Papers by Keyword: Self-Similarity

Abstract: Using a fractal analysis approach to study plant leaf venation and stem sections, we find that plants use very intelligent scaffolding strategies to tune mechanical strength of leaves and stems. Within plant organs, specialized types of tissues with different mechanical properties have evolved. Ideally, the biopolymers cellulose, hemicelluloses and lignin present in plant cell walls confer mechanical rigidity to plant tissues, but our studies reveal that the manner these biopolymers are distributed in the tissue matrix hold the key to the mechanical rigidity of the tissues. We have developed an algorithm to determine fractal dimension of the scaffolding matrix and the well-known box counting algorithm to calculate fractal dimensions of leaf venation in high resolution images of reticulate–veined leaves and optical microscope image of cellulose, hemicellulose, and lignin-stained cross sections of Turbina corymbosa. We found that in leaves with reticulate venation, veins form a scaffolding matrix imparting mechanical rigidity to leaves, and have a fractal dimension close to 1.0 for leaves which have less bending resistance, compared to fractal dimensions close to 1.7 for leaves which have higher bending resistance. Deriving this idea from plants, we use evaporation instability to develop scaffolding matrix with fractal dimensions higher than 1.5 in polymer films. This can form the basis of an efficient strategy to devise thin, stand-alone polymer films with tunable bending stiffness.

Abstract: Self-similar solution of two-dimensional problem of interaction between a plane longitudinal shock wave and free boundary of elastic half-space is considered. It is suggested that the intensity of this wave is constant. Feasible combinations of wave surfaces which may be generated in elastic medium as a result of such interaction are investigated. Choosing of unique physically admissible mode of deformation propagation from among mathematically possible wave patterns is related to shockwave evolutionary condition and the second law of thermodynamics.

Abstract: The investigation on the sensitivity of the flows to the initial conditions was carried with varying grid resolutions, turbulence models and perturbations. The Direct Numerical Simulation study of Pantano and Sarkar [1] was taken as the reference study and the computational model used in this study was built with a similar configuration of theirs except for the perturbations used. Important results were arrived pertaining to the effect of initial conditions on the turbulent properties and the turbulent structures of the flow.

Abstract: Cluster evolution tracking and dimensionality reduction have been studied intensively but separately in the time decayed and high dimensional stream data environment during the past decades. However, the interaction between the cluster evolution and the dimensionality reduction is the most common scenario in the time decayed stream data. Therefore, the dimensionality reduction should interact with cluster operation in the endless life cycle of stream data. In this paper, we first investigate the interaction between dimensionality reduction and cluster evolution in the high dimensional time decayed stream data. Then, we integrate the on-line sequential forward fractal dimensionality reduction technique with self-adaptive technique for cluster evolution tracking based on multi-fractal. Our performance experiments over a number of real and synthetic data sets illustrate the effectiveness and efficiency provided by our approach.

Abstract: In the present work it is revealed by modified Potts model simulations and theoretical considerations that self-similarity is a feature of junction controlled grain growth as it can be found in nanocrystalline materials. To this aim the influence of the grain junctions – boundary faces, triple lines and quadruple points – on grain growth is analyzed by attributing each type of junction an own specific energy and mobility yielding nine types of growth kinetics, each characterized by a self-similar scaling form of the growth law and a corresponding self-similar grain size distribution.

Abstract: Most researches regard the real traffic has self_similarity,so traditional model based passion or Markov can’t adapt to the real traffic.In order to resolve these problems,the estimation is used based on Hurst parameter to detect DoS attack,researching on the affect of Hurst paramerter change brought by DoS attack,By analyzing the 1998 DARPA intrusion detection evaluation dataset show that this method detect DoS attack,and is more reliable on the recognition of all kinds of DoS attack than any other method based on measure precision.

Abstract: Load forecasting based on fractal extrapolation is a very important method. However, traditional methods exists several disadvantages such as vertical scale factor difficult to calculate, low-precision, difficult to use. Therefore, a method is proposed combined with self-similarity theory and fractal extrapolation theory to solve the above problems. In this paper, the self-similarity of electrical load historical data is analyzed using multi-resolution wavelet firstly. Then use the Hurst parameter values to calculate vertical scaling factors based on the values of Hurst parameter and the other four parameters of Iterative Function Systems (IFS) affine transformation. At last the electrical load forecasting curve was generated by the iterations system. Considering the actual practical application, the algorithm was used to forecast electrical load based on fractal extrapolation. The computer simulation resulted that this algorithm has advantages of high-precision, less-sample demands, less-interpolation points and easy to use.

Abstract: Fractal model is applicable to describe the complex shapes of nature. Self-similarity is the basic feature of fractal. Anomaly detection of network traffic is the key to security and reliability of network. In this paper, a new algorithm for anomaly detection of network traffic based on fractal technology is proposed. It can achieve higher precision with less space and time complexity. Theoretical analysis and experiments show that the method can discover the abnormal network traffic accurately and efficiently.

Abstract: In allusion to the disadvantage of having to obtain the number of clusters in advance and the sensitivity to selecting initial clustering centers in the K-means algorithm, an improved K-means algorithm is proposed, that the cluster centers and the number of clusters are dynamically changing. The new algorithm determines the cluster centers by calculating the density of data points and shared nearest neighbor similarity, and controls the clustering categories by using the average shared nearest neighbor self-similarity.The experimental results of IRIS testing data set show that the algorithm can select the cluster cennters and can distinguish between different types of cluster efficiently.

Abstract: The objective of this paper is to consider the use of fractal geometry as a tool for the study of non-smooth and discontinuous objects for which Euclidean coordinate is not able to fully describe their shapes. We categorized the methods for computing fractal dimension with a discussion into that. We guide readers up to the point they can dig into the literature, but with more advanced methods that researchers are developing. Considerations show that is necessary to understand the numerous theoretical and experimental results concerning searching of the conformality before evaluating the fractal dimension to our own objects. We suggested examining a cloud of points of growth of fracture surface at laboratory using CATIA - Digitized Shape Editor software in order to reconstruct the surface (CAD model). Then, the author carried out measurement/calculation of more accurate fractal dimension which are introduced by [1] in the other paper as Part II.