identify the occurrence of a peak in the median frequency of AE as a harbinger of plastic instability leading to necking. It is suggested that access to the fractal dimension provided by AE measurements and by surface topography analysis makes these techniques important tools for monitoring the evolution of the dislocation structure during plastic deformation—both as stand-alone methods and especially when used in tandem.

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.

Fractal dimension analysis of complexity in Ligeti piano pieces

Science.gov (United States)

Bader, Rolf

2005-04-01

Fractal correlation dimensional analysis has been performed with whole solo piano pieces by Gyrgy Ligeti at every 50ms interval of the pieces. The resulting curves of development of complexity represented by the fractal dimension showed up a very reasonable correlation with the perceptional density of events during these pieces. The seventh piece of Ligeti's ``Musica ricercata'' was used as a test case. Here, each new part of the piece was followed by an increase of the fractal dimension because of the increase of information at the part changes. The second piece ``Galamb borong,'' number seven of the piano Etudes was used, because Ligeti wrote these Etudes after studying fractal geometry. Although the piece is not fractal in the strict mathematical sense, the overall structure of the psychoacoustic event-density as well as the detailed event development is represented by the fractal dimension plot.

Helicalised fractals

OpenAIRE

Saw, Vee-Liem; Chew, Lock Yue

2013-01-01

We formulate the helicaliser, which replaces a given smooth curve by another curve that winds around it. In our analysis, we relate this formulation to the geometrical properties of the self-similar circular fractal (the discrete version of the curved helical fractal). Iterative applications of the helicaliser to a given curve yields a set of helicalisations, with the infinitely helicalised object being a fractal. We derive the Hausdorff dimension for the infinitely helicalised straight line ...

a Fractal Network Model for Fractured Porous Media

Science.gov (United States)

Xu, Peng; Li, Cuihong; Qiu, Shuxia; Sasmito, Agus Pulung

2016-04-01

The transport properties and mechanisms of fractured porous media are very important for oil and gas reservoir engineering, hydraulics, environmental science, chemical engineering, etc. In this paper, a fractal dual-porosity model is developed to estimate the equivalent hydraulic properties of fractured porous media, where a fractal tree-like network model is used to characterize the fracture system according to its fractal scaling laws and topological structures. The analytical expressions for the effective permeability of fracture system and fractured porous media, tortuosity, fracture density and fraction are derived. The proposed fractal model has been validated by comparisons with available experimental data and numerical simulation. It has been shown that fractal dimensions for fracture length and aperture have significant effect on the equivalent hydraulic properties of fractured porous media. The effective permeability of fracture system can be increased with the increase of fractal dimensions for fracture length and aperture, while it can be remarkably lowered by introducing tortuosity at large branching angle. Also, a scaling law between the fracture density and fractal dimension for fracture length has been found, where the scaling exponent depends on the fracture number. The present fractal dual-porosity model may shed light on the transport physics of fractured porous media and provide theoretical basis for oil and gas exploitation, underground water, nuclear waste disposal and geothermal energy extraction as well as chemical engineering, etc.

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

A transfer matrix method for the analysis of fractal quantum potentials

International Nuclear Information System (INIS)

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

2005-01-01

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

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

International Nuclear Information System (INIS)

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

1984-08-01

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

A transfer matrix method for the analysis of fractal quantum potentials

Energy Technology Data Exchange (ETDEWEB)

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

2005-07-01

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

Fractal Dimension Analysis of Subcortical Gray Matter Structures in Schizophrenia.

Directory of Open Access Journals (Sweden)

Guihu Zhao

Full Text Available A failure of adaptive inference-misinterpreting available sensory information for appropriate perception and action-is at the heart of clinical manifestations of schizophrenia, implicating key subcortical structures in the brain including the hippocampus. We used high-resolution, three-dimensional (3D fractal geometry analysis to study subtle and potentially biologically relevant structural alterations (in the geometry of protrusions, gyri and indentations, sulci in subcortical gray matter (GM in patients with schizophrenia relative to healthy individuals. In particular, we focus on utilizing Fractal Dimension (FD, a compact shape descriptor that can be computed using inputs with irregular (i.e., not necessarily smooth surfaces in order to quantify complexity (of geometrical properties and configurations of structures across spatial scales of subcortical GM in this disorder. Probabilistic (entropy-based information FD was computed based on the box-counting approach for each of the seven subcortical structures, bilaterally, as well as the brainstem from high-resolution magnetic resonance (MR images in chronic patients with schizophrenia (n = 19 and age-matched healthy controls (n = 19 (age ranges: patients, 22.7-54.3 and healthy controls, 24.9-51.6 years old. We found a significant reduction of FD in the left hippocampus (median: 2.1460, range: 2.07-2.18 vs. median: 2.1730, range: 2.15-2.23, p<0.001; Cohen's effect size, U3 = 0.8158 (95% Confidence Intervals, CIs: 0.6316, 1.0, the right hippocampus (median: 2.1430, range: 2.05-2.19 vs. median: 2.1760, range: 2.12-2.21, p = 0.004; U3 = 0.8421 (CIs: 0.5263, 1, as well as left thalamus (median: 2.4230, range: 2.40-2.44, p = 0.005; U3 = 0.7895 (CIs: 0.5789, 0.9473 in schizophrenia patients, relative to healthy individuals. Our findings provide in-vivo quantitative evidence for reduced surface complexity of hippocampus, with reduced FD indicating a less complex, less regular GM surface detected in

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 ...

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.

Fractal and multifractal analyses of bipartite networks

Science.gov (United States)

Liu, Jin-Long; Wang, Jian; Yu, Zu-Guo; Xie, Xian-Hua

2017-03-01

Bipartite networks have attracted considerable interest in various fields. Fractality and multifractality of unipartite (classical) networks have been studied in recent years, but there is no work to study these properties of bipartite networks. In this paper, we try to unfold the self-similarity structure of bipartite networks by performing the fractal and multifractal analyses for a variety of real-world bipartite network data sets and models. First, we find the fractality in some bipartite networks, including the CiteULike, Netflix, MovieLens (ml-20m), Delicious data sets and (u, v)-flower model. Meanwhile, we observe the shifted power-law or exponential behavior in other several networks. We then focus on the multifractal properties of bipartite networks. Our results indicate that the multifractality exists in those bipartite networks possessing fractality. To capture the inherent attribute of bipartite network with two types different nodes, we give the different weights for the nodes of different classes, and show the existence of multifractality in these node-weighted bipartite networks. In addition, for the data sets with ratings, we modify the two existing algorithms for fractal and multifractal analyses of edge-weighted unipartite networks to study the self-similarity of the corresponding edge-weighted bipartite networks. The results show that our modified algorithms are feasible and can effectively uncover the self-similarity structure of these edge-weighted bipartite networks and their corresponding node-weighted versions.

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

Science.gov (United States)

Macintosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan

2013-05-01

Animal behaviour exhibits fractal structure in space and time. Fractal properties in animal space-use have been explored extensively under the Lévy flight foraging hypothesis, but studies of behaviour change itself through time are rarer, have typically used shorter sequences generated in the laboratory, and generally lack critical assessment of their results. We thus performed an in-depth analysis of fractal time in binary dive sequences collected via bio-logging from free-ranging little penguins (Eudyptula minor) across full-day foraging trips (216 data points; 4 orders of temporal magnitude). Results from 4 fractal methods show that dive sequences are long-range dependent and persistent across ca. 2 orders of magnitude. This fractal structure correlated with trip length and time spent underwater, but individual traits had little effect. Fractal time is a fundamental characteristic of penguin foraging behaviour, and its investigation is thus a promising avenue for research on interactions between animals and their environments.

Three-dimensional fractal geometry for gas permeation in microchannels

NARCIS (Netherlands)

Malankowska, Magdalena; Schlautmann, Stefan; Berenschot, Erwin J.W.; Tiggelaar, Roald M.; Pina, Maria Pilar; Mallada, Reyes; Tas, Niels R.; Gardeniers, Han

2018-01-01

The novel concept of a microfluidic chip with an integrated three-dimensional fractal geometry with nanopores, acting as a gas transport membrane, is presented. The method of engineering the 3D fractal structure is based on a combination of anisotropic etching of silicon and corner lithography. The

Unified Mie and fractal scattering by cells and experimental study on application in optical characterization of cellular and subcellular structures.

Science.gov (United States)

Xu, Min; Wu, Tao T; Qu, Jianan Y

2008-01-01

A unified Mie and fractal model for light scattering by biological cells is presented. This model is shown to provide an excellent global agreement with the angular dependent elastic light scattering spectroscopy of cells over the whole visible range (400 to 700 nm) and at all scattering angles (1.1 to 165 deg) investigated. Mie scattering from the bare cell and the nucleus is found to dominate light scattering in the forward directions, whereas the random fluctuation of the background refractive index within the cell, behaving as a fractal random continuous medium, is found to dominate light scattering at other angles. Angularly dependent elastic light scattering spectroscopy aided by the unified Mie and fractal model is demonstrated to be an effective noninvasive approach to characterize biological cells and their internal structures. The acetowhitening effect induced by applying acetic acid on epithelial cells is investigated as an example. The changes in morphology and refractive index of epithelial cells, nuclei, and subcellular structures after the application of acetic acid are successfully probed and quantified using the proposed approach. The unified Mie and fractal model may serve as the foundation for optical detection of precancerous and cancerous changes in biological cells and tissues based on light scattering techniques.

Dimensional analysis, scaling and fractals

International Nuclear Information System (INIS)

Timm, L.C.; Reichardt, K.; Oliveira Santos Bacchi, O.

2004-01-01

straight line, can be divided into N identical parts, so that each part is a new straight line segment represented in a scale r = 1/N of the original segment. With the indispensable aid of computers, fractal geometry is developing very fast in several areas of knowledge, including arts, as a new tool to better understand nature. In agronomic research it is used to study the dynamic processes that occur in soils (water, solute, heat and gas movements), soil structure, plant architecture and development, drainage of watersheds, etc. Fractal models that simulate soil structure are also used to better understand soil behaviour. The fractal characteristic of several soil attributes has led to the use of these new technologies in substitution to several empirical procedures

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.

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.

Fractals for Geoengineering

Science.gov (United States)

Oleshko, Klaudia; de Jesús Correa López, María; Romero, Alejandro; Ramírez, Victor; Pérez, Olga

2016-04-01

The effectiveness of fractal toolbox to capture the scaling or fractal probability distribution, and simply fractal statistics of main hydrocarbon reservoir attributes, was highlighted by Mandelbrot (1995) and confirmed by several researchers (Zhao et al., 2015). Notwithstanding, after more than twenty years, it's still common the opinion that fractals are not useful for the petroleum engineers and especially for Geoengineering (Corbett, 2012). In spite of this negative background, we have successfully applied the fractal and multifractal techniques to our project entitled "Petroleum Reservoir as a Fractal Reactor" (2013 up to now). The distinguishable feature of Fractal Reservoir is the irregular shapes and rough pore/solid distributions (Siler, 2007), observed across a broad range of scales (from SEM to seismic). At the beginning, we have accomplished the detailed analysis of Nelson and Kibler (2003) Catalog of Porosity and Permeability, created for the core plugs of siliciclastic rocks (around ten thousand data were compared). We enriched this Catalog by more than two thousand data extracted from the last ten years publications on PoroPerm (Corbett, 2012) in carbonates deposits, as well as by our own data from one of the PEMEX, Mexico, oil fields. The strong power law scaling behavior was documented for the major part of these data from the geological deposits of contrasting genesis. Based on these results and taking into account the basic principles and models of the Physics of Fractals, introduced by Per Back and Kan Chen (1989), we have developed new software (Muukíl Kaab), useful to process the multiscale geological and geophysical information and to integrate the static geological and petrophysical reservoir models to dynamic ones. The new type of fractal numerical model with dynamical power law relations among the shapes and sizes of mesh' cells was designed and calibrated in the studied area. The statistically sound power law relations were established

Shower fractal dimension analysis in a highly-granular calorimeter

CERN Document Server

Ruan, M

2014-01-01

We report on an investigation of the self-similar structure of particle showers recorded at a highly-granular calorimeter. On both simulated and experimental data, a strong correlation between the number of hits and the spatial scale of the readout channels is observed, from which we define the shower fractal dimension. The measured fractal dimension turns out to be strongly dependent on particle type, which enables new approaches for particle identification. A logarithmic dependence of the particle energy on the fractal dimension is also observed.

Fractals everywhere

CERN Document Server

Barnsley, Michael F

2012-01-01

""Difficult concepts are introduced in a clear fashion with excellent diagrams and graphs."" - Alan E. Wessel, Santa Clara University""The style of writing is technically excellent, informative, and entertaining."" - Robert McCartyThis new edition of a highly successful text constitutes one of the most influential books on fractal geometry. An exploration of the tools, methods, and theory of deterministic geometry, the treatment focuses on how fractal geometry can be used to model real objects in the physical world. Two sixteen-page full-color inserts contain fractal images, and a bonus CD of

Long-Range Order and Fractality in the Structure and Organization of Eukaryotic Genomes

Science.gov (United States)

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.

Space-coiling fractal metamaterial with multi-bandgaps on subwavelength scale

Science.gov (United States)

Man, Xianfeng; Liu, Tingting; Xia, Baizhan; Luo, Zhen; Xie, Longxiang; Liu, Jian

2018-06-01

Acoustic metamaterials are remarkably different from conventional materials, as they can flexibly manipulate and control the propagation of sound waves. Unlike the locally resonant metamaterials introduced in earlier studies, we designed an ultraslow artificial structure with a sound speed much lower than that in air. In this paper, the space-coiling approach is proposed for achieving artificial metamaterial for extremely low-frequency airborne sound. In addition, the self-similar fractal technique is utilized for designing space-coiling Mie-resonance-based metamaterials (MRMMs) to obtain a band-dispersive spectrum. The band structures of two-dimensional (2D) acoustic metamaterials with different fractal levels are illustrated using the finite element method. The low-frequency bandgap can easily be formed, and multi-bandgap properties are observed in high-level fractals. Furthermore, the designed MRMMs with higher order fractal space coiling shows a good robustness against irregular arrangement. Besides, the proposed artificial structure was found to modify and control the radiation field arbitrarily. Thus, this work provides useful guidelines for the design of acoustic filtering devices and acoustic wavefront shaping applications on the subwavelength scale.

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

DEFF Research Database (Denmark)

Andronache, Ion; Fensholt, Rasmus; Ahammer, Helmut

2017-01-01

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

Fractal Geometry and Stochastics V

CERN Document Server

Falconer, Kenneth; Zähle, Martina

2015-01-01

This book brings together leading contributions from the fifth conference on Fractal Geometry and Stochastics held in Tabarz, Germany, in March 2014. The book is divided into five sections covering different facets of this fast developing area: geometric measure theory, self-similar fractals and recurrent structures, analysis and algebra on fractals, multifractal theory, and random constructions. There are state-of-the-art surveys as well as papers highlighting more specific recent advances. The authors are world-experts who present their topics comprehensibly and attractively. The book provides an accessible gateway to the subject for newcomers as well as a reference for recent developments for specialists. Authors include: Krzysztof Barański, Julien Barral, Kenneth Falconer, De-Jun Feng, Peter J. Grabner, Rostislav Grigorchuk, Michael Hinz, Stéphane Jaffard, Maarit Järvenpää, Antti Käenmäki, Marc Kesseböhmer, Michel Lapidus, Klaus Mecke, Mark Pollicott,  Michał Rams, Pablo Shmerkin, and András Te...

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.

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

Science.gov (United States)

Bai, Yanan; Huang, Ning; Sun, Lina

2018-06-01

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

A conservation law, entropy principle and quantization of fractal dimensions in hadron interactions

Science.gov (United States)

Zborovský, I.

2018-04-01

Fractal self-similarity of hadron interactions demonstrated by the z-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable z is a function of the momentum fractions x1 and x2 of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions ya and yb of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the z-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

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

Directory of Open Access Journals (Sweden)

Jian Xiong

2015-01-01

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

Fractal mechanism for characterizing singularity of mode shape for damage detection

Energy Technology Data Exchange (ETDEWEB)

Cao, M. S. [Department of Engineering Mechanics, Hohai University, Nanjing 210098 (China); Ostachowicz, W. [Institute of Fluid-Flow Machinery, Polish Academy of Sciences, ul. Fiszera 14, 80-952 Gdansk (Poland); Faculty of Automotive and Construction Machinery, Warsaw University of Technology, Narbutta 84, 02-524 Warsaw (Poland); Bai, R. B., E-mail: bairunbo@gmail.com [Department of Engineering Mechanics, Shandong Agricultural University, Taian 271000 (China); Radzieński, M. [Institute of Fluid-Flow Machinery, Polish Academy of Sciences, ul. Fiszera 14, 80-952 Gdansk (Poland)

2013-11-25

Damage is an ordinary physical phenomenon jeopardizing structural safety; damage detection is an ongoing interdisciplinary issue. Waveform fractal theory has provided a promising resource for detecting damage in plates while presenting a concomitant problem: susceptibility to false features of damage. This study proposes a fractal dimension method based on affine transformation to address this problem. Physical experiments using laser measurement demonstrate that this method can substantially eliminate false features of damage and accurately identify complex cracks in plates, providing a fundamental mechanism that brings the merits of waveform fractal theory into full play in structural damage detection applications.

Structure-function relationship of skeletal muscle provides inspiration for design of new artificial muscle

Science.gov (United States)

Gao, Yingxin; Zhang, Chi

2015-03-01

A variety of actuator technologies have been developed to mimic biological skeletal muscle that generates force in a controlled manner. Force generation process of skeletal muscle involves complicated biophysical and biochemical mechanisms; therefore, it is impossible to replace biological muscle. In biological skeletal muscle tissue, the force generation of a muscle depends not only on the force generation capacity of the muscle fiber, but also on many other important factors, including muscle fiber type, motor unit recruitment, architecture, structure and morphology of skeletal muscle, all of which have significant impact on the force generation of the whole muscle or force transmission from muscle fibers to the tendon. Such factors have often been overlooked, but can be incorporated in artificial muscle design, especially with the discovery of new smart materials and the development of innovative fabrication and manufacturing technologies. A better understanding of the physiology and structure-function relationship of skeletal muscle will therefore benefit the artificial muscle design. In this paper, factors that affect muscle force generation are reviewed. Mathematical models used to model the structure-function relationship of skeletal muscle are reviewed and discussed. We hope the review will provide inspiration for the design of a new generation of artificial muscle by incorporating the structure-function relationship of skeletal muscle into the design of artificial muscle.

Bridging Three Orders of Magnitude: Multiple Scattered Waves Sense Fractal Microscopic Structures via Dispersion

Science.gov (United States)

Lambert, Simon A.; Näsholm, Sven Peter; Nordsletten, David; Michler, Christian; Juge, Lauriane; Serfaty, Jean-Michel; Bilston, Lynne; Guzina, Bojan; Holm, Sverre; Sinkus, Ralph

2015-08-01

Wave scattering provides profound insight into the structure of matter. Typically, the ability to sense microstructure is determined by the ratio of scatterer size to probing wavelength. Here, we address the question of whether macroscopic waves can report back the presence and distribution of microscopic scatterers despite several orders of magnitude difference in scale between wavelength and scatterer size. In our analysis, monosized hard scatterers 5 μ m in radius are immersed in lossless gelatin phantoms to investigate the effect of multiple reflections on the propagation of shear waves with millimeter wavelength. Steady-state monochromatic waves are imaged in situ via magnetic resonance imaging, enabling quantification of the phase velocity at a voxel size big enough to contain thousands of individual scatterers, but small enough to resolve the wavelength. We show in theory, experiments, and simulations that the resulting coherent superposition of multiple reflections gives rise to power-law dispersion at the macroscopic scale if the scatterer distribution exhibits apparent fractality over an effective length scale that is comparable to the probing wavelength. Since apparent fractality is naturally present in any random medium, microstructure can thereby leave its fingerprint on the macroscopically quantifiable power-law exponent. Our results are generic to wave phenomena and carry great potential for sensing microstructure that exhibits intrinsic fractality, such as, for instance, vasculature.

The pore structure and fractal characteristics of shales with low thermal maturity from the Yuqia Coalfield, northern Qaidam Basin, northwestern China

Science.gov (United States)

Hou, Haihai; Shao, Longyi; Li, Yonghong; Li, Zhen; Zhang, Wenlong; Wen, Huaijun

2018-03-01

The continental shales from the Middle Jurassic Shimengou Formation of the northern Qaidam Basin, northwestern China, have been investigated in recent years because of their shale gas potential. In this study, a total of twenty-two shale samples were collected from the YQ-1 borehole in the Yuqia Coalfield, northern Qaidam Basin. The total organic carbon (TOC) contents, pore structure parameters, and fractal characteristics of the samples were investigated using TOC analysis, low-temperature nitrogen adsorption experiments, and fractal analysis. The results show that the average pore size of the Shimengou shales varied from 8.149 nm to 20.635 nm with a mean value of 10.74 nm, which is considered mesopore-sized. The pores of the shales are mainly inkbottle- and slit-shaped. The sedimentary environment plays an essential role in controlling the TOC contents of the low maturity shales, with the TOC values of shales from deep to semi-deep lake facies (mean: 5.23%) being notably higher than those of the shore-shallow lake facies (mean: 0.65%). The fractal dimensions range from 2.4639 to 2.6857 with a mean of 2.6122, higher than those of marine shales, which indicates that the pore surface was rougher and the pore structure more complex in these continental shales. The fractal dimensions increase with increasing total pore volume and total specific surface area, and with decreasing average pore size. With increasing TOC contents in shales, the fractal dimensions increase first and then decrease, with the highest value occurring at 2% of TOC content, which is in accordance with the trends between the TOC and both total specific surface area and total pore volume. The pore structure complexity and pore surface roughness of these low-maturity shales would be controlled by the combined effects of both sedimentary environments and the TOC contents.

Evaluation of peri-implant bone using fractal analysis

International Nuclear Information System (INIS)

Jung, Yun Hoa

2005-01-01

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

THE FRACTAL MARKET HYPOTHESIS

Directory of Open Access Journals (Sweden)

FELICIA RAMONA BIRAU

2012-05-01

Full Text Available In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and of course, the manner in which they interpret that information may be different. Also, Fractal Market Hypothesis refers to the way that liquidity and investment horizons influence the behaviour of financial investors.

THE FRACTAL MARKET HYPOTHESIS

OpenAIRE

FELICIA RAMONA BIRAU

2012-01-01

In this article, the concept of capital market is analysed using Fractal Market Hypothesis which is a modern, complex and unconventional alternative to classical finance methods. Fractal Market Hypothesis is in sharp opposition to Efficient Market Hypothesis and it explores the application of chaos theory and fractal geometry to finance. Fractal Market Hypothesis is based on certain assumption. Thus, it is emphasized that investors did not react immediately to the information they receive and...

