Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 7

Fractals Related Abstracts

7 A Novel Antenna Design for Telemedicine Applications

Authors: Amar Partap Singh Pharwaha, Shweta Rani


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: Fractals, BFO, electrical permittivity, Koch curve

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6 On the Design of Wearable Fractal Antenna

Authors: Amar Partap Singh Pharwaha, Shweta Rani


This paper is aimed at proposing a rhombus shaped wearable fractal antenna for wireless communication systems. The geometrical descriptors of the antenna have been obtained using bacterial foraging optimization (BFO) for wide band operation. The method of moment based IE3D software has been used to simulate the antenna and observed that miniaturization of 13.08% has been achieved without degrading the resonating properties of the proposed antenna. An analysis with different substrates has also been done in order to evaluate the effectiveness of electrical permittivity on the presented structure. The proposed antenna has low profile, light weight and has successfully demonstrated wideband and multiband characteristics for wearable electronic applications.

Keywords: Fractals, BFO, electrical permittivity, bandwidth, wearable antenna

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5 Aggregation of Fractal Aggregates Inside Fractal Cages in Irreversible Diffusion Limited Cluster Aggregation Binary Systems

Authors: Zakiya Shireen, Sujin B. Babu


Irreversible diffusion-limited cluster aggregation (DLCA) of binary sticky spheres was simulated by modifying the Brownian Cluster Dynamics (BCD). We randomly distribute N spheres in a 3D box of size L, the volume fraction is given by Φtot = (π/6)N/L³. We identify NA and NB number of spheres as species A and B in our system both having identical size. In these systems, both A and B particles undergo Brownian motion. Irreversible bond formation happens only between intra-species particles and inter-species interact only through hard-core repulsions. As we perform simulation using BCD we start to observe binary gels. In our study, we have observed that species B always percolate (cluster size equal to L) as expected for the monomeric case and species A does not percolate below a critical ratio which is different for different volume fractions. We will also show that the accessible volume of the system increases when compared to the monomeric case, which means that species A is aggregating inside the cage created by B. We have also observed that for moderate Φtot the system undergoes a transition from flocculation region to percolation region indicated by the change in fractal dimension from 1.8 to 2.5. For smaller ratio of A, it stays in the flocculation regime even though B have already crossed over to the percolation regime. Thus, we observe two fractal dimension in the same system.

Keywords: Fractals, percolation, BCD, sticky spheres

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4 Using Fractal Architectures for Enhancing the Thermal-Fluid Transport

Authors: Debjyoti Banerjee, Surupa Shaw


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, Heat Transfer Enhancement, constructal theory, pumping power enhancement

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3 Generic Early Warning Signals for Program Student Withdrawals: A Complexity Perspective Based on Critical Transitions and Fractals

Authors: Sami Houry


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: Fractals, critical transitions, generic early warning signals, program student withdrawal

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2 Fractal Behaviour of Earthquake Sequences in Himalaya

Authors: Kamal, Adil Ahmad


Earthquakes are among the most versatile natural and dynamic processes, and hence a fractal model is considered to be the best representative of the same. We present a novel method to process and analyse information hidden in earthquake sequences using Fractal Dimensions and Iterative Function Systems (IFS). Spatial and temporal variations in the fractal dimensions of seismicity observed around the Indian peninsula in last 30 years are studied. This was used as a possible precursor before large earthquakes in the region. IFS images for observed seismicity in the Himalayan belt were also obtained. We scan the whole data set and coarse grain of a selected window to reduce it to four bins. A critical analysis of four-cornered chaos-game clearly shows that the spatial variation in earthquake occurrences in Himalayan range is not random. Two subzones of Himalaya have a tendency to follow each other in time.

Keywords: Fractals, Earthquakes, Himalaya, iterated function systems

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1 PathoPy2.0: Application of Fractal Geometry for Early Detection and Histopathological Analysis of Lung Cancer

Authors: Rhea Kapoor


Fractal dimension provides a way to characterize non-geometric shapes like those found in nature. The purpose of this research is to estimate Minkowski fractal dimension of human lung images for early detection of lung cancer. Lung cancer is the leading cause of death among all types of cancer and an early histopathological analysis will help reduce deaths primarily due to late diagnosis. A Python application program, PathoPy2.0, was developed for analyzing medical images in pixelated format and estimating Minkowski fractal dimension using a new box-counting algorithm that allows windowing of images for more accurate calculation in the suspected areas of cancerous growth. Benchmark geometric fractals were used to validate the accuracy of the program and changes in fractal dimension of lung images to indicate the presence of issues in the lung. The accuracy of the program for the benchmark examples was between 93-99% of known values of the fractal dimensions. Fractal dimension values were then calculated for lung images, from National Cancer Institute, taken over time to correctly detect the presence of cancerous growth. For example, as the fractal dimension for a given lung increased from 1.19 to 1.27 due to cancerous growth, it represents a significant change in fractal dimension which lies between 1 and 2 for 2-D images. Based on the results obtained on many lung test cases, it was concluded that fractal dimension of human lungs can be used to diagnose lung cancer early. The ideas behind PathoPy2.0 can also be applied to study patterns in the electrical activity of the human brain and DNA matching.

Keywords: Image Processing, Lung cancer, Fractals, histopathological analysis, Minkowski dimension

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