Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Everyday incivility: towards a benchmark

Commonplace incivility is a topic of longstanding interest within social theory, perhaps best exemplified by Goffman's studies of the interaction order. Nevertheless we know very little about its distribution and expression in everyday life. Current empirical work is dominated by criminological agendas. These tend to focus on more serious and illegal activities rather than minor deviant acts that are simply inconsiderate or rude. The paper reports findings from a focus group study conducted in Melbourne, Australia that set out to benchmark everyday incivilities. The results suggest that perpetrators of incivility have a surprisingly broad social distribution as does the range of locales that might be characterised as 'high risk'. Turning to the work of Putnam and Wolfe, we call for a research focus on low-level incivilities as key symptoms of the state of civic virtue and the strength of moral ties within civil society. Drawing on Virilio, Bauman and Durkheim, it is suggested that the experience of incivility is underpinned by the growth of freedom and movement in contemporary urban settings, and has ambivalent implications that not only invoke boundary maintenance and retreatism, but also offer the possibility for boundary expansion and tolerance of difference.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimen- sioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation that improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.