Excitation of a conserved lattice gas model as a possible toy model for granular systems

Abstract

We present an excited CLG model in order to better represent a granular setup on a 1D lattice. The proposed model takes into account multiple particle to particle interactions in each time step by use of a block cellular automaton with a Margolus neighborhood, as compared to the original model which only acted on one particle every iteration. This allows for a more realistic simulation of granular systems. We found that the time it takes before the system reaches a steady state, T_a, follows an exponential trend. We also found that our model no longer approaches a steady state at a critical density of ρ_c ≈ 0.37. Any values of ρ > ρ_c exhibit a constant state of movement. We further evolve the system by adding shaking using a probabilistic cellular automata (PCA), which employs the probabilities m and c that we defined to be the probability of migration and cohesiveness, respectively. Here we found that both play an equal role in the dynamics of the system. Such a setup can be used for further studies in measuring temperature in granular systems.