Multi-scale Modelling of Computers Made from Excitable Chemical Droplets

Here we review and extend models on different scales for a computing architecture made from networks of excitable chemical droplets. The model system of the Belousov-Zhabotinsky (BZ) reaction enclosed in lipid-coated droplets in oil is used to study signal transmission dynamics of chemical computers and their modelling. The excitable medium oscillates in the sub-excitable, excitable or self-exciting regimes, leading to excitation pulses that spread over the medium and can be used for information processing. We review a homogeneous differential equation model, the spatially extended partial differential equation model and a cellular automaton model of the chemical reaction and propose a new high level modelling approach for the droplets, which uses discrete states and potentially stochastic transition functions to represent the complex chemical state of each droplet. We show how the parameters like oscillation periods, diffusion coefficients and wave propagation speed for the models can be deduced from the lower level models and from experimental data. Furthermore we offer an outlook on the currently ongoing work and the role of the different modelling and simulation scopes within.