Relevant bibliographies by topics / Fractal modelling

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers

Academic literature on the topic 'Fractal modelling'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 April 2022

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Journal articles on the topic "Fractal modelling"

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Chen, Yanguang. "Characterizing Growth and Form of Fractal Cities with Allometric Scaling Exponents." Discrete Dynamics in Nature and Society 2010 (2010): 1–22. http://dx.doi.org/10.1155/2010/194715.

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Fractal growth is a kind of allometric growth, and the allometric scaling exponents can be employed to describe growing fractal phenomena such as cities. The spatial features of the regular fractals can be characterized by fractal dimension. However, for the real systems with statistical fractality, it is incomplete to measure the structure of scaling invariance only by fractal dimension. Sometimes, we need to know the ratio of different dimensions rather than the fractal dimensions themselves. A fractal-dimension ratio can make an allometric scaling exponent (ASE). As compared with fractal dimension, ASEs have three advantages. First, the values of ASEs are easy to be estimated in practice; second, ASEs can reflect the dynamical characters of system's evolution; third, the analysis of ASEs can be made through prefractal structure with limited scale. Therefore, the ASEs based on fractal dimensions are more functional than fractal dimensions for real fractal systems. In this paper, the definition and calculation method of ASEs are illustrated by starting from mathematical fractals, and, then, China's cities are taken as examples to show how to apply ASEs to depiction of growth and form of fractal cities.
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LAI, PENG-JEN. "HOW TO MAKE FRACTAL TILINGS AND FRACTAL REPTILES." Fractals 17, no. 04 (December 2009): 493–504. http://dx.doi.org/10.1142/s0218348x09004533.

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Intensive research on fractals began around 1980 and many new discoveries have been made. However, the connection between fractals, tilings and reptiles has not been thoroughly explored. This paper shows that a method, similar to that used to construct irregular tilings in ℜ2 can be employed to construct fractal tilings. Five main methods, including methods in Escher style paintings and the Conway criterion are used to create the fractal tilings. Also an algorithm is presented to generate fractal reptiles. These methods provide a more geometric way to understand fractal tilings and fractal reptiles and complements iteration methods.
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LAPIDUS, MICHEL L. "FRACTALS AND VIBRATIONS: CAN YOU HEAR THE SHAPE OF A FRACTAL DRUM?" Fractals 03, no. 04 (December 1995): 725–36. http://dx.doi.org/10.1142/s0218348x95000643.

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We study various aspects of the question “Can one hear the shape of a fractal drum?”, both for “drums with fractal boundary” (or “surface fractals”) and for “drums with fractal membrane” (or “mass fractals”).
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SUZUKI, MASUO. "FRACTAL FORM ANALYSIS." Fractals 04, no. 03 (September 1996): 237–39. http://dx.doi.org/10.1142/s0218348x96000327.

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CHEN, YAN-GUANG. "FRACTAL TEXTURE AND STRUCTURE OF CENTRAL PLACE SYSTEMS." Fractals 28, no. 01 (February 2020): 2050008. http://dx.doi.org/10.1142/s0218348x20500085.

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The boundaries of central place models proved to be fractal lines, which compose fractal texture of central place networks. However, the fractal texture cannot be verified by empirical analyses based on observed data. On the other hand, fractal structure of central place systems in the real world can be empirically confirmed by positive studies, but there are no corresponding models. The spatial structure of classic central place models bears Euclidean dimension [Formula: see text] rather than fractal dimensions [Formula: see text]. This paper is devoted to deriving structural fractals of central place models from the textural fractals. The method is theoretical deduction based on the dimension rules of fractal sets. The main results and findings are as follows. First, the central place fractals were formulated by the [Formula: see text] numbers and [Formula: see text] numbers. Second, three structural fractal models were constructed for central place systems according to the corresponding fractal dimensions. Third, the classic central place models proved to comprise Koch snowflake curve, Sierpinski space filling curve, and Gosper snowflake curve. Moreover, the traffic principle plays a leading role in urban and rural settlements evolution. A conclusion was reached that the textural fractal dimensions of central place models can be converted into the structural fractal dimensions and vice versa, and the structural dimensions can be directly used to appraise human settlement distributions in reality. Thus, the textural fractals can be indirectly employed to characterize the systems of human settlements.
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Avery, I., F. R. Hall, and C. E. N. Sturgess. "Fractal modelling of materials." Journal of Materials Processing Technology 80-81 (August 1998): 565–71. http://dx.doi.org/10.1016/s0924-0136(98)00124-1.

