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Please note that this seminar will take place online via Zoom. You can connect to this seminar via the following link:

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In this talk we present analytical studies of active gels and cell motility. ÌýWe start from a briefÌý Ìýoverview of out-of-equilibrium active matter systems (e.g., active gels, bacterial suspensions, etc.) andÌý mathematicalÌý challengesÌý in theirÌý modeling and analysis.

Next we present three minimal models of active gels: a phase-field model and two free boundary models. While having a minimal set of parameters and variables, these models capture key biophysical phenomena such as persistent & turning motion, and spontaneous symmetry breaking. The main focus of the talk is stability analysis of our recently developed 2D Hele-Shaw type free boundary (FBP) model. Bifurcation analysis of this model reveals the transition from sub- to supercritical bifurcations of the rest states to traveling waves and bistability in subcritical bifurcation.Ìý We show that this transition occurs due to the gradient coupling, which is a signature mathematical feature of ÌýÌýactive matter. Our analysis is based on the center manifold consideration for the underlying non-linear dynamical system. The challenges in the stability analysis are due active terms in the FBP model that manifestsÌý as the Ìýnon self-adjoint form of the corresponding linearized operator.

In summary, we identify the key mathematical structures behind the models of active matter such as gradient coupling, reduction of the vectorial models to a scalar Liouville type equations, Keller-Segel cross-diffusion in free boundary settings, and center manifold analysis of Ìýfree boundary models.

If time permits,Ìý we will discuss recent work in progress on free boundary models of tissue growthÌý (joint withÌý J. Casademunt, et al) and numerics (with A. Safsten).

These are joint works with V. Rybalko (ILTPE, Kharkiv, Ukraine) and J. Fuhrman (PSU & Mainz, Germany).

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