EXTENDED SELF SIMILARITY OF PASSIVE SCALAR IN RAYLEIGH-BNARD CONVECTION FLOW BASED ON WAVELET TRANSFORM

Wavetet transform was used to analyze the scaling law of temperature data (passive scalar) in Rayleigh-Bénard convection flow from two aspects. The first one was to utilize the method of extended self similarity, presented first by Benzi et al., to study the scaling exponent of temperature data. The obtained results show that the inertial range is much wider than that one determined directly from the conventional structure function, and find the obtained scaling exponent agrees well with the one obtained from the temperature data in an experiment of wind tunnel. The second one was that, by extending the formula which was proposed by A. Arneodo et al. for extracting the scaling exponent ζ(q) of velocity data to temperature data, a newly defined formula which is also based on wavelet transform, and can determine the scaling exponent ξ(q) of temperature data was proposed. The obtained results demonstrate that by using the method which is named as WTMM (wavelet transform maximum modulus) ξ(q) correctly can be extracted.

Study of Self-Similarity in Variable Bit Rate Video Sources

Variable bit rate(VBR)video will be the predominant application in the future's multimedia communication networks.Understanding the characteristics of VBR video is important for us to utilize network resources effectively.A brief description of MPEG 1 video sources is given.The essentials of self similarity and long range dependence are also presented.Furthermore,some methods of estimating Hurst parameter are described in details.We analyze an hour long MPEG 1 video trace,and the details of statistical results are discussed.The results highlight that the trace generated by MPEG 1 code has both the short range dependence and long range dependence structures.

Einstein’s Dark Energy via Similarity Equivalence, ‘tHooft Dimensional Regularization and Lie Symmetry Groups

Realizing the physical reality of ‘tHooft’s self similar and dimensionaly regularized fractal-like spacetime as well as being inspired by a note worthy anecdote involving the great mathematician of Alexandria, Pythagoras and the larger than life man of theoretical physics Einstein, we utilize some deep mathematical connections between equivalence classes of equivalence relations and E-infinity theory quotient space. We started from the basic principles of self similarity which came to prominence in science with the advent of the modern theory of nonlinear dynamical systems, deterministic chaos and fractals. This fundamental logico-mathematical thread related to partially ordered sets is then applied to show how the classical Newton’s kinetic energy E = 1/2mv2 leads to Einstein’s celebrated maximal energy equation E = mc2 and how in turn this can be dissected into the ordinary energy density E(O) = mc2/22 and the dark energy density E(D) = mc2(21/22) of the cosmos where m is the mass;v is the velocity and c is the speed of light. The important role of the exceptional Lie symmetry groups and ‘tHooft-Veltman-Wilson dimensional regularization in fractal spacetime played in the above is also highlighted. The author hopes that the unusual character of the analysis and presentation of the present work may be taken in a positive vein as seriously attempting to propose a different and new way of doing theoretical physics by treating number theory, set theory, group theory, experimental physics as well as conventional theoretical physics on the same footing and letting all these diverse tools lead us to the answer of fundamental questions without fear of being labelled in one way or another.

AN FFT-BASED SELF-SIMILAR TRAFFIC GENERATOR

The self similarity of the network traffic has great influences on the performance. But there are few analytical or even numerical solutions for such a model. So simulation becomes the most efficient method for research. Fractal Gaussian noise (FGN) is the most popularly used self similar model. This paper presented an FGN generator based on fast Fourier transform (FFT). The study indicates that this algorithm is fairly fast and accurate.

RF MEMS Based Reconfigurable Rectangular Slotted Self Similar Antenna

Wireless communication systems which require flexibility and reconfigurability in antenna systems faces main problems like antenna performance, size, weight and cost. A wide band Frequency Reconfigurable Rectangular Slotted Self Similar Antenna has been proposed in this paper. The rectangular slotted patch is repeated for two iterations at different scales and is separated by means of Radio Frequency Micro Electro Mechanical Systems (RF MEMS) switches in order to provide reconfigurability. The antenna can operate in three frequency bandsi.e. K-band, Ku-band and Ka-band by altering the states of RF MEMS switches. To avoid fringing effects and to improve antenna performance, quarter wavelength (λ/4) spacing is required between the antenna and the ground plane. However, a Reconfigurable Antenna requires different λ/4 spacing which is difficult to achieve using a common ground plane. So the Frequency Reconfigurable antenna is integrated with high impedance surface (HIS) like Electronic Band Gap (EBG) structures to suppress standing waves and surface waves with a unified profile thickness of 1.75 mm. The overall dimension of the proposed antenna along with RF MEMS Switch, feed element and HIS is about 8 mm × 8 mm × 1.75 mm. The simulated results of the proposed antenna reveal enhancement in antennas performance like Voltage Standing Wave Ratio (VSWR), Front to Back Ratio (FBR) and bandwidth when it is placed over HIS EBG. Also the radiation patterns of the proposed antenna when placed over EBG shows the suppression of side lobe and backward radiation.

