Multifractal analysis of ultrasonically machined surfaces of cylindrical quartz crystals: the effect of the abrasive grits

2021 ◽  
Author(s):  
Ştefan Ţălu ◽  
Pedro Luiz Guzzo ◽  
Bandar Astinchap ◽  
Hamta Ghanbaripour
Keyword(s):  
Surface Topography ◽  
Multifractal Spectrum ◽  
Grit Size ◽  
Mean Deviation ◽  
Quartz Crystals ◽  
Box Counting ◽  
Cutting Rate ◽  
Measured Profile ◽  
Box Counting Method ◽  
Machined Surfaces

Abstract Since synthetic quartz is essential to produce 3-D resonators for numerous applications in precision electronics, in this work the surface topography of cylindrical quartz bars is investigated using the multifractal technique. The cylindrical bars were manufactured with ultrasonic machining using with five SiC grits ranging from 6 to 50 µm. The machined surfaces were initially characterized by contact profilometry and scanning electron microscopy (SEM). The multifractality of the machined surfaces was scrutinized using a box-counting method applied to the images obtained with 500X magnification. The multifractal spectrum indicated that the fractal dimension f(α) and the width of the fractal spectrum Δα are dependent on the grit size, but this dependence is not monotonic. The lowest (negative) value for Δf(α) was found for 25 µm grits indicating that for these grits the lower frequency events (grooves with tens µm width occurring along the USM direction) controls the surface topography much more than high frequency events related to brittle microcracking. The abrasive wear due to the continuous slurry recycling in lateral tool-workpiece interfaces contributed to smooth the groove texture as well as the sharpness of microscopic indentations, which remained observed on the surfaces machined with 50 µm grits. The opposite paths observed for the arithmetical mean deviation of the measured profile (Ra) and Δf(α) parameters with the cutting rate measured for each grit size were valuable to differentiate flat-rough and unlevelled-rough topographies in quartz bars.

scholarly journals Multifractal Analysis of River Networks in an Urban Catchment on the Taihu Plain, China

Water ◽  
2019 ◽  
Vol 11 (11) ◽  
pp. 2283 ◽  
Author(s):  
Jie Xiang ◽  
Youpeng Xu ◽  
Jia Yuan ◽  
Qiang Wang ◽  
Jie Wang ◽  
...  
Keyword(s):  
Multifractal Analysis ◽  
Decisive Role ◽  
Multifractal Spectrum ◽  
Temporal Variations ◽  
Yangtze River Delta ◽  
River Networks ◽  
Urban Catchment ◽  
Box Counting ◽  
Multifractal Theory ◽  
Box Counting Method

Multifractal analysis was successfully used to investigate the structure of river networks. In this paper, we performed a multifractal analysis of river networks in an urban catchment that is located on the Taihu Plain in the lower part of the Yangtze River Delta, China. Spatial and temporal variations in the river networks during the period 1960–2010 were investigated. The generalized multifractal dimensions (Dq) and the multifractal spectrum (f(α)) were calculated using a box-counting method. The results indicate that: (i) the river networks in Wuchengxiyu (WXCY), Yangchengdianmao (YCDM), and Hangjiahu (HJH) had obvious multifractal features with capacity dimensions between 1.90 and 1.91 during the period 1960–2010. The multifractal spectrums are asymmetrical inverted-hook-shaped curves with a dominant left arm. The variation in the singularity component (∆α) changed the most in WCXY (an increase of ~ 7.9%), and the height variation in the multifractal spectrum (∆f) increased by ~ 17.5% in HJH; (ii) the changes in ∆α and ∆f of the tributaries in the three areas during the period 1960–2010 were consistent with those of the overall river network, demonstrating the decisive role that the tributaries play in the complexity of the river networks; (iii) compared to the natural factors, the influences of urbanization on the river networks significantly changed with a higher urbanization level; and (iv) there were no border effects. Further applications of multifractal theory in analyses of the relationship between a flood-forming regime and the multifractal structures of river networks will attract more attention. Generally, this approach, when successfully applied to studies of changes in river networks, is of theoretical significance for better describing and quantifying the evolution of river networks’ structures.