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

Fractal Globule as a model of DNA folding in eukaryotes

Science.gov (United States)

Imakaev, Maksim; Mirny, Leonid

2012-02-01

A recent study (Lieberman-Aiden et al., Science, 2009) observed that the structure of the genome, on the scale of a few megabases, is consistent with a fractal globule. The fractal globule is a quasi-equilibrium state of a polymer after a rapid collapse. First proposed theoretically in 1988, this structure had never been simulated. Fractal globule was seen as a state, in which each subchain is compact, and doesn't mix with other subchains due to their mutual unentanglement (topological constraints). We use GPU-assisted dynamics to create fractal globules of different sizes and observe their dynamics. Our simulations confirm that a polymer after rapid collapse has compact subchains. We measure the scaling of looping probability of a subchain with it's length, and observe the remarkably robust inverse proportionality. Dynamic simulation of the equilibration of this state show that it exhibits Rose type subdiffusion. Due to diffusion, fractal globule quickly degrades to a quasi-equilibrium state, in which subchains of a polymer are mixed, but topologically unentangled. We propose that separation of spatial and topological equilibration of a polymer chain might have implications in different fields of physics.

Aqueous synthesis of LiFePO4 with Fractal Granularity

Science.gov (United States)

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

2016-06-01

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

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

Science.gov (United States)

Reza Namazi, H.

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

Mitered fractal trees: constructions and properties

NARCIS (Netherlands)

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

Naturaleza fractal en redes de cristales de grasas

Directory of Open Access Journals (Sweden)

Gómez Herrera, C.

2004-06-01

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

Fractal based curves in musical creativity: A critical annotation

Science.gov (United States)

Georgaki, Anastasia; Tsolakis, Christos

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

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

Science.gov (United States)

Miller, Bruce N; Rouet, Jean-Louis; Le Guirriec, Emmanuel

2007-09-01

Observations of galaxies over large distances reveal the possibility of a fractal distribution of their positions. The source of fractal behavior is the lack of a length scale in the two body gravitational interaction. However, even with new, larger, sample sizes from recent surveys, it is difficult to extract information concerning fractal properties with confidence. Similarly, three-dimensional N-body simulations with a billion particles only provide a thousand particles per dimension, far too small for accurate conclusions. With one-dimensional models these limitations can be overcome by carrying out simulations with on the order of a quarter of a million particles without compromising the computation of the gravitational force. Here the multifractal properties of two of these models that incorporate different features of the dynamical equations governing the evolution of a matter dominated universe are compared. For each model at least two scaling regions are identified. By employing criteria from dynamical systems theory it is shown that only one of them can be geometrically significant. The results share important similarities with galaxy observations, such as hierarchical clustering and apparent bifractal geometry. They also provide insights concerning possible constraints on length and time scales for fractal structure. They clearly demonstrate that fractal geometry evolves in the mu (position, velocity) space. The observed patterns are simply a shadow (projection) of higher-dimensional structure.

Fractals and foods.

Science.gov (United States)

Peleg, M

1993-01-01

Fractal geometry and related concepts have had only a very minor impact on food research. The very few reported food applications deal mainly with the characterization of the contours of agglomerated instant coffee particles, the surface morphology of treated starch particles, the microstructure of casein gels viewed as a product limited diffusion aggregation, and the jagged mechanical signatures of crunchy dry foods. Fractal geometry describes objects having morphological features that are scale invariant. A demonstration of the self-similarity of fractal objects can be found in the familiar morphology of cauliflower and broccoli, both foods. Processes regulated by nonlinear dynamics can exhibit a chaotic behavior that has fractal characteristics. Examples are mixing of viscous fluids, turbulence, crystallization, agglomeration, diffusion, and possibly food spoilage.

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)

[Features of fractal dynamics EEG of alpha-rhythm in patients with neurotic and neurosis-like disorders].

Science.gov (United States)

Shul'ts, E V; Baburin, I N; Karavaeva, T A; Karvasarskiĭ, B D; Slezin, V B

2011-01-01

Fifty-five patients with neurotic and neurosis-like disorders and 20 healthy controls, aged 17-64 years, have been examined. The basic research method was electroencephalography (EEG) with the fractal analysis of alpha power fluctuations. In patients, the changes in the fractal structure were of the same direction: the decrease of fractal indexes of low-frequency fluctuations and the increase of fractal indexes of mid-frequency fluctuations. Patients with neurosis-like disorders, in comparison to those with neurotic disorders, were characterized by more expressed (quantitative) changes in fractal structures of more extended character. It suggests the presence of deeper pathological changes in patients with neurosis-like disorders.

A possible dynamical process leading to fractal structures

Indian Academy of Sciences (India)

In this paper, we propose a stochastic evolution of the early Universe which can lead to a fractal correlation in galactic distribution in the Universe. The stochastic equation of state, due to fluctuating creation rates of various components in a many-component fluid, leads to a fluctuating expansion rate for the Universe in the ...

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

Science.gov (United States)

Sala, Nicoletta

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

Fractals and the Large-Scale Structure in the Universe

Indian Academy of Sciences (India)

of fractals. Measuring the Length of a Curve. Consider the problem of measuring the length of a ..... a two dimensional smooth surface embedded in 3 dimen- ... interesting measure of a I-dimensional object is its length and not the volume.

Structural, biochemical, cellular, and functional changes in skeletal muscle extracellular matrix with aging

DEFF Research Database (Denmark)

Kragstrup, Tue Wenzel; Kjaer, M; Mackey, A L

2011-01-01

The extracellular matrix (ECM) of skeletal muscle is critical for force transmission and for the passive elastic response of skeletal muscle. Structural, biochemical, cellular, and functional changes in skeletal muscle ECM contribute to the deterioration in muscle mechanical properties with aging......-links and a buildup of advanced glycation end-product cross-links. Altered mechanotransduction, poorer activation of satellite cells, poorer chemotactic and delayed inflammatory responses, and a change in modulators of the ECM are important cellular changes. It is possible that the structural and biochemical changes...... in skeletal muscle ECM contribute to the increased stiffness and impairment in force generated by the contracting muscle fibers seen with aging. The cellular interactions provide and potentially coordinate an adaptation to mechanical loading and ensure successful regeneration after muscle injury. Some...

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.

Fractal physiology and the fractional calculus: a perspective.

Science.gov (United States)

West, Bruce J

2010-01-01

This paper presents a restricted overview of Fractal Physiology focusing on the complexity of the human body and the characterization of that complexity through fractal measures and their dynamics, with fractal dynamics being described by the fractional calculus. Not only are anatomical structures (Grizzi and Chiriva-Internati, 2005), such as the convoluted surface of the brain, the lining of the bowel, neural networks and placenta, fractal, but the output of dynamical physiologic networks are fractal as well (Bassingthwaighte et al., 1994). The time series for the inter-beat intervals of the heart, inter-breath intervals and inter-stride intervals have all been shown to be fractal and/or multifractal statistical phenomena. Consequently, the fractal dimension turns out to be a significantly better indicator of organismic functions in health and disease than the traditional average measures, such as heart rate, breathing rate, and stride rate. The observation that human physiology is primarily fractal was first made in the 1980s, based on the analysis of a limited number of datasets. We review some of these phenomena herein by applying an allometric aggregation approach to the processing of physiologic time series. This straight forward method establishes the scaling behavior of complex physiologic networks and some dynamic models capable of generating such scaling are reviewed. These models include simple and fractional random walks, which describe how the scaling of correlation functions and probability densities are related to time series data. Subsequently, it is suggested that a proper methodology for describing the dynamics of fractal time series may well be the fractional calculus, either through the fractional Langevin equation or the fractional diffusion equation. A fractional operator (derivative or integral) acting on a fractal function, yields another fractal function, allowing us to construct a fractional Langevin equation to describe the evolution of a

Fractal design concepts for stretchable electronics.

Science.gov (United States)

Fan, Jonathan A; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J; Huang, Yonggang; Rogers, John A

2014-01-01

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

Fractal design concepts for stretchable electronics

Science.gov (United States)

Fan, Jonathan A.; Yeo, Woon-Hong; Su, Yewang; Hattori, Yoshiaki; Lee, Woosik; Jung, Sung-Young; Zhang, Yihui; Liu, Zhuangjian; Cheng, Huanyu; Falgout, Leo; Bajema, Mike; Coleman, Todd; Gregoire, Dan; Larsen, Ryan J.; Huang, Yonggang; Rogers, John A.

2014-02-01

Stretchable electronics provide a foundation for applications that exceed the scope of conventional wafer and circuit board technologies due to their unique capacity to integrate with soft materials and curvilinear surfaces. The range of possibilities is predicated on the development of device architectures that simultaneously offer advanced electronic function and compliant mechanics. Here we report that thin films of hard electronic materials patterned in deterministic fractal motifs and bonded to elastomers enable unusual mechanics with important implications in stretchable device design. In particular, we demonstrate the utility of Peano, Greek cross, Vicsek and other fractal constructs to yield space-filling structures of electronic materials, including monocrystalline silicon, for electrophysiological sensors, precision monitors and actuators, and radio frequency antennas. These devices support conformal mounting on the skin and have unique properties such as invisibility under magnetic resonance imaging. The results suggest that fractal-based layouts represent important strategies for hard-soft materials integration.

Simultaneous realization of slow and fast acoustic waves using a fractal structure of Koch curve.

Science.gov (United States)

Ding, Jin; Fan, Li; Zhang, Shu-Yi; Zhang, Hui; Yu, Wei-Wei

2018-01-24

An acoustic metamaterial based on a fractal structure, the Koch curve, is designed to simultaneously realize slow and fast acoustic waves. Owing to the multiple transmitting paths in the structure resembling the Koch curve, the acoustic waves travelling along different paths interfere with each other. Therefore, slow waves are created on the basis of the resonance of a Koch-curve-shaped loop, and meanwhile, fast waves even with negative group velocities are obtained due to the destructive interference of two acoustic waves with opposite phases. Thus, the transmission of acoustic wave can be freely manipulated with the Koch-curve shaped structure.

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

CERN Document Server

Lapidus, Michel L; Žubrinić, Darko

2017-01-01

This monograph gives a state-of-the-art and accessible treatment of a new general higher-dimensional theory of complex dimensions, valid for arbitrary bounded subsets of Euclidean spaces, as well as for their natural generalization, relative fractal drums. It provides a significant extension of the existing theory of zeta functions for fractal strings to fractal sets and arbitrary bounded sets in Euclidean spaces of any dimension. Two new classes of fractal zeta functions are introduced, namely, the distance and tube zeta functions of bounded sets, and their key properties are investigated. The theory is developed step-by-step at a slow pace, and every step is well motivated by numerous examples, historical remarks and comments, relating the objects under investigation to other concepts. Special emphasis is placed on the study of complex dimensions of bounded sets and their connections with the notions of Minkowski content and Minkowski measurability, as well as on fractal tube formulas. It is shown for the f...

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.

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

CERN Document Server

Lapidus, Michael L

1999-01-01

A fractal drum is a bounded open subset of R. m with a fractal boundary. A difficult problem is to describe the relationship between the shape (geo­ metry) of the drum and its sound (its spectrum). In this book, we restrict ourselves to the one-dimensional case of fractal strings, and their higher dimensional analogues, fractal sprays. We develop a theory of complex di­ mensions of a fractal string, and we study how these complex dimensions relate the geometry with the spectrum of the fractal string. We refer the reader to [Berrl-2, Lapl-4, LapPol-3, LapMal-2, HeLapl-2] and the ref­ erences therein for further physical and mathematical motivations of this work. (Also see, in particular, Sections 7. 1, 10. 3 and 10. 4, along with Ap­ pendix B. ) In Chapter 1, we introduce the basic object of our research, fractal strings (see [Lapl-3, LapPol-3, LapMal-2, HeLapl-2]). A 'standard fractal string' is a bounded open subset of the real line. Such a set is a disjoint union of open intervals, the lengths of which ...

Research on the fractal structure in the Chinese stock market

Science.gov (United States)

Zhuang, Xin-tian; Huang, Xiao-yuan; Sha, Yan-li

2004-02-01

Applying fractal theory, this paper probes and discusses self-similarity and scale invariance of the Chinese stock market. It analyses three kinds of scale indexes, i.e., autocorrelation index, Hurst index and the scale index on the basis of detrended fluctuation analysis (DFA) algorithm and promotes DFA into a recursive algorithm. Using the three kinds of scale indexes, we conduct empirical research on the Chinese Shanghai and Shenzhen stock markets. The results indicate that the rate of returns of the two stock markets does not obey the normal distribution. A correlation exists between the stock price indexes over time scales. The stock price indexes exhibit fractal time series. It indicates that the policy guide hidden at the back influences the characteristic of the Chinese stock market.

Persistent fluctuations in stride intervals under fractal auditory stimulation.

Science.gov (United States)

Marmelat, Vivien; Torre, Kjerstin; Beek, Peter J; Daffertshofer, Andreas

2014-01-01

Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.

FRACTAL ANALYSIS OF PHYSICAL ADSORPTION ON SURFACES OF ACID ACTIVATED BENTONITES FROM SERBIA

Directory of Open Access Journals (Sweden)

Ljiljana Rožić

2008-11-01

Full Text Available Solid surfaces are neither ideally regular, that is, morphological and energeticcally homogeneous, nor are they fully irregular or fractal. Instead, real solid surfaces exhibit a limited degree of organization quantified by the fractal dimension, D. Fractal analysis was applied to investigate the effect of concentrations of HCl solutions on the structural and textural properties of chemically activated bentonite from southern Serbia. Acid treatment of bentonites is applied in order to remove impurities and various exchangeable cations from bentonite clay. Important physical changes in acid-activated smectite are the increase of the specific surface area and of the average pore volume, depending on acid strength, time and temperature of a treatment. On the basis of the sorption-structure analysis, the fractal dimension of the bentonite surfaces was determined by Mahnke and Mögel method. The fractal dimension evaluated by this method was 2.11 for the AB3 and 1.94 for the AB4.5 sample. The estimation of the values of the fractal dimension of activated bentonites was performed in the region of small pores, 0.5 nm < rp < 2 nm.

Electromagnetism on anisotropic fractal media

Science.gov (United States)

Ostoja-Starzewski, Martin

2013-04-01

Basic equations of electromagnetic fields in anisotropic fractal media are obtained using a dimensional regularization approach. First, a formulation based on product measures is shown to satisfy the four basic identities of the vector calculus. This allows a generalization of the Green-Gauss and Stokes theorems as well as the charge conservation equation on anisotropic fractals. Then, pursuing the conceptual approach, we derive the Faraday and Ampère laws for such fractal media, which, along with two auxiliary null-divergence conditions, effectively give the modified Maxwell equations. Proceeding on a separate track, we employ a variational principle for electromagnetic fields, appropriately adapted to fractal media, so as to independently derive the same forms of these two laws. It is next found that the parabolic (for a conducting medium) and the hyperbolic (for a dielectric medium) equations involve modified gradient operators, while the Poynting vector has the same form as in the non-fractal case. Finally, Maxwell's electromagnetic stress tensor is reformulated for fractal systems. In all the cases, the derived equations for fractal media depend explicitly on fractal dimensions in three different directions and reduce to conventional forms for continuous media with Euclidean geometries upon setting these each of dimensions equal to unity.

Inkjet-Printed Ultra Wide Band Fractal Antennas

KAUST Repository

Maza, Armando Rodriguez

2012-05-01

In this work, Paper-based inkjet-printed Ultra-wide band (UWB) fractal antennas are presented. Three new designs, a combined UWB fractal monopole based on the fourth order Koch Snowflake fractal which utilizes a Sierpinski Gasket fractal for ink reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics. It is shown that fractals prove to be a successful method of reducing fabrication cost in inkjet printed antennas while retaining or enhancing printed antenna performance.

Quantitative multi-scale analysis of mineral distributions and fractal pore structures for a heterogeneous Junger Basin shale

International Nuclear Information System (INIS)

Wang, Y.D.; Ren, Y.Q.; Hu, T.; Deng, B.; Xiao, T.Q.; Liu, K.Y.; Yang, Y.S.

2016-01-01

Three dimensional (3D) characterization of shales has recently attracted wide attentions in relation to the growing importance of shale oil and gas. Obtaining a complete 3D compositional distribution of shale has proven to be challenging due to its multi-scale characteristics. A combined multi-energy X-ray micro-CT technique and data-constrained modelling (DCM) approach has been used to quantitatively investigate the multi-scale mineral and porosity distributions of a heterogeneous shale from the Junger Basin, northwestern China by sub-sampling. The 3D sub-resolution structures of minerals and pores in the samples are quantitatively obtained as the partial volume fraction distributions, with colours representing compositions. The shale sub-samples from two areas have different physical structures for minerals and pores, with the dominant minerals being feldspar and dolomite, respectively. Significant heterogeneities have been observed in the analysis. The sub-voxel sized pores form large interconnected clusters with fractal structures. The fractal dimensions of the largest clusters for both sub-samples were quantitatively calculated and found to be 2.34 and 2.86, respectively. The results are relevant in quantitative modelling of gas transport in shale reservoirs

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

Random walk through fractal environments

OpenAIRE

Isliker, H.; Vlahos, L.

2002-01-01

We analyze random walk through fractal environments, embedded in 3-dimensional, permeable space. Particles travel freely and are scattered off into random directions when they hit the fractal. The statistical distribution of the flight increments (i.e. of the displacements between two consecutive hittings) is analytically derived from a common, practical definition of fractal dimension, and it turns out to approximate quite well a power-law in the case where the dimension D of the fractal is ...

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

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.

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-03-10

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

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

Science.gov (United States)

Squarcina, Letizia; De Luca, Alberto; Bellani, Marcella; Brambilla, Paolo; Turkheimer, Federico E.; Bertoldo, Alessandra

2015-02-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders.

Fractal analysis of MRI data for the characterization of patients with schizophrenia and bipolar disorder

International Nuclear Information System (INIS)

Squarcina, Letizia; Bellani, Marcella; De Luca, Alberto; Bertoldo, Alessandra; Brambilla, Paolo; Turkheimer, Federico E

2015-01-01

Fractal geometry can be used to analyze shape and patterns in brain images. With this study we use fractals to analyze T1 data of patients affected by schizophrenia or bipolar disorder, with the aim of distinguishing between healthy and pathological brains using the complexity of brain structure, in particular of grey matter, as a marker of disease. 39 healthy volunteers, 25 subjects affected by schizophrenia and 11 patients affected by bipolar disorder underwent an MRI session. We evaluated fractal dimension of the brain cortex and its substructures, calculated with an algorithm based on the box-count algorithm. We modified this algorithm, with the aim of avoiding the segmentation processing step and using all the information stored in the image grey levels. Moreover, to increase sensitivity to local structural changes, we computed a value of fractal dimension for each slice of the brain or of the particular structure. To have reference values in comparing healthy subjects with patients, we built a template by averaging fractal dimension values of the healthy volunteers data. Standard deviation was evaluated and used to create a confidence interval. We also performed a slice by slice t-test to assess the difference at slice level between the three groups. Consistent average fractal dimension values were found across all the structures in healthy controls, while in the pathological groups we found consistent differences, indicating a change in brain and structures complexity induced by these disorders. (paper)

Fractals and chaos

CERN Document Server

Earnshow, R; Jones, H

1991-01-01

This volume is based upon the presentations made at an international conference in London on the subject of 'Fractals and Chaos'. The objective of the conference was to bring together some of the leading practitioners and exponents in the overlapping fields of fractal geometry and chaos theory, with a view to exploring some of the relationships between the two domains. Based on this initial conference and subsequent exchanges between the editors and the authors, revised and updated papers were produced. These papers are contained in the present volume. We thank all those who contributed to this effort by way of planning and organisation, and also all those who helped in the production of this volume. In particular, we wish to express our appreciation to Gerhard Rossbach, Computer Science Editor, Craig Van Dyck, Production Director, and Nancy A. Rogers, who did the typesetting. A. J. Crilly R. A. Earnshaw H. Jones 1 March 1990 Introduction Fractals and Chaos The word 'fractal' was coined by Benoit Mandelbrot i...

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.

Science.gov (United States)

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.

Evolution of fractality in space plasmas of interest to geomagnetic activity

Science.gov (United States)

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

2018-03-01

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

Persistent fluctuations in stride intervals under fractal auditory stimulation.

Directory of Open Access Journals (Sweden)

Vivien Marmelat

Full Text Available Stride sequences of healthy gait are characterized by persistent long-range correlations, which become anti-persistent in the presence of an isochronous metronome. The latter phenomenon is of particular interest because auditory cueing is generally considered to reduce stride variability and may hence be beneficial for stabilizing gait. Complex systems tend to match their correlation structure when synchronizing. In gait training, can one capitalize on this tendency by using a fractal metronome rather than an isochronous one? We examined whether auditory cues with fractal variations in inter-beat intervals yield similar fractal inter-stride interval variability as isochronous auditory cueing in two complementary experiments. In Experiment 1, participants walked on a treadmill while being paced by either an isochronous or a fractal metronome with different variation strengths between beats in order to test whether participants managed to synchronize with a fractal metronome and to determine the necessary amount of variability for participants to switch from anti-persistent to persistent inter-stride intervals. Participants did synchronize with the metronome despite its fractal randomness. The corresponding coefficient of variation of inter-beat intervals was fixed in Experiment 2, in which participants walked on a treadmill while being paced by non-isochronous metronomes with different scaling exponents. As expected, inter-stride intervals showed persistent correlations similar to self-paced walking only when cueing contained persistent correlations. Our results open up a new window to optimize rhythmic auditory cueing for gait stabilization by integrating fractal fluctuations in the inter-beat intervals.

Super Water-Repellent Fractal Surfaces of a Photochromic Diarylethene Induced by UV Light

Science.gov (United States)

Izumi, Norikazu; Minami, Takayuki; Mayama, Hiroyuki; Takata, Atsushi; Nakamura, Shinichiro; Yokojima, Satoshi; Tsujii, Kaoru; Uchida, Kingo

2008-09-01

Photochromic diarylethene forms super water-repellent surfaces upon irradiation with UV light. Microfibril-like crystals grow on the solid diarylethene surface after UV irradiation, and the contact angle of water on the surface becomes larger with increasing surface roughness with time. The fractal analysis was made by the box-counting method for the rough surfaces. There are three regions in the roughness size having the fractal dimension of ca. 2.4 (size of roughness smaller than 5 µm), of ca. 2.2 (size of roughness between 5-40 µm), and of ca. 2.0 (size of roughness larger than 40 µm). The fractal dimension of ca. 2.4 was due to the fibril-like structures generated gradually by UV irradiation on diarylethene surfaces accompanied with an increase in the contact angle. The surface structure with larger fractal dimension mainly contributes to realizing the super water-repellency of the diarylethene surfaces. This mechanism of spontaneous formation of fractal surfaces is similar to that for triglyceride and alkylketene dimer waxes.

Revelation of the Sun Self-Similarity Skeletal Structures

International Nuclear Information System (INIS)

Rantsev-Kartinov, V.A.

