1/f Noise in sliding friction under wear conditions: the role of debris.

It has been shown that the friction force time series in sliding friction under wear conditions is self-similar and has a 1/f power spectrum. Albeit a variety of models, mostly inspired in the field of earthquakes, has been explored, an important factor was overlooked: the role of debris. This Letter describes sliding friction experiments on steel with alumina pins, carried out with and without debris blowing, that prove the role of loose debris in determining the 1/f character of the friction force. A damped-forced harmonic oscillator with two friction terms, one purely random and another inversely proportional to the amount of loose debris, calculated by means of a modified sandpile model, is proposed to describe the dynamics of friction under wear conditions.

Debris and 1/f noise in sliding friction dynamics under wear conditions.

Friction force time series showing irregular fluctuations have been since long considered one of the possible stick-slip regimes in sliding friction. However, it has not been until recently that a 1/f power spectrum in friction force time series derived from sliding friction experiments under wear conditions has been identified. A variety of models, mostly inspired in the field of earthquakes, has been explored, without reaching a fully satisfactory explanation of that behavior. Recently, the present authors have reported results of sliding friction experiments on steel with alumina pins, carried out with and without debris blowing, that proved the role of loose debris in determining the 1/f character of the friction force. A damped-forced harmonic oscillator with two friction terms was proposed to describe the dynamics of friction under wear conditions: one purely random, which accounts for surface roughness, and another inversely proportional to the amount of loose debris that was calculated by means of a modified sand-pile model. This paper presents a full discussion of the experiments that allowed to reach that conclusion and of the model proposed to rationalize the results. In addition, the results of experiments devised to understand the transition from friction with debris to friction without debris (experiment initiated without blowing and after some time switching on blowing) and vice versa are reported. The results of further studies of the wear track are presented, namely, the variation in the track width with sliding distance and results of chemical analyses and surface roughness measurements of the track, for both with or without debris blowing experiments. These additional data give further support to the crucial role of debris in the 1/f character of the friction force.

Network community structure and loop coefficient method.

A modular structure, in which groups of tightly connected nodes could be resolved as separate entities, is a property that can be found in many complex networks. In this paper, we propose a algorithm for identifying communities in networks. It is based on a local measure, so-called loop coefficient that is a generalization of the clustering coefficient. Nodes with a large loop coefficient tend to be core inner community nodes, while other vertices are usually peripheral sites at the borders of communities. Our method gives satisfactory results for both artificial and real-world graphs, if they have a relatively pronounced modular structure. This type of algorithm could open a way of interpreting the role of nodes in communities in terms of the local loop coefficient, and could be used as a complement to other methods.

Efficiency of informational transfer in regular and complex networks.

We analyze the process of informational exchange through complex networks by measuring network efficiencies. Aiming to study nonclustered systems, we propose a modification of this measure on the local level. We apply this method to an extension of the class of small worlds that includes declustered networks and show that they are locally quite efficient, although their clustering coefficient is practically zero. Unweighted systems with small-world and scale-free topologies are shown to be both globally and locally efficient. Our method is also applied to characterize weighted networks. In particular we examine the properties of underground transportation systems of Madrid and Barcelona and reinterpret the results obtained for the Boston subway network.