Search results for: fractal analysis

Authors: Vramori Mitra, Bornali Sarma, Arun K. Sarma

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Recurrence is a ubiquitous feature of any real dynamical system. The states in phase space trajectory of a system have an inherent tendency to return to the same state or its close state after certain time laps. Recurrence quantification analysis technique, based on this fundamental feature of a dynamical system, detects evaluation of state under variation of control parameter of the system. The paper presents the investigation of nonlinear dynamical behavior of plasma floating potential fluctuations obtained by using a Langmuir probe in different magnetic field under the variation of discharge voltages. The main measures of recurrence quantification analysis are considered as determinism, linemax and entropy. The increment of the DET and linemax variables asserts that the predictability and periodicity of the system is increasing. The variable linemax indicates that the chaoticity is being diminished with the slump of magnetic field while increase of magnetic field enhancing the chaotic behavior. Fractal property of the plasma time series estimated by DFA technique (Detrended fluctuation analysis) reflects that long-range correlation of plasma fluctuations is decreasing while fractal dimension is increasing with the enhancement of magnetic field which corroborates the RQA analysis.

Keywords: detrended fluctuation analysis, chaos, phase space, recurrence

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Authors: Sibashish Baksi, Ujjaini Sarkar, Sudeshna Saha

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In the present study, hydrolysis of Pinus roxburghi wood powder was carried out with Viscozyme, and kinetics of the hydrolysis has been investigated. Finely ground sawdust is submerged into 2% aqueous peroxide solution (pH=11.5) and pretreated through autoclaving, probe sonication, and alkaline peroxide pretreatment. Afterward, the pretreated material is subjected to hydrolysis. A chain of experiments was executed with delignified biomass (50 g/l) and varying enzyme concentrations (24.2–60.5 g/l). In the present study, 14.32 g/l of glucose, along with 7.35 g/l of xylose, have been recovered with a viscozyme concentration of 48.8 g/l and the same condition was treated as optimum condition. Additionally, thermal deactivation of viscozyme has been investigated and found to be gradually decreasing with escalated enzyme loading from 48.4 g/l (dissociation constant= 0.05 h⁻¹) to 60.5 g/l (dissociation constant= 0.02 h⁻¹). The hydrolysis reaction is a pseudo first-order reaction, and therefore, the rate of the hydrolysis can be expressed as a fractal-like kinetic equation that communicates between the product concentration and hydrolytic time t. It is seen that the value of rate constant (K) increases from 0.008 to 0.017 with augmented enzyme concentration from 24.2 g/l to 60.5 g/l. Greater value of K is associated with stronger enzyme binding capacity of the substrate mass. However, escalated concentration of supplied enzyme ensures improved interaction with more substrate molecules resulting in an enhanced de-polymerization of the polymeric sugar chains per unit time which eventually modifies the physiochemical structure of biomass. All fractal dimensions are in between 0 and 1. Lower the value of fractal dimension, more easily the biomass get hydrolyzed. It can be seen that with increased enzyme concentration from 24.2 g/l to 48.4 g/l, the values of fractal dimension go down from 0.1 to 0.044. This indicates that the presence of more enzyme molecules can more easily hydrolyze the substrate. However, an increased value has been observed with a further increment of enzyme concentration to 60.5g/l because of diffusional limitation. It is evident that the hydrolysis reaction system is a heterogeneous organization, and the product formation rate depends strongly on the enzyme diffusion resistances caused by the rate-limiting structures of the substrate-enzyme complex. Value of the rate constant increases from 1.061 to 2.610 with escalated enzyme concentration from 24.2 to 48.4 g/l. As the rate constant is proportional to Fick’s diffusion coefficient, it can be assumed that with a higher concentration of enzyme, a larger amount of enzyme mass dM diffuses into the substrate through the surface dF per unit time dt. Therefore, a higher rate constant value is associated with a faster diffusion of enzyme into the substrate. Regression analysis of time curves with various enzyme concentrations shows that diffusion resistant constant increases from 0.3 to 0.51 for the first two enzyme concentrations and again decreases with enzyme concentration of 60.5 g/l. During diffusion in a differential scale, the enzyme also experiences a greater resistance during diffusion of larger dM through dF in dt.

Keywords: viscozyme, glucose, fractal kinetics, thermal deactivation

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Authors: Surupa Shaw, Debjyoti Banerjee

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Enhancing heat transfer in compact volumes is a challenge when constrained by cost issues, especially those associated with requirements for minimizing pumping power consumption. This is particularly acute for electronic chip cooling applications. Technological advancements in microelectronics have led to development of chip architectures that involve increased power consumption. As a consequence packaging, technologies are saddled with needs for higher rates of power dissipation in smaller form factors. The increasing circuit density, higher heat flux values for dissipation and the significant decrease in the size of the electronic devices are posing thermal management challenges that need to be addressed with a better design of the cooling system. Maximizing surface area for heat exchanging surfaces (e.g., extended surfaces or “fins”) can enable dissipation of higher levels of heat flux. Fractal structures have been shown to maximize surface area in compact volumes. Self-replicating structures at multiple length scales are called “Fractals” (i.e., objects with fractional dimensions; unlike regular geometric objects, such as spheres or cubes whose volumes and surface area values scale as integer values of the length scale dimensions). Fractal structures are expected to provide an appropriate technology solution to meet these challenges for enhanced heat transfer in the microelectronic devices by maximizing surface area available for heat exchanging fluids within compact volumes. In this study, the effect of different fractal micro-channel architectures and flow structures on the enhancement of transport phenomena in heat exchangers is explored by parametric variation of fractal dimension. This study proposes a model that would enable cost-effective solutions for thermal-fluid transport for energy applications. The objective of this study is to ascertain the sensitivity of various parameters (such as heat flux and pressure gradient as well as pumping power) to variation in fractal dimension. The role of the fractal parameters will be instrumental in establishing the most effective design for the optimum cooling of microelectronic devices. This can help establish the requirement of minimal pumping power for enhancement of heat transfer during cooling. Results obtained in this study show that the proposed models for fractal architectures of microchannels significantly enhanced heat transfer due to augmentation of surface area in the branching networks of varying length-scales.

