Estimation of Fractal Dimension and Statistical Tools for Surface Evaluation

2014 ◽  
pp. 43-53
Author(s):  
Vlastimil Hotař ◽  
Petr Salač ◽  
Ondřej Matúšek
Keyword(s):  
Fractal Dimension ◽  
Statistical Tools

scholarly journals Surface Evaluation by Estimation of Fractal Dimension and Statistical Tools

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Vlastimil Hotar ◽  
Petr Salac
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Complex Surface ◽  
Complete Analysis ◽  
Complex Data ◽  
Statistical Tools ◽  
Statistical Tool ◽  
Industrial Practice ◽  
Structured Surfaces ◽  
Analyse Data

Structured and complex data can be found in many applications in research and development, and also in industrial practice. We developed a methodology for describing the structured data complexity and applied it in development and industrial practice. The methodology uses fractal dimension together with statistical tools and with software modification is able to analyse data in a form of sequence (signals, surface roughness), 2D images, and dividing lines. The methodology had not been tested for a relatively large collection of data. For this reason, samples with structured surfaces produced with different technologies and properties were measured and evaluated with many types of parameters. The paper intends to analyse data measured by a surface roughness tester. The methodology shown compares standard and nonstandard parameters, searches the optimal parameters for a complete analysis, and specifies the sensitivity to directionality of samples for these types of surfaces. The text presents application of fractal geometry (fractal dimension) for complex surface analysis in combination with standard roughness parameters (statistical tool).

Use of fractals to describe microstructures of porous thick-film platinum electrodes

1992 ◽  
Vol 50 (1) ◽  
pp. 314-315
Author(s):  
Steven D. Toteda
Keyword(s):  
Fractal Dimension ◽  
Power Plants ◽  
Electrical Response ◽  
Cubic Phase ◽  
Platinum Electrodes ◽  
Fine Grained ◽  
Impedance Response ◽  
Platinum Particles ◽  
Energy Surfaces ◽  
Highly Porous

Zirconia oxygen sensors, in such applications as power plants and automobiles, generally utilize platinum electrodes for the catalytic reaction of dissociating O2 at the surface. The microstructure of the platinum electrode defines the resulting electrical response. The electrode must be porous enough to allow the oxygen to reach the zirconia surface while still remaining electrically continuous. At low sintering temperatures, the platinum is highly porous and fine grained. The platinum particles sinter together as the firing temperatures are increased. As the sintering temperatures are raised even further, the surface of the platinum begins to facet with lower energy surfaces. These microstructural changes can be seen in Figures 1 and 2, but the goal of the work is to characterize the microstructure by its fractal dimension and then relate the fractal dimension to the electrical response. The sensors were fabricated from zirconia powder stabilized in the cubic phase with 8 mol% percent yttria. Each substrate was sintered for 14 hours at 1200°C. The resulting zirconia pellets, 13mm in diameter and 2mm in thickness, were roughly 97 to 98 percent of theoretical density. The Engelhard #6082 platinum paste was applied to the zirconia disks after they were mechanically polished ( diamond). The electrodes were then sintered at temperatures ranging from 600°C to 1000°C. Each sensor was tested to determine the impedance response from 1Hz to 5,000Hz. These frequencies correspond to the electrode at the test temperature of 600°C.

Comment on "On the fractal dimension of stream networks"

1990 ◽  
Vol 26 (9) ◽  
pp. 2243-2244 ◽  
Author(s):  
David G. Tarboton
Keyword(s):  
Fractal Dimension ◽  
Stream Networks

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.

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

THE BALANCE OF PROBABILITY: STATISTICS AND THE DIACHRONIC STUDY OF ANCIENT HEBREW

2017 ◽  
Vol 25 (2) ◽  
pp. 927-960
Author(s):  
Jarod Jacobs
Keyword(s):  
Dead Sea Scrolls ◽  
Dead Sea ◽  
Biblical Hebrew ◽  
Large Datasets ◽  
Dual Function ◽  
Statistical Tools ◽  
Masoretic Text ◽  
Linguistic Research ◽  
Recent Debate ◽  
Diachronic Study

In this article, I discuss three statistical tools that have proven pivotal in linguistic research, particularly those studies that seek to evaluate large datasets. These tools are the Gaussian Curve, significance tests, and hierarchical clustering. I present a brief description of these tools and their general uses. Then, I apply them to an analysis of the variations between the “biblical” DSS and our other witnesses, focusing upon variations involving particles. Finally, I engage the recent debate surrounding the diachronic study of Biblical Hebrew. This article serves a dual function. First, it presents statistical tools that are useful for many linguistic studies. Second, it develops an analysis of the he-locale, as it is used in the “biblical” Dead Sea Scrolls, Masoretic Text, and Samaritan Pentateuch. Through that analysis, this article highlights the value of inferential statistical tools as we attempt to better understand the Hebrew of our ancient witnesses.

Quantitative Image Analysis of Fractal-like Thin Films of Organic Semiconductors

2018 ◽  
Author(s):  
Weikun Zhu ◽  
Erfan Mohammadi ◽  
Ying Diao
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Image Analysis ◽  
Fractal Dimension ◽  
Organic Semiconductors ◽  
Film Growth ◽  
Electronic Device ◽  
Significant Control ◽  
Semiconductor Thin Films ◽  
Two Parameters

Morphology modulation offers significant control over organic electronic device performance. However, morphology quantification has been rarely carried out via image analysis. In this work, we designed a MATLAB program to evaluate two key parameters describing morphology of small molecule semiconductor thin films: fractal dimension and film coverage. We then employ this program in a case study of meniscus-guided coating of 2,7-dioctyl[1]benzothieno[3,2-b][1]benzothiophene (C<sub>8</sub>-BTBT) under various conditions to analyze a diverse and complex morphology set. The evolution of morphology in terms of fractal dimension and film coverage was studied as a function of coating speed. We discovered that combined fractal dimension and film coverage can quantitatively capture the key characteristics of C<sub>8</sub>-BTBT thin film morphology; change of these two parameters further inform morphology transition. Furthermore, fractal dimension could potentially shed light on thin film growth mechanisms.

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