Fractal Concepts Research Articles

An integrated neuro-genetic approach incorporating the Taguchi method for product design

Product design is a multidisciplinary activity that requires the integration of concurrent engineering approaches into a design process that secures competitive advantages in product quality. In concurrent engineering, the Taguchi method has demonstrated an efficient design approach for product quality improvement. However, the Taguchi method intuitively uses parameters and levels in measuring the optimum combination of design parameter values, which might not guarantee that the final solution is the most optimal. This work proposes an integrated procedure that involves neural network training and genetic algorithm simulation within the Taguchi quality design process to aid in searching for the optimum solution with more precise design parameter values for improving the product development. The concept of fractals in computer graphics is also considered in the generation of product form alternatives to demonstrate its application in product design. The stages in the general approach of the proposed procedures include: (1) use of the Taguchi experimental design procedure, (2) analysis of the neural network and genetic algorithm process, and (3) generation of design alternatives. An electric fan design is used as an example to describe the development and explore the applicability of the proposed procedures. The results indicate that the proposed procedures could enhance the efficiency of product design efforts by approximately 7.8%. It is also expected that the proposed design procedure will provide designers with a more effective approach to product development.

Fractal kinetic behavior of plasmin on the surface of fibrin meshwork.

Intravascular fibrin clots are resolved by plasmin acting at the interface of gel phasesubstrate and fluid-borne enzyme. The classic Michaelis.Menten kinetic scheme cannot describe satisfactorily this heterogeneous-phase proteolysis because it assumes homogeneous well-mixed conditions. A more suitable model for these spatial constraints,known as fractal kinetics, includes a time-dependence of the Michaelis coefficient Km(F) = Km0F (1+ t)h, where h is a fractal exponent of time, t. The aim of the present study was to build up and experimentally validate a mathematical model for surface-acting plasmin that can contribute to a better understanding of the factors that influence fibrinolytic rates. The kinetic model was fitted to turbidimetric data for fibrinolysis under various conditions. The model predicted Km0(F) = 1.98 μM and h = 0.25 for fibrin composed of thin fibers and Km0(F) = 5.01 μM and h = 0.16 for thick fibers in line with a slower macroscale lytic rate (due to a stronger clustering trend reflected in the h value) despite faster cleavage of individual thin fibers (seen as lower Km0(F) ). ε-Aminocaproic acid at 1 mM or 8 U/mL carboxypeptidase-B eliminated the time-dependence of Km F and increased the lysis rate suggesting a role of C-terminal lysines in the progressive clustering of plasmin. This fractal kinetic concept gained structural support from imaging techniques. Atomic force microscopy revealed significant changes in plasmin distribution on a patterned fibrinogen surface in line with the time-dependent clustering of fluorescent plasminogen in confocal laser microscopy. These data from complementary approaches support a mechanism for loss of plasmin activity resulting from C-terminal lysine-dependent redistribution of enzyme molecules on the fibrin surface.

The fractal nature of maps and mapping

A fractal can be simply understood as a set or pattern in which there are far more small things than large ones, for example, far more small geographic features than large ones on the earth surface, or far more large-scale maps than small-scale maps for a geographic region. This article attempts to argue and provide evidence for the fractal nature of maps and mapping. It is the underlying fractal structure of geographic features, either natural or man-made, that make reality mappable, large-scale maps generalizable, and cities imageable. The fractal nature is also what underlies the beauty of maps. After introducing some key fractal concepts such as recursion, self-similarity, scaling ratio, and scaling exponent, this article demonstrates that fractal thought is rooted in long-standing map-making practices such as series maps subdivision, visual hierarchy, and Töpfer’s radical law. Drawing on previous studies on head/tail breaks, mapping can be considered a head/tail breaks process; that is to divide things around an average, according to their geometric, topological and/or semantic properties, into the head (for those above the average) and the tail (for those below the average), and recursively continue the dividing process for the head for map generalization, statistical mapping, and cognitive mapping. Given the fractal nature of maps and mapping, cartography should be considered a perfect combination of science and art, and scaling must be formulated as a law of cartography or that of geography in general.

