Explicitly defined fractal interpolation functions with variable parameters

Serpa, Cristina; Buescu, Jorge

doi:10.1016/j.chaos.2015.01.023

Cited by 35 publications

(22 citation statements)

References 20 publications

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“…The fractal analysis of real images was performed by using the technique based on a new affine fractal regression model. This process exploits certain mathematical formulations [2][3][4] designated for obtaining the coefficients of the equations system that best fit the data. The modeled system is:…”

Section: Mathematical Fractal Analysis Techniquementioning

confidence: 99%

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Fractal Nature of Advanced Ni-Based Superalloys Solidified on Board the International Space Station

et al. 2021

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Materials science is highly significant in space program investigation, energy production and others. Therefore, designing, improving and predicting advanced material properties is a crucial necessity. The high temperature creep and corrosion resistance of Ni-based superalloys makes them important materials for turbine blades in aircraft engines and land-based power plants. The investment casting process of turbine blades is costly and time consuming, which makes process simulations a necessity. These simulations require fundamental models for the microstructure formation. In this paper, we present advanced analytical techniques in describing the microstructures obtained experimentally and analyzed on different sample’s cross-sectional images. The samples have been processed on board the International Space Station using the MSL-EML device based on electromagnetic levitation principles. We applied several aspects of fractal analysis and obtained important results regarding fractals and Hausdorff dimensions related to the surface and structural characteristics of CMSX-10 samples. Using scanning electron microscopy (SEM), Zeiss LEO 1550, we analyzed the microstructure of samples solidified in space and successfully performed the fractal reconstruction of the sample’s morphology. We extended the fractal analysis on the microscopic images based on samples solidified on earth and established new frontiers on the advanced structures prediction.

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Section: Mathematical Fractal Analysis Techniquementioning

confidence: 99%

“…In fact, it is proved [4] that such functions have a mathematical fractal structure, meaning that the plot of their graph is a fractal curve. Theoretical mathematical properties and explicit solutions are provided [2,3]. This model is originated by the system constructed by [5].…”

Section: Mathematical Fractal Analysis Techniquementioning

confidence: 99%

Fractal Nature of Advanced Ni-Based Superalloys Solidified on Board the International Space Station

et al. 2021

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“…and they are often too irregular to have any smooth differentiable structure defined on them, which results in delivering the methods and techniques of ordinary calculus powerless and inapplicable. Some approaches have been developed to deal with this inapplicability by means of fractional derivatives [6,10,21,23,24,34,38,42], fractional spaces [1,7,20,35], harmonic analysis [2,5,8,22,25,37,39], and measure theory, non-standard methods, and stochastic process [3, 29-31, 36, 40]. Yet, there has still been a gap in the literature on how to develop an appropriate calculus mainly related to the disconnected fractal subsets of R .…”

Section: Introductionmentioning

confidence: 99%

General characteristics of a fractal Sturm–Liouville problem

Cetinkaya¹,

Golmankhaneh²

2021

Turk J Math

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In this paper, we consider a regular fractal Sturm-Liouville boundary value problem. We prove the selfadjointness of the differential operator which is generated by the F α -derivative introduced in [32]. We obtained the F αanalogue of Liouville's theorem, and we show some properties of eigenvalues and eigenfunctions. We present examples to demonstrate the efficiency and applicability of the obtained results. The findings of this paper can be regarded as a contribution to an emerging field.

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“…Since wind speed fluctuation has very stochastic and unpredictably in nature, it is good to apply chaos theory based on fractal dimensions [13]. By this methodology the wind speed was modelled by the Weierstrass function with a fractal graph [14].…”

Section: Introductionmentioning

confidence: 99%

Estimation of fractal representation of wind speed fluctuation by artificial neural network with different training algorothms

Petković

Nikolić

Mitić

et al. 2017

Flow Measurement and Instrumentation

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Cite this article as: Dalibor Petković, Vlastimir Nikolić, Vojislav V. Mitić and Ljubiša Kocić, Estimation of fractal representation of wind speed fluctuation by artificial neural network with different training algorothms, Flow Measurement and Instrumentation, http://dx. AbstractSince the wind speed fluctuation could cause large instability in wind energy systems it is crucial to develop a method for precise estimation of the wind speed fluctuation. Fractal interpolation of the wind speed could be used to improve the accuracy of the estimation of the wind speed fluctuation. Based on the self-similarity feature, the fractal interpolation could be established from internal to external interval. In this article fractal interpolation was used to improve the wind speed fluctuation estimation by soft computing methods. Artificial neural network (ANN) with different training algorithms were used in order to estimate the wind speed fluctuation based on the fractal interpolation. Highlights The fluctuation of wind speed affects energy conversion of wind energy systems.  Fractal characteristics of the wind speed series were analyzed.  An improved fractal interpolation to predict the wind speed series.  Prediction of the wind speed fractal representation was established.

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Explicitly defined fractal interpolation functions with variable parameters

Cited by 35 publications

References 20 publications

Fractal Nature of Advanced Ni-Based Superalloys Solidified on Board the International Space Station

Fractal Nature of Advanced Ni-Based Superalloys Solidified on Board the International Space Station

General characteristics of a fractal Sturm–Liouville problem

Estimation of fractal representation of wind speed fluctuation by artificial neural network with different training algorothms

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