Surface thermodynamics, surface stress, equations at surfaces and triple lines for deformable bodies

International audienceThe thermodynamics and mechanics of the surface of a deformable body are studied here, following and refining the general approach of Gibbs. It is first shown that the 'local' thermodynamic variables of the state of the surface are only the temperature, the chemical potentials and the surface strain tensor (true thermodynamic variables, for a viscoelastic solid or a viscous fluid). A new definition of the surface stress is given and the corresponding surface thermodynamics equations are presented. The mechanical equilibrium equation at the surface is then obtained. It involves the surface stress and is similar to the Cauchy equation for the volume. Its normal component is a generalization of the Laplace equation. At a (body-fluid-fluid) triple contact line, two equations are obtained, which represent: (i) the equilibrium of the forces (surface stresses) for a triple line fixed on the body; (ii) the equilibrium relative to the motion of the line with respect to the body. This last equation leads to a strong modification of Young's classical capillary equation

Green's formula and singularity at a triple contact line. Example of finite-displacement solution

International audienceThe various equations at the surfaces and triple contact lines of a deformable body are obtained from a variational condition, by applying Green's formula in the whole space and on the Riemannian surfaces. The surface equations are similar to the Cauchy's equations for the volume, but involve a special definition of the 'divergence' (tensorial product of the covariant derivatives on the surface and the whole space). The normal component of the divergence equation generalizes the Laplace's equation for a fluid-fluid interface. Assuming that Green's formula remains valid at the contact line (despite the singularity), two equations are obtained at this line. The first one expresses that the fluid-fluid surface tension is equilibrated by the two surface stresses (and not by the volume stresses of the body) and suggests a finite displacement at this line (contrary to the infinite-displacement solution of classical elasticity, in which the surface properties are not taken into account). The second equation represents a strong modification of Young's capillary equation. The validity of Green's formula and the existence of a finite-displacement solution are justified with an explicit example of finite-displacement solution in the simple case of a half-space elastic solid bounded by a plane. The solution satisfies the contact line equations and its elastic energy is finite (whereas it is infinite for the classical elastic solution). The strain tensor components generally have different limits when approaching the contact line under different directions. Although Green's formula cannot be directly applied, because the stress tensor components do not belong to the Sobolev space H1(V), it is shown that this formula remains valid. As a consequence, there is no contribution of the volume stresses at the contact line. The validity of Green's formula plays a central role in the theory

Water nanoelectrolysis: A simple model

A simple model of water nanoelectrolysis-defined as the nanolocalization at a single point of any electrolysis phenomenon-is presented. It is based on the electron tunneling assisted by the electric field through the thin film of water molecules ($\sim$0.3 nm thick) at the surface of a tip-shaped nanoelectrode (micrometric to nanometric curvature radius at the apex). By applying, e.g., an electric potential V 1 during a finite time t 1 , and then the potential --V 1 during the same time t 1 , we show that there are three distinct regions in the plane (t 1 , V 1): one for the nanolocalization (at the apex of the nanoelectrode) of the electrolysis oxidation reaction, the second one for the nanolocalization of the reduction reaction, and the third one for the nanolocalization of the production of bubbles. These parameters t 1 and V 1 completely control the time at which the electrolysis reaction (of oxidation or reduction) begins, the duration of this reaction, the electrolysis current intensity (i.e., the tunneling current), the number of produced O 2 or H 2 molecules, and the radius of the nanolocalized bubbles. The model is in good agreement with our experiments

About de "Concerto for Viola and Orchestra" of Ángel Oliver Pina. An introduction to the analysis of his music

