A mathematical model for the continuous culture of microorganisms utilizing inhibitory substrates, Biotechnol. Bioeng, vol.10, issue.6, pp.707-723, 1968. ,
Optimal industrial reactor design: development of a multiobjective optimization method based on a posteriori performance parameters calculated from CFD flow solutions, Adv. Eng. Softw, vol.91, issue.C, pp.23-35, 2016. ,
Aerodynamic design via control theory, J. Sci. Comput, vol.3, issue.3, pp.233-260, 1988. ,
Bioreactor shape optimisation. modeling, simulation, and shape optimization of a simple bioreactor for water treatment, Les STIC pour l'environnement, pp.125-141, 2011. ,
URL : https://hal.archives-ouvertes.fr/hal-00858579
Application of computational fluid dynamics for modeling and designing photobioreactors for microalgae production: A review, Comput. Electron. Agr, vol.76, issue.2, pp.131-147, 2011. ,
Shape optimization in ship hydrodynamics using computational fluid dynamics, Comput. Methods Appl. Mech. Eng, vol.196, issue.1-3, pp.634-651, 2006. ,
Microalgal reactors: A review of enclosed system designs and performances, Biotechnol. Prog, vol.22, issue.6, pp.1490-1506, 2006. ,
Modeling and geometry optimization of photochemical reactors: Single-and multi-lamp reactors for UVH 2 O 2 AOP systems, Chem. Eng. Sci, vol.96, pp.174-189, 2013. ,
Mathematical modeling and optimization of bioreactors and liquid crystals, 2017. ,
Existence and uniqueness of solution of a continuous flow bioreactor model with two species, pp.357-377, 2016. ,
Asymptotic stability of a coupled advection-diffusion-reaction system arising in bioreactor processes, Electr. J. Differ. Equ, vol.2017, issue.194, pp.1-26, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01607898
Modeling and optimization of activated sludge bioreactors for wastewater treatment taking into account spatial inhomogeneities, J. Process Contr, vol.54, pp.118-128, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01171033
The stream-line motion of fluid in a curved pipe, Lond. Edinb. Dubl. Phil. Mag. Sci, vol.5, issue.2, pp.673-695, 1928. ,
Multi-objective optimization using evolutionary algorithms, Wiley Interscience Series in Systems and Optimization, 2001. ,
Remarks on the preceding paper by Crespo, Ivorra and Ramos on the stability of bioreactor processes, Electr. J. Differ. Equ, vol.2017, issue.195, pp.1-25, 2017. ,
Automatic control of bioprocesses, ISTE, 2010. ,
Dynamical modelling and estimation in wastewater treatment processes, 2001. ,
Shape optimization with computational fluid dynamics, Adv. Eng. Softw, vol.36, issue.9, pp.607-613, 2005. ,
Curves and surfaces for computer-aided geometric design: A practical guide, Computer science and scientific computing, 2014. ,
High-performance computing for the optimization of high-pressure thermal treatments in food industry, J. Supercomput, 2018. ,
Minimal time sequential batch reactors with bounded and impulse controls for one or more species, SIAM J. Control Optim, vol.47, issue.6, pp.2827-2856, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00857823
Numerical methods for nonlinear variational problems, Scientific Computation, 2013. ,
Genetic algorithms in search, optimization, and machine learning, Artificial Intelligence, 1989. ,
Optimization of a pumping ship trajectory to clean oil contamination in the open sea, Math. Comput. Model, vol.54, issue.1, pp.477-489, 2011. ,
The brownian diffusion of dormant and germinating spores of bacillus megaterium, J. Appl. Bacteriol, vol.60, issue.3, pp.227-232, 1986. ,
The optimal design of two interconnected (bio)chemical reactors revisited, Comput. Chem. Eng, vol.30, issue.1, pp.70-82, 2005. ,
The chemostat: Mathematical theory of microorganism cultures, 2017. ,
URL : https://hal.archives-ouvertes.fr/hal-01539446
Optimal design of interconnected bioreactors: New results, AIChE J, vol.49, issue.6, pp.1433-1450, 2003. ,
Minimum tank volumes for CFST bioreactors in series, Can. J. Chem. Eng, vol.67, issue.5, pp.818-824, 1989. ,
On the modelling and simulation of high pressure processes and inactivation of enzymes in food engineering, Mathematical Models and Methods in Applied Sciences, vol.19, issue.12, pp.2203-2229, 2009. ,
Shape optimization of geotextile tubes for sandy beach protection, Int. J. Numer. Meth. Eng, vol.74, issue.8, pp.1262-1277, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-00411912
Application of the laminar navier-stokes equations for solving 2d and 3d pathfinding problems with static and dynamic spatial constraints: Implementation and validation in comsol multiphysics, J. Sci. Comput, vol.74, issue.2, pp.1163-1187, 2018. ,
