scholarly journals Fractal Analysis of Morphological Parameters of the Structure Materials

2019 ◽  
Author(s):  
Константин Макаренко ◽  
Konstantin Makarenko ◽  
Александр Никитин ◽  
Alexander Nikitin
Keyword(s):  
Elementary Particle ◽  
Fractal Analysis ◽  
Ductile Iron ◽  
Crystallization Process ◽  
Morphological Characteristics ◽  
Fractal Dimensions ◽  
Structural Materials ◽  
Morphological Parameters ◽  
Graphite Cell ◽  
Mesh Method

It is proposed to use the methods of fractal analysis to determine the morphological characteristics of the structure of structural materials. The questions of fractal aggregation of particles in the process of crystallization of ductile iron are considered, an austenitic-graphite cell is used as an elementary particle. Based on the mesh method, images of the microstructure of ductile irons are analysed and conclusions are drawn about the similarity of the nature of the process of their crystallization and fractal aggregation of particles. Based on the calculated fractal dimensions, a theory is proposed to explain the features of the crystallization process of ductile irons.

FRACTAL ANALYSIS FOR CRYSTAL LAYER STRUCTURE AND IMPURITY DISTRIBUTION RESEARCH OF MELT CRYSTALLIZATION

Fractals ◽  
2015 ◽  
Vol 23 (01) ◽  
pp. 1540002 ◽  
Author(s):  
DA-PENG LU ◽  
YI LIU ◽  
GAOHONG HE ◽  
XIAO-BIN JIANG
Keyword(s):  
Fractal Analysis ◽  
Crystallization Process ◽  
Layer Structure ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Impurity Distribution ◽  
Migration Behavior ◽  
Crystal Layer ◽  
Melt Crystallization ◽  
Porous Crystal

Fractal analysis for crystal layer structure formation and impurity distribution of melt crystallization was conducted in this paper. The fractal dimensions were introduced to analyze the structural property of the porous crystal layer and the melt phase migration behavior. The analysis results met the experimental results with a satisfactory agreement. The introduction of fractal theory was contributed to develop novel aspect on the separation effect evaluation on melt crystallization process.

Structure characterization of ground calcium carbonate flocs by fractal analysis and their effects on handsheet properties

TAPPI Journal ◽  
2013 ◽  
Vol 12 (3) ◽  
pp. 17-23 ◽  
Author(s):  
WANHEE IM ◽  
HAK LAE LEE ◽  
HYE JUNG YOUN ◽  
DONGIL SEO
Keyword(s):  
Fractal Analysis ◽  
Structural Characteristics ◽  
Fractal Dimensions ◽  
Strength Loss ◽  
Structure Characterization ◽  
Uniform Size ◽  
Cross Sectional ◽  
Floc Size ◽  
Mass Fractal ◽  
Handsheet Properties

Preflocculation of filler particles before their addition to pulp stock provides the most viable and practical solution to increase filler content while minimizing strength loss. The characteristics of filler flocs, such as floc size and structure, have a strong influence on preflocculation efficiency. The influence of flocculant systems on the structural characteristics of filler flocs was examined using a mass fractal analysis method. Mass fractal dimensions of filler flocs under high shear conditions were obtained using light diffraction spectroscopy for three different flocculants. A single polymer (C-PAM), a dual cationic polymer (p-DADMAC/C-PAM) and a C-PAM/micropolymer system were used as flocculants, and their effects on handsheet properties were investigated. The C-PAM/micropolymer system gave the greatest improvement in tensile index. The mass fractal analysis showed that this can be attributed to the formation of highly dense and spherical flocs by this flocculant. A cross-sectional analysis of the handsheets showed that filler flocs with more uniform size were formed when a C-PAM/micropolymer was used. The results suggest that a better understanding of the characteristics of preflocculated fillers and their influence on the properties of paper can be gained based on a fractal analysis.

