Optimal routing strategy based on the minimum information path

In this paper, we propose a new routing strategy based on the minimum information path, named the optimal routing (OR) strategy, to improve the transportation capacity of scale-free networks. We define the average routing centrality degree of the node to analyze the traffic load on nodes of different degree. We analyze the transportation capacity by using the critical values of R_c, the average packet travel time, and the average path length. Both theoretical and experimental results show that the capacity of the network under our strategy will be maximized when the packet-delivery rate of the node is directly proportional to the degree.     

The effect of TTL on the information traffic

In real communication protocols, the information packets have a finite Time-to-Live (TTL) to avoid the waste of network resources, such as infinite loop induced by routing error or too long transferring time. In this paper, we introduce TTL into the information traffic model on Barabási-Albert scale-free networks under local routing strategy and focus on its effect on the network capacity measured by the critical point (R_c) of phase transition from free flow to congestion. Simulations show that the network capacity and the communication velocity are improved. However, some packets are dropped before they arrived at destinations. It is found that the share of successfully arrived packets monotonously increases with the increment of TTL and it is considerably acceptable if TTL is not very small. We also examine the effect of TTL on the positive-feedback preference (PFP) internet model and the results are alike. Our work may be helpful in quantifying the effect of packet lifetime in real communication networks and in routing strategy designing.     

一类基于随机行走机理的优化路由改进策略

在对随机行走过程的研究中发现:单个粒子通过某条特定路径的时间正比于该路径上所有节点度的连乘积.据此,文章提出基于随机行走机理的优化路由改进策略.该策略以节点度连乘积最小化为原则,通过调节可变参数,建立节点处理能力均匀分布的情况下最佳路由策略.通过分析比较不同路由策略条件下平均路由介数中心度,网络的临界负载量,平均路径长度以及平均搜索信息量等性能指标,研究结果表明,此改进路由策略在保证网络平均路径长度较少增加的前提下,使网络的传输能力获得最大幅度的提升. 关键词： 复杂网络 路由策略 负载传输     

Traffic dynamics in scale-free networks with limited packet-delivering capacity

We propose a limited packet-delivering capacity model for traffic dynamics in scale-free networks. In this model, the total node’s packet-delivering capacity is fixed, and the allocation of packet-delivering capacity on node i is proportional to , where k_i is the degree of node i and ? is a adjustable parameter. We have applied this model on the shortest path routing strategy as well as the local routing strategy, and found that there exists an optimal value of parameter ? leading to the maximal network capacity under both routing strategies. We provide some explanations for the emergence of optimal ?.     

Traffic dynamics based on an efficient routing strategy on scale free networks

In this paper, we propose a new routing strategy on the basis of the so-called next-nearest-neighbor search strategy by introducing a preferential delivering exponent α. It is found that by tuning the parameter α, the scale-free network capacity measured by the order parameter is considerably enhanced compared to the normal next-nearest-neighbor strategy. Traffic dynamics both near and far away from the critical generating rate R_c are discussed, and it is found that the behavior of 1/f-like noise of the load time series not only depends on the generating rate R but also on the parameter α. We also investigate R_c as functions of C (capacity of nodes), m (connectivity density) and N (network size). Due to the low cost of acquiring next-nearest-neighbor information and the strongly improved network capacity, our strategy may be useful for the protocol designing of modern communication networks.     

Energy dependence of multiplicity in proton-nucleus collisions and models of multiparticle production

This is a continuation of our earlier investigation (Gurtuet al 1974Phys. Lett. 50 B 391) on multiparticle production in proton-nucleus collisions based on an exposure of emulsion stack to 200 GeV/c beam at the NAL. It is found that the ratioR _em = 〈n _s〉/〈n _ch〉, where 〈n _ch〉 is the charged particle multiplicity in pp-collisions, increases slowly from about 1 at 10 GeV/c to 1·6 at 68 GeV/c and attains a constant value of 1·71 ± 0·04 in the region 200 to 8000 GeV/c. Furthermore,R _em = 1·71 implies an effectiveA-dependence ofR _A =A ^0.18,i.e., a very weak dependence. Predictions ofR _em on various models are discussed and compared with the emulsion data. Data seem to favour models of hadron-nucleon collisions in which production of particles takes place through adouble step mechanism,e.g., diffractive excitation, hydrodynamical and energy flux cascade as opposed to models which envisage instantaneous production.     