Keywords: fractals, microelectronics, constructal theory, heat transfer enhancement, pumping power enhancement

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Authors: Amal Maazoun, Abderrazak Mezghani, Ali Ben Moussa

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Aerogel consists of a ramified and inter-connected solid skeleton enclosing a very important number of nano-sized pores filled with air that occupies most of the volume and makes very low density. The thermal conductivity of this material can reach lower values than those of any other material, and it changes with the type of the aerogel and its composition. So, in order to explain the causes of the super-insulation of our material and to determine the factors in which depends on its conductivity we used a numerical simulation. We have developed a numerical code that generates random fractal structure of silica aerogel with pre-defined concentration, properties of the backbone and the gas in the pores as well as the size of the particles. The calculation of the conductivity at any point of domain shows that it is not constant and that it depends on the pore size and the location in the pore. A numerical method based on resolution by inversion of block tridiagonal matrices is used to calculate the equivalent thermal conductivity of the whole fractal structure. The average conductivity calculated for each concentration is in good agreement with those of typical aerogels. And we found that the equivalent thermal conductivity of a silica aerogel depends strongly not only on the porosity but also on the tortuosity of the solid backbone.

Keywords: aerogel, fractal structure, numerical study, porous media, thermal conductivity

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Authors: U. Paniveni

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A few parameters of supergranular cells are studied using intensity patterns from the Kodaikanal Solar Observatory and Dopplergrams from SOHO. The turbulent aspect of the solar supergranulation is established by examining the interrelationships amongst the parameters characterizing a supergranular cell, namely size, lifetime, area, perimeter, fractal dimension, and horizontal flow velocity. The complexity of supergranular cells depicted by their fractal dimension is indicative of their non-laminar characteristics. The findings corroborate Kolmogorov’s theory of turbulence. Some parameters of supergranular cells also show a latitudinal dependence. Supergranulation is a synonym of convective phenomenon and hence can shed light on the physical conditions in the convection zone of the Sun. It plays a major role in the transport and dispersal of magnetic fields that may have a relation to the phases of the solar cycle.

Keywords: sun, granulation, convection, turbulence

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Authors: Yadwinder Kumar, Priyanka Rani Amandeep Singh

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In this paper the design of a multiband pre-fractal micro strip antenna with proximity coupling feed is presented. The proposed antenna resonates on seven different frequencies that are 2.6 GHz, 5.1 GHz, 9.4 GHz, 11.5 GHz, 13.8 GHz, 16.3 GHz, and 18.6 GHz. Simulated results presented here shows that the minimum return loss is achieved at the 16.3 GHz frequency which is up to 37 dB. Also the maximum band width of 700 MHz is achieved by the frequency bands 13.4 GHz to 14.1 GHz, 15.9 GHz to 16.6 GHz and 18.2 GHz to 18.9 GHz. The proposed feed line is sandwiched between two substrate layers and increases in the bandwidth of antenna has been observed up to 13% in comparison of micro strip feed line. Effect of key design parameters such as variation in substrate material, substrate height and feeding technique on antenna S-parameter have been investigated and discussed.

Keywords: fractal antenna, pre-fractals, micro strip antenna, ISM band, electromagnetic coupling, VSWR

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Authors: Lu Lin

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Urbanization has reshaped physical environment, energy consumption and carbon emission of the urban area. China is a typical developing country under a rapid urbanization process and is the world largest carbon emission country. This study aims to explore the correlation between urban form and carbon emission caused by urban energy consumption in China. 287 provincial-level and prefecture-level cities are studied in 2000, 2005, and 2010. Compact ratio index, shape index, and fractal dimension index are used to quantify urban form. Geographically weighted regression (GWR) model is employed to explore the relationship between urban form, energy consumption, and related carbon emission. The results show the average compact ratio index decreased from 2000 to 2010 which indicates urban in China sprawled. The average fractal dimension index increases by 3%, indicating the spatial layouts of China's cities were more complicated. The results by the GWR model show that shape index and fractal dimension index had a non-significant relationship with carbon emission by urban energy consumption. However, compact urban form reduced carbon emission. The findings of this study will help policy-makers make sustainable urban planning and reduce urban carbon emission.

