scholarly journals Comments on “On the Relationship Between Fractal Dimension and the Performance of Multi-Resonant Dipole Antennas Using Koch Curves”

2004 ◽  
Vol 52 (6) ◽  
pp. 1626-1627 ◽  
Author(s):  
J.M. Gonzalez-Arbesu ◽  
J.M. Rius ◽  
J. Romeu
Keyword(s):  
Fractal Dimension ◽  
Dipole Antennas ◽  
The Relationship

An analysis of fractal dimension and tortuosity based on 2D numerical reconstruction model of reservoir rocks

2019 ◽  
Vol 7 (4) ◽  
pp. SJ1-SJ6 ◽  
Author(s):  
Liang Luo ◽  
Jiahong Jin ◽  
Wei Wei ◽  
Jianchao Cai
Keyword(s):  
Fractal Dimension ◽  
Oil And Gas ◽  
Universal Method ◽  
Structure Generation ◽  
Reservoir Rocks ◽  
Numerical Reconstruction ◽  
The Monte Carlo Method ◽  
Microstructure Parameters ◽  
Rock Model ◽  
The Relationship

The microstructure of reservoir rocks plays an important role in oil and gas accumulation and production. We examine a universal method to evaluate these properties of rocks, such as pore tortuosity, matrix porosity, and connectivity, and we respectively construct a 2D numerical reconstruction rock model with different microstructure parameters by the Monte Carlo method and the quartet structure generation set method. We further study the heterogeneity (characterized by fractal dimension and tortuosity) of the constructed image for reservoir rocks by the numerical and theoretical analysis and obtain the formulas for fractal dimension and tortuosity versus porosity. The simulation results show that the logarithmic relation is between the pore fractal dimension and porosity, and the relationship between tortuosity and porosity has the form of power. This process provided an important method to advance 2D reconstruction technology of reservoir rocks and effectively determine the relationship between microstructure and porosity.

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

scholarly journals Shape matters: morphological metrics of glioblastoma imaging abnormalities as biomarkers of prognosis

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Lee Curtin ◽  
Paula Whitmire ◽  
Haylye White ◽  
Kamila M. Bond ◽  
Maciej M. Mrugala ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Tumor Location ◽  
Primary Brain Tumor ◽  
Resonance Imaging ◽  
Significant Relationships ◽  
Biological Phenomena ◽  
Microenvironmental Factors ◽  
Magnetic Resonance Imaging Mri ◽  
The Relationship ◽  
Standard Magnetic Resonance Imaging

AbstractLacunarity, a quantitative morphological measure of how shapes fill space, and fractal dimension, a morphological measure of the complexity of pixel arrangement, have shown relationships with outcome across a variety of cancers. However, the application of these metrics to glioblastoma (GBM), a very aggressive primary brain tumor, has not been fully explored. In this project, we computed lacunarity and fractal dimension values for GBM-induced abnormalities on clinically standard magnetic resonance imaging (MRI). In our patient cohort (n = 402), we connect these morphological metrics calculated on pretreatment MRI with the survival of patients with GBM. We calculated lacunarity and fractal dimension on necrotic regions (n = 390), all abnormalities present on T1Gd MRI (n = 402), and abnormalities present on T2/FLAIR MRI (n = 257). We also explored the relationship between these metrics and age at diagnosis, as well as abnormality volume. We found statistically significant relationships to outcome for all three imaging regions that we tested, with the shape of T2/FLAIR abnormalities that are typically associated with edema showing the strongest relationship with overall survival. This link between morphological and survival metrics could be driven by underlying biological phenomena, tumor location or microenvironmental factors that should be further explored.

Microstructure of Agglomerates of Nanometer Particles

1995 ◽  
Vol 380 ◽  
Author(s):  
Alfred P. Weber ◽  
James D. Thorne ◽  
Sheldon K. Friedlander
Keyword(s):  
Fractal Dimension ◽  
Laser Ablation ◽  
Coordination Number ◽  
Computer Simulations ◽  
Large Fraction ◽  
Low Density ◽  
Nanometer Particles ◽  
The Relationship

ABSTRACTThe microstructure of an agglomerate can be characterized by the coordination number. The relationship between the fractal dimension and the coordination number of agglomerates of nanometer particles was investigated in experiments and computer simulations. The results for silver agglomerates formed by laser ablation agreed well with the simulations. The coordination number is low for low density fractals because of the large fraction of surface particles which have fewer bonds. The sensitivity of the coordination number to the fractal dimension increases with increasing fractal dimension.

scholarly journals Charge accumulation in thunderstorm clouds: fractal dynamic model

2019 ◽  
Vol 127 ◽  
pp. 01001 ◽  
Author(s):  
Tembulat Kumykov
Keyword(s):  
Fractal Dimension ◽  
Comparative Study ◽  
Dynamic Model ◽  
Model Equation ◽  
Fractal Structure ◽  
Analytic Solution ◽  
Numerical Calculations ◽  
Charge Accumulation ◽  
Dynamic Charge ◽  
The Relationship

The paper considers a fractal dynamic charge accumulation model in thunderstorm clouds in view of the fractal dimension. Analytic solution to the model equation has been found. Using numerical calculations we have shown the relationship between the charge accumulation and the medium with the fractal structure. A comparative study of thunderstorm electrification mechanisms have been performed.

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