Mathematical model of shallow water self-purification process

Abstract The paper covers the model of shallow water self-purification processes. The proposed mathematical model of biological kinetics is based on a system of non-stationary convection-diffusion-reaction equations with nonlinear terms, taking into account the water flow movement, gravitational sedimentation of impurities, microturbulent diffusion, and the detritus decomposition as a result of activity the aerobic and anaerobic bacteria. Discretization is performed on the basis of a linear combination of central and Upwind Leapfrog difference schemes, which makes it possible to increase the solution accuracy of biological kinetics problem at large values of the grid Péclet number (Peh > 2). To solve high-dimensional SLAEs, a modified alternating-triangular method was used.

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On the time dependent mathematical model of ateroma plaque formation

Jornada de Jóvenes Investigadores del I3A ◽

10.26754/jji-i3a.201401732 ◽

1970 ◽

Vol 1 ◽

pp. 10-11

Author(s):

Myriam Cilla ◽

Estefanía Peña ◽

Miguel Ángel Martínez

Keyword(s):

Mathematical Model ◽

Stokes Equations ◽

Plaque Formation ◽

Diffusion Reaction ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Convection Diffusion ◽

Atheroma Plaque ◽

Plaque Growth ◽

Reaction Equations

A mathematical model to reproduce the atheroma plaque growth is presented. This model employs the Navier-Stokes equations and Darcy's law for fluid dynamics, convection-diffusion-reaction equations for modeling the mass balance in the lumen and intima, and the Kedem-Katchalsky equations for the interfacial coupling at membranes, i.e., endothelium.

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A Mixed-Culture Model of a Probiotic Biofilm Control System

Computational and Mathematical Methods in Medicine ◽

10.1080/17486700902789355 ◽

2010 ◽

Vol 11 (2) ◽

pp. 99-118 ◽

Cited By ~ 12

Author(s):

Hermann J. Eberl ◽

Hassan Khassehkhan ◽

Laurent Demaret

Keyword(s):

Mathematical Model ◽

Microbial Control ◽

Diffusion Reaction ◽

Simulation Studies ◽

Convection Diffusion ◽

Culture Model ◽

High Concentrations ◽

The Mathematical Model ◽

Reaction Equations ◽

Lactic Acids

We present a mathematical model and computer simulations for the control of a pathogenic biofilm by a probiotic biofilm. This is a substantial extension of a previous model of control of a pathogenic biofilm by microbial control agents that are suspended in the aqueous bulk phase (H. Khassehkhan and H.J. Eberl, Comp. Math. Meth. Med, 9(1) (2008), pp. 47–67). The mathematical model is a system of double-degenerate diffusion–reaction equations for the microbial biomass fractions probiotics, pathogens and inert bacteria, coupled with convection–diffusion–reaction equations for two growth controlling substrates, protonated lactic acids and hydrogen ions (pH). The latter are produced by the bacteria and become detrimental at high concentrations. In simulation studies, we find that the site of attachment of probiotics in the flow channel is crucial for success and efficacy of the probiotic control mechanism.

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