2005-01-01

The analysis of databases of photographic images of a surface of the Sun, its atmosphere and the closest its space environment taken at various spatial resolutions and for various types of radiation of a surface of the Sun by means of a method multilevel dynamic contrasting, has revealed presence skeletal structures as on the Sun directly such and in its environment. It is demonstrated the revealed a global structures of the Sun and powerful ejections of mass of its corona, as well as the structures of its atmosphere, protuberances, sun-spots and a globular structures of its photosphere

Lévy processes on a generalized fractal comb

Science.gov (United States)

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)

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

Science.gov (United States)

Sharma, Vijay

2009-09-10

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

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

Science.gov (United States)

Omilion, Alexis; Ibrahim, Mounir; Zhang, Wei

2017-11-01

Fractal square grids offer a unique solution for passive flow control as they can produce wakes with a distinct turbulence intensity peak and a prolonged turbulence decay region at the expense of only minimal pressure drop. While previous studies have solidified this characteristic of fractal square grids, how the number of scales (or fractal iterations N) affect turbulence production and decay of the induced wake is still not well understood. The focus of this research is to determine the relationship between the fractal iteration N and the turbulence produced in the wake flow using well-controlled water-tunnel experiments. Particle Image Velocimetry (PIV) is used to measure the instantaneous velocity fields downstream of four different fractal grids with increasing number of scales (N = 1, 2, 3, and 4) and a conventional single-scale grid. By comparing the turbulent scales and statistics of the wake, we are able to determine how each iteration affects the peak turbulence intensity and the production/decay of turbulence from the grid. In light of the ability of these fractal grids to increase turbulence intensity with low pressure drop, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.

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

Science.gov (United States)

Balankin, Alexander S.; Bory-Reyes, Juan; Shapiro, Michael

2016-02-01

One way to deal with physical problems on nowhere differentiable fractals is the mapping of these problems into the corresponding problems for continuum with a proper fractal metric. On this way different definitions of the fractal metric were suggested to account for the essential fractal features. In this work we develop the metric differential vector calculus in a three-dimensional continuum with a non-Euclidean metric. The metric differential forms and Laplacian are introduced, fundamental identities for metric differential operators are established and integral theorems are proved by employing the metric version of the quaternionic analysis for the Moisil-Teodoresco operator, which has been introduced and partially developed in this paper. The relations between the metric and conventional operators are revealed. It should be emphasized that the metric vector calculus developed in this work provides a comprehensive mathematical formalism for the continuum with any suitable definition of fractal metric. This offers a novel tool to study physics on fractals.

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

Thermal properties of bodies in fractal and cantorian physics

International Nuclear Information System (INIS)

Zmeskal, Oldrich; Buchnicek, Miroslav; Vala, Martin

2005-01-01

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

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

Science.gov (United States)

Rhea, Christopher K; Kiefer, Adam W; D'Andrea, Susan E; Warren, William H; Aaron, Roy K

2014-08-01

Fractal patterns characterize healthy biological systems and are considered to reflect the ability of the system to adapt to varying environmental conditions. Previous research has shown that fractal patterns in gait are altered following natural aging or disease, and this has potential negative consequences for gait adaptability that can lead to increased risk of injury. However, the flexibility of a healthy neurological system to exhibit different fractal patterns in gait has yet to be explored, and this is a necessary step toward understanding human locomotor control. Fifteen participants walked for 15min on a treadmill, either in the absence of a visual stimulus or while they attempted to couple the timing of their gait with a visual metronome that exhibited a persistent fractal pattern (contained long-range correlations) or a random pattern (contained no long-range correlations). The stride-to-stride intervals of the participants were recorded via analog foot pressure switches and submitted to detrended fluctuation analysis (DFA) to determine if the fractal patterns during the visual metronome conditions differed from the baseline (no metronome) condition. DFA α in the baseline condition was 0.77±0.09. The fractal patterns in the stride-to-stride intervals were significantly altered when walking to the fractal metronome (DFA α=0.87±0.06) and to the random metronome (DFA α=0.61±0.10) (both p<.05 when compared to the baseline condition), indicating that a global change in gait dynamics was observed. A variety of strategies were identified at the local level with a cross-correlation analysis, indicating that local behavior did not account for the consistent global changes. Collectively, the results show that a gait dynamics can be shifted in a prescribed manner using a visual stimulus and the shift appears to be a global phenomenon. Copyright © 2014 Elsevier B.V. All rights reserved.

Fractal corrections of BaTiO3-ceramic sintering parameters

Directory of Open Access Journals (Sweden)

Mitić V.V.

2014-01-01

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

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

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

Directory of Open Access Journals (Sweden)

Ion Andronache

2017-02-01

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

Contour fractal analysis of grains

Science.gov (United States)

Guida, Giulia; Casini, Francesca; Viggiani, Giulia MB

2017-06-01

Fractal analysis has been shown to be useful in image processing to characterise the shape and the grey-scale complexity in different applications spanning from electronic to medical engineering (e.g. [1]). Fractal analysis consists of several methods to assign a dimension and other fractal characteristics to a dataset describing geometric objects. Limited studies have been conducted on the application of fractal analysis to the classification of the shape characteristics of soil grains. The main objective of the work described in this paper is to obtain, from the results of systematic fractal analysis of artificial simple shapes, the characterization of the particle morphology at different scales. The long term objective of the research is to link the microscopic features of granular media with the mechanical behaviour observed in the laboratory and in situ.

Fractal-Markovian scaling of turbulent bursting process in open channel flow

International Nuclear Information System (INIS)

Keshavarzi, Ali Reza; Ziaei, Ali Naghi; Homayoun, Emdad; Shirvani, Amin

2005-01-01

The turbulent coherent structure of flow in open channel is a chaotic and stochastic process in nature. The coherence structure of the flow or bursting process consists of a series of eddies with a variety of different length scales and it is very important for the entrainment of sediment particles from the bed. In this study, a fractal-Markovian process is applied to the measured turbulent data in open channel. The turbulent data was measured in an experimental flume using three-dimensional acoustic Doppler velocity meter (ADV). A fractal interpolation function (FIF) algorithm was used to simulate more than 500,000 time series data of measured instantaneous velocity fluctuations and Reynolds shear stress. The fractal interpolation functions (FIF) enables to simulate and construct time series of u', v', and u'v' for any particular movement and state in the Markov process. The fractal dimension of the bursting events is calculated for 16 particular movements with the transition probability of the events based on 1st order Markov process. It was found that the average fractal dimensions of the streamwise flow velocity (u') are; 1.73, 1.74, 1.71 and 1.74 with the transition probability of 60.82%, 63.77%, 59.23% and 62.09% for the 1-1, 2-2, 3-3 and 4-4 movements, respectively. It was also found that the fractal dimensions of Reynold stress u'v' for quadrants 1, 2, 3 and 4 are 1.623, 1.623, 1.625 and 1.618, respectively

An event driven algorithm for fractal cluster formation

NARCIS (Netherlands)

González, S.; Gonzalez Briones, Sebastián; Thornton, Anthony Richard; Luding, Stefan

2011-01-01

A new cluster based event-driven algorithm is developed to simulate the formation of clusters in a two dimensional gas: particles move freely until they collide and "stick" together irreversibly. These clusters aggregate into bigger structures in an isotompic way, forming fractal structures whose

An event driven algorithm for fractal cluster formation

NARCIS (Netherlands)

González, S.; Thornton, Anthony Richard; Luding, Stefan

2010-01-01

A new cluster based event-driven algorithm is developed to simulate the formation of clusters in a two dimensional gas: particles move freely until they collide and "stick" together irreversibly. These clusters aggregate into bigger structures in an isotompic way, forming fractal structures whose

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)

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

Science.gov (United States)

Zeng, Qiang

2017-10-01

Determining the size of nuclei on complex surfaces remains a big challenge in aspects of biological, material and chemical engineering. Here the author reported a simple method to estimate the size of the nuclei in contact with complex (fractal) surfaces. The established approach was based on the assumptions of contact area proportionality for determining nucleation density and the scaling congruence between nuclei and surfaces for identifying contact regimes. It showed three different regimes governing the equations for estimating the nucleation site density. Nuclei in the size large enough could eliminate the effect of fractal structure. Nuclei in the size small enough could lead to the independence of nucleation site density on fractal parameters. Only when nuclei match the fractal scales, the nucleation site density is associated with the fractal parameters and the size of the nuclei in a coupling pattern. The method was validated by the experimental data reported in the literature. The method may provide an effective way to estimate the size of nuclei on fractal surfaces, through which a number of promising applications in relative fields can be envisioned.

Encounters with chaos and fractals

CERN Document Server

Gulick, Denny

2012-01-01

Periodic Points Iterates of Functions Fixed Points Periodic Points Families of Functions The Quadratic Family Bifurcations Period-3 Points The Schwarzian Derivative One-Dimensional Chaos Chaos Transitivity and Strong Chaos Conjugacy Cantor Sets Two-Dimensional Chaos Review of Matrices Dynamics of Linear FunctionsNonlinear Maps The Hénon Map The Horseshoe Map Systems of Differential Equations Review of Systems of Differential Equations Almost Linearity The Pendulum The Lorenz System Introduction to Fractals Self-Similarity The Sierpiński Gasket and Other "Monsters"Space-Filling Curves Similarity and Capacity DimensionsLyapunov Dimension Calculating Fractal Dimensions of Objects Creating Fractals Sets Metric Spaces The Hausdorff Metric Contractions and Affine Functions Iterated Function SystemsAlgorithms for Drawing Fractals Complex Fractals: Julia Sets and the Mandelbrot Set Complex Numbers and Functions Julia Sets The Mandelbrot Set Computer Programs Answers to Selected Exercises References Index.

Psicodiagnóstico fractal

OpenAIRE

Moghilevsky, Débora Estela

2011-01-01

A lo largo de los últimos años del siglo veinte se ha desarrollado la teoría de la complejidad. Este modelo relaciona las ciencias duras tales como la matemática, la teoría del caos, la física cuántica y la geometría fractal con las llamadas seudo ciencias. Dentro de este contexto podemos definir la Psicología Fractal como la ciencia que estudia los aspectos psíquicos como dinámicamente fractales.

Structure of skeletal muscles after hypokinesia and physical loading of middle aerobic power

Directory of Open Access Journals (Sweden)

Serg Popel’

2014-11-01

Full Text Available In the article is shown that determined degree of destructive changes in skeletal muscles is in direct dependence on the term of hypokinesiа limitation. Application of kinesiotherapy intensifies the repair processes and substantially reduces the terms of renewal of structurally-functional properties of skeletal muscles after hypokinesiа.

Theory of potentiostatic current transients for coupled catalytic reaction at random corrugated fractal electrode

International Nuclear Information System (INIS)

Jha, Shailendra K.; Kant, Rama

2010-01-01

We developed a mathematical model for the first order homogeneous catalytic chemical reaction coupled with an electron transfer (EC') on a rough working electrode. Results are obtained for the various roughness models of electrode corrugations, viz., (i) roughness as an exact periodic function, (ii) roughness as a random function with known statistical properties, and (iii) roughness as a random function with statistical self-affine fractality over a finite range of length scales. Method of Green's function is used in the formulation to obtain second-order perturbation (in roughness profile) expressions for the concentration, the local current density and the current transients. A general operator structure between these quantities and arbitrary roughness profile is emphasized. The statistically averaged (randomly rough) electrode response is obtained by an ensemble averaging over all possible surface configurations. An elegant mathematical formula between the average electrochemical current transient and surface structure factor or power-spectrum of roughness is obtained. This formula is used to obtain an explicit equation for the current on an approximately self-affine (or realistic) fractal electrode with a limited range of length scales of irregularities. This description of realistic fractal is obtained by cutoff power law power-spectrum of roughness. The realistic fractal power-spectrum consists of four physical characteristics, viz., the fractal dimension (D H ), lower (l) and upper (L) cutoff length scales of fractality and a proportionality factor (μ), which is related to the topothesy or strength of fractality. Numerical calculations are performed on final results to understand the effect of catalytic reaction and fractal morphological characteristics on potentiostatic current transients.

Design of LTCC Based Fractal Antenna

KAUST Repository

AdbulGhaffar, Farhan

2010-09-01

The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array has been designed for the first time on Low Temperature Co-fired Ceramic (LTCC) based substrate. LTCC provides a suitable platform for the development of these antennas due to its properties of vertical stack up and embedded passives. The complete antenna concept involves integration of this fractal antenna array with a Fresnel lens antenna providing a total gain of 15dB which is appropriate for medium range radar applications. The thesis also presents a comparison between the designed fractal antenna and a conventional patch antenna outlining the advantages of fractal antenna over the later one. The fractal antenna has a bandwidth of 1.8 GHz which is 7.5% of the centre frequency (24GHz) as compared to 1.9% of the conventional patch antenna. Furthermore the fractal design exhibits a size reduction of 53% as compared to the patch antenna. In the end a sensitivity analysis is carried out for the fractal antenna design depicting the robustness of the proposed design against the typical LTCC fabrication tolerances.

2-D Fractal Carpet Antenna Design and Performance

Science.gov (United States)

Barton, C. C.; Tebbens, S. F.; Ewing, J. J.; Peterman, D. J.; Rizki, M. M.

2017-12-01

A 2-D fractal carpet antenna uses a fractal (self-similar) pattern to increase its perimeter by iteration and can receive or transmit electromagnetic radiation within its perimeter-bounded surface area. 2-D fractals are shapes that, at their mathematical limit (infinite iterations) have an infinite perimeter bounding a finite surface area. The fractal dimension describes the degree of space filling and lacunarity which quantifies the size and spatial distribution of open space bounded by a fractal shape. A key aspect of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that are very compact, wideband and multiband. As the number of iterations increases, the antenna operates at higher and higher frequencies. Manifestly different from traditional antenna designs, a fractal antenna can operate at multiple frequencies simultaneously. We have created a MATLAB code to generate deterministic and stochastic modes of Sierpinski carpet fractal antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, number of iterations, and lacunarities have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance

2-D Fractal Wire Antenna Design and Performance

Science.gov (United States)

Tebbens, S. F.; Barton, C. C.; Peterman, D. J.; Ewing, J. J.; Abbott, C. S.; Rizki, M. M.

2017-12-01

A 2-D fractal wire antenna uses a fractal (self-similar) pattern to increase its length by iteration and can receive or transmit electromagnetic radiation. 2-D fractals are shapes that, at their mathematical limit (of infinite iterations) have an infinite length. The fractal dimension describes the degree of space filling. A fundamental property of fractal antennas lies in iteration (repetition) of a fractal pattern over a range of length scales. Iteration produces fractal antennas that can be very compact, wideband and multiband. As the number of iterations increases, the antenna tends to have additional frequencies that minimize far field return loss. This differs from traditional antenna designs in that a single fractal antenna can operate well at multiple frequencies. We have created a MATLAB code to generate deterministic and stochastic modes of fractal wire antennas with a range of fractal dimensions between 1 and 2. Variation in fractal dimension, stochasticity, and number of iterations have been computationally tested using COMSOL Multiphysics software to determine their effect on antenna performance.

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.

Fractal-Based Image Analysis In Radiological Applications

Science.gov (United States)

Dellepiane, S.; Serpico, S. B.; Vernazza, G.; Viviani, R.

1987-10-01

We present some preliminary results of a study aimed to assess the actual effectiveness of fractal theory and to define its limitations in the area of medical image analysis for texture description, in particular, in radiological applications. A general analysis to select appropriate parameters (mask size, tolerance on fractal dimension estimation, etc.) has been performed on synthetically generated images of known fractal dimensions. Moreover, we analyzed some radiological images of human organs in which pathological areas can be observed. Input images were subdivided into blocks of 6x6 pixels; then, for each block, the fractal dimension was computed in order to create fractal images whose intensity was related to the D value, i.e., texture behaviour. Results revealed that the fractal images could point out the differences between normal and pathological tissues. By applying histogram-splitting segmentation to the fractal images, pathological areas were isolated. Two different techniques (i.e., the method developed by Pentland and the "blanket" method) were employed to obtain fractal dimension values, and the results were compared; in both cases, the appropriateness of the fractal description of the original images was verified.

The Sun-Earth connect 2: Modelling patterns of a fractal Sun in time and space using the fine structure constant

Science.gov (United States)

Baker, Robert G. V.

2017-02-01

Self-similar matrices of the fine structure constant of solar electromagnetic force and its inverse, multiplied by the Carrington synodic rotation, have been previously shown to account for at least 98% of the top one hundred significant frequencies and periodicities observed in the ACRIM composite irradiance satellite measurement and the terrestrial 10.7cm Penticton Adjusted Daily Flux data sets. This self-similarity allows for the development of a time-space differential equation (DE) where the solutions define a solar model for transmissions through the core, radiative, tachocline, convective and coronal zones with some encouraging empirical and theoretical results. The DE assumes a fundamental complex oscillation in the solar core and that time at the tachocline is smeared with real and imaginary constructs. The resulting solutions simulate for tachocline transmission, the solar cycle where time-line trajectories either 'loop' as Hermite polynomials for an active Sun or 'tail' as complementary error functions for a passive Sun. Further, a mechanism that allows for the stable energy transmission through the tachocline is explored and the model predicts the initial exponential coronal heating from nanoflare supercharging. The twisting of the field at the tachocline is then described as a quaternion within which neutrinos can oscillate. The resulting fractal bubbles are simulated as a Julia Set which can then aggregate from nanoflares into solar flares and prominences. Empirical examples demonstrate that time and space fractals are important constructs in understanding the behaviour of the Sun, from the impact on climate and biological histories on Earth, to the fractal influence on the spatial distributions of the solar system. The research suggests that there is a fractal clock underpinning solar frequencies in packages defined by the fine structure constant, where magnetic flipping and irradiance fluctuations at phase changes, have periodically impacted on the

Fractal analysis of sulphidic mineral

Directory of Open Access Journals (Sweden)

Miklúšová Viera

2002-03-01

Full Text Available In this paper, the application of fractal theory in the characterization of fragmented surfaces, as well as the mass-size distributions are discussed. The investigated mineral-chalcopyrite of Slovak provenience is characterised after particle size reduction processes-crushing and grinding. The problem how the different size reduction methods influence the surface irregularities of obtained particles is solved. Mandelbrot (1983, introducing the fractal geometry, offered a new way of characterization of surface irregularities by the fractal dimension. The determination of the surface fractal dimension DS consists in measuring the specific surface by the BET method in several fractions into which the comminuted chalcopyrite is sieved. This investigation shows that the specific surface of individual fractions were higher for the crushed sample than for the short-term (3 min ground sample. The surface fractal dimension can give an information about the adsorption sites accessible to molecules of nitrogen and according to this, the value of the fractal dimension is higher for crushed sample.The effect of comminution processes on the mass distribution of particles crushed and ground in air as well as in polar liquids is also discussed. The estimation of fractal dimensions of particles mass distribution is done on the assumption that the particle size distribution is described by the power-law (1. The value of fractal dimension for the mass distribution in the crushed sample is lower than in the sample ground in air, because it is influenced by the energy required for comminution.The sample of chalcopyrite was ground (10min in ethanol and i-butanol [which according to Ikazaki (1991] are characterized by the parameter µ /V, where µ is its dipole moment and V is the molecular volume. The values of µ /V for the used polar liquids are of the same order. That is why the expressive differences in particle size distributions as well as in the values of

Fractality and the law of the wall

Science.gov (United States)

Xu, Haosen H. A.; Yang, X. I. A.

2018-05-01

Fluid motions in the inertial range of isotropic turbulence are fractal, with their space-filling capacity slightly below regular three-dimensional objects, which is a consequence of the energy cascade. Besides the energy cascade, the other often encountered cascading process is the momentum cascade in wall-bounded flows. Despite the long-existing analogy between the two processes, many of the thoroughly investigated aspects of the energy cascade have so far received little attention in studies of the momentum counterpart, e.g., the possibility of the momentum-transferring scales in the logarithmic region being fractal has not been considered. In this work, this possibility is pursued, and we discuss one of its implications. Following the same dimensional arguments that lead to the D =2.33 fractal dimension of wrinkled surfaces in isotropic turbulence, we show that the large-scale momentum-carrying eddies may also be fractal and non-space-filling, which then leads to the power-law scaling of the mean velocity profile. The logarithmic law of the wall, on the other hand, corresponds to space-filling eddies, as suggested by Townsend [The Structure of Turbulent Shear Flow (Cambridge University Press, Cambridge, 1980)]. Because the space-filling capacity is an integral geometric quantity, the analysis presented in this work provides us with a low-order quantity, with which, one would be able to distinguish between the logarithmic law and the power law.

Nonlinear dynamics, fractals, cardiac physiology and sudden death

Science.gov (United States)

Goldberger, Ary L.

1987-01-01

The authors propose a diametrically opposite viewpoint to the generally accepted tendency of equating healthy function with order and disease with chaos. With regard to the question of sudden cardiac death and chaos, it is suggested that certain features of dynamical chaos related to fractal structure and fractal dynamics may be important organizing principles in normal physiology and that certain pathologies, including ventricular fibrillation, represent a class of 'pathological periodicities'. Some laboratory work bearing on the relation of nonlinear analysis to physiological and pathophysiological data is briefly reviewed, with tentative theories and models described in reference to the mechanism of ventricular fibrillation.

Bilipschitz embedding of homogeneous fractals

OpenAIRE

Lü, Fan; Lou, Man-Li; Wen, Zhi-Ying; Xi, Li-Feng

2014-01-01

In this paper, we introduce a class of fractals named homogeneous sets based on some measure versions of homogeneity, uniform perfectness and doubling. This fractal class includes all Ahlfors-David regular sets, but most of them are irregular in the sense that they may have different Hausdorff dimensions and packing dimensions. Using Moran sets as main tool, we study the dimensions, bilipschitz embedding and quasi-Lipschitz equivalence of homogeneous fractals.

Effect of fractal silver electrodes on charge collection and light distribution in semiconducting organic polymer films

Energy Technology Data Exchange (ETDEWEB)

Chamousis, RL; Chang, LL; Watterson, WJ; Montgomery, RD; Taylor, RP; Moule, AJ; Shaheen, SE; Ilan, B; van de Lagemaat, J; Osterloh, FE

2014-08-21

Living organisms use fractal structures to optimize material and energy transport across regions of differing size scales. Here we test the effect of fractal silver electrodes on light distribution and charge collection in organic semiconducting polymer films made of P3HT and PCBM. The semiconducting polymers were deposited onto electrochemically grown fractal silver structures (5000 nm x 500 nm; fractal dimension of 1.71) with PEDOT:PSS as hole-selective interlayer. The fractal silver electrodes appear black due to increased horizontal light scattering, which is shown to improve light absorption in the polymer. According to surface photovoltage spectroscopy, fractal silver electrodes outperform the flat electrodes when the BHJ film thickness is large (>400 nm, 0.4 V photovoltage). Photocurrents of up to 200 microamperes cm(-2) are generated from the bulk heterojunction (BHJ) photoelectrodes under 435 nm LED (10-20 mW cm(-2)) illumination in acetonitrile solution containing 0.005 M ferrocenium hexafluorophosphate as the electron acceptor. The low IPCE values (0.3-0.7%) are due to slow electron transfer to ferrocenium ion and due to shunting along the large metal-polymer interface. Overall, this work provides an initial assessment of the potential of fractal electrodes for organic photovoltaic cells.

Recognition of fractal graphs

NARCIS (Netherlands)

Perepelitsa, VA; Sergienko, [No Value; Kochkarov, AM

1999-01-01

Definitions of prefractal and fractal graphs are introduced, and they are used to formulate mathematical models in different fields of knowledge. The topicality of fractal-graph recognition from the point of view, of fundamental improvement in the efficiency of the solution of algorithmic problems

Fractal analysis of Xylella fastidiosa biofilm formation

Science.gov (United States)

Moreau, A. L. D.; Lorite, G. S.; Rodrigues, C. M.; Souza, A. A.; Cotta, M. A.

