Quantitative characterization of kaolinite dispersibility in styrene–butadiene rubber composites by fractal dimension

A fractal method was introduced to quantitatively characterize the dispersibility of modified kaolinite (MK) and precipitated silica (PS) in styrene–butadiene rubber (SBR) matrix based on the lower magnification transmission electron microscopic images. The fractal dimension (FD) is greater, and the dispersion is worse. The fractal results showed that the dispersibility of MK in the latex blending sample is better than that in the mill blending samples. With the increase of kaolinite content, the FD increases from 1.713 to 1.800, and the dispersibility of kaolinite gradually decreases. There is a negative correlation between the dispersibility and loading content. With the decrease of MK and increase of PS, the FD significantly decreases from 1.735 to 1.496 and the dipersibility of kaolinite remarkably increases. The hybridization can improve the dispersibility of fillers in polymer matrix. The FD can be used to quantitatively characterize the aggregation and dispersion of kaolinite sheets in rubber matrix.

Use of running fractal dimension for the analysis of changing patterns in electroencephalograms

Running fractal dimensions were measured on four channels of an electroencephalogram (EEG) recorded from a normal volunteer. The changes in the background activity due to eye closure were clearly differentiated by the fractal method. The compressed spectral array (CSA) and the running fractal dimensions of the EEG showed corresponding changes with respect to change in the background activity. The fractal method was also successful in detecting low amplitude spikes and the changes in the patterns in the EEG. The effects of different window lengths and shifts on the running fractal dimension have also been studied. The utility of fractal method for EEG data compression is highlighted.

Análise espaço temporal da dimensão fractal de matas ciliares na alta bacia do rio Passa Cinco - centro Leste do Estado de São Paulo

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Predicting flow and transport in highly heterogeneous alluvial aquifers

Successful prediction of groundwater flow and solute transport through highly heterogeneous aquifers has remained elusive due to the limitations of methods to characterize hydraulic conductivity (K) and generate realistic stochastic fields from such data. As a result, many studies have suggested that the classical advective-dispersive equation (ADE) cannot reproduce such transport behavior. Here we demonstrate that when high-resolution K data are used with a fractal stochastic method that produces K fields with adequate connectivity, the classical ADE can accurately predict solute transport at the macrodispersion experiment site in Mississippi. This development provides great promise to accurately predict contaminant plume migration, design more effective remediation schemes, and reduce environmental risks. Key Points Non-Gaussian transport behavior at the MADE site is unraveledADE can reproduce tracer transport in heterogeneous aquifers with no calibrationNew fractal method generates heterogeneous K fields with adequate connectivity

石油二次运移的物理与数值模拟实验及其应用

Facing the problems met in studies on predominant hydrocarbon migration pathways, experiments and numerical simulating were done in this thesis work to discuss the migration mechanisms. The aim is to analyze quantitatively the pathway pattern in basin scale and to estimate the hydrocarbon loss on the pathway that offer useful information for confirming the potential hydrocarbon accumulation. Based on our understandings on hydrocarbon migration and the fluid dynamic theory, a series of migration experiments were designed to observe the phenomena where kerosene is used as draining phase driven only by buoyancy force that expulses pore water. These experiments allow to study the formation of migration pathways, the distribution of non-wetting oil along these pathways, and the re-utilizing of previously existing pathways marked by residual traces etc. The types of pattern for migration pathways may be characterized by a phase diagram using two dimensionless numbers: the capillary number and the Bond number. The NMR technique is used to measure the average saturation of residual oil within the pathways. Based our experiment works and percolation concept, a numerical simulation model were proposed and realized. This model is therefore called as BP (Buoyancy Percolation) simulator, since buoyancy is taken as the main driving force in hydrocarbon migration. To make sure that BP model is applicable to simulate the process of oil secondary migration, the experimental phenomena are compared with those simulated with BP model by fractal method, and the result is positive. After then, we use BP simulator to simulate the process of migration of oil in the porous media saturated with water at different scale. And the results seem similar to those cited in literatures. In addition, our software is applied in Paris basin to predict the pathway of hydrocarbon migration happened in the Middle Jurassic reservoirs. It is found that the results obtained with our BP model are generally agree with Hindle (1997) and Bekeles'(1999), but our simulated migration pathway pattern and migration direction seem more reasonable than theirs.

胜利油田低渗透砂岩油藏非均质地质建模

Guided by geological theories, the author analyzed factual informations and applied advanced technologies including logging reinterpretation, predicting of fractal-based fracture network system and stochastic modeling to the low permeable sandstone reservoirs in Shengli oilfield. A new technology suitable for precious geological research and 3D heterogeneity modeling was formed through studies of strata precious correlation, relation between tectonic evolution and fractural distribution, the control and modification of reservoirs diagenesis, logging interpretation mathematical model, reservoir heterogeneity, and so on. The main research achievements are as follows: (1) Proposed four categories of low permeable reservoirs, which were preferable, general, unusual and super low permeable reservoir, respectively; (2) Discussed ten geological features of the low permeable reservoirs in Shengli area; (3) Classified turbidite fan of Es_3 member of the Area 3 in Bonan oilfield into nine types of lithological facies, and established the facies sequences and patterns; (4) Recognized that the main diagenesis were compaction, cementation and dissolution, among which the percent compaction was up to 50%~90%; (5) Divided the pore space in ES_3 member reservoir into secondary pores with dissolved carbonate cement and residual intergranular pores strongly compacted and cemented; (6) Established logging interpretation mathematical model guided by facies- control modeling theory; (7) Predicted the fracture distribution in barriers using fractal method; (8) Constructed reservoir structural model by deterministic method and the 3D model of reservoir parameters by stochastic method; (9) Applied permeability magnitudes and directions to describe the fractures' effect on fluid flow, and presented four different fractural configurations and their influence on permeability; (10) Developed 3D modeling technology for the low permeable sandstone reservoirs. The research provided reliable geological foundation for the establishment and modification of development plans in low permeable sandstone reservoirs, improved the development effect and produced more reserves, which provided technical support for the stable and sustained development of Shengli Oilfield.

