Guaranteed and robust a posteriori error estimates for singularly perturbed reaction-diffusion problems

International audienceWe derive a posteriori error estimates for singularly perturbed reaction-diffusion problems which yield a guaranteed upper bound on the discretization error and are fully and easily computable. Moreover, they are also locally efficient and robust in the sense that they represent local lower bounds for the actual error, up to a generic constant independent in particular of the reaction coefficient. We present our results in the framework of the vertex-centered finite volume method but their nature is general for any conforming method, like the piecewise linear finite element one. Our estimates are based on a H(div)-conforming reconstruction of the diffusive flux in the lowest-order Raviart-Thomas space linked with mesh dual to the original simplicial one, previously introduced by the last author in the pure diffusion case. They also rely on elaborated Poincaré, Friedrichs, and trace inequalities-based auxiliary estimates designed to cope optimally with the reaction dominance. In order to bring down the ratio of the estimated and actual overall energy error as close as possible to the optimal value of one, independently of the size of the reaction coefficient, we finally develop the ideas of local minimizations of the estimators by local modifications of the reconstructed diffusive flux. The numerical experiments presented confirm the guaranteed upper bound, robustness, and excellent efficiency of the derived estimates

Diseño de una red de logística inversa para envases de Tetra Pak® en la ciudad de Manizales

El alto nivel de consumo de la sociedad actual ha llevado a una creciente generación de residuos de todo tipo, lo que a su vez ha generado un deterioro medioambiental progresivo, dado que el nivel de aprovechamiento no compensa los niveles de generación. En Colombia, si bien existe una legislación para buscar el aprovechamiento de los residuos, se evidencia que no es llevado a la práctica con rigor. Por ello, se ha perdido en gran medida la oportunidad de generar valor y a la vez disminuir el impacto ambiental a partir del aprovechamiento de los residuos que se generan. Este trabajo se concentra en estudiar cómo en la ciudad de Manizales es posible aportar a la disminución del impacto ambiental por la generación de residuos de envases de Tetra Pak®, dada la oportunidad latente de generar valor a partir de este residuo en Colombia. Ello se dará gracias al diseño de una red de logística inversa que permita la recolección y alistamiento de este tipo de residuos para su posterior aprovechamiento en plantas a nivel nacional que se dedican a la producción de materiales derivadosAbstract : The high consumption levels in our current society has led to an increasing waste generation, which has consequently generated a progressive environmental damage as the recovery levels do not compensate generation levels. In Colombia, even though there is a legislation striving to increasing waste recovery, it is not properly applied. Thus, the opportunity of value generation and environmental impact decrease by recovering waste has been lost in great measure. This work is focused on studying how in Manizales city it is possible to contribute to the environmental impact decrease due to Tetra Pak® waste generation, given the unrealized opportunity of value generation through the recovery of this specific waste in Colombia. This will be possible thanks to the design of a reverse logistics network that allows gathering this material in order to prepare it to be processed in different plants around the country that are dedicated to the production of byproductsMaestrí