Este artículo propone, como asunto principal, el análisis de ciertos aspectos fundamentales del «Concierto para viola y orquesta» de Ángel Oliver Pina, principalmente los relacionados con la estructura de la obra, el trasfondo oculto de sus correspondencias interválicas, la articulación de la unidad formal y la función ordenadora de la instrumentación. Desde el análisis de la partitura señalamos, paralelamente, algunos de los rasgos propios del estilo compositivo de Oliver Pina y comentamos someramente su adscripción estética. Como compositor, su música destaca por su rigor constructivo y por el afán, no premeditado, de hacerse comprensible al oyente. De aquí que, estéticamente, el total de su obra, salvo excepciones, no pueda clasificarse ni como vanguardista ni como conservadora. De su independencia y originalidad creativas surge una música caracterizada por una expresividad que anida en un sentido interior del discurso y que no hace ostentación innecesaria de recursos y resultados meramente sonoros. La identificación del hombre y su música es, por momentos, absoluta y eso habla de la autenticidad que recorre los rincones de su obra. El «Concierto para viola», la única partitura de gran formato escrita por Ángel Oliver para instrumento solista y orquesta, es una clara muestra de todo cuanto decimos.As a main subject, this article proposes the analysis of certain essential aspects of the "Concert for viola and orchestra" of Ángel Oliver Pina. The analysis is focused, principally, on those realms related with the structure of the work, the secret background of the correspondences among the notes and intervals, the articulation of the formal unity and the structural function of the instrumentation. In parallel, and from an analysis of the score, some features of his own style as a composer is shown; and his esthetic assignement is also shortly commented. As a composer, his music stands out for its constructive rigour and for his not deliberate desire of being understandable to the listener. That is the reason why esthetically, all of his work, only with a few exceptions, cannot be qualified neither characterized by an expressiveness that nests a speech with a sense of interior, arises; a music that does not take advantage of merely sonorous resources and results. The identification of the man and his music is, at times, total. This fact reflects the authenticity of his work. The "Concert for viola", the only score of large format for a soloist instrument and orchestra, written by Ángel Oliver Pina is a clear example of this proposal

Control de tensiones para convertidores de cuatro hilos con cargas desequilibradas y no lineales

La evolución hacia los sistemas eléctricos futuros parece tender a la creación de microrredes. Esta nueva configuración de los sistemas eléctricos se alza como una solución plausible a los problemas de integración de energías renovables y generación distribuida, permitiendo además la alimentación de zonas aisladas. Las principales dificultades que se presentan en la implementación de las microrredes residen en el control de la tensión y la frecuencia, ya que la inercia de estos sistemas es muy baja o nula. Además, una de las características de las microrredes es la capacidad de mantener alimentadas las cargas aún cuando se encuentre aislada de la red principal, para este modo de funcionamiento es necesario que un nodo ejerza de nudo slack, estableciendo la referencia de tensión. El presente proyecto se centra en el control de tensión en niveles de distribución, de bajo voltaje. El objetivo es programar un algoritmo de control que actúe sobre un inversor conectado a un bus de tensión continua de potencia infinita. La función de este algoritmo es la de sintetizar a la salida del inversor las tensiones de fase requeridas para que en el punto común de acoplamiento (PCC) los voltajes de fase sean tres ondas sinusoidales puras de 230Vrms, pulsando a 50Hz y desfasadas entre ellas 120 . Alcanzar el objetivo de controlar cada fase de tensión independientemente requiere disponer de tres grados de libertad en las acciones de control, por lo que se vuelve estrictamente necesario el uso de un inversor trifásico de cuatro hilos y cuatro ramas. Concretamente se selecciona un convertidor 4LVSC en configuración de dos niveles y puente completo. A la salida de este inversor se encuentra un filtro LC y se considera que los condensadores están conectados directamente al PCC, por lo que será sobre estos elementos que se medirá las tensiones de fase. Para realizar el control se parte de la medida de la tensión de los condensadores transformándola a un marco de referencia abg. La primera etapa que actúa es un separador de secuencias escrito como un observador de Luenberger. Esta etapa considera el principio de superposición para extraer el contenido armónico y secuencial de las ondas de tensión medidas. A continuación, los errores entre cada componente y su referencia alimentan múltiples controladores resonantes sintonizados a las frecuencias más problemáticas con el objetivo de conseguir las características citadas de la tensión en bornes de los condensadores. Las sintonización de todas las ganancias se consigue aplicando la solución LQR del problema de control óptimo a un espacio de estados ampliado qué contiene la dinámica de la planta, el separador de secuencias y el control resonante. El algoritmo resultante se pone a prueba en simulación y en entorno de laboratorio. Estos resultados son presentados y comparados con la normativa española de calidad de baja tensión.World’s electric power system evolution towards future electrical systems seems to tend to the implementation of microgrids. This technology stands as a solution to the problems of renewable energy sources integration and distributed generation as well as it allows feeding isolated areas. The low electrical inertia of these systems causes that voltage and frequency control difficulties increase. In addition, an interesting microgrid characteristic is the ability to maintain loads feeded even when the system is isolated from the main grid. During this operation mode it is necessary that one node works as slack establishing a voltage reference. This project is focused on voltage control at low voltage distribution levels. The aim is to get a control algorithm for a power converter connected to an infinite power DC bus. The algorithm may calculate the phase voltages required so that in the point of common coupling (PCC) the phase voltages are three pure sinusoidal waves of 230Vrms, 50Hz and shifted 120 between them. Achieving the objective of controlling each voltage phase independently requires having three degrees of freedom in the control actions, so it becomes strictly necessary to use a three-phase inverter with four wires and four legs. Specifically, a 4LVSC power converter is selected in two-level full bridge configuration. At the output of this inverter is connected an LC filter and it is considered that the capacitors are connected directly to the PCC, so it will be across these elements where the phase voltages will be measured. To carry out the control, we start by measuring the voltage across the capacitors and transforming this measure to an abg reference frame. The first stage that acts is a voltage sequence estimator written as a Luenberger’s observer. This stage considers the superposition principle to extract the harmonic and sequential content of the measured voltage waves. Next, the errors between each component and its reference feed multiple resonant controllers tuned to the most problematic frequencies in order to achieve the abovementioned characteristics of the voltage across the capacitors. The tuning of all the gains is achieved by applying the LQR solution of the optimal control problem to an expanded state space that contains the plant, the sequence estimator and the resonant controller dynamics. The resulting algorithm is tested in simulation and in a laboratory environment. The results are presented and compared with the Spanish regulation of low voltage quality.Universidad de Sevilla. Máster en Sistemas de Energía Eléctric

