scholarly journals Intergranular area microalloyed aluminium-silicate ceramics fractal analysis

2013 ◽  
Vol 45 (1) ◽  
pp. 117-126 ◽  
Author(s):  
J. Purenovic ◽  
V.V. Mitic ◽  
Lj. Kocic ◽  
V. Pavlovic ◽  
M. Randjelovic ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Electrical Properties ◽  
Fractal Analysis ◽  
Fractal Nature ◽  
Place Making ◽  
Richardson Method ◽  
Micro Morphology ◽  
Solid System ◽  
Aluminium Silicate

Porous aluminium-silicate ceramics, modified by alloying with magnesium and microalloying with alluminium belongs to a group of advanced multifunctional ceramics materials. This multiphase solid-solid system has predominantly amorphous microstructure and micro morphology. Intergranular and interphase areas are very complex, because they represent areas, where numbered processes and interactions take place, making new boundaries and regions with fractal nature. Fractal analysis of intergranular microstructure has included determination of ceramic grain fractal dimension by using Richardson method. Considering the fractal nature of intergranular contacts, it is possible to establish correlation between material electrical properties and fractal analysis, as a tool for future correlation with microstructure characterization.

Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of study: Charak area,IRAN)

2005 ◽  
Vol 1 (1) ◽  
pp. 21-24
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cfor the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area

scholarly journals Electrical properties and microstructure fractal analysis of magnesium-modified aluminium-silicate ceramics

2011 ◽  
Vol 43 (2) ◽  
pp. 193-204 ◽  
Author(s):  
J. Purenovic ◽  
V.V. Mitic ◽  
Lj. Kocic ◽  
V.B. Pavlovic ◽  
V. Paunovic ◽  
...  
Keyword(s):  
Fractal Analysis ◽  
Sintering Temperature ◽  
Electrical Characterization ◽  
Porous Ceramics ◽  
Before And After ◽  
High Degree ◽  
Highly Porous ◽  
Aluminium Silicate

The addition of Mg2(NO)3 and some active additives, composed of Al salts, to the mixtures of kaolinite and bentonite can provide clay compositions which, after sintering at high temperatures, produce very porous ceramics with microcrystalline and amorphous regions and highly developed metalized surfaces (mainly with magnesium surplus). Characterization of sintered samples was done before and after treatment in ?synthetic water?, i.e. in aqueous solution of arsenic-salt. Microstructure investigations have revealed non-uniform and highly porous structure with broad distribution of grain size, specifically shaped grains and high degree of agglomeration. Electrical characterization was estimated by determining dielectric constant and electrical resistivity in function of active additives amount and sintering temperature. Fractal analysis has included determination of grain contour fractal dimension.

scholarly journals Relation between geometry of fracture surfaces and impact work of wood composite materials

2006 ◽  
Vol 54 (2) ◽  
pp. 91-96
Author(s):  
Eva Přemyslovská ◽  
Petr Koňas
Keyword(s):  
Fractal Dimension ◽  
Composite Materials ◽  
Fractal Analysis ◽  
Wood Composite ◽  
Fracture Surfaces ◽  
Box Counting ◽  
Counting Methods ◽  
Richardson Method ◽  
Proportional Relationship

The aim of this work is description of geometry of fracture surfaces of wood composite materials (cement-bonded particleboard, gypsum-bonded fibreboard and wood particleboard) using fractal analysis and exploration relation between fractal dimension and impact work. Fractal dimension determinated by filtration, volumetric and robust Box-Counting methods and Richardson method is different considering type of material and method. Proportional relationship between fractal dimension (computed by robust BC method) and impact work of mentioned materials was found in other cases non-proportional relationships were founded.

scholarly journals FRACTAL ANALYSIS OF MODELS OF TEXTS OF DIFFERENT STYLES SUBMITTED INTEGER EQUIDISTANT SEQUENCES NUMBER OF LETTERS IN WORDS

2021 ◽  
Vol 295 (2) ◽  
pp. 26-34
Author(s):  
ROMA KAMINSKYY ◽  
◽  
NATALIYA SHAKHOVSKA ◽  
BOHDAN KHUDOBA ◽  
◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Point Of View ◽  
Mathematical Representation ◽  
Unknown Parameters ◽  
Artistic Style ◽  
Spoken Text ◽  
Cumulative Summation ◽  
The Relationship

