Glassiness in cellular Potts model of biological tissue is controlled by disordered energy landscape

Glassy dynamics in a confluent monolayer is indispensable in morphogenesis, wound healing, bronchial asthma, and many others; a detailed theoretical understanding for such a system is, therefore, important. We combine numerical simulations of a cellular Potts model and an analytical study based on random first order transition (RFOT) theory of glass, develop a comprehensive theoretical framework for a confluent glassy system, and show that glassiness is controlled by the underlying disordered energy landscape. Our study elucidates the crucial role of geometric constraints in bringing about two distinct regimes in the dynamics, as the target perimeter P0 is varied. The extended RFOT theory provides a number of testable predictions that we verify in our simulations. The unusual sub-Arrhenius relaxation results from the distinctive interaction potential arising from the perimeter constraint in a regime controlled by geometric restriction. Fragility of the system decreases with increasing P0 in the low-P0 regime, whereas the dynamics is independent of P0 in the other regime. The mechanism, controlling glassiness in a confluent system, is different in our study in comparison with vertex model simulations, and can be tested in experiments.

Non-Critical Open Strings Beyond the Semiclassical Approximation

We studied the lowest order quantum corrections to the macroscopic wave functions Γ(A,ℓ) of non-critical string theory using the semiclassical expansion of Liouville theory. By carefully taking the perimeter constraint into account we obtained a new type of boundary condition for the Liouville field which is compatible with the reparametrization invariance of the boundary and which is not only a mixture of Dirichlet and Neumann types but also involves an integral of an exponential of the Liouville field along the boundary. This condition contains an unknown function of A/ℓ2. We determined this function by computing part of the one-loop corrections to Γ(A,ℓ).