The analysis of fracture profiles of soil using fractal geometry

Soil Research ◽  
1992 ◽  
Vol 30 (3) ◽  
pp. 291 ◽  
Author(s):  
IM Young ◽  
JW Crawford
Keyword(s):  
Statistical Method ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Significant Proportion ◽  
Roughness Parameter ◽  
Fractal Dimensions ◽  
Fracture Path ◽  
Apparent Length ◽  
Traditional Statistical Method

The fracture profiles of three soils (taken from Dexter and Horn 1988) are analysed according to their fractal dimensions D. D, which is a measure of how the 'apparent' length of a fracture path increases with decreasing ruler size, is found to be a good quantifier of the tortuousity of fracture paths. The fractal analysis is compared with a more traditional statistical method of analysing fracture profiles. It is shown that the latter method, unlike fractal analysis, can omit a significant proportion of a tortuous fracture path and therefore leads to an underestimate of any roughness parameter.

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.

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

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.

Fractal analysis and control of the competition model

2016 ◽  
Vol 09 (03) ◽  
pp. 1650045 ◽  
Author(s):  
Mianmian Zhang ◽  
Yongping Zhang
Keyword(s):  
Feedback Control ◽  
Mathematical Models ◽  
Fractal Analysis ◽  
Fractal Geometry ◽  
Julia Set ◽  
Julia Sets ◽  
Competition Model ◽  
Simulation Results ◽  
Population Competition ◽  
And Control

Lotka–Volterra population competition model plays an important role in mathematical models. In this paper, Julia set of the competition model is introduced by use of the ideas and methods of Julia set in fractal geometry. Then feedback control is taken on the Julia set of the model. And synchronization of two different Julia sets of the model with different parameters is discussed, which makes one Julia set change to be another. The simulation results show the efficacy of these methods.

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 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.

Moisture adsorption thermodynamics of wood from fractal-geometry approach

Holzforschung ◽  
2004 ◽  
Vol 58 (3) ◽  
pp. 274-279 ◽  
Author(s):  
J. Cao ◽  
D.P. Kamdem
Keyword(s):  
Thermodynamic Properties ◽  
Moisture Content ◽  
Adsorption Isotherms ◽  
Fractal Geometry ◽  
Moisture Sorption ◽  
Fractal Dimensions ◽  
Future Research ◽  
Differential Heat ◽  
Internal Surfaces ◽  
Differential Heat Of Adsorption

Abstract The fractal-geometry approach was used to calculate the thermodynamic properties of moisture sorption by wood from the adsorption isotherms in this study. The results were compared with those from an isosteric approach and a calorimetric approach. The adsorption isotherms of Southern yellow pine (Pinus spp.) were measured at 4, 15, 30, and 40°C to provide source data for the calculation of both fractal-geometry and isosteric approaches. The results show that the fractal dimensions of the internal surfaces of wood vary between 2.4 and 2.5. The curves of the differential heat of adsorption −∆H against moisture content from the fractal-geometry approach are similar to those from calorimetric measurements in previous research. The −∆H values from the isosteric approach increased with moisture content within a moisture content range up to 3%. And, at moisture contents higher than 3%, the −∆H values from this method are much higher than those from the fractal-geometry approach and calorimetric approach. As a result, the fractal-geometry approach is applicable to calculate the differential thermodynamic properties of moisture sorption by wood in future research.