Modelling and optimization applied to the design of fast hydrodynamic focusing microfluidic mixer for protein folding, J. Math. Industry, vol.8, issue.4, 2018. ,
Design sensitivity and mixing uniformity of a micro-fluidic mixer, Phys. Fluids, vol.28, issue.1, p.12005, 1994. ,
Semi-deterministic vs. genetic algorithms for global optimization of multichannel optical filters, Int. J. Comput. Sci. Eng, vol.2, issue.3, pp.170-178, 2006. ,
A multi-layer line search method to improve the initialization of optimization algorithms, Eur. J. Oper. Res, vol.42, issue.2, pp.711-720, 2009. ,
URL : https://hal.archives-ouvertes.fr/hal-01206339
Semi-deterministic and genetic algorithms for global optimization of microfluidic protein folding devices, Int. J. Numer. Meth. Eng, vol.66, issue.2, pp.319-333, 2006. ,
Semideterministic global optimization method: Application to a control problem of the burgers equation, J. Optimiz. Theory Appl, vol.135, issue.3, pp.549-561, 2007. ,
Two-and three-dimensional modeling and optimization applied to the design of a fast hydrodynamic focusing microfluidic mixer for protein folding, Phys. Fluids, vol.25, issue.3, p.32001, 1994. ,
Finite difference methods for ordinary and partial differential equations: Steady-state and time-dependent problems, Society for Industrial and Applied Mathematics, 2007. ,
Optimal design for continuous stirred tank reactors in series using Michaelis Menten kinetics, Biotechnol. Bioeng, vol.24, issue.5, pp.1217-1220, 1982. ,
Multidisciplinary shape optimization in aerodynamics and electromagnetics using genetic algorithms, Int. J. Numer. Methods Fluids, vol.30, issue.2, pp.149-159, 1999. ,
Hybrid method for aerodynamic shape optimization in automotive industry, Comput. Fluids, vol.33, issue.5-6, pp.849-858, 2004. ,
Aerodynamics Design and Genetic Algorithms for Optimization of Airship Bodies, JSME Int. J. Ser. B Fluids Therm. Eng, vol.46, issue.4, pp.610-617, 2003. ,
Numerical optimization, 2 nd ed, 2006. ,
Competition between nitrospira spp. and nitrobacter spp. in nitrite-oxidizing bioreactors, Biotechnol. Bioeng, vol.95, issue.1, pp.169-175, 2006. ,
Optimal shape design for elliptic systems, Springer series in computational physics, 1984. ,
Hybridization of a multi-objective genetic algorithm, a neural network and a classical optimizer for a complex design problem in fluid dynamics, Comput. Methods in Appl. Mech. Eng, vol.186, issue.2-4, pp.403-420, 2000. ,
Mixing and hydrodynamics investigation using CFD in a square-sectioned torus reactor in batch and continuous regimes, Chem. Eng. J, vol.137, issue.2, pp.386-395, 2008. ,
URL : https://hal.archives-ouvertes.fr/hal-02534190
Productivity optimization of microalgae cultivation in a batch photobioreactor process, Math. Methods Appl. Sci, pp.1-21, 2017. ,
Introducción al análisis matemático del método de elementos finitos, 2012. ,
A robust and efficient global optimization algorithm for planar competitive location problems, Optim. Method Soft, vol.23, issue.5, pp.21-53, 2008. ,
Assessment of laboratory methods for quantifying aqueous bacterial diffusion, 1999. ,
A new tubular reactor for mass production of microalgae outdoors, J. Appl. Phycol, vol.5, issue.3, pp.327-332, 1993. ,
Optimality of affine control system of several species in competition on a sequential batch reactor, Int. J. Control, vol.87, issue.9, pp.1877-1885, 2014. ,
Genetic algorithms: Basic ideas, variants and analysis, 2007. ,
Characterization of a flat plate photobioreactor for the production of microalgae, Chem. Eng. J, vol.138, issue.1-3, pp.136-147, 2008. ,
Environmental hydrology, Water Science and Technology Library, 2013. ,
The theory of the chemostat. in cambridge studies in mathematical biology, vol.13, 1995. ,
Diffusion in biofilms, J. Bacteriol, vol.185, issue.5, pp.1485-1491, 2003. ,
World student series, 1971. ,
Efficiency of sunlight utilization: Tubular versus flat photobioreactors, Biotechnol. Bioeng, vol.57, issue.2, pp.187-197, 1998. ,
Mechanistic modeling of nitrite accumulation and nitrogen oxide gas emissions during nitrification, J. Environ. Qual, vol.29, issue.6, pp.1741-1751, 2000. ,
Global optimization algorithms -theory and application, 2009. ,
Computational investigation of fluid dynamics in a recently developed centrifugal impeller bioreactor, Biochemical Engineering Journal, vol.38, issue.3, pp.406-413, 2008. ,
An object-oriented graphics interface design and optimization software for cross-sectional shape of automobile body, Adv. Eng. Softw, vol.64, pp.1-10, 2013. ,
, Departamento de Matematica Aplicada a la Ingeniería Industrial
, E-mail: maria.crespo@upm.es 2 Instituto de Matemática Interdisciplinar & Departamento de Análisis Matemático y Matemática Aplicada, +34 913377370, vol.3, p.28040