Incorporating Cellular Stochasticity in Solidxe2x80x93Fluid Mixture Biofilm Models The dynamics of cellular aggregates is driven by the interplay of mechanochemical processes and cellular activity. Although deterministic models may capture mechanical features, local chemical fluctuations trigger random cell responses, which determine the overall evolution. Incorporating stochastic cellular behavior in macroscopic models of biological media is a challenging task. Herein, we propose hybrid models for bacterial biofilm growth, which couple a two phase solidfluid mixture description of mechanical and chemical fields with a dynamic energy budgetbased cellular automata treatment of bacterial activity. Thin film and plate approximations for the relevant interfaces allow us to obtain numerical solutions exhibiting behaviors observed in experiments, such as accelerated spread due to water intake from the environment, wrinkle formation, undulated contour development, and the appearance of inhomogeneous distributions of differentiated bacteria performing varied tasks.

Stochastic homogenization of multicontinuum heterogeneous flows Abstract   We consider a multicontinuum model in porous media applications, which is described as a system of coupled flow equations. The coupling between different continua depends on many factors and its modeling is important for porous media applications. The coefficients depend on particle deposition that is described in term of a stochastic process solution of an SDE. The stochastic process is considered to be faster than the flow motion and we introduce timespace scales to model the problem. Our goal is to pass to the limit in time and space and to find an associated averaged system. This is an averaginghomogenization problem, where the averages are computed in terms of the invariant measure associated to the fast motion and the spatial variable. We use the techniques developed in our previous paper (Bessaih et al., 2019) to model the interactions between the continua and derive the averaged model problem that can be used in many applications.