Mathematical Approaches in Biofilm Research

细菌生物膜是浸泡在界面上的微生物沉积，在任何环境条件支持细菌生命的地方形成。许多环境工程技术在废水处理、土壤修复或最近的生物燃料生产等领域利用了它们的特性。另一方面，在医学上，它们主要被认为是有害的，因为它们是难以用抗生素治疗的持续性感染的原因。在工业环境中，它们可能会造成损害，例如生物结垢或生物腐蚀。数学建模已成为生物膜研究的重要工具。这项研究计划旨在为这一发展做出贡献。它涉及数学模型的形成、它们的分析以及它们在数值模拟实验中的使用。将要使用的方法来自偏微分方程组和科学计算领域。这将涉及高度退化的拟线性抛物型系统及其数值解，以及多尺度建模和模拟技术。将解决的具体问题包括群体感应抑制和细菌串扰模型、用于从非食用植物材料生产作为运输燃料的纤维素乙醇的纤维素分解生物膜模型，以及用于土壤清理的生物修复过程模型。该计划的重点是在数学科学、生物学、工程学和计算重叠的领域对本科生和研究生进行研究培训。

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.