High-performance distribution of limited resources via a dynamical reallocation scheme

Using the context of routing efficiency in a complex scale-free network, we study the problem of how a limited amount of resources should be distributed to the nodes in a network so as to achieve a better performance, without imposing a certain pre-determined distribution. A dynamical reallocation scheme, based on the willingness of sharing resources with a busy neighboring node, is proposed as a tool for allowing an initially uniform distribution of resource to evolve to a high-performance distribution. The resulting distribution gives a critical packet generation rate R_c that is significantly enhanced when compared with evenly distributing the same amount of resources on the nodes. There emerges a relation between the resource allocated to a node and the degree of the node in the form of . The exponent γ is found to vary with the packet generation rate R. For R<R_c, γ takes on a high value and shows a weak dependence on R; for R>R_c, γ drops with R; and for R?R_c, γ saturates. For good performance, the values of γ indicate a behavior different from that linear in k, as often assumed in previous studies. The resource distribution is also analyzed in terms of the betweenness of the nodes.     

On the critical packet injection rate of a preferential next-nearest neighbor routing traffic model on Barabási-Albert networks

Recently, Yin et al. [Eur. Phys. J. B 49, 205 (2006)] introduced an efficient small-world network traffic model using preferential next-nearest neighbor routing strategy with the so-called path iteration avoidance (PIA) rule to study the jamming transition of internet. Here we study their model without PIA rule by a mean-field analysis which carefully divides the message packets into two types. Then, we argue that our mean-field analysis is also applicable in the presence of PIA rule in the limit of a large number of nodes in the network. Our analysis gives an explicit expression of the critical packet injection rate R_c as a function of a bias parameter of the routing strategy α in their model with or without PIA rule. In particular, we predict a sudden change in R_c at a certain value of α. These predictions agree quite well with our extensive computer simulations.     

非晶态超导体的声子谱参数λ,〈ω〉和〈ω2〉与霍耳系数之间的经验关系

在大量的非过渡金属和合金中,非晶态超导体的声子谱参数λ,<ω>和<ω²>与霍耳系数R_H之间存在着一个经验关系:在R_H=-3.5—-4.0×10^-11m³/As之间存在着λ,<ω>和<ω²>的最大值。上述声子谱参数与相应的液态金属的霍耳系数R_HL之间也存在着一个和上述类似的经验关系。最后讨论了非晶态超导体的转变温度T_c的提高问题。 关键词：     

Effect of chemical ordering on the crystallization behavior of Se90Te10−xSnx (x=2, 4, 6, and 8) chalcogenide glasses

