The Totally Asymmetric Simple Exclusion Process (TASEP) is an important example of a particle system driven by an irreversible Markov chain. In this paper we give a simple yet rigorous derivation of the chain stationary measure in the case of parallel updating rule. In this parallel framework we then consider the blockage problem (aka slow bond problem). We find the exact expression of the current for an arbitrary blockage intensity in the case of the so-called rule-184 cellular automaton, i.e. a parallel tasep where at each step all particles free-to-move are actually moved. Finally, we investigate through numerical experiments the conjecture that for parallel updates other than rule-184 the current may be non-analytic in the blockage intensity around the value epsilon = 0.
Scoppola, B., Lancia, C., Mariani, R. (2015). On the Blockage Problem and the Non-analyticity of the Current for Parallel TASEP on a Ring. JOURNAL OF STATISTICAL PHYSICS, 161(4), 843-858 [10.1007/s10955-015-1352-4].
On the Blockage Problem and the Non-analyticity of the Current for Parallel TASEP on a Ring
Scoppola B.;Lancia C.;Mariani R.
2015-01-01
Abstract
The Totally Asymmetric Simple Exclusion Process (TASEP) is an important example of a particle system driven by an irreversible Markov chain. In this paper we give a simple yet rigorous derivation of the chain stationary measure in the case of parallel updating rule. In this parallel framework we then consider the blockage problem (aka slow bond problem). We find the exact expression of the current for an arbitrary blockage intensity in the case of the so-called rule-184 cellular automaton, i.e. a parallel tasep where at each step all particles free-to-move are actually moved. Finally, we investigate through numerical experiments the conjecture that for parallel updates other than rule-184 the current may be non-analytic in the blockage intensity around the value epsilon = 0.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
