| Abstract [eng] |
This thesis investigates the mathematical modeling, numerical solution and visualization of structure formation in bioluminescent bacteria in two and three spatial dimensions. The aim of the thesis is to construct 2D, coupled surface and 3D numerical models based on the chemotaxis model of luminous bacteria presented in [BLŠ15], to analyse the influence of model parameters on the formed structures and to develop an interactive method for visualizing the results in three-dimensional space. The models are solved using the finite difference method. The computational subsystem is implemented in C++, while the analysis and visualization subsystem is implemented in Python. A parametric analysis is carried out to investigate how bacterial concentration structures depend on diffusion, chemotactic sensitivity, nutrient-related parameters and other model coefficients. The results show that parameter changes have a clear influence on the shape, intensity and spatial distribution of bacterial concentration structures. The coupled surface model can be useful as an intermediate pseudo-spatial analysis method, but it cannot fully replace the complete 3D model when accurate volumetric interactions are important. |
