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The bifurcated, ordered Cayley tree with disorder and frustration as a model for relaxing granular media is examined numerically. Surprisingly, only exponential time dependencies are found despite frustration. Extensions to bidirectional models are discussed extensively and qualitatively new behavior is detected.

In this paper a local trade web (LTW) in the Asia-Pacific region is examined using the data derived from the United Nations and the International Monetary Fund. The topology of the LTW has been specified, based upon which the impacts of US financial crisis on the structural and behavior pattern of the LTW are further investigated. The major findings are given as follows. Firstly, the LTW is much more integrated than the global trade web; secondly, after the financial crisis, the fundamental structure of the network remains relatively stable but the strength of the web has been changed and the structure of the web has evolved over time. Economic implications for what have been observed are also discussed.

In this paper, topology monitoring of growing networks is studied. When some new nodes are added into a network, the topology of the network is changed, which needs to be monitored in many applications. Some auxiliary systems (network monitors) are designed to achieve this goal. Both linear feedback control and adaptive strategy are applied to designing such network monitors. Based on the Lyapunov function method via constructing a potential or energy function decreasing along any solution of the system, and the LaSalle's invariance principle, which is a generalization of the Lyapunov function method, some sufficient conditions for achieving topology monitoring are obtained. Illustrative examples are provided to demonstrate the effectiveness of the new method.

We study the searching efficiency of complex networks considering node's visual range within which a node can see its neighbors and knows the topology. We firstly introduce the network generating models and searching strategies. Using the generating function method, in both random networks and scale-free networks we derive the most-effective-visual-range (MEVR) which means every step of random walkers can find most of new nodes and we also obtain the searching-cost (SC) under visual range. To validate the generating function method, we perform simulations in random networks and scale-free networks. We also explain why the deviation between numerical simulation and theoretical prediction in scale-free networks is much larger than that in random networks. By studying the visual range of nodes in the networks, the results open the possibility to learn about the searching on networks with unknown topologies.

In the present paper, a variation of the widespread model of diffusion-limited aggregation (DLA) is presented. Unlike the traditional DLA model, where particles are attached to the aggregate whenever they touch it, we here restrict attachment by reducing the number of available bonds of the particles. This subtle change in the model changes the topological properties of the resulting aggregate.

By using a binary mixture of particles, with different coordination number, the fractal dimension (d_f), the spectral dimension (d_s) and the random walk dimension (d_w) are studied as a function of particle-type ratio. The behavior of the system shows non-negligible deviation from the traditional model.

We investigate vacuum transitions in lattice higgs models at finite temperature. The 2 dimensional U(1) Higgs model is used as a toy model. In the 4 dimensional SU(2) Higgs model the region of the phase transition and temperatures above it are considered. The couplings (β, κ, λ) = (2.25, 0.27, 0.5) and (8.0, 0.12996, 0.0017235) correspond to masses in lattice units (a_σm_H, a_σm_w) of (0.02, 0.05) and (0.2,0.2), respectively. The algorithm is described and a parallelized version is proposed. Taking the influence of the finite lattice into account we discuss temperature effects. We compare our results with perturbative estimates and claim that they link low and high temperature approximations.