Optimal design for active self-assembly system

Two key issues in stochastic self-assembly are whether the system will converge to the desirable global equilibrium and how quickly it converges. In this paper an optimal self assembly design approach, which guarantees the unique desirable convergence and provides the fastest convergence rate, is proposed for active self-assembly systems. We adopt a Markov chain to model the self-assembly system. Based on the convergence theory of a Markov chain, we solve an optimization problem in which minimizing a certain function involved in the Markov chain results in both maximum yield of the target assemblies at the equilibrium and optimal convergence rate to the desired equilibrium. Several examples are carried out to further illustrate the importance and the effectiveness of the proposed approach.