Research interests:
Research interests:
- Population biology
- Dynamical systems; periodic semi-flows; monotone dynamical systems
- Mathematical modelling
- Optimal control
- Bayesian models
More details:
More details:
My research interests lie in the analysis and control of mathematical models arising from population biology in its widest sense. Using the theory of dynamical systems, I aim to answer questions related to the long-term behavior of such models. For example "Does a population survive?", "Can two interacting species coexist?", or "Does a population oscillate in the long-term?". I am particularly interested in the application of the theories of monotone dynamical systems, periodic semi-flows, and the theory of persistence.
My research interests lie in the analysis and control of mathematical models arising from population biology in its widest sense. Using the theory of dynamical systems, I aim to answer questions related to the long-term behavior of such models. For example "Does a population survive?", "Can two interacting species coexist?", or "Does a population oscillate in the long-term?". I am particularly interested in the application of the theories of monotone dynamical systems, periodic semi-flows, and the theory of persistence.
Understanding the long-term behavior of population models leads to interesting control problems in the context of industrial biotechnology, wastewater treatment, bioenergy, production, or epidemiology. For example, "How to lead an undesired population (e.g. mosquitoes) to extinction?", "How to maximize the removal of contaminants in wastewater?", or "How to maximize the production of a fermentation product?". I use the theory of control (mainly optimal control) to answer to these questions.
Understanding the long-term behavior of population models leads to interesting control problems in the context of industrial biotechnology, wastewater treatment, bioenergy, production, or epidemiology. For example, "How to lead an undesired population (e.g. mosquitoes) to extinction?", "How to maximize the removal of contaminants in wastewater?", or "How to maximize the production of a fermentation product?". I use the theory of control (mainly optimal control) to answer to these questions.
PhD Thesis (2016-2019)
PhD Thesis (2016-2019)
Dissertation title: Modeling, analysis, and control of microalgae growth in dense cultures
Dissertation title: Modeling, analysis, and control of microalgae growth in dense cultures
Defense date: May 13th 2019
Defense date: May 13th 2019
Jury:
Jury:
- Supervisor : Antoine Sciandra (antoine.sciandra@obs-vlfr.fr) (Laboratoire d'Oceanographie de Villefranche)
List of publications
List of publications
Journal Articles
Journal Articles
Carlos Martínez, Bruno Assis Pessi, Olivier Bernard, Optimal production of microalgae in the presence of grazers , Journal of Process Control, 118, 153-164, (2022) https://doi.org/10.1016/j.jprocont.2022.09.001
Carlos Martínez, Bruno Assis Pessi, Olivier Bernard, Optimal production of microalgae in the presence of grazers , Journal of Process Control, 118, 153-164, (2022) https://doi.org/10.1016/j.jprocont.2022.09.001
Carlos Martínez, Eugenio Cinquemani, Hidde de Jong, Jean-Luc Gouzé, Optimal protein production by a synthetic microbial consortium: Coexistence, distribution of labor, and syntrophy, Preprint (Accepted in Journal of Mathematical Biology, 2023), https://doi.org/10.1101/2022.01.12.476046
Carlos Martínez, Eugenio Cinquemani, Hidde de Jong, Jean-Luc Gouzé, Optimal protein production by a synthetic microbial consortium: Coexistence, distribution of labor, and syntrophy, Preprint (Accepted in Journal of Mathematical Biology, 2023), https://doi.org/10.1101/2022.01.12.476046
