Solar flare cellular automata interpreted as discretized MHD equations
H. Isliker, A. Anastasiadis, D. Vassiliadis, L. Vlahos · 1998
We show that the Cellular Automaton (CA) model for Solar flares of Lu and Hamilton (1991) can be understood as the solution to a particular partial differential equation (PDE), which describes diffusion in a localized region in space if a cer- tain instability threshold is met, together with a slowly acting source term. This equation is then compared to the induction equation of MHD, the equation which governs the energy re- lease process in solar flares. The similarities and differences are discussed. We make some suggestions how improved Cellular Automaton models might be constructed on the basis of MHD, and how physical units can be introduced in the existing respec- tive Cellular Automaton models. The introduced formalism of recovering equations from Cellular Automata models is rather general and can be applied to other situations as well. subsystems. The essence of the CA approach to such systems is to assume that the global dynamics, if described statistically, are not sensitive to the details of the elementary processes, the system has the property that most local information gets lost if viewed globally. The 'classical' approach to complex systems, on the other hand, is analytical: from a precise description of the elementary processes — in the optimum case involving the fundamental laws of physics, i.e. differential equations — one tries to understand a process globally. Both approaches have drawbacks and advantages. The CA approach does not explain what happens locally or over short time intervals, but it allows to understand the statistics of the global behaviour. The analyt- ical approach may reveal insights into the local processes, but coupling this understanding to a global description is practically not feasible, mainly due to the large number of (in astrophysics even unobserved) boundary conditions. In this sense, the two ap- proaches can be considered as complementary, and a description