A Microcontact Model Developed for Asperity Heights With a Variable Profile Fractal Dimension, a Surface Fractal Dimension, Topothesy, and Non-Gaussian Distribution

2008 ◽  
Author(s):  
Jen Luen Liou ◽  
Jen Fin Lin
Keyword(s):  
Fractal Dimension ◽  
Cross Sections ◽  
Fractal Dimensions ◽  
Surface Fractal Dimension ◽  
Surface Fractal ◽  
Deformation Regime ◽  
Circular Contour ◽  
The Mean ◽  
Non Gaussian ◽  
The Relationship

The cross sections formed by the contact asperities of two rough surfaces at an interference are island-shaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds+1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying with the mean separation (or the interference at the rough surface) between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformations are derived and the inceptions of the elastoplastic deformation regime and the fully plastic deformation regime are redefined using the equality of two expressions established in two different ways for the number of contact spots (N).

A Microcontact Model Developed for Asperity Heights with a Variable Profile Fractal Dimension, A Surface Fractal Dimension, Topothesy, and Non-Gaussian Distribution

2009 ◽  
Vol 25 (1) ◽  
pp. 103-115
Author(s):  
J. L. Liou ◽  
J. F. Lin
Keyword(s):  
Fractal Dimension ◽  
Contact Area ◽  
Distribution Functions ◽  
Real Contact Area ◽  
Contact Deformation ◽  
Surface Fractal Dimension ◽  
Surface Fractal ◽  
Deformation Regime ◽  
The Mean ◽  
Non Gaussian

AbstractThe cross sections formed by the contact asperities of two rough surfaces at an interference are islandshaped, rather than having the commonly assumed circular contour. These island-shaped contact surface contours show fractal behavior with a profile fractal dimension Ds. The surface fractal dimension for the asperity heights is defined as D and the topothesy is defined as G. In the study of Mandelbrot, the relationship between D and Ds was given as D = Ds + 1 if these two fractal dimensions are obtained before contact deformation. In the present study, D, G, and Ds are considered to be varying with the mean separation (or the interference at the rough surface) between two contact surfaces. The D-Ds relationships for the contacts at the elastic, elastoplastic, and fully plastic deformations are derived and the inceptions of the elastoplastic deformation regime and the fully plastic deformation regime are redefined using the equality of two expressions established in two different ways for the number of contact spots (N). The contact parameters, including the total contact force and the real contact area, were evaluated when the size distribution functions (n) for the three deformation regimes were available. The results indicate that both the D and Ds parameters in these deformation regimes increased with increasing the mean separation (d*). The initial plasticity index before contact deformation (ψ)0 is also a factor of importance to the predictions of the contact load (F*t) and contact area (At*) between the model of variable D and G, non-Gaussian asperity heights and circular contact area and the present model of variable D and G, non-Gaussian asperity heights and fractal contact area.

scholarly journals Relevance of coral geometry in the outcomes of the coral-algal benthic war

2018 ◽  
Author(s):  
Emma E. George ◽  
James Mullinix ◽  
Fanwei Meng ◽  
Barbara Bailey ◽  
Clinton Edwards ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Surface Area ◽  
Essential Element ◽  
Fractal Dimensions ◽  
Environmental Conservation ◽  
Microbial Composition ◽  
Surface Area Ratio ◽  
Surface Fractal Dimension ◽  
Surface Fractal ◽  
The Mean