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PE, JOSEPH L. "ANA'S GOLDEN FRACTAL." Fractals 11, no. 04 (December 2003): 309–13. http://dx.doi.org/10.1142/s0218348x03002269.

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In his fascinating book Wonders of Numbers, Clifford Pickover introduces the Ana sequence and fractal, two self-referential constructions arising from the use of language. This paper answers Pickover's questions on the relative composition of sequence terms and the dimension of the fractal. In the process, it introduces a novel way of obtaining fractals from iterative set operations. Also, it presents a beautiful variant of the Ana constructions involving the golden ratio. In conclusion, it suggests ways of constructing similar fractals for the Morse-Thue and "Look and Say" sequences.
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Coppens, Marc-Olivier, and Gilbert F. Froment. "The Effectiveness of Mass Fractal Catalysts." Fractals 05, no. 03 (September 1997): 493–505. http://dx.doi.org/10.1142/s0218348x97000395.

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Many porous catalysts have a fractal surface, but only rarely do they have a fractal volume, the main exceptions being extremely porous aerogels. It has been suggested that a fractal shape of their volume would be ideal, because it has an infinite area per unit mass that is easily accessible by the reactants. This paper investigates the efficiency of mass fractals by comparing them with nonfractal catalysts. It is found that the specific surface areas of comparable nonfractal catalysts are of the same order of magnitude, if not higher than those of mass fractals. Despite the high effectiveness factor of mass fractals due to the exceptionally easy accessibility of their active sites, production in a nonfractal catalyst is often higher than in a mass fractal, because of the high porosity of the latter. For some strongly diffusion limited reactions, especially in mesoporous catalysts, an added mass fractal macroporosity, with a finite scaling regime, would increase the yields beyond what is possible with a nonfractal catalyst. Nonetheless, when transport through viscous flow in macropores is very rapid the effective reaction rates in classical bimodal catalysts are higher than in fractal catalysts with their high macroporosity.
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Semkow, Thomas M. "Neighborhood Volume for Bounded, Locally Self-Similar Fractals." Fractals 05, no. 01 (March 1997): 23–33. http://dx.doi.org/10.1142/s0218348x97000048.

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We derive the formulas for neighborhood volume (Minkowski volume in d-dimensions) for fractals which have a curvature bias and are thus bounded. Both local surface fractal dimension and local mass fractal dimension are included as well as a radius of the neighborhood volume comparable with the size of the fractal. We consider two types of the neighborhood volumes: simplified and generalized, as well as the volumes below and above the fractal boundary. The formulas derived are generalizations of the equations for isotropic unbounded fractals. Based on the simplified-volume concept, we establish the procedure for calculating a distribution of physical quantities on bounded fractals and apply it to the distribution of trace elements in soil particles. Using the concept of the generalized volume, we show how an expectation value of a physical process can be calculated on bounded fractals, and apply it to the radon emanation from solid particles.
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TATOM, FRANK B. "THE RELATIONSHIP BETWEEN FRACTIONAL CALCULUS AND FRACTALS." Fractals 03, no. 01 (March 1995): 217–29. http://dx.doi.org/10.1142/s0218348x95000175.