Deeper insights into fractal concepts applied to liquid-phase adsorption dynamics

In this work, the superior accuracy of “fractal-like kinetic models” with respect to their classical counterparts in interpreting cadmium adsorption dynamics on both raw and beneficiated (by means of mechanical sieving and CO2/steam gasification) combustion fly ashes has been validated. Results showed that classical and “fractal-like kinetic models” produce comparable outputs only for low fractional adsorption degrees (generally lower than 0.5); this was ascribed to a likely more homogeneous pollutant concentration in the particle outer shells. On the other hand, for longer adsorption times a less random pollutant intraparticle distribution should be responsible for a fractal-like behaviour. Additionally, for beneficiated ashes, the generally higher values of fractal pseudo-first order model rate coefficients (the model that produced best fitting results) with respect to what was observed for the parent sorbent, were linked to both the reduction of the particle diameter and the porosity development induced by the activation treatments, determining faster diffusion paths for the pollutant.

Fractal and multifractal analysis on pore structure in cement paste

The capillary pore structure in cement paste is critical to the transport property, to which various durability problems of concrete are closely related. A novel characterization of pore structure in cement paste has to account for its intrinsic heterogeneity, i.e., the disordered porous media. In this paper, we present some results about the application of fractal and multifractal analysis on simulated pore structure of cement paste, where some hydration factors including the water to cement ratio and the degree of cement hydration are discussed in terms of the fractal dimension and the multifractal spectrum. Results indicate that the concepts of fractal and multifractal are feasible in characterizing the heterogeneity of pore structure in cement paste. Moreover, it is confirmed that compared to the fractal concept, the multifractal concept allows a relatively more reasonable characterization, where the size distribution and the spatial arrangement of pore are addressed without any priori assumptions.

Reducing risk of closed loop control of blood glucose in artificial pancreas using fractional calculus.

Healthcare costs in the US are among the highest in the world. Chronic diseases such as diabetes significantly contribute to these extensive costs. Despite technological advances to improve sensing and actuation devices, we still lack a coherent theory that facilitates the design and optimization of efficient and robust medical cyber-physical systems for managing chronic diseases. In this paper, we propose a mathematical model for capturing the complex dynamics of blood glucose time series (e.g., time dependent and fractal behavior) observed in real world measurements via fractional calculus concepts. Building upon our time dependent fractal model, we propose a novel model predictive controller for an artificial pancreas that regulates insulin injection. We verify the accuracy of our controller by comparing it to conventional non-fractal models using real world measurements and show how the nonlinear optimal controller based on fractal calculus concepts is superior to non-fractal controllers in terms of average risk index and prediction accuracy.

Fractional structure «mixing - transport» as an open system

In the context of a research area “open systems physics”, fractional structure “mixing – transport” as an open system is proposed. The studies of power-law nonlocality and power-law memory, allowing to create mathematical methods, successfully used in transport (transfer) systems are considered.Interaction paradigm of geoinformation space with fractional structure “mixing – transport” is proposed. It is shown that the interaction is crystallized into fractional structure “transport - mixing – transport”, formalization of which is presented as an open system model. It is noted that due to the complexity of the open system, the formation of various structures, such as Levy processes and random walks in fractal time is possible in it.A base for understanding anomalous transport, adequate to Levy flights, is an association with superdiffusion processes, considered in transport theory.It is noted that in describing the properties of systems with fractal structure, representations of Euclidean geometry cannot be used. There is a need to analyze these processes in terms of the fractional dimension geometry. Systems with fractal feature are characterized by effects such as memory, complex spatial mixing processes and self-organization.Using the new research area - open systems physics, which integrates the fields such as synergy, dissipative structures, deterministic chaos, fractal concept introduces a new level of understanding in implementing complex tasks at interdisciplinary level.A new vision of the open system, which is characterized by coherent Lagrangian structure (stable and unstable manifolds of fixed points and periodic orbits) and finite-time Lyapunov exponent is shown.Based on the ideology of the nonlinear recursive analysis and the Poincare theory, visual images of Poincare fractional-order diagrams for the cases of the interference component influence in various frequency ranges are first acquired. Moreover, numerical characteristics of the fractional-order fractal dimension and the average Poincare recurrence time are obtained.

Paradigmatic Constants and Structural­Semantic Patterns of Digital Culture

Analyses paradigmatic foundations of digital culture that supersedes the (post)postmodern. It reveals paradigmatic constants and structural­semantic patterns of digital culture from the perspective of digital humanities and fractal conception in particular and suggests an explanation of diversity of local cultural configurations, peculiarities of socio­cultural transmission and periodic actualisation of socio­cultural attractors of the past epochs.

