Multiscale modeling, analysis and simulation of reaction-diffusion processes in porous media. Application to carbohydrat

Lehrstuhl für Angewandte Mathematik

FAU Kontaktperson:
Prechtel, Alexander Dr.
Neuß, Maria PD Dr.
Ray, Nadja Dr.
Elbinger, Tobias


We consider porous media consisting of
different components separated by interfaces. Inside of each component
diffusion and nonlinear reaction processes take place. The exchange of
substances at interfaces is controlled by the concentrations on both
sides of the interface via nonlinear transmission conditions. At
interfaces also nonlinear reaction and surface diffusion can occur. We
start from microscopic descriptions, where the geometry of medium, the
processes inside the components, and the transmission conditions at the
interfaces are are resolved. Then, under suitable conditions on the
distribution of the components inside the medium (e.g. periodic, locally
periodic or stochastic distribution), we derive effective
approximations by using techniques of multiscale analysis and
homogenization. Hereby, existing techniques have to be further developed
to cope with the special feature of our models, e.g. nonlinear
transmission conditions on microscopic interfaces.

models are applied to the mathematical modeling of metabolic and
regulatory processes in living cells, where biochemical species are
exchanged between organelles (like mitochondria or plastids) and
cytoplasm through organellar membranes, or are attached to membranes,
where they undergo enzymatic reactions. In this context, the
nonlinearities are given by kinetics corresponding to multi-species
enzyme catalyzed reactions, which are generalizations of the classical
Michaelis-Menten kinetics for multi-species reactions.

concerning metabolic reaction networks and spatial enzyme organization,
as well as experimental data are provided by our collaboration partners
Uwe Sonnewald and Lars Voll (Biochemistry Department, University
Erlangen-Nuremberg). Based on these experimental information, the
effective models are simulated numerically. A main aim for our
investigations is the identification of the impact of metabolic
channeling on the carbon partitioning between starch, sucrose and
respiration in Arabidopsis leaves.


(DFG RU 2179 “MAD Soil - Microaggregates: Formation and turnover of the structural building blocks of soils”):
Mechanistische Modellierung der Formation und Konsolidierung von Mikroaggregaten in Böden
Dr. Alexander Prechtel; Dr. Nadja Ray
(01.01.2016 - 31.12.2019)

Zuletzt aktualisiert 2019-17-04 um 14:47