Mathematical model for elastic beams with longitudinally variable depth

In this work we introduce a new mathematical model for elastic beams with a cross-section of constant width and longitudinally variable depth, obtained from the classical three-dimensional linear elasticity problem by using an asymptotic expansion method. We characterize the first- and second-order displacements and the first-order stress field, giving results related to existence, uniqueness and convergence for the limit model solution. Finally, we present the computations for a classical example

Problemas de control en procesos de eutrofización

El aumento de los niveles de nitrógeno y fósforo (nutrientes principales para determinadas algas) en grandes masas de agua debido a la acción contaminante del hombre, puede traer consigo una disminución de la calidad del agua (procesos de eutrofización). En este trabajo estudiamos un m´etodo de control de esta clase de procesos, basado en el uso de biorreactores (tanques en donde se desarrollarán una serie de procesos que reducirán los niveles de nitrógeno y/o fósforo del agua por debajo de unos umbrales máximos). Matemáticamente estos métodos de control se pueden formular como problemas de control óptimo con restricciones sobre el estado en donde las ecuaciones de estado son un tipo de sistema de ecuaciones cuasilineales

Controlling eutrophication by means of water recirculation: an optimal control perspective

In this work, the artificial recirculation of water is presented and analyzed, from the perspective of the optimal control of partial differential equations, as a tool to prevent eutrophication effects in large waterbodies. A novel formulation of the environmental problem, based on the coupling of nonlinear models for hydrodynamics, water temperature and concentrations of the different species involved in the eutrophication processes, is introduced. After a complete and rigorous analysis of the existence of optimal solutions, a full numerical algorithm for their computation is proposed. Finally, some numerical results for a realistic scenario are shown, in order to prove the efficiency of our approach.Xunta de Galicia | Ref. ED431C 2019/02Agencia Estatal de Investigación | Ref. MTM2016-75140-

Algal cultivation for bioenergy production: first mathematical modelling results in raceways

The most used algae cultivation systems are the open-channel raceway ponds for their low maintenance and energy costs. Raceways allow algal cultivation using wastewater, where algae mass can be employed as source for bioenergy production. One of the main external factors influencing algal productivity is the velocity of the liquid inside the pond, that can be easily controlled by the position and/or rotational speed of the turning paddle wheel, and by the height of water. In this work we introduce a novel methodology to automate the optimization of the design of raceway ponds based on techniques of optimal control of partial differential equations. So, we formulate the problem as a control problem where the state system is given by the coupled nonlinear equations for hydrodynamics and algae/nitrogen/phosphorus concentrations, and the objective function to be maximized represents the global concentration of algae at final time. We present here a detailed, rigorous mathematical formulation of the optimal control problem, we propose a numerical algorithm for its resolution, and we show some preliminary computational results related to the numerical modelling of the problem

Escolio de la envolvente

La envolvente arquitectónica es uno de los elementos que más caracterizan a las construcciones de cada tiempo. La búsqueda de eficiencia energética para los edificios ha extremado en las últimas décadas la importancia de cualificarla por su condición de filtro entre el ambiente exterior y el interior. En el trasdós de los edificios antiguos se puede leer la identidad entre el sistema resistente y el sistema espacial: los muros, las columnas, las bóvedas, los arcos conforman el espacio, y el paso de la luz a través de los huecos exteriores y de articulación interior es la más clara expresión de su cualidad espacio_temporal. También en la compartimentación del espacio interior, aplicando el mismo sistema constructivo que en la fachada, lograba el diseño de dichos edificios su consistencia entre construcción y espacio arquitectónico. La independencia de los sistemas de soporte y de cerramiento de la edificación ha dado lugar, en algunos casos de la práctica profesional, a una pérdida de ident ificación del espacio arquitectónico como interrelación de la estructura resistente y la envolvente construida.The architectural envelope is one of the elements that characterize constructions of different eras. Being a filter between the outside environment and the interior, it has been put in the forefront of the quest for the energy efficient building. In inside face of the old buildings it can be read the identity of the resistant system and the spatial system: the walls, columns, domes, arches make up the space, and the light pass through the outer openings and articulation inside is the clearest expression of its space_time quality. Partitioning of interior space, applying the same construction system as in the façade, would accomplish the design of such consistency in buildings between construction and architectural space. The independence of the support and building enclosure systems has resulted, in some professional practices, in a loss of identification of the architectural space as strong interrelationship between structure and envelope built

Bilevel optimal control of urban traffic-related air pollution by means of Stackelberg strategies

