Matière et Systèmes Complexes, Paris, France
Architecture of Optimal Pipe Networks
Marc Durand
Finding the most efficient pipe network is an issue arising in a wide variety of contexts. One can cite, among others, the water, natural gas and power supply of a city, and the design of labs-on-chips or microfluidic devices. Moreover, this problem also appears in theoretical works intending to describe the architecture of the vascular systems of living organisms. In this presentation, we establish basic properties on the structure of pipe networks minimizing the total dissipation rate under a global constraint on the total pipe volume (or lateral surface area). Although this problem is likely to be NP-hard - meaning that the optimal network cannot be found without an exhaustive search of all the possible solutions ~V general features on the geometry [1] and topology [2] of the optimal network can be established analytically. These results suggest an explanation for the observed architectures in the vascular systems of various living organisms. Applications to various physical situations are also discussed.
[1] M. Durand, "Architecture of optimal transport networks ", Phys. Rev. E 73, 016116 (2006).
[2] M. Durand, "Architecture of optimal transport networks subject to a global constraint", Phys. Rev. Lett. 98, 088701 (2007).

Institute for Condensed Matter Physics, Lviv, Ukraine
Attack vulnerability of public transport networks
C. von Ferber, T. Holovatch, Yu. Holovatch, V. Palchykov
Complex networks demonstrate very different behaviour depending on the attack (removing their nodes/links) scenario. Of special interest are scale-free networks, which are extremely robust being attacked randomly and vulnerable against targeted attacks. In a recent study of the public transport networks (PTN) of 14 major cities of the world we have shown that these networks may exhibit scale-free behaviour [physics/0608125, to appear in Physica A]. In our further analysis, which is a subject of this report, we study how do the properties of PTN change when their constituent are removed. We apply different attack strategies and elaborate vulnerability criterion that allows to choose which of the strategies applied is the most effective one. We extract correlations between the resilience threshold of the PTN against targeted attacks and their architecture. Another outcome of our study is that the algorithms involved allow for a search of community structure as well as to analyze growing network properties.

VON FERBER Christian
AMRC Coventry University
Modelling Metropolis public transport
C. von Ferber, T. Holovatch, Yu. Holovatch, V. Palchykov
We present results of a survey of public transport networks (PTN) of selected 14 major cities of the world with PTN sizes ranging between 2000 and 46000 stations and develop an evolutionary model of these networks. The structure of PTNs is revealed in terms of a set of of neighbourhood relations both for the routes and the stations.
The networks defined in this way display distinguishing properties due to the constraints of the embedding 2D geographical space and the structure of the cities. In addition to the standard characteristics of complex networks like the number of nearest neighbours, mean path length, and clustering we observe features specific to PTNs. While other networks with real-world links like cables or neurons embedded in two or three dimensions often show similar behavior, these can be studied in detail in our present case. Geographical data for the routes reveal surprising self-avoiding walk (SAW) properties that we relate to the optimisation of surface coverage. We propose and simulate an evolutionary growth model of PTN based on effectively interacting SAWs that reproduces the key features.
[physics/0608125, to appear in Physica A]