scholarly journals Application of the Fractal Dimension Calculation Technique to Determine the Shape of Selected Monchepluton Intrusion Crystals (NE Fennoscandia)

Minerals ◽  
2021 ◽  
Vol 11 (10) ◽  
pp. 1140
Author(s):  
Miłosz Huber ◽  
Klaudia Stępniewska
Keyword(s):  
Fractal Dimension ◽  
Fractal Dimensions ◽  
Mean Value ◽  
Computational Technique ◽  
Calculation Technique ◽  
Euhedral Crystal ◽  
The Mean ◽  
Crystal Boundaries

Thirty-eight samples of minerals from Paleoproterozoic Layered PGE Intrusion Monchepluton, located in NE Fennoscandia, were tested. An automated computational technique was used which involved counting the sides superimposed on vectorized graphics using separated crystal boundaries. The results were obtained for olivine, orthopyroxene, clinopyroxene, and plagioclase. On this basis, an interpretation of the mineral box fractal dimension was made, along with an interpretation of its nature in the rock in which it was found. The performed calculations were applied to the sampling positions, and maps of changes in fractal dimensions were prepared. The nature of the minerals studied was correlated with the type of rocks present in Monchepluton. Then, the fractal dimensions were scaled to a percentage scale determining the mean value for the euhedral crystal as 100%, and a map was obtained representing the advancement of secondary processes after summing these data for all four investigated minerals. This method was analyzed and its advantages and limitations shown.

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).

scholarly journals An Investigation of Fractal Characteristics of Marine Shales in the Southern China from Nitrogen Adsorption Data

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Jian Xiong ◽  
Xiangjun Liu ◽  
Lixi Liang
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Southern China ◽  
Fractal Dimensions ◽  
Nitrogen Adsorption ◽  
Mean Value ◽  
Relative Pressure ◽  
Pore Surface ◽  
Adsorption Sites ◽  
Fractal Characteristics

We mainly focus on the Permian, Lower Cambrian, Lower Silurian, and Upper Ordovician Formation; the fractal dimensions of marine shales in southern China were calculated using the FHH fractal model based on the low-pressure nitrogen adsorption analysis. The results show that the marine shales in southern China have the dual fractal characteristics. The fractal dimensionD1at low relative pressure represents the pore surface fractal characteristics, whereas the fractal dimensionD2at higher relative pressure describes the pore structure fractal characteristics. The fractal dimensionsD1range from 2.0918 to 2.718 with a mean value of 2.4762, and the fractal dimensionsD2range from 2.5842 to 2.9399 with a mean value of 2.8015. There are positive relationships between fractal dimensionD1and specific surface area and total pore volume, whereas the fractal dimensionsD2have negative correlation with average pore size. The larger the value of the fractal dimensionD1is, the rougher the pore surface is, which could provide more adsorption sites, leading to higher adsorption capacity for gas. The larger the value of the fractal dimensionD2is, the more complicated the pore structure is, resulting in the lower flow capacity for gas.

FRACTAL ANALYSIS OF DENDRITIC ARBORISATION PATTERNS OF STALKED AND ISLET NEURONS IN SUBSTANTIA GELATINOSA OF DIFFERENT SPECIES

Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 1-7 ◽  
Author(s):  
NEBOJŠA T. MILOŠEVIĆ ◽  
DUŠAN RISTANOVIĆ ◽  
JOVAN B. STANKOVIĆ ◽  
RADMILA GUDOVIĆ
Keyword(s):  
Fractal Dimension ◽  
Fractal Analysis ◽  
Islet Cells ◽  
Fractal Dimensions ◽  
Substantia Gelatinosa ◽  
Neuronal Populations ◽  
Box Counting ◽  
Morphological Descriptor ◽  
The Mean ◽  
Box Counting Method

Through analysis of the morphology of dendritic arborisation of neurons from the substantia gelatinosa of dorsal horns from four different species, we have established that two types of cells (stalked and islet) are always present. The aim of the study was to perform the intra- and/or inter-species comparison of these two neuronal populations by fractal analysis, as well as to clarify the importance of the fractal dimension as an objective and usable morphological parameter. Fractal analysis was carried out adopting the box-counting method. We have shown that the mean fractal dimensions for the stalked cells are significantly different between species. The same is true for the mean fractal dimensions of the islet cells. Still, no significant differences were found for the fractal dimensions of the stalked and islet cells within a particular species. The human species has shown as the only exception where fractal dimensions of these two types of cells differ significantly. This study shows once more that the fractal dimension is a useful and sensitive morphological descriptor of neuronal structures and differences between them.