Architectural Bias in Recurrent Neural Networks: Fractal Analysis

2003 ◽  
Vol 15 (8) ◽  
pp. 1931-1957 ◽  
Author(s):  
Peter Tiňo ◽  
Barbara Hammer
Keyword(s):  
Neural Networks ◽  
Fractal Analysis ◽  
Recurrent Neural Networks ◽  
Markov Models ◽  
Fractal Dimensions ◽  
Transition Diagram ◽  
Activation Patterns ◽  
Box Counting ◽  
Fractal Clusters ◽  
Finite State

We have recently shown that when initialized with “small” weights, recurrent neural networks (RNNs) with standard sigmoid-type activation functions are inherently biased toward Markov models; even prior to any training, RNN dynamics can be readily used to extract finite memory machines (Hammer & Tiňo, 2002; Tiňo, Čerňanský, &Beňušková, 2002a, 2002b). Following Christiansen and Chater (1999), we refer to this phenomenon as the architectural bias of RNNs. In this article, we extend our work on the architectural bias in RNNs by performing a rigorous fractal analysis of recurrent activation patterns. We assume the network is driven by sequences obtained by traversing an underlying finite-state transition diagram&a scenario that has been frequently considered in the past, for example, when studying RNN-based learning and implementation of regular grammars and finite-state transducers. We obtain lower and upper bounds on various types of fractal dimensions, such as box counting and Hausdorff dimensions. It turns out that not only can the recurrent activations inside RNNs with small initial weights be explored to build Markovian predictive models, but also the activations form fractal clusters, the dimension of which can be bounded by the scaled entropy of the underlying driving source. The scaling factors are fixed and are given by the RNN parameters.

scholarly journals PECULIARITIES OF THE RADIO SIGNALS AND HINDRANCES IN THE NAVIGATION SYSTEM OF THE REMOTE-PILOTED VEHICLES

2018 ◽  
Vol 8 (1) ◽  
pp. 40-43 ◽  
Author(s):  
Mykola Mykyjchuk ◽  
Volodymyr Markiv
Keyword(s):  
Control System ◽  
Fractal Analysis ◽  
Navigation System ◽  
Fractal Dimensions ◽  
Vehicle Control ◽  
Vital Role ◽  
Environment Research ◽  
Radio Signals

The article dwells upon the peculiarities of radio signals concerning the use of remote-piloted vehicles. It is highlighted that it is important take into consideration the fractal analysis of remote-piloted vehicles based on diverse fractal dimensions. The significance of remote-piloted vehicle control system investigation based on radio signals is presented. Also it is highlighted that there are many hindrances during the remote-piloted vehicle flight and it is important to take them into consideration and develop methods in order to omit them. Also the vital role of remote-piloted vehicles in different spheres of life, for example, in environment research is depicted.

Morphological Characteristics and Physical & Mechanical Properties of seeds of small-seeded crops

2020 ◽  
pp. 27-35
Author(s):  
Elchyn Aliiev ◽  
◽  
Christina Lupko ◽  
Keyword(s):  
Mechanical Properties ◽  
Coefficient Of Friction ◽  
Morphological Characteristics ◽  
Physical And Mechanical Properties ◽  
Specific Weight ◽  
Test Material ◽  
Effective Diameter ◽  
Morphological Parameters ◽  
Separation Processes ◽  
The Coefficient Of Friction

To create a database and systematize the seeds of samples of small-seeded crops, it is necessary to determine the patterns of influence of morphological parameters on their physical and mechanical properties. The development of the latest technologies and technical devices for cleaning and separation is possible due to the understanding of the characteristic morphological parameters for each of the small-seeded crops. The aim of the research is to determine the physical and mechanical properties of the seed material of small-seeded crops (mustard, flax, ryegrass, rapeseed), necessary to increase the efficiency of their cleaning and separation processes. To achieve this goal, a plan of experimental research was developed, which provided for the determination of physical and mechanical parameters of seeds of small-seeded crops, namely: indicators that characterize the flowability of seeds (angle of natural bias); frictional properties of seeds (static coefficient of friction); porosity (density) and density; size and mass characteristics of seeds (length, width, thickness, effective diameter, weight of 1000 seeds). It is established that the physical and mechanical properties of seeds of small-seeded crops are greatly influenced by its humidity. With increasing humidity, the performance of the test material increases. This is due to the fact that with increasing humidity, the shape of the seed almost turns into a spherical, which, in turn, leads to an increase in the curvature of the surface and reduce the points of contact between the seeds. As a result, the angle of natural inclination increases. The coefficient of friction of seeds of small-seeded crops depends on the roughness of the friction surface and decreases with increasing humidity. This is due to the fact that with increasing humidity decreases the forces of molecular attraction of the seed coat to the surface of the material. Seed density increases with increasing humidity. From this we can conclude that the absorption of moisture by the investigated material increases the total weight of the seed, and as a result - increases its specific weight.

