A NOVEL METHOD TO IDENTIFY THE SCALING REGION OF ROUGH SURFACE PROFILE

Fractals ◽  
2019 ◽  
Vol 27 (02) ◽  
pp. 1950011
Author(s):  
ZHIYING CHEN ◽  
YONG LIU ◽  
PING ZHOU
Keyword(s):  
Fractal Dimension ◽  
Rough Surface ◽  
Surface Profile ◽  
Fractal Dimensions ◽  
Second Derivative ◽  
Logarithmic Curve ◽  
Margin Of Error ◽  
Scaling Region ◽  
Novel Method ◽  
First Time

Scaling region identification is of great importance in calculating the fractal dimension of a rough surface profile. A new method used to identify the scaling region is presented to improve the calculation accuracy of fractal dimension. In this method, the second derivative of the double logarithmic curve is first calculated and the [Formula: see text]-means algorithm method is adopted to identify the scaling region for the first time. Then the margin of error is reasonably set to get a possible scaling region. Finally, the [Formula: see text]-means method is used again to obtain a more accurate scaling region. The effectiveness of the proposed method is compared with the existing methods. Both the simulation and experimental results show that the proposed method provides more precise results for extracting the scaling regions and leads to a higher calculation precision of fractal dimensions.

Quantitative Analysis for Micro Geometrical Characteristic of Rough Surface Profile Based on Fractal Theory

2010 ◽  
Vol 154-155 ◽  
pp. 19-22
Author(s):  
Xiu Juan Yang ◽  
Zhi Qian Xu ◽  
Xiang Zhen Yan
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Quantitative Analysis ◽  
Rough Surface ◽  
Vertical Section ◽  
Fractal Theory ◽  
Surface Profile ◽  
Fractal Dimensions ◽  
Geometrical Characteristic ◽  
Accuracy Requirement

In this paper, a quantitative analysis for the micro geometrical characteristic of rough surface profile is researched with the fractal theory. Firstly, the fractal dimensions of profile curves under different surface roughness are obtained by using the vertical section method, and then the theoretical relationship between the surface roughness and the fractal dimension is built. Secondly, according to the surface profile curve composed of many triangle peaks, the angles and heights of them are calculated to study the micro geometrical size. Through their variation laws changing with the fractal parameters, the calculation formulas of their average values related to fractal dimension are obtained by using mathematics regression tools. Finally, combing three theoretical relationships built above, the geometrical characteristic of the rough surface profile can be calculated with the surface roughness and accuracy requirement known.

scholarly journals The Impact of Nano-Al2O3 on the Physical and Strength Properties as Well as on the Morphology of Cement Composite Crack Surfaces in the Early and Later Maturation Age

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4441
Author(s):  
Wioleta Iskra-Kozak ◽  
Janusz Konkol
Keyword(s):  
Fractal Dimension ◽  
Surface Profile ◽  
Fractal Dimensions ◽  
Cement Composite ◽  
Fracture Morphology ◽  
Strength Properties ◽  
Hardened Cement ◽  
Physical Strength ◽  
Binder Ratio ◽  
The Impact

This article presents the effect of aluminum nanoxide on the physical, strength and structural properties of cement mortars. The mortars were made with a water to binder ratio of 0.5 and a binder to sand ratio of 1:3; and 1%, 2%, 3% and 4% of aluminum nanoxide, respectively, were used by cement weight. First, the consistency of nano-Al2O3 mortars was tested. Next, after 7 days of sample maturation, compressive and flexural strength tests were carried out and continued after 28 and 90 days of the maturing of the mortars. The best test results were obtained for mortars with the addition of 1% aluminum nanoxide, the compressive strength of which increased by about 20% compared to the reference mortars. The water absorption and rising capillary tests as well as SEM observations were also performed. Another aim of the article is the analysis of the fracture morphology of nano-Al2O3 modified mortars. It is assumed that a change of the microstructure of the hardened cement paste affects not only the properties of the modified mortars but also the roughness of the fractures formed as a result of the destruction of the surface. Roughness analysis was performed with methods and tools relevant to fractal geometry. The fractographic analysis showed a significant influence of the modifier in the form of nano-Al2O3 on the values of fractal dimensions. The lowest values of the fractal dimension D and the fractal dimension of the DRP roughness profile of the fracture surface profile lines were obtained for nano-Al2O3 modified mortars. The conducted research proved the fractal dimension to be a parameter extremely sensitive to modifications of mortar composition as well as changes related to the maturation time.