ANN-Based Wheat Chlorophyll Density Estimation Using Canopy Hyperspectral Vegetation Indices

2012 ◽  
Vol 500 ◽  
pp. 243-249
Author(s):  
Da Cheng Wang ◽  
Luo Rui Sen ◽  
Ji Hua Wang ◽  
Cun Jun Li ◽  
Dong Yan Zhang ◽  
...  
Keyword(s):  
Neural Network ◽  
Statistical Method ◽  
Prediction Models ◽  
Vegetation Indices ◽  
Remote Sensing Data ◽  
Leaf Chlorophyll ◽  
The Neural Network ◽  
Spectral Vegetation Indices ◽  
Artificial Neural Network Ann ◽  
Traditional Statistical Method

Canopy leaf Chlorophyll Density is a key index for evaluating crop potential photosynthetic efficiency and nutritional stress. Leaf Chlorophyll Density estimate using canopy hyperspectral vegetation indices provides a rapid and non-destructive method to evaluate yield predictions. A systematic comparison of two approaches to estimate Chlorophyll Density using 6 spectral vegetation indices (VIs) was presented in this study. In this study, the traditional statistical method based on power regression analyses was compared to the emerging computationally powerful techniques based on artificial neural network (ANN). The regression models of TCARI 、SAVI 、MSAVI and RDVIgreen were found to be more suitable for predicting Chlorophyll Density when only traditional statistical method was used especially TCARI and RDVI. ANN method was more appropriate to develop prediction models. The comparisons between these two methods were based on analysis of the statistic parameters. Results obtained using Root Mean Square Error (RMSE) for ANNs were significantly lower than the traditional method. From this analysis it is concluded that the neural network is more robust to train and estimate crop Chlorophyll Density from remote sensing data.

Application of Fractal Geometry to Fracture Forensics, Research and Production

2006 ◽  
Vol 45 ◽  
pp. 1646-1651 ◽  
Author(s):  
J.J. Mecholsky Jr.
Keyword(s):  
Fractal Analysis ◽  
Fractal Geometry ◽  
Crack Size ◽  
Structural Parameter ◽  
New Materials ◽  
Scale Invariant ◽  
Prepared Material ◽  
Reasonable Approach ◽  
Self Similar ◽  
Production Problems

The fracture surface records past events that occur during the fracture process by leaving characteristic markings. The application of fractal geometry aids in the interpretation and understanding of these events. Quantitative fractographic analysis of brittle fracture surfaces shows that these characteristic markings are self-similar and scale invariant, thus implying that fractal analysis is a reasonable approach to analyzing these surfaces. The fractal dimensional increment, D*, is directly proportional to the fracture energy, γ, during fracture for many brittle materials, i.e., γ = ½ E a0 D* where E is the elastic modulus and a0 is a structural parameter. Also, D* is equal to the crack-size-to-mirror-radius ratio. Using this information can aid in identifying toughening mechanisms in new materials, distinguishing poorly fabricated from well prepared material and identifying stress at fracture for field failures. Examples of the application of fractal analysis in research, fracture forensics and solving production problems are discussed.

scholarly journals The Solutions to the Uncertainty Problem of Urban Fractal Dimension Calculation

Entropy ◽  
2019 ◽  
Vol 21 (5) ◽  
pp. 453 ◽  
Author(s):  
Chen
Keyword(s):  
Fractal Dimension ◽  
Spatial Analysis ◽  
Fractal Geometry ◽  
Fractal Dimensions ◽  
Dimension Estimation ◽  
Scale Free ◽  
Factors Influencing ◽  
Calculation Results ◽  
Fractal Patterns ◽  
Main Factors

Fractal geometry provides a powerful tool for scale-free spatial analysis of cities, but the fractal dimension calculation results always depend on methods and scopes of the study area. This phenomenon has been puzzling many researchers. This paper is devoted to discussing the problem of uncertainty of fractal dimension estimation and the potential solutions to it. Using regular fractals as archetypes, we can reveal the causes and effects of the diversity of fractal dimension estimation results by analogy. The main factors influencing fractal dimension values of cities include prefractal structure, multi-scaling fractal patterns, and self-affine fractal growth. The solution to the problem is to substitute the real fractal dimension values with comparable fractal dimensions. The main measures are as follows. First, select a proper method for a special fractal study. Second, define a proper study area for a city according to a study aim, or define comparable study areas for different cities. These suggestions may be helpful for the students who take interest in or have already participated in the studies of fractal cities.

Sign in / Sign up

Export Citation Format

Share Document