Keywords: carbon emission, GWR model, urban energy consumption, urban form

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Authors: Shreemoyee Sarkar, Vikhyat Chadha

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In this paper, the local fractal properties and chaotic properties of financial time series are investigated by calculating two exponents, the Local Hurst Exponent: LHE and Lyapunov Exponent in a moving time window of a financial series.y. For the purpose of this paper, the Dow Jones Industrial Average (DIJA) and S&P 500, two of the major indices of United States have been considered. The behaviour of the above-mentioned exponents prior to some major crashes (1998 and 2008 crashes in S&P 500 and 2002 and 2008 crashes in DIJA) is discussed. Also, the optimal length of the window for obtaining the best possible results is decided. Based on the outcomes of the above, an attempt is made to predict the crashes and accuracy of such an algorithm is decided.

Keywords: local hurst exponent, lyapunov exponent, market crash prediction, time series chaos, time series local fractal properties

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Authors: Ibrahim Alsendid, Rob Sturman, Benjamin Sharp

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In this paper, we consider a family of 2-dimensional nonlinear area-preserving transformations on the torus. A single parameter η varies between 0 and 1, taking the transformation from a hyperbolic toral automorphism to the “Cerbelli-Giona” map, a system known to exhibit multifractal properties. Here we study the multifractal properties of the family of maps. We apply a box-counting method by defining a grid of boxes Bi(δ), where i is the index and δ is the size of the boxes, to quantify the distribution of stable and unstable manifolds of the map. When the parameter is in the range 0.51< η <0.58 and 0.68< η <1 the map is ergodic; i.e., the unstable and stable manifolds eventually cover the whole torus, although not in a uniform distribution. For accurate numerical results, we require correspondingly accurate construction of the stable and unstable manifolds. Here we use the piecewise linearity of the map to achieve this, by computing the endpoints of line segments that define the global stable and unstable manifolds. This allows the generalized fractal dimension Dq, and spectrum of dimensions f(α), to be computed with accuracy. Finally, the intersection of the unstable and stable manifold of the map will be investigated and compared with the distribution of periodic points of the system.

Keywords: Discrete-time dynamical systems, Fractal geometry, Multifractal behaviour of the Perturbed map, Multifractal of Dynamical systems

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Authors: Shankha Sanyal, Archi Banerjee, Sayan Biswas, Sourya Sengupta, Sayan Nag, Ranjan Sengupta, Dipak Ghosh

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The term ‘gestalt’ has been widely used in the field of psychology which defined the perception of human mind to group any object not in part but as a 'unified' whole. Music, in general, is polyphonic - i.e. a combination of a number of pure tones (frequencies) mixed together in a manner that sounds harmonious. The study of human brain response due to different frequency groups of the acoustic signal can give us an excellent insight regarding the neural and functional architecture of brain functions. Hence, the study of music cognition using neuro-biosensors is becoming a rapidly emerging field of research. In this work, we have tried to analyze the effect of different frequency bands of music on the various frequency rhythms of human brain obtained from EEG data. Four widely popular Rabindrasangeet clips were subjected to Wavelet Transform method for extracting five resonant frequency bands from the original music signal. These frequency bands were initially analyzed with Detrended/Adaptive Fractal analysis (DFA/AFA) methods. A listening test was conducted on a pool of 100 respondents to assess the frequency band in which the music becomes non-recognizable. Next, these resonant frequency bands were presented to 20 subjects as auditory stimulus and EEG signals recorded simultaneously in 19 different locations of the brain. The recorded EEG signals were noise cleaned and subjected again to DFA/AFA technique on the alpha, theta and gamma frequency range. Thus, we obtained the scaling exponents from the two methods in alpha, theta and gamma EEG rhythms corresponding to different frequency bands of music. From the analysis of music signal, it is seen that loss of recognition is proportional to the loss of long range correlation in the signal. From the EEG signal analysis, we obtain frequency specific arousal based response in different lobes of brain as well as in specific EEG bands corresponding to musical stimuli. In this way, we look to identify a specific frequency band beyond which the music becomes non-recognizable and below which in spite of the absence of other bands the music is perceivable to the audience. This revelation can be of immense importance when it comes to the field of cognitive music therapy and researchers of creativity.

Keywords: AFA, DFA, EEG, gestalt in music, Hurst exponent

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Authors: Tushnik Sarkar, Mofazzal H. Khondekar, Subrata Banerjee

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This paper investigates the nature of the fluctuation of the daily average Solar wind speed time series collected over a period of 2492 days, from 1^st January, 1997 to 28^th October, 2003. The degree of self-similarity and scalability of the Solar Wind Speed signal has been explored to characterise the signal fluctuation. Multi-fractal Detrended Fluctuation Analysis (MFDFA) method has been implemented on the signal which is under investigation to perform this task. Furthermore, the singularity spectra of the signals have been also obtained to gauge the extent of the multifractality of the time series signal.