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The general relationship between fractional calculus and fractals is explored. Based on prior investigations dealing with random fractal processes, the fractal dimension of the function is shown to be a linear function of the order of fractional integro-differentiation. Emphasis is placed on the proper application of fractional calculus to the function of the random fractal, as opposed to the trail. For fractional Brownian motion, the basic relations between the spectral decay exponent, Hurst exponent, fractal dimension of the function and the trail, and the order of the fractional integro-differentiation are developed. Based on an understanding of fractional calculus applied to random fractal functions, consideration is given to an analogous application to deterministic or nonrandom fractals. The concept of expressing each coordinate of a deterministic fractal curve as a “pseudo-time” series is investigated. Fractional integro-differentiation of such series is numerically carried out for the case of quadric Koch curves. The resulting time series produces self-similar patterns with fractal dimensions which are linear functions of the order of the fractional integro-differentiation. These curves are assigned the name, fractional Koch curves. The general conclusion is reached that fractional calculus can be used to precisely change or control the fractal dimension of any random or deterministic fractal with coordinates which can be expressed as functions of one independent variable, which is typically time (or pseudo-time).
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Dissertations / Theses on the topic "Fractal modelling"

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Gregotski, Mark Edward. "Fractal stochastic modelling of airborne magnetic data." Thesis, McGill University, 1989. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=74300.

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Airborne magnetic field data exhibit downward continued power spectra of the form $1/f sp beta$ (where f is the spatial frequency and $ beta$ is a non-negative real number). This form of spectrum is observed for magnetic data recorded over a range of sampling scales from various areas of the Canadian Shield. Two scaling regimes have been discovered. The first has a $ beta$ value near 3 for wavelengths $ sbsp{ sim}{$25 km. These results suggest a "variable fractal" description of the distribution of near-surface magnetic sources.
From a data modelling viewpoint, the magnetic measurements are derived from a linear superposition of a deterministic system function and a stochastic excitation process. A symmetric operator corresponds to the system function, and the near-surface magnetic source distribution represents the excitation process. The deconvolution procedure assumes an autoregressive (AR) system function and proceeds iteratively using bi-directional AR (BDAR) filtering in one dimension, which is extended to four-pass AR filtering in two dimensions. The traditional assumption of a spectrally white innovation is used in the deconvolution procedure. The data are modified prior to deconvolution by a Fourier domain prewhitening technique, to account for the long wavelength content of the fractal innovation. Deconvolution of the modified data produces the system function, which is removed from the original data to produce the near-surface magnetic source distribution. This distribution serves as a susceptibility map which can be used for enhancing magnetic field anomalies and geological mapping. Thus, the statistical descriptions of near-surface magnetic sources are useful for modelling airborne magnetic data in "shield-type" geologic environments.
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Nilsen, Christopher. "Fractal modelling of turbulent flows : Subgrid modelling for the Burgers equation." Thesis, Norges teknisk-naturvitenskapelige universitet, Institutt for energi- og prosessteknikk, 2011. http://urn.kb.se/resolve?urn=urn:nbn:no:ntnu:diva-13916.

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The stochastically forced Burgers equation shares some of the same characteristics as the three-dimensional Navier-Stokes equations. Because of this it is sometimes used as a model equation for turbulence. Simulating the stochastically forced Burgers equation with low resolution can be considered as a one dimensional model of a three-dimensional large eddy simulation, and can be used to evaluate subgrid models. Modified versions of subgrid models using the fractal interpolation technique are presented here and tested in low resolution simulations of the stochastically forced Burgers equations. The results are compared with high resolution simulations, then low resolution simulations first using the dynamic Smagorinsky model and then using no subgrid model other than the numerical dissipation of the convective flux discretisation scheme. The fractal models perform reasonably well and most of the large scale features from the high resolution simulations are reproduced by corresponding simulations with low resolution. The performance of the fractal models is not, however, better than the performance of the dynamic Smagorinsky model. Therefore one might say that although the fractal models give promising results, it is not obvious that they are in any way superior to the traditional models. Also the low resolution simulation with the dissipative convective scheme performs well, suggesting that numerical dissipation can be sufficient as a subgrid model in one dimension.The solutions to the stochastically forced Burgers equation follow a k^(-5/3) energy spectrum, but high order statistics are not similar to real turbulence, due to the complete domination of shocks. Thus the stochastically forced Burgers equation might not be a suitable model for turbulence. It is not likely that the complexity of three-dimensional subgrid modelling is sufficiently represented by the one-dimensional case either.
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Lauren, Michael Kyle. "The fractal modelling of turbulent surface-layer winds." Thesis, University of Auckland, 1999. http://hdl.handle.net/2292/1106.

