Fabrizio Davì, Marco Paggi and Alessio Gizzi

Reaction-Diffusion-Drift equations (RDD) and their variational formulation, which leads to Gradient Flows, have important applications in many different fields: from the mechanics of coupled multifield problem to the classical chemical kinetics to more, and unfortunately famous, applications to epidemic disease propagation. Even if we limit ourselves to the field of mechanical applications, they can model electrical and chemical interactions within continuum bodies as in soft active media electrophysiology, as well as problems of charged particle diffusion, as in semiconductors and scintillating crystals. 

The underlying physics is in some cases (for instance, elasto-mechanical luminescent materials or electro-mechanics of muscles) is still to be completely understood, and in these cases, the continuum and phenomenological approach can be useful to give a simpler but not simplistic picture of the whole problem. The specialistic mathematical aspects, which deal with topics like, e.g., the Wasserstein Measures amongst the others, are in many cases also to be completely studied and understood, and the whole field is very promising for new achievement and discoveries. 

This interdisciplinary MS could attract people from the Mechanics community as well as Physicists interested in phenomenological models and Mathematicians focusing on modelling and simulation of RDD systems in nature and technology. 

Keywords: Coupled Multiphysics Problems; Reaction-Diffusion-Drift equations; Gradient flows; Electrochemical interactions in continua; Soft active media; Luminescent continua; Population dynamics and epidemics; Entropic methods; Wasserstein measures.