Modeling and simulation of a bacterial biofilm that is controlled by pH and protonated lactic acids.
Khassehkhan, Hassan, Eberl, Hermann J. (2008)
Computational & Mathematical Methods in Medicine
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Displaying similar documents to “A finite difference scheme for a degenerated diffusion equation arising in microbial ecology.”
Modeling and simulation of a bacterial biofilm that is controlled by pH and protonated lactic acids.
Discretization methods with analytical characteristic methods for advection-diffusion-reaction equations and 2d applications
Jürgen Geiser (2009)
ESAIM: Mathematical Modelling and Numerical Analysis
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Our studies are motivated by a desire to model long-time simulations of possible scenarios for a waste disposal. Numerical methods are developed for solving the arising systems of convection-diffusion-dispersion-reaction equations, and the received results of several discretization methods are presented. We concentrate on linear reaction systems, which can be solved analytically. In the numerical methods, we use large time-steps to achieve long simulation times of about 10 000 years. We...
Diffusion with dissolution and precipitation in a porous medium: Mathematical analysis and numerical approximation of a simplified model
Nicolas Bouillard, Robert Eymard, Raphaele Herbin, Philippe Montarnal (2007)
ESAIM: Mathematical Modelling and Numerical Analysis
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Modeling the kinetics of a precipitation dissolution reaction occurring in a porous medium where diffusion also takes place leads to a system of two parabolic equations and one ordinary differential equation coupled with a stiff reaction term. This system is discretized by a finite volume scheme which is suitable for the approximation of the discontinuous reaction term of unknown sign. Discrete solutions are shown to exist and converge towards a weak solution of the continuous...
A new deterministic spatio-temporal continuum model for biofilm development.
Eberl, Hermann J., Parker, David F., van Loosdrecht, Mark C.M. (2001)
Journal of Theoretical Medicine
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A mixed-culture model of a probiotic biofilm control system.
Eberl, Hermann J., Khassehkhan, Hassan, Demaret, Laurent (2010)
Computational & Mathematical Methods in Medicine
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Numerical simulation of chemotactic bacteria aggregation via mixed finite elements
Americo Marrocco (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We start from a mathematical model which describes the collective motion of bacteria taking into account the underlying biochemistry. This model was first introduced by Keller-Segel [13]. A new formulation of the system of partial differential equations is obtained by the introduction of a new variable (this new variable is similar to the quasi-Fermi level in the framework of semiconductor modelling). This new system of P.D.E. is approximated via a mixed finite element technique. The...
Increasing the Calculation Speed of an Acceleration Scheme for an Age-Structured Diffusion Model Повишаване на изчислителната скорост на ускорена схема за възрастово структуриран дифузионен модел
Boyadzhiev, Doychin, Pelovska, Galena (2011)
Union of Bulgarian Mathematicians
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Дойчин Бояджиев, Галена Пеловска - В статията се предлага оптимизиран алгоритъм, който е по-бърз в сравнение с по- рано описаната ускорена (модифицирана STS) диференчна схема за възрастово структуриран популационен модел с дифузия. Запазвайки апроксимацията на модифицирания STS алгоритъм, изчислителното времето се намаля почти два пъти. Това прави оптимизирания метод по-предпочитан за задачи с нелинейност или с по-висока размерност. In this paper we propose an optimized...