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Multiscaling analysis and cascade simulation techniques, which form part of the more general field of fractals, are introduced as a method for characterising and simulating surface-layer winds, particularly for time scales associated with the energy-containing range. This type of analysis consists of determining the power-law parameter of the spectrum of the data, and the scaling of the statistical moments. These techniques were applied to determine how the statistics depended on the duration (or scale) of the fluctuations in wind speed, the atmospheric conditions, and the topography of the site. It was found that the parameterisations produced using multiscaling analysis characterised differences in the statistics for each of these cases. Furthermore, the fractal cascade simulation techniques used provided simple methods for reproducing these statistics. This analysis is followed by an investigation into the robustness of some of these results. In particular, the data is examined for the existence of self-similar distributions of the cascade weighting factor, W. Such self-similar analysis allows the direct simulation of the data via a cascade. Cascade models have the virtue of being able to reproduce statistical properties such as intermittency, and in particular, the nesting of intermittency from different wavenumber bands in the same region of space. The existence of these properties in both the experimental and simulated data is investigated, with consideration given to the consequence of the results for simulation techniques. One notable discovery is the failure of these methods to reproduce the bias in the distribution of the gradients in the wind velocity field. This result has important implications for all workers dealing with simulation of geophysical data by fractal cascades. Finally, a brief numerical experiment is carried out to both demonstrate how this bias may be exploited to construct a model, and to test some of the analysis techniques presented on non-cascade based data. While not a particularly convincing simulator of turbulence, the model nevertheless displays some interesting turbulence-like characteristics.
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Vera, Epiphany. "Fractal modelling of residual in linear predictive coding of speech." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1999. http://www.collectionscanada.ca/obj/s4/f2/dsk1/tape8/PQDD_0006/MQ41642.pdf.

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Arfeen, Muhammad Asad. "Contributions to modelling of internet traffic by fractal renewal processes." Thesis, University of Canterbury. Department of Computer Science & Software Engineering, 2014. http://hdl.handle.net/10092/10194.

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The principle of parsimonious modelling of Internet traffic states that a minimal number of descriptors should be used for its characterization. Until early 1990s, the conventional Markovian models for voice traffic had been considered suitable and parsimonious for data traffic as well. Later with the discovery of strong correlations and increased burstiness in Internet traffic, various self-similar count models have been proposed. But, in fact, such models are strictly mono-fractal and applicable at coarse time scales, whereas Internet traffic modelling is about modelling traffic at fine and coarse time scales; modelling traffic which can be mono and multi-fractal; modelling traffic at interarrival time and count levels; modelling traffic at access and core tiers; and modelling all the three structural components of Internet traffic, that is, packets, flows and sessions. The philosophy of this thesis can be described as: “the renewal of renewal theory in Internet traffic modelling”. Renewal theory has a great potential in modelling statistical characteristics of Internet traffic belonging to individual users, access and core networks. In this thesis, we develop an Internet traffic modelling framework based on fractal renewal processes, that is, renewal processes with underlying distribution of interarrival times being heavy-tailed. The proposed renewal framework covers packets, flows and sessions as structural components of Internet traffic and is applicable for modelling the traffic at fine and coarse time scales. The properties of superposition of renewal processes can be used to model traffic in higher tiers of the Internet hierarchy. As the framework is based on renewal processes, therefore, Internet traffic can be modelled at both interarrival times and count levels.
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Yasrebi, Amir Bijan. "Determination of an ultimate pit limit utilising fractal modelling to optimise NPV." Thesis, University of Exeter, 2014. http://hdl.handle.net/10871/18449.

