scholarly journals Fractal dimension of coastline of Australia

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Akhlaq Husain ◽  
Jaideep Reddy ◽  
Deepika Bisht ◽  
Mohammad Sajid
Keyword(s):  
Fractal Dimension ◽  
Parallel Processing ◽  
Programming Language ◽  
Power Law ◽  
Fractal Geometry ◽  
Parallel Computer ◽  
Processing Algorithm ◽  
Computational Results ◽  
Random Fractal

AbstractCoastlines are irregular in nature having (random) fractal geometry and are formed by various natural activities. Fractal dimension is a measure of degree of geometric irregularity present in the coastline. A novel multicore parallel processing algorithm is presented to calculate the fractal dimension of coastline of Australia. The reliability of the coastline length of Australia is addressed by recovering the power law from our computational results. For simulations, the algorithm is implemented on a parallel computer for multi-core processing using the QGIS software, R-programming language and Python codes.

Role of Fractal Geometry in Roughness Characterization and Contact Mechanics of Surfaces

1990 ◽  
Vol 112 (2) ◽  
pp. 205-216 ◽  
Author(s):  
A. Majumdar ◽  
B. Bhushan
Keyword(s):  
Fractal Dimension ◽  
Size Distribution ◽  
Power Law ◽  
Magnetic Tape ◽  
Fractal Geometry ◽  
Rough Surfaces ◽  
Statistical Parameters ◽  
Length Scales ◽  
Imperfect Contact ◽  
Contact Spots

A proper characterization of the multiscale topography of rough surfaces is very crucial for understanding several tribological phenomena. Although the multiscale nature of rough surfaces warrants a scale-independent characterization, conventional techniques use scale-dependent statistical parameters such as the variances of height, slope and curvature which are shown to be functions of the surface magnification. Roughness measurements on surfaces of magnetic tape, smooth and textured magnetic thin film rigid disks, and machined stainless steel surfaces show that their spectra follow a power law behavior. Profiles of such surfaces are, therefore, statistically self-affine which implies that when repeatedly magnified, increasing details of roughness emerge and appear similar to the original profile. This paper uses fractal geometry to characterize the multiscale self-affine topography by scale-independent parameters such as the fractal dimension. These parameters are obtained from the spectra of surface profiles. It was observed that surface processing techniques which produce deterministic texture on the surface result in non-fractal structure whereas those producing random texture yield fractal surfaces. For the magnetic tape surface, statistical parameters such as the r.m.s. peak height and curvature and the mean slope, which are needed in elastic contact models, are found to be scale-dependent. The imperfect contact between two rough surfaces is composed of a large number of contact spots of different sizes. The fractal representation of surfaces shows that the size-distribution of the multiscale contact spots follows a power law and is characterized by the fractal dimension of the surface. The surface spectra and the spot size-distribution follow power laws over several decades of length scales. Therefore, the fractal approach has the potential to predict the behavior of a surface phenomenon at a particular length scale from the observations at other length scales.

Application of Fractal Geometry in the Evaluation of Surface Microtexture of Soil Particles

2015 ◽  
Vol 797 ◽  
pp. 238-245
Author(s):  
Sylwia Szerakowska ◽  
Maria Jolanta Sulewska ◽  
Edward Stanisław Oczeretko ◽  
Jerzy Trzciński ◽  
Barbara Woronko
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Solid Phase ◽  
Complex Nature ◽  
Mathematical Tool ◽  
Soil Behaviour ◽  
Difficult Issue ◽  
Shape Of Particles

The shape of particles building the solid phase of soils is an important factor influencing soil behaviour. Three parameters defining the characteristics of particle shape: roundness, angularity and texture are the most commonly analyzed. The most difficult issue is texture determination due to its complex nature. Quantitative evaluation of this parameter creates serious problems, however, is not impossible. A new mathematical tool, such as fractal geometry, may be helpful. Through the use of power law, fractal analysis allows to designate fractal dimension that specifies the complexity of the tested object.

Light-scattering studies of aggregation

1989 ◽  
Vol 423 (1864) ◽  
pp. 89-102 ◽  
Keyword(s):  
Fractal Dimension ◽  
Light Scattering ◽  
Dynamic Light Scattering ◽  
Power Law ◽  
Fractal Geometry ◽  
Linear Growth ◽  
Fractal Dimensions ◽  
Power Law Model ◽  
Aggregate Distribution ◽  
Scattering Measurements

We discuss dynamic and static light-scattering measurements made during slow (reaction-limited) aggregation of model colloids and immune complex forming proteins. Analysis of the results leads to an understanding of the random aggregates formed in terms of a fractal geometry and measurement of the fractal dimension. Differences in the measured fractal dimensions of the model and protein systems are discussed. The aggregation appears to follow ‘Smoluchowski-like’ kinetics as measured by a near linear growth of the low-angle light scattering with time. However, the dynamic light-scattering results support a simple power-law model for the aggregate distribution and allow an estimate of this power law to be made.

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 The fractal dimension of the tree of life

2014 ◽  
Author(s):  
Xiaofei Lv ◽  
Yuping Wu ◽  
Bin Ma
Keyword(s):  
Fractal Dimension ◽  
Power Law ◽  
Fractal Dimensions ◽  
Predictive Modelling ◽  
Tree Of Life ◽  
Fundamental Question ◽  
Theoretical Studies ◽  
Structure Pattern ◽  
Intermediate Size ◽  
Taxonomic Groups

The structure pattern of the tree of life clues on the key ecological issues; hence knowing the fractal dimension is the fundamental question in understanding the tree of life. Yet the fractal dimension of the tree of life remains unclear since the scale of the tree of life has hypergrown in recent years. Here we show that the tree of life display a consistent power-law rules for inter- and intra-taxonomic levels, but the fractal dimensions were different among different kingdoms. The fractal dimension of hierarchical structure (Dr) is 0.873 for the entire tree of life, which smaller than the values of Dr for Animalia and Plantae but greater than the values of Dr for Fungi, Chromista, and Protozoa. The hierarchical fractal dimensions values for prokaryotic kingdoms are lower than for other kingdoms. The Dr value for Viruses was lower than most eukaryotic kingdoms, but greater than prokaryotes. The distribution of taxa size is governed by fractal diversity but skewed by overdominating taxa with large subtaxa size. The proportion of subtaxa in taxa with small and large sizes was greater than in taxa with intermediate size. Our results suggest that the distribution of subtaxa in taxa can be predicted with fractal dimension for the accumulating taxa abundance rather than the taxa abundance. Our study determined the fractal dimensions for inter- and intra-taxonomic levels of the present tree of life. These results emphases the need for further theoretical studies, as well as predictive modelling, to interpret the different fractal dimension for different taxonomic groups and skewness of taxa with large subtaxa size.

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