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Multi-scale Modelling of Computers Made from Excitable Chemical Droplets
Gerd Gruenert, Jan Szymanski, Julian Holley, Gabi Escuela, Alexandra Diemi, Bashar Ibrahimi, Andrew Adamatzky, Jerzy Gorecki and Peter Dittrichi

Here we review and extend models on different scales for a computing architecture made from networks of excitable chemical droplets. A system of lipid covered droplets containing reagents of the Belousov-Zhabotinsky (BZ) reaction has been used in our experiments as model system to study the signal transmission dynamics of chemical computers and their modelling. A chemical medium in sub-excitable, excitable or self-exciting (oscillating) regimes supports propagating excitation pulses. These pulses can be used for information coding and processing. In the manuscript we review models that can be applied to describe the time evolution of a medium composed of droplets: we discuss a homogeneous differential equation model, a spatially extended partial differential equation model and a cellular automaton model of the chemical reaction. Furthermore, we propose a new high level modelling approach for the droplets, that discretises the chemical states and considers stochasticity in the transition functions. We demonstrate how the values of experimentally measured quantities like oscillation periods, diffusion coefficients and wave propagation speeds can be deduced from the lower level models. Furthermore we offer an outlook on the currently ongoing work and the role of the different modelling and simulation scopes within.

Keywords: Multi-scale modelling, Belousov-Zhabotinsky reaction, chemical droplets, reaction-diffusion, stochastic simulation, deterministic simulation

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