Reaction flow artificial chemistries

Artificial chemistries have been analysed mostly under the precondition of a well-stirred reaction vessel. In other words, the localisation of molecules is ignored for simplicity. Here we drop this assumption and replace it with a spatial distribution of molecules given by a flow, i.e. molecules move according to a given vector field. This can be seen as a particular type of dynamics. It also gives additional parameters to the control over the development of the chemistry over time. In particular, the modelling of membranes and transport processes which occur in cells, for example, can be described using continuous vector fields instead of giving a discrete formulation. We give some examples and ideas for analysing such chemistries via a stochastic simulation, a PDE and chemical organisations.