2009-07-01

We have investigated the growth process of Xylella fastidiosa biofilms inoculated on a glass. The size and the distance between biofilms were analyzed by optical images; a fractal analysis was carried out using scaling concepts and atomic force microscopy images. We observed that different biofilms show similar fractal characteristics, although morphological variations can be identified for different biofilm stages. Two types of structural patterns are suggested from the observed fractal dimensions Df. In the initial and final stages of biofilm formation, Df is 2.73±0.06 and 2.68±0.06, respectively, while in the maturation stage, Df=2.57±0.08. These values suggest that the biofilm growth can be understood as an Eden model in the former case, while diffusion-limited aggregation (DLA) seems to dominate the maturation stage. Changes in the correlation length parallel to the surface were also observed; these results were correlated with the biofilm matrix formation, which can hinder nutrient diffusion and thus create conditions to drive DLA growth.

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

International Nuclear Information System (INIS)

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

2012-01-01

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

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

Electrical conductivity modeling in fractal non-saturated porous media

Science.gov (United States)

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

2016-12-01

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

Aqueous synthesis of LiFePO4 with Fractal Granularity

OpenAIRE

Cab?n-Huertas, Zahilia; Ayyad, Omar; Dubal, Deepak P.; G?mez-Romero, Pedro

2016-01-01

Lithium iron phosphate (LiFePO4) electrodes with fractal granularity are reported. They were made from a starting material prepared in water by a low cost, easy and environmentally friendly hydrothermal method, thus avoiding the use of organic solvents. Our method leads to pure olivine phase, free of the impurities commonly found after other water-based syntheses. The fractal structures consisted of nanoparticles grown into larger micro-sized formations which in turn agglomerate leading to hi...

Effective Thermal Conductivity of Open Cell Polyurethane Foam Based on the Fractal Theory

Directory of Open Access Journals (Sweden)

Kan Ankang

2013-01-01

Full Text Available Based on the fractal theory, the geometric structure inside an open cell polyurethane foam, which is widely used as adiabatic material, is illustrated. A simplified cell fractal model is created. In the model, the method of calculating the equivalent thermal conductivity of the porous foam is described and the fractal dimension is calculated. The mathematical formulas for the fractal equivalent thermal conductivity combined with gas and solid phase, for heat radiation equivalent thermal conductivity and for the total thermal conductivity, are deduced. However, the total effective heat flux is the summation of the heat conduction by the solid phase and the gas in pores, the radiation, and the convection between gas and solid phase. Fractal mathematical equation of effective thermal conductivity is derived with fractal dimension and vacancy porosity in the cell body. The calculated results have good agreement with the experimental data, and the difference is less than 5%. The main influencing factors are summarized. The research work is useful for the enhancement of adiabatic performance of foam materials and development of new materials.

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

Energy Technology Data Exchange (ETDEWEB)

Clausse, A; Delmastro, D F

1991-12-31

This work presents a description of the research lines carried out by the authors on chaos and fractal theories, oriented to the nuclear field. The possibilities that appear in the nuclear security branch where the information deriving from chaos and fractal techniques may help to the development of better criteria and more reliable designs, are of special importance. (Author). [Espanol] En este trabajo se presenta una descripcion de las lineas de investigacion que los autores estan llevando a cabo en teoria de caos y fractales orientadas al campo nuclear. Es de especial importancia las posibilidades que se abren en el area de la seguridad nuclear, en donde la informacion proveniente de las tecnicas de caos y fractales pueden ayudar al desarrollo de mejores criterios y disenos mas confiables. (Autor).

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)

arXiv Generalized Fragmentation Functions for Fractal Jet Observables

CERN Document Server

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...

Fractal modeling of fluidic leakage through metal sealing surfaces

Science.gov (United States)

Zhang, Qiang; Chen, Xiaoqian; Huang, Yiyong; Chen, Yong

2018-04-01

This paper investigates the fluidic leak rate through metal sealing surfaces by developing fractal models for the contact process and leakage process. An improved model is established to describe the seal-contact interface of two metal rough surface. The contact model divides the deformed regions by classifying the asperities of different characteristic lengths into the elastic, elastic-plastic and plastic regimes. Using the improved contact model, the leakage channel under the contact surface is mathematically modeled based on the fractal theory. The leakage model obtains the leak rate using the fluid transport theory in porous media, considering that the pores-forming percolation channels can be treated as a combination of filled tortuous capillaries. The effects of fractal structure, surface material and gasket size on the contact process and leakage process are analyzed through numerical simulations for sealed ring gaskets.

A Novel Ancient Coin-Like Fractal Multiband Antenna for Wireless Applications

Directory of Open Access Journals (Sweden)

Zhen Yu

2017-01-01

Full Text Available This study proposes a novel square-circle structure fractal multibroadband planar antenna, similar to an ancient Chinese coin-like structure, for second generation (2G, third generation (3G, fourth generation (4G, WLAN, and navigation wireless applications. The device is based on the principles and structural features of conventional monopole antenna elements, combined with the advantages of microstrip antennas and fractal geometry. A fractal method was presented for circular nested square slotted structures, similar to an ancient Chinese copper coin. The proposed antenna adapted five iterations on a fractal structure radiator, which covers more than ten mobile applications in three broad frequency bands with a bandwidth of 70% (1.43–2.97 GHz for DCS1800, TD-SCDMA, WCDMA, CDMA2000, LTE33-41, Bluetooth, GPS (Global Positioning System, BDS (BeiDou Navigation Satellite System, GLONSS (Global Navigation Satellite System, GALILEO (Galileo Satellite Navigation System, and WLAN frequency bands, 16.32% (3.32–3.91 GHz for LTE42, LTE43, and WiMAX frequency bands, and 10.92% (4.85–5.41 GHz for WLAN frequency band. The proposed antenna was fabricated on a 1.6 mm thick G10/FR4 substrate with a dielectric constant of 4.4 and a size of 88.5 × 60 mm2. The measurement results reveal that the omnidirectional radiation patterns achieve a gain of 1.16–3.75 dBi and an efficiency of 40–72%. The good agreement between the measurement results and simulation validates the proposed design approach and satisfies the requirements for various wireless applications.

Two and Three-Phases Fractal Models Application in Soil Saturated Hydraulic Conductivity Estimation

Directory of Open Access Journals (Sweden)

ELNAZ Rezaei abajelu

2017-03-01

Full Text Available Introduction: Soil Hydraulic conductivity is considered as one of the most important hydraulic properties in water and solutionmovement in porous media. In recent years, variousmodels as pedo-transfer functions, fractal models and scaling technique are used to estimate the soil saturated hydraulic conductivity (Ks. Fractal models with two subset of two (solid and pore and three phases (solid, pore and soil fractal (PSF are used to estimate the fractal dimension of soil particles. The PSF represents a generalization of the solid and pore mass fractal models. The PSF characterizes both the solid and pore phases of the porous material. It also exhibits self-similarity to some degree, in the sense that where local structure seems to be similar to the whole structure.PSF models can estimate interface fractal dimension using soil pore size distribution data (PSD and soil moisture retention curve (SWRC. The main objective of this study was to evaluate different fractal models to estimate the Ksparameter. Materials and Methods: The Schaapetal data was used in this study. The complex consists of sixty soil samples. Soil texture, soil bulk density, soil saturated hydraulic conductivity and soil particle size distribution curve were measured by hydrometer method, undistributed soil sample, constant head method and wet sieve method, respectively for all soil samples.Soil water retention curve were determined by using pressure plates apparatus.The Ks parameter could be estimated by Ralws model as a function of fractal dimension by seven fractal models. Fractal models included Fuentes at al. (1996, Hunt and Gee (2002, Bird et al. (2000, Huang and Zhang (2005, Tyler and Wheatcraft (1990, Kutlu et al. (2008, Sepaskhah and Tafteh (2013.Therefore The Ks parameter can be estimated as a function of the DS (fractal dimension by seven fractal models (Table 2.Sensitivity analysis of Rawls model was assessed by making changes±10%, ±20% and±30%(in input parameters

Fractal profit landscape of the stock market.

Science.gov (United States)

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 geometry mathematical foundations and applications

CERN Document Server

Falconer, Kenneth

2013-01-01

The seminal text on fractal geometry for students and researchers: extensively revised and updated with new material, notes and references that reflect recent directions. Interest in fractal geometry continues to grow rapidly, both as a subject that is fascinating in its own right and as a concept that is central to many areas of mathematics, science and scientific research. Since its initial publication in 1990 Fractal Geometry: Mathematical Foundations and Applications has become a seminal text on the mathematics of fractals.  The book introduces and develops the general theory and applica

Determination of effective thermal conductivity for polyurethane foam by use of fractal method

Institute of Scientific and Technical Information of China (English)

SHI Mingheng; LI Xiaochuan; CHEN Yongping

2006-01-01

The microstructure of polyurethane foam is disordered, which influences the foam heat conduction process significantly. In this paper foam structure is described by using the local area fractal dimension in a certain small range of length scales. An equivalent element cell is constructed based on the local fractal dimensions along the directions parallel and transverse to the heat flux. By use of fractal void fraction a simplified heat conduction model is proposed to calculate the effective thermal conductivity of polyurethane foam. The predicted effective thermal conductivity agrees well with the experimental data.

Fractal nature of hydrocarbon deposits. 2. Spatial distribution

International Nuclear Information System (INIS)

Barton, C.C.; Schutter, T.A; Herring, P.R.; Thomas, W.J.; Scholz, C.H.

1991-01-01

Hydrocarbons are unevenly distributed within reservoirs and are found in patches whose size distribution is a fractal over a wide range of scales. The spatial distribution of the patches is also fractal and this can be used to constrain the design of drilling strategies also defined by a fractal dimension. Fractal distributions are scale independent and are characterized by a power-law scaling exponent termed the fractal dimension. The authors have performed fractal analyses on the spatial distribution of producing and showing wells combined and of dry wells in 1,600-mi 2 portions of the Denver and Powder River basins that were nearly completely drilled on quarter-mile square-grid spacings. They have limited their analyses to wells drilled to single stratigraphic intervals so that the map pattern revealed by drilling is representative of the spatial patchiness of hydrocarbons at depth. The fractal dimensions for the spatial patchiness of hydrocarbons in the two basins are 1.5 and 1.4, respectively. The fractal dimension for the pattern of all wells drilled is 1.8 for both basins, which suggests a drilling strategy with a fractal dimension significantly higher than the dimensions 1.5 and 1.4 sufficient to efficiently and economically explore these reservoirs. In fact, the fractal analysis reveals that the drilling strategy used in these basins approaches a fractal dimension of 2.0, which is equivalent to random drilling with no geologic input. Knowledge of the fractal dimension of a reservoir prior to drilling would provide a basis for selecting and a criterion for halting a drilling strategy for exploration whose fractal dimension closely matches that of the spatial fractal dimension of the reservoir, such a strategy should prove more efficient and economical than current practice

Fractal electrodynamics via non-integer dimensional space approach

Science.gov (United States)

Tarasov, Vasily E.

2015-09-01

Using the recently suggested vector calculus for non-integer dimensional space, we consider electrodynamics problems in isotropic case. This calculus allows us to describe fractal media in the framework of continuum models with non-integer dimensional space. We consider electric and magnetic fields of fractal media with charges and currents in the framework of continuum models with non-integer dimensional spaces. An application of the fractal Gauss's law, the fractal Ampere's circuital law, the fractal Poisson equation for electric potential, and equation for fractal stream of charges are suggested. Lorentz invariance and speed of light in fractal electrodynamics are discussed. An expression for effective refractive index of non-integer dimensional space is suggested.

A Double-Minded Fractal

Science.gov (United States)

Simoson, Andrew J.

2009-01-01

This article presents a fun activity of generating a double-minded fractal image for a linear algebra class once the idea of rotation and scaling matrices are introduced. In particular the fractal flip-flops between two words, depending on the level at which the image is viewed. (Contains 5 figures.)

Single-Image Super-Resolution Based on Rational Fractal Interpolation.

Science.gov (United States)

Zhang, Yunfeng; Fan, Qinglan; Bao, Fangxun; Liu, Yifang; Zhang, Caiming

2018-08-01

This paper presents a novel single-image super-resolution (SR) procedure, which upscales a given low-resolution (LR) input image to a high-resolution image while preserving the textural and structural information. First, we construct a new type of bivariate rational fractal interpolation model and investigate its analytical properties. This model has different forms of expression with various values of the scaling factors and shape parameters; thus, it can be employed to better describe image features than current interpolation schemes. Furthermore, this model combines the advantages of rational interpolation and fractal interpolation, and its effectiveness is validated through theoretical analysis. Second, we develop a single-image SR algorithm based on the proposed model. The LR input image is divided into texture and non-texture regions, and then, the image is interpolated according to the characteristics of the local structure. Specifically, in the texture region, the scaling factor calculation is the critical step. We present a method to accurately calculate scaling factors based on local fractal analysis. Extensive experiments and comparisons with the other state-of-the-art methods show that our algorithm achieves competitive performance, with finer details and sharper edges.

Conference on Fractals and Related Fields III

CERN Document Server

Seuret, Stéphane

2017-01-01

This contributed volume provides readers with an overview of the most recent developments in the mathematical fields related to fractals, including both original research contributions, as well as surveys from many of the leading experts on modern fractal theory and applications. It is an outgrowth of the Conference of Fractals and Related Fields III, that was held on September 19-25, 2015 in île de Porquerolles, France. Chapters cover fields related to fractals such as harmonic analysis, multifractal analysis, geometric measure theory, ergodic theory and dynamical systems, probability theory, number theory, wavelets, potential theory, partial differential equations, fractal tilings, combinatorics, and signal and image processing. The book is aimed at pure and applied mathematicians in these areas, as well as other researchers interested in discovering the fractal domain.

Inkjet-Printed Ultra Wide Band Fractal Antennas

KAUST Repository

Maza, Armando Rodriguez

2012-01-01

reduction, a Cantor-based fractal antenna which performs a larger bandwidth compared to previously published UWB Cantor fractal monopole antenna, and a 3D loop fractal antenna which attains miniaturization, impedance matching and multiband characteristics

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.

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.

The Application of Fractal and Multifractal Theory in Hydraulic-Flow-Unit Characterization and Permeability Estimation

Science.gov (United States)

Chen, X.; Yao, G.; Cai, J.

2017-12-01

Pore structure characteristics are important factors in influencing the fluid transport behavior of porous media, such as pore-throat ratio, pore connectivity and size distribution, moreover, wettability. To accurately characterize the diversity of pore structure among HFUs, five samples selected from different HFUs (porosities are approximately equal, however permeability varies widely) were chosen to conduct micro-computerized tomography test to acquire direct 3D images of pore geometries and to perform mercury injection experiments to obtain the pore volume-radii distribution. To characterize complex and high nonlinear pore structure of all samples, three classic fractal geometry models were applied. Results showed that each HFU has similar box-counting fractal dimension and generalized fractal dimension in the number-area model, but there are significant differences in multifractal spectrums. In the radius-volume model, there are three obvious linear segments, corresponding to three fractal dimension values, and the middle one is proved as the actual fractal dimension according to the maximum radius. In the number-radius model, the spherical-pore size distribution extracted by maximum ball algorithm exist a decrease in the number of small pores compared with the fractal power rate rather than the traditional linear law. Among the three models, only multifractal analysis can classify the HFUs accurately. Additionally, due to the tightness and low-permeability in reservoir rocks, connate water film existing in the inner surface of pore channels commonly forms bound water. The conventional model which is known as Yu-Cheng's model has been proved to be typically not applicable. Considering the effect of irreducible water saturation, an improved fractal permeability model was also deduced theoretically. The comparison results showed that the improved model can be applied to calculate permeability directly and accurately in such unconventional rocks.

Fractals, malware, and data models

Science.gov (United States)

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.

Fractal dimension of turbulent black holes

Science.gov (United States)

Westernacher-Schneider, John Ryan

2017-11-01

We present measurements of the fractal dimension of a turbulent asymptotically anti-de Sitter black brane reconstructed from simulated boundary fluid data at the perfect fluid order using the fluid-gravity duality. We argue that the boundary fluid energy spectrum scaling as E (k )˜k-2 is a more natural setting for the fluid-gravity duality than the Kraichnan-Kolmogorov scaling of E (k )˜k-5 /3, but we obtain fractal dimensions D for spatial sections of the horizon H ∩Σ in both cases: D =2.584 (1 ) and D =2.645 (4 ), respectively. These results are consistent with the upper bound of D =3 , thereby resolving the tension with the recent claim in Adams et al. [Phys. Rev. Lett. 112, 151602 (2014), 10.1103/PhysRevLett.112.151602] that D =3 +1 /3 . We offer a critical examination of the calculation which led to their result, and show that their proposed definition of the fractal dimension performs poorly as a fractal dimension estimator on one-dimensional curves with known fractal dimension. Finally, we describe how to define and in principle calculate the fractal dimension of spatial sections of the horizon H ∩Σ in a covariant manner, and we speculate on assigning a "bootstrapped" value of fractal dimension to the entire horizon H when it is in a statistically quasisteady turbulent state.

The nano-fractal structured tungsten oxides films with high thermal stability prepared by the deposition of size-selected W clusters

Energy Technology Data Exchange (ETDEWEB)

Park, Eun Ji; Kim, Young Dok [Sungkyunkwan University, Department of Chemistry, Suwon (Korea, Republic of); Dollinger, Andreas; Huether, Lukas; Blankenhorn, Moritz; Koehler, Kerstine; Gantefoer, Gerd [Konstanz University, Department of Physics, Constance (Germany); Seo, Hyun Ook [Sangmyung University, Department of Chemistry and Energy Engineering, Seoul (Korea, Republic of)

2017-06-15

Size-selected W{sub n}{sup -} clusters (n = 1650) were deposited on the highly ordered pyrolytic graphite surface at room temperature under high vacuum conditions by utilizing a magnetron sputtering source and a magnet sector field. Moreover, geometrical structure and surface chemical states of deposited clusters were analyzed by in situ scanning tunneling microscopy (STM) and X-ray photoelectron spectroscopy, respectively. The formation of 2-D islands (lateral size ∝150 nm) with multiple dendritic arms was observed by STM, and the structure of the individual W{sub 1650} clusters survived within the dendritic arms. To study the thermal stability of the nano-fractal structure under the atmospheric conditions, the sample was brought to the ambient air conditions and sequentially post-annealed at 200, 300, and 500 C in the air. The nano-fractal structure was maintained after the 1st post-annealing process at 200 C for 1 h in the air, and the subsequent 2nd post-annealing at 300 C (for 1 h, in the air) also did not induce any noticeable change in the topological structure of the sample. The topological changes were observed only after the further post-annealing at a higher temperature (at 500 C, 1 h) in the air. We show high potential use of these nano-structured films of tungsten oxides in ambient conditions. (orig.)

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

Science.gov (United States)

Gao, Xu-Zhen; Pan, Yue; Zhao, Meng-Dan; Zhang, Guan-Lin; Zhang, Yu; Tu, Chenghou; Li, Yongnan; Wang, Hui-Tian

2018-01-22

We introduce a general fractal lattice growth model, significantly expanding the application scope of the fractal in the realm of optics. This model can be applied to construct various kinds of fractal "lattices" and then to achieve the design of a great diversity of fractal vector optical fields (F-VOFs) combinating with various "bases". We also experimentally generate the F-VOFs and explore their universal focusing behaviors. Multiple focal spots can be flexibly enginnered, and the optical tweezers experiment validates the simulated tight focusing fields, which means that this model allows the diversity of the focal patterns to flexibly trap and manipulate micrometer-sized particles. Furthermore, the recovery performance of the F-VOFs is also studied when the input fields and spatial frequency spectrum are obstructed, and the results confirm the robustness of the F-VOFs in both focusing and imaging processes, which is very useful in information transmission.

Pre-Service Teachers' Concept Images on Fractal Dimension

Science.gov (United States)

Karakus, Fatih

2016-01-01

The analysis of pre-service teachers' concept images can provide information about their mental schema of fractal dimension. There is limited research on students' understanding of fractal and fractal dimension. Therefore, this study aimed to investigate the pre-service teachers' understandings of fractal dimension based on concept image. The…

Fractal THz metamaterials

DEFF Research Database (Denmark)

Malureanu, Radu; Jepsen, Peter Uhd; Xiao, S.

2010-01-01

applications. THz radiation can be employed for various purposes, among them the study of vibrations in biological molecules, motion of electrons in semiconductors and propagation of acoustic shock waves in crystals. We propose here a new THz fractal MTM design that shows very high transmission in the desired...... frequency range as well as a clear differentiation between one polarisation and another. Based on theoretical predictions we fabricated and measured a fractal based THz metamaterial that shows more than 60% field transmission at around 1THz for TE polarized light while the TM waves have almost 80% field...... transmission peak at 0.6THz. One of the main characteristics of this design is its tunability by design: by simply changing the length of the fractal elements one can choose the operating frequency window. The modelling, fabrication and characterisation results will be presented in this paper. Due to the long...

Static friction between rigid fractal surfaces.

Science.gov (United States)

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.

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.

Investigation of porosity and fractal properties of the sintered metal and semiconductor layers in the MDS capacitor structure

Directory of Open Access Journals (Sweden)

Skatkov Leonid

2012-01-01

Full Text Available MDS capacitor (metal - dielectric - semiconductor is a structure in which metal plate is represented by compact bulk-porous pellets of niobium sintered powder, and semiconductor plate - by pyrolytic layer of MnO2. In the present paper we report the results of investigation of microporosity of sintered Nb and pyrolytic MnO2 and also the fractal properties of semiconductor layer.

Shape characteristics of equilibrium and non-equilibrium fractal clusters.

Science.gov (United States)

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

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)

Fractal Analysis of Rock Joint Profiles

Science.gov (United States)

Audy, Ondřej; Ficker, Tomáš

2017-10-01

Surface reliefs of rock joints are analyzed in geotechnics when shear strength of rocky slopes is estimated. The rock joint profiles actually are self-affine fractal curves and computations of their fractal dimensions require special methods. Many papers devoted to the fractal properties of these profiles were published in the past but only a few of those papers employed a convenient computational method that would have guaranteed a sound value of that dimension. As a consequence, anomalously low dimensions were presented. This contribution deals with two computational modifications that lead to sound fractal dimensions of the self-affine rock joint profiles. These are the modified box-counting method and the modified yard-stick method sometimes called the compass method. Both these methods are frequently applied to self-similar fractal curves but the self-affine profile curves due to their self-affine nature require modified computational procedures implemented in computer programs.

A random walk through fractal dimensions

CERN Document Server

Kaye, Brian H

2008-01-01

Fractal geometry is revolutionizing the descriptive mathematics of applied materials systems. Rather than presenting a mathematical treatise, Brian Kaye demonstrates the power of fractal geometry in describing materials ranging from Swiss cheese to pyrolytic graphite. Written from a practical point of view, the author assiduously avoids the use of equations while introducing the reader to numerous interesting and challenging problems in subject areas ranging from geography to fine particle science. The second edition of this successful book provides up-to-date literature coverage of the use of fractal geometry in all areas of science.From reviews of the first edition:''...no stone is left unturned in the quest for applications of fractal geometry to fine particle problems....This book should provide hours of enjoyable reading to those wishing to become acquainted with the ideas of fractal geometry as applied to practical materials problems.'' MRS Bulletin

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.

