| Abstract: |
| Active phase separation leads to behaviors that significantly differ from those of classical systems. Instead of the usual coarsening, where larger droplets grow at the expense of smaller ones, chemically active mixtures can maintain stable populations of finite-sized droplets, which may even grow, divide, or form more complex structures. These dynamics have been proposed as simple models for protocells and early self-organizing biological structures.
In this talk, I present a mathematical framework for active droplet dynamics based on two complementary descriptions: the phase-field Cahn--Hilliard equation and its sharp-interface limit given by the Mullins--Sekerka free-boundary problem. I discuss the relation between these models, address questions of well-posedness and stability in symmetric settings, and conclude with numerical simulations illustrating phenomena such as droplet division and shell formation. |
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