# Performance Study of Two Serial Interconnected Chemostats with Mortality

TL;DR: In this paper , the authors considered the model of two chemostats in series when a biomass mortality is considered in each vessel and compared the performance of the serial configuration with a single chemostat with the same total volume.

About: This article is published in Bulletin of Mathematical Biology.The article was published on 2022-08-28 and is currently open access. It has received 2 citations till now. The article focuses on the topics: Medicine & Chemostat.

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TL;DR: In this paper , the authors considered the production of biomass of two interconnected chemostats in series with biomass mortality and a growth kinetic of the biomass described by an increasing function, and compared the productivity of a single chemostat with the same mortality rate and with volume equal to the sum of the volumes of the two Chemostats.

Abstract: This paper considers the production of biomass of two interconnected chemostats in series with biomass mortality and a growth kinetic of the biomass described by an increasing function. A comparison is made with the productivity of a single chemostat with the same mortality rate and with volume equal to the sum of the volumes of the two chemostats. We determine the operating conditions under which the productivity of the serial configuration is greater than the productivity of the single chemostat. Moreover, the differences and similarities in the results corresponding to the case with mortality and the one without mortality, are highlighted. The mortality leads to surprising results where the productivity of a steady state where the bacteria are washed out in the first chemostat is greater than the one where the bacteria are present in both chemostats.

1 citations

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TL;DR: In this article , a model of two interconnected chemostats in series, characterized by biomass mortality, is discussed, and a comparison is established with a single chemostat of the same total volume in two different cases, that are with or without mortality rate.

Abstract: This paper discusses a model of two interconnected chemostats in series, characterized by biomass mortality. A comparison is established with a single chemostat of the same total volume in two different cases, that are with or without mortality rate. The outlet substrate concentration and the biogas flow rate are the main criteria for comparison. According to conditions depending on the operating parameters and the distribution of the total volume, our results show which structure, the series of the two chemostats or the single chemostat, performs better in terms of minimizing the outlet substrate concentration or maximizing the biogas flow rate, and this with or without account of mortality. Moreover, the differences and similarities in the results corresponding to the case with mortality and the one without mortality, are highlighted.

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01 Jan 1998TL;DR: In this article, the first two chapters furnish, besides their concrete assertions, a methodology for later problems connected with partial differential equa-tions. But this is not done merely to give the old theorems a second proof.

Abstract: Many theorems of this chapter are very similar to the corresponding theorems of the preceding chapter. If we nevertheless devote a new chapter to an old subject, this will be justified by a new method. This method deals with differential equations and inequalities, whereas earlier the corresponding integral equations stood in the foreground. This is not done merely to give the old theorems a second proof. Rather, both of these first two chapters furnish, besides their concrete assertions, a methodology for later problems connected with partial differential equations. Chapter III, devoted to hyperbolic differential equations, contains in essence a translation of Chapter I into several dimensions, while the theory of the parabolic equations in Chapter IV is closely connected to the present Chapter II.

793 citations

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TL;DR: In this article, the Fundamental Theorem of Calculus gives us an important connection between differential equations and integrals, and modern numerical methods automatically determine the step sizes hn = tn+1 − tn so that the estimated error in the numerical solution is controlled by a specified tolerance.

Abstract: together with the initial condition y(t0) = y0 A numerical solution to this problem generates a sequence of values for the independent variable, t0, t1, . . . , and a corresponding sequence of values for the dependent variable, y0, y1, . . . , so that each yn approximates the solution at tn yn ≈ y(tn), n = 0, 1, . . . Modern numerical methods automatically determine the step sizes hn = tn+1 − tn so that the estimated error in the numerical solution is controlled by a specified tolerance. The Fundamental Theorem of Calculus gives us an important connection between differential equations and integrals.

751 citations

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TL;DR: In this article, a model of exploitative competition of n species in a chemostat for a single, essential, nonreproducing, growth-limiting resource is considered.

Abstract: A model of exploitative competition of n species in a chemostat for a single, essential, nonreproducing, growth-limiting resource is considered. S. B. Hsu [SIAM J. Appl. Math., 34 (1978), pp. 760–763] applies LaSalle’s extension theorem of Lyapunov stability theory to study the asymptotic behavior of solutions in the special case that the response functions are modeled by Michaelis–Menten dynamics. G. J. Butler and G. S. K. Wolkowicz [SIAM J. Appl. Math., 45 (1985), pp. 138–151], on the other hand, allow more general response functions (including monotone and nonmonotone functions), but their analysis requires the assumption that the death rates of all the species are negligible in comparison with the washout rate, and hence can be ignored. By means of Lyapunov stability theory, the global dynamics of the model for a large class of response functions are studied, including both monotone and nonmonotone functions (though it is not as general as the class studied by Butler and Wolkowicz) and the results in ...

242 citations

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TL;DR: A competition model between n species in a chemostat that incorporates both monotone and nonmonotone general response functions and distinct removal rates is considered, showing that only the species with the lowest break-even concentration survives.

Abstract: In this paper, we consider a competition model between n species in a chemostat that incorporates both monotone and nonmonotone general response functions and distinct removal rates. We show that only the species with the lowest break-even concentration survives, provided that the variation of distinct removal rates relative to the flow rate of the chemostat can be controlled by either the difference between the two lowest break-even concentrations or by a parameter based on the structure of response functions. LaSalle's extension theorem of the Lyapunov stability theory and fluctuation lemma are the main tools.

109 citations