We propose a minimal mathematical model to explain long-range coordination of dynamics of multiple cells in epithelial spreading, which may be induced, under different conditions, by a chemical signal, or mechanically induced strain, or both. The model is based on chemo-mechanical interactions including a chemical effect of strain, chemically induced polarization and active traction, and interaction between polarized cells. The results, showing kinase concentration distribution and cell displacement, velocity, and stress fields, allow us to reproduce qualitatively available experimental data and distinguish between distinct dynamical patterns observed under conditions of injury or unconstraining.

The structure formation of convection rolls in Maxwellian fluids that are heated from below in a Rayleigh-Bénard setup is investigated close to onset with a simple few-modes ansatz and by solving the hydrodynamic field equations with a finite-difference method. Depending on the magnitude of the viscoelastic relaxation time one can have besides stationary convection also oscillatory patterns in the form of standing or traveling waves. The existence and stability regions of these convection structures are determined. The convection behavior of the model is compared with the results of full numerical simulations. Furthermore, the effect of modulating the heating periodically in time on the stability of the quiescent conductive state of the fluid and on its convection behavior is investigated as a function of the fluid's viscoelasticity.

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