A methodology to model arbitrary holes and material interfaces (inclusions) without meshing the internal boundaries is proposed. The numerical method couples the level set method (S.
SummaryThe role of quorum sensing in Pseudomonas aeruginosa biofilm formation is unclear. Some researchers have shown that quorum sensing is important for biofilm development, while others have indicated it has little or no role. In this study, the contribution of quorum sensing to biofilm development was found to depend upon the nutritional environment. Depending upon the carbon source, quorum-sensing mutant strains (lasIrhlI and lasRrhlR) either exhibited a pronounced defect early in biofilm formation or formed biofilms identical to the wild-type strain. Quorum sensing was then shown to exert its nutritionally conditional control of biofilm development through regulation of swarming motility. Examination of pilA and fliM mutant strains further supported the role of swarming motility in biofilm formation. These data led to a model proposing that the prevailing nutritional conditions dictate the contributions of quorum sensing and swarming motility at a key juncture early in biofilm development.
SUMMARYAn algorithm which couples the level set method (LSM) with the extended ÿnite element method (X-FEM) to model crack growth is described. The level set method is used to represent the crack location, including the location of crack tips. The extended ÿnite element method is used to compute the stress and displacement ÿelds necessary for determining the rate of crack growth. This combined method requires no remeshing as the crack progresses, making the algorithm very e cient. The combination of these methods has a tremendous potential for a wide range of applications. Numerical examples are presented to demonstrate the accuracy of the combined methods.
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