Microscopic position and structure of a shock in CA 184 V. Belitsky 1 and G.M. Sch¨ utz 2 May 9, 2011 1 Instituto de Matem´ atica e Est´ atistica, Universidade de S˜ aoPaulo, Rua do Mat˜ao, 1010, CEP 05508-090, S˜ ao Paulo - SP, Brazil Email: belitsky@ime.usp.br 2 Theoretical Soft Matter and Biophysics, Institute of Complex Systems, Forschungszen- trum J¨ ulich, 52425 J¨ ulich, Germany Email: g.schuetz@fz-juelich.de Abstract We consider the time evolution of the cellular automaton CA 184 with random initial conditions. We derive a partial differential equa- tion that describes the macroscopic time evolution of the coarse grained local density and we study some solutions of this equation, in par- ticular shock solutions and rarefaction-type solutions for initial step profiles. In order to elucidate the emergence of the large scale hy- drodynamic behaviour we define a microscopic position of a shock and find its mean velocity, its diffusion coefficient and the microscopic structure of the shock as seen from this position. Keywords: cellular automata, hydrodynamic limit, shock, second class particle MSC2010 classification codes: 82C20. Secondary: 60K35, 82C23 1