Active particles with delayed attractions form quaking crystallites ^(a)

Abstract

Perception-reaction delays have experimentally been found to cause a spontaneous circling of microswimmers around a fixed target particle. Here we investigate a many-body version of such an experiment with Brownian-dynamics simulations of active particles in a plane. For short delays, they form a hexagonal crystallite around the target. The bifurcation to a chiral dynamical phase, seen for longer delays, maps onto that for a single active particle. Different angular velocities at different distances from the target induce shear stresses that grow with increasing delay. By exciting shear bands, they shake and intermittently break the rotating crystallite. For long delays, it detaches from the target to circle around it near the preferred single-particle orbit as a compact spinning satellite, trembling from what could be called tidal quakes.

Matrix numerical method for probability densities of stochastic delay differential equations

“…Examples range from feedback-controlled Brownian particles [2][3][4][5] and robots [6][7][8] over various biological [9][10][11][12][13] and physical [14][15][16] systems to finance [17]. SDDEs also successfully describe instabilities in car traffic [18] and recently, they have been applied to model other manybody nonequilibrium phenomena with time-delayed interactions such as flocking or swarming [19][20][21][22][23][24][25][26][27].…”

Harnessing synthetic active particles for physical reservoir computing

“…A retarded propulsion towards an immobilized target particle creates a self-organized non-linear dynamical system that is, despite the strong Brownian noise, capable of predicting chaotic time series such as Mackey–Glass and Lorenz series when used as a physical node in a reservoir computer. The key element of this physical recurrent node is a time delay realizing a retarded interaction 27 , 53 , 54 that creates the fading memory as a basic requirement for reservoir computing 8 . It also provides the coupling of the active particle dynamics to its past allowing to implement virtual nodes living on a single physical active particle system via time-multiplexing 12 , 44 .…”