AbstractCorals have built reefs on the benthos for millennia, becoming an essential element in marine ecosystems. Climate change and human impact, however, are favoring the invasion of non-calcifying benthic algae and reducing coral coverage. Corals rely on energy derived from photosynthesis and heterotrophic feeding, which depends on their surface area, to defend their outer perimeter. But the relation between geometric properties of corals and the outcome of competitive coral-algal interactions is not well known. To address this, 50 coral colonies interacting with algae were sampled in the Caribbean island of Curaçao. 3D and 2D digital models of corals were reconstructed to measure their surface area, perimeter, and polyp sizes. A box counting algorithm was applied to calculate their fractal dimension. The perimeter and surface dimensions were statistically non-fractal, but differences in the mean surface fractal dimension captured relevant features in the structure of corals. The mean fractal dimension and surface area were negatively correlated with the percentage of losing perimeter and positively correlated with the percentage of winning perimeter. The combination of coral perimeter, mean surface fractal dimension, and coral species explained 19% of the variability of losing regions, while the surface area, perimeter, and perimeter-to-surface area ratio explained 27% of the variability of winning regions. Corals with surface fractal dimensions smaller than two and small perimeters displayed the highest percentage of losing perimeter, while corals with large surface areas and low perimeter-to-surface ratios displayed the largest percentage of winning perimeter. This study confirms the importance of fractal surface dimension, surface area, and perimeter of corals in coral-algal interactions. In combination with non-geometrical measurements such as microbial composition, this approach could facilitate environmental conservation and restoration efforts on coral reefs.

DISTINCT FRACTAL CHARACTERISTICS OF MONOMER AND MULTIMER PROTEINS

Fractals ◽  
2010 ◽  
Vol 18 (02) ◽  
pp. 207-214 ◽  
Author(s):  
DANA CRACIUN ◽  
ADRIANA ISVORAN ◽  
R. D. REISZ ◽  
N. M. AVRAM
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Structural Characteristics ◽  
Fractal Dimensions ◽  
The Other ◽  
Mean Values ◽  
Surface Fractal Dimension ◽  
Surface Fractal ◽  
Fractal Characteristics ◽  
The Mean

Within this study we have calculated the surface fractal dimension (Ds) and the backbone fractal dimensions associated to the local folding (D1) and to the global folding (D2) for two unbiased sets of 50 proteins each, one for monomer and the other for homo- multimer proteins. The mean surface fractal dimension is Ds = 2.29 ± 0.02 for monomers and Ds = 2.21 ± 0.01 for multimers, the two means being significantly different. The mean backbone fractal dimensions associated to the local folding are D1 = 1.34 ± 0.14 for monomers and D1 = 1.33 ± 0.11 for multimers and those associated to the global folding are D2 = 1.33 ± 0.05 for monomers and D2 = 1.29 ± 0.04 for multimers, respectively. There are not significant differences between the mean values of the backbone fractal dimensions corresponding to monomers and multimers. These results suggest that there are different structural characteristics between monomer and multimer proteins only concerning their surface roughness, with multimers being smoother than monomers.

scholarly journals TECHNIQUE FOR DETERMINATION OF SURFACE FRACTAL DIMENSION AND MORPHOLOGY OF MESOPOROUS TITANIA USING DYNAMIC FLOW ADSORPTION AND ITS CHARACTERIZATION

2010 ◽  
Vol 9 (1) ◽  
pp. 13-17
Author(s):  
Silvester Tursiloadi
Keyword(s):  
Fractal Dimension ◽  
Adsorption Isotherm ◽  
Surface Morphology ◽  
Average Pore Size ◽  
Fractal Dimensions ◽  
Nano Particles ◽  
Dynamic Flow ◽  
N2 Adsorption ◽  
Surface Fractal Dimension ◽  
Surface Fractal

A technique to determine the surface fractal dimension of mesoporous TiO­2 using a dynamic flow adsorption instrument is described. Fractal dimension is an additional technique to characterize surface morphology. Surface fractal dimension, a quantitative measurement of surface ruggedness, can be determined by adsorbing a homologous series of adsorbates onto an adsorbent sample of mesoporous TiO­2. Titania wet gel prepared by hydrolysis of Ti-alkoxide was immersed in the flow of supercritical CO2 at 60 °C and the solvent was extracted.  Mesoporous TiO­2 consists of anatase nano-particles, about 5nm in diameter, have been obtained. After calcination at 600 °C, the average pore size of the extracted gel, about 20nm in diameter, and the pore volume, about 0.35cm3g-1, and the specific surface area, about 58 m2g-1. Using the N2 adsorption isotherm, the surface fractal dimension, DS, has been estimated according to the Frenkel-Halsey-Hill (FHH) theory. The N2 adsorption isotherm for the as-extracted aerogel indicates the mesoporous structure. Two linear regions are found for the FHH plot of the as-extracted aerogel. The estimated surface fractal dimensions are about 2.49 and 2.68. Both of the DS  values indicate rather complex surface morphology. The TEM observation shows that there are amorphous and crystalline particles. Two values of DS may be attributed to these two kinds of particles. The two regions are in near length scales, and the smaller DS, DS =2.49, for the smaller region. This result indicates that there are two kinds of particles, probably amorphous and anatase particles as shown by the TEM observation.     Keywords: surface fractal dimensions, CO2 supercritically extraction, sol-gel, aerogel, titania