Golpour Dehsari, A., Šmejkal, M., Čech, M., Acácio dos Santos, R., Souza, A. T., Martinez, C., ... & Blabolil, P. Similarities and differences in fish community composition accessed by electrofishing, gill netting, seining, trawling, and water eDNA metabarcoding in temperate reservoirs. Frontiers in Ecology and Evolution, 600 (2022) https://doi.org/10.3389/fevo.2022.913279
Carlos Martínez, Jean-Luc Gouzé, Global dynamics of the chemostat with overflow metabolism, Journal of Mathematical Biology, 82(13), (2021), https://doi.org/10.1007/s00285-021-01566-6
Carlos Martínez, Jean-Luc Gouzé, Global dynamics of the chemostat with overflow metabolism, Journal of Mathematical Biology, 82(13), (2021), https://doi.org/10.1007/s00285-021-01566-6
Carlos Martínez, Francis Mairet, Olivier Bernard, Dynamics of the periodically forced light-limited Droop model, Journal of Differential Equations, 269(4), 3890-3913, (2020) https://doi.org/10.1016/j.jde.2020.03.020
Carlos Martínez, Francis Mairet, Olivier Bernard, Dynamics of the periodically forced light-limited Droop model, Journal of Differential Equations, 269(4), 3890-3913, (2020) https://doi.org/10.1016/j.jde.2020.03.020
Carlos Martínez, Andrés Avila, Francis Mairet, Leslie Meier, David Jeison, Modeling and analysis of an absorption column connected to a microalgae culture, SIAM Journal on Applied Mathematics, 80(2), 772-791, (2020) https://doi.org/10.1137/18M1225641
Carlos Martínez, Andrés Avila, Francis Mairet, Leslie Meier, David Jeison, Modeling and analysis of an absorption column connected to a microalgae culture, SIAM Journal on Applied Mathematics, 80(2), 772-791, (2020) https://doi.org/10.1137/18M1225641
Leslie Meier, Carlos Martínez, Carlos Vilchez, Olivier Bernard, David Jeison, Evaluation of the feasibility of photosynthetic biogas upgrading: Simulation of a large-scale system, Energy, 189, 116313, (2019) https://doi.org/10.1016/j.energy.2019.116313
Leslie Meier, Carlos Martínez, Carlos Vilchez, Olivier Bernard, David Jeison, Evaluation of the feasibility of photosynthetic biogas upgrading: Simulation of a large-scale system, Energy, 189, 116313, (2019) https://doi.org/10.1016/j.energy.2019.116313
Carlos Martínez, Olivier Bernard, and Francis Mairet, Theory of turbid microalgae cultures, Journal of Theoretical Biology, 456, 190-200, (2018), https://doi.org/10.1016/j.jtbi.2018.07.016
Carlos Martínez, Olivier Bernard, and Francis Mairet, Theory of turbid microalgae cultures, Journal of Theoretical Biology, 456, 190-200, (2018), https://doi.org/10.1016/j.jtbi.2018.07.016
Brian D Shoener, Stephanie M Schramm, Fabrice Béline, Olivier Bernard, Carlos Martínez, Benedek G Plosz, Spencer Snowling, Jean-Philippe Steyer, Borja Valverde-Pérez, Dorottya Wagner, Jeremy S Guest, Microalgae and cyanobacteria modeling in water resource recovery facilities: A critical review, Water Research X, 100024, (2018) https://doi.org/10.1016/j.wroa.2018.100024
Brian D Shoener, Stephanie M Schramm, Fabrice Béline, Olivier Bernard, Carlos Martínez, Benedek G Plosz, Spencer Snowling, Jean-Philippe Steyer, Borja Valverde-Pérez, Dorottya Wagner, Jeremy S Guest, Microalgae and cyanobacteria modeling in water resource recovery facilities: A critical review, Water Research X, 100024, (2018) https://doi.org/10.1016/j.wroa.2018.100024
Conference proceedings (peer reviewed, indexed by WoS)
Conference proceedings (peer reviewed, indexed by WoS)
Carlos Martínez, Allan de Souza, Jan Kubečka, Fish eradication in freshwater ecosystems by repeated fishing , IFAC-PapersOnline, 55 (20), 659-664, (2022) https://doi.org/10.1016/j.ifacol.2022.09.171
10th Vienna International Conference on Mathematical Modelling (MATHMOD 2022), Vienna, Austria
Carlos Martínez, Allan de Souza, Jan Kubečka, Fish eradication in freshwater ecosystems by repeated fishing , IFAC-PapersOnline, 55 (20), 659-664, (2022) https://doi.org/10.1016/j.ifacol.2022.09.171
10th Vienna International Conference on Mathematical Modelling (MATHMOD 2022), Vienna, Austria
