The effect of gravity on self-similarity of Worthington jet after water entry of a two-dimensional wedge

The effect of gravity on the self-similarity of jet shape at late stage of Worthington jet development is investigated by experiment in the study.In addition,the particle image velocimetry(PIV)method is introduced to analyze the development of flow field.There is a linear scaling regarding the axial velocity of the jet and the scaling coefficient increases with the Froude number.

Self-similarity of complex networks under centrality-based node removal strategy

Real-world networks exhibit complex topological interactions that pose a significant computational challenge to analyses of such networks.Due to limited resources,there is an urgent need to develop dimensionality reduction techniques that can significantly reduce the structural complexity of initial large-scale networks.In this paper,we propose a subgraph extraction method based on the node centrality measure to reduce the size of the initial network topology.Specifically,nodes with smaller centrality value are removed from the initial network to obtain a subgraph with a smaller size.Our results demonstrate that various real-world networks,including power grids,technology,transportation,biology,social,and language networks,exhibit self-similarity behavior during the reduction process.The present results reveal the selfsimilarity and scale invariance of real-world networks from a different perspective and also provide an effective guide for simplifying the topology of large-scale networks.

The Golden Ratio Theorem: A Framework for Interchangeability and Self-Similarity in Complex Systems

The Golden Ratio Theorem, deeply rooted in fractal mathematics, presents a pioneering perspective on deciphering complex systems. It draws a profound connection between the principles of interchangeability, self-similarity, and the mathematical elegance of the Golden Ratio. This research unravels a unique methodological paradigm, emphasizing the omnipresence of the Golden Ratio in shaping system dynamics. The novelty of this study stems from its detailed exposition of self-similarity and interchangeability, transforming them from mere abstract notions into actionable, concrete insights. By highlighting the fractal nature of the Golden Ratio, the implications of these revelations become far-reaching, heralding new avenues for both theoretical advancements and pragmatic applications across a spectrum of scientific disciplines.

An Intrusion Alarming System Based on Self-Similarity of Network Traffic

Intrusion detection system ean make effective alarm for illegality of networkusers, which is absolutely necessarily and important to build security environment of communicationbase service According to the principle that the number of network traffic can affect the degree ofself-similar traffic, the paper investigates the variety of self-similarity resulted fromunconventional network traffic. A network traffic model based on normal behaviors of user isproposed and the Hursl parameter of this model can be calculated. By comparing the Hurst parameterof normal traffic and the self-similar parameter, we ean judge whether the network is normal or notand alarm in time.

On the Self-Similarity in Biological Processes

We show that the processes described by Avrami functions are self-similar. A comparative function characterizes a self-similar process by a certain Avrami exponent. We define the self-similar categories of some well-known biological processes. The method to determine the Avrami exponent by choosing the comparative function is demonstrated on the diffusion model of the growth of nuclei. We generalize the results.

Measurement of Characteristic Self-Similarity and Self-Diversity for Complex Mechanical Systems

Based on similarity science and complex system theory,a new concept of characteristic self-diversity and corre- sponding relations between self-similarity and self-diversity for complex mechanical systems are presented in this paper.Methods of system self-similarity and self-diversity measure between main system and sub-system are studied.Numerical calculations show that the characteristic self-similarity and self-diversity measure method is validity.A new theory and method of self-similarity and self- diversity measure for complexity mechanical system is presented.

A MODEL OF RANDOM PARTICLES CONSTRUCTED BY THE PRINCIPLE OF SELF-SIMILARITY AND ITS APPLICATION

A model of random particles constructed by the operation of self-similarity in fractalgeometry is presented.The correlation function of the number density has been obtained andcan be used conveniently in theoretical study and computer simulation for wave interaction withrandom media.As an example,this model has been applied to calculate analytically the rangedependence of volume scattering in radar echoes.The result agrees with that of Rastogi andScheucher’s simulation.

Self-similarity of spanwise rotational motions’population trends in decelerating open-channel flow

Decelerating open-channel flow is a type of flow that gradually moves forward with decreasing velocity and increasing water depth.Although all flow parameters change along the streamwise direction,previous studies have revealed that these parameters’vertical distributions at different sections can be universally described with a single profile when being nondimensionalised by appropriate scales.This study focuses on the population trends of spanwise rotational motions at various sections along the main flow direction by particle imaging velocimetry(PIV)measurement.The wall-normal population distributions of density,radius,swirling strength,and convection velocity of the prograde and retrograde motions show similar trends in uniform open-channel flows.The dimensionless representation is invariant along the main flow direction.This study’s results indicate the self-similar characteristic of population trends of spanwise rotational motions prevails in decelerating open-channel flow.

An Enhanced Nonlocal Self-Similarity Technique for Fabric Defect Detection

Fabric defect detection has been an indispensable and important link in fabric production,many studies on the development of vision based automated inspection techniques have been reported.The main drawback of existing methods is that they can only inspect a particular type of fabric pattern in controlled environment.Recently,nonlocal self-similarity(NSS)based method is used for fabric defect detection.This method achieves good defect detection performance for small defects with uneven illumination,the disadvantage of NNS based method is poor for detecting linear defects.Based on this reason,we improve NSS based defect detection method by introducing a gray density function,namely an enhanced NSS(ENSS)based defect detection method.Meanwhile,mean filter is applied to smooth images and suppress noise.Experimental results prove the validity and feasibility of the proposed NLRA algorithm.

