Fig. 4: Instability and transition of the active fluid with ϕ = 0.5.
From: Shaping active matter from crystalline solids to active turbulence
a An oscillatory active flow self-organizes via instability at Pe = 5, when the dense population of disks shifts periodically between the corners (this snapshot) and the center (SI Sec. III.F) of the domain. b History of domain-averaged absolute pressure \({\langle | {\Phi }_{{{{{{{{\rm{E}}}}}}}}}| \rangle }_{xy}\) and speed \({\langle | {{{{{{{{\bf{U}}}}}}}}}_{{{{{{{{\rm{E}}}}}}}}}| \rangle }_{xy}\) of the active fluid implies the absence and emergence of a self-organized flow at Pe = 3 and Pe = 5, respectively. c Wave-like spatiotemporal evolution of x-averaged pressure \({\langle {\Phi }_{{{{{{{{\rm{E}}}}}}}}}\rangle }_{x}\) and velocity component \({\langle {V}_{{{{{{{{\rm{E}}}}}}}}}\rangle }_{x}\) at Pe = 5. d Corrugated kymograph of \({\Phi }_{{{{{{{{\rm{E}}}}}}}}}{| }_{x=\frac{L}{2}}\) sampled along the median x = L/2 when Pe = 5 (upper) versus its disrupted counterpart for Pe = 10 (lower). e History of \({\langle {\Phi }_{{{{{{{{\rm{E}}}}}}}}}{| }_{x=\frac{L}{2}}\rangle }_{y}\) depicts the evolution and saturation of disturbances mimicking those of their canonical hydrodynamic analog. f, when Pe = 10, disks form clusters that breakdown the wave patterns. The clusters are characterized by the number Nclu of their constituting disks. g Cluster size distribution function \({{{{{{{\mathcal{P}}}}}}}}({N}_{{{{{{{{\rm{clu}}}}}}}}})\), and its fitted curves following \({{{\mathcal{P}}}}({{N}_{{{\rm{clu}}}}})={{{{\mathcal{C}}}}_{1}}{{N}_{{{\rm{clu}}}}^{-{{{\mathcal{C}}}}_{2}}}\exp \left(-{{N}_{{{\rm{clu}}}}}/{{N}_{{{\rm{clu}}}}^{ \nmid }}\right)\) defined in SI Sec. I.D. See Source data.