scholarly journals Postnatal Development of the Retina in Rats Exposed to Hyperoxia: A Fractal Analysis

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Anne Claudia Ştefănuţ ◽  
Ştefan Ţălu ◽  
Viorel Miclăuş ◽  
Adriana Mureşan ◽  
Remus Moldovan ◽  
...  
Keyword(s):  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Control Group ◽  
Newborn Rats ◽  
Vascular Abnormalities ◽  
Retinal Layers ◽  
Fractal Analyses ◽  
Group 10 ◽  
Box Counting Method ◽  
Experimental Group

Purpose. The aim of this study was to investigate and quantify changes in the newborn rats retinal layers during the hyperoxia (80% O2) exposure using fractal analysis. Materials and Methods. This study was conducted on two groups of 20 newborn rats: a control (normal) group (10 rats) and an experimental group (10 rats). The control group was composed of 10 newborn rats, which were placed at 12 hours after birth, in a pediatric incubator, together with their mother, in conditions of normoxia for 21 days. The experimental group consisted of 10 newborn rats, which were placed at 12 hours after birth, in a pediatric incubator with their mother, in conditions of normoxia for 7 days, then 7 days of hyperoxia (80% O2) for 22.5 hours/day, and then 7 days in conditions of normoxia. Slaughtering of the rats was performed on day 21 and the eye globes were harvested in order to perform histopathological examinations. The fractal analyses of the retinal digital images were performed using the fractal analysis software Image J, and the fractal dimensions were calculated using the standard box-counting method. Results. Microscopic examination revealed a normal development of the retina in the control group. In the experimental group, all the animals exposed to hyperoxia revealed both structural and vascular abnormalities on entire retina. Conclusions. The results showed that the fractal analysis is a valuable tool to quantify histoarchitectural changes in the newborn rats retinal layers during the hyperoxia (80% O2).

Cake porosity analysis using 1D–3D fractal dimensions in coagulation–microfiltration of NOM

2015 ◽  
Vol 71 (5) ◽  
pp. 740-746
Author(s):  
G. S. Raspati ◽  
T. O. Leiknes
Keyword(s):  
Natural Organic Matter ◽  
Fractal Analysis ◽  
Membrane Fouling ◽  
Fractal Dimensions ◽  
The Other ◽  
Transmembrane Pressure ◽  
Process Conditions ◽  
Iron Based ◽  
Cake Porosity ◽  
Porosity Analysis

Fouling during coagulation–ceramic microfiltration of natural organic matter was investigated. Two process configurations (inline coagulation (IC) and tank coagulation (TC)) and two process conditions (types of coagulants–aluminum-based PAX and iron-based PIX–and G-values) were studied. The rate of irreversible fouling corresponding to the increase of initial transmembrane pressure after backwash of IC-PAX was lowest followed by TC-PAX and TC-PIX, while the performance of IC-PIX was found worst. The 1D and 2D fractal analysis revealed that flocs from IC were morphologically different from those of TC, leading to different filtration characteristics. The 3D fractal analysis revealed two groups of morphologically similar flocs: one led to successful filtration experiments, whereas the other led to unsuccessful ones. Cake porosity was found dependent on the floc morphology. Thus, such an approach was found complementary with fouling analysis by means of a membrane fouling model and minimization of fouling phenomenon was achieved by combining the two approaches.

Fractals in physical geography

1996 ◽  
Vol 20 (2) ◽  
pp. 178-191 ◽  
Author(s):  
Jay Gao ◽  
Zong-guo Xia
Keyword(s):  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Great Depth ◽  
Physical Geography ◽  
Topographic Features ◽  
Straight Line ◽  
Mathematical Algorithms ◽  
Determination Methods ◽  
Landform Regions ◽  
Geomorphic Processes

Since the fractal concept was introduced to measuring coastline length over three decades ago, fractal analysis has been prolifically applied to many topographic studies. A number of mathematical algorithms are now available to determine the fractal dimension for both linear and areal features. These determination methods require one or more straight-line segments to fit the Richardson's plot. A close examination of the literature shows that not all topographic features are fractal at all scales studied. While the multifractal nature of some geographical phenomena has been explored in great depth, it is not completely understood why some terrains are better modelled with fractal geometry than others. Fractal analysis has been successfully used to measure and characterize irregular linear features such as coastlines and shorelines, to describe and characterize landforms, and to delineate landform regions statistically. Fractal analysis can also be used to produce terrain simulations with a known dimension against which hypotheses can be tested. These studies fail to link fractal dimensions to the underlying geomorphic processes. The failure stems from the fact that there is no one-to-one relationship between geomorphic processes and the landforms they shape.

