Coupled Nonlinear Ginzburg-Landau and Mechanics Model for Martensitic Transformations in Polycrystals

Las transformaciones martensíticas (MT) se definen como un cambio en la estructura del cristal para formar una fase coherente o estructuras de dominio multivariante, a partir de la fase inicial con la misma composición, debido a pequeños intercambios o movimientos atómicos cooperativos. En el siglo pasado se han descubierto MT en diferentes materiales partiendo desde los aceros hasta las aleaciones con memoria de forma, materiales cerámicos y materiales inteligentes. Todos muestran propiedades destacables como alta resistencia mecánica, memoria de forma, efectos de superelasticidad o funcionalidades ferroicas como la piezoelectricidad, electro y magneto-estricción etc. Varios modelos/teorías se han desarrollado en sinergia con el desarrollo de la física del estado sólido para entender por qué las MT generan microstructuras muy variadas y ricas que muestran propiedades muy interesantes. Entre las teorías mejor aceptadas se encuentra la Teoría Fenomenológica de la Cristalografía Martensítica (PTMC, por sus siglas en inglés) que predice el plano de hábito y las relaciones de orientación entre la austenita y la martensita. La reinterpretación de la teoría PTMC en un entorno de mecánica del continuo (CM-PTMC) explica la formación de los dominios de estructuras multivariantes, mientras que la teoría de Landau con dinámica de inercia desentraña los mecanismos físicos de los precursores y otros comportamientos dinámicos. La dinámica de red cristalina desvela la reducción de la dureza acústica de las ondas de tensión de red que da lugar a transformaciones débiles de primer orden en el desplazamiento. A pesar de las diferencias entre las teorías estáticas y dinámicas dado su origen en diversas ramas de la física (por ejemplo mecánica continua o dinámica de la red cristalina), estas teorías deben estar inherentemente conectadas entre sí y mostrar ciertos elementos en común en una perspectiva unificada de la física. No obstante las conexiones físicas y diferencias entre las teorías/modelos no se han tratado hasta la fecha, aun siendo de importancia crítica para la mejora de modelos de MT y para el desarrollo integrado de modelos de transformaciones acopladas de desplazamiento-difusión. Por lo tanto, esta tesis comenzó con dos objetivos claros. El primero fue encontrar las conexiones físicas y las diferencias entre los modelos de MT mediante un análisis teórico detallado y simulaciones numéricas. El segundo objetivo fue expandir el modelo de Landau para ser capaz de estudiar MT en policristales, en el caso de transformaciones acopladas de desplazamiento-difusión, y en presencia de dislocaciones. Comenzando con un resumen de los antecedente, en este trabajo se presentan las bases físicas de los modelos actuales de MT. Su capacidad para predecir MT se clarifica mediante el ansis teórico y las simulaciones de la evolución microstructural de MT de cúbicoatetragonal y cúbicoatrigonal en 3D. Este análisis revela que el modelo de Landau con representación irreducible de la deformación transformada es equivalente a la teoría CM-PTMC y al modelo de microelasticidad para predecir los rasgos estáticos durante la MT, pero proporciona una mejor interpretación de los comportamientos dinámicos. Sin embargo, las aplicaciones del modelo de Landau en materiales estructurales están limitadas por su complejidad. Por tanto, el primer resultado de esta tesis es el desarrollo del modelo de Landau nolineal con representación irreducible de deformaciones y de la dinámica de inercia para policristales. La simulación demuestra que el modelo propuesto es consistente fcamente con el CM-PTMC en la descripción estática, y también permite una predicción del diagrama de fases con la clásica forma ’en C’ de los modos de nucleación martensítica activados por la combinación de temperaturas de enfriamiento y las condiciones de tensión aplicada correlacionadas con la transformación de energía de Landau. Posteriomente, el modelo de Landau de MT es integrado con un modelo de transformación de difusión cuantitativa para elucidar la relajación atómica y la difusión de corto alcance de los elementos durante la MT en acero. El modelo de transformaciones de desplazamiento y difusión incluye los efectos de la relajación en borde de grano para la nucleación heterogenea y la evolución espacio-temporal de potenciales de difusión y movilidades químicas mediante el acoplamiento de herramientas de cálculo y bases de datos termo-cinéticos de tipo CALPHAD. El modelo se aplica para estudiar la evolución microstructural de aceros al carbono policristalinos procesados por enfriamiento y partición (Q&