published_or_final_version / Botany / Master / Master of Philosophy

L’objet de cette thèse est l’étude de certains problèmes liés à l’ingénierie des bioprocédés, en particulier l’analyse du comportement et de la culture optimale des microalgues et la connexion de plusieurs bioréacteurs. Trois problèmes sont proposés et analysés. Le première est basé sur une étude récente dans laquelle les auteurs modifient le modèle classique du Monod en incorporant l’incidence de la lumière sur la dynamique à travers le rôle de la croissance de la biomasse. L’idée est d’étudier un problème plus général de l’optimisation non linéaire qui considère maximisation de la biomasse moyenne de microalgues en fonction du temps, pour des intervalles de temps différents. La difficulté mathématique qui se pose est lié à la discontinuité des intervalles de temps qui rend la fonction à optimiser non différentiable. Ce manque de régularité comprend la formulation d’un problème d’optimisation non-lisse. Dans le deuxième problème, un modèle réduit du réservoir microalgues avec nitrification est analysé, en supposant que les microalgues peuvent se développer à partir de la consommation de nitrate et d’ammonium, de préférence par l’ammonium. La limitation de la lumière par l’auto-ombrage est également inclus dans le taux de croissance du microalgues comme inhibition non compétitive. En réduisant le système en utilisant la théorie des systèmes asymptotiquement autonomes, il peut être considéré comme une perturbation d’un système de deux espèces en compétition pour un substrat. Par conséquent, nous utilisons un résultat de systèmes perturbés non-évanescentes pour obtenir un théorème de stabilité pour la coexistence.Le dernier problème est lié aux systèmes compartimentés. Il est prouvé que pour une grande classe de systèmes entrées-sorties positifs de dimension finie, représentant transport et diffusion de soluté entre des compartiments mobiles et immobiles, il existe des représentations MINC (multiple interacting continua) et MRMT (multi-rate mass transfer) algébriquement équivalentes. En outre, des méthodes explicites sont donnés pour construire ces représentations équivalentes, où la contrôlabilité des systèmes joue un rôle important. / The purpose of this thesis is to study some problems that arise from bioprocess engineering, in particular the behaviour analysis and optimal cultivation of microalgae and the connection of multiple bioreactors. The thesis consists of three problems. The first is based on a recent study in which the authors extend the classical Monod model incorporating light incidence on the dynamics through the role of biomass growth. The idea is to study a more general problem of nonlinear optimization which considers maximization average biomass of microalgae versus time, for different time intervals. The mathematical difficulty that arises is related to that discontinuity of the time intervals which causes non differentiability in some domain points. This lack of regularity involves the formulation of a non-smooth optimization problem. In the second problem, a reduced mathematical model of a microalgal pond with nitrification is analyzed, assuming that microalgae can grow either by ammonium consumption or by nitrate consuming, with preference for ammonium. Light limitation by self-shading is also included in the growth rate of microalgae as a noncompetitive inhibition.It is feasible to reduce the system using the theory of asymptotically autonomous systems and the limiting system obtained can be considered as a perturbation of a system of two species competing for a substrate. So, we use a result of non-vanishing perturbated systems to obtain a strong stability theorem for equilibrium coexistence. The last problem is related to compartmental systems. It is proved that for a large class of finite dimensional input-output positive systems that represent networks of transport and diffusion of solute in mobile and immobile compartments, there exist MINC (multiple interacting continua) and MRMT (multirate mass transfer) algebraically equivalent representations. Moreover, we provide explicit methods to construct these representations, where controllability property is playing a crucial role.

Orientador: Lucia Helena Sipauba Tavares / Resumo: A microalga Haematococcus pluvialis apresenta elevado interesse biotecnológico e comercial devido sua capacidade de síntese de compostos de alto valor e composição nutricional rica em proteínas, aminoácidos e outros compostos. Dentre os entraves em sua produção comercial, a obtenção de elevada biomassa tem sido o foco de diversas pesquisa que buscam otimizar o cultivo desta espécie. O cultivo mixotrófico é uma ferramenta que pode auxiliar na obtenção de elevadas produtividades, no entanto a fonte de carbono utilizada nestes cultivos deve ser adequada e disponibilizada de forma correta para completa absorção. O melaço de cana de açúcar é uma fonte de carbono rica em sacarose e nutrientes podendo ser empregado no cultivo de H. pluvialis, no entanto, requer pré-tratamento antes de seu uso. A hidrólise auxilia na redução das moléculas de sacarose em glicose e frutose, aumentando a disponibilidade de carbono e facilitando sua assimilação. Comparado ao melaço in natura, a hidrolise do melaço demonstrou melhores resultados aumentando a produtividade e alta composição bioquímica. Outra ferramenta importante utilizada na otimização dos cultivos algais em condições mixotróficas é o uso de ciclos de luz, uma vez que a luminosidade está relacionada diretamente ao metabolismo algal auxiliando na assimilação dos nutrientes e do carbono. O período de iluminação fornecida varia de espécie para espécie, podendo ou não ser necessário. Neste estudo e para estas condições de cultivo, foram obser... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: The Haematococcus pluvialis microalgae displays high biotechnological and commercial interest due to its capacity to synthesize high nutritional value in protein, amino acids and other compounds. Besides the difficulties in commercial production, the obtaining of high biomass amounts has been the objective of several researches which seek to optimize the production of this species. The mixotrophic culture is a tool which may improve the obtention of higher productivity. However, the carbon source for the cultures have to be adequate and has to be in an available form in order to be completely absorbed. The cane molasse is a carbon source rich in saccharose and nutrients and might be employed in H. pluvialis culture. Nevertheless, it requires a pre-treatment for its use. The hydrolysis promotes the reduction of saccharose molecules into glycose and fructose, improving the carbon availability and assimilation. In comparison to in natura molasses, the hydrolysis improved the results by increasing productivity. Light cycle is another important tool for algae culture in mixotrophic conditions, since light is directly related to the algae metabolism, which improves the carbon and nutrients assimilation. The light interval varies according to species and may or may not be necessary to be employed. In this study, an increase in biomass and biochemical composition was observed when H. pluvialis was exposed to light cycles. The best results were obtained with a 20:4 hours cycle (light/... (Complete abstract click electronic access below) / Doutor