Air contamination and road congestion are two major problems in modern cities. Both are closely related and present the same source: traffic flow. To deal with these problems, governments impose traffic restrictions preventing the entry of vehicles into sensitive areas, with the final goal of decreasing pollution levels. Unfortunately, these restrictions force drivers to look for alternative routes that usually generate traffic congestions, resulting in longer travel times and higher levels of contamination. In this work, blending computational modelling and optimal control of partial differential equations, we formulate and analyse a bilevel optimal control problem with air pollution and drivers’ travel time as objectives and look for optimal solutions in the sense of Stackelberg. In this setting, the leader (local government) implements traffic restrictions meanwhile the follower (drivers set) acts choosing travel preferences against leader constraints. We discretize the problem and propose a numerical algorithm to solve it, combining genetic-elitist algorithms and interior-point methods. Finally, computational results for a realistic case posed in the Guadalajara Metropolitan Area (Mexico) are shown.Sistema Nacional de Investigadores | Ref. SNI-52768Programa para el Desarrollo Profesional Docente | Ref. PRODEP/103.5/16/8066Xunta de Galicia | Ref. ED431C 2018/50

Optimizing the design of an estuarine water quality monitoring network by optimal control techniques

In this work, we propose a novel methodology in order to automatically optimize the location of the sampling points for a water quality monitoring network in an estuary, in such a way that any unknown pollution source can be identified (both in intensity and location) from the data supplied by those sampling points. In the central part of the article, after a rigorous mathematical formulation of the environmental problem, the full details of its numerical implementation are given. Finally, we present and analyze the results when applying the above proposed technique to study a real case in Ría of Vigo (northwestern Spain).Agencia Estatal de Investigación | Ref. TED2021-129324B-I00Universidade de Vigo/CISU

Designing an ecologically optimized road corridor surrounding restricted urban areas: a mathematical methodology

The use of optimization techniques for the optimal design of roads and railways has increased in recent years. The environmental impact of a layout is usually given in terms of the land use where it runs (avoiding some ecologically protected areas), without taking into account air pollution (in these or other sensitive areas) due to vehicular traffic on the road. This work addresses this issue and proposes an automatic method for obtaining a specific corridor (optimal in terms of air pollution), where the economically optimized road must be designed in a later stage. Combining a 1D traffic simulation model with a 2D air pollution model, and using classical techniques for optimal control of partial differential equations, the problem is formulated and solved in the framework of Mixed Integer Nonlinear Programming. The usefulness of this approach is shown in a real case study posed in a region that suffers from serious episodes of environmental pollution, the Guadalajara Metropolitan Area (México)Xunta de Galicia | Ref. ED431C 2018/50Sistema Nacional de Investigadores | Ref. SNI-52768Programa para el Desarrollo Profesional Docente | Ref. PRODEP/103.5/16/806

Mathematical analysis and numerical resolution of a heat transfer problem arising in water recirculation

This work is devoted to the analysis and resolution of a well-posed mathematical model for several processes involved in the artificial circulation of water in a large waterbody. This novel formulation couples the convective heat transfer equation with the modified Navier–Stokes system following a Smagorinsky turbulence model, completed with a suitable set of mixed, nonhomogeneous boundary conditions of diffusive, convective and radiative type. We prove several theoretical results related to existence of solution, and propose a full algorithm for its computation, illustrated with some realistic numerical examples.Ministerio de Economía y Competitividad | Ref. MTM2015-65570-PXunta de Galicia | Ref. ED431D 2017/1

Controlling eutrophication by means of water recirculation: An optimal control perspective

In this work, the artificial recirculation of water is presented and analyzed, from the perspective of the optimal control of partial differential equations, as a tool to prevent eutrophication effects in large waterbodies. A novel formulation of the environmental problem, based on the coupling of nonlinear models for hydrodynamics, water temperature and concentrations of the different species involved in the eutrophication processes, is introduced. After a complete and rigorous analysis of the existence of optimal solutions, a full numerical algorithm for their computation is proposed. Finally, some numerical results for a realistic scenario are shown, in order to prove the efficiency of our approachThe authors would like to thank the anonymous referees for their interesting comments, suggestions and corrections, as they have greatly contributed to improve the quality of the manuscript. The authors were partially supported by Xunta de Galicia, Spain, project ED431C 2019/02, and by the Agencia Estatal de Investigación (AEI) of Spain under grant MTM2016-75140-P, co-financed by the European Community fund FEDERS