Eventos Anais de eventos
COBEM 2023
27th International Congress of Mechanical Engineering
Mechanical Effects on Turing Pattern Formation in Bulk Diffusion and Surface Reaction-diffusion Systems
Submission Author:
Francisco S. Forte Neto , PA
Co-Authors:
Francisco S. Forte Neto, Fernando Pereira Duda
Presenter: Fernando Pereira Duda
doi://10.26678/ABCM.COBEM2023.COB2023-2217
Abstract
The coupling between bulk diffusion and surface reaction-diffusion is a critical factor underlying many complex behaviors observed in fields like material science and biology, including phenomena such as chemical pattern formation and oscillations. This study investigates how this coupling is influenced by mechanical effects resulting from bulk diffusion occurring within an elastic solid. In particular, we address the role played by this mechanochemical interplay in the formation of Turing's patterns using a reaction kinetics model of the Fitzhugh--Nagumo type. To achieve this objective, we perform numerical simulations of the nonlinear system of equations using a mixed finite element implementation in the COMSOL Multiphysics platform. The proposed numerical formulation is applied to the investigation of pattern formation on the surface of a sphere. The results suggest that a pressure load applied to the surface has a stabilizing effect, suppressing pattern formation in the bulk variable.
Keywords
bulk-diffusion, surface reaction-diffusion, Fitzhugh–Nagumo kinetics, mechanochemical coupling