Carlos Martínez, Bruno Assis Pessi, Olivier Bernard, Dynamics and productivity of microalgae in presence of predators, IFAC-PapersOnline, 54 (3), 673-678, (2021) https://doi.org/10.1016/j.ifacol.2021.08.319
11th IFAC Symposium on Advance Control of Chemical Processes (ADCHEM), June 2021
Carlos Martínez, Bruno Assis Pessi, Olivier Bernard, Dynamics and productivity of microalgae in presence of predators, IFAC-PapersOnline, 54 (3), 673-678, (2021) https://doi.org/10.1016/j.ifacol.2021.08.319
11th IFAC Symposium on Advance Control of Chemical Processes (ADCHEM), June 2021
Carlos Martínez, Jean-Luc Gouzé, Optimal control of a fed-batch reactor with overflow metabolism, 53 (2), 16820-16825, (2020) IFAC-PapersOnline, https://doi.org/10.1016/j.ifacol.2020.12.1167
21st World Congress of the International Federation of Automatic Control (IFAC), Berlin, Germany
Carlos Martínez, Jean-Luc Gouzé, Optimal control of a fed-batch reactor with overflow metabolism, 53 (2), 16820-16825, (2020) IFAC-PapersOnline, https://doi.org/10.1016/j.ifacol.2020.12.1167
21st World Congress of the International Federation of Automatic Control (IFAC), Berlin, Germany
Carlos Martínez, Francis Mairet, Luis Plaza, Antoine Sciandra, Olivier Bernard, Quantifying the potential of microalgae to remove nutrients from wastewater, IFAC-PapersOnLine, 52 (26), 287-292, (2019) https://doi.org/10.1016/j.ifacol.2019.12.272
8th IFAC Conference on Foundations of Systems Biology in Engineering (FOSBE), Valencia, Spain
Carlos Martínez, Francis Mairet, Luis Plaza, Antoine Sciandra, Olivier Bernard, Quantifying the potential of microalgae to remove nutrients from wastewater, IFAC-PapersOnLine, 52 (26), 287-292, (2019) https://doi.org/10.1016/j.ifacol.2019.12.272
8th IFAC Conference on Foundations of Systems Biology in Engineering (FOSBE), Valencia, Spain
Carlos Martínez, Olivier Bernard, Pierre Martinon, Francis Mairet, Dynamics and Control of a Periodically Forced Microalgae Culture, IFAC-PapersOnLine, 52 (1), 922-927, (2019) https://doi.org/10.1016/j.ifacol.2019.06.180
12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems (DYCOPS), Florianopolis-SC, Brasil
Carlos Martínez, Olivier Bernard, Pierre Martinon, Francis Mairet, Dynamics and Control of a Periodically Forced Microalgae Culture, IFAC-PapersOnLine, 52 (1), 922-927, (2019) https://doi.org/10.1016/j.ifacol.2019.06.180
12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems (DYCOPS), Florianopolis-SC, Brasil
Carlos Martínez, Olivier Bernard, and Francis Mairet, Maximizing microalgae productivity in a light-limited chemostat, IFAC-PapersOnLine, 51(2), 735-740, (2018) https://doi.org/10.1016/j.ifacol.2018.04.001
9th Vienna International Conference on Mathematical Modelling (MATHMOD 2018), Vienna, Austria
Carlos Martínez, Olivier Bernard, and Francis Mairet, Maximizing microalgae productivity in a light-limited chemostat, IFAC-PapersOnLine, 51(2), 735-740, (2018) https://doi.org/10.1016/j.ifacol.2018.04.001
9th Vienna International Conference on Mathematical Modelling (MATHMOD 2018), Vienna, Austria
Carlos Martínez, Olivier Bernard, and Francis Mairet, Maximizing microalgae productivity by shading outdoor cultures, IFAC-PapersOnLine, 50(1), 8734-8739, (2017) https://doi.org/10.1016/j.ifacol.2017.08.1725
20th World Congress of the International Federation of Automatic Control (IFAC), Toulouse, France
Carlos Martínez, Olivier Bernard, and Francis Mairet, Maximizing microalgae productivity by shading outdoor cultures, IFAC-PapersOnLine, 50(1), 8734-8739, (2017) https://doi.org/10.1016/j.ifacol.2017.08.1725
20th World Congress of the International Federation of Automatic Control (IFAC), Toulouse, France
Reviews: Journal of Biological Systems, Algal Research, Hydrobiologia, Mathematics, International Journal of Phytoremediation.
Reviews: Journal of Biological Systems, Algal Research, Hydrobiologia, Mathematics, International Journal of Phytoremediation.