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The speed and complexity of globalisation and reduction of natural resources on the one hand, and interests of large multinational corporations on the other, necessitates proper management of mineral resources and consumption. The need for scientific research and application of new methodologies and approaches to maximise Net Present Value (NPV) within mining operations is essential. In some cases, drill core logging in the field may result in an inadequate level of information and subsequent poor diagnosis of geological phenomenon which may undermine the delineation or separation of mineralised zones. This is because the interpretation of individual loggers is subjective. However, modelling based on logging data is absolutely essential to determine the architecture of an orebody including ore distribution and geomechanical features. For instance, ore grades, density and RQD values are not included in conventional geological models whilst variations in a mineral deposit are an obvious and salient feature. Given the problems mentioned above, a series of new mathematical methods have been developed, based on fractal modelling, which provide a more objective approach. These have been established and tested in a case study of the Kahang Cu-Mo porphyry deposit, central Iran. Recognition of different types of mineralised zone in an ore deposit is important for mine planning. As a result, it is felt that the most important outcome of this thesis is the development of an innovative approach to the delineation of major mineralised (supergene and hypogene) zones from ‘barren’ host rock. This is based on subsurface data and the utilisation of the Concentration-Volume (C-V) fractal model, proposed by Afzal et al. (2011), to optimise a Cu-Mo block model for better determination of an ultimate pit limit. Drawing on this, new approaches, referred to Density–Volume (D–V) and RQD-Volume (RQD-V) fractal modelling, have been developed and used to delineate rock characteristics in terms of density and RQD within the Kahang deposit (Yasrebi et al., 2013b; Yasrebi et al., 2014). From the results of this modelling, the density and RQD populations of rock types from the studied deposit showed a relationship between density and rock quality based on RQD values, which can be used to predict final pit slope. Finally, the study introduces a Present Value-Volume (PV-V) fractal model in order to identify an accurate excavation orientation with respect to economic principals and ore grades of all determined voxels within the obtained ultimate pit limit in order to achieve an earlier pay-back period.
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Wohlberg, Brendt. "Fractal image compression and the self-affinity assumption : a stochastic signal modelling perspective." Doctoral thesis, University of Cape Town, 1996. http://hdl.handle.net/11427/9475.

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Bibliography: p. 208-225.
Fractal image compression is a comparatively new technique which has gained considerable attention in the popular technical press, and more recently in the research literature. The most significant advantages claimed are high reconstruction quality at low coding rates, rapid decoding, and "resolution independence" in the sense that an encoded image may be decoded at a higher resolution than the original. While many of the claims published in the popular technical press are clearly extravagant, it appears from the rapidly growing body of published research that fractal image compression is capable of performance comparable with that of other techniques enjoying the benefit of a considerably more robust theoretical foundation. . So called because of the similarities between the form of image representation and a mechanism widely used in generating deterministic fractal images, fractal compression represents an image by the parameters of a set of affine transforms on image blocks under which the image is approximately invariant. Although the conditions imposed on these transforms may be shown to be sufficient to guarantee that an approximation of the original image can be reconstructed, there is no obvious theoretical reason to expect this to represent an efficient representation for image coding purposes. The usual analogy with vector quantisation, in which each image is considered to be represented in terms of code vectors extracted from the image itself is instructive, but transforms the fundamental problem into one of understanding why this construction results in an efficient codebook. The signal property required for such a codebook to be effective, termed "self-affinity", is poorly understood. A stochastic signal model based examination of this property is the primary contribution of this dissertation. The most significant findings (subject to some important restrictions} are that "self-affinity" is not a natural consequence of common statistical assumptions but requires particular conditions which are inadequately characterised by second order statistics, and that "natural" images are only marginally "self-affine", to the extent that fractal image compression is effective, but not more so than comparable standard vector quantisation techniques.
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Cottet, Arnaud J. "Modelling of ceramic matrix composite microstructure using a 2-D fractal spatial particle distribution." Diss., Georgia Institute of Technology, 2003. http://hdl.handle.net/1853/12928.

