Global Attractor for a Reaction-Diffusion Model Arising in Biological Dynamic in 3D Soil Structure

Partial Differential Equations (PDEs) play a crucial role as tools for modeling and comprehending intricate natural processes, notably within the domain of biology. This research explores the domain of microbial activity within the complex matrix of 3D soil structures, providing valuable understanding into both the existence and uniqueness of solutions and the asymptotic behavior of the corresponding PDE model. Our investigation results in the discovery of a global attractor, a fundamental feature with significant implications for long-term system behavior. To enhance the clarity of our findings, numerical simulations are employed to visually illustrate the attributes of this global attractor.

Segmentation of 3D pore space from CT images using curvilinear skeleton: application to numerical simulation of microbial decomposition

Recent advances in 3D X-ray Computed Tomographic (CT) sensors have stimulated research efforts to unveil the extremely complex micro-scale processes that control the activity of soil microorganisms. Voxel-based description (up to hundreds millions voxels) of the pore space can be extracted, from grey level 3D CT scanner images, by means of simple image processing tools. Classical methods for numerical simulation of biological dynamics using mesh of voxels, such as Lattice Boltzmann Model (LBM), are too much time consuming. Thus, the use of more compact and reliable geometrical representations of pore space can drastically decrease the computational cost of the simulations. Several recent works propose basic analytic volume primitives (e.g. spheres, generalized cylinders, ellipsoids) to define a piece-wise approximation of pore space for numerical simulation of draining, diffusion and microbial decomposition. Such approaches work well but the drawback is that it generates approximation errors. In the present work, we study another alternative where pore space is described by means of geometrically relevant connected subsets of voxels (regions) computed from the curvilinear skeleton. Indeed, many works use the curvilinear skeleton (3D medial axis) for analyzing and partitioning 3D shapes within various domains (medicine, material sciences, petroleum engineering, etc.) but only a few ones in soil sciences. Within the context of soil sciences, most studies dealing with 3D medial axis focus on the determination of pore throats. Here, we segment pore space using curvilinear skeleton in order to achieve numerical simulation of microbial decomposition (including diffusion processes). We validate simulation outputs by comparison with other methods using different pore space geometrical representations (balls, voxels).