A NUMERICAL STUDY ON FRACTAL DIMENSIONS OF CURRENT STREAMLINES IN TWO-DIMENSIONAL AND THREE-DIMENSIONAL PORE FRACTAL MODELS OF POROUS MEDIA

Fractals ◽  
2015 ◽  
Vol 23 (01) ◽  
pp. 1540012 ◽  
Author(s):  
WEI WEI ◽  
JIANCHAO CAI ◽  
XIANGYUN HU ◽  
PING FAN ◽  
QI HAN ◽  
...  
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Numerical Study ◽  
Three Dimensional ◽  
Fractal Dimensions ◽  
Simple Relation ◽  
Two Dimensional ◽  
Random Walker ◽  
Fractal Models ◽  
Novel Method

The fractal dimension of random walker (FDRW) is an important parameter for description of electrical conductivity in porous media. However, it is somewhat empirical in nature to calculate FDRW. In this paper, a simple relation between FDRW and tortuosity fractal dimension (TFD) of current streamlines is derived, and a novel method of computing TFD for different generations of two-dimensional Sierpinski carpet and three-dimensional Sierpinski sponge models is presented through the finite element method, then the FDRW can be accordingly predicted; the proposed relation clearly shows that there exists a linear relation between pore fractal dimension (PFD) and TFD, which may have great potential in analysis of transport properties in fractal porous media.

scholarly journals Numerical Simulation and Accuracy Verification of Surface Morphology of Metal Materials Based on Fractal Theory

Materials ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4158
Author(s):  
Xiaokai Mu ◽  
Wei Sun ◽  
Chong Liu ◽  
Bo Yuan ◽  
Yunlong Wang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Fractal Dimension ◽  
Surface Morphology ◽  
Fractal Theory ◽  
Surface Profile ◽  
Reference Value ◽  
Fractal Dimensions ◽  
Current Method ◽  
Simulation Method ◽  
Surface Morphologies

This paper presents a numerical simulation method to determine the surface morphology characteristics of metallic materials. First, a surface profiler (NV5000 5022s) was used to measure the surface, and the morphology data thereof were characterized. Second, fractal theory was used to simulate the surface profile for different fractal dimensions D and scale coefficients G, and statistical analyses of different surface morphologies were carried out. Finally, the fractal dimension D of the simulated morphology and the actual morphology were compared. The analysis showed that the error of fractal dimension D between the two morphologies was less than 10%; meanwhile, the comparison values of the characterization parameters of the simulated morphology and the actual morphology were approximately equal, and the errors were below 6%. Therefore, the current method used to evaluate the surface morphologies of parts processed by the grinding/milling method can be replaced by the simulated method using the corresponding parameters. This method makes it possible to theorize about the surface morphologies of machined parts, and provides a theoretical basis and reference value for the surface morphology design of materials, with the potential to improve the assembly quality of products.

Fractal Characterization of Corroded Surface Profile in Reinforcing Steel Bars

2010 ◽  
Vol 163-167 ◽  
pp. 3118-3121 ◽  
Author(s):  
Yi Dong Xu ◽  
Chun Xiang Qian
Keyword(s):  
Fractal Dimension ◽  
Surface Profile ◽  
Fractal Dimensions ◽  
Corrosion Damage ◽  
Absolute Measurement ◽  
Reinforcing Steel ◽  
Multi Scale ◽  
Steel Bars ◽  
Fractal Characteristics

Based on fractal geometry theory and surface roughness characterization technology, this paper presents the fractal characterization of nonuniform corrosion degree of corroded reinforcing steel bars. The surface profile curves of different corroded reinforcing steel bars were obtained and their fractal dimensions were calculated in order to describe the fractal characteristics. As is shown by the results, the surface profile curves of rebar have statistical fractal feature. However, fractal dimension is not sensitive to small changes in profile curves. By combining fractal dimension D with scale parameter C, characteristic profile parameter r* is derived to characterize the surface profile of corroded reinforcing steel bars sensitively, which realized the unity of multi-scale similarity measurement and absolute measurement. The results of this analysis will become the basis for corrosion damage evolution of corroded reinforcing steel bars.

THE THREE-POINT SINUOSITY METHOD FOR CALCULATING THE FRACTAL DIMENSION OF MACHINED SURFACE PROFILE

Fractals ◽  
2015 ◽  
Vol 23 (02) ◽  
pp. 1550016 ◽  
Author(s):  
YUANKAI ZHOU ◽  
YAN LI ◽  
HUA ZHU ◽  
XUE ZUO ◽  
JIANHUA YANG
Keyword(s):  
Fractal Dimension ◽  
Surface Profile ◽  
Structural Complexity ◽  
Variation Method ◽  
Real Surface ◽  
Machined Surface ◽  
Box Counting ◽  
Scaling Region ◽  
Fractal Characteristics ◽  
Surface Profiles

The three-point sinuosity (TPS) method is proposed to calculate the fractal dimension of surface profile accurately. In this method, a new measure, TPS is defined to present the structural complexity of fractal curves, and has been proved to follow the power law. Thus, the fractal dimension can be calculated through the slope of the fitted line in the log–log plot. The Weierstrass–Mandelbrot (W–M) fractal curves, as well as the real surface profiles obtained by grinding, sand blasting and turning, are used to validate the effectiveness of the proposed method. The calculation values are compared to those obtained from root-mean-square (RMS) method, box-counting (BC) method and variation method. The results show that the TPS method has the widest scaling region, the least fit error and the highest accuracy among the methods examined, which demonstrates that the fractal characteristics of the fractal curves can be well revealed by the proposed method.