Passage through X-ray protection having the structure of homogeneous fractals

OpenAIRE

Churikov Viktor Anatolyevich

2014-01-01

In this paper we generalize the law of Bouguer-Lambert in the case of a homogeneous fractal. With detailed analysis in terms of d-output operator generalized law of BouguerLambert-Beer law, which in particular includes the classical law of optics Bouguer-LambertBeer.

A Study on the Mechanical Properties of the Representative Volume Element in Fractal Porous Media

Directory of Open Access Journals (Sweden)

Jianjun Liu

2017-01-01

Full Text Available Natural porous structure is extremely complex, and it is of great significance to study the macroscopic mechanical response of the representative volume element (RVE with the microstructure of porous media. The real porous media RVE is generated by an improved quartet structure generation set (QSGS, and the connectivity of the reconstructed porous media models is analyzed. The fractal dimension of the RVE is calculated by the box-counting method, which considers the different porosity, different fractal dimension, and different mechanical properties of the matrix. Thus, the stress-strain curves of the RVE in the elastoplastic stage under different conditions are obtained. The results show that when the matrix mechanics are consistent, the mechanical properties of the porous media RVE are negatively correlated with the porosity and fractal dimension; when the difference between the porosity and fractal dimension increases, the trend is more obvious. The mechanical properties of the RVE have a positive correlation with the modulus of elasticity of the matrix, though the correlation with Poisson’s ratio of the matrix is weak. The fractal dimension of complex porous media can better predict the RVE mechanical characteristics than the porosity.

Determination of Irreducible Water Saturation from nuclear magnetic resonance based on fractal theory — a case study of sandstone with complex pore structure

Science.gov (United States)

Peng, L.; Pan, H.; Ma, H.; Zhao, P.; Qin, R.; Deng, C.

2017-12-01

The irreducible water saturation (Swir) is a vital parameter for permeability prediction and original oil and gas estimation. However, the complex pore structure of the rocks makes the parameter difficult to be calculated from both laboratory and conventional well logging methods. In this study, an effective statistical method to predict Swir is derived directly from nuclear magnetic resonance (NMR) data based on fractal theory. The spectrum of transversal relaxation time (T2) is normally considered as an indicator of pore size distribution, and the micro- and meso-pore's fractal dimension in two specific range of T2 spectrum distribution are calculated. Based on the analysis of the fractal characteristics of 22 core samples, which were drilled from four boreholes of tight lithologic oil reservoirs of Ordos Basin in China, the positive correlation between Swir and porosity is derived. Afterwards a predicting model for Swir based on linear regressions of fractal dimensions is proposed. It reveals that the Swir is controlled by the pore size and the roughness of the pore. The reliability of this model is tested and an ideal consistency between predicted results and experimental data is found. This model is a reliable supplementary to predict the irreducible water saturation in the case that T2 cutoff value cannot be accurately determined.

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.

Thermodynamics for Fractal Statistics

OpenAIRE

da Cruz, Wellington

1998-01-01

We consider for an anyon gas its termodynamics properties taking into account the fractal statistics obtained by us recently. This approach describes the anyonic excitations in terms of equivalence classes labeled by fractal parameter or Hausdorff dimension $h$. An exact equation of state is obtained in the high-temperature and low-temperature limits, for gases with a constant density of states.

Fractal geometry and computer graphics

CERN Document Server

Sakas, Georgios; Peitgen, Heinz-Otto; Englert, Gabriele

1992-01-01

Fractal geometry has become popular in the last 15 years, its applications can be found in technology, science, or even arts. Fractal methods and formalism are seen today as a general, abstract, but nevertheless practical instrument for the description of nature in a wide sense. But it was Computer Graphics which made possible the increasing popularity of fractals several years ago, and long after their mathematical formulation. The two disciplines are tightly linked. The book contains the scientificcontributions presented in an international workshop in the "Computer Graphics Center" in Darmstadt, Germany. The target of the workshop was to present the wide spectrum of interrelationships and interactions between Fractal Geometry and Computer Graphics. The topics vary from fundamentals and new theoretical results to various applications and systems development. All contributions are original, unpublished papers.The presentations have been discussed in two working groups; the discussion results, together with a...

Plant Identification Based on Leaf Midrib Cross-Section Images Using Fractal Descriptors.

Directory of Open Access Journals (Sweden)

Núbia Rosa da Silva

Full Text Available The correct identification of plants is a common necessity not only to researchers but also to the lay public. Recently, computational methods have been employed to facilitate this task, however, there are few studies front of the wide diversity of plants occurring in the world. This study proposes to analyse images obtained from cross-sections of leaf midrib using fractal descriptors. These descriptors are obtained from the fractal dimension of the object computed at a range of scales. In this way, they provide rich information regarding the spatial distribution of the analysed structure and, as a consequence, they measure the multiscale morphology of the object of interest. In Biology, such morphology is of great importance because it is related to evolutionary aspects and is successfully employed to characterize and discriminate among different biological structures. Here, the fractal descriptors are used to identify the species of plants based on the image of their leaves. A large number of samples are examined, being 606 leaf samples of 50 species from Brazilian flora. The results are compared to other imaging methods in the literature and demonstrate that fractal descriptors are precise and reliable in the taxonomic process of plant species identification.

Fractal analysis of electrolytically-deposited palladium hydride dendrites

International Nuclear Information System (INIS)

Bursill, L.A.; Julin, Peng; Xudong, Fan.

1990-01-01

The fractal scaling characteristics of the surface profile of electrolytically-deposited palladium hydride dendritic structures have been obtained using conventional and high resolution transmission electron microscopy. The results are in remarkable agreement with the modified diffusion-limited aggregation model. 19 refs., 3 tabs., 13 figs

Correlation of optical properties with the fractal microstructure of black molybdenum coatings

Energy Technology Data Exchange (ETDEWEB)

Barrera, Enrique; Gonzalez, Federico [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Rodriguez, Eduardo [Area de Computacion y Sistemas, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico); Alvarez-Ramirez, Jose, E-mail: jjar@xanum.uam.mx [Area de Energia, Division de Ciencias Basicas e Ingenieria, Universidad Autonoma Metropolitana-Iztapalapa, Apartado Postal 55-534, Mexico, D.F. 09340 (Mexico)

2010-01-01

Coating is commonly used for improving the optical properties of surfaces for solar collector applications. The coating morphology depends on the deposition conditions, and this determines the final optical characteristics. Coating morphologies are irregular and of fractal nature, so a suitable approach for its characterization should use methods borrowed from fractal analysis. The aim of this work is to study the fractal characteristics of black molybdenum coatings on copper and to relate the fractal parameters to the optical properties. To this end, coating surfaces were prepared via immersion in a solution of ammonium paramolybdate for different deposition periods. The fractal analysis was carried out for SEM and AFM images of the coating surface and the fractal properties were obtained with a recently developed high-dimensional extension of the well-known detrended fluctuation analysis (DFA). The most salient parameter drawn from the application of the DFA is the Hurst index, a parameter related to the roughness of the coating surface, and the multifractality index, which is related to the non-linearity features of the coating morphology. The results showed that optical properties, including absorptance and emittance, are decreasing functions of the Hurst and multifractality indices. This suggests that coating surfaces with high absorptance and emittance values are related to complex coating morphologies conformed within a non-linear structure.

Symmetric intersections of Rauzy fractals | Sellami | Quaestiones ...

African Journals Online (AJOL)

In this article we study symmetric subsets of Rauzy fractals of unimodular irreducible Pisot substitutions. The symmetry considered is re ection through the origin. Given an unimodular irreducible Pisot substitution, we consider the intersection of its Rauzy fractal with the Rauzy fractal of the reverse substitution. This set is ...

Fractal dimension analysis of malignant and benign endobronchial ultrasound nodes

International Nuclear Information System (INIS)

Fiz, José Antonio; Monte-Moreno, Enrique; Andreo, Felipe; Auteri, Santiago José; Sanz-Santos, José; Serra, Pere; Bonet, Gloria; Castellà, Eva; Manzano, Juan Ruiz

2014-01-01

Endobronchial ultrasonography (EBUS) has been applied as a routine procedure for the diagnostic of hiliar and mediastinal nodes. The authors assessed the relationship between the echographic appearance of mediastinal nodes, based on endobronchial ultrasound images, and the likelihood of malignancy. The images of twelve malignant and eleven benign nodes were evaluated. A previous processing method was applied to improve the quality of the images and to enhance the details. Texture and morphology parameters analyzed were: the image texture of the echographies and a fractal dimension that expressed the relationship between area and perimeter of the structures that appear in the image, and characterizes the convoluted inner structure of the hiliar and mediastinal nodes. Processed images showed that relationship between log perimeter and log area of hilar nodes was lineal (i.e. perimeter vs. area follow a power law). Fractal dimension was lower in the malignant nodes compared with non-malignant nodes (1.47(0.09), 1.53(0.10) mean(SD), Mann–Whitney U test p < 0.05)). Fractal dimension of ultrasonographic images of mediastinal nodes obtained through endobronchial ultrasound differ in malignant nodes from non-malignant. This parameter could differentiate malignat and non-malignat mediastinic and hiliar nodes

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

Science.gov (United States)

Wang, Xujing; Becker, Frederick F.; Gascoyne, Peter R. C.

2010-01-01

The scale-invariant property of the cytoplasmic membrane of biological cells is examined by applying the Minkowski–Bouligand method to digitized scanning electron microscopy images of the cell surface. The membrane is found to exhibit fractal behavior, and the derived fractal dimension gives a good description of its morphological complexity. Furthermore, we found that this fractal dimension correlates well with the specific membrane dielectric capacitance derived from the electrorotation measurements. Based on these findings, we propose a new fractal single-shell model to describe the dielectrics of mammalian cells, and compare it with the conventional single-shell model (SSM). We found that while both models fit with experimental data well, the new model is able to eliminate the discrepancy between the measured dielectric property of cells and that predicted by the SSM. PMID:21198103

Fractal reactor: An alternative nuclear fusion system based on nature's geometry

International Nuclear Information System (INIS)

Siler, T. L.

2007-01-01

The author presents his concept of the Fractal Reactor, which explores the possibility of building a plasma fusion power reactor based on the real geometry of nature [fractals], rather than the virtual geometry that Euclid postulated around 330 BC; nearly every architect of our plasma fusion devices has been influenced by his three-dimensional geometry. The idealized points, lines, planes, and spheres of this classical geometry continue to be used to represent the natural world and to describe the properties of all geometrical objects, even though they neither accurately nor fully convey nature's structures and processes. The Fractal Reactor concept contrasts the current containment mechanisms of both magnetic and inertial containment systems for confining and heating plasmas. All of these systems are based on Euclidean geometry and use geometrical designs that, ultimately, are inconsistent with the Non-Euclidean geometry and irregular, fractal forms of nature (3). The author explores his premise that a controlled, thermonuclear fusion energy system might be more effective if it more closely embodies the physics of a star

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

Science.gov (United States)

Feng, Yongjiu; Liu, Miaolong; Tong, Xiaohua

2007-06-01

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

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.

Poiseuille equation for steady flow of fractal fluid

Science.gov (United States)

Tarasov, Vasily E.

2016-07-01

Fractal fluid is considered in the framework of continuous models with noninteger dimensional spaces (NIDS). A recently proposed vector calculus in NIDS is used to get a description of fractal fluid flow in pipes with circular cross-sections. The Navier-Stokes equations of fractal incompressible viscous fluids are used to derive a generalization of the Poiseuille equation of steady flow of fractal media in pipe.

Análisis fractal de las catedrales góticas españolas

Directory of Open Access Journals (Sweden)

Samper, A.

2014-06-01

Full Text Available Euclidean geometry, and especially “phi” and “pi” ratios, were used in Gothic buildings to give them structure, proportion and beauty. Moreover the euclidean elements there are complexes structures in Spanish Gothic Cathedrals: effectiveness to occupy space, roughness and amount of details that constitute its structures. The best tool to describe these ideas is available in Fractal geometry through the use of the so-called “fractal dimension” ratio. This is a geometric parameter, which provides a measure of these concepts. The ratio is not exclusively related with the euclidean elements, but instead it is also brought about by the final construction project of these cathedrals. In the present paper we prove that the Spanish Gothic Cathedrals do not only follow euclidean geometric patterns, but they also show another specific pattern dictated by their fractal dimension.En las construcciones góticas la Geometría Euclídea, y en especial los ratios phi y pi, fue usada para dotarles de estructura, proporción y belleza; sin embargo, además de los elementos euclídeos existen otros conceptos complejos en las construcciones de las catedrales góticas: efectividad de ocupar espacio, rugosidad y escabrosidad de los detalles que constituyen sus estructuras. La mejor herramienta para describir estos conceptos la ofrece la Geometría Fractal a través del ratio llamado «dimensión fractal». Se trata de un parámetro geométrico, que da una medida de esos conceptos; y que no es atribuible únicamente a elementos euclídeos, sino que además viene generado por el resultado arquitectónico final de estas construcciones. Con el presente estudio mostramos que las Catedrales Góticas Españolas no sólo se rigen por los patrones geométricos euclídeos, sino que además poseen otro patrón característico, que viene determinado por su dimensión fractal.

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volume 1 of Eric Hammel's Fractal Dimensions, Volume 2 is filled wit

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1, 2, and 3 of Eric Hammel's Fractal Dimensions, Volume 4 is

Fractal dimensions the digital art of Eric Hammel

CERN Document Server

Hammel, Eric

2014-01-01

The concept behind fractal geometry is extremely difficult to explain . . . but easy to see and enjoy. Eric Hammel, a professional author of military history books, is unable to explain fractals in a way that will be clear to anyone else, but most mathematicians can't explain fractals in language most people can understand. The simplest explanation is that fractals are graphic representations of high-order mathematical formulas that repeat patterns to infinity.Don't get hung up on the math. It's really all in the seeing. Like Volumes 1 and 2 of Eric Hammel's Fractal Dimensions, Volume 3 is fil

Renormalization, unstable manifolds, and the fractal structure of mode locking

International Nuclear Information System (INIS)

Cvitanovic, P.; Jensen, M.H.; Kadanoff, L.P.; Procaccia, I.

1985-01-01

The apparent universality of the fractal dimension of the set of quasiperiodic windings at the onset of chaos in a wide class of circle maps is described by construction of a universal one-parameter family of maps which lies along the unstable manifold of the renormalization group. The manifold generates a universal ''devil's staircase'' whose dimension agrees with direct numerical calculations. Applications to experiments are 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

Fractal nature of aluminum alloys substructures under creep and its implications

Science.gov (United States)

Fernández, R.; Bruno, G.; González-Doncel, G.

2018-04-01

The present work offers an explanation for the variation of the power-law stress exponent, n, with the stress σ normalized to the shear modulus G in aluminum alloys. The approach is based on the assumption that the dislocation structure generated with deformation has a fractal nature. It fully explains the evolution of n with σ/G even beyond the so-called power law breakdown region. Creep data from commercially pure Al99.8%, Al-3.85%Mg, and ingot AA6061 alloy tested at different temperatures and stresses are used to validate the proposed ideas. Finally, it is also shown that the fractal description of the dislocation structure agrees well with current knowledge.

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.

Quantitative Fractal Evaluation of Herbicide Effects on the Water-Absorbing Capacity of Superabsorbent Polymers

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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%.

A holistic approach to determine tree structural complexity based on laser scanning data and fractal analysis.

Science.gov (United States)

Seidel, Dominik

2018-01-01

The three-dimensional forest structure affects many ecosystem functions and services provided by forests. As forests are made of trees it seems reasonable to approach their structure by investigating individual tree structure. Based on three-dimensional point clouds from laser scanning, a newly developed holistic approach is presented that enables to calculate the box dimension as a measure of structural complexity of individual trees using fractal analysis. It was found that the box dimension of trees was significantly different among the tested species, among trees belonging to the same species but exposed to different growing conditions (at gap vs. forest interior) or to different kinds of competition (intraspecific vs. interspecific). Furthermore, it was shown that the box dimension is positively related to the trees' growth rate. The box dimension was identified as an easy to calculate measure that integrates the effect of several external drivers of tree structure, such as competition strength and type, while simultaneously providing information on structure-related properties, like tree growth.

Variability of fractal dimension of solar radio flux

Science.gov (United States)

Bhatt, Hitaishi; Sharma, Som Kumar; Trivedi, Rupal; Vats, Hari Om

2018-04-01

In the present communication, the variation of the fractal dimension of solar radio flux is reported. Solar radio flux observations on a day to day basis at 410, 1415, 2695, 4995, and 8800 MHz are used in this study. The data were recorded at Learmonth Solar Observatory, Australia from 1988 to 2009 covering an epoch of two solar activity cycles (22 yr). The fractal dimension is calculated for the listed frequencies for this period. The fractal dimension, being a measure of randomness, represents variability of solar radio flux at shorter time-scales. The contour plot of fractal dimension on a grid of years versus radio frequency suggests high correlation with solar activity. Fractal dimension increases with increasing frequency suggests randomness increases towards the inner corona. This study also shows that the low frequency is more affected by solar activity (at low frequency fractal dimension difference between solar maximum and solar minimum is 0.42) whereas, the higher frequency is less affected by solar activity (here fractal dimension difference between solar maximum and solar minimum is 0.07). A good positive correlation is found between fractal dimension averaged over all frequencies and yearly averaged sunspot number (Pearson's coefficient is 0.87).

Pairs Generating as a Consequence of the Fractal Entropy: Theory and Applications

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Alexandru Grigorovici

2017-03-01

Full Text Available In classical concepts, theoretical models are built assuming that the dynamics of the complex system’s stuctural units occur on continuous and differentiable motion variables. In reality, the dynamics of the natural complex systems are much more complicated. These difficulties can be overcome in a complementary approach, using the fractal concept and the corresponding non-differentiable theoretical model, such as the scale relativity theory or the extended scale relativity theory. Thus, using the last theory, fractal entropy through non-differentiable Lie groups was established and, moreover, the pairs generating mechanisms through fractal entanglement states were explained. Our model has implications in the dynamics of biological structures, in the form of the “chameleon-like” behavior of cholesterol.

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.

Effect of pore structure on anomalous behaviour of the lithium intercalation into porous V2O5 film electrode using fractal geometry concept

International Nuclear Information System (INIS)

Jung, Kyu-Nam; Pyun, Su-Il

2006-01-01

The effect of pore structure on anomalous behaviour of the lithium intercalation into porous V 2 O 5 film electrode has been investigated in terms of fractal geometry by employing ac-impedance spectroscopy combined with N 2 gas adsorption method and atomic force microscopy (AFM). For this purpose, porous V 2 O 5 film electrodes with different pore structures were prepared by the polymer surfactant templating method. From the analysis of N 2 gas adsorption isotherms and the triangulation analysis of AFM images, it was found that porous V 2 O 5 surfaces exhibited self-similar scaling properties with different fractal dimensions depending upon amount of the polymer surfactant in solution and the spatial cut-off ranges. All the ac-impedance spectra measured on porous V 2 O 5 film electrodes showed the non-ideal behaviour of the charge-transfer reaction and the diffusion reaction, which resulted from the interfacial capacitance dispersion and the frequency dispersion of the diffusion impedance, respectively. From the comparison between the surface fractal dimensions by using N 2 gas adsorption method and AFM, and the analysis of ac-impedance spectra by employing a constant phase element (CPE), it is experimentally confirmed that the lithium intercalation into porous V 2 O 5 film electrode is crucially influenced by the pore surface irregularity and the film surface irregularity

HDAC4 preserves skeletal muscle structure following long-term denervation by mediating distinct cellular responses.

Science.gov (United States)

Pigna, Eva; Renzini, Alessandra; Greco, Emanuela; Simonazzi, Elena; Fulle, Stefania; Mancinelli, Rosa; Moresi, Viviana; Adamo, Sergio

2018-02-24

Denervation triggers numerous molecular responses in skeletal muscle, including the activation of catabolic pathways and oxidative stress, leading to progressive muscle atrophy. Histone deacetylase 4 (HDAC4) mediates skeletal muscle response to denervation, suggesting the use of HDAC inhibitors as a therapeutic approach to neurogenic muscle atrophy. However, the effects of HDAC4 inhibition in skeletal muscle in response to long-term denervation have not been described yet. To further study HDAC4 functions in response to denervation, we analyzed mutant mice in which HDAC4 is specifically deleted in skeletal muscle. After an initial phase of resistance to neurogenic muscle atrophy, skeletal muscle with a deletion of HDAC4 lost structural integrity after 4 weeks of denervation. Deletion of HDAC4 impaired the activation of the ubiquitin-proteasome system, delayed the autophagic response, and dampened the OS response in skeletal muscle. Inhibition of the ubiquitin-proteasome system or the autophagic response, if on the one hand, conferred resistance to neurogenic muscle atrophy; on the other hand, induced loss of muscle integrity and inflammation in mice lacking HDAC4 in skeletal muscle. Moreover, treatment with the antioxidant drug Trolox prevented loss of muscle integrity and inflammation in in mice lacking HDAC4 in skeletal muscle, despite the resistance to neurogenic muscle atrophy. These results reveal new functions of HDAC4 in mediating skeletal muscle response to denervation and lead us to propose the combined use of HDAC inhibitors and antioxidant drugs to treat neurogenic muscle atrophy.

Design of LTCC Based Fractal Antenna

KAUST Repository

AdbulGhaffar, Farhan

2010-01-01

The thesis presents a Sierpinski Carpet fractal antenna array designed at 24 GHz for automotive radar applications. Miniaturized, high performance and low cost antennas are required for this application. To meet these specifications a fractal array

Development of Fractal Pattern Making Application using L-System for Enhanced Machine Controller

Directory of Open Access Journals (Sweden)

Gunawan Alexander A S

2014-03-01

Full Text Available One big issue facing the industry today is an automated machine lack of flexibility for customization because it is designed by the manufacturers based on certain standards. In this research, it is developed customized application software for CNC (Computer Numerically Controlled machines using open source platform. The application is enable us to create designs by means of fractal patterns using L-System, developed by turtle geometry interpretation and Python programming languages. The result of the application is the G-Code of fractal pattern formed by the method of L-System. In the experiment on the CNC machine, the G-Code of fractal pattern which involving the branching structure has been able to run well.

Bifurcation and Fractal of the Coupled Logistic Map

Science.gov (United States)

Wang, Xingyuan; Luo, Chao

The nature of the fixed points of the coupled Logistic map is researched, and the boundary equation of the first bifurcation of the coupled Logistic map in the parameter space is given out. Using the quantitative criterion and rule of system chaos, i.e., phase graph, bifurcation graph, power spectra, the computation of the fractal dimension, and the Lyapunov exponent, the paper reveals the general characteristics of the coupled Logistic map transforming from regularity to chaos, the following conclusions are shown: (1) chaotic patterns of the coupled Logistic map may emerge out of double-periodic bifurcation and Hopf bifurcation, respectively; (2) during the process of double-period bifurcation, the system exhibits self-similarity and scale transform invariability in both the parameter space and the phase space. From the research of the attraction basin and Mandelbrot-Julia set of the coupled Logistic map, the following conclusions are indicated: (1) the boundary between periodic and quasiperiodic regions is fractal, and that indicates the impossibility to predict the moving result of the points in the phase plane; (2) the structures of the Mandelbrot-Julia sets are determined by the control parameters, and their boundaries have the fractal characteristic.

