Critical behaviour of annihilating random walk of two species with exclusion in one dimension

The $A+A\to 0$, $B+B\to 0 $ process with exclusion between the differentkinds is investigated here numerically. Before treating this model explicitly,we study the generalized Domany-Kinzel cellular automaton model of Hinrichsenon the line of the parameter space where only compact clusters can grow. Thesimplest version is treated with two absorbing phases in addition to the activeone. The two kinds of kinks which arise in this case do not react leading tokinetics differing from standard annihilating random walk of two species. Timedependent simulations are presented here to illustrate the differences causedby exclusion in the scaling properties of usually discussed characteristicquantities. The dependence on the density and composition of the initial stateis most apparent. Making use of the parallelism between this process anddirected percolation limited by a reflecting parabolic surface we argue thatthe two kinds of kinks exert marginal perturbation on each other leading todeviations from standard annihilating random walk behavior.