Theoretical and computational studies of some bioreactor models

Abstract

International audienceWe study certain classical basic models for bioreactor simulation in case of batch mode withdecay. It is shown that in many cases the two-dimensional differential system describingthe dynamics of the substrate and biomass concentrations can be reduced to an algebraicequation for the biomass together with a single differential equation for the substrate.Then from an analogy with the Henri–Michaelis–Menten enzyme kinetic mechanism asimple model is proposed for a bioreactor in batch mode with decay. Two more modelsare also proposed taking into account the phases of microbial growth. Some propertiesof these two models are studied and compared to classical Monod type models usingcomputer simulations

Modelo Semifísico de Base Fenomenológica del Proceso Continuo de Fermentación Alcohólica

“…Se refiere a encontrar las ecuaciones que permitan calcular el mayor número de parámetros en cada Sistema de Proceso. Para la velocidad de crecimiento celular: Se utiliza una cinética que contiene efectos inhibitorios de concentración de sustrato, concentración de producto y concentración de biomasa (Clarke;Akpa, 2012;Alt y Markov;Dodić et al, 2012;Tian et al, 2011;Ccopa et al, 2006;Schügerl y Bellgardt, 2000):…”

Building reaction kinetic models for amiloid fibril growth

“…From (25) we have f + c = k c c. Assuming that the monomer m is abundant in a time interval ∆ we can apply the QSSA principle and assume that c is approximately equal to 0 in ∆, and accordingly, in ∆ we have approximately f = k c c [1], [4], [5], [13], [32], [35], [36], [37]. Hence, for some t * ∈ ∆ we have f (t * ) = k c c (t * ) = 0, hence function f has inflection and has a sigmoidal form.…”

“…Here the transition of the aggregated monomer P into fibril follows the decay-saturation mechanism (1). Applying the mass action law we obtain the ODE system…”

A family of recurrence generated sigmoidal functions based on the Log-logistic function. Some approximation aspects

“…Since then the logistic function finds applications in many scientific fields, including biology, ecology, population dynamics, chemistry, demography, economics, geoscience, mathematical psychology, probability, sociology, political science, financial mathematics, statistics, fuzzy set theory, insurance mathematics, debugging and test theory to name a few [5]- [37].…”