scholarly journals Fractal analysis of bentonite modified with heteropoly acid using nitrogen sorption and mercury intrusion porosimetry

2011 ◽  
Vol 76 (10) ◽  
pp. 1403-1410 ◽  
Author(s):  
Srdjan Petrovic ◽  
Zorica Vukovic ◽  
Tatjana Novakovic ◽  
Zoran Nedic ◽  
Ljiljana Rozic
Keyword(s):  
Fractal Dimension ◽  
Specific Surface ◽  
Surface Area ◽  
Specific Surface Area ◽  
Heteropoly Acid ◽  
Mercury Intrusion Porosimetry ◽  
Fractal Dimensions ◽  
Surface Fractal Dimension ◽  
Mercury Intrusion ◽  
Surface Fractal

Experimental adsorption isotherms were used to evaluate the specific surface area and the surface fractal dimensions of acid-activated bentonite samples modified with a heteropoly acid (HPW). The aim of the investigations was to search for correlations between the specific surface area and the geometric heterogeneity, as characterized by the surface fractal dimension and the content of added acid. In addition, mercury intrusion was employed to evaluate the porous microstructures of these materials. The results from the Frankel-Halsey-Hill method showed that, in the p/p0 region from 0.75 to 0.96, surface fractal dimension increased with increasing content of heteropoly acid. The results from mercury intrusion porosimetry (MIP) data showed the generation of mesoporous structures with important topographical modifications, indicating an increase in the roughness (fractal geometry) of the surface of the solids as a consequence of the modification with the heteropoly acid. By comparison, MIP is preferable for the characterization because of its wide effective probing range.

Variation in Fractal Properties and Non-Gaussian Distributions of Microcontact Between Elastic-Plastic Rough Surfaces With Mean Surface Separation

2005 ◽  
Vol 73 (1) ◽  
pp. 143-152 ◽  
Author(s):  
Jung Ching Chung ◽  
Jen Fin Lin
Keyword(s):  
Fractal Dimension ◽  
Power Spectrum ◽  
Gaussian Distribution ◽  
Experimental Results ◽  
Fractal Parameters ◽  
Spectrum Function ◽  
The Mean ◽  
Non Gaussian ◽  
The Relationship ◽  
Scaling Coefficient

The fractal parameters (fractal dimension and topothesy), describing the contact behavior of rough surface, were considered as constant in the earlier models. However, their results are often significantly different from the experimental results. In the present study, these two roughness parameters have been derived analytically as a function of the mean separation first, then they are found with the aid of the experimental results. By equating the structure functions developed in two different ways, the relationship among the scaling coefficient in the power spectrum function, the fractal dimension, and topothesy of asperity heights can be established. The variation of topothesy can be determined when the fractal dimension and the scaling coefficient have been obtained from the experimental results of the number of contact spots and the power spectrum function at different mean separations. The probability density function of asperity heights, achieved at a different mean separation, was obtained from experimental results as a non-Gaussian distribution; it is expressed as a function of the skewness and the kurtosis. The relationship between skewness and mean separation can be established through the fitting of experimental results by this non-Gaussian distribution. For a sufficiently small mean separation, either the total load or the real contact area predicted by variable fractal parameters, as well as non-Gaussian distribution, is greater than that predicted by constant fractal parameters, as well as Gaussian distribution. The difference between these two models is significantly enhanced as the mean separation becomes small.

