Abstract
A lattice version of the driven inelastic Maxwell gas is studied in one dimension with periodic boundary conditions. Each site of the lattice is assigned with a scalar “velocity,” . Nearest neighbors on the lattice interact, with a rate , according to an inelastic collision rule. External driving, occurring with a rate , sustains a steady state in the system. A set of closed coupled equations for the evolution of the variance and the two-point correlation is found. Steady-state values of the variance, as well as spatial correlation functions, are calculated. It is shown exactly that the correlation function decays exponentially with distance, and the correlation length for a large system is determined. Furthermore, the spatiotemporal correlation can also be obtained. We find that there is an interior region , where has a time-dependent form, whereas in the exterior region , the correlation function remains the same as the initial form. exhibits second-order discontinuity at the transition points , and these transition points move away from the with a constant speed.
- Received 22 July 2016
- Revised 6 November 2016
DOI:https://doi.org/10.1103/PhysRevE.95.022115
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