scholarly journals Grain textural analysis across a range of glacial facies

1999 ◽  
Vol 28 ◽  
pp. 111-117 ◽  
Author(s):  
A. Khatwa ◽  
J. K. Hart ◽  
A. J. Payne
Keyword(s):  
Particle Size ◽  
Fractal Dimension ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Diagnostic Criteria ◽  
Fractal Dimensions ◽  
Textural Analysis ◽  
Significant Difference ◽  
The Mean

AbstractA technique proposed by Hooke and Iverson (1995) to identify deformed subglacial sediments is reviewed and tested, based on two main objectives. First, an investigation of whether the fractal dimension can distinguish between non-deformed and deformed facies; for which we compare supraglacial and subglacial facies explicitly. Second, an evaluation of whether the fractal dimension can be used as a diagnostic criteria to discriminate between different styles and degrees of basal deformation. This is tested using a range of sediments from the deformation continuum suggested by Hart and Boulton (1991b). Sixteen subglacial samples were selected from Quaternary sites in England and three supraglacial samples from the modern Haut Glacier d’Arolla, Switzerland. The mean fractal dimension for the subglacial diamicton matrix facies was 2.92, similar to findings of 2.90 by Hooke and Iverson (1995) for their basal tills. The supraglacial facies displayed a mean fractal dimension of 2.83, which is unusually high for facies which are assumed to be undeformed. A Mann—Whitney U test showed that fractal dimensions of supraglacial and subglacial diamicton matrix facies were not significantly different. No significant difference was found between the fractal dimensions of the different tectonic facies within the subglacial group. It may be impossible to separate the subglacial and supraglacial facies because of complex debris paths within the glacier. Grain fracture or parent lithology may affect the particle-size distribution of subglacial facies.

scholarly journals Anatomical Considerations and Study of the Fractal Dimension around the Posterior Superior Alveolar Artery

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1177
Author(s):  
Yolanda Guerrero-Sánchez ◽  
Francisco José Gómez García ◽  
Manuel Fernández-Martínez ◽  
Blanca Pallarés Martínez ◽  
Pia López-Jornet
Keyword(s):  
Fractal Dimension ◽  
Maxillary Sinus ◽  
Fractal Dimensions ◽  
Tissue Structure ◽  
Cone Beam ◽  
P Value ◽  
Linear Relationships ◽  
The Mean ◽  
Edentulous Patients ◽  
The One

The Posterior Superior Alveolar Artery (PSAA) provides vascular support to molars, gingiva, and maxillary sinus. A tear of the PSAA may cause profuse hemorrhages which may lead to complications at a surgical level. As such, it becomes crucial to anatomically analyse several features regarding the PSAA as well as the area surrounding it. In this paper, we are particularly interested in the study of the complexity of the periodontal tissue structure which appears close to the location of the PSAA. A total amount of 400 cone beam computed tomography (CBCT) scans (two per subject) were performed to explore the presence of the PSAA, the thickness of the Schneider’s membrane, and the existence of septa. Several parameters were evaluated including the location of the artery in the maxillary sinus, the distance from the PSAA to the alveolar ridge, the thickness of the membrane, the diameter of the cavities produced by the septa, and the fractal dimension of the trabecular tissue that surrounds the PSAA. They were found strong linear relationships between Distal and Central Measures (a Pearson’s R 2 = 0.9952 ), Mesial and Central Measures ( R 2 = 0.9950 ), and Distal and Mesial Measure ( R 2 = 0.997 ). We hypothesised that the loss of dental pieces would imply a distinct complexity of the trabecular tissue structure surrounding the PSAA. In this way, a p-value equal to 0.001 was provided by the Mann-Whitney test, which supports our hypothesis. Furthermore, the mean of the fractal dimensions of the group of edentulous patients (equal to 1.56 ) was found to be lower than the one of the group of non-edentulous patients (equal to 1.61 ) with small standard deviations in both cases. Our study suggests that accurate calculations of the fractal dimension combined with the use of CBCT do provide valuable information regarding the area that surrounds the PSAA.

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.