Keywords: detrended fluctuation analysis, generalized hurst exponent, holder exponents, multifractal exponent, multifractal spectrum, singularity spectrum, time series analysis

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Authors: Dhanuj M. Gandikota

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Sensor-derived three-dimensional (3D) point clouds of trees are invaluable in remote sensing analysis for the accurate measurement of key structural metrics, bio-inventory values, spatial planning/visualization, and ecological modeling. Machine learning (ML) holds the potential in addressing the restrictive tradeoffs in cost, spatial coverage, resolution, and information gain that exist in current point cloud sensing methods. Terrestrial laser scanning (TLS) remains the highest fidelity source of both canopy and below-canopy structural features, but usage is limited in both coverage and cost, requiring manual deployment to map out large, forested areas. While aerial laser scanning (ALS) remains a reliable avenue of LIDAR active remote sensing, ALS is also cost-restrictive in deployment methods. Space-borne photogrammetry from high-resolution satellite constellations is an avenue of passive remote sensing with promising viability in research for the accurate construction of vegetation 3-D point clouds. It provides both the lowest comparative cost and the largest spatial coverage across remote sensing methods. However, both space-borne photogrammetry and ALS demonstrate technical limitations in the capture of valuable below-canopy point cloud data. Looking to minimize these tradeoffs, we explored a class of powerful ML algorithms called Deep Learning (DL) that show promise in recent research on 3-D point cloud reconstruction and interpolation. Our research details the efficacy of applying these DL techniques to reconstruct accurate below-canopy point clouds from space-borne and aerial remote sensing through learned patterns of tree species fractal symmetry properties and the supplementation of locally sourced bio-inventory metrics. From our dataset, consisting of tree point clouds obtained from TLS, we deconstructed the point clouds of each tree into those that would be obtained through ALS and satellite photogrammetry of varying resolutions. We fed this ALS/satellite point cloud dataset, along with the simulated local bio-inventory metrics, into the DL point cloud reconstruction architectures to generate the full 3-D tree point clouds (the truth values are denoted by the full TLS tree point clouds containing the below-canopy information). Point cloud reconstruction accuracy was validated both through the measurement of error from the original TLS point clouds as well as the error of extraction of key structural metrics, such as crown base height, diameter above root crown, and leaf/wood volume. The results of this research additionally demonstrate the supplemental performance gain of using minimum locally sourced bio-inventory metric information as an input in ML systems to reach specified accuracy thresholds of tree point cloud reconstruction. This research provides insight into methods for the rapid, cost-effective, and accurate construction of below-canopy tree 3-D point clouds, as well as the supported potential of ML and DL to learn complex, unmodeled patterns of fractal tree growth symmetry.

Keywords: deep learning, machine learning, satellite, photogrammetry, aerial laser scanning, terrestrial laser scanning, point cloud, fractal symmetry

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Authors: Sanjeet Kumar Singh, Shanatanu Bhattacharaya

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Design of high- efficiency low, frequency (<1000Hz) soundproof window or wall absorber which is transparent to airflow is presented. Due to the massive rise in human population and modernization, environmental noise has significantly risen globally. Prolonged noise exposure can cause severe physiological and psychological symptoms like nausea, headaches, fatigue, and insomnia. There has been continuous growth in building construction and infrastructure like offices, bus stops, and airports due to urban population. Generally, a ventilated window is used for getting fresh air into the room, but at the same time, unwanted noise comes along. Researchers used traditional approaches like noise barrier mats in front of the window or designed the entire window using sound-absorbing materials. However, this solution is not aesthetically pleasing, and at the same time, it's heavy and not adequate for low-frequency noise shielding. To address this challenge, we design a transparent hexagonal panel based on Sierpiński fractal triangle, which is aesthetically pleasing, demonstrates normal incident sound absorption coefficient more than 0.96 around 700 Hz and transmission loss around 23 dB while maintaining e air circulation through triangular cutout. Next, we present a concept of fabrication of large acoustic panel for large-scale applications, which lead to suppressing the urban noise pollution.

Keywords: acoustic metamaterials, noise, functional materials, ventilated

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Authors: Sanjeet Kumar Singh, Shantanu Bhatacharya

Abstract:

Design of high-efficiency low, frequency (<1000Hz) soundproof window or wall absorber which is transparent to airflow is presented. Due to the massive rise in human population and modernization, environmental noise has significantly risen globally. Prolonged noise exposure can cause severe physiological and psychological symptoms like nausea, headaches, fatigue, and insomnia. There has been continuous growth in building construction and infrastructure like offices, bus stops, and airports due to the urban population. Generally, a ventilated window is used for getting fresh air into the room, but at the same time, unwanted noise comes along. Researchers used traditional approaches like noise barrier mats in front of the window or designed the entire window using sound-absorbing materials. However, this solution is not aesthetically pleasing, and at the same time, it's heavy and not adequate for low-frequency noise shielding. To address this challenge, we design a transparent hexagonal panel based on the Sierpiński fractal triangle, which is aesthetically pleasing and demonstrates a normal incident sound absorption coefficient of more than 0.96 around 700 Hz and transmission loss of around 23 dB while maintaining e air circulation through the triangular cutout. Next, we present a concept of fabrication of large acoustic panels for large-scale applications, which leads to suppressing urban noise pollution.

