Stochastic finite elements: a spectral approach
Stochastic finite elements: a spectral approach
The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
SIAM Journal on Scientific Computing
Random coefficient differential equation models for bacterial growth
Mathematical and Computer Modelling: An International Journal
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Biofilms are colonies of bacteria that attach to surfaces by producing extracellular polymer substances. They may cause serious infections in humans and animals, and also cause problems in hydraulic machinery. In this paper we model the growth of a biofilm established on a medical implant. We assume that the biofilm's growth is given by a logistic reaction term with the growth rate being a random variable with a given distribution. This way we take into account the variability in the bacterial populations, and the measurement and experimental errors. The diffusion coefficient of the microbes is also taken to be random. A stochastic spectral representation of the parameters and the unknown stochastic process is used, together with the polynomial chaos method, to obtain a system of partial differential equations, which is integrated numerically to obtain the evolution of the mean and higher-order moments with respect to time. Some examples are presented.