scholarly journals Skin Lesion Classification Based on Surface Fractal Dimensions and Statistical Color Cluster Features Using an Ensemble of Machine Learning Techniques

Cancers ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 5256
Author(s):  
Simona Moldovanu ◽  
Felicia Anisoara Damian Michis ◽  
Keka C. Biswas ◽  
Anisia Culea-Florescu ◽  
Luminita Moraru
Keyword(s):  
Neural Network ◽  
Fractal Dimension ◽  
Skin Cancer ◽  
Skin Lesion ◽  
Fractal Dimensions ◽  
Color Distribution ◽  
Surface Fractal Dimension ◽  
Color Features ◽  
Surface Fractal ◽  
Lesion Classification

(1) Background: An approach for skin cancer recognition and classification by implementation of a novel combination of features and two classifiers, as an auxiliary diagnostic method, is proposed. (2) Methods: The predictions are made by k-nearest neighbor with a 5-fold cross validation algorithm and a neural network model to assist dermatologists in the diagnosis of cancerous skin lesions. As a main contribution, this work proposes a descriptor that combines skin surface fractal dimension and relevant color area features for skin lesion classification purposes. The surface fractal dimension is computed using a 2D generalization of Higuchi’s method. A clustering method allows for the selection of the relevant color distribution in skin lesion images by determining the average percentage of color areas within the nevi and melanoma lesion areas. In a classification stage, the Higuchi fractal dimensions (HFDs) and the color features are classified, separately, using a kNN-CV algorithm. In addition, these features are prototypes for a Radial basis function neural network (RBFNN) classifier. The efficiency of our algorithms was verified by utilizing images belonging to the 7-Point, Med-Node, and PH2 databases; (3) Results: Experimental results show that the accuracy of the proposed RBFNN model in skin cancer classification is 95.42% for 7-Point, 94.71% for Med-Node, and 94.88% for PH2, which are all significantly better than that of the kNN algorithm. (4) Conclusions: 2D Higuchi’s surface fractal features have not been previously used for skin lesion classification purpose. We used fractal features further correlated to color features to create a RBFNN classifier that provides high accuracies of classification.

scholarly journals On Similarity of Seismo Magnetic Power Density and Pressure Head Fractal Dimension for Characterizing Shajara Reservoirs of the Permo-Carboniferous Shajara Formation, Saudi Arabia

2020 ◽  
pp. 1-8
Author(s):  
Khalid Elyas Mohamed Elameen Alkhidir ◽  
Keyword(s):  
Fractal Dimension ◽  
Power Density ◽  
Functional Relationship ◽  
Fractal Dimensions ◽  
Pressure Head ◽  
Density Maximum ◽  
Phase Saturation ◽  
Head Pressure ◽  
Second Procedure ◽  
The Relationship

The quality and assessment of a reservoir can be documented in details by the application of seismo magnetic power density. This research aims to calculate fractal dimension from the relationship among seismo magnetic power density, maximum seismo magnetic power density and wetting phase saturation and to approve it by the fractal dimension derived from the relationship among inverse pressure head * pressure head and wetting phase saturation. Two equations for calculating the fractal dimensions have been employed. The first one describes the functional relationship between wetting phase saturation, seismo magnetic power density, maximum seismo magnetic power density and fractal dimension. The second equation implies to the wetting phase saturation as a function of pressure head and the fractal dimension. Two procedures for obtaining the fractal dimension have been utilized. The first procedure was done by plotting the logarithm of the ratio between seismo magnetic power density and maximum seismo magnetic power density versus logarithm wetting phase saturation. The slope of the first procedure = 3- Df (fractal dimension). The second procedure for obtaining the fractal dimension was determined by plotting the logarithm (inverse of pressure head and pressure head) versus the logarithm of wetting phase saturation. The slope of the second procedure = Df -3. On the basis of the obtained results of the fabricated stratigraphic column and the attained values of the fractal dimension, the sandstones of the Shajara reservoirs of the Shajara Formation were divided here into three units

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