Advanced Workstations for Research in Computational Biomathematics

随着越来越多的生物和物理细节被包含在数学模型中，计算机模拟和数值分析在数学生物学中变得越来越重要。这方面的一个例子是细菌生物膜，这是由拟议设备支持的研究计划中的焦点之一。它们在许多环境工程应用中发挥着重要作用，如废水处理和土壤修复，在这些应用中它们是有益的，但在医药中，它们是细菌感染的持久原因，或者在食品科学和技术中，它们可能导致产品变质和健康风险。它们的数学描述导致了具有奇异性的高度非线性偏微分方程组，其数值处理仍然是计算机模拟中的一个挑战。这些困难的确切性质取决于所考虑的现象。在单物种生物膜中，人们关心的是描述生物膜结构的运动界面的形成。沿着这些界面会形成陡峭的生物量梯度，这可能会降低计算算法的速度，特别是如果几个这样的界面合并和结合的话。如果包括几个物种，其中一个面临交叉扩散通量的额外挑战，该通量描述了一个物种的存在如何影响另一个物种的空间扩展。在这两种情况下，模型都是高度非线性和僵硬的扩散-反应系统。另一方面，如果研究细菌菌落水平对现场规模过程的影响，根据反应器的类型，可能会得到双曲线平衡定律，其具体挑战可能是描述生物记录的体积填充奇点，再次需要小的时间步长。此外，这些领域的规模模型仍然需要一些菌落规模过程的分辨率，最明显的是正确地描述生物膜菌落和周围水相之间的底物通量，以便能够正确地解释生物膜的生长。虽然这显然只是一个次要的细节，但持续和重复地解决这些子规模问题的需要成为模拟时间的决定因素。*这项基础设施拨款支持的其他研究涉及蜜蜂的健康和福祉，以及如何在面临次要压力(如暴露于环境农药)的情况下改善蜂箱的越冬条件，或者如何改进蜜蜂疾病的补救方法。*随着模型的复杂性随着越来越多的细节被纳入，计算的挑战和要求增加了，而且很容易超过现成的个人计算机和笔记本电脑的能力。这笔赠款将允许购买高级多处理器/多核工作站来应对这些挑战。*

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.********