Long-period modulated superstructures in Pd-12.5 at.%Ce and Pd-15 at.%Ce alloys

1990 ◽  
Vol 48 (4) ◽  
pp. 164-165
Author(s):  
Noriyuki Kuwano ◽  
Masaru Itakura ◽  
Kensuke Oki
Keyword(s):  
Electron Microscopy ◽  
Mean Value ◽  
Heavy Elements ◽  
Arc Furnace ◽  
X Ray ◽  
Long Period ◽  
Ultra High Purity ◽  
Heat Treated ◽  
Atomic Scattering ◽  
The Mean

Pd-Ce alloys exhibit various anomalies in physical properties due to mixed valences of Ce, and the anomalies are thought to be strongly related with the crystal structures. Since Pd and Ce are both heavy elements, relative magnitudes of (fcc-fpd) are so small compared with <f> that superlattice reflections, even if any, sometimes cannot be detected in conventional x-ray powder patterns, where fee and fpd are atomic scattering factors of Ce and Pd, and <f> the mean value in the crystal. However, superlattices in Pd-Ce alloys can be analyzed by electron microscopy, thanks to the high detectability of electron diffraction. In this work, we investigated modulated superstructures in alloys with 12.5 and 15.0 at.%Ce.Ingots of Pd-Ce alloys were prepared in an arc furnace under atmosphere of ultra high purity argon. The disc specimens cut out from the ingots were heat-treated in vacuum and electrothinned to electron transparency by a jet method.

Partition Coefficient Ratios and Tumour Perfusion Studied with 85mKr and 133Xe

1987 ◽  
Vol 26 (06) ◽  
pp. 253-257
Author(s):  
M. Mäntylä ◽  
J. Perkkiö ◽  
J. Heikkonen
Keyword(s):  
Partition Coefficient ◽  
Partition Coefficients ◽  
Regional Blood Flow ◽  
Blood Perfusion ◽  
Compartmental Analysis ◽  
Malignant Tumour ◽  
Mean Value ◽  
Perfusion Rate ◽  
Biological Variables ◽  
The Mean

The relative partition coefficients of krypton and xenon, and the regional blood flow in 27 superficial malignant tumour nodules in 22 patients with diagnosed tumours were measured using the 85mKr- and 133Xe-clearance method. In order to minimize the effect of biological variables on the measurements the radionuclides were injected simultaneously into the tumour. The distribution of the radiotracers was assumed to be in equilibrium at the beginning of the experiment. The blood perfusion was calculated by fitting a two-exponential function to the measuring points. The mean value of the perfusion rate calculated from the xenon results was 13 ± 10 ml/(100 g-min) [range 3 to 38 ml/(100 g-min)] and from the krypton results 19 ± 11 ml/(100 g-min) [range 5 to 45 ml/(100 g-min)]. These values were obtained, if the partition coefficients are equal to one. The equations obtained by using compartmental analysis were used for the calculation of the relative partition coefficient of krypton and xenon. The partition coefficient of krypton was found to be slightly smaller than that of xenon, which may be due to its smaller molecular weight.

Detection of Soluble Fibrin Monomer Complexes in Blood by Means of Protamine Sulphate Test

1968 ◽  
Vol 20 (01/02) ◽  
pp. 044-049 ◽  
Author(s):  
B Lipiński ◽  
K Worowski
Keyword(s):  
Human Subjects ◽  
Coronary Thrombosis ◽  
Mean Value ◽  
Healthy Human ◽  
Protamine Sulphate ◽  
Soluble Fibrin ◽  
Fibrin Monomer ◽  
Dog Plasma ◽  
The Mean ◽  
Precipitable Protein

SummaryIn the present paper described is a simple test for detecting soluble fibrin monomer complexes (SFMC) in blood. The test consists in mixing 1% protamine sulphate with diluted oxalated plasma or serum and reading the optical density at 6190 Å. In experiments with dog plasma, enriched with soluble fibrin complexes, it was shown that OD read in PS test is proportional to the amount of fibrin recovered from the precipitate. It was found that SFMC level in plasma increases in rabbits infused intravenously with thrombin and decreases after injection of plasmin with streptokinase. In both cases PS precipitable protein in serum is elevated indicating enhanced fibrinolysis. In healthy human subjects the mean value of OD readings in plasma and sera were found to be 0.30 and 0.11, while in patients with coronary thrombosis they are 0.64 and 0.05 respectively. The origin of SFMC in circulation under physiological and pathological conditions is discussed.

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