As models for biological molecular motors, Brownian motors have been studied recently by many workers, and their physical properties such as velocity, efficiency, and so on, have been investigated. They have also attracted much interest in an application to nanoscale technology. It is significant to study more complex systems, that is, coupled Brownian motors, in detail, since Brownian motors with a single particle have been mainly studied until now. In this paper, we consider Brownian motors coupled mutually with elastic springs, and investigate the dynamics of the model and the efficiency of energy conversion. In particular, we find that the center of the mass of the elastically coupled particles moves faster than the corresponding single-particle model, and also that the efficiency of the coupled-particle model is larger than that of the single-particle model.

We investigate a new efficient packet routing strategy which mitigates traffic congestion on complex networks. In order to avoid congestion, we minimize the maximum betweenness, which is a measure for concentration of routing paths passing through a node in the network. Danila et al. propose a packet routing strategy in which, instead of shortest paths, they used efficient paths, which are the paths with the minimum total summations of weights assigned to nodes in the respective paths. They use a heuristic algorithm in which the weights are updated step by step by using the information of betweenness of each node in every step and the respective total summations of weights for paths through the nodes with large degrees become comparatively large. Thus passage through such nodes, where congestion almost occurs, is likely to be avoided in their algorithm. The convergence time by their algorithm is, however, quite long. In this paper, we propose a new efficient heuristic algorithm which balances traffic on networks by achieving minimization of the maximum betweenness in the much smaller number of iteration steps for convergence than that by the algorithm of Danila et al.Recently, communication networks such as the Internet reach a huge scale and a lot of data pass through the networks. Although some attempts to optimize information traffic are made in real computer networks, they are not systematic. Therefore, development of efficient packet routing strategies optimal for transport is one of the most important problems in the study of computer networks. Until now, however, transport routing strategies used on computer networks have been solely determined based on the shortest paths. Real computer networks, however, display scale-free features and have poor performance for traffic flow on routing based on the shortest path strategy (SPS). The reason is because traffic concentrates on hubs, nodes with a great many degrees, and congestion is prone to occur there when we send traffic by the SPS because many shortest paths pass through hubs on scale-free networks [4]. It is especially important that we find the routing strategy which can bear as much traffic as possible without congestion in scale-free networks. Thus it is necessary to devise routing strategies to avoid hubs efficiently in place of those based on the SPS.Many studies on information transport on complex networks have attracted a great deal of interest in recent years [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. investigate routing in wireless ad hoc communication.In this paper, we investigate packet routing strategies to mitigate traffic congestion in complex networks. In order to avoid congestion, nodes passed through by a great many routing paths should be bypassed. Concentration of routing paths to a node is measured with betweenness, which is calculated with the fast algorithm by Newman [20], and Newman and Girvan [21]. If we minimize the maximum betweenness, which is the largest one of all the nodes in the network, with an improvement...

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