Speaker
Description
Hwa–Kardar "running' sandpile model was an attempt to construct a continuous stochastic equation (an effective coarse-grained large-scale description), the derivation of which is based solely on conservation laws, relevant symmetries and dimensionality considerations, in order to capture the hypothetical mechanism behind self-organized criticality, namely, transport in a driven diffusive system with anisotropy and conservation. While the model does not include one of the important features of self-organized criticality – separation of time scales – and cannot adequately differentiate between discrete sandpile models, it allows to apply the well-developed methods of quantum field theory to the problem of self-organized criticality.
The very popular concept of self-organized criticality was initially based on specially designed discrete models; now it is considered one of the strongest contenders for the mechanism behind emergent complexity in Nature as it might explain self-similar spatio-temporal correlations in the infrared (large distances, long times) range believed to be observed in a startlingly big number of systems.
In this talk, asymptotic behaviour of a self-organized critical system subjected to a number of different moving random environments is analyzed using field theoretic renormalization group approach. The system is described by the anisotropic continuous Hwa–Kardar model while the medium is described by "synthetic" Gaussian ensembles due to Kraichnan and Avellaneda–Majda and their generalizations (general spatial dimension $d$ and finite correlation time), and the isotropic Navier–Stokes equation with a random stirring force of a very general form that covers, in particular, the overall shaking of the system and, in some limiting case, turbulent motion.
The obtained results reveal complex patterns of possible critical behaviour including: the lack of a fully nontrivial regime, for which nonlinear terms from both coupled equations would be simultaneously relevant in the sense of Wilson, non-universality, strong dependence on the type of random noise, non-conventional anisotropic scaling behaviour with a kind of dimensional transmutation, curves of simultaneously stable fixed points and so on.
