Optimal transport and control of active drops

Suraj Shankar, Vidya Raju, and L. Mahadevan

PNAS

Transportation, in its broadest sense, is an important task in many fields, including engineering, physics, biology, and economics, and a great deal is known about optimal and efficient strategies to move matter, energy, and information around. But can we craft similar optimal protocols to transport autonomously moving (active) matter, such as self-propelled drops or migrating cells? We develop an optimal control framework to transport active fluid drops with the least amount of energy dissipated, by manipulating the spatio-temporal profile of its internal active stresses. By combining numerical solutions and analytical insight, we uncover simple principles and characteristic trade-offs that govern the optimal policies, suggesting general strategies for optimal transportation in a wide variety of synthetic and biological active systems.

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