Fractals: a very short introduction

Preface 1. The fractal concept 2. Self-similarity 3. Fractal dimension 4. Julia sets and the Mandelbrot set 5. Random walks and Brownian motion 6. Fractals in the real world 7. A little history Further reading

An allometric scaling relation based on logistic growth of cities

The relationships between urban area and population size have been empirically demonstrated to follow the scaling law of allometric growth. This allometric scaling is based on exponential growth of city size and can be termed “exponential allometry”, which is associated with the concepts of fractals. However, both city population and urban area comply with the course of logistic growth rather than exponential growth. In this paper, I will present a new allometric scaling based on logistic growth to solve the above mentioned problem. The logistic growth is a process of replacement dynamics. Defining a pair of replacement quotients as new measurements, which are functions of urban area and population, we can derive an allometric scaling relation from the logistic processes of urban growth, which can be termed “logistic allometry”. The exponential allometric relation between urban area and population is the approximate expression of the logistic allometric equation when the city size is not large enough. The proper range of the allometric scaling exponent value is reconsidered through the logistic process. Then, a medium-sized city of Henan Province, China, is employed as an example to validate the new allometric relation. The logistic allometry is helpful for further understanding the fractal property and self-organized process of urban evolution in the right perspective.

DESIGN AND SIMULATION OF SIERPINSKI CARPET FRACTAL ANTENNA AND COMPARISION OF DIFFERENT FEEDS

The rapid growth in wireless communication has led to need of antennas with increased bandwidth, high gain and low profile. In this paper, a multi band microstrip antenna is designed by applying fractal concept to a rectangular microstrip antenna. The antennas properties gain, and return loss, are studied to achieve better performance. The designed antenna is compared for different feeding techniques and the results are analyzed. This antenna is designed and simulated by using HFSS software.

Fractal monopole antenna with electromagnetic bandgap structure for UWB applications

This article presents the design and performance measures of a fractal monopole antenna with band rejection characteristics for ultrawide band applications. Fractal concept is incorporated to miniaturize the antenna dimension and to enhance its radiation and broadband properties. Mushroom type electromagnetic bandgap structures are introduced near the micristrip feed line to reject the WLAN frequency band. The proposed antenna operates in the frequency range 3.2–12.4 GHz with average gain of 5 dB and maximum efficiency of 97.6%. The rejection band ranges from 5.09 to 5.97 GHz. Consistent radiation characteristics exist within the operating band. The performance of the proposed antenna is confirmed by simulation and experimental results. © 2014 Wiley Periodicals, Inc. Microwave Opt Technol Lett 56:1872–1874, 2014

On the scaling law analysis of nanodimensional LiF thin film surfaces

The surface characteristics of nanodimensional LiF films deposited at different substrate temperature were investigated and scaling law analysis was performed using fractal concept. The interface width, average roughness, height–height correlation, lateral correlation length, roughness exponent and fractal dimension were determined to characterize the observed surface. The computed results show that the film deposited at higher substrate temperature has higher surface roughness, whereas the fractal analysis using height–height correlation function reveals that the value of fractal dimension decreases as the substrate temperature during deposition increases.

Morphology of Koch Fractal Antenna

Antenna is paramount element for the radio communication entity using radio frequency and microwaves. In twenty-first century wireless communication systems, there is a demand for wider bandwidth, multiband and low profile antennas for both commercial and military purposes. This has initiated antenna analysis in various directions; one of them is using fractal shaped antenna elements. Fractal concepts have emerged and advanced as a unique technique for designing compact UWB antennas, because of the self-similarityand space-filling attributes. In a fractal antenna, the multiple frequencies of operation depend on the total dimensions of the design and the scale factor. There are varied fractal geometries that have been found to be favorable in developing novel and new models for antennas. In this paper we will be discussing one such type of fractal antennas i.e. the Koch structure. Koch antenna can be designed with a triangle, rectangle and pentagon as its initiator. Their geometry and parameters have been analyzed in this paper.Â

Evolution of neotectonic activity of East Anatolian Fault System (EAFS) in Bingöl pull-apart basin, based on fractal dimension and morphometric indices

This study is an attempt of a semi-automatic geomorphological GIS analysis based on morphometric indices. In the study, 10-m-resolution Digital Elevation Models (DEMs) are used to assess the neotectonic signals regarding the recent topographic developments and to attach additional significance to active tectonics in the Bingöl basin area. The methodology incorporates the determination of the structural similarities of the faults in the basins using fractal concepts and the application of four morphometric indices (Stream Power Index (SP), Multi-resolution Index of Valley Bottom Flatness (MRVBF), Terrain Ruggedness Index (TRI) and Valley Width-to-Height Ratio (Vf)). In order to detect the deviation from spatial randomness of the applied indices, the weighted correlation coefficient Moran’s I is used and the results are interpreted at a confidence interval of 99%. The spatial distribution of integrated index values is evaluated with the tectonically active fault zones in order to determine the probable activity and the structural deformation in the basin.The applied methodology reveals that the fractal analysis of the fault lines and the spatial analysis of the morphometric indices proved to be effective tools in analyzing the tectonic influence of the fault system on the basin area. Within the basin area, a relatively lesser degree of tectonic activity is observed, in contrast with the high tectonic activity outside the basin.

