Application of Wavelet Transformation in Analysis of Multiplicity Phase Space

Using the wavelet transformation, the probability distribution for the multiplicity phase space which is obtained by simulation from random cascading α model is discussed. We find that using the wavelet transformation the probability moments and the correlation moments for the experimental data of the multiplicity phase space probability distribution canbe directly analysed. An actual calculation mathod is suggested.     

The rapidity distribution of the cascade inside deuteron in πd high energy collisions

The problem of the existence of internuclear cascade and its characteristics are analysed in the π^? d experiment at 205 GeV/c. Two versions of the additive quark model are used to obtain the mean multiplicity and the rapidity distribution of charged particles produced through cascading. It is shown that the cascading effect does exist. The particles produced through this effect have the rapidity distribution very similar as in elementary low energy hadron-nucleon interactions. Both the rapidity distribution and the mean multiplicity do not depend on the version of the additive quark model which was used to obtain them.     

基于超图的超网络相继故障分析

分析了快递超网络和电子元件超网络的相继故障扩散方式, 结合超图理论提出了2-section 图分析法和线图分析法, 并仿真分析了无标度超网络耦合映像格子的相继故障进程. 结果表明: 无标度超网络对外部攻击表现出了既鲁棒又脆弱的特性. 针对相继故障的不同扩散方式, 无标度超网络的相继故障行为表现出不同的特点. 超网络的相继故障行为和超网络的超度以及超边度分布有密切的联系, 也和超网络中超边的个数有关. 通过和同规模的Barabasi-Albert (BA)无标度网络对比, 在同一种攻击方式下同规模的无标度超网络都比BA 无标度网络表现出了更强的鲁棒性. 另外, 基于超边扩散的相继故障进程比基于节点扩散的相继故障进程更加缓慢.     

Intermittency and small scale resummation

A method of sampling fluctuations in sub-dimensional phase space of (possibly fractal) dimensionD is proposed. Applied to random cascading models of multi-particle production, it gives aD-dependent nonlinear equation for the generating function of particle multiplicities in the sub-domain, whose solutions lead to new properties, e.g. the correction effects of very small scale ressumations on the generic intermittent fluctuations of the model, the unexpected possibility of non vanishing intermittency after dimensional projection and the connection of KNO scaling violations with a structural phase transition. A phenomenological discussion of \(\bar p\) p SPS data allows one to exhibit a simple fragmentation model describing both local and global multiplicity fluctuations observed in these reactions, and compare it with theoretical gluon cascading.     

Intermittency in multiparticle production at high energy

We present predictions of random cascading models for multiparticle production at high energy. Standard and correlated factorial moments in rapidity are shown to provide stringent tests of the intermittency patterns characteristic of random cascades. Using the central limit theorem we show how to test directly for the existence of a cascading process. Finally, we discuss how to take into account statistical corrections.     

Cascading failure in Watts-Strogatz small-world networks

In this paper, we study the cascading failure in Watts-Strogatz small-world networks. We find that this network model has a heterogeneous betweenness distribution, although its degree distribution is homogeneous. Further study shows that this small-world network is robust to random attack but fragile to intentional attack, in the cascading failure scenario. With comparison to standard random graph and scale-free networks, our result indicates that the robust yet fragile property in the cascading failure scenario is mainly related to heterogeneous betweenness, rather than the network degree distribution. Thus, it suggests that we have to be very careful when we use terms such as homogeneous network and heterogeneous network, unless the distribution we refer to is specified.     

Load-dependent random walks on complex networks

Load-dependent random walks are used to investigate the evolution of load distribution in transportation network systems. The walkers hop to a node according to node load of the last time step. The preference of walks leads to a change in the load distribution. It changes from degree-dependent distribution in the case of non-preference walks to eigenvector-centrality-dependent distribution. By numerical simulations, it is shown that the network heterogeneity has a influence on the effect of walk preference. In the cascading failure phenomenon, an appropriate degree correlation can guarantee a low risk of cascading failures.     