Keywords: acoustic metamaterials, ventilation, urban noise pollution, noise control

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Authors: Liuhui Zhu, Peng Zeng

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With the rapid development in China, the urbanization has entered the transformation and promotion stage, and its direction of development has shifted to overall regional synergy. China has a large number of towns and villages, with comparative small scale and scattered distribution, which always support and provide resources to cities leading to urban-rural opposition, so it is difficult to achieve common development in a single town or village. In this context, the regional development should focus more on towns and villages to form a synergetic system, joining the regional association with cities. Thus, the paper raises the question about how to effectively organize towns and villages system to regulate the resource allocation and improve the comprehensive value of the regional area. To answer the question, it is necessary to find a suitable research unit and analysis of its present situation of towns and villages system for optimal development. By combing relevant researches and theoretical models, the county is the most basic administrative unit in China, which can directly guide and regulate the development of towns and villages, so the paper takes county as the research unit. Following the theoretical concept of ‘three structures and one network’, the paper concludes the research framework to analyse the present situation of towns and villages system, including scale structure, functional structure, spatial structure, and organization network. The analytical methods refer to the fractal theory and gravity model, using statistics and spatial data. The scale structure analyzes rank-size dimensions and uses the principal component method to calculate the comprehensive scale of towns and villages. The functional structure analyzes the functional types and industrial development of towns and villages. The spatial structure analyzes the aggregation dimension, network dimension, and correlation dimension of spatial elements to represent the overall spatial relationships. In terms of organization network, from the perspective of entity and ono-entity, the paper analyzes the transportation network and gravitational network. Based on the present situation analysis, the optimization strategies are proposed in order to achieve a synergetic relationship between towns and villages in the county area. The paper uses Suning county in the Beijing-Tianjin-Hebei region as a case study to apply the research framework and methods and then proposes the optimization orientations. The analysis results indicate that: (1) The Suning county is lack of medium-scale towns to transfer effect from towns to villages. (2) The distribution of gravitational centers is uneven, and the effect of gravity is limited only for nearby towns and villages. The gravitational network is not complete, leading to economic activities scattered and isolated. (3) The overall development of towns and villages system is immature, staying at ‘single heart and multi-core’ stage, and some specific optimization strategies are proposed. This study provides a regional view for the development of towns and villages and concludes the research framework and methods of towns and villages system for forming an effective synergetic relationship between them, contributing to organize resources and stimulate endogenous motivation, and form counter magnets to join the urban-rural integration.

Keywords: towns and villages system, organization structure, county area, fractal theory, gravity model

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Authors: Ozgu Hafizoglu

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Analogy is an essential tool of human cognition that enables connecting diffuse and diverse systems with attributional, deep structural, casual relations that are essential to learning, to innovation in artificial worlds, and to discovery in science. Cognitive Model of Analogy (CMA) leads and creates information pattern transfer within and between domains and disciplines in science. This paper demonstrates the Cognitive Model of Analogy (CMA) as an evolutionary approach to scientific research. The model puts forward the challenges of deep uncertainty about the future, emphasizing the need for flexibility of the system in order to enable reasoning methodology to adapt to changing conditions. In this paper, the model of analogical reasoning is created based on brain cells, their fractal, and operational forms within the system itself. Visualization techniques are used to show correspondences. Distinct phases of the problem-solving processes are divided thusly: encoding, mapping, inference, and response. The system is revealed relevant to brain activation considering each of these phases with an emphasis on achieving a better visualization of the brain cells: glial cells, axons, axon terminals, and neurons, relative to matching conditions of analogical reasoning and relational information. It’s found that encoding, mapping, inference, and response processes in four-term analogical reasoning are corresponding with the fractal and operational forms of brain cells: glial, axons, and neurons.

Keywords: analogy, analogical reasoning, cognitive model, brain and glials

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Authors: Saad M. Darwish, Adel A. El-Zoghabi, Moustafa F. Ashry

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The popularity of the Internet and the availability of powerful computers and high-speed networks as low-cost commodity components are changing the way we use computers today. These technical opportunities have led to the possibility of using geographically distributed and multi-owner resources to solve large-scale problems in science, engineering, and commerce. Recent research on these topics has led to the emergence of a new paradigm known as Grid computing. To achieve the promising potentials of tremendous distributed resources, effective and efficient load balancing algorithms are fundamentally important. Unfortunately, load balancing algorithms in traditional parallel and distributed systems, which usually run on homogeneous and dedicated resources, cannot work well in the new circumstances. In this paper, the concept of a fast fractal transform in heterogeneous grid computing based on R-tree and the domain-range entropy is proposed to improve fault tolerance and load balancing algorithm by improve connectivity, communication delay, network bandwidth, resource availability, and resource unpredictability. A novel two-dimension figure of merit is suggested to describe the network effects on load balance and fault tolerance estimation. Fault tolerance is enhanced by adaptively decrease replication time and message cost while load balance is enhanced by adaptively decrease mean job response time. Experimental results show that the proposed method yields superior performance over other methods.

Keywords: Grid computing, load balancing, fault tolerance, R-tree, heterogeneous systems

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Authors: Steven D. P Moore

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A novel method referred to asKýklos(Ky) dimensional geometry is proposed as an entity specific core geometric dimensional measurement system. Ky geometric measures can constructscaled multi-dimensionalmodels using regular and irregular sets in IRn. This entity specific-derived geometric measurement system shares similar fractal methods in which a ‘fractal transformation operator’ is applied to a set S to produce a union of N copies. The Kýklos’ inputs use 1D geometry as a core measure. One-dimensional inputs include the radius interval of a circle/sphere or the semiminor/semimajor axes intervals of an ellipse or spheroid. These geometric inputs have finite values that can be measured by SI distance units. The outputs for each interval are divided and subdivided 1D subcomponents with a union equal to the interval geometry/length. Setting a limit of subdivision iterations creates a finite value for each 1Dsubcomponent. The uniqueness of this method is captured by allowing the simplest 1D inputs to define entity specific subclass geometric core measurements that can also be used to derive length measures. Current methodologies for celestial based measurement of time, as defined within SI units, fits within this methodology, thus combining spatial and temporal features into geometric core measures. The novel Ky method discussed here offers geometric measures to construct scaled multi-dimensional structures, even models. Ky classes proposed for consideration include celestial even subatomic. The application of this offers incredible possibilities, for example, geometric architecture that can represent scaled celestial models that incorporates planets (spheroids) and celestial motion (elliptical orbits).