Quantitative Mixing Analysis of Laminar Flow in Circle Grid Perforated Plate with 50% Porosity Static Mixer

The applications of the static mixers are widely applied in many industries to obtain the desired type of mixing. In this context, to perform the mixing process should have two different fluids that also have different properties which will combines it in a single equipment to make an another fluid. The main objective of this research study is to propose a new approach of fractal concept (circle grid perforated plate) for internal rapid mixing by determining the coefficient of variation (COV). This study was implemented by fully numerical simulations. The simulations of mixing fluid were carried out with the help of commercial computational fluid dynamic (CFD) package ANSYS CFX 14.0 software. The simulation was done primarily in cylindrical pipe with insertions of circle grid perforated plate with porosity of 50%. Three levels of laminar flow have been chosen to result in Reynolds numbers (Re) equal to 100, 200 and 400. The effectiveness of circle grid perforated plate static mixer has been evaluated by comparing the homogeneity level of mixing fluids to the Kenics static mixer that readily available in industries applications. Based on the research findings, the COV value for circle grid perforated plate with 50% porosity at Re 100 was 0.0744 which is out of the range while Reynolds number at 200 and 400 were 0.0483 and 0.0247 respectively which are in the range in term of reasonable target of mixing homogeneity. The values of COV between 0.01 and 0.05 are the reasonable target for many applications. In term of manufacturing cost and energy loss due to static mixer, definitely this new approach of 50% porosity circle grid perforated plate is better design compared to the Kenics static mixer because of lower number of inserts and simpler design of static mixer to produce.

Modelling the combustion of a sub-micron aluminium particle

We pose the following question: ‘Within the context of the classical shrinking-core model for sub-micron aluminium combustion, allowing only for the diffusion of atomic oxygen (no aluminium diffusion), but with two non-classical ingredients (large Knudsen number heat losses to the ambient atmosphere and a fractal reacting surface), are the solutions consistent with four experimental facts and data sets: (i) burn times; (ii) particle temperatures; (iii) maximum temperatures independent of particle size for small Damköhler numbers; and (iv) also for small Damköhler numbers a burn law of the form d1 − ν–t (where d is the particle diameter and ν ∼ 0.7 or so)?’ In the analysis we first consider a non-fractal model and scale the lengths with (where is the diffusion coefficient and k is the reaction-rate constant) and time with (where ρ− is the aluminium density and co is a characteristic value of the O density within the alumina). Burn times are calculated which follow a linear d–t law for small values of kL/D(L = D/2), the Damköhler number, and a quadratic d2–t law for large values of . Enhanced temperatures (greater than the ambient) arise for small values of with maximum values that are size independent. Since the small Damköhler d–t law does not agree with experimental data, we introduce a fractal concept into the model, as this can generate a burn law of the observed form. However, we then find that the maximum temperature is not independent of particle size.

FRACTAL PROPERTY OF ADMINISTRATION

To understand the constant increase in administrati on, we need a new approach to the administration. F or many years, the administration has intensified as a closed science, associated only with economics, la w and political science. However, this approach did not b ring anything good, because almost nothing in the administration has improved. Therefore, it is neces sary to connect the administration with the natural sciences which give the best description of the wor ld around us. Because of this the concept of fracta ls gives us a good insight primarily why administratio n tends to increase and why the job in the administ ration of people outside the church seems meaningless, complicated and full of paperwork.

Conceptual Modeling Methodology of Multifunction Sensors on the Basis of a Fractal Approach

The problems of the multifunction sensors development make inefficient of design traditional methods application. Work purpose is an effective approach creation to the analysis and synthesis of sensors physical functional principle and creation on its basis mathematical, algorithmic and informational software for multifunction quantity sensors conceptual design automation. Authors propose the problem solution method based on fractal approach application to the theory of energy and information circuit models. For this purpose the physical functional principle sensor modeling fractal concept and mechanisms of its realization are created. This work results are new computer technique, software for the automatic synthesis of the multifunction sensors physical functional principle and two new multifunction sensors utility models automatically generated by developed software.

Fractal design concepts for stretchable electronics

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.