Microscopic position and structure of a shock in CA 184

Abstract

We consider the time evolution of the cellular automaton CA 184 with random initial conditions. We derive a partial differential equation that describes the macroscopic time evolution of the coarse-grained local density and we study some solutions of this equation, in particular shock solutions and rarefaction-type solutions for initial step profiles. In order to elucidate the emergence of the large-scale hydrodynamic 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.

Exact domain wall theory for deterministic TASEP with parallel update

“…The constant D differs from the one found by Belitsky et al [26], which applies to a particular type of shock. It is also different from that of SDWT.…”

“…Note that the constant D given above differs from the one found by Belitsky et al [31], which actually applies to a particular type of shock. Our exact expression ( 12),( 16) for D disagrees with that of SDWT and also with equation ( 56) from [23], conjectured on the basis of an exact calculation.…”

“…We introduce a marker that will turn out to play the role of a domain wall. We say that the leftmost particle ever to have been blocked carries a flag similar to the shock marker introduced in [31]. If no particle in the system has ever been blocked, the flag occupies by convention a virtual site L + 1.…”

Self-duality and shock dynamics in the n-species priority ASEP

“…This may allow for finding dualities and non-Abelian symmetries in these processes. Our results also indicate a link between current fluctuations [78,73,3,46,58,40,20] and the dynamics of shocks [69,9,8,10,22] via self-duality since for both problems the same duality functions are used.…”

Duality, supersymmetry and non-conservative random walks

“…Recent applications of duality for the study of physical properties of classical IPS include current fluctuations, shock motion, and heat conduction [9][10][11][12][13][14][15][16][17][18][19][20]. An interesting J. Stat.…”