Keywords: Kyklos, geometry, measurement, celestial, dimension

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Authors: R. Korchiyne, A. Sbihi, S. M. Farssi, R. Touahni, M. Tahiri Alaoui

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Trabecular bone structure is important texture in the study of osteoporosis. Legendre multifractal spectrum can reflect the complex and self-similarity characteristic of structures. The main objective of this paper is to develop a new technique of medical image classification based on Legendre multifractal spectrum. Novel features have been developed from basic geometrical properties of this spectrum in a supervised image classification. The proposed method has been successfully used to classify medical images of bone trabeculations, and could be a useful supplement to the clinical observations for osteoporosis diagnosis. A comparative study with existing data reveals that the results of this approach are concordant.

Keywords: multifractal analysis, medical image, osteoporosis, fractal dimension, Legendre spectrum, supervised classification

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Authors: Marina Benito-Parejo, Raul Perez-Lopez, Miguel Herraiz, Carolina Guardiola-Albert, Cesar Martinez

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Persistency, long-term memory and randomness are intrinsic properties of time-series of earthquakes. The Rescaled Range Analysis (RS-Analysis) was introduced by Hurst in 1956 and modified by Mandelbrot and Wallis in 1964. This method represents a simple and elegant analysis which determines the range of variation of one natural property (the seismic energy released in this case) in a time interval. Despite the simplicity, there is complexity inherent in the property measured. The cumulative curve of the energy released in time is the well-known fractal geometry of a devil’s staircase. This geometry is used for determining the maximum and minimum value of the range, which is normalized by the standard deviation. The rescaled range obtained obeys a power-law with the time, and the exponent is the Hurst value. Depending on this value, time-series can be classified in long-term or short-term memory. Hence, an algorithm has been developed for compiling the RS-Analysis for time series of earthquakes by days. Completeness time distribution and locally stationarity of the time series are required. The interest of this analysis is their application for a complex seismic crisis where different earthquakes take place in clusters in a short period. Therefore, the Hurst exponent has been obtained for the seismic crisis of Alhoceima (Mediterranean Sea) of January-March, 2016, where at least five medium-sized earthquakes were triggered. According to the values obtained from the Hurst exponent for each cluster, a different mechanical origin can be detected, corroborated by the focal mechanisms calculated by the official institutions. Therefore, this type of analysis not only allows an approach to a greater understanding of a seismic series but also makes possible to discern different types of seismic origins.

Keywords: Alhoceima crisis, earthquake time series, Hurst exponent, rescaled range analysis

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Authors: Li Hung-Hui, Chen Chi-Chieh, Yang Zon-Yee

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This study aims to explore the impact energy absorption in the fragmented processes of rock samples during the split-Hopkinson-pressure-bar tests. Three kinds of rock samples including granite, marble and sandstone were tested. The impact energy absorptions were calculated according to the incident, reflected and transmitted strain wave histories measured by a oscilloscope. The degree of fragment rocks after tests was quantified by the box dimension of the fractal theory. The box dimension of rock fragments was obtained from the particle size distribution curve by the sieve analysis. The results can be concluded that: (1) the degree of rock fragments after tests can be well described by the value of box dimension; (2) with the impact energy absorption increasing, the degrees of rock fragments are varied from the very large fragments to very small fragments, and the corresponding box dimension varies from 2.9 to 1.2.

Keywords: SHPB test, energy absorption, rock fragments, impact loading, box dimension

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Authors: Ana M. Korol, Bibiana Riquelme, Osvaldo A. Rosso

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Since erythrocyte deformability analysis is mostly qualitative, the development of quantitative nonlinear methods is crucial for restricting subjectivity in the study of cell behaviour. An electro-optic mechanic system called erythrodeformeter has been developed and constructed in our laboratory in order to evaluate the erythrocytes' viscoelasticity. A numerical method formulated on the basis of fractal approximation for ordinary (OBM) and fractionary Brownian motion (FBM), as well as wavelet transform analysis, are proposed to distinguish chaos from noise based on the assumption that diffractometric data involves both deterministic and stochastic components, so it could be modelled as a system of bounded correlated random walk. Here we report studies on 25 donors: 4 alpha thalassaemic patients, 11 beta thalassaemic patients, and 10 healthy controls non-alcoholic and non-smoker individuals. The Correlation Coefficient, a nonlinear parameter, showed evidence of the changes in the erythrocyte deformability; the Wavelet Entropy could quantify those differences which are detected by the light diffraction patterns. Such quantifiers allow a good deal of promise and the possibility of a better understanding of the rheological erythrocytes aspects and also could help in clinical diagnosis.

