Optimal transport of an active particle near a plane wall

Abstract: The control of active colloidal particles via optical traps is a cornerstone for research of matter at the micron and nanometer scale. A central challenge in this domain is the derivation of optimal transport protocols that minimize the mean work required to move a particle over a finite-time interval. Here we present a Ritz method in which open-loop protocols are constructed from a global basis of Chebyshev polynomials and optimised by a genetic algorithm. We apply the method to study optimal transport of an active particle, which is modelled as a force-dipole (or a stresslet) near a no-slip wall. The methodology is validated in the limits of zero activity and infinite wall separation, where it successfully recovers the known analytical protocols and the theoretical minimum work. Crucially, we demonstrate that the presence of the boundary breaks the time-reversal symmetry of the optimal protocol found in bulk solutions. This symmetry breaking is shown to be a complex function of the transport direction and the particle's intrinsic activity. Because the presented approach requires only the capability to simulate stochastic trajectories, it offers a robust, principled framework for optimizing transport protocols in complex fluid environments that remain inaccessible to exact analytical treatment.