Ternary Se₉₀Te_10−xSn_x (x=2, 4, 6, and 8) chalcogenide glassy alloys have been prepared by melt quenching technique. Various crystallization parameters, such as onset (T_c) and peak (T_p) crystallization temperatures, activation energy of crystallization (E_c) and Avrami exponent (n) have been determined for these alloys. T_c and T_p have been determined directly from the non-isothermal differential scanning calorimeter (DSC) thermograms. The value of E_c has been calculated from the variation of both T_c and T_p with the heating rate (β) according to Kissinger, Takhor, Augis–Bennett and Ozawa models while Augis–Bennett method has been used to deduce the value of n for the studied samples. The obtained values of the crystallization parameters have been correlated with the character and the energy of the chemical bonds through the calculation of the heteronuclear bond energies of the constituent atoms using Pauling principle. In addition to that, Tichy–Ticha model was used to estimate the mean bond energy of the average cross-linking per atom 〈E_cl〉, the average bond energy per atom of the remaining matrix 〈E_rm〉, and the overall mean bond energy 〈E〉 of the studied glasses. Results reveal that both of T_c and T_p decreases with increases Sn content. This is may be attributed to the decreasing in the overall mean bond energy 〈E〉. Besides, the plot of E_c (and also T_g) against 〈E〉 was found to be non linear, which contradicts the well known linear correlation between E_c and T_g with 〈E〉 as suggested by Tichy–Ticha model. This discrepancy may be due to the fact that the Tichy–Ticha linear correlation model was based on the assumption of covalent glassy network, while in the present glassy alloys, Se–Te binary doped with heavy elements such as Sn exhibit iono-covalent bonding. The calculated values of the ionicity are in support of this argument.     

A model for cascading failures in scale-free networks with a breakdown probability

Considering that not all overload nodes will be removed from networks due to some effective measures to protect them, we propose a new cascading model with a breakdown probability. Adopting the initial load of a node j to be L_j=[k_j(∑_m∈Γjk_m)]^α with k_j and Γ_j being the degree of the node j and the set of its neighboring nodes, respectively, where α is a tunable parameter, we investigate the relationship between some parameters and universal robustness characteristics against cascading failures on scale-free networks. According to a new measure originated from a phase transition from the normal state to collapse, the numerical simulations show that Barabási-Albert (BA) networks reach the strongest robustness level against cascading failures when the tunable parameter α=0.5, while not relating to the breakdown probability. We furthermore explore the effect of the average degree 〈k〉 for network robustness, thus obtaining a positive correlation between 〈k〉 and network robustness. We then analyze the effect of the breakdown probability on the network robustness and confirm by theoretical predictions this universal robustness characteristic observed in simulations. Our work may have practical implications for controlling various cascading-failure-induced disasters in the real world.     

Momentenanalyse derR 2-Nullphononen-Linie in NaF unter einaxialem Druck

The R₂ zero-phonon absorption line 4480 Å in NaF at 4.2 °K and 23 °K is studied under uniaxial stress along 〈100〉 and 〈100〉. According to the F₃ model of theR center the R₂ line is found to be due to a transition between a degenerate ground state (²E) and a nondegenerate excited state (²A) of this center. Instead of a splitting into single components under stress, changes in line shape are observed which are analyzed by means of the method of moments. The zeroth and first moment of the line are calculated as functions of the magnitude of stress and temperature. The theoretical moments are found to be in good agreement with those determined from the experimental data. From a comparison of the measured moments with the theoretical expressions the stress splitting parameters are obtained which describe the removal of both the orientational and the orbital degeneracy of theR center under uniaxial stress. The corresponding strain parameters of the R² line in NaF are compared with those in other alkali halides.     

Study of the effective transverse momentum of partons in the proton using prompt photons in photoproduction at HERA

The photoproduction of prompt photons, together with an accompanying jet, has been measured with the ZEUS detector at HERA using an integrated luminosity of 38.6 pb⁻¹. A study of the effective transverse momentum, 〈k_T〉, of partons in the proton, as modelled within the framework of the PYTHIA Monte Carlo, gives a value of 〈k_T〉=1.69±0.18^+0.18_−0.20 GeV for the γp centre-of-mass energy range 134<W<251 GeV. This result is in agreement with the previously observed trend in hadron–hadron scattering for 〈k_T〉 to rise with interaction energy.     