Keywords: red blood cells, deformability, nonlinear dynamics, chaos theory, wavelet trannsform

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Authors: Mounir Zili

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We will introduce a new extension of the Brownian motion, that could serve to get a good model of many natural phenomena. It is a linear combination of a finite number of sub-fractional Brownian motions; that is why we will call it the mixed sub-fractional Brownian motion. We will present some basic properties of this process. Among others, we will check that our process is non-markovian and that it has non-stationary increments. We will also give the conditions under which it is a semi-martingale. Finally, the main features of its sample paths will be specified.

Keywords: fractal dimensions, mixed gaussian processes, sample paths, sub-fractional brownian motion

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Authors: Sami Houry

Abstract:

Complex systems exhibit universal characteristics as they near a tipping point. Among them are common generic early warning signals which precede critical transitions. These signals include: critical slowing down in which the rate of recovery from perturbations decreases over time; an increase in the variance of the state variable; an increase in the skewness of the state variable; an increase in the autocorrelations of the state variable; flickering between different states; and an increase in spatial correlations over time. The presence of the signals has management implications, as the identification of the signals near the tipping point could allow management to identify intervention points. Despite the applications of the generic early warning signals in various scientific fields, such as fisheries, ecology and finance, a review of literature did not identify any applications that address the program student withdrawal problem at the undergraduate distance universities. This area could benefit from the application of generic early warning signals as the program withdrawal rate amongst distance students is higher than the program withdrawal rate at face-to-face conventional universities. This research specifically assessed the generic early warning signals through an intensive case study of undergraduate program student withdrawal at a Canadian distance university. The university is non-cohort based due to its system of continuous course enrollment where students can enroll in a course at the beginning of every month. The assessment of the signals was achieved through the comparison of the incidences of generic early warning signals among students who withdrew or simply became inactive in their undergraduate program of study, the true positives, to the incidences of the generic early warning signals among graduates, the false positives. This was achieved through significance testing. Research findings showed support for the signal pertaining to the rise in flickering which is represented in the increase in the student’s non-pass rates prior to withdrawing from a program; moderate support for the signals of critical slowing down as reflected in the increase in the time a student spends in a course; and moderate support for the signals on increase in autocorrelation and increase in variance in the grade variable. The findings did not support the signal on the increase in skewness of the grade variable. The research also proposes a new signal based on the fractal-like characteristic of student behavior. The research also sought to extend knowledge by investigating whether the emergence of a program withdrawal status is self-similar or fractal-like at multiple levels of observation, specifically the program level and the course level. In other words, whether the act of withdrawal at the program level is also present at the course level. The findings moderately supported self-similarity as a potential signal. Overall, the assessment of the signals suggests that the signals, with the exception with the increase of skewness, could be utilized as a predictive management tool and potentially add one more tool, the fractal-like characteristic of withdrawal, as an additional signal in addressing the student program withdrawal problem.

Keywords: critical transitions, fractals, generic early warning signals, program student withdrawal

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Authors: Hikari Ryu, Yuki Fukuda, Kento Oishi, Chiharu Igarashi, Shogo Kiryu

Abstract:

Recently, wireless power transfer has been developed in various fields. Magnetic coupling is popular for feeding power at a relatively short distance and at a lower frequency. Electro-magnetic wave coupling at a high frequency is used for long-distance power transfer. The wireless power transfer has attracted attention in e-textile fields. Rigid batteries are required for many body-worn electric systems at the present time. The technology enables such batteries to be removed from the systems. Flexible coils have been studied for such applications. Coils with a high Q factor are required in the magnetic-coupling power transfer. Antennas with low return loss are needed for the electro-magnetic coupling. Litz wire is so flexible to fabricate coils and antennas sewn on fabric and has low resistivity. In this study, the electric characteristics of some coils and antennas fabricated with the Litz wire by using two sewing techniques are investigated. As examples, a coil and an antenna are described. Both were fabricated with 330/0.04 mm Litz wire. The coil was a planar coil with a square shape. The outer side was 150 mm, the number of turns was 15, and the pitch interval between each turn was 5 mm. The Litz wire of the coil was overstitched with a sewing machine. The coil was fabricated as a receiver coil for a magnetic coupled wireless power transfer. The Q factor was 200 at a frequency of 800 kHz. A wireless power system was constructed by using the coil. A power oscillator was used in the system. The resonant frequency of the circuit was set to 123 kHz, where the switching loss of power FETs was small. The power efficiencies were 0.44 – 0.99, depending on the distance between the transmitter and receiver coils. As an example of an antenna with a sewing technique, a fractal pattern antenna was stitched on a 500 mm x 500 mm fabric by using a needle punch method. The pattern was the 2nd-oder Vicsec fractal. The return loss of the antenna was -28 dB at a frequency of 144 MHz.

