Advanced Workstations for Research in Computational Biomathematics

随着数学模型中包含越来越多的生物和物理细节，计算机模拟和数值分析在数学生物学中变得越来越重要。 细菌生物膜是一个例子，这是拟议设备支持的研究计划的重点之一。它们在许多环境工程应用中发挥着重要作用，例如废水处理和土壤修复，在这些应用中，它们是有益的，但也在医学中，它们是细菌感染的持久原因，或在食品科学和技术中，它们可能导致产品腐败和健康风险。* 它们的数学描述导致了高度非线性的偏微分方程，具有奇异性，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，人们关注的是描述生物膜结构的移动界面的形成。沿着这些界面形成陡峭的生物量梯度，这会减慢计算算法，特别是如果几个这样的界面合并和联合收割机。如果包括几个物种，则面临交叉扩散通量的额外挑战，交叉扩散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，模型是高度非线性和刚性的扩散反应系统。另一方面，如果研究细菌菌落水平效应对现场规模过程的作用，则取决于反应器类型，可能最终得到双曲线平衡定律，其具体挑战可能是描述生物堵塞的体积填充奇异性，再次需要小的时间步长。此外，这些领域规模的模型仍然需要解决一些菌落规模的过程，最值得注意的是正确地描述生物膜菌落和周围的水相之间的底物通量，以便能够正确地考虑生物膜的生长。 虽然这只是作为一个明显的小细节进入平衡方程，但需要不断重复地解决这些子尺度问题，这成为模拟时间的决定因素。这项基础设施补助金支持的其他研究涉及蜜蜂的健康和福祉，以及如何改善蜂箱中的越冬条件或如何在面临次级压力（如暴露于环境杀虫剂）时改善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的加入而增加，计算挑战和要求也在增加，并且很容易超过现成的个人计算机和笔记本电脑的能力。这笔赠款将用于购买先进的多处理器/多核工作站，以应对这些挑战。*

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.********