A Novel High Efficiency Fractal Multiview Video Codec

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Shiping Zhu

2015-01-01

Full Text Available Multiview video which is one of the main types of three-dimensional (3D video signals, captured by a set of video cameras from various viewpoints, has attracted much interest recently. Data compression for multiview video has become a major issue. In this paper, a novel high efficiency fractal multiview video codec is proposed. Firstly, intraframe algorithm based on the H.264/AVC intraprediction modes and combining fractal and motion compensation (CFMC algorithm in which range blocks are predicted by domain blocks in the previously decoded frame using translational motion with gray value transformation is proposed for compressing the anchor viewpoint video. Then temporal-spatial prediction structure and fast disparity estimation algorithm exploiting parallax distribution constraints are designed to compress the multiview video data. The proposed fractal multiview video codec can exploit temporal and spatial correlations adequately. Experimental results show that it can obtain about 0.36 dB increase in the decoding quality and 36.21% decrease in encoding bitrate compared with JMVC8.5, and the encoding time is saved by 95.71%. The rate-distortion comparisons with other multiview video coding methods also demonstrate the superiority of the proposed scheme.

Fractal physiology and the fractional calculus: a perspective

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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.

A fractal-based image encryption system

KAUST Repository

Abd-El-Hafiz, S. K.; Radwan, Ahmed Gomaa; Abdel Haleem, Sherif H.; Barakat, Mohamed L.

2014-01-01

single-fractal image and statistical analysis is performed. A general encryption system utilising multiple fractal images is, then, introduced to improve the performance and increase the encryption key up to hundreds of bits. This improvement is achieved

Fractal and Morphological Characteristics of Single Marble Particle Crushing in Uniaxial Compression Tests

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Yidong Wang

2015-01-01

Full Text Available Crushing of rock particles is a phenomenon commonly encountered in geotechnical engineering practice. It is however difficult to study the crushing of rock particles using classical theory because the physical structure of the particles is complex and irregular. This paper aims at evaluating fractal and morphological characteristics of single rock particle. A large number of particle crushing tests are conducted on single rock particle. The force-displacement curves and the particle size distributions (PSD of crushed particles are analysed based on particle crushing tests. Particle shape plays an important role in both the micro- and macroscale responses of a granular assembly. The PSD of an assortment of rocks are analysed by fractal methods, and the fractal dimension is obtained. A theoretical formula for particle crushing strength is derived, utilising the fractal model, and a simple method is proposed for predicting the probability of particle survival based on the Weibull statistics. Based on a few physical assumptions, simple equations are derived for determining particle crushing energy. The results of applying these equations are tested against the actual experimental data and prove to be very consistent. Fractal theory is therefore applicable for analysis of particle crushing.

Mitigating HZE Radiation-Induced Deficits in Marrow-Derived Mesenchymal Progenitor Cells and Skeletal Structure

Science.gov (United States)

Globus, Ruth K.; Schreurs, Ann-Sofie; Shirazi-Fard, Yasaman; Terada, Masahiro; Alwood, Joshua; Halloran, Bernard; Tahimic, Candice

2016-01-01

Future long-duration space exploration beyond the earths magnetosphere will increase human exposure to space radiation and associated risks to skeletal health. We hypothesize that oxidative stress resulting from radiation exposure causes progressive bone loss and dysfunction in associated tissue. In animal studies, increased free radical formation is associated with pathological changes in bone structure, enhanced bone resorption, reduced bone formation and decreased bone mineral density, which can lead to skeletal fragility.

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.

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.

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.

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.

Monitoring of dry sliding wear using fractal analysis

NARCIS (Netherlands)

Zhang, Jindang; Regtien, Paulus P.L.; Korsten, Maarten J.

2005-01-01

Reliable online monitoring of wear remains a challenge to tribology research as well as to the industry. This paper presents a new method for monitoring of dry sliding wear using digital imaging and fractal analysis. Fractal values, namely fractal dimension and intercept, computed from the power

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

Science.gov (United States)

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

2006-12-01

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

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

A fractal model of effective stress of porous media and the analysis of influence factors

Science.gov (United States)

Li, Wei; Zhao, Huan; Li, Siqi; Sun, Wenfeng; Wang, Lei; Li, Bing

2018-03-01

The basic concept of effective stress describes the characteristics of fluid and solid interaction in porous media. In this paper, based on the theory of fractal geometry, a fractal model was built to analyze the relationship between the microstructure and the effective stress of porous media. From the microscopic point of view, the influence of effective stress on pore structure of porous media was demonstrated. Theoretical analysis and experimental results show that: (i) the fractal model of effective stress can be used to describe the relationship between effective stress and the microstructure of porous media; (ii) a linear increase in the effective stress leads to exponential increases in fractal dimension, porosity and pore number of the porous media, and causes a decreasing trend in the average pore radius.

Fractal Information by Means of Harmonic Mappings and Some Physical Implications

Directory of Open Access Journals (Sweden)

Maricel Agop

2016-04-01

Full Text Available Considering that the motions of the complex system structural units take place on continuous, but non-differentiable curves, in the frame of the extended scale relativity model (in its Schrödinger-type variant, it is proven that the imaginary part of a scalar potential of velocities can be correlated with the fractal information and, implicitly, with a tensor of “tensions”, which is fundamental in the construction of the constitutive laws of material. In this way, a specific differential geometry based on a Poincaré-type metric of the Lobachevsky plane (which is invariant to the homographic group of transformations and also a specific variational principle (whose field equations represent an harmonic map from the usual space into the Lobachevsky plane are generated. Moreover, fractal information (which is made explicit at any scale resolution is produced, so that the field variables define a gravitational field. This latter situation is specific to a variational principle in the sense of Matzner–Misner and to certain Ernst-type field equations, the fractal information being contained in the material structure and, thus, in its own space associated with it.

Evaluation of bridge instability caused by dynamic scour based on fractal theory

International Nuclear Information System (INIS)

Lin, Tzu-Kang; Shian Chang, Yu; Wu, Rih-Teng; Chang, Kuo-Chun

2013-01-01

Given their special structural characteristics, bridges are prone to suffer from the effects of many hazards, such as earthquakes, wind, or floods. As most of the recent unexpected damage and destruction of bridges has been caused by hydraulic issues, monitoring the scour depth of bridges has become an important topic. Currently, approaches to scour monitoring mainly focus on either installing sensors on the substructure of a bridge or identifying the physical parameters of a bridge, which commonly face problems of system survival or reliability. To solve those bottlenecks, a novel structural health monitoring (SHM) concept was proposed by utilizing the two dominant parameters of fractal theory, including the fractal dimension and the topothesy, to evaluate the instability condition of a bridge structure rapidly. To demonstrate the performance of this method, a series of experiments has been carried out. The function of the two parameters was first determined using data collected from a single bridge column scour test. As the fractal dimension gradually decreased, following the trend of the scour depth, it was treated as an alternative to the fundamental frequency of a bridge structure in the existing methods. Meanwhile, the potential of a positive correlation between the topothesy and the amplitude of vibration data was also investigated. The excellent sensitivity of the fractal parameters related to the scour depth was then demonstrated in a full-bridge experiment. Moreover, with the combination of these two parameters, a safety index to detect the critical scour condition was proposed. The experimental results have demonstrated that the critical scour condition can be predicted by the proposed safety index. The monitoring system developed greatly advances the field of bridge scour health monitoring and offers an alternative choice to traditional scour monitoring technology. (paper)

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 ...

A new surface fractal dimension for displacement mode shape-based damage identification of plate-type structures

Science.gov (United States)

Shi, Binkai; Qiao, Pizhong

2018-03-01

Vibration-based nondestructive testing is an area of growing interest and worthy of exploring new and innovative approaches. The displacement mode shape is often chosen to identify damage due to its local detailed characteristic and less sensitivity to surrounding noise. Requirement for baseline mode shape in most vibration-based damage identification limits application of such a strategy. In this study, a new surface fractal dimension called edge perimeter dimension (EPD) is formulated, from which an EPD-based window dimension locus (EPD-WDL) algorithm for irregularity or damage identification of plate-type structures is established. An analytical notch-type damage model of simply-supported plates is proposed to evaluate notch effect on plate vibration performance; while a sub-domain of notch cases with less effect is selected to investigate robustness of the proposed damage identification algorithm. Then, fundamental aspects of EPD-WDL algorithm in term of notch localization, notch quantification, and noise immunity are assessed. A mathematical solution called isomorphism is implemented to remove false peaks caused by inflexions of mode shapes when applying the EPD-WDL algorithm to higher mode shapes. The effectiveness and practicability of the EPD-WDL algorithm are demonstrated by an experimental procedure on damage identification of an artificially-induced notched aluminum cantilever plate using a measurement system of piezoelectric lead-zirconate (PZT) actuator and scanning laser Doppler vibrometer (SLDV). As demonstrated in both the analytical and experimental evaluations, the new surface fractal dimension technique developed is capable of effectively identifying damage in plate-type structures.

Fractal analytical approach of urban form based on spatial correlation function

International Nuclear Information System (INIS)

Chen, Yanguang

2013-01-01

Highlights: ► Many fractal parameter relations of cities can be derived by scaling analysis. ► The area-radius scaling of cities suggests a spatial correlation function. ► Spectral analysis can be used to estimate fractal dimension values of urban form. ► The valid range of fractal dimension of urban form comes between 1.5 and 2. ► The traditional scale concept will be replaced by scaling concept in geography. -- Abstract: Urban form has been empirically demonstrated to be of scaling invariance and can be described with fractal geometry. However, the rational range of fractal dimension value and the relationships between various fractal indicators of cities are not yet revealed in theory. By mathematical deduction and transform (e.g., Fourier transform), I find that scaling analysis, spectral analysis, and spatial correlation analysis are all associated with fractal concepts and can be integrated into a new approach to fractal analysis of cities. This method can be termed ‘3S analyses’ of urban form. Using the 3S analysis, I derived a set of fractal parameter equations, by which different fractal parameters of cities can be linked up with one another. Each fractal parameter has its own reasonable extent of values. According to the fractal parameter equations, the intersection of the rational ranges of different fractal parameters suggests the proper scale of the fractal dimension of urban patterns, which varies from 1.5 to 2. The fractal dimension equations based on the 3S analysis and the numerical relationships between different fractal parameters are useful for geographers to understand urban evolution and potentially helpful for future city planning

International Conference and Workshop on Fractals and Wavelets

CERN Document Server

Barnsley, Michael; Devaney, Robert; Falconer, Kenneth; Kannan, V; PB, Vinod

2014-01-01

Fractals and wavelets are emerging areas of mathematics with many common factors which can be used to develop new technologies. This volume contains the selected contributions from the lectures and plenary and invited talks given at the International Workshop and Conference on Fractals and Wavelets held at Rajagiri School of Engineering and Technology, India from November 9-12, 2013. Written by experts, the contributions hope to inspire and motivate researchers working in this area. They provide more insight into the areas of fractals, self similarity, iterated function systems, wavelets and the applications of both fractals and wavelets. This volume will be useful for the beginners as well as experts in the fields of fractals and wavelets.

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

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.

Fractal flow design how to design bespoke turbulence and why

CERN Document Server

Vassilicos, Christos

2016-01-01

This book focuses on turbulent flows generated and/or influenced by multiscale/fractal structures. It consists of six chapters which demonstrate, each one in its own way, how such structures and objects can be used to design bespoke turbulence for particular applications and also how they can be used for fundamental studies of turbulent flows.

Chaos and fractals an elementary introduction

CERN Document Server

Feldman, David P

2012-01-01

For students with a background in elementary algebra, this text provides a vivid introduction to the key phenomena and ideas of chaos and fractals, including the butterfly effect, strange attractors, fractal dimensions, Julia sets and the Mandelbrot set, power laws, and cellular automata.

Geometria fractal em física do solo Fractal geometry in soil physics

Directory of Open Access Journals (Sweden)

O.O.S. Bacchi

1993-09-01

Full Text Available A geometria fractal tem sido aplicada nos mais diversos ramos da ciencia, mostrando grande potencial na descrição de estruturas altamente complexas. A sua aplicação em ciência do solo tem despertado grande interesse e vem se intensificando nos últimos anos. Apesar da sua divulgação através da literatura científica internacional, de conhecido acesso por parte dos pesquisadores brasileiros, o assunto parece não ter merecido ainda a nossa atenção, a contar pela ausência do tema em nossas revistas especializadas. Tratamos aqui da conceituação básica dessa nova abordagem e de algumas aplicações em física do solo.Fractal geometry has been applied on different branches of science, showing high potential in describing complex structures. Its applications in soil science have received large attention and have been intensified in the last few years. Inspite of the large number of internationally published papers, the subject seems not having received the same attention by Brazilian soil scientists, as verified by the absence of the subject in our scientific journals. This paper presents the basic concepts of this new tool and some of its applications in soil physics.

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)

Paper-based inkjet-printed ultra-wideband fractal antennas

KAUST Repository

Maza, Armando Rodriguez

2012-01-01

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

Effective degrees of freedom of a random walk on a fractal

Science.gov (United States)

Balankin, Alexander S.

2015-12-01

We argue that a non-Markovian random walk on a fractal can be treated as a Markovian process in a fractional dimensional space with a suitable metric. This allows us to define the fractional dimensional space allied to the fractal as the ν -dimensional space Fν equipped with the metric induced by the fractal topology. The relation between the number of effective spatial degrees of freedom of walkers on the fractal (ν ) and fractal dimensionalities is deduced. The intrinsic time of random walk in Fν is inferred. The Laplacian operator in Fν is constructed. This allows us to map physical problems on fractals into the corresponding problems in Fν. In this way, essential features of physics on fractals are revealed. Particularly, subdiffusion on path-connected fractals is elucidated. The Coulomb potential of a point charge on a fractal embedded in the Euclidean space is derived. Intriguing attributes of some types of fractals are highlighted.

Power Load Prediction Based on Fractal Theory

OpenAIRE

Jian-Kai, Liang; Cattani, Carlo; Wan-Qing, Song

2015-01-01

The basic theories of load forecasting on the power system are summarized. Fractal theory, which is a new algorithm applied to load forecasting, is introduced. Based on the fractal dimension and fractal interpolation function theories, the correlation algorithms are applied to the model of short-term load forecasting. According to the process of load forecasting, the steps of every process are designed, including load data preprocessing, similar day selecting, short-term load forecasting, and...

Time Series Analysis OF SAR Image Fractal Maps: The Somma-Vesuvio Volcanic Complex Case Study

Science.gov (United States)

Pepe, Antonio; De Luca, Claudio; Di Martino, Gerardo; Iodice, Antonio; Manzo, Mariarosaria; Pepe, Susi; Riccio, Daniele; Ruello, Giuseppe; Sansosti, Eugenio; Zinno, Ivana

2016-04-01

The fractal dimension is a significant geophysical parameter describing natural surfaces representing the distribution of the roughness over different spatial scale; in case of volcanic structures, it has been related to the specific nature of materials and to the effects of active geodynamic processes. In this work, we present the analysis of the temporal behavior of the fractal dimension estimates generated from multi-pass SAR images relevant to the Somma-Vesuvio volcanic complex (South Italy). To this aim, we consider a Cosmo-SkyMed data-set of 42 stripmap images acquired from ascending orbits between October 2009 and December 2012. Starting from these images, we generate a three-dimensional stack composed by the corresponding fractal maps (ordered according to the acquisition dates), after a proper co-registration. The time-series of the pixel-by-pixel estimated fractal dimension values show that, over invariant natural areas, the fractal dimension values do not reveal significant changes; on the contrary, over urban areas, it correctly assumes values outside the natural surfaces fractality range and show strong fluctuations. As a final result of our analysis, we generate a fractal map that includes only the areas where the fractal dimension is considered reliable and stable (i.e., whose standard deviation computed over the time series is reasonably small). The so-obtained fractal dimension map is then used to identify areas that are homogeneous from a fractal viewpoint. Indeed, the analysis of this map reveals the presence of two distinctive landscape units corresponding to the Mt. Vesuvio and Gran Cono. The comparison with the (simplified) geological map clearly shows the presence in these two areas of volcanic products of different age. The presented fractal dimension map analysis demonstrates the ability to get a figure about the evolution degree of the monitored volcanic edifice and can be profitably extended in the future to other volcanic systems with

Fractal dynamics in self-evaluation reveal self-concept clarity.

Science.gov (United States)

Wong, Alexander E; Vallacher, Robin R; Nowak, Andrzej

2014-10-01

The structural account of self-esteem and self-evaluation maintains that they are distinct constructs. Trait self-esteem is stable and is expressed over macro timescales, whereas state self-evaluation is unstable and experienced on micro timescales. We compared predictions based on the structural account with those derived from a dynamical systems perspective on the self, which maintains that self-esteem and self-evaluation are hierarchically related and share basic dynamic properties. Participants recorded a 3-minute narrative about themselves, then used the mouse paradigm (Vallacher, Nowak, Froehlich, & Rockloff, 2002) to track the momentary self-evaluation in their narrative. Multiple methods converged to reveal fractal patterns in the resultant temporal patterns, indicative of nested timescales that link micro and macro selfevaluation and thus supportive of the dynamical account. The fractal dynamics were associated with participants' self-concept clarity, suggesting that the hierarchical relation between macro self-evaluation (self-esteem) and momentary self-evaluation is predicted by the coherence of self-concept organization.

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.

Fractal Feature of Particle-Size Distribution in the Rhizospheres and Bulk Soils during Natural Recovery on the Loess Plateau, China

Science.gov (United States)

Song, Zilin; Zhang, Chao; Liu, Guobin; Qu, Dong; Xue, Sha

2015-01-01

The application of fractal geometry to describe soil structure is an increasingly useful tool for better understanding the performance of soil systems. Only a few studies, however, have focused on the structure of rhizospheric zones, where energy flow and nutrient recycling most frequently occur. We used fractal dimensions to investigate the characteristics of particle-size distribution (PSD) in the rhizospheres and bulk soils of six croplands abandoned for 1, 5, 10, 15, 20, and 30 years on the Loess Plateau of China and evaluated the changes over successional time. The PSDs of the rhizospheres and the fractal dimensions between rhizosphere soil and bulk soils during the natural succession differed significantly due to the influence of plant roots. The rhizospheres had higher sand (0.05–1.00 mm) contents, lower silt (soils during the early and intermediate successional stages (1–15 years). The fractal dimensions of the rhizosphere soil and bulk soil ranged from 2.102 to 2.441 and from 2.214 to 2.459, respectively, during the 30-year restoration. Rhizospheric clay and silt contents and fractal dimension tended to be higher and sand content tended to be lower as abandonment age increased, but the bulk soils had the opposite trend. Linear regression analysis indicated that the fractal dimensions of both the rhizospheres and bulk soils were significantly linearly correlated with clay, sand, organic-carbon, and total-nitrogen contents, with R 2 ranging from 0.526 to 0.752 (Psoil and bulk soil. The fractal dimension was a sensitive and useful index for quantifying changes in the properties of the different soil zones. This study will greatly aid the application of the fractal method for describing soil structure and nutrient status and the understanding of the performance of rhizospheric zones during ecological restoration. PMID:26368339

Miniature thermal matches: from nanoheaters to reactive fractals

International Nuclear Information System (INIS)

Rebholz, Claus; Gunduz, Ibrahim Emre; Ando, Teiichi; Doumanidis, Charalabos C

2015-01-01

Fine thermal actuation by miniature heat sources enables applications from electronics fabrication to tumor cauterization. This paper introduces the concept of nanoheaters, i.e., reactive bimetallic material dots (0D), ignited electrically to exothermically release precise heat amounts where and when needed. This concept is extended to nanoheater wires (1D) and foils (2D), as well as bulk nanoheaters (3D) manufactured via ball milling and ultrasonic consolidation of nickel and aluminum powders. The fractal structure of such powders and consolidates, with self-similar, multiscale Apollonian or lamellar packaging, is discovered to hold the key for their ignition sensitivity: nanoscale structures ignite first, to produce enough heat and raise the temperature of submicron formations, which then ignite microscale regions and so on; while inert areas quench and arrest the self-propagating exothermic reaction. Therefore, such engineered fractal reactive heaters lend themselves to affordable, high-throughput manufacture and controllable, safe, efficient, supplyless in situ thermal release. This can be transformative for innovations from self-healing composites and self-heating packages to underwater construction and mining. (paper)

Fractal model of polarization switching kinetics in ferroelectrics under nonequilibrium conditions of electron irradiation

Science.gov (United States)

Maslovskaya, A. G.; Barabash, T. K.

2018-03-01

The paper presents the results of the fractal and multifractal analysis of polarization switching current in ferroelectrics under electron irradiation, which allows statistical memory effects to be estimated at dynamics of domain structure. The mathematical model of formation of electron beam-induced polarization current in ferroelectrics was suggested taking into account the fractal nature of domain structure dynamics. In order to realize the model the computational scheme was constructed using the numerical solution approximation of fractional differential equation. Evidences of electron beam-induced polarization switching process in ferroelectrics were specified at a variation of control model parameters.

Waterspout as a result of the ocean skeletal structures

Science.gov (United States)

Rantsev-Kartinov, Valentin A.

2004-11-01

An analysis of databases of photographic images of oceanic surface, taken from various altitudes and for various types of rough ocean surface, reduced to a revealing the presence of oceanic skeletal structures (OSS) = http://www.arxiv.org/ftp/physics/papers/0401/0401139.pdf [1] Rantsev-Kartinov V.A., Preprint. The OSSs presumably differ from the formerly found skeletal structures (SS) (Phys. Lett. A 306 (2002) 175) only by the fact that OSS are filled in with the closely packed blocks of a smaller size, up to capillary sizes. It is suggested [1] the dust produced by the volcanic activity forms the SS of powerful clouds due to of atmospheric electricity. The fall-out of such SSs on the oceanic surface is a material source of OSS. It is suggested that an OSS block [1] in the form of vertically oriented floating cylinder may be a stimulator of waterspout (WS). The main body of the WS may be interpreted as a special type of atmospheric aerosol dusty plasma, and its column - as a long-lived filament, being formed in the process of electric breakdown between the cloud and oceanic surface. The charged water drops aerosol may behave similar to microdust and lift upward to the cloud by the electrostatic force. Suggested a capillary-electrostatic model of the WS permits to interpret many effects connected with the WS.

The fractal spatial distribution of pancreatic islets in three dimensions: a self-avoiding growth model

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)

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

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

3D-Printed Super-Wideband Spidron Fractal Cube Antenna with Laminated Copper

Directory of Open Access Journals (Sweden)

Oh Heon Kwon

2017-09-01

Full Text Available In this paper, a 3D-printed super-wideband (SWB Spidron fractal cube antenna is proposed. The Spidron fractal configuration is utilized as a self-complementary structure on each face of a 3D frame to attain SWB characteristics. The antenna is excited through a tapered microstrip balun for both mode transforming and impedance matching. A prototype of the proposed antenna, including the 3D frame fabricated with the help of a 3D printer and Spidron fractal patches made of copper tape, is experimentally verified. The measured −10 dB reflection ratio bandwidth is 34:1 (0.44–15.38 GHz. The peak gain varies from 3.42 to 9.29 dBi within the operating frequency bandwidth. The measured radiation patterns are nearly omnidirectional at all operating frequency bands.