CT Image Analysis on the Meso-Damage of Construction Waste Recycled Brick

2012 ◽  
Vol 588-589 ◽  
pp. 1930-1933
Author(s):  
Guo Song Han ◽  
Hai Yan Yang ◽  
Xin Pei Jiang
Keyword(s):  
Fractal Dimension ◽  
Strain Curve ◽  
Ct Image ◽  
Stress Strain Curve ◽  
Crack Evolution ◽  
Construction Waste ◽  
Box Counting ◽  
Industrial Ct ◽  
Ct Image Analysis ◽  
Box Counting Method

Based on industrial CT technique, Meso-mechanical experiment was conducted on construction waste recycled brick to get the real-time CT image and stress-strain curve of brick during the loading process. Box counting method was used to calculate the fractal dimension of the inner pore transfixion and crack evolution. The results showed that lots of pore in the interfacial transition zone mainly resulted in the damage of the brick. With the increase of stress, the opening through-pore appeared and crack expanded, and the fractal dimension increased.

Fractal and Convolutional Analysis for Deep Atmospheric Turbulence Using Machine Learning

2021 ◽  
Author(s):  
Nicholas Dudu ◽  
Arturo Rodriguez ◽  
Gael Moran ◽  
Jose Terrazas ◽  
Richard Adansi ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Atmospheric Turbulence ◽  
Isotropic Turbulence ◽  
Passive Scalar ◽  
Counting Method ◽  
Data Set ◽  
Box Counting ◽  
Box Counting Dimension ◽  
Self Similar ◽  
Box Counting Method

Abstract Atmospheric turbulence studies indicate the presence of self-similar scaling structures over a range of scales from the inertial outer scale to the dissipative inner scale. A measure of this self-similar structure has been obtained by computing the fractal dimension of images visualizing the turbulence using the widely used box-counting method. If applied blindly, the box-counting method can lead to misleading results in which the edges of the scaling range, corresponding to the upper and lower length scales referred to above are incorporated in an incorrect way. Furthermore, certain structures arising in turbulent flows that are not self-similar can deliver spurious contributions to the box-counting dimension. An appropriately trained Convolutional Neural Network can take account of both the above features in an appropriate way, using as inputs more detailed information than just the number of boxes covering the putative fractal set. To give a particular example, how the shape of clusters of covering boxes covering the object changes with box size could be analyzed. We will create a data set of decaying isotropic turbulence scenarios for atmospheric turbulence using Large-Eddy Simulations (LES) and analyze characteristic structures arising from these. These could include contours of velocity magnitude, as well as of levels of a passive scalar introduced into the simulated flows. We will then identify features of the structures that can be used to train the networks to obtain the most appropriate fractal dimension describing the scaling range, even when this range is of limited extent, down to a minimum of one order of magnitude.

Research on a precise differential box-counting method of eliminating image background

2016 ◽  
Author(s):  
Kexue Lai ◽  
Tao He ◽  
Cancan Li ◽  
Weisong Zhou ◽  
Liangen Yang
Keyword(s):  
Counting Method ◽  
Box Counting ◽  
Box Counting Method

scholarly journals Application of An Exponential Mathematical Law of Cardiac Dynamics In 16 Hours

2021 ◽  
Author(s):  
Javier Oswaldo Rodríguez Velásquez ◽  
Sandra Catalina Correra Herrera ◽  
Yesica Tatiana Beltrán Gómez ◽  
Jorge Gómez Rojas ◽  
Signed Esperanza Prieto Bohórquez ◽  
...  
Keyword(s):  
Kappa Coefficient ◽  
Medical Attention ◽  
Chaotic Attractors ◽  
Counting Method ◽  
Statistical Validation ◽  
Overlapping Grids ◽  
Box Counting ◽  
Cardiac Dynamics ◽  
Box Counting Method ◽  
Time Required

Abstract Introduction and objectives: nonlinear dynamics and fractal geometry have allowed the advent of an exponential mathematical law applicable to diagnose cardiac dynamics in 21 hours, however, it would be beneficial to reduce the time required to diagnose cardiac dynamics with this method in critical scenarios, in order to detect earlier complications that may require medical attention. The objective of this research is to confirm the clinical applicability of the mathematical law in 16 hours, with a comparative study against the Gold Standard. Methods: There were taken 450 electrocardiographic records of healthy patients and with cardiac diseases. A physical-mathematical diagnosis was applied to study cardiac dynamics, which consists of generating cardiac chaotic attractors based on the sequence of heart rate values during 16 hours, which were then measured with two overlapping grids according to the Box-Counting method to quantify the spatial occupation and the fractal dimension of each cardiac dynamic, with its respective statistical validation. Results: The occupation spaces of normal dynamics calculated in 16 hours were compatible with previous parameters established, evidencing the precision of the methodology to differentiate normality from abnormality. Sensitivity and specificity values of 100% were found, as well as a Kappa coefficient of 1. Conclusions: it was possible to establish differences between cardiac dynamics for 16 hours, suggesting that this method could be clinically applicable to analyze and diagnose cardiac dynamics in real time.

