![]() ![]() Only a small subset of the full domain ( 1 / 16 th zoomed-in region) is shown. (a) and (b) illustrate the polarity field (left panels) and the corresponding velocity field (right panels) characterized by streamlines (solid black lines) colored by the normalized vorticity ω / ω max. There are no such peaks for the kurtosis of the rms velocity, which indicates there is no equivalent crossover regime. In between, the crossover is characterized by very rare formation and annihilation events, as evidenced by the peaks in κ (blue highlighted areas). ![]() For small activity levels, there are no defects at all and κ is set by convention to − 3. For large activity levels, κ ( ρ d ) ≃ 0, which indicates the population of defects is typically equilibriumlike and follows a normal distribution law. The excess kurtosis κ i values of both quantities are also represented at the bottom. Results were averaged over time and for ten simulations from different initial conditions the error bars stand for the corresponding standard deviation. Active turbulence arises as soon as the activity is nonzero, but topological defects form and persist in the polarity field only beyond a finite threshold in both contractile ( ζ 0). Shown here are the averaged defect density (blue dots) and the rms velocity (orange dots) in units of V p = A K / η, characterizing the passive relaxation velocity of the polar particles. These findings reveal a dynamical crossover between distinct spatiotemporal organization patterns in polar active matter.Ĭrossover from defect-free to defect-laden active turbulence upon increasing strength of active stresses. Despite the distinct symmetry features between these two active turbulence regimes, the flow fluctuations exhibit universal statistical scaling behaviors at large scales, while the spectrum of polarity fluctuations decays exponentially at small length scales compared to the active energy injection length. By stability analyses of the topological charge density field, we provide theoretical insights on the criterion for the crossover to the defect-laden active turbulent state. ![]() Interestingly, we show that concurrent to the crossover from defect-free to defect-laden active turbulence is the restoration of the previously broken SO ( 2 ) symmetry signaled by the fast decay of the two-point correlations. Here, we reveal a crossover between defect-free active turbulence and active turbulence laden with topological defects. Coherent flows of self-propelled particles are characterized by vortices and jets that sustain chaotic flows, referred to as active turbulence. ![]()
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