The dynamics of interacting domain walls, regarded as a system of particles which are biased to move towards their nearest neighbors and annihilate when they meet, have been studied in the recent past. We study the effect of the presence of a fraction $r$ of quenched impurities (which act as rigid walkers) on the dynamics. Here, in the case where two domain walls or one impurity and one domain wall happen to be on the same site, both get simultaneously annihilated. It is found that for any nonzero value of $r$, the dynamical behavior changes as the surviving fraction of particles $\rho \left(t\right)$ attains a constant value. $\rho \left(t\right)t^{\alpha }$ shows a universal behavior when plotted against $r^{\beta }{t}^{\alpha }$ with $\alpha ,\beta$ values depending on whether the particles are rigid or nonrigid. Also, the values differ for the biased and unbiased cases. The timescale associated with the particle decay shows that it varies with $r$ in a power-law manner with an exponent $\approx \frac{\beta }{\alpha }$ as expected.

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• Random walks
• Monte Carlo methods