Rapidity gap correlations in short range order models

We show that short range order models relate the multiplicity distribution produced in a rapidity interval R of the central region, to the distribution of such intervals which all contain a fixed multiplicity N. This is an asymptotic result which furthermore implies that the asymptotic behavior of the Mueller moments be related to certain rapidity gap correlation moments. The behavior of these gap correlations in specific models depends in a direct way on the assumptions made about clustering and about the range of the interaction.     

Tolerance of edge cascades with coupled map lattices methods

This paper studies the cascading failure on random networks and scale-free networks by introducing the tolerance parameter of edge based on the coupled map lattices methods. The whole work focuses on investigating some indices including the number of failed edges, dynamic edge tolerance capacity and the perturbation of edge. In general, it assumes that the perturbation is attributed to the normal distribution in adopted simulations. By investigating the effectiveness of edge tolerance in scale-free and random networks, it finds that the larger tolerance parameter λ can more efficiently delay the cascading failure process for scale-free networks than random networks. These results indicate that the cascading failure process can be effectively controlled by increasing the tolerance parameter λ. Moreover, the simulations also show that, larger variance of perturbation can easily trigger the cascading failures than the smaller one. This study may be useful for evaluating efficiency of whole traffic systems, and for alleviating cascading failure in such systems.     

An overview of shadowed fading wireless channels in terms of a cascaded approach

Wireless channels suffer from short term fading and shadowing simultaneously. While simple models of short term fading are based on the Nakagami-m distribution, short term fading can also be described as a cascading process allowing the modeling of wireless channels having worse fading than what exists in Nakagami-m channels. Shadowing, on the other hand, has been traditionally modeled as a lognormal process, making the analysis of shadowed fading channels cumbersome. Taking note of the fact that the lognormal density arises out of a multiplicative process, it was shown that shadowing can also be modeled as a cascading process. Utilizing such a vision of shadowing, this work provides an overview of a unified cascaded approach to model wireless channels when short term fading and shadowing are simultaneously present. The degradation in such shadowed fading channels is estimated in terms of error rates and outage probabilities. Results are compared to those of the exact model based on lognormal density as well as random number simulation. Analysis demonstrates that error rates and outage probabilities obtained using the exact model (lognormal model for shadowing) agree very well with those obtained through the composite cascaded model as well as random number simulations.     

Phase space dependence of the multiplicity distribution in π+ andpp collisions at 250 GeV/c

The charged particle multiplicity distribution has been studied for non-single-diffractive π⁺ p andpp collisions at \(\sqrt s = 22\) GeV, for full phase space as well as for intervals in rapidity, azimuthal angle and transverse momentum. In general, the multiplicity distribution is well described by a negative binomial. From comparison of the distribution for negative or positive particles to that of all charged particles, cascading is favoured as an interpretation over stimulated emission. Interesting consequences follow from a comparison of our results to those at collider energies and toe ⁺ e ^? data at comparable energy. Furthermore, evidence is given that the multiplicity distribution is not exactly of negative binomial type in every (connected or disconnected) phase space region.     

Multiplicity distribution at 104 GeV and the two-component models

We present the multiplicity distribution in pp collisions at 10⁴ GeV and compare with it the predictions of the two-component models. It is concluded that the data seem to rule out all those models which predict a dip in the multiplicity distribution at this energy. The data indicate that within the framework of two-component models the average multiplicity of the “diffractive’ component must also grow with energy so as to avoid the appearance of a bimodal multiplicity distribution at 10⁴ GeV.     

Two models of quantum random walk

We present an overview of two models of quantum random walk. In the first model, the discrete quantum random walk, we present the explicit solution for the recurring amplitude of the quantum random walk on a one-dimensional lattice. We also introduce a new method of solving the problem of random walk in the most general case and use it to derive the hitting amplitude for quantum random walk on the hypercube. The second is a special model based on a local interaction between neighboring spin-1/2 particles on a one-dimensional lattice. We present explicit results for the relevant quantities and obtain an upper bound on the speed of convergence to limiting probability distribution.     

