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We study the dynamics of circular active particles (AP) on a two dimensionalperiodic undulated surface. Each particle has an internal energy mechanismwhich is modeled by an active friction force and it is controlled by anactivity parameter $v_0$. It acts as negative friction if the speed of theparticle is smaller than $v_0$ and normal friction otherwise. Surfaceundulation is modeled by the periodic undulation of fixed amplitude andwavelength and is measured in terms of a dimensionless ratio of amplitude andwavelength, $\bar{h}$. The dynamics of the particle is studied for differentactivities, $v_0$ and surface undulations (SU), $\bar{h}$. Three types ofparticle dynamics are observed on varying activity and SU. For small $v_0\lesssim 0.1$ and $\bar{h}$ $\gtrsim 0.8$, particles remain confined in asurface minimum, for moderate $v_0 \lesssim \bar{h}$, dynamics of particleshows an intermediate subdiffusion to late time diffusion and for large $v_0\gtrsim \bar{h}$, it shows initial superdiffusion to late time diffusion. Forall $v_0$'s and $\bar{h} \lesssim 0.2$, the dynamics of particle, satisfies theGreen-Kubo relation between the effective diffusivity and velocityauto-correlation function. Systematic deviation is found on increasing$\bar{h}$. Hence, an effective equilibrium can be established for a range ofsystem parameters in this nonequilibirum system.

Dynamics of a collection of active particles on a two-dimensional periodic undulated surface