Diseño de blends de combustibles basado en propiedades termodinámicas

La valorización de la biomasa es un área en permanente evolución, relevante de investigación y que continuará atrayendo el interés del sector industrial a medida que más y más consumidores estén preocupados por el impacto ambiental del uso de recursos fósiles no renovables. Señal de ello son las grandes inversiones realizadas por la industria química tradicional (BASF, DUPONT, Braskem, Mitsubishi, entre otras) en nuevas vías de síntesis de químicos y materiales, a partir de recursos renovables. Además, existen beneficios económicos significativos si en futuros desarrollos tecnológicos se procesa biomasa residual. El notable potencial de la biomasa, como fuente alternativa de productos químicos, combustibles y materiales demanda nuevas tecnologías para procesar eficientemente materias primas complejas y diversas. Por su parte, impulsar el desarrollo de biorrefinerías eficientes obliga a integrar el diseño de nuevos procesos con el diseño de productos innovadores que faciliten la inserción de estos en el mercado. En este contexto, es importante el desarrollo de modelos termodinámicos predictivos y de algoritmos de simulación de propiedades de mezclas robustos, tanto en el ámbito productivo (diseño y simulación de biorrefinerías) como en el de blends de combustibles, que permitan predecir el desempeño de biocombustibles al ser utilizados, por ejemplo, como aditivos de combustibles convencionales. Esta tesis realiza dos contribuciones principales: 1) modelado del equilibrio de fases de sistemas involucrados en la conversión de biomasa, dirigida a la síntesis de biocombustibles y 2) desarrollo de herramientas para el diseño de productos multicomponentes que, en particular, se aplican al diseño de mezclas de combustibles y biocombustibles. El Capítulo 1 brinda una visión general sobre las tendencias actuales en biorrefinerías y biocombustibles. Se presentan los compuestos que constituyen la plataforma de biobasadas y sus principales rutas de conversión a biocombustibles. En esta tesis se amplía el al- VIII cance de la Ecuación de Estado a Contribución Grupal con Asociación (GCA-EoS). Este modelo ha sido aplicado con éxito a la descripción del comportamiento de fases de mezclas que involucran biocombustibles de primera generación (etanol y biodiesel) y numerosos productos naturales. En el Capítulo 2, luego de describir el modelo termodinámico GCAEoS, su base teórica y tabla de parámetros, se discuten las principales estrategias de parametrización desarrolladas durante este trabajo de tesis. El Capítulo 3 presenta el modelado del equilibrio entre fases de mezclas de CO2 con las series homólogas de n-alcanos y n-alcoholes. Estos sistemas son de particular interés para el desarrollo de tecnologías intensificadas por presión que están siendo altamente aplicadas en la síntesis de compuestos biobasados y donde el CO2 es el solvente por excelencia. El Capítulo 4 desarrolla el trabajo realizado en torno a extender la tabla de parámetros de la GCA-EoS a nuevos biocombustibles furánicos. Por último, el Capítulos 5 está dedicado al modelado termodinámico de éteres con alcanos y alcoholes. Esta extensión se aplica a la predicción del equilibrio de fases de sistemas constituidos por compuestos polifuncionales como poliéteres y glicol éteres. En la segunda parte de la tesis, la GCA-EoS se aplica a la simulación de propiedades de blends y se integra a una herramienta de diseño de productos multicomponentes basado en propiedades termodinámicas. En el Capítulo 6 se presentan los algoritmos desarrollados para simular matemáticamente ensayos experimentales que determinan las principales propiedades reguladas por normas nacionales e internacionales. Finalmente, el Capítulo 7 presenta el algoritmo de optimización, basado en técnicas metaheurísticas, que permite encontrar mezclas sustitutas que cumplan con un conjunto de propiedades especificadas para el combustible (presión de vapor Reid, curva de destilación y perfil de composición PIANOX). El diseño de blends es una aplicación de interés particular para esta tesis; sin embargo, está claro que la herramienta desarrollada puede ser extendida y aplicada al diseño de productos multicomponentes en una diversidad de aplicaciones.Currently, biomass valorization is a research field of growing interest and has gain special attention in the industrial sector as more and more consumers are concerned about the environmental impact of using non-renewable fossil resources. Sign of it are the large investments done by the traditional chemical industry (BASF, DUPONT, Braskem, Mitsubishi) in new synthesis routes of chemicals and materials from renewable resources. Moreover, significant economic benefits can be achieved if future technological developments process residual biomass. Biomass potential as an alternative source of chemical, fuels and materials require new technologies capable of efficiently process complex and inhomogeneous raw materials. On the other hand, boosting the development of efficient biorefineries requires integrating the design of new processes with the design of innovative products that facilitate the insertion of these in the market. In this context predictive thermodynamic models and robust property simulation algorithms are required for both, process and product conceptual design and optimization. This thesis makes two main contributions for the development of: 1) a thermodynamic model for biorefineries, with focus on biofuel synthesis and 2) a tool for multicomponent product design, specifically applied to fuel/biofuel blends design. Chapter 1 provides an overview about current trends in biorefineries and biofuels. It also introduces the main platform chemicals obtained from biomass processing and their further conversion routes towards biofuels. In this thesis the scope of application of the Group Contribution with Association Equation of State (GCA-EoS) is extended in the biorefineries context and to include new biofuels. This thermodynamic model has been successfully applied to mixtures involving first generation biofuels (bioethanol and biodiesel) and several natural products. Chapter 2 describes the GCA-EoS model, its theoretical bases and discusses the parametrization strategies developed during this research work. Chapter 3 reviews the modeling of CO2 phase behavior with the n-alkane and n-alcohol homologous series. These systems are of interest for developing pressure intensified technologies highly applied in the synthesis of platform chemicals. Chapter 4 is focus on extending GCAEoS table of parameters to new furanic biofuels. Finally, Chapter 5 introduces the thermodynamic modeling of ethers with alkanes and alcohols, extension of the GCA-EoS that allows predicting the phase behavior of systems including polyfunctional compounds such as polyether and glycol ethers, also considered next generation biofuels. In the second part of this thesis, the GCA-EoS is applied to the simulation of fuel blend properties and the development of a tool for designing blends based on thermodynamic properties. The developed algorithms for modeling experimental tests methods, regulated by national and international standards, are presented in Chapter 6. Finally, Chapter 7 presents an optimization algorithm based on metaheuristics techniques that allows searching for surrogate mixtures that fulfill specified fuel properties (Reid vapor pressure, distillation curve and PIANOX composition). Beyond blend design, the tools developed in this thesis could be extended and applied to other multicomponent product design.Fil: Gonzalez Prieto, Mariana. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Planta Piloto de Ingeniería Química. Universidad Nacional del Sur. Planta Piloto de Ingeniería Química; Argentin