DNA Sequence Representation methods

DNA sequence representation methods are used to denote a gene structure effectively and help in similarities/dissimilarities analysis of coding sequences. Many different kinds of representations have been proposed in the literature. They can be broadly classified into Numerical, Graphical, Geometrical and Hybrid representation methods. DNA structure and function analysis are made easy with graphical and geometrical representation methods since it gives visual representation of a DNA structure. In numerical method, numerical values are assigned to a sequence and digital signal processing methods are used to analyze the sequence. Hybrid approaches are also reported in the literature to analyze DNA sequences. This paper reviews the latest developments in DNA Sequence representation methods. We also present a taxonomy of various methods. A comparison of these methods where ever possible is also done

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

A quasi-likelihood method for fractal-dimension estimation

We propose a simple method of constructing quasi-likelihood functions for dependent data based on conditional-mean-variance relationships, and apply the method to estimating the fractal dimension from box-counting data. Simulation studies were carried out to compare this method with the traditional methods. We also applied this technique to real data from fishing grounds in the Gulf of Carpentaria, Australia

Fractal boundaries of basin of attraction of Newton-Raphson method in helicopter trim

A key problem in helicopter aeroelastic analysis is the enormous computational time required for a numerical solution of the nonlinear system of algebraic equations required for trim, particularly when free wake models are used. Trim requires calculation of the main rotor and tail rotor controls and the vehicle attitude which leads to the six steady forces and moments about the helicopter center of gravity to be zero. An appropriate initial estimate of the trim state is needed for successful helicopter trim. This study aims to determine the control inputs that can have considerable effect on the convergence of trim solution in the aeroelastic analysis of helicopter rotors by investigating the basin of attraction of the nonlinear equations (set of initial guess points from which the nonlinear equations converge). It is illustrated that the three main rotor pitch controls of collective pitch, longitudinal cyclic pitch and lateral cyclic pitch have a significant contribution to the convergence of the trim solution. Trajectories of the Newton iterates are shown and some ideas for accelerating the convergence of a trim solution in the aeroelastic analysis of helicopters are proposed. It is found that the basins of attraction can have fractal boundaries. (C) 2010 Elsevier Ltd. All rights reserved.

Computing Fractal Dimension of Signals using Multiresolution Box-counting Method

In this paper, we have developed a method to compute fractal dimension (FD) of discrete time signals, in the time domain, by modifying the box-counting method. The size of the box is dependent on the sampling frequency of the signal. The number of boxes required to completely cover the signal are obtained at multiple time resolutions. The time resolutions are made coarse by decimating the signal. The loglog plot of total number of boxes required to cover the curve versus size of the box used appears to be a straight line, whose slope is taken as an estimate of FD of the signal. The results are provided to demonstrate the performance of the proposed method using parametric fractal signals. The estimation accuracy of the method is compared with that of Katz, Sevcik, and Higuchi methods. In ddition, some properties of the FD are discussed.

Fractal dimension method for delamination detection in composite beams

A new delaminated composite beam element is formulated for Timoshenko as well as Euler-Bernoulli beam models. Shape functions are derived from Timoshenko functions; this provides a unified formulation for slender to moderately deep beam analyses. The element is simple and easy to implement, results are on par with those from free mode delamination models. Katz fractal dimension method is applied on the mode shapes obtained from finite element models, to detect the delamination in the beam. The effect of finite element size on fractal dimension method of delamination detection is quantified.

A hybrid fractal video compression method

Fractal image compression is a relatively recent image compression method. Its extension to a sequence of motion images is important in video compression applications. There are two basic fractal compression methods, namely the cube-based and the frame-based methods, being commonly used in the industry. However there are advantages and disadvantages in both methods. This paper proposes a hybrid algorithm highlighting the advantages of the two methods in order to produce a good compression algorithm for video industry. Experimental results show the hybrid algorithm improves the compression ratio and the quality of decompressed images.

Adaptive partition and hybrid method in fractal video compression

Fractal image compression is a relatively recent image compression method, which is simple to use and often leads to a high compression ratio. These advantages make it suitable for the situation of a single encoding and many decoding, as required in video on demand, archive compression, etc. There are two fundamental fractal compression methods, namely, the cube-based and the frame-based methods, being commonly studied. However, there are advantages and disadvantages in both methods. This paper gives an extension of the fundamental compression methods based on the concept of adaptive partition. Experimental results show that the algorithms based on adaptive partition may obtain a much higher compression ratio compared to algorithms based on fixed partition while maintaining the quality of decompressed images.