Workshop ADIW02 — Mathematical and Computational Modelling of Anti-Diffusive Phenomena

Anti-diffusive phenomena are the remarkable processes whereby up-gradient transport leads to large-scale structure formation. Such self-organization can occur through coarsening, coalescence, a flux between different scales, or a combination of the above. It is particularly striking in systems which are chaotic or turbulent, where there is no known organizing principle such as minimization of energy or a long-wave instability. From the jets on Jupiter to sand ripples on dunes to drop coalescence, large-scale formation can occur in systems of very different scale and physical origin, including oceanographic and atmospheric flows, magnetically-confined plasmas, and active and multiphase fluids. Despite the ubiquity of the phenomena, many open questions remain: are there universal mechanisms underlying the formation and sustainment of large-scale structures, shared by these systems? Is there a common mathematical characterization? What determines the scale to which the structures grow and their resulting shape? What is the feedback between chaotic fluctuations and the large-scale structure? How do bifurcations between different large-scale structures occur in chaotic systems? How are such transitions affected by internal and external perturbations? If the system is bi-stable, are there universal transition paths in such self-organizing systems? The aim of the workshop is to bring together experts from different fields, working on related phenomena from different perspectives, to shed light on these questions.

Topics: Anti-diffusive dynamics: from sub-cellular to astrophysical scales