Precursors of catastrophe in the BTW, Manna and random fiber bundle models of failure

We have studied precursors of the global failure in some self-organised critical models of sand-pile (in BTW and Manna models) and in the random fiber bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed number of sand grains (heights) to any central site of the stable pile, the local dynamics starts and continues for an average relaxation time (\tau) and an average number of topplings (\Delta) spread over a radial distance (\xi). We find that these quantities all depend on the average height (h_{av}) of the pile and they all diverge as (h_{av}) approaches the critical height (h_{c}) from below: (\Delta) (\sim (h_{c}-h_{av}))(^{-\delta}), (\tau \sim (h_{c}-h_{av})^{-\gamma}) and (\xi) (\sim) ((h_{c}-h_{av})^{-\nu}). Numerically we find (\delta \simeq 2.0), (\gamma \simeq 1.2) and (\nu \simeq 1.0) for both BTW and Manna model in two dimensions. In the strained RFB model we find that the breakdown susceptibility (\chi) (giving the differential increment of the number of broken fibers due to increase in external load) and the relaxation time (\tau), both diverge as the applied load or stress (\sigma) approaches the network failure threshold (\sigma_{c}) from below: (\chi) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}) and (\tau) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}). These self-organised dynamical models of failure therefore show some definite precursors with robust power laws long before the failure point. Such well-characterised precursors should help predicting the global failure point of the systems in advance.Comment: 13 pages, 9 figures (eps

Grain Surface Models and Data for Astrochemistry

AbstractThe cross-disciplinary field of astrochemistry exists to understand the formation, destruction, and survival of molecules in astrophysical environments. Molecules in space are synthesized via a large variety of gas-phase reactions, and reactions on dust-grain surfaces, where the surface acts as a catalyst. A broad consensus has been reached in the astrochemistry community on how to suitably treat gas-phase processes in models, and also on how to present the necessary reaction data in databases; however, no such consensus has yet been reached for grain-surface processes. A team of ∼25 experts covering observational, laboratory and theoretical (astro)chemistry met in summer of 2014 at the Lorentz Center in Leiden with the aim to provide solutions for this problem and to review the current state-of-the-art of grain surface models, both in terms of technical implementation into models as well as the most up-to-date information available from experiments and chemical computations. This review builds on the results of this workshop and gives an outlook for future directions