Towards thermomechanics of fractal media

Science.gov (United States)

Ostoja-Starzewski, Martin

2007-11-01

Hans Ziegler’s thermomechanics [1,2,3], established half a century ago, is extended to fractal media on the basis of a recently introduced continuum mechanics due to Tarasov [14,15]. Employing the concept of internal (kinematic) variables and internal stresses, as well as the quasiconservative and dissipative stresses, a field form of the second law of thermodynamics is derived. In contradistinction to the conventional Clausius Duhem inequality, it involves generalized rates of strain and internal variables. Upon introducing a dissipation function and postulating the thermodynamic orthogonality on any lengthscale, constitutive laws of elastic-dissipative fractal media naturally involving generalized derivatives of strain and stress can then be derived. This is illustrated on a model viscoelastic material. Also generalized to fractal bodies is the Hill condition necessary for homogenization of their constitutive responses.

Undergraduate Experiment with Fractal Diffraction Gratings

Science.gov (United States)

Monsoriu, Juan A.; Furlan, Walter D.; Pons, Amparo; Barreiro, Juan C.; Gimenez, Marcos H.

2011-01-01

We present a simple diffraction experiment with fractal gratings based on the triadic Cantor set. Diffraction by fractals is proposed as a motivating strategy for students of optics in the potential applications of optical processing. Fraunhofer diffraction patterns are obtained using standard equipment present in most undergraduate physics…

Self-interacting polymer chains terminally anchored to adsorbing surfaces of three-dimensional fractal lattices

Science.gov (United States)

Živić, I.; Elezović-Hadžić, S.; Milošević, S.

2018-01-01

We have studied the adsorption problem of self-attracting linear polymers, modeled by self-avoiding walks (SAWs), situated on three-dimensional fractal structures, exemplified by 3d Sierpinski gasket (SG) family of fractals as containers of a poor solvent. Members of SG family are enumerated by an integer b (b ≥ 2), and it is assumed that one side of each SG fractal is an impenetrable adsorbing surface. We calculate the critical exponents γ1 ,γ11, and γs, which are related to the numbers of all possible SAWs with one, both, and no ends anchored to the adsorbing boundary, respectively. By applying the exact renormalization group (RG) method (for the first three members of the SG fractal family, b = 2 , 3, and 4), we have obtained specific values of these exponents, for θ-chain and globular polymer phase. We discuss their mutual relations and relations with corresponding values pertinent to extended polymer chain phase.

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....

Evaluation of surface fractal dimension of carbon for plasma-facing material damaged by hydrogen plasma

International Nuclear Information System (INIS)

Nishino, Nobuhiro

1997-01-01

The surface structure of the plasma facing materials (PFM) changes due to plasma-surface interaction in a nuclear fusion reactor. Usually B 4 C coated graphite block are used as PFM. In this report, the surface fractal was applied to study the surface structure of plasma-damaged PFM carbon. A convenient flow-type adsorption apparatus was developed to evaluate the surface fractal dimension of materials. Four branched alkanol molecules with different apparent areas were used as the probe adsorbates. The samples used here were B 4 C coated isotopic graphite which were subjected to hydrogen plasma for various periods of exposure. The monolayer capacities of these samples for alkanols were determined by applying BET theory. The surface fractal dimension was calculated using the monolayer capacities and molecular areas for probe molecules and was found to increase from 2 to 3 with the plasma exposure time. (author)

A Mathematical Model of a Novel 3D Fractal-Inspired Piezoelectric Ultrasonic Transducer.

Science.gov (United States)

Canning, Sara; Walker, Alan J; Roach, Paul A

2016-12-17

Piezoelectric ultrasonic transducers have the potential to operate as both a sensor and as an actuator of ultrasonic waves. Currently, manufactured transducers operate effectively over narrow bandwidths as a result of their regular structures which incorporate a single length scale. To increase the operational bandwidth of these devices, consideration has been given in the literature to the implementation of designs which contain a range of length scales. In this paper, a mathematical model of a novel Sierpinski tetrix fractal-inspired transducer for sensor applications is presented. To accompany the growing body of research based on fractal-inspired transducers, this paper offers the first sensor design based on a three-dimensional fractal. The three-dimensional model reduces to an effective one-dimensional model by allowing for a number of assumptions of the propagating wave in the fractal lattice. The reception sensitivity of the sensor is investigated. Comparisons of reception force response (RFR) are performed between this novel design along with a previously investigated Sierpinski gasket-inspired device and standard Euclidean design. The results indicate that the proposed device surpasses traditional design sensors.

Quantitative assessment of early diabetic retinopathy using fractal analysis.

Science.gov (United States)

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

2009-01-01

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

Matlab fractal techniques used to study the structural degradation caused by alpha radiation to laser mirrors

Science.gov (United States)

Ioan, M.-R.

2018-01-01

Almost all optical diagnostic systems associated with classical particle accelerators or with new state-of-the-art particle accelerators, such as those developed within the European Collaboration ELI-NP (Extreme Light Infrastructure-Nuclear Physics) (involving extreme power laser beams), contain in their infrastructure high quality laser mirrors, used for their reflectivity and/or their partial transmittance. These high quality mirrors facilitate the extraction and handling of optical signals. When optical mirrors are exposed to high energy ionizing radiation fields, their optical and structural properties will change over time and their functionality will be affected, meaning that they will provide imprecise information. In some experiments, being exposed to mixed laser and accelerated particle beams, the deterioration of laser mirrors is even more acute, since the destruction mechanisms of both types of beams are cumulated. The main task of the work described in this paper was to find a novel specific method to analyse and highlight such degradation processes. By using complex fractal techniques integrated in a MATLAB code, the effects induced by alpha radiation to laser mirrors were studied. The fractal analysis technique represents an alternative approach to the classical Euclidean one. It can be applied for the characterization of the defects occurred in mirrors structure due to their exposure to high energy alpha particle beams. The proposed method may be further integrated into mirrors manufacturing process, as a testing instrument, to obtain better quality mirrors (enhanced resistance to high energy ionizing beams) by using different types of reflective coating materials and different deposition techniques. Moreover, the effect of high energy alpha ionizing particles on the optical properties of the exposed laser mirrors was studied by using spectrophotometric techniques.

Fractals and spectra related to fourier analysis and function spaces

CERN Document Server

Triebel, Hans

1997-01-01

Fractals and Spectra Hans Triebel This book deals with the symbiotic relationship between the theory of function spaces, fractal geometry, and spectral theory of (fractal) pseudodifferential operators as it has emerged quite recently. Atomic and quarkonial (subatomic) decompositions in scalar and vector valued function spaces on the euclidean n-space pave the way to study properties (compact embeddings, entropy numbers) of function spaces on and of fractals. On this basis, distributions of eigenvalues of fractal (pseudo)differential operators are investigated. Diverse versions of fractal drums are played. The book is directed to mathematicians interested in functional analysis, the theory of function spaces, fractal geometry, partial and pseudodifferential operators, and, in particular, in how these domains are interrelated. ------ It is worth mentioning that there is virtually no literature on this topic and hence the most of the presented material is published here the first time. - Zentralblatt MATH (…) ...

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.

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

Using Peano Curves to Construct Laplacians on Fractals

Science.gov (United States)

Molitor, Denali; Ott, Nadia; Strichartz, Robert

2015-12-01

We describe a new method to construct Laplacians on fractals using a Peano curve from the circle onto the fractal, extending an idea that has been used in the case of certain Julia sets. The Peano curve allows us to visualize eigenfunctions of the Laplacian by graphing the pullback to the circle. We study in detail three fractals: the pentagasket, the octagasket and the magic carpet. We also use the method for two nonfractal self-similar sets, the torus and the equilateral triangle, obtaining appealing new visualizations of eigenfunctions on the triangle. In contrast to the many familiar pictures of approximations to standard Peano curves, that do no show self-intersections, our descriptions of approximations to the Peano curves have self-intersections that play a vital role in constructing graph approximations to the fractal with explicit graph Laplacians that give the fractal Laplacian in the limit.

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

Science.gov (United States)

Calcagni, Gianluca

2016-04-01

We clarify what it means to have a spacetime fractal geometry in quantum gravity and show that its properties differ from those of usual fractals. A weak and a strong definition of multi-scale and multi-fractal spacetimes are given together with a sketch of the landscape of multi-scale theories of gravitation. Then, in the context of the fractional theory with q-derivatives, we explore the consequences of living in a multi-fractal spacetime. To illustrate the behavior of a non-relativistic body, we take the entertaining example of a sea turtle. We show that, when only the time direction is fractal, sea turtles swim at a faster speed than in an ordinary world, while they swim at a slower speed if only the spatial directions are fractal. The latter type of geometry is the one most commonly found in quantum gravity. For time-like fractals, relativistic objects can exceed the speed of light, but strongly so only if their size is smaller than the range of particle-physics interactions. We also find new results about log-oscillating measures, the measure presentation and their role in physical observations and in future extensions to nowhere-differentiable stochastic spacetimes.

Human Development VII: A Spiral Fractal Model of Fine Structure of Physical Energy Could Explain Central Aspects of Biological Information, Biological Organization and Biological Creativity

Directory of Open Access Journals (Sweden)

Søren Ventegodt

2006-01-01

Full Text Available In this paper we have made a draft of a physical fractal essence of the universe, a sketch of a new cosmology, which we believe to lay at the root of our new holistic biological paradigm. We present the fractal roomy spiraled structures and the energy-rich dancing “infinite strings” or lines of the universe that our hypothesis is based upon. The geometric language of this cosmology is symbolic and both pre-mathematical and pre-philosophical. The symbols are both text and figures, and using these we step by step explain the new model that at least to some extent is able to explain the complex informational system behind morphogenesis, ontogenesis, regeneration and healing. We suggest that it is from this highly dynamic spiraled structure that organization of cells, organs, and the wholeness of the human being including consciousness emerge. The model of ““dancing fractal spirals” carries many similarities to premodern cultures descriptions of the energy of the life and universe. Examples are the Native American shamanistic descriptions of their perception of energy and the old Indian Yogis descriptions of the life-energy within the body and outside. Similar ideas of energy and matter are found in the modern superstring theories. The model of the informational system of the organism gives new meaning to Bateson’s definition of information: “A difference that makes a difference”, and indicates how information-directed self-organization can exist on high structural levels in living organisms, giving birth to their subjectivity and consciousness.

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...

On the Isomorphism between Dissipative Systems, Fractal Self-Similarity and Electrodynamics. Toward an Integrated Vision of Nature

Directory of Open Access Journals (Sweden)

Giuseppe Vitiello

2014-05-01

Full Text Available In electrodynamics there is a mutual exchange of energy and momentum between the matter field and the electromagnetic field and the total energy and momentum are conserved. For a constant magnetic field and harmonic scalar potential, electrodynamics is shown to be isomorph to a system of damped/amplified harmonic oscillators. These can be described by squeezed coherent states which in turn are isomorph to self-similar fractal structures. Under the said conditions of constant magnetic field and harmonic scalar potential, electrodynamics is thus isomorph to fractal self-similar structures and squeezed coherent states. At a quantum level, dissipation induces noncommutative geometry with the squeezing parameter playing a relevant role. Ubiquity of fractals in Nature and relevance of coherent states and electromagnetic interaction point to a unified, integrated vision of Nature.

A Physiologically Based, Multi-Scale Model of Skeletal Muscle Structure and Function

Science.gov (United States)

Röhrle, O.; Davidson, J. B.; Pullan, A. J.

2012-01-01

Models of skeletal muscle can be classified as phenomenological or biophysical. Phenomenological models predict the muscle’s response to a specified input based on experimental measurements. Prominent phenomenological models are the Hill-type muscle models, which have been incorporated into rigid-body modeling frameworks, and three-dimensional continuum-mechanical models. Biophysically based models attempt to predict the muscle’s response as emerging from the underlying physiology of the system. In this contribution, the conventional biophysically based modeling methodology is extended to include several structural and functional characteristics of skeletal muscle. The result is a physiologically based, multi-scale skeletal muscle finite element model that is capable of representing detailed, geometrical descriptions of skeletal muscle fibers and their grouping. Together with a well-established model of motor-unit recruitment, the electro-physiological behavior of single muscle fibers within motor units is computed and linked to a continuum-mechanical constitutive law. The bridging between the cellular level and the organ level has been achieved via a multi-scale constitutive law and homogenization. The effect of homogenization has been investigated by varying the number of embedded skeletal muscle fibers and/or motor units and computing the resulting exerted muscle forces while applying the same excitatory input. All simulations were conducted using an anatomically realistic finite element model of the tibialis anterior muscle. Given the fact that the underlying electro-physiological cellular muscle model is capable of modeling metabolic fatigue effects such as potassium accumulation in the T-tubular space and inorganic phosphate build-up, the proposed framework provides a novel simulation-based way to investigate muscle behavior ranging from motor-unit recruitment to force generation and fatigue. PMID:22993509

A physiologically based, multi-scale model of skeletal muscle structure and function

Directory of Open Access Journals (Sweden)

Oliver eRöhrle

2012-09-01

Full Text Available Models of skeletal muscle can be classified as phenomenological or biophysical. Phenomenological models predict the muscle's response to a specified input based on experimental measurements. Prominent phenomenological models are the Hill-type muscle models, which have been incorporated into rigid-body modelling frameworks, and three-dimensional continuum-mechanical models. Biophysically based models attempt to predict the muscle's response as emerging from the underlying physiology of the system. In this contribution, the conventional biophysically based modelling methodology is extended to include several structural and functional characteristics of skeletal muscle. The result is a physiologically based, multi-scale skeletal muscle finite element model that is capable of representing detailed, geometrical descriptions of skeletal muscle fibres and their grouping. Together with a well-established model of motor unit recruitment, the electro-physiological behaviour of single muscle fibres within motor units is computed and linked to a continuum-mechanical constitutive law. The bridging between the cellular level and the organ level has been achieved via a multi-scale constitutive law and homogenisation. The effect of homogenisation has been investigated by varying the number of embedded skeletal muscle fibres and/or motor units and computing the resulting exerted muscle forces while applying the same excitatory input. All simulations were conducted using an anatomically realistic finite element model of the Tibialis Anterior muscle. Given the fact that the underlying electro-physiological cellular muscle model is capable of modelling metabolic fatigue effects such as potassium accumulation in the T-tubular space and inorganic phosphate build-up, the proposed framework provides a novel simulation-based way to investigate muscle behaviour ranging from motor unit recruitment to force generation and fatigue.

Association between stride time fractality and gait adaptability during unperturbed and asymmetric walking.

Science.gov (United States)

Ducharme, Scott W; Liddy, Joshua J; Haddad, Jeffrey M; Busa, Michael A; Claxton, Laura J; van Emmerik, Richard E A

2018-04-01

Human locomotion is an inherently complex activity that requires the coordination and control of neurophysiological and biomechanical degrees of freedom across various spatiotemporal scales. Locomotor patterns must constantly be altered in the face of changing environmental or task demands, such as heterogeneous terrains or obstacles. Variability in stride times occurring at short time scales (e.g., 5-10 strides) is statistically correlated to larger fluctuations occurring over longer time scales (e.g., 50-100 strides). This relationship, known as fractal dynamics, is thought to represent the adaptive capacity of the locomotor system. However, this has not been tested empirically. Thus, the purpose of this study was to determine if stride time fractality during steady state walking associated with the ability of individuals to adapt their gait patterns when locomotor speed and symmetry are altered. Fifteen healthy adults walked on a split-belt treadmill at preferred speed, half of preferred speed, and with one leg at preferred speed and the other at half speed (2:1 ratio asymmetric walking). The asymmetric belt speed condition induced gait asymmetries that required adaptation of locomotor patterns. The slow speed manipulation was chosen in order to determine the impact of gait speed on stride time fractal dynamics. Detrended fluctuation analysis was used to quantify the correlation structure, i.e., fractality, of stride times. Cross-correlation analysis was used to measure the deviation from intended anti-phasing between legs as a measure of gait adaptation. Results revealed no association between unperturbed walking fractal dynamics and gait adaptability performance. However, there was a quadratic relationship between perturbed, asymmetric walking fractal dynamics and adaptive performance during split-belt walking, whereby individuals who exhibited fractal scaling exponents that deviated from 1/f performed the poorest. Compared to steady state preferred walking

Skeletal muscle tissue engineering: methods to form skeletal myotubes and their applications.

Science.gov (United States)

Ostrovidov, Serge; Hosseini, Vahid; Ahadian, Samad; Fujie, Toshinori; Parthiban, Selvakumar Prakash; Ramalingam, Murugan; Bae, Hojae; Kaji, Hirokazu; Khademhosseini, Ali

2014-10-01

Skeletal muscle tissue engineering (SMTE) aims to repair or regenerate defective skeletal muscle tissue lost by traumatic injury, tumor ablation, or muscular disease. However, two decades after the introduction of SMTE, the engineering of functional skeletal muscle in the laboratory still remains a great challenge, and numerous techniques for growing functional muscle tissues are constantly being developed. This article reviews the recent findings regarding the methodology and various technical aspects of SMTE, including cell alignment and differentiation. We describe the structure and organization of muscle and discuss the methods for myoblast alignment cultured in vitro. To better understand muscle formation and to enhance the engineering of skeletal muscle, we also address the molecular basics of myogenesis and discuss different methods to induce myoblast differentiation into myotubes. We then provide an overview of different coculture systems involving skeletal muscle cells, and highlight major applications of engineered skeletal muscle tissues. Finally, potential challenges and future research directions for SMTE are outlined.

A Tutorial Review on Fractal Spacetime and Fractional Calculus

Science.gov (United States)

He, Ji-Huan

2014-11-01

This tutorial review of fractal-Cantorian spacetime and fractional calculus begins with Leibniz's notation for derivative without limits which can be generalized to discontinuous media like fractal derivative and q-derivative of quantum calculus. Fractal spacetime is used to elucidate some basic properties of fractal which is the foundation of fractional calculus, and El Naschie's mass-energy equation for the dark energy. The variational iteration method is used to introduce the definition of fractional derivatives. Fractal derivative is explained geometrically and q-derivative is motivated by quantum mechanics. Some effective analytical approaches to fractional differential equations, e.g., the variational iteration method, the homotopy perturbation method, the exp-function method, the fractional complex transform, and Yang-Laplace transform, are outlined and the main solution processes are given.

Structural and fractal properties of particles emitted from spark ignition engines.

Science.gov (United States)

Chakrabarty, Rajan K; Moosmüller, Hans; Arnott, W Patrick; Garro, Mark A; Walker, John

2006-11-01

Size, morphology, and microstructure of particles emitted from one light-duty passenger vehicle (Buick Century; model year 1990; PM (particulate matter) mass emission rate 3.1 mg/km) and two light-duty trucks (Chevrolet C2; model year 1973; PM mass emission rate 282 mg/km, and Chevrolet El Camino; model year 1976; PM mass emission rate 31 mg/km), running California's unified driving cycles (UDC) on a chassis dynamometer, were studied using scanning electron microscopy (SEM). SEM images yielded particle properties including three-dimensional density fractal dimensions, monomer and agglomerate number size distributions, and three different shape descriptors, namely aspect ratio, root form factor, and roundness. The density fractal dimension of the particles was between 1.7 and 1.78, while the number size distribution of the particles placed the majority of the particles in the accumulation mode (0.1-0.3 microm). The shape descriptors were found to decrease with increasing particle size. Partial melting of particles, a rare and previously unreported phenomenon, was observed upon exposure of particles emitted during phase 2 of the UDC to the low accelerating voltage electron beam of the SEM. The rate of melting was quantified for individual particles, establishing a near linear relationship between the melting rate and the organic carbon 1 to elemental carbon ratio.

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.

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

Investigation into How 8th Grade Students Define Fractals

Science.gov (United States)

Karakus, Fatih

2015-01-01

The analysis of 8th grade students' concept definitions and concept images can provide information about their mental schema of fractals. There is limited research on students' understanding and definitions of fractals. Therefore, this study aimed to investigate the elementary students' definitions of fractals based on concept image and concept…

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.

Fractal dimension of cantori

International Nuclear Information System (INIS)

Li, W.; Bak, P.

1986-01-01

At a critical point the golden-mean Kolmogorov-Arnol'd-Moser trajectory of Chirikov's standard map breaks up into a fractal orbit called a cantorus. The transition describes a pinning of the incommensurate phase of the Frenkel-Kontorowa model. We find that the fractal dimension of the cantorus is D = 0 and that the transition from the Kolmogorov-Arnol'd-Moser trajectory with dimension D = 1 to the cantorus is governed by an exponent ν = 0.98. . . and a universal scaling function. It is argued that the exponent is equal to that of the Lyapunov exponent

Constructing and applying the fractal pied de poule (houndstooth)

NARCIS (Netherlands)

Feijs, L.M.G.; Toeters, M.J.; Hart, G.; Sarhangi, R.

2013-01-01

Time is ready for a fractal version of pied de poule; it is almost "in the air". Taking inspiration from the Cantor set, and using the analysis of the classical pattern, we obtain a family of elegant new fractal Pied de Poules. We calculate the fractal dimension and develop an attractive fashion

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)

Fractal dimensions from a 3-dimensional intermittency analysis in e+e- annihilation

International Nuclear Information System (INIS)

Behrend, H.J.; Criegee, L.; Field, J.H.; Franke, G.; Jung, H.; Meyer, J.; Podobrin, O.; Schroeder, V.; Winter, G.G.; Bussey, P.J.; Campbell, A.J.; Hendry, D.; Lumsdon, S.J.; Skillicorn, I.O.; Ahme, J.; Blobel, V.; Feindt, M.; Fenner, H.; Harjes, J.; Koehne, J.H.; Peters, J.H.; Spitzer, H.; Weihrich, T.; Boer, W. de; Buschhorn, G.; Grindhammer, G.; Gunderson, B.; Kiesling, C.; Kotthaus, R.; Kroha, H.; Lueers, D.; Oberlack, H.; Schacht, P.; Scholz, S.; Wiedenmann, W.; Davier, M.; Grivaz, J.F.; Haissinski, J.; Journe, V.; Le Diberder, F.; Veillet, J.J.; Cozzika, G.; Ducros, Y.; Alexander, G.; Beck, A.; Bella, G.; Grunhaus, J.; Klatchko, A.; Levy, A.; Milstene, C.

1990-10-01

The intermittency structure of multihadronic e + e - annihilation is analyzed by evaluating the factorial moments F 2 -F 5 in 3-dimensional Lorentz invariant phase space as a function of the resolution scale. We interpret our data in the language of fractal objects. It turns out that the fractal dimension depends on the resolution scale in a way that can be attributed to geometrical resolution effects and dynamical effects, such as the π 0 Dalitz decay. The LUND 7.2 hadronization model provides an excellent description of the data. There is no indication of unexplained multiplicity fluctuations in small phase space regions. (orig.)