ON THE MODIFICATION OF FRACTAL SELF-SPACE DURING CELL DIFFERENTIATION OR TUMOR PROGRESSION

Fractals ◽  
2000 ◽  
Vol 08 (02) ◽  
pp. 195-203 ◽  
Author(s):  
PRZEMYSLAW WALISZEWSKI ◽  
JERZY KONARSKI ◽  
MARCIN MOLSKI
Keyword(s):  
Tumor Progression ◽  
Cancer Cells ◽  
Expansion Coefficient ◽  
Single Cells ◽  
Collective State ◽  
Global Features ◽  
Box Counting ◽  
2D System ◽  
Box Counting Method ◽  
Dynamic Relationships

A novel parameter called expansion coefficient has been defined to measure both connectivity and collectivity in a population of cells conquering the available space and self-organizing into tissue patterns of the higher order. Connectivity (i.e. interconnectedness) denotes that there are complex dynamic relationships, not just structural, static ones, in a population of cells enabling the emergence of global features in the system that would never appear in single cells existing out of the system. Collectivity denotes that all interconnected cells interact in a common mode. Evolution of this coefficient during differentiation or tumor progression was investigated by the box-counting method. The population of control or retinoid-treated primary cancer cells cultured in the monolayer (i.e. quasi-2D) system possessed fractal dimension and self-similarity. However, the expansion coefficient was close to zero, indicating that connectivity was low, and no collective state emerged. A significant change of the coefficient occurred when primary cells formed aggregates, quasi-3D systems with increased connectivity, and during treatment of the aggregates with retinoid resulting in a collective state (i.e. in differentiation of cells). Those statistical features were lost during tumor progression. All populations of the secondary cancer cells possessed integer dimension and the expansion coefficient was equal to zero.

scholarly journals Surface Topography-Based Positioning Accuracy of Maxillary Templates Fabricated by the CAD/CAM Technique for Orthognathic Surgery without an Intermediate Splint

2019 ◽  
Vol 9 (22) ◽  
pp. 4928
Author(s):  
Jeong Han ◽  
Soon Hwang
Keyword(s):  
Surface Topography ◽  
Computer Aided Design ◽  
Orthognathic Surgery ◽  
Mean Deviation ◽  
Lateral Direction ◽  
Positioning Accuracy ◽  
Actual Position ◽  
Computer Aided ◽  
Cad Cam ◽  
The Mean

Computer-aided design/computer-aided manufacturing (CAD/CAM)-based maxillary templates can transfer a surgical plan accurately only when the template is positioned correctly. Our study aimed to evaluate the positioning accuracy of the CAD/CAM-based template for maxillary orthognathic surgery using dry skulls. After reconstruction of a three-dimensional (3D) virtual skull model, a surface-based surgical template for Le Fort I osteotomy was designed and fabricated using CAD/CAM and 3D printing technology. To determine accuracy, the deviation of the template between the planned and the actual position and the fitness of the template were evaluated. The mean deviation was 0.41 ± 0.30 mm in the medio-lateral direction, 0.55 ± 0.59 mm in the antero-posterior direction, and 0.69 ± 0.59 mm in the supero-inferior direction. The root mean square deviation between the planned and the actual position of the template was 1.21 ± 0.54 mm. With respect to the fitness of the template, the mean distance between the inner surface of the template and the underlying bone surface was 0.76 ± 0.24 mm. CAD/CAM-based templates showed precise positioning and good fitness. These results suggest that surface topography-based CAD-CAM templates can be considered as an alternative solution in replacing the traditional intermediate splints for the transfer of surgical plans.

scholarly journals Study on the Fractal Dimension and Growth Time of the Electrical Treeing Degradation at Different Temperature and Moisture

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Youping Fan ◽  
Dai Zhang ◽  
Jingjiao Li
Keyword(s):  
Fractal Dimension ◽  
Tree Growth ◽  
Fractal Dimensions ◽  
Moisture Level ◽  
Growth Time ◽  
Counting Method ◽  
Box Counting ◽  
Electrical Trees ◽  
Box Counting Method ◽  
Electrical Treeing

The paper aims to understand how the fractal dimension and growth time of electrical trees change with temperature and moisture. The fractal dimension of final electrical trees was estimated using 2-D box-counting method. Four groups of electrical trees were grown at variable moisture and temperature. The relation between growth time and fractal dimension of electrical trees were summarized. The results indicate the final electrical trees can have similar fractal dimensions via similar tree growth time at different combinations of moisture level and temperature conditions.

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