Critical points and transitions in an electric power transmission model for cascading failure blackouts

Cascading failures in large-scale electric power transmission systems are an important cause of blackouts. Analysis of North American blackout data has revealed power law (algebraic) tails in the blackout size probability distribution which suggests a dynamical origin. With this observation as motivation, we examine cascading failure in a simplified transmission system model as load power demand is increased. The model represents generators, loads, the transmission line network, and the operating limits on these components. Two types of critical points are identified and are characterized by transmission line flow limits and generator capability limits, respectively. Results are obtained for tree networks of a regular form and a more realistic 118-node network. It is found that operation near critical points can produce power law tails in the blackout size probability distribution similar to those observed. The complex nature of the solution space due to the interaction of the two critical points is examined.(c) 2002 American Institute of Physics.     

Intra-nuclear cascading in deep inelastic scattering of 150 GeV muons in emulsion

An experimental search is presented for the existence of intra-nuclear cascading which, for small values of the Bjorken scaling variable ω, is the only mechanism of particle multiplication in the target nucleus. Our data indicate that cascading does exist as one of the effective mechanisms of particle multiplication in μ-nucleus collisions. No significant variation of the observed multiplicity with ω is observed.     

Conditional Entropy and Mutual Information in Random Cascading Processes

The conditional entropy and mutual information of two neighboring generations of division are proposed to use as characteristics in analyzing the random cascading mechanism in multiparticle production.It is shown that these characteristics are effective in examining the exsistence and property of self-similar cascading.     

Exploring the robustness of urban bus network: A case from Southern China

The robustness of urban bus network is essential to a city that heavily relies on buses as its main transportation solution. In this paper, the urban bus network has been modeled as a directed and space L network, and Changsha, a transportation hub of nearly 8 million people and hundreds of bus lines in southern China, is taken as a case. Based on the quantitative analyses of the topological properties, it is found that Changsha urban bus network is a scale-free network, not a small-world network. To evaluate the robustness of the network, five scenarios of network failure are simulated, including a random failure and four types of intentional attacks that differed in key node identification methods (i.e., unweighted degree or betweenness centrality) and attack strategies (i.e., normal or cascading attack). It is revealed that intentional attacks are more destructive than a random failure, and cascading attacks are more disruptive than normal attacks in the urban bus network. In addition, the key nodes identification methods are found to play a critical role in the robustness of the urban bus network. Specifically, cascading attack could be more disruptive when the betweenness centrality is used to identify key nodes; in contrast, normal attack could be more disruptive when the unweighted degree is used to identify key nodes. Our results could provide reference for risk management of urban bus network.     

HBT correlations and charge ratios in multiple production of pions

The influence of the HTB effect on the multiplicity distribution and charge ratios of independently produced pions is studied. It is shown that, for a wide class of models, there is a critical point, where the average number of pions becomes very large and the multiplicity distribution becomes very broad. In this regime unusual charge ratios (“centauros”, “anticentauros”) are strongly enhanced. The prospects for reaching this regime are discussed. Received: 25 March 1998 / Published online: 21 August 1998     

Proton interactions with high multiplicity

Project Thermalization is aimed to study the proton-proton interaction with high multiplicity of secondary particles. The region of high multiplicity is especially actual at present. We expect the manifestation of the secondary particle collective behavior at this region. The experimentally measured topological cross section was corrected for apparatus acceptance and detection efficiency. These data are in good agreement with gluon dominance model. The comparison with other models is also done and shows no essential deviations. There is evidence that Bose-Einstein condensation can formed at high total multiplicity region.     

Negative binomials and multiplicity distributions in 250 GeV/cK + and π+ interactions on Al and Au nuclei

The negative binomial distribution (NBD) is fitted to all charged and to negative particle multiplicity distributions in restricted rapidity intervals, both in the forward and backward c.m. hemispheres of positive meson interactions on Al and Au nuclei. For negative particle multiplicity distributions, the NBD parameters are also determined as a function ofn _g, the number of grey tracks, corresponding to varying number of intranuclear collisions. The data are interpreted in terms of the clan picture of Giovannini and Van Hove and compared to the MCMHA and Fritiof models. Both models reproduce quite well the global multiplicity distributions, but not when sub-samples are considered with fixed number of grey tracks. Regularities are better visible on the parton than on the particle level.