scholarly journals FRACTAL ANALYSIS OF TRABECULAR BONE: A STANDARDISED METHODOLOGY

2011 ◽  
Vol 19 (1) ◽  
pp. 45 ◽  
Author(s):  
Ian Parkinson ◽  
Nick Fazzalari
Keyword(s):  
Fractal Dimension ◽  
Trabecular Bone ◽  
Fractal Analysis ◽  
Fractal Dimensions ◽  
Box Counting ◽  
Cell Tissue ◽  
Image Analyser ◽  
Model Independent ◽  
Box Counting Method ◽  
Image Orientation

A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge). The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.

scholarly journals Correlation between cardiac magnetic resonance feature tracking derived left ventricular strain and morphological characteristics of non-ischemic dilated cardiomyopathy at baseline and follow-up

2021 ◽  
Vol 42 (Supplement_1) ◽  
Author(s):  
E Pozo Osinalde ◽  
J Urmeneta Ulloa ◽  
J L Rodriguez Hernandez ◽  
L Perez De Isla ◽  
H Martinez Fernandez ◽  
...  
Keyword(s):  
Cardiac Magnetic Resonance ◽  
Magnetic Resonance ◽  
Feature Tracking ◽  
Systolic Function ◽  
Morphological Characteristics ◽  
Strain Analysis ◽  
Left Ventricular ◽  
Morphological Parameters ◽  
Non Ischemic Dilated Cardiomyopathy

Abstract Background Left ventricular (LV) strain from echocardiography is a known useful predictor of LVEF recovery in non-ischemic dilated cardiomyopathy (NIDCM). More recently, feature tracking (FT) has allowed LV myocardial deformation analysis using conventional cardiac magnetic resonance (CMR) cine sequences. Purpose Our aim is to establish the correlation between LV strain values from CMR-FT at diagnosis and morphological parameters at baseline and during follow-up. Methods Consecutive patients with NIDCM who underwent CMR were retrospectively collected. All the studies were performed in a 1.5 Tesla magnet following a standard acquisition protocol of conventional SSFP cine sequences in long and short axis. Global longitudinal, circumferential and radial strain (GLS, GCS and GRS, respectively) were obtained with a dedicated FT software. Correlation with CMR morphological parameters at baseline were evaluated. Likewise, in the cases with follow-up echocardiogram association between FT LV strain and evolution of morphofunctional variables was explored. Results CMR-FT strain analysis was performed in 98 patients (age 68±13 years, 72% males) with NIDCM. They showed severe LV dilatation (LVEDVi= 133.6±33.4 mL/m2) and systolic dysfunction (LVEF= 29.5±9.6%) at baseline. Myocardial fibrosis was detected in 38.8% of the patients with late gadolium enhancement (LGE) sequence. All the basal CMR morphological characteristics were significantly correlated with FT strain analysis (Table), even more markedly for GCS. However, there was no association of baseline morphofunctional parameters with LGE. An echocardiogram was performed in 85.7% of the patients during the follow-up (2.4 [1.8–3.4] years), with an LVEF &gt;50% in the 25.5% of the cases. These patients with preserved LVEF in the evolution showed better GCS (−9 vs −7.1%; p=0.019) at baseline, with no differences in the other FT LV strain parameters. Despite less fibrosis in LGE (16.1% vs 37.7%; p=0.037), none of the baseline morphofunctional CMR parameters (LVEF, LVEDVi...) were associated with systolic function restoration. In multivariate analysis, GCS was the only independent predictor (OR 1.16; p=0.045) of LVEF recovery among imaging variables. Conclusions All the FT derived LV strain values were correlated with the degree of basal morphofunctional involvement in NIDCM. Furthermore, GCS emerged as an independent imaging predictor of LV systolic function restoration in our series. FUNDunding Acknowledgement Type of funding sources: None. Table 1. Correlation between myocardial deformation values by feature tracking and morphofunctional variables in basal CMR.

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