Rubber–Road Contact: Comparison of Physics-Based Theory and Indoor Experiments

2016 ◽  
Vol 44 (3) ◽  
pp. 150-173 ◽  
Author(s):  
Mehran Motamedi ◽  
Saied Taheri ◽  
Corina Sandu
Keyword(s):  
Rough Surface ◽  
Practical Importance ◽  
Surface Profile ◽  
Surface Characteristics ◽  
Mechanical Analysis ◽  
Friction Model ◽  
Rubber Friction ◽  
Optical Profilometer ◽  
Viscoelastic Modulus ◽  
Longitudinal Slip

ABSTRACT For tire designers, rubber friction is a topic of pronounced practical importance. Thus, development of a rubber–road contact model is of great interest. In this research, to predict the effectiveness of the tread compound in a tire as it interacts with the pavement, the physics-based multiscale rubber-friction theories developed by B. Persson and M. Klüppel were studied. The strengths of each method were identified and incorporated into a consolidated model that is more comprehensive and proficient than any single, existing, physics-based approach. In the present work, the friction coefficient was estimated for a summer tire tread compound sliding on sandpaper. The inputs to the model were the fractal properties of the rough surface and the dynamic viscoelastic modulus of rubber. The sandpaper-surface profile was measured accurately using an optical profilometer. Two-dimensional parameterization was performed using one-dimensional profile measurements. The tire tread compound was characterized via dynamic mechanical analysis. To validate the friction model, a laboratory-based, rubber-friction test that could measure the friction between a rubber sample and any arbitrary rough surface was designed and built. The apparatus consisted of a turntable, which can have the surface characteristics of choice, and a rubber wheel in contact with the turntable. The wheel speed, as well as the turntable speed, could be controlled precisely to generate the arbitrary values of longitudinal slip at which the dynamic coefficient of friction was measured. The correlation between the simulation and the experimental results was investigated.

Organic Reactivity Control by Means of Neighboring Groups and Organometallics. A Personal Account

1994 ◽  
Vol 59 (1) ◽  
pp. 1-74 ◽  
Author(s):  
Pavel Kočovský
Keyword(s):  
Transition Metals ◽  
Cyclopropane Ring ◽  
Allylic Substitutions ◽  
Recent Developments ◽  
Cardioactive Drug ◽  
Novel Method ◽  
Metal Catalyzed ◽  
Electrophilic Additions ◽  
Near Future ◽  
First Time

This review summarizes the main topics of our research and covers the period of the last 15 years. The prime interest is focused on various ways of controlling the regio- and stereoselectivity of selected organic reactions, in particular electrophilic additions, cleavage of cyclopropane rings, and allylic substitutions by means of neighboring groups and/or transition and non-transition metals. In the first part, the factors governing the course of electrophilic additions are assessed, culminating in the formulation of selection rules for the reactivity of cyclohexene systems, and in a concise synthesis of the natural cardioactive drug, strophanthidin. These studies also contribute to a better understanding of the mechanisms of electrophilic additions. The second part describes recent developments in the stereo- and regiocontrolled cleavage of cyclopropane rings by non-transition metals (Tl and Hg), and the reactivity and transmetalation (with Pd) of the primary products. This methodology has resulted in novel routes to unique polycyclic structures, and will have synthetic applications in the near future. Evidence for the stereospecific "corner" cleavage of the cyclopropane ring has been provided for the first time for Tl and later for Hg. The third part deals with transition metal-catalyzed allylic substitution. Evidence for a new "syn" mechanism for the formation of the intermediate (π-allyl)palladium complex has been provided, which runs counter to the generally accepted "anti" mechanism. A novel method for a Pd-catalyzed allylic oxidation has been developed and employed in the synthesis of natural sesquiterpenes. The increasing importance of transition and non-transition metals for synthetic organic chemistry is demonstrated by their unique reactivity in a number of the papers included in this review.

FRACTAL DIMENSION, PRIMES, AND THE PERSISTENCE OF MEMORY

2003 ◽  
Vol 06 (02) ◽  
pp. 241-249
Author(s):  
JOSEPH L. PE
Keyword(s):  
Number Theory ◽  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Distinguishing Characteristic ◽  
Local Behavior ◽  
Remarkable Similarity ◽  
Recursive Procedures

Many sequences from number theory, such as the primes, are defined by recursive procedures, often leading to complex local behavior, but also to graphical similarity on different scales — a property that can be analyzed by fractal dimension. This paper computes sample fractal dimensions from the graphs of some number-theoretic functions. It argues for the usefulness of empirical fractal dimension as a distinguishing characteristic of the graph. Also, it notes a remarkable similarity between two apparently unrelated sequences: the persistence of a number, and the memory of a prime. This similarity is quantified using fractal dimension.

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