Supercloseness on graded meshes for Q1 finite element approximation of a reaction–diffusion equation

In this paper we analyze the standard piece-wise bilinear finite element approximation of a model reaction–diffusion problem. We prove supercloseness results when appropriate graded meshes are used. The meshes are those introduced in Durán and Lombardi (2005) [8] but with a stronger restriction on the graduation parameter. As a consequence we obtain almost optimal error estimates in the L 2 -norm thus completing the error analysis given in Durán and Lombardi (2005).Fil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santalo". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santalo"; ArgentinaFil: Lombardi, Ariel Luis. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de General Sarmiento; ArgentinaFil: Prieto, Mariana Ines. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Superconvergence for finite element approximation of a convection-diffusion equation using graded meshes

In this paper we analyse the approximation of a model convection-diffusion equation by standard bilinear finite elements using the graded meshes introduced in Durán & Lombardi (2006, Finite element approximation of convection-diffusion problems using graded meshes. Appl. Numer. Math., 56, 1314-1325). Our main goal is to prove superconvergence results of the type known for standard elliptic problems, namely, that the difference between the finite element solution and the Lagrange interpolation of the exact solution, in the ε-weighted H 1-norm, is of higher order than the error itself. The constant in our estimate depends only weakly on the singular perturbation parameter. As a consequence of the superconvergence result we obtain optimal order error estimates in the L 2-norm. Also we show how to obtain a higher order approximation by a local postprocessing of the computed solution.Fil: Durán, Rodrigo Gonzalo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; ArgentinaFil: Lombardi, Ariel Luis. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Prieto, Mariana Ines. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentin

Mixed methods for degenerate elliptic problems and application to fractional Laplacian

We analyze the approximation by mixed finite element methods of solutions of equations of the form −div (a∇u) = g, where the coefficient a = a(x) can degenerate going to zero or infinity. First, we extend the classic error analysis to this case provided that the coefficient a belongs to the Muckenhoupt class A2. The analysis developed applies to general mixed finite element spaces satisfying the standard commutative diagram property, whenever some stability and interpolation error estimates are valid in weighted norms. Next, we consider in detail the case of Raviart–Thomas spaces of arbitrary order, obtaining optimal order error estimates for simplicial elements in any dimension and for convex quadrilateral elements in the two dimensional case, in both cases under a regularity assumption on the family of meshes. For the lowest order case we show that the regularity assumption can be removed and prove anisotropic error estimates which are of interest in problems with boundary layers. Finally we apply the results to a problem arising in the solution of the fractional Laplace equation.Fil: Cejas, María Eugenia. Universidad Nacional de La Plata. Departamento de Matemática, Facultad de Ciencias Exactas. Centro de Matemática La Plata ; ArgentinaFil: Duran, Ricardo Guillermo. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Prieto, Mariana Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentin

Design of a laboratory system for the prediction of wireline tool sticking

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1999.Includes bibliographical references (leaves 101-102).by Cecilia Mariana Prieto.S.M