Control convertidor dc-ac de 100kW

[Castellà]: Este proyecto desarrolla un estudio y diseño de un inversor trifásico que trabaja como fuente de corriente conectado a red. Tanto a nivel de hardware (los elementos físicos necesarios para su funcionamiento) como el desarrollo del software de control. A nivel de hardware se explicará la función de los componentes y estudiará la necesidad y las variables que determinan su dimensionado. Al mismo tiempo, el uso de convertidores de potencia conectados a red requiere la implementación de un adecuado sistema de filtrado. Es por este motivo que en este proyecto se dedicarán unas líneas al diseño de este. A nivel de software se pretende desarrollar una evolución, en cuanto a complejidad, del sistema de control así como las etapas necesarias para el desempeño de su función. Se presentarán los resultados obtenidos mediante la simulación de los circuitos y los resultados experimentales del testeo de un inversor real. Las etapas de control y software se realizarán para un inversor de 100kW, mientras que el dimensionado de los elementos de hardware se llevará a cabo para uno de 50kW. Finalmente, los ensayos realizados sobre el inversor serán realizados controlando un convertidor de 10kW.[English]: This project develops the study and design of a three-phase inverter connected to the grid working as a current source. Both hardware level (the physical elements necessary for its operation) as the development of the control software. About the hardware level, the role of the components and the need for their existence will be explained as the variables that determine its sizing. The use of power converters connected to the grid requires the implementation of a suitable filtering system. For this reason, a few lines of this project will try to explain the filter design. The study about de software level will try to develop an evolution, in terms of complexity, of the control system as well as the steps needed to carry out its work. The results obtained by simulating the circuits and experimental results of testing will be presented and compared. Control stages and software will be performed for a 100kW inverter; however, the sizing of the hardware elements will be calculated for one of 50kW. Finally, testing of the inverter will be carried out by controlling a 10kW converter