Density phase separation and order-disorder transition in a collection of polar self-propelled particles

We study the order-disorder transition in a collection of polar self-propelled particles, interacting through a distance dependent short range alignment interaction. A distance dependent interaction parameter $a_0$ is introduced such that on decreasing $a_0$ interaction decay faster with distance $d$ and for $a_0=1.0$ model reduces to Vicsek's type. For all $a_0>0.0$, system shows a transition from disorder to long ranged ordered state. We find another phase transition from phase separated to nonphase separated state with decreasing $a_0$: at the same time order-disorder transition changes from discontinuous to continuous type. Hence density phase separation plays an important role in predicting the nature of order-disorder transition. We also calculate the two-point density structure factor using coarse-grained hydrodynamic equations of motion with an introduction of a density dependent alignment term in the equation introduced by Toner and Tu \cite{tonertu}. Density structure factor shows a divergence at a critical wave-vector $q_c$, which decreases with decreasing density dependent alignment term. Alignment term in the coarse-grained equation plays the same role as the distance dependent parameter $a_0$ in the microscopic simulation. Our results can be tested in many biological systems: where particle have tendency to interact strongly with their closest neighbours.