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.

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.

scholarly journals CELLULAR AUTOMATA MODELING OF IMPURITIES SEGREGATION IN THE MELT CRYSTALLIZATION PROCESS

2015 ◽  
pp. 216-226
Author(s):  
Liliya Shumylyak ◽  
Vladimir Zhikharevich ◽  
Sergey Ostapov
Keyword(s):  
Cellular Automata ◽  
Impurity Concentration ◽  
Concentration Distribution ◽  
Crystallization Process ◽  
Impurity Distribution ◽  
Melt Crystallization ◽  
Directional Crystallization ◽  
Cellular Automata Model ◽  
Basic Approach ◽  
Binary Solutions

The paper deals with the issue of the construction of a cellular automata model of the directional crystallization of binary solutions process. The basic approach and general methodology for the development of cellular automata models are examined. This allowed to obtain the spatial distribution of the studied characteristics. The paper gives an overview of available techniques on the problem, outlines the arguments in favor of a cellular automata method. The occurring processes of redistribution of impurities concentration and overcooling are emphasized. Previously known idea of a mechanism of the melt concentration overcooling is considered. The results of the calculation of impurity concentration distribution along the track of the sample during crystallization are presented. Dependence of the phase transition melting temperature on the value of the impurity concentration is determined on the basis of the calculated impurity distribution. Graphic examples of the varieties of uneven impurity distribution as a result of overcooling concentration of the melt are given.

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.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

Effect of Electrical Aging on the Trap Parameter of HVAC XLPE Cable Insulation

2014 ◽  
Vol 672-674 ◽  
pp. 769-772
Author(s):  
Wei Wei Li ◽  
Qiang Shi ◽  
Chi Wu
Keyword(s):  
Crystallization Process ◽  
Melt Crystallization ◽  
Depolarization Current ◽  
Cable Insulation ◽  
Trap Charge ◽  
Xlpe Cable ◽  
Trap Parameter ◽  
Start Up ◽  
Electrical Aging ◽  
Two Peaks

The effect of electrical aging on the trap parameter of HVAC XLPE cable insulation was investigated in this work. Thermally Stimulated Current (TSC) was used to measure depolarization current. The variation of trap parameter was calculated by means of start-up method based on the Gaussian fitting curve of TSC data. It was found that, the activation energy and the amount of trap charge obtained from TSC peak at 243K and 348K were increased after electrical aging, which may be benefit to characterize the degree of aging. The amount of trap charge in the two peaks increases as the increase of oxide dipole after electrical aging. And charge trapped described by the TSC peak at melting temperature increased after aging. It is considered that the increase of charge in the TSC peak can be attributed to the release of trap charge in the melt crystallization process, which corresponds to the α relaxation process in XLPE insulation.

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 Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

scholarly journals FRACTAL APPROACH TO MECHANICAL AND ELECTRICAL PROPERTIES OF GRAPHENE/SIC COMPOSITES

2021 ◽  
Vol 19 (2) ◽  
pp. 271
Author(s):  
Yu-Ting Zuo ◽  
Hong-Jun Liu
Keyword(s):  
Carbon Nanotubes ◽  
Electrical Properties ◽  
Fractal Theory ◽  
Bright Light ◽  
Fractal Dimensions ◽  
Mechanical Analysis ◽  
New Era ◽  
Fractal Approach ◽  
Mechanical And Electrical Properties ◽  
Sic Composites

Graphene and carbon nanotubes have a Steiner minimum tree structure, which endows them with extremely good mechanical and electronic properties. A modified Hall-Petch effect is proposed to reveal the enhanced mechanical strength of the SiC/graphene composites, and a fractal approach to its mechanical analysis is given.  Fractal laws for the electrical conductivity of graphene, carbon nanotubes and graphene/SiC composites are suggested using the two-scale fractal theory. The Steiner structure is considered as a cascade of a fractal pattern. The theoretical results show that the two-scale fractal dimensions and the graphene concentration play an important role in enhancing the mechanical and electrical properties of graphene/SiC composites. This paper sheds a bright light on a new era of the graphene-based materials.

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