Seminario di Adrian Muntean (TU/e)
Titolo: Case studies in averaging Smoluchovski-like interactions
The talk has two remotely connected parts: Firstly, we present a continuum PDE-ODE model for collagen self-assembly describing the interplay betweenthe change in the polymer distribution and the evolution of monomers. We endow the model with periodiccoefficients, where the small parameter is interpreted in this context as the ratio of lengths of monomers and fibrils. After applying a fixed-point homogenization argument and proving corrector estimates, we use the microscopic information incorporated in the first order correctors to explain the so-called turbidity measurement.
Secondly, we present a PDE model for the continuum motion of populations of hot colloidal particles at thepore scale inside a heterogeneous (periodic or locally-periodic) porous material. The focus is now on deriving macroscopic equations and the corresponding effective transport coefficien ts that account for the intimate interplay between the Smoluchowski aggregation and dissolution of size classes and the deposition of the biggest colloid populations on the pores surface in the presence of diffusion/dispersion. To reach this goal, we combine gradient-like estimates for both the temperature and the concentration of colloidal populations with the concept of two-scale convergence by Nguetseng and Allaire. In both cases, we compare qualitatively our multiscale modelling, mathematical analysis, and simulation results with experimental data. This work on collagen growth is jointly with B. van Lith and C. Storm (Eindhoven), while the approach on the motion of hot colloids in porous media is a work together with O. Krehel (Eindhoven) and T. Aiki (Tokyo). References and Literature for Further Reading:  B.S. van Lith, A. Muntean, A. Muntean: A continuummodel for hierarchical fibril assembly. Europhysics Letters (EPL), 106 (2014), 08004.  O. Krehel, T. Aiki, A. Muntean: A thermo-diffusion system with Smoluchowski interactions : well-posedness and homogenization. Networks and Heterogeneous Media, to appear, (2014)