Caffeine's Vascular Mechanisms of Action

Caffeine is the most widely consumed stimulating substance in the world. It is found in coffee, tea, soft drinks, chocolate, and many medications. Caffeine is a xanthine with various effects and mechanisms of action in vascular tissue. In endothelial cells, it increases intracellular calcium stimulating the production of nitric oxide through the expression of the endothelial nitric oxide synthase enzyme. Nitric oxide is diffused to the vascular smooth muscle cell to produce vasodilation. In vascular smooth muscle cells its effect is predominantly a competitive inhibition of phosphodiesterase, producing an accumulation of cAMP and vasodilation. In addition, it blocks the adenosine receptors present in the vascular tissue to produce vasoconstriction. In this paper the main mechanisms of action of caffeine on the vascular tissue are described, in which it is shown that caffeine has some cardiovascular properties and effects which could be considered beneficial

Effect of the Fe Nanoparticles Generated by Pulsed Plasma in Liquid in the Catalyzed Ozone Removal of Phenolphthalein

We have synthesized, in this work, zero valent iron (ZVI) nanoparticles to improve the efficiency of degradation of phenolphthalein catalyzed by ozone in aqueous solution. The Fe nanoparticles were obtained using the pulsed plasma in liquid (PPL) method with water as the liquid medium. Such nanoparticles have a mean size of 12 nm and are composed of ~80% Fe0, while the rest are a mixture of Fe+2 and Fe+3 oxides. The degradation of phenolphthalein was carried on a glass reactor injecting a constant amount of ozone and introducing different concentrations of Fe nanoparticles to the system. When using pure ozone, the percentage of degradation of phenolphthalein measured by colorimetry after one hour of reaction was 84%. However, when Fe nanoparticles are used, such percentage can be as high as 98% in 50 minutes of reaction. Furthermore, the degradation rate constant was 0.0334 min−1 with only ozone and it can be as high as 0.0733 min−1 with Fe nanoparticles. Finally, the total mineralization of phenolphthalein was obtained by total organic carbon (TOC) determinations. It is shown that when using only ozone, we obtained a percentage of mineralization of 49% and 96% when using the highest concentration of Fe nanoparticles

Fluxo de comunicação e partilha de dados entre agências criativas e agências de meios

Num mercado em constante evolução como o da Publicidade, é necessário encontrar ferramentas e métodos que permitam aos profissionais acompanhar o seu progresso. O Fluxo de Comunicação e Partilha de dados é fundamental para que isto seja possível. A base e o objetivo do Marketing e da Publicidade é a comunicação, sendo fulcral que, quem com esta trabalha diariamente utilize os seus expertises na área não só para o momento de passar a mensagem ao consumidor, mas como para realizar o seu trabalho em parceria com os diferentes departamentos envolvidos no processo. A presente investigação, tem como objetivo compreender de que forma a partilha de dados e o fluxo de comunicação entre diferentes departamentos como o criativo e o analítico, influenciam a eficiência das campanhas publicitárias. Como metodologia utilizou a análise bibliográfica e entrevista de forma a comprovar a teoria encontrada através de diversos autores. Os resultados obtidos revelaram à autora, que existe uma grande necessidade de criar sinergias entre os diferentes departamentos, de forma a desenvolver estratégias publicitárias de excelência. A pesquisa mostra também que apesar de algo relutantes alguns dos profissionais da área, demostra haver abertura para que se façam avanços naquilo que são parcerias entre agências 360.In a market where there is constant evolution, like the Advertisement one, it is necessary to find tools and methods that allow the professionals to accompany its progress. The Flux of Communication and Data Sharing is fundamental for this to be possible. The base and goal of Marketing and Advertisement is the communication, being crucial that, the ones who work with it every day, use their expertise in the area, not only to pass their message to the consumer, but also, to do their work alongside the different departments involved in the process. The present investigation has the goal to understand the way how data sharing and the flux of communication between the various departments, like the creative and analytical, influence the efficiency of the advertisement campaigns. As methodology for this research, the bibliographic analysis and the process of interviews were used to prove the theory found based on the work of other authors. The results obtained show the author that there is a need to crate synergy between the different departments, to be able to develop advertisement strategies in excellence. The research shows that, even if some of the professionals in the area are skeptical, there is space in the area for big developments to be done in the partnerships between 360º agencies