Manuscript on simulating interacting active droplets
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We uploaded a preprint on the main results from Ajinkya’s PhD thesis on arxiv. In this slightly technical work, we propose a new numerical algorithm to simulate interacting active droplets.
The main idea of the algorithm is to only simulate the relevant degrees of freedom, which in our case are droplet radii & positions as well as large-scale information about the background field. This reduced set of variables can be evolved in time much faster than the usual fine-grained fields necessary for a full description of the phase separation process, e.g., using a Cahn-Hilliard equation. We are now in a position to simulate systems of much larger size for longer evolution times, optionally also with (active) chemical turnover and imposed chemical gradients; see the inset. To develop the algorithm, and in particular couple the dynamics of the droplets to the background field, we leveraged analytical results to bridge length scales. In the future, this approach will allow us to explorer dynamics that are relevant to the behavior of droplets in biological cells and other challenging situations that were previously not numerically accessible.