Inspecting plastic deformation of Pd by means of fractal geometry

International Nuclear Information System (INIS)

Eftekhari, Ali

2007-01-01

The influence of phase transformation-induced plastic deformation in Pd|H system on the electrode surface was investigated. Since the Pd surface is subject of severe plastic deformation during this process, the structure and roughness of the electrode surface significantly change. Quantitative analysis of the electrode surfaces for comparative study of such changes is a valuable tool to inspect the plastic deformation induced. Fractal dimension can be used as a quantitative measure for this purpose. Since inappropriate methods may lead to significant errors, an appropriate approach was proposed for the determination of fractal dimensions in such systems. It was demonstrated that the surface roughness generated is mainly due to the plastic deformation induced, not the other side processes, as the electrodes were coated with a uniform layer of gold with thickness smaller than 10 nm. Since plastic deformation is due to hydrogen insertion/extraction and occurs in atomic-scale, it is necessary to divide structural changes appeared in nano- and micro-scale

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.

A fractal analytical model for the permeabilities of fibrous gas diffusion layer in proton exchange membrane fuel cells

International Nuclear Information System (INIS)

Xiao, Boqi; Fan, Jintu; Ding, Feng

2014-01-01

The study of water and gas transport through fibrous gas diffusion layer (GDL) is important to the optimization of proton exchange membrane fuel cells (PEMFCs). In this work, analytical models of dimensionless permeability, and water and gas relative permeabilities of fibrous GDL in PEMFCs are derived using fractal theory. In our models, the structure of fibrous GDL is characterized in terms of porosity, tortuosity fractal dimension (D T ), pore area fractal dimensions (d f ), water phase (d f,w ) and gas phase (d f,g ) fractal dimensions. The predicted dimensionless permeability, water and gas relative permeabilities based on the proposed models are in good agreement with experimental data and predictions of numerical simulations reported in the literature. The model reveals that, although water phase and gas phase fractal dimensions strongly depend on porosity, the water and gas relative permeabilities are independent of porosity and are a function of water saturation only. It is also shown that the dimensionless permeability decreases significantly with the increase of tortuosity fractal dimension. On the other hand, there is only a small decrease in the water and gas relative permeabilities when tortuosity fractal dimension increases. One advantage of the proposed analytical model is that it contains no empirical constant, which is normally required in past models

Fractal tomography and its application in 3D vision

Science.gov (United States)

Trubochkina, N.

2018-01-01

A three-dimensional artistic fractal tomography method that implements a non-glasses 3D visualization of fractal worlds in layered media is proposed. It is designed for the glasses-free 3D vision of digital art objects and films containing fractal content. Prospects for the development of this method in art galleries and the film industry are considered.

Clypeotheca, a new skeletal structure in scleractinian corals: a potential stress indicator

Science.gov (United States)

Nothdurft, L. D.; Webb, G. E.

2009-03-01

Physiological responses to environmental stress are increasingly well studied in scleractinian corals. This work reports a new stress-related skeletal structure we term clypeotheca. Clypeotheca was observed in several live-collected common reef-building coral genera and a two to three kya subfossil specimen from Heron Reef, Great Barrier Reef and consists of an epitheca-like skeletal wall that seals over the surface of parts of the corallum in areas of stress or damage. It appears to form from a coordinated process wherein neighboring polyps and adjoining coenosarc seal themselves off from the surrounding environment as they contract and die. Clypeotheca forms from inward skeletal centripetal growth at the edges of corallites and by the merging of flange-like outgrowths that surround individual spines over the surface of the coenosteum. Microstructurally, the merged flanges are similar to upside-down dissepiments and true epitheca. Clypeotheca is interpreted primarily as a response to stress that may help protect the colony from invasion of unhealthy tissues by parasites or disease by retracting tissues in areas that have become unhealthy for the polyps. Identification of skeletal responses of corals to environmental stress may enable the frequency of certain types of environmental stress to be documented in past environments. Such data may be important for understanding the nature of reef dynamics through intervals of climate change and for monitoring the effects of possible anthropogenic stress in modern coral reef habitats.

Wetting characteristics of 3-dimensional nanostructured fractal surfaces

Science.gov (United States)

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

2017-01-01

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

Teaching about Fractals.

Science.gov (United States)

Willson, Stephen J.

1991-01-01

Described is a course designed to teach students about fractals using various teaching methods including the computer. Discussed are why the course drew students, prerequisites, clientele, textbook, grading, computer usage, and the syllabus. (KR)

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.

Fractal study of Ni-Cr-Mo alloy for dental applications: effect of beryllium

Energy Technology Data Exchange (ETDEWEB)

Eftekhari, Ali

2003-12-30

Different Ni-based alloys with various compositions were prepared by varying the amounts of beryllium. Effect of the amount of beryllium added to the alloy on its corrosion in an electrolyte solution of artificial saliva was investigated. Fractal dimension was used as a quantitative factor for surface analysis of the alloys before and after storage in the artificial salvia. The fractal dimensions of the electrode surfaces were determined by means of the most reliable method in this context viz. time dependency of the diffusion-limited current for a system involving 'diffusion towards electrode surface'. The results showed that increase of the beryllium amount in the alloy composition significantly increases the alloy corrosion. It is accompanied by increase of the fractal dimension and roughness of the electrode surface, whereas a smooth and shiny surface is required for dentures. From the methodology point of view, the approach utilized for fractal analysis of the alloy surfaces (Au-masking of metallic surfaces) is a novel and efficient method for study of denture surfaces. Generally, this approach is of interest for corrosion studies of different metals and alloys, particularly where changes in surface structure have a significant importance.

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

International Nuclear Information System (INIS)

Ren Xincheng; Guo Lixin

2008-01-01

A normalized two-dimensional band-limited Weierstrass fractal function is used for modelling the dielectric rough surface. An analytic solution of the scattered field is derived based on the Kirchhoff approximation. The variance of scattering intensity is presented to study the fractal characteristics through theoretical analysis and numerical calculations. The important conclusion is obtained that the diffracted envelope slopes of scattering pattern can be approximated as a slope of linear equation. This conclusion will be applicable for solving the inverse problem of reconstructing rough surface and remote sensing. (classical areas of phenomenology)

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.

Fractal analysis for studying the evolution of forests

International Nuclear Information System (INIS)

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

2016-01-01

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

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

Directory of Open Access Journals (Sweden)

Tyler M Reese

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

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

Science.gov (United States)

Tarasov, Vasily E.

2015-01-01

Using a generalization of vector calculus for space with non-integer dimension, we consider elastic properties of fractal materials. Fractal materials are described by continuum models with non-integer dimensional space. A generalization of elasticity equations for non-integer dimensional space, and its solutions for the equilibrium case of fractal materials are suggested. Elasticity problems for fractal hollow ball and cylindrical fractal elastic pipe with inside and outside pressures, for rotating cylindrical fractal pipe, for gradient elasticity and thermoelasticity of fractal materials are solved.

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.

Desaturation of skeletal muscle structural and depot lipids in obese individuals during a very-low-calorie diet intervention

DEFF Research Database (Denmark)

Haugaard, Steen B; Vaag, Allan; Høy, Carl-Erik

2007-01-01

would decrease saturated fatty acids (FAs) and increase long-chain polyunsaturated FAs (LCPUFAs) in muscular structural lipids, as such changes have been associated with improved insulin sensitivity. RESEARCH METHODS AND PROCEDURES: Skeletal muscle biopsies (vastus lateralis) were obtained from 13 obese...... during the VLCD. DISCUSSION: Desaturation of both muscle cell membrane phospholipid and IMTG was significant but modest during a VLCD in obese subjects. Further research must delineate whether such changes in skeletal muscle structural and depot lipid composition themselves are enough to promote...

Desaturation of skeletal muscle structural and depot lipids in obese individuals during a very-low-calorie diet intervention

DEFF Research Database (Denmark)

Haugaard, S.B.; Vaag, A.; Høy, Carl-Erik

2007-01-01

would decrease saturated fatty acids (FAs) and increase long-chain polyunsaturated FAs (LCPUFAs) in muscular structural lipids, as such changes have been associated with improved insulin sensitivity. Research Methods and Procedures: Skeletal muscle biopsies (vastus lateralis) were obtained from 13 obese....... Discussion: Desaturation of both muscle cell membrane phospholipid and IMTG was significant but modest during a VLCD in obese subjects. Further research must delineate whether such changes in skeletal muscle structural and depot lipid composition themselves are enough to promote the observed improvements...

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...

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

Energy Technology Data Exchange (ETDEWEB)

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

2015-06-15

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

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.

International Conference on Advances of Fractals and Related Topics

CERN Document Server

Lau, Ka-Sing

2014-01-01

This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.   

A fractal derivative model for the characterization of anomalous diffusion in magnetic resonance imaging

Science.gov (United States)

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

A new numerical approximation of the fractal ordinary differential equation

Science.gov (United States)

Atangana, Abdon; Jain, Sonal

2018-02-01

The concept of fractal medium is present in several real-world problems, for instance, in the geological formation that constitutes the well-known subsurface water called aquifers. However, attention has not been quite devoted to modeling for instance, the flow of a fluid within these media. We deem it important to remind the reader that the concept of fractal derivative is not to represent the fractal sharps but to describe the movement of the fluid within these media. Since this class of ordinary differential equations is highly complex to solve analytically, we present a novel numerical scheme that allows to solve fractal ordinary differential equations. Error analysis of the method is also presented. Application of the method and numerical approximation are presented for fractal order differential equation. The stability and the convergence of the numerical schemes are investigated in detail. Also some exact solutions of fractal order differential equations are presented and finally some numerical simulations are presented.

A diffusivity model for predicting VOC diffusion in porous building materials based on fractal theory

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.

Short-term prediction method of wind speed series based on fractal interpolation

International Nuclear Information System (INIS)

Xiu, Chunbo; Wang, Tiantian; Tian, Meng; Li, Yanqing; Cheng, Yi

2014-01-01

Highlights: • An improved fractal interpolation prediction method is proposed. • The chaos optimization algorithm is used to obtain the iterated function system. • The fractal extrapolate interpolation prediction of wind speed series is performed. - Abstract: In order to improve the prediction performance of the wind speed series, the rescaled range analysis is used to analyze the fractal characteristics of the wind speed series. An improved fractal interpolation prediction method is proposed to predict the wind speed series whose Hurst exponents are close to 1. An optimization function which is composed of the interpolation error and the constraint items of the vertical scaling factors in the fractal interpolation iterated function system is designed. The chaos optimization algorithm is used to optimize the function to resolve the optimal vertical scaling factors. According to the self-similarity characteristic and the scale invariance, the fractal extrapolate interpolation prediction can be performed by extending the fractal characteristic from internal interval to external interval. Simulation results show that the fractal interpolation prediction method can get better prediction result than others for the wind speed series with the fractal characteristic, and the prediction performance of the proposed method can be improved further because the fractal characteristic of its iterated function system is similar to that of the predicted wind speed series

Inverted fractal analysis of TiO{sub x} thin layers grown by inverse pulsed laser deposition

Energy Technology Data Exchange (ETDEWEB)

Égerházi, L., E-mail: egerhazi.laszlo@gmail.com [University of Szeged, Faculty of Medicine, Department of Medical Physics and Informatics, Korányi fasor 9., H-6720 Szeged (Hungary); Smausz, T. [University of Szeged, Faculty of Science, Department of Optics and Quantum Electronics, Dóm tér 9., H-6720 Szeged (Hungary); Bari, F. [University of Szeged, Faculty of Medicine, Department of Medical Physics and Informatics, Korányi fasor 9., H-6720 Szeged (Hungary)

2013-08-01

Inverted fractal analysis (IFA), a method developed for fractal analysis of scanning electron microscopy images of cauliflower-like thin films is presented through the example of layers grown by inverse pulsed laser deposition (IPLD). IFA uses the integrated fractal analysis module (FracLac) of the image processing software ImageJ, and an objective thresholding routine that preserves the characteristic features of the images, independently of their brightness and contrast. IFA revealed f{sub D} = 1.83 ± 0.01 for TiO{sub x} layers grown at 5–50 Pa background pressures. For a series of images, this result was verified by evaluating the scaling of the number of still resolved features on the film, counted manually. The value of f{sub D} not only confirms the fractal structure of TiO{sub x} IPLD thin films, but also suggests that the aggregation of plasma species in the gas atmosphere may have only limited contribution to the deposition.

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.

Finite Element Method Simulations of the Near-Field Enhancement at the Vicinity of Fractal Rough Metallic Surfaces

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

Paper-based inkjet-printed ultra-wideband fractal antennas

KAUST Repository

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

2012-01-01

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

Two-layer radio frequency MEMS fractal capacitors in PolyMUMPS for S-band applications

KAUST Repository

Elshurafa, Amro M.

2012-07-23

In this Letter, the authors fabricate for the first time MEMS fractal capacitors possessing two layers and compare their performance characteristics with the conventional parallel-plate capacitor and previously reported state-of-the-art single-layer MEMS fractal capacitors. Explicitly, a capacitor with a woven structure and another with an interleaved configuration were fabricated in the standard PolyMUMPS surface micromachining process and tested at S-band frequencies. The self-resonant frequencies of the fabricated capacitors were close to 10GHz, which is better than that of the parallel-plate capacitor, which measured only 5.5GHz. Further, the presented capacitors provided a higher capacitance when compared with the state-of-the-art-reported MEMS fractal capacitors created using a single layer at the expense of a lower quality factor. © 2012 The Institution of Engineering and Technology.

Applications of fractals in ecology.

Science.gov (United States)

Sugihara, G; M May, R

1990-03-01

Fractal models describe the geometry of a wide variety of natural objects such as coastlines, island chains, coral reefs, satellite ocean-color images and patches of vegetation. Cast in the form of modified diffusion models, they can mimic natural and artificial landscapes having different types of complexity of shape. This article provides a brief introduction to fractals and reports on how they can be used by ecologists to answer a variety of basic questions, about scale, measurement and hierarchy in, ecological systems. Copyright © 1990. Published by Elsevier Ltd.

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.

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...

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.

The Impact of The Fractal Paradigm on Geography

Science.gov (United States)

De Cola, L.

2001-12-01

Being itself somewhat fractal, Benoit Mandelbrot's magnum opus THE FRACTAL GEOMETRY OF NATURE may be deconstructed in many ways, including geometrically, systematically, and epistemologically. Viewed as a work of geography it may be used to organize the major topics of interest to scientists preoccupied with the understanding of real-world space in astronomy, geology, meteorology, hydrology, and biology. We shall use it to highlight such recent geographic accomplishments as automated feature detection, understanding urban growth, and modeling the spread of disease in space and time. However, several key challenges remain unsolved, among them: 1. It is still not possible to move continuously from one map scale to another so that objects change their dimension smoothly. I.e. as a viewer zooms in on a map the zero-dimensional location of a city should gradually become a 2-dimensional polygon, then a network of 1-dimensional streets, then 3-dimensional buildings, etc. 2. Spatial autocorrelation continues to be regarded more as an econometric challenge than as a problem of scaling. Similarities of values among closely-spaced observation is not so much a problem to be overcome as a source of information about spatial structure. 3. Although the fractal paradigm is a powerful model for data analysis, its ideas and techniques need to be brought to bear on the problems of understanding such hierarchies as ecosystems (the flow networks of energy and matter), taxonomies (biological classification), and knowledge (hierarchies of bureaucratic information, networks of linked data, etc).

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)

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

Identify the Rotating Stall in Centrifugal Compressors by Fractal Dimension in Reconstructed Phase Space

Directory of Open Access Journals (Sweden)

Le Wang

2015-11-01

Full Text Available Based on phase space reconstruction and fractal dynamics in nonlinear dynamics, a method is proposed to extract and analyze the dynamics of the rotating stall in the impeller of centrifugal compressor, and some numerical examples are given to verify the results as well. First, the rotating stall of an existing low speed centrifugal compressor (LSCC is numerically simulated, and the time series of pressure in the rotating stall is obtained at various locations near the impeller outlet. Then, the phase space reconstruction is applied to these pressure time series, and a low-dimensional dynamical system, which the dynamics properties are included in, is reconstructed. In phase space reconstruction, C–C method is used to obtain the key parameters, such as time delay and the embedding dimension of the reconstructed phase space. Further, the fractal characteristics of the rotating stall are analyzed in detail, and the fractal dimensions are given for some examples to measure the complexity of the flow in the post-rotating stall. The results show that the fractal structures could reveal the intrinsic dynamics of the rotating stall flow and could be considered as a characteristic to identify the rotating stall.

An efficient fractal image coding algorithm using unified feature and DCT

International Nuclear Information System (INIS)

Zhou Yiming; Zhang Chao; Zhang Zengke

2009-01-01

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

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

International Nuclear Information System (INIS)

Chen Yanguang

2009-01-01

A pair of nonlinear programming models is built to explain the fractal structure of systems of cities and those of rivers. The hierarchies of cities can be characterized by a set of exponential functions, which is identical in form to the Horton-Strahler's laws of the river networks. Four power laws can be derived from these exponential functions. The evolution of both systems of cities and rivers are then represented as nonlinear dual programming models: to maximize information entropy subject to a certain energy use or to minimize energy dissipation subject to certain information capacity. The optimal solutions of the programming problems are just the exponential equations associated with scaling relations. By doing so, fractals and the self-organized criticality marked by the power laws are interpreted using the idea from the entropy-maximization principle, which gives further weight to the suggestion that optimality of the system as a whole defines the dynamical origin of fractal forms in both nature and society.

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

Characterisation of human non-proliferativediabetic retinopathy using the fractal analysis

Directory of Open Access Journals (Sweden)

Carmen Alina Lupaşcu

2015-08-01

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

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.

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

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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.

Fractal analysis of bone architecture at distal radius

International Nuclear Information System (INIS)

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

2005-01-01

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

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

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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

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

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Li, Xiaohong; Chen, Peiwen; Chen, Feng; Wang, Zijia

2018-04-01

To quantify the spatiotemporal distribution of passenger flow and the characteristics of an urban rail transit network, we introduce four radius fractal dimensions and two branch fractal dimensions by combining a fractal approach with passenger flow assignment model. These fractal dimensions can numerically describe the complexity of passenger flow in the urban rail transit network and its change characteristics. Based on it, we establish a fractal quantification method to measure the fractal characteristics of passenger follow in the rail transit network. Finally, we validate the reasonability of our proposed method by using the actual data of Beijing subway network. It has been shown that our proposed method can effectively measure the scale-free range of the urban rail transit network, network development and the fractal characteristics of time-varying passenger flow, which further provides a reference for network planning and analysis of passenger flow.

Analyzing fractal property of species abundance distribution and diversity indexes.

Science.gov (United States)

Su, Qiang

2016-03-07

Community diversity is usually characterized by numerical indexes; however it indeed depends on the species abundance distribution (SAD). Diversity indexes and SAD are based on the same information but treating as separate themes. Ranking species abundance from largest to smallest, the decreasing pattern can give the information about the SAD. Frontier proposed such SAD might be a fractal structure, and first applied the Zipf-Mandelbrot model to the SAD study. However, this model fails to include the Zipf model, and also fails to ensure an integer rank. In this study, a fractal model of SAD was reconstructed, and tested with 104 community samples from 8 taxonomic groups. The results show that there was a good fit of the presented model. Fractal parameter (p) determines the SAD of a community. The ecological significance of p relates to the "dominance" of a community. The correlation between p and classical diversity indexes show that Shannon index decreases and Simpson index increases as p increases. The main purpose of this paper is not to compare with other SADs models; it simply provides a new interpretation of SAD model construction, and preliminarily integrates diversity indexes and SAD model into a broader perspective of community diversity. Copyright © 2015 Elsevier Ltd. All rights reserved.

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...

Ulam method and fractal Weyl law for Perron-Frobenius operators

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Ermann, L.; Shepelyansky, D. L.

2010-06-01

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

Insulator Contamination Forecasting Based on Fractal Analysis of Leakage Current

Directory of Open Access Journals (Sweden)

Bing Luo

2012-07-01

Full Text Available In this paper, an artificial pollution test is carried out to study the leakage current of porcelain insulators. Fractal theory is adopted to extract the characteristics hidden in leakage current waveforms. Fractal dimensions of the leakage current for the security, forecast and danger zones are analyzed under four types of degrees of contamination. The mean value and the standard deviation of the fractal dimension in the forecast zone are calculated to characterize the differences. The analysis reveals large differences in the fractal dimension of leakage current under different contamination discharge stages and degrees. The experimental and calculation results suggest that the fractal dimension of a leakage current waveform can be used as a new indicator of the discharge process and contamination degree of insulators. The results provide new methods and valid indicators for forecasting contamination flashovers.

Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China

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Xiang Niu

2015-12-01

Full Text Available Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD and soil water retention curve (WRC under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1 the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM > Pinus thunbergii Parl. (PTP > Juglans rigia Linn. (JRL > abandoned grassland (ABG; (2 the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL were significantly higher than that in ABG, and mixed forests (QRM and PPM were higher than that in pure forests (PTP and JRL; (3 the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4 the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure.

Fractal Characteristics of Soil Retention Curve and Particle Size Distribution with Different Vegetation Types in Mountain Areas of Northern China

Science.gov (United States)

Niu, Xiang; Gao, Peng; Wang, Bing; Liu, Yu

2015-01-01

Based on fractal theory, the fractal characteristics of soil particle size distribution (PSD) and soil water retention curve (WRC) under the five vegetation types were studied in the mountainous land of Northern China. Results showed that: (1) the fractal parameters of soil PSD and soil WRC varied greatly under each different vegetation type, with Quercus acutissima Carr. and Robina pseudoacacia Linn. mixed plantation (QRM) > Pinus thunbergii Parl. and Pistacia chinensis Bunge mixed plantation (PPM) > Pinus thunbergii Parl. (PTP) > Juglans rigia Linn. (JRL) > abandoned grassland (ABG); (2) the soil fractal dimensions of woodlands (QRM, PPM, PTP and JRL) were significantly higher than that in ABG, and mixed forests (QRM and PPM) were higher than that in pure forests (PTP and JRL); (3) the fractal dimension of soil was positively correlated with the silt and clay content but negatively correlated with the sand content; and (4) the fractal dimension of soil PSD was positively correlated with the soil WRC. These indicated that the fractal parameters of soil PSD and soil WRC could act as quantitative indices to reflect the physical properties of the soil, and could be used to describe the influences of the Return Farmland to Forests Projects on soil structure. PMID:26633458

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)

Fractal universe and quantum gravity.

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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.

Synergetics and fractals in tribology

CERN Document Server

Janahmadov, Ahad Kh

2016-01-01

This book examines the theoretical and practical aspects of tribological process using synergy, fractal and multifractal methods, and the fractal and multifractal models of self-similar tribosystems developed on their basis. It provides a comprehensive analysis of their effectiveness, and also considers the method of flicker noise spectroscopy with detailed parameterization of surface roughness friction. All models, problems and solutions are taken and tested on the set of real-life examples of oil-gas industry. The book is intended for researchers, graduate students and engineers specialising in the field of tribology, and also for senior students of technical colleges.

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

Experimental Study and Fractal Analysis on the Anisotropic Performance of Explosively Welded Interfaces of 304 Stainless Steel/245 Carbon Steel

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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.

A fractal-based image encryption system

KAUST Repository