Inhomogeneous activity enhances density phase separation in active model B

We study the binary phase separation in active model B, on a two-dimensional substrate with inhomogeneous activity. The activity was introduced with a maximum value at the center of the box and spread as a Bivariate-Gaussian distribution as we move away from the center. The system was studied for three different intensities of the distribution. Towards the boundary of the box, activity is zero or the model is similar to the passive model B. We start from the random homogeneous distribution of density of particles, and the system evolves towards a structured distribution of density. With time, density starts to phase separately with maximum density at the center of the box and decreases as we move away from the center of the box. The width of the density profile at the center increases as a power lawexponent{\alpha}(t) remains close between 2/3 to 3/4 up to some moderate time and then decays to zero in the steady state. Hence, our result shows the response of density in an active binary system with respect to the patterned substrate. It can be used to design devices useful for the trapping and segregation of active particles.