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McClean, Colin John. "The scale-free and scale-bound properties of land surfaces : fractal analysis and specific geomorphometry from digital terrain models." Thesis, Durham University, 1990. http://etheses.dur.ac.uk/5999/.

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The scale-bound view of landsurfaces, being an assemblage of certain landforms, occurring within limited scale ranges, has been challenged by the scale-free characteristics of fractal geometry. This thesis assesses the fractal model by examining the irregularity of landsurface form, for the self-affine behaviour present in fractional Brownian surfaces. Different methods for detecting self-affine behaviour in surfaces are considered and of these the variogram technique is shown to be the most effective. It produces the best results of two methods tested on simulated surfaces, with known fractal properties. The algorithm used has been adapted to consider log (altitude variance) over a sample of log (distances) for: complete surfaces; subareas within surfaces; separate directions within surfaces. Twenty seven digital elevation models of landsurfaces arc re-examined for self- affine behaviour. The variogram results for complete surfaces show that none of these are self-affine over the scale range considered. This is because of dominant slope lengths and regular valley, spacing within areas. For similar reasons subarea analysis produces the non-fractal behaviour of markedly different variograms for separate subareas. The linearity of landforms in many areas, is detected by the variograms for separate directions. This indicates that the roughness of landsurfaces is anisotropic, unlike that of fractal surfaces. Because of difficulties in extracting particular landforms from their landsurfaces, no clear links between fractal behaviour, and landform size distribution could be established. A comparative study shows the geomorphometric parameters of fractal surfaces to vary with fractal dimension, while the geomorphometry of landsurfaces varies with the landforms present. Fractal dimensions estimated from landsurfaces do not correlate with geomorphometric parameters. From the results of this study, real landsurfaces would not appear to be scale- free. Therefore, a scale-bound approach towards landsurfaces would seem to be more appropriate to geomorphology than the fractal alternative.
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Sithebe, Nomcebo Princess. "Flocculation modelling of differential sedimentation based on fundamental physics of settling particles and fractal theory." Diss., University of Pretoria, 2013. http://hdl.handle.net/2263/40841.

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Sedimentation is a fundamental operation in wastewater treatment works. A rational design of sedimentation tanks is currently achieved by plotting iso-percentile (iso-percentage) concentration removal profiles from flocculent settling data. A major drawback of the graphical iso-percentage method is that the iso-percentile lines are often manually interpolated and are mere hand drawn estimations. This is because the settling behaviour of sludge particles is highly non-linear. The manual analytical process is therefore very tedious, inaccurate and subjective. Hence, an optimised design of sedimentation tanks is necessary in order to eliminate the errors incurred during data analysis. In this study, a mechanistic iso-percentile flocculent model (referred to as the velocity flocculation model) is developed to simulate the behaviour of flocculating colloidal particles in turbid water. This model is based on the physical meanings of flocculent settling particles and on fractal theory. It is formulated to produce automated iso-percentile curves which are fundamental in the design of sedimentation tanks. The iso-percentile model was vertically integrated into a velocity model to produce a model expressing the velocity of particles as a function of removal rate. The velocity model has an obvious advantage over the iso-percentile model in that it is easy to contextualize. It can be reverted back to the iso-percentile trajectory analysis eliminating the need for extensive data interpolation and may in future eliminate the need for settling column analysis altogether. In the current study, the integrated velocity form is used to predict instantaneous flocculent settling velocity of fine suspended particles under near quiescent conditions. This is vital since it is difficult to obtain velocity values in-situ or directly from sedimentation tanks. Model validity and competency was tested by a direct comparison with existing literature models, such as Ozer’s model and Ramatsoma and Chirwa’s model. Model comparison was based on the goodness of fit, the least sum of square errors and mathematical consistency with known flocculent settling behaviour. The newly developed iso-percentile model achieved a more accurate simulation of physical experimental data, did not violate any of the mathematical constraints and yielded lower sum of square errors than originally achieved by Ozer and Ramatsoma and Chirwa. Notably, the proposed velocity model offers a distinctive advantage over conventional interpolated-iso-percentile based models which are prone to numerical errors during interpolation. Its performance (velocity model) was compared against Je and Chang’s velocity model. Higher velocity values were observed for the new model than for Je and Chang’s model implying that empirically based models would tend to under-predict the velocity values. The model developed in this study brings us one step closer to achieving full automation of the settling tank and clarifier design.
Dissertation (MEng)--University of Pretoria, 2013.
gm2014
Chemical Engineering
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Books on the topic "Fractal modelling"

