Luciano Aguilera-Vázquez

This paper develops a variational analysis of projected optimization over nonconvex constraint sets, with emphasis on the geometry and regularity of the metric projection. For a closed feasible set, the metric projection is treated as a set-valued mapping whose loss of local uniqueness may induce nonsmoothness and nonunique feasible continuations. Projection multiplicity and local projection regularity are related to the differentiability properties of the squared distance function, tangent-normal geometry, and first-order stationarity. These relationships provide a geometric characterization of regimes in which projected dynamics are locally single-valued or may branch. Smooth embedded manifolds arise as a locally regular case, where the existence of tubular neighborhoods ensures local uniqueness of the metric projection and the corresponding stationarity condition reduces to the vanishing of the Riemannian gradient. This framework, termed Nonconvex Constraint Geometry (NCG), connects set-valued projection, variational regularity, nonsmoothness, and manifold-constrained optimization within a unified geometric setting.

Efficient biomass harvesting remains one of the primary barriers to the commercial feasibility of large-scale microalgal production. This study investigates the effect of different culture media on the surface physicochemical properties of Tetradesmus sp., with emphasis on their role in natural aggregation. Cultures were grown for 30 days under controlled light and temperature conditions using Blue Green 11 (BG11), Tris–acetate–phosphate (TAP), and deionized water supplemented with Bayfolan^® fertilizer. Surface hydrophobicity was assessed through microbial adhesion to solvents (MATS) and contact angle analysis, electrokinetic properties were evaluated by zeta potential measurements, and cell surface chemistry was characterized by attenuated total reflectance (ATR) sampling methodology for Fourier Transform Infrared (FTIR) spectroscopy. Across all treatments, Tetradesmus sp. exhibited inherent hydrophobicity, but Bayfolan^® supplementation yielded the highest contact angle (49.0 ± 0.9°) and the least negative free energy of interaction (ΔGsws = −26.36 mJ·m⁻²), indicating a stronger tendency toward self-aggregation. Zeta potential values remained consistently negative (−10 to −14 mV), with no significant variation among media, suggesting that hydrophobic interactions rather than electrostatic forces govern aggregation. ATR-FTIR spectra confirmed the presence of lipids, proteins, and carbohydrates, with changes in peak intensities reflecting metabolic adjustments to media composition. These results demonstrate that low-cost Bayfolan^® supplementation enhances surface hydrophobicity and aggregation, providing a sustainable strategy to facilitate biomass recovery and reduce harvesting costs in microalgal biorefineries.

The current high cost of producing green hydrogen, for use as an energy vector, has motivated the search for the development of non-conventional technologies for its production, joining forces on the path towards energy transition. Hydrogen production by aluminum corrosion in aqueous acid solutions seems to be a promising alternative. In order to evaluate its technical feasibility, a kinetic study was carried out, analyzing the impact of HCl concentration (1.125 to 1.75 M) on the aluminum corrosion capacity under the presence of a saline environment and using a promoter, fitting the proposed models to the data obtained through experimental runs. Although other studies use the shrinking core model to describe the kinetics of this type of reaction, in most cases, it does not fit well with the experimental data and needs to be modified. Finally, by considering the corrosion dynamics (variations in diffusion coefficients and shell thickness) in the kinetic model equations, it was possible to describe its behavior. For low HCl concentrations, a single resistance controls the reaction of the particle throughout; however, for high HCl concentrations, a combination of related equations must be used. The results of this study enable viable continuous reactor designs for a given amount of green hydrogen production.

Flux Balance Analysis (FBA) is a constraint-based method that is commonly used to guide metabolites through restricting pathways that often involve conditions such as anaplerotic cycles like Calvin, reversible or irreversible reactions, and nodes where metabolic pathways branch. The method can identify the best conditions for one course but fails when dealing with the pathways of multiple metabolites of interest. Recent studies on metabolism consider it more natural to optimize several metabolites simultaneously rather than just one; moreover, they point out the use of metaheuristics as an attractive alternative that extends FBA to tackle multiple objectives. However, the literature also warns that the use of such techniques must not be wild. Instead, it must be subject to careful fine-tuning and selection processes to achieve the desired results. This work analyses the impact on the quality of the pathways built using the NSGAII and MOEA/D algorithms and several novel optimization models; it conducts a study on two case studies, the pigment biosynthesis and the node in glutamate metabolism of the microalgae Chlorella vulgaris, under three culture conditions (autotrophic, heterotrophic, and mixotrophic) while optimizing for three metabolic intermediaries as independent objective functions simultaneously. The results show varying performances between NSGAII and MOEA/D, demonstrating that the selection of an optimization model can greatly affect predicted phenotypes.

Given the need to improve bioenergy production processes, it is necessary to focus on low-cost culture media and environmental conditions of radiation and temperature. The Scenedesmus dimorphus species was cultured in eutrophicated lagoon water and Bayfolan 0.3% as culture media under four photoperiods with the objective of evaluating the biomass productivity, bioremediation capacity and influence of illumination on the composition and lipid content. It is concluded that the increase of light hours in the culture with eutrophicated lagoon water produces a decrease in the biomass productivity and COD removal percentage. The highest biomass productivity was obtained in photoperiod F1 (10.5:13.5) hours L:O, 0.053 ± 0.0015 g/L day and a removal of 95.6%. Bayfolan 0.3% with F2 (11.5:12.5) and F3 (12.5:11.5) did not show significant differences in the biomass productivity and COD removal. The increase in light hours in the photoperiod induced an increase of 1.01% and 2.84% of saturated fatty acids and 0.8% and 2.14% of monounsaturated fatty acids, as well as a decrease of 3.85% and 2.88% of polyunsaturated fatty acids in eutrophicated lagoon water and Bayfolan 0.3%, respectively.

The production of biodiesel from microalgae faces several problems to be solved, among them is the necessity of increasing their lipid content, optimizing the harvesting, and improving the conversion of lipids to bioenergy, therefore reducing the energy cost of the production process prior to its commercial launch. Research focused on optimizing the biodiesel production process known as transesterification has various objectives such as eliminating the biomass drying stage, unifying the extraction and transesterification stages, improving the reaction yield using supercritical conditions, providing heating with microwave and ultrasonic radiation, reusing enzymatic and heterogeneous catalysts, among others. This chapter aims to summarize the advances that have been achieved with the various operating conditions for the in situ, direct, and supercritical oil transesterification process of microalgae from the genera Chlorella, Scenedesmus, Spirulina, and Nannochloropsis.

Nowadays, there has been an increase in the usage of renewable energies, due to the environmental situation in our planet. Among the existing renewable energies, the photovoltaic energy is an attractive alternative. However, it has an intermittent production due to the environmental factors involved in its process. Particularly partial shading can make photovoltaic arrays consume energy instead of producing it. Also, it is useful to register the environmental factors, in order to implement control measurements. For this reason, in order to measure and register real-time temperature and irradiance precisely, a low-cost Data Acquisition System (DAS) is proposed. The implemented DAS has a wireless communication system, which allows the user to have a database through an interface. Subsequently the available power is calculated through a simplified math model, and used along with the irradiance and temperature as attributes. Finally, the data is classified through Data Mining techniques, such as k-means and ID3, and later used to predict whether the bypass diode remains connected or not.