On the behaviour of a rumour process with random stifling

We propose a realistic generalization of the Maki-Thompson rumour model by assuming that each spreader ceases to propagate the rumour right after being involved in a random number of stifling experiences. We consider the process with a general initial configuration and establish the asymptotic behaviour (and its fluctuation) of the ultimate proportion of ignorants as the population size grows to $\infty$. Our approach leads to explicit formulas so that the limiting proportion of ignorants and its variance can be computed.Comment: 12 pages, to appear in Environmental Modelling & Softwar

Effect of the intermolecular thermal motions on the tail of the electronic density of states in polyacene crystals

The thermal fluctuation of the intermolecular hopping integral in the series of polyacene crystals (naphthalene, anthracene, tetracene, pentacene) was evaluated computationally using a combined molecular dynamics and quantum chemistry approach. It was shown that these large fluctuations can manifest themselves in a temperature-dependent relatively broad tail of the density of states extending from the valence band into the gap. It was also shown that this tail accounts for a large fraction of all states in the valence band and therefore it may be essential for accurately describing the charge transport and optical properties