“…The behavior of the system consisting of motile microswimmers (artificial self-propelled Janus particles or sperm cells) and passive species (synthetic beads or immotile sperm cells and debris) is simulated by numerically integrating the overdamped Langevin equations: 16,21,22,32,33,35–37,39,40
for i , j running from 1 to the total number N of particles, active and passive; v 0 is self-velocity of active particles. Here, ξ i 0 ( t ) = ( ξ i 0, x ( t ), ξ i 0, y ( t )) is a 2D thermal Gaussian noise with correlation functions 〈 ξ 0, α ( t )〉 = 0, 〈 ξ 0, α ( t ) ξ 0, β ( t )〉 = 2 D T δ αβ δ ( t ), where α , β = x , y and D T is the translational diffusion constant of a passive particle at fixed temperature; ξ θ ( t ) is an independent 1D Gaussian noise with correlation functions 〈 ξ θ ( t )〉 = 0 and 〈 ξ θ ( t ) ξ θ (0)〉 = 2 D R δ ( t ) that models the fluctuations of the propulsion angle θ .…”