30,142 research outputs found
Spectral properties of the trap model on sparse networks
One of the simplest models for the slow relaxation and aging of glasses is
the trap model by Bouchaud and others, which represents a system as a point in
configuration-space hopping between local energy minima. The time evolution
depends on the transition rates and the network of allowed jumps between the
minima. We consider the case of sparse configuration-space connectivity given
by a random graph, and study the spectral properties of the resulting master
operator. We develop a general approach using the cavity method that gives
access to the density of states in large systems, as well as localisation
properties of the eigenvectors, which are important for the dynamics. We
illustrate how, for a system with sparse connectivity and finite temperature,
the density of states and the average inverse participation ratio have
attributes that arise from a non-trivial combination of the corresponding mean
field (fully connected) and random walk (infinite temperature) limits. In
particular, we find a range of eigenvalues for which the density of states is
of mean-field form but localisation properties are not, and speculate that the
corresponding eigenvectors may be concentrated on extensively many clusters of
network sites.Comment: 41 pages, 15 figure
Centrality and connectivity in public transport networks and their significance for transport sustainability in cities
The promotion of public transport as a backbone of mobility in urban agglomerations, or at least as an alternative to the dominance of the automobile, has become a prominent policy focus in most large cities around the world. However, while some cities have been successful in shifting car journeys onto rail and buses, others are struggling despite considerable effort to make public transport more attractive. This paper provides a brief overview of success factors for public transport and then takes the configuration of public transport networks as a vantage point for policy evaluation. The development of centrality and connectivity indicators for the public transport network of Melbourne's north-eastern suburbs delivers an instrument for assessing the congruence of the systems with the geographical structure of central areas and urban activities in these cities. It is hypothesised that a higher number of convenient transfer points and a choice of routes to users (network connectivity), as well as a high degree of spatial overlap and integration between public transport infrastructure and urban activity centres and corridors (centrality of facilities) will lead to a greater role for public transport in the mobility patterns of the city as a whole
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