This paper presents the results of fractal analysis of models of texts of different styles. Integer numerical sequences, the elements of which are the number of letters in the words of the text, are used as models. An algorithm for calculating the exact value of the fractal dimension is presented, which provided the determination of the exact value of the Hirst index. In addition, the value of the power dependence constant R / S is calculated. The obtained indicators in the aspect of fractality fully describe the objects of research. This method is in fact a logical implementation of the known procedures of fractal analysis and its advantage is that it provides a rigorous mathematical representation of the values of the fractal dimension, the Hirst index and the constant in relation to the indicators of variation. The essence of his presentation is, first of all, as a warning to researchers against misinterpretation of the relationship R / S, because many researchers ignore the existence of a constant for this relationship. Indeed, this relation is a function with two unknown parameters and cannot be directly determined. With regard to the fractal dimension, we can point out that the least important is the conversational style, and the most – poetic. In other words, the model of colloquial text is the smallest part of its environment, poetic – the largest. From the point of view of Hirst’s index, the model of the spoken text contains a trend, while the model of the poem has a character closer to the random one. The largest scope of the cumulative series has a model of spoken text, and the smallest – a model of artistic style of the text. Since the cumulative series is a sequential (cumulative) summation of the sequence of deviations of elements from its arithmetic mean, its scope will depend on the presence of groups of elements of the sequence with very large deviations. Artistic style has the least significance of scope.

The Percolation Phenomenon and Fractal Dimension of Natural Silicates

2015 ◽  
Vol 365 ◽  
pp. 128-135
Author(s):  
Maria A. Vasilyeva ◽  
Yuri A. Gusev ◽  
Valery G. Shtyrlin ◽  
Yury N. Osin
Keyword(s):  
Fractal Dimension ◽  
Electron Micrographs ◽  
Fractal Analysis ◽  
Dielectric Spectroscopy ◽  
Fractal Dimensions ◽  
Adsorbed Water ◽  
Ambient Air ◽  
Silicate Structure ◽  
Percolation Phenomenon

Many physical effects, such asdcconductivity and percolation, depend on the morphology of the silicate structure and its relationship to adsorbed water. These effects play an important role in numerous technological applications, in geology, oil-extracting industry, and other practical fields. In this study, all the samples: natural montmorillonite, kaolinite, and сlinoptilolite with different exchangeable cations in their structures, – were stored in ambient air humidity. The investigation was carried by using two separate techniques, namely Dielectric Spectroscopy and a fractal analysis of electron micrographs. The aims of this work were to analyze the complex relaxation behavior of the relaxation process in temperature range –70°C ÷ +70°C and to determine the fractal dimensions of silicates from the dielectric response at percolation. Dielectric measurements in the frequency range of 1 Hz ÷ 1 MHz were performed using a BDS 80 Dielectric Spectrometer based on an Alpha Impedance Analyzer (Novocontrol). The micrographs were analyzed using a special Matlab based program. The analysis of aspects of the dielectric relaxation spectra related to percolation was used for the determination of the numerical characteristics of geometric heterogeneity of natural silicates. The percolation temperatures of the studied samples were determined. The percolation phenomenon in the silicates is related to the transfer of the electric excitation within the developed network of open pores due to the migration of protons and ions along the surface of connected pores on the outer surfaces of the granules. The analysis of these processes allows one to extract the fractal dimensions associated with the migration of charge carriers within the porous medium. Fractal dimensions of the silicates calculated in two ways: from dielectric spectroscopy study and from fractal analysis of the micrographs, – are in good agreement with each other. It was demonstrated that conventional method of the spatial fractal dimension determination using fractal analysis of electron micrographs leads to overestimation in the case of spatial fractal bounded by a surface fractal. The dielectric spectroscopy method is free from such overestimation.

scholarly journals Potential of Fractal Analysis of Earthquakes through Wavelet Analysis and Determination of b Value as an Aftershock Precursor: A Case Study Using Earthquake Data between 2003 and 2011 in Turkey

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
V. Srivardhan ◽  
Uppala Srinu
Keyword(s):  
Fractal Dimension ◽  
Wavelet Analysis ◽  
Fractal Analysis ◽  
B Value ◽  
High Accuracy ◽  
Elegant Method ◽  
Stress Accumulation ◽  
Earthquake Data

The b value of earthquakes is very useful to forecast the occurrence of aftershocks in a given region. The b value characterizes the release of energy due to stress accumulation in the rocks through an earthquake and is a direct indicator for the prediction of aftershocks in the region. Wavelet based fractal analysis is used in this study to determine the b value by calculating the fractal dimension. This method guarantees high accuracy results through a limited dataset. The objective of this work was to demonstrate an elegant method for the determination of the b value after an earthquake and predict the occurrence of aftershocks with high accuracy. Repeated earthquakes were analyzed between 2003 and 2011 in Turkey and the b value was found for these earthquakes. The results gave an indication that the b value of the mainshock and its aftershocks are different and aftershocks occur in the region when the b value of the mainshock deviates significantly from 0.5, and aftershocks keep occurring until the b value of the earthquake approaches close to 0.5 for this region.

scholarly journals Optimal Density Determination of Bouguer Anomaly Using Fractal Analysis (Case of Study: Charak Area, Iran)

2013 ◽  
Vol 2 (7) ◽  
pp. 80-85
Author(s):  
Hamid Reza Samadi
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Host Rock ◽  
Bouguer Anomaly ◽  
Research Area ◽  
Density Difference ◽  
Optimal Density

In exploration geophysics the main and initial aim is to determine density of under-research goals which have certain density difference with the host rock. Therefore, we state a method in this paper to determine the density of bouguer plate, the so-called variogram method based on fractal geometry. This method is based on minimizing surface roughness of bouguer anomaly. The fractal dimension of surface has been used as surface roughness of bouguer anomaly. Using this method, the optimal density of Charak area insouth of Hormozgan province can be determined which is 2/7 g/cm^3for the under-research area. This determined density has been used to correct and investigate its results about the isostasy of the studied area and results well-coincided with the geology of the area and dug exploratory holes in the text area.