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Kaandorp, Jaap A. Fractal Modelling. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6.

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Fractal modelling: Growth and form in biology. Berlin: Springer-Verlag, 1994.

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1959-, Castillo Oscar, ed. Modelling, simulation and control of non-linear dynamical systems: An intelligent approach using soft computing and fractal theory. London: Taylor & Francis, 2002.

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Kaandorp, Jaap A. Modelling growth forms of biological objects using fractals. Meppel, the Netherlands: Printed by Krips Repro, 1992.

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Chaos and order in the capital markets: A new view of cycles, prices, and market volatility. New York: Wiley, 1991.

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Chaos and order in the capital markets: A new view of cycles, prices, and market volatility. 2nd ed. New York: Wiley, 1996.

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Kaandorp, Jaap A. Fractal Modelling: Growth and Form in Biology. Springer, 2012.

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Wei, Wei, Liehui Zhang, and Jianchao Cai. Modelling of Flow and Transport in Fractal Porous Media. Elsevier, 2020.

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Modelling of Flow and Transport in Fractal Porous Media. Elsevier, 2021. http://dx.doi.org/10.1016/c2018-0-02631-6.

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Melin, Patricia, and Oscar Castillo. Modelling, Simulation and Control of Non-linear Dynamical Systems: An Intelligent Approach Using Soft Computing and Fractal Theory (Numerical Insights, 2). CRC, 2001.

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Book chapters on the topic "Fractal modelling"

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Kaandorp, Jaap A. "Introduction." In Fractal Modelling, 1–6. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_1.

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Kaandorp, Jaap A. "Methods for Modelling Biological Objects." In Fractal Modelling, 7–53. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_2.

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Kaandorp, Jaap A. "2D Models of Growth Forms." In Fractal Modelling, 55–101. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_3.

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Kaandorp, Jaap A. "A Comparison of Forms." In Fractal Modelling, 103–27. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_4.

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Kaandorp, Jaap A. "3D Models of Growth Forms." In Fractal Modelling, 129–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_5.

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Kaandorp, Jaap A. "Final Conclusions." In Fractal Modelling, 189–95. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/978-3-642-57922-6_6.

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Appleby, S. "Fractal Populations." In Modelling Future Telecommunications Systems, 22–44. Boston, MA: Springer US, 1996. http://dx.doi.org/10.1007/978-1-4615-2049-8_3.

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Walters, Glenn D. "The Fractal Nature of Lifestyles." In Modelling the Criminal Lifestyle, 53–74. Cham: Springer International Publishing, 2017. http://dx.doi.org/10.1007/978-3-319-57771-5_3.

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Pardo-Igúzquiza, Eulogio, Juan José Durán, Pedro Robledo, Carolina Guardiola, Juan Antonio Luque, and Sergio Martos. "Fractal Modelling of Karst Conduits." In Lecture Notes in Earth System Sciences, 217–20. Berlin, Heidelberg: Springer Berlin Heidelberg, 2013. http://dx.doi.org/10.1007/978-3-642-32408-6_50.

