Advanced Workstations for Research in Computational Biomathematics

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Computer simulations and numerical analysis become more and more important in Mathematical Biology, as more and more biological and physical detail is included in mathematical models. An example for this, which is one of the focus points in the research program supported by the proposed equipment, are bacterial biofilms. These play an important role in many environmental engineering applications, such as wastewater treatment and soil remediation, where they are beneficially used, but also in medicine where they are a persistent cause of bacterial infection, or in food science and technology, where they can induce product spoilage and health risks. ***Their mathematical description leads to highly nonlinear partial differential equations, with singularities, the numerical treatment of which remains a challenge in computer simulations. The exact nature of these difficulties depends on the phenomenon under consideration. In single-species biofilms one is concerned with the formation of moving interfaces that describe biofilm structure. Along these interfaces steep biomass gradients develop which can slow down computational algorithms, in particular if several such interfaces merge and combine. If several species are included one faces the additional challenge of cross-diffusion fluxes which describe how the presence of one species affects spatial expansion of the other one. In both scenarios the models are highly nonlinear and stiff diffusion-reaction systems. On the other hand, if one studies the role of bacterial colony level effects on field scale processes, depending on the reactor type, one may end up with hyperbolic balance laws, the specific challenges of which can be volume filling singularities that describe bioclogging, requiring again small time steps. Moreover, these fields scale models still require the resolution of some colony scale processes, most notably to correctly describe substrate fluxes between the biofilm colony and the surrounding aqueous phase in order to be able to correctly account for biofilm growth. While this enters the balance equation only as an apparently minor detail, the need to continuously and repeatedly solve these sub-scale problems becomes a determinant for simulation time.******Other research supported by this infrastructure grant is concerned with the health and well-being of honeybees and the question how overwintering conditions in beehives can be improved or how remedial approaches for honeybee diseases can be improved in the face of secondary stressors, such as exposure to environmental pesticides.******As the complexity of the models has increased with more and more detail incorporated, the computational challenges and requirements increase and easily surpass the abilities of off-the-shelf personal computers and laptops. This grant will allow the purchase of advance multi-processor/multi-core workstations to tackle these challenges.********