Heterogeneity of Cerebral Blood Flow: a Fractal Approach

2000 ◽  
Vol 39 (02) ◽  
pp. 37-42 ◽  
Author(s):  
P. Hartikainen ◽  
J. T. Kuikka
Keyword(s):  
Blood Flow ◽  
Cerebral Blood Flow ◽  
Fractal Dimension ◽  
Frontal Lobe ◽  
Fractal Analysis ◽  
Relative Dispersion ◽  
Emission Computed Tomography ◽  
Brain Blood Flow ◽  
Healthy Controls ◽  
Fractal Approach

Summary Aim: We demonstrate the heterogeneity of regional cerebral blood flow using a fractal approach and singlephoton emission computed tomography (SPECT). Method: Tc-99m-labelled ethylcysteine dimer was injected intravenously in 10 healthy controls and in 10 patients with dementia of frontal lobe type. The head was imaged with a gamma camera and transaxial, sagittal and coronal slices were reconstructed. Two hundred fifty-six symmetrical regions of interest (ROIs) were drawn onto each hemisphere of functioning brain matter. Fractal analysis was used to examine the spatial heterogeneity of blood flow as a function of the number of ROIs. Results: Relative dispersion (= coefficient of variation of the regional flows) was fractal-like in healthy subjects and could be characterized by a fractal dimension of 1.17 ± 0.05 (mean ± SD) for the left hemisphere and 1.15 ± 0.04 for the right hemisphere, respectively. The fractal dimension of 1.0 reflects completely homogeneous blood flow and 1.5 indicates a random blood flow distribution. Patients with dementia of frontal lobe type had a significantly lower fractal dimension of 1.04 ± 0.03 than in healthy controls. Conclusion: Within the limits of spatial resolution of SPECT, the heterogeneity of brain blood flow is well characterized by a fractal dimension. Fractal analysis may help brain scientists to assess age-, sex- and laterality-related anatomic and physiological changes of brain blood flow and possibly to improve precision of diagnostic information available for patient care.

Structural Conductivity of Carbon Nanotubes

2008 ◽  
Vol 59 (10) ◽  
pp. 1169-1171 ◽  
Author(s):  
Zoltan Borsos ◽  
Viorel-Puiu Paun ◽  
Irinel Casian Botez ◽  
Cristina-Maria Stoica ◽  
Petrica Vizureanu ◽  
...  
Keyword(s):  
Carbon Nanotubes ◽  
Fractal Dimension ◽  
Electrical Properties ◽  
Transport Properties ◽  
Structural Form ◽  
Structural Symmetry

In this paper, the explicit connection between the high structural symmetry of the carbon nanotubes and the electrical properties is studied. An interesting path effect on the transport properties will be proved. For a bidimensional lattice, the conductivity sx depends on the structural form, which determines the shape of electron path, respectively it is direct proportional to the fractal dimension of this path.

scholarly journals Fractal Dimension and Retinal Pathology: A Meta-Analysis

2021 ◽  
Vol 11 (5) ◽  
pp. 2376
Author(s):  
Sam Yu ◽  
Vasudevan Lakshminarayanan
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Meta Analysis ◽  
Scientific Evidence ◽  
Retinal Disease ◽  
Clinical Value ◽  
Disease Category ◽  
Normal Individuals ◽  
Retinal Pathology ◽  
Meta Analyses

Due to the fractal nature of retinal blood vessels, the retinal fractal dimension is a natural parameter for researchers to explore and has garnered interest as a potential diagnostic tool. This review aims to summarize the current scientific evidence regarding the relationship between fractal dimension and retinal pathology and thus assess the clinical value of retinal fractal dimension. Following the PRISMA guidelines, a literature search for research articles was conducted in several internet databases (EMBASE, MEDLINE, Web of Science, Scopus). This led to a result of 28 studies included in the final review, which were analyzed via meta-analysis to determine whether the fractal dimension changes significantly in retinal disease versus normal individuals. From the meta-analysis, summary effect sizes and 95% confidence intervals were derived for each disease category. The results for diabetic retinopathy and myopia suggest decreased retinal fractal dimension for those pathologies with the association for other diseases such as diabetes mellitus, hypertension, and glaucoma remaining uncertain. Due to heterogeneity in imaging/fractal analysis setups used between studies, it is recommended that standardized retinal fractal analysis procedures be implemented in order to facilitate future meta-analyses.

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