# Binary phase separation in a collection of self-propelled particle with variable speed

## TL;DR

This paper investigates the collective behavior and phase separation in a binary mixture of self-propelled particles with variable speeds, revealing four distinct phases and the independence of transition nature from speed variability.

## Contribution

It introduces a variable speed parameter into the Vicsek model for self-propelled particles and explores the resulting phase behavior in mixed systems, extending understanding of active matter dynamics.

## Key findings

- System exhibits disorder-to-ordered transition regardless of speed variability.
- Four distinct phases identified based on order and density parameters.
- Transition characteristics are independent of the variable speed parameter.

## Abstract

We study the collective behavior of binary mixture of self-propelled particles. Particles moves along their heading direction with {\it variable speed} and interact through short range alignment interaction. A variable speed parameter $\gamma >0$ is introduced such that for $\gamma=0.0$ model reduces to {\it constant speed} Vicsek's model. We mix the particles with two different $\gamma$'s and study the steady state behavior of the mixture for different choice of $\gamma$'s and noise strength. One of the $\gamma$ is kept fixed to $1.0$ and another one is varied from small $0.0$ to larger values $8.0$. Properties of system is characterise by two types of order parameters (i) orientation order parameter, which is a measure of ordering in the system and (ii) density order parameter, which measures the phase separation is the system. For all set of $\gamma$'s, system shows a transition from disorder-to-ordered state on the variation of noise strength. The nature of transition and critical noise is independent of value of $\gamma$, which is also supported from coarse-grained hydrodynamic study. On the variation of system parameters, ($\gamma$'s, $\eta$), we find four distinct phases, (i) ordered phase separated, (ii) ordered mixed, (iii) disordered mixed and (iv) disordered phase segragated. Our study shade light on different phases of mixture of different types of active particles.