Keywords: e-textile, flexible coils and antennas, Litz wire, wireless power transfer

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Authors: I. Hosni, L. Bennaceur Farah, N. Saber, R Bennaceur

Abstract:

Soil moisture content is a key variable in many environmental sciences. Even though it represents a small proportion of the liquid freshwater on Earth, it modulates interactions between the land surface and the atmosphere, thereby influencing climate and weather. Accurate modeling of the above processes depends on the ability to provide a proper spatial characterization of soil moisture. The measurement of soil moisture content allows assessment of soil water resources in the field of hydrology and agronomy. The second parameter in interaction with the radar signal is the geometric structure of the soil. Most traditional electromagnetic models consider natural surfaces as single scale zero mean stationary Gaussian random processes. Roughness behavior is characterized by statistical parameters like the Root Mean Square (RMS) height and the correlation length. Then, the main problem is that the agreement between experimental measurements and theoretical values is usually poor due to the large variability of the correlation function, and as a consequence, backscattering models have often failed to predict correctly backscattering. In this study, surfaces are considered as band-limited fractal random processes corresponding to a superposition of a finite number of one-dimensional Gaussian process each one having a spatial scale. Multiscale roughness is characterized by two parameters, the first one is proportional to the RMS height, and the other one is related to the fractal dimension. Soil moisture is related to the complex dielectric constant. This multiscale description has been adapted to two-dimensional profiles using the bi-dimensional wavelet transform and the Mallat algorithm to describe more correctly natural surfaces. We characterize the soil surfaces and sub-surfaces by a three layers geo-electrical model. The upper layer is described by its dielectric constant, thickness, a multiscale bi-dimensional surface roughness model by using the wavelet transform and the Mallat algorithm, and volume scattering parameters. The lower layer is divided into three fictive layers separated by an assumed plane interface. These three layers were modeled by an effective medium characterized by an apparent effective dielectric constant taking into account the presence of air pockets in the soil. We have adopted the 2D multiscale three layers small perturbations model including, firstly air pockets in the soil sub-structure, and then a vegetable canopy in the soil surface structure, that is to simulate the radar backscattering. A sensitivity analysis of backscattering coefficient dependence on multiscale roughness and new soil moisture has been performed. Later, we proposed to change the dielectric constant of the multilayer medium because it takes into account the different moisture values of each layer in the soil. A sensitivity analysis of the backscattering coefficient, including the air pockets in the volume structure with respect to the multiscale roughness parameters and the apparent dielectric constant, was carried out. Finally, we proposed to study the behavior of the backscattering coefficient of the radar on a soil having a vegetable layer in its surface structure.

Keywords: multiscale, bidimensional, wavelets, backscattering, multilayer, SPM, air pockets

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Authors: Amar Partap Singh Pharwaha, Shweta Rani

Abstract:

To develop a reliable and cost effective communication platform for the telemedicine applications, novel antenna design has been presented using bacterial foraging optimization (BFO) technique. The proposed antenna geometry is achieved by etching a modified Koch curve fractal shape at the edges and a square shape slot at the center of the radiating element of a patch antenna. It has been found that the new antenna has achieved 43.79% size reduction and better resonating characteristic than the original patch. Representative results for both simulations and numerical validations are reported in order to assess the effectiveness of the developed methodology.

Keywords: BFO, electrical permittivity, fractals, Koch curve

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Authors: A. Hakimiyan, H. Namazi

Abstract:

Human behavior is defined as a range of behaviors exhibited by humans who are influenced by different internal or external sources. Human behavior is the subject of much research in different areas of psychology and neuroscience. Despite some advances in studies related to forecasting of human behavior, there are not many researches which consider the effect of the time delay between the presence of stimulus and the related human response. Analysis of EEG signal as a fractal time series is one of the major tools for studying the human behavior. In the other words, the human brain activity is reflected in his EEG signal. Artificial Neural Network has been proved useful in forecasting of different systems’ behavior especially in engineering areas. In this research, a time delay neural network is trained and tested in order to forecast the human EEG signal and subsequently human behavior. This neural network, by introducing a time delay, takes care of the lagging time between the occurrence of the stimulus and the rise of the subsequent action potential. The results of this study are useful not only for the fundamental understanding of human behavior forecasting, but shall be very useful in different areas of brain research such as seizure prediction.

Keywords: human behavior, EEG signal, time delay neural network, prediction, lagging time

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Authors: Anca Radulescu, Danae Evans

Abstract:

The relationship between a network’s hardwiring and its emergent dynamics are central to neuroscience. We study the principles of this correspondence in a canonical setup (in which network nodes exhibit well-studied complex quadratic dynamics), then test their universality in biological networks. By extending methods from discrete dynamics, we study the effects of network connectivity on temporal patterns, encapsulating long-term behavior into the rich topology of network Mandelbrot sets. Then elements of fractal geometry can be used to predict and classify network behavior.

Keywords: canonical model, complex dynamics, dynamic networks, fractals, Mandelbrot set, network connectivity

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Authors: Emanuel Guariglia

Abstract:

In this paper we deal with Chebyshev wavelets. We analyze their properties computing their Fourier transform. Moreover, we discuss the differential properties of Chebyshev wavelets due the connection coefficients. The differential properties of Chebyshev wavelets, expressed by the connection coefficients (also called refinable integrals), are given by finite series in terms of the Kronecker delta. Moreover, we treat the p-order derivative of Chebyshev wavelets and compute its Fourier transform. Finally, we expand the mother wavelet in Taylor series with an application both in fractional calculus and fractal geometry.

Keywords: Chebyshev wavelets, Fourier transform, connection coefficients, Taylor series, local fractional derivative, Cantor set

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