Fractal analysis of canopy architectures of Acacia angustissima, Gliricidia sepium, and Leucaena collinsii for estimation of aboveground biomass in a short rotation forest in eastern Zambia

A study was conducted at Msekera Regional Agricultural Research Station in eastern Zambia to （1） describe canopy branching properties of Acacia angustissima, Gliricidia sepium and Leucaena collinsii in short rotation forests, （2） test the existence of self similarity from repeated iteration of a structural unit in tree canopies, （3） examined intra-specifie relationships between functional branching characteristics, and （4） determine whether allometric equations for relating aboveground tree biomass to fractal properties could accurately predict aboveground biomass. Measurements of basal diameter （Din0） at 10em aboveground and total height （H）, and aboveground biomass of 27 trees were taken, but only nine trees representative of variability of the stand and the three species were processed for functional branching analyses （FBA） of the shoot systems. For each species, fractal properties of three trees, includ- ing fractal dimension （Dfract）, bifurcation ratios （p） and proportionality ratios （q） of branching points were assessed. The slope of the linear re- gression ofp on proximal diameter was not significantly different （P 〈 0.01） from zero and hence the assumption that p is independent of scale, a pre-requisite for use of fraetal branching rules to describe a fraetal tree canopy, was fulfilled at branching orders with link diameters 〉1.5 cm. The proportionality ration q for branching patterns of all tree species was constant at all scales. The proportion of q values 〉0.9 （fq） was 0.8 for all species. Mean fraetal dimension （Df^ct） values （1.5-1.7） for all species showed that branching patterns had an increasing magnitude of intricacy. Since Dfraet values were 〉1.5, branching patterns within species were self similar. Basal diameter （D10）, proximal diameter and Dfraet described most of variations in aboveground biomass, suggesting that allometric equa- tions for relating aboveground tree biomass to fractal properties could accurately predict aboveground biomass. Thus, assessed Acacia, Gliri- cidia and Leucaena trees were fractals and their branching propertiescould be used to describe variability in size and aboveground biomass.

Implementation of Efficient Burst Assembly Algorithm with Traffic Prediction

This paper reports on the implementation of efficient burst assembly algorithms and traffic prediction. The ultimate goal is to propose a new burst assembly algorithm which is based on time-burst length （hybrid） threshold with traffic prediction to reduce burst assembly delay in OBS （Optical Burst Switching） networks. Research has shown that traffic always change from time to time, hence, any measure that is put in place should be able to adapt to such changes. With our implemented burst assembly algorithm, the traffic rate is predicted and the predicted rate is used to dynamically adjust the burst assembly length. This work further investigates the impact of the proposed algorithm on traffic self similarity.

Nonlinear morphological characteristics of debris flow in Dongcheng area of Helong,Jilin

Helong City is located in the northeastern Changbai Mountain with a poor geological environment,there often occur debris flows,collapses and landslides;especially debris flows restrict the local economic development. Based on fractal theory and the surveying data of 34 debris flows,the authors studied fractal feature of debris flow gully and its various situations of fractal dimensions in different observation scales. The nonlinear relation reveals the development of non-uniformity and self similarity of debris flow gully.

ON THE SELF-SIMILARITY OF A JET IN CROSSFLOW

The RNG k εturbulence model is adopted to investigate a turbulent round jet issuing into crossflow, with the Reynolds number at jet exit of Re=6000 and jet to crossflow velocity ratio of r=8. With the CFD code, FLUENT, the relations of dimensional analysis are successfully reproduced and the calculated coefficients agree well with the experimental measurements of Wong (1991) and Chu (1996). The investigations are then taken on the velocity, stream function and vorticity at the far field of the jet. It shows that at least within the covered range herein, the jet at the far field is self similar.