Another Important Parameter’s Research on Estimating Self-Similarity

It is convincingly demonstrated by numerous studies that the self-similarity of modern multimedia network traffic is presented by Hurst parameter (H). The specific performance is that the similar degree is higher along with the increase of H when H is between 0.5 and 1. However, it is doubtable that whether the complicated process of self-similarity can be described comprehensively by the parameter H only. Therefore, another important parameter cf has been proposed based on the discrete wavelet decomposition in this paper. The significance of the parameters is provided and the performance of the self-similarity process is described better.

On Self-Similarity of Top Production at Tevatron

This paper presents the results of analysis of the D? 1.0 fb-1 data on top-quark differential cross section measurements at the Fermilab Tevatron collider at √s= 1960 GeV in the framework of z-scaling approach. The flavor independence of scaling function Ψ(z)observed in pp and pp interactions over a wide collision energy range √s= 19-1960 GeV has been verified. This property of Ψ(z) was found for different hadrons – from π-mesons up to Υ particles. The flavor independence of Ψ(z) is used as indication on self-similarity of the top-quark production. A tendency to saturation of Ψ(z) at low z for top-quark production has been confirmed. Momentum fraction x1 of the incoming (anti)protons as a function of the scaled transverse momentum pT/m and masses of heavy mesons is studied. We anticipate that the data on low- and high-pT inclusive spectra of the top-quark production at the Tevatron and LHC energies could be of interest to verify self-similarity over a wide range of masses and different flavor content of produced particles.

Density-based ship detection in SAR images:Extension to a self-similarity perspective

Nonlocal self-similarity is an important property of Synthetic Aperture Radar(SAR)images to characterize the repetitiveness of features embodied by SAR images within nonlocal areas and has been used for enhancement of SAR images.Existing SAR ship detectors often independently handle small sub-images cropped from a large marine SAR image and do not exploit the nonlocal self-similarity therein.In this paper,we propose a new ship detector from the perspective of nonlocal self-similarity in SAR images to improve the ship detection performance,basically including three stages:prescreening,intra-cue calculation,and inter-cue calculation.In the prescreening stage,we design a new Histogram-based Density(HD)feature to rapidly select candidate sub-images potentially containing ship targets from a large SAR image.In the intra-cue calculation stage,target cues within a single candidate sub-image are extracted.In the inter-cue calculation stage,thanks to the nonlocal self-similarity among different candidate sub-images in terms of density features,we innovatively extract a weighted superpixel-HD map to obtain accumulated intracues across all the candidate sub-images.Finally,for each candidate sub-image,we fuse its inter-cue and intra-cue to obtain final detection results.Experimental results based on real SAR images show that our newly proposed method provides a better target-to-clutter contrast and ship detection performance than those of other state-of-the-art detection approaches.

Spatiotemporal self-similar solutions for the nonautonomous (3+1)-dimensional cubic-quintic Gross-Pitaevskii equation

With the help of similarity transformation, we obtain analytical spatiotemporal self-similar solutions of the nonautonomous （3＋1）-dimensional cubic-quintic Gross-Pitaevskii equation with time-dependent diffraction, nonlinearity, harmonic potential and gain or loss when two constraints are satisfied. These constraints between the system parameters hint that self-similar solutions form and transmit stably without the distortion of shape based on the exact balance between the diffraction, nonlinearity and the gain/loss. Based on these analytical results, we investigate the dynamic behaviours in a periodic distributed amplification system.

THE REGULARITY OF RANDOM GRAPH DIRECTED SELF-SIMILAR SETS

A set in Rd is called regular if its Hausdorff dimension coincides with its upper box counting dimension. It is proved that a random graph-directed self-similar set is regular a.e..

MULTIRESOLUTION ANALYSIS, SELF-SIMILAR TILINGS AND HAAR WAVELETS ON THE HEISENBERG GROUP

In this article, the properties of multiresolution analysis and self-similar tilings on the Heisenberg group are studied. Moreover, we establish a theory to construct an orthonormal Haar wavelet base in L^2（H^d） by using self-similar tilings for the acceptable dilations on the Heisenberg group.

SELF-SIMILAR SOLUTIONS AND BLOW-UP PHENOMENA FOR A TWO-COMPONENT SHALLOW WATER SYSTEM

In this article, we consider a two-component nonlinear shallow water system, which includes the famous 2-component Camassa-Holm and Degasperis-Procesi equations as special cases. The local well-posedess for this equations is established. Some sufficient conditions for blow-up of the solutions in finite time are given. Moreover, by separation method, the self-similar solutions for the nonlinear shallow water equations are obtained, and which local or global behavior can be determined by the corresponding Emden equation.

ON THE SELF-SIMILAR SOLUTIONS OF THE MAGNETO-HYDRO-DYNAMIC EQUATIONS

In this paper, we show that, for the three dimensional incompressible magnetohydro-dynamic equations, there exists only trivial backward self-similar solution in L^p（R^3） for p ≥ 3, under some smallness assumption on either the kinetic energy of the self-similar solution related to the velocity field, or the magnetic field. Second, we construct a class of global unique forward self-similar solutions to the three-dimensional MHD equations with small initial data in some sense, being homogeneous of degree -1 and belonging to some Besov space, or the Lorentz space or pseudo-measure space, as motivated by the work in [5].

The Exact Measure Functions of the Images for a Class of Self-Similar Processes

Let X= (Ω, ■, ■_t, X_t,, θ_t, p~x) be a self-similar Markov process on (0,∞) with non-decreasing path. The exact Hausdorff and Packing measure functions of the image X([0,t] ) are obtained.