Emergence and melting of active vortex crystals

Abstract

Melting of two-dimensional (2D) equilibrium crystals is a complex phenomenon characterized by the sequential loss of positional and orientational order. In contrast to passive systems, active crystals can self-assemble and melt into an active fluid by virtue of their intrinsic motility and inherent non-equilibrium stresses. Currently, the non-equilibrium physics of active crystallization and melting processes is not well understood. Here, we establish the emergence and investigate the melting of self-organized vortex crystals in 2D active fluids using a generalized Toner-Tu theory. Performing extensive hydrodynamic simulations, we find rich transition scenarios. On small domains, we identify a hysteretic transition as well as a transition featuring temporal coexistence of active vortex lattices and active turbulence, both of which can be controlled by self-propulsion and active stresses. On large domains, an active vortex crystal with solid order forms within the parameter range corresponding to active vortex lattices. The melting of this crystal proceeds through an intermediate hexatic phase. Generally, these results highlight the differences and similarities between crystalline phases in active fluids and their equilibrium counterparts.

Mesoscopic simulations of active nematics

“…In stochastic, particle-based algorithms, diffusion dominates over advection, making these suitable for the small Péclet number limit. This is in contrast to hydrodynamic solvers, such as pseudo-spectral methods ( 45 ), which do not inherently account for diffusion and, thus, operate in the large Péclet number limit where advection dominates. MPCD allows for both advection and diffusion and, thus, is suitable for simulations of systems with moderate Péclet numbers.…”

Lagrangian Manifestation of Anomalies in Active Turbulence

“…The simulations are performed for 5 × 10 5 iterations with time-steps δt = 0.001 and, in some cases, δt = 0.0002 for higher temporal resolution. We choose Γ 0 = 0.045, Γ 2 = Γ 3 0 , β = 0.5, and λ = 3.5, consistent with earlier studies [16,22,[31][32][33]. The flow, after a spinup time of 2 × 10 4 iterations, is seeded with 1 × 10 5 randomly distributed tracers which evolve as dx/dt = u(x(t)), with x(t) being the tracer location at time t. We use a fourth-order Runge-Kutta scheme, along with a bilinear interpolation scheme to obtain the fluid velocity at the particle positions u(x(t)), to evolve the tracers.…”

Optimal turbulent transport in microswimmer suspensions

“…However, it is largely unexplored how the complex emerging large-scale flow patterns, which are typical for such microswimmer suspensions, impact the mixing and transport properties of these non-equilibrium systems. Here, we quantify active fluid transport in the framework of an experimentally validated model for polar active fluids, which enables a precise control of the flow states ranging from vortex lattices [16][17][18][19][20][21][22] to active turbulence [21][22][23][24][25][26], either externally, e.g. through obstacles [17,19,20,27,28], or by changing the fluid parameters [18,21,22].…”