Study of data on the associated momentum on the trigger side in highP T hadron production

The British-French-Scandinavian collaboration has recently studied the non trigger charged mean momentum in different rapidity regions on the trigger hemisphere, 〈p _x〉, in the collision of two hadrons at the CERN Intersecting Storing Rings (ISR). In particular, they give for the rapidity regions |y|<0.5 and |y|<1 the values of the slope, α, of 〈p _x〉 with the trigger momentum,p _T ^t . Several authors have analysed those values of α in the framework of hard scattering models which predict values independent ofp _T ^t for 〈z _c〉, the longitudinal momentum fraction of the outgoing hard scattered system taken by the trigger. From this analysis they give estimates of 〈z _c〉 of very difficult reconcilliation with those calculated in the Feynman, Field and Fox hard scattering model or in the QCD treatment of highp _T hadron production. The authors of the present paper have looked for, and found, other data whose model independent analysis is more feasible than that of the data mentioned above. More specifically, we analyse in the framework of the hard scattering models, but otherwise model independently, data on 〈p _x〉 in two other rapidity regions (|y|<3, 2<|y|<3) and find that consistence of the average slopes, α, in these two regions is only achieved with mean values of 〈z _c〉 significantly, increasing withp _T ^t and close in value to those obtained by Feynman et al. [6, 7].     

Impulse approximation in QCD,Parton's pT-distribution and application to deep inelastic process

The recently formulated theory of the impulse approximation in QCD is developed further. The integro-differential equation describing the evolution of the parton's distribution function is solved. The formalism is applied to compute R = σ_L/σ_T in deep inelastic electron scattering and the average transverse momentum 〈k_T〉 of the Drell-Yan pairs. The cross section formula for the latter process is significantly different from the one recently conjectured. Agreement with recent data is good in both cases.     

Transverse momentum in Drell-Yan processes

We study the transverse momentum distribution of muon pairs from Drell-Yan processes in QCD. In particular the dependence of 〈k_⊥²〉 on Q² is considered. QCD predicts an approximately linear rise of 〈k_⊥²〉 with S or Q² only at fixed τ = Q²/S. The slope as a function of τ is quantitatively studied for P$\text{P}$ and P-nucleus scattering. The most recent data showing a rather flat 〈k_⊥²〉 in Q² at fixed S are found to be consistent with QCD.     

Effects of attachment preferences on coevolution of opinions and networks

In the coevolution of network structures and opinion formation, we investigate the effects of a mixed population with distinctive relinking preferences on both the convergence time and the network structures. It has been found that a heterogeneous network structure is easier to be reached with more high-degree-preferential (HDP) nodes. There exists high correlation between the convergence time and the network heterogeneity. The heterogeneous degree distribution caused by preferential attachment accelerates the convergence to a consensus state and the shortened convergence time inhibits the occurrence of the following disquieting situation that occurs in a continuously evolving network: with preferential attachment and long-time evolvement, most of the nodes would become separated and only a few leaders would have immediate neighbors. Analytical calculations based on mean field theory reveal that both the transition point p_tr and the consensus time τ depend upon the standard deviation of the degree distribution σ_d. p_tr increases while τ decreases with the rise of σ_d. Functions of p_tr=〈k〉/(〈k〉+1) and are found. Theoretical analyses are in accordance with simulation data.     

Range-energy relation of electrons in a KCl crystal

The range of electron in KCl 〈100〉 and KCl 〈110〉 crystals in the energy between 30 and 60 keV have been experimentally determined. The data fit an equation of the type, R = kEⁿ. The values of k and n exhibit crystalline orientation dependence.     

A local-world node deleting evolving network model

A new type network growth rule which comprises node addition with the concept of local-world connectivity and node deleting is studied. A series of theoretical analysis and numerical simulation to the LWD network are conducted in this Letter. Firstly, the degree distribution p(k) of this network changes no longer pure scale free but truncates by an exponential tail and the truncation in p(k) increases as pa decreases. Secondly, the connectivity is tighter, as the local-world size M increases. Thirdly, the average path length L increases and the clustering coefficient 〈C〉 decreases as generally node deleting increases. Finally, 〈C〉 trends up when the local-world size M increases, so as to kmax. Hence, the expanding local-world can compensate the infection of the node deleting.