Mathematical Approaches in Biofilm Research

细菌生物膜是微生物在浸没界面上的沉积物，无论环境条件如何维持细菌的生命。许多环境工程技术利用它们的特性，如废水处理，土壤修复或最近的生物燃料生产。 另一方面，在医学背景下，它们主要被认为是有害的，作为难以用抗生素治疗的持续感染的原因。在工业环境中，它们可以造成损害，例如通过生物污染或生物腐蚀。 数学建模已成为生物膜研究的重要工具。这项研究计划旨在促进这一发展。 它涉及数学模型的制定，它们的分析，以及它们在数值模拟实验中的应用。将使用的方法来自偏微分方程和科学计算领域。 这将涉及高度退化的拟线性抛物系统及其数值解，以及多尺度建模和模拟技术。具体的问题，将解决包括群体感应抑制和细菌串扰模型，模型的纤维素分解生物膜，用于生产纤维素乙醇从非食用植物材料作为运输燃料，和模型的生物修复过程中使用的土壤的清理。 该计划的重点是学生的研究培训，无论是在本科和研究生水平，在数学科学，生物学，工程和计算重叠的领域。

Bacterial biofilms are microbial depositions on immersed interfaces that form wherever environmental conditions sustain bacterial life. Many environmental engineering technologies utilise their properties, in areas like wastewater treatment, soil remediation, or more recently biofuel production. On the other hand, in a medical context they are mainly considered detrimental, as a cause of persistent infections that are difficult to treat with antibiotics. In an industrial context they can cause damage, e.g by biofouling or biocorrosion. Mathematical modeling has become an important tool in biofilm research. This research program seeks to contribute to this development. It involves the formulation of mathematical models, their analysis, and their use in numerical simulation experiments. The methods that will be utilised stem from fields of Partial Differential Equations and Scientific Computing. This will involve highly degenerate quasilinear parabolic systems and their numerical solution, as well as multiscale modeling and simulation techniques. Specific problems that will be addressed include models of quorum sensing inhibition and bacterial cross-talk, models of cellulolytic biofilms that are utilised in the production of cellulosic ethanol from non-edible plant material as a transportation fuel, and models of bioremediation processes that are utilised in the clean up of soils. A focus of the program is research training of students, both on the undergraduate and graduate level, in an area in which mathematical sciences, biology, engineering, and computation overlap.