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Trethewey, K. R., and P. R. Roberge. "Towards Improved Quantitative Characterization of Corroding Surfaces Using Fractal Models." In Modelling Aqueous Corrosion, 443–63. Dordrecht: Springer Netherlands, 1994. http://dx.doi.org/10.1007/978-94-011-1176-8_21.

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Conference papers on the topic "Fractal modelling"

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Coloşi, Tiberiu, and Steliana Codreanu. "A new method of modelling and numerical simulation of nonlinear dynamical systems." In Chaotic, fractal, and nonlinear signal processing. AIP, 1996. http://dx.doi.org/10.1063/1.51011.

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Burkovets, D. M., O. P. Maksimyak, and K. I. Nestina. "Modelling of light scattering by fractal clusters." In SPIE Proceedings, edited by Malgorzata Kujawinska and Oleg V. Angelsky. SPIE, 2008. http://dx.doi.org/10.1117/12.797011.

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Yun, Chen, and Gao Ruidong. "A New Fractal Hyperspectral Image Compression Algorithm." In 2nd International Conference on Modelling, Identification and Control. Paris, France: Atlantis Press, 2015. http://dx.doi.org/10.2991/mic-15.2015.32.

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Tafti, Pouya Dehghani, Ricard Delgado-Gonzalo, Aurelien F. Stalder, and Michael Unser. "Fractal modelling and analysis of flow-field images." In 2010 7th IEEE International Symposium on Biomedical Imaging: From Nano to Macro. IEEE, 2010. http://dx.doi.org/10.1109/isbi.2010.5490416.

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Potapov, A. A., E. N. Matveev, V. A. Potapov, and A. V. Laktyunkin. "Mathematical and physics modelling of fractal antennas and fractal frequency selective surfaces and volumes for the fractal radio systems." In 2nd European Conference on Antennas and Propagation (EuCAP 2007). Institution of Engineering and Technology, 2007. http://dx.doi.org/10.1049/ic.2007.1192.

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Bagmanov, Valeriy H., Sergey V. Dyblenko, Klaus Janschek, Anton E. Kiselev, Albert H. Sultanov, and Valeriy V. Tchernykh. "Fractal approach to mathematical modelling of space observation data." In SPIE Proceedings, edited by Vladimir A. Andreev, Vladimir A. Burdin, Oleg G. Morozov, and Albert H. Sultanov. SPIE, 2008. http://dx.doi.org/10.1117/12.801495.

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"EEG/SEEG SIGNAL MODELLING USING FREQUENCY AND FRACTAL ANALYSIS." In International Conference on Bio-inspired Systems and Signal Processing. SciTePress - Science and and Technology Publications, 2012. http://dx.doi.org/10.5220/0003780302490253.

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Kinsner, Witold, and Epiphany Vera. "Fractal modelling of residues in linear predictive coding of speech." In 2009 8th IEEE International Conference on Cognitive Informatics (ICCI). IEEE, 2009. http://dx.doi.org/10.1109/coginf.2009.5250762.

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Guo, Y. "Efficient modelling of novel fractal loaded electromagnetic band gap arrays." In Fifth IEE International Conference on Computation in Electromagnetics - CEM 2004. IEE, 2004. http://dx.doi.org/10.1049/cp:20040484.

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Maric, A., G. Radosavljevic, M. Zivanov, Lj Zivanov, G. Stojanovic, M. Mayer, A. Jachimowicz, and F. Keplinger. "Modelling and Characterisation of Fractal Based RF Inductors on Silicon Substrate." In 2008 International Conference on Advanced Semiconductor Devices and Microsystems (ASDAM). IEEE, 2008. http://dx.doi.org/10.1109/asdam.2008.4743314.

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