Research on Fault Tolerant Scheduling Algorithms of Web Cluster Based on Probability

Aiming at the soft real-lime fault tolerant demand of critical webapplications at present, such as E-commerce, a new fault tolerant scheduling algorithm based onprobability is proposed. To achieve fault tolerant scheduling, the primary/slave backuptechnology isapplied on the basis of task's self similar accessing characteristics, when the primary taskcompleted successfully, the resources allocated for the slave task are reclaimed, thus advancingsystem's efficiency. Experimental results demonstrate on the premise of satisfying system's certainfault tolerant probability, task's schcdulabi-listic probability is improved, especially, the highertask's self similar degree is, the more obviously the utilization of system resources is enhanced.

The Advances of the Research for Random Recursive Sets(Ⅰ)

We introduce the probability properties of random recursive sets systematically in this paper. The main contents include convergence, zero\|one law and support of distribution and self\|similarity.Hutchinson constructed a class of strictly self\|similar sets and got many important results on fractal properties.Graf investigated the fractal properties of a special statistically self\|similar set. We have investigated various self\|similar sets and their probability properties and fractal properties.\;

PRIMARY RESEARCH ON FRACTAL GEOMETRY OF MERIDIAN THEORY

In meridian theory of traditional Chinese medicine (TCM), the geometrical descriptions can be traced back to the remote ancient times in China, mainly in The Yellow Emperor’s Internal Classic (The Internal Classic in short). Euclid’s geometry, topology and other classic mathematics are all at their wit’s end to explain the high complexity and non clinear phenomenon of the meridian. In recent over 2000 years, the meridian phenomenon has been being the challenge to fundamental mathematics. Fractral geometry, founded by Mandelbrot (1975), is a branch of learning for investigating irregular geometrical curves. It has successfully solved some qualitative and quantitative problems about the topographical structure of molecular Brown’s movement curve and other irregular complicated curves and geometrical characters. The characteristics of geometrical topographical structure of meridian and its phenomenon belong to the research category of Fractal Geometry. The author of this paper believes that Fractal Geometry may provide a useful mathematical tool and a possible way for revealing the enigma of acup moxibustion meridian theory. The human body is of basic characters of Fractal Geometry in structure, while meridian is the expression form of Fractal structure of the human body. The basic Fractal geometrical characters of meridian are: self similarity, self affinity, symmetry, minute structure and self avoidance, which has been applied for thousands of years in clinic, such as “taking the acupoints on the right side of the body in cases of disorders appearing on the left side and vice versa". The basic characters of meridians are 1) symmetry of the 12 regular meridians on the bilateral sides of the body (symmetry); 2) similarity in characters and actions of acupoints of the same one meridian (self similarity); 3) taking acupoints on the lower part of the body when disorders occurring on the upper part of the body; and taking acupoints on the upper part of the body if disorders appearing on the lower part (self affinity); 4) micro acupuncture system including hand acupuncture, foot acupuncture, scalp acupuncture, auricular acupuncture and eye acupuncture (minute structure); and 5) systematical running of needling sensation (self avoidance).

Modeling and analysis of self-similar traffic source based on fractal-binomial-noise-driven Poisson process

This article explores the short-range dependence （SRD） and the long-range dependence （LRD） of self-similar traffic generated by the fractal-binomial-noise-driven Poisson process （FBNDP） model and lays emphasis on the former. By simulation, the SRD decaying trends with the increase of Hurst value and peak rate are obtained, respectively. After a comprehensive analysis of accuracy of self-similarity intensity, the optimal range of peak rate is determined by taking into account the time cost, the accuracy of self-similarity intensity, and the effect of SRD.

Design and Realization of Software for Guard Against DDoS Based on Self-Similar and Optimization Filter

This paper proposes a distributed denial-of-service attack detection method based on self similar and wavelet analysis. This method adopts an optimized transmission control protocol cookie technology for filter optimization in order to accurately detect and efficiently filter the traffic of distributed denial-of-service attack. This paper presents the design of our software, and describes all important algorithms of detection and filtering. Experimental results showed that our method has only a low delay to detect abnormal traffic of distributed denial-of-service attacks, and with a high percentage o f filtering.

An Equivalent Condition for the Self Similar Sets on the Real Line to Have Best Coverings

In this paper, an equivalent condition for the self similar sets on the real line to have best coverings is given. As a result, it partly gives answer to the conjecture which was posed by Zhou and Feng [Zhou, Z. L., Feng, L.： Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17（2）, 493-502 （2004）].

Elementary Waves of Two-dimensional Steady Isentropic Flow

A self similar solution is developed for two dimensional, steady, isentropic and inviscid flow. Some fundamental properties are clarified for centered simple waves R and shock waves S. The present paper provides further theoretical analysis to clarify the results obtained by Glimm et al. using theoretical and computational methods.