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See supplemental material: movie 1 and 2 respectively are the motion of topological active particles with \(k N N\) interaction and \(V T\) interaction in \(\rho_o = 0\). Movie 3 and 4 respectively are the motion of topological active particles with \(k N N\) interaction and \(V T\) interaction in \(\rho_o = 0.5\). Movie 5 and 6 respectively are the motion of topological active particles with \(k N N\) interaction and \(V T\) interaction in \(\rho_o = 1\). Other parameters: self-propulsion speed \(v_0 = 0.1\), time step \(\Delta t = 0.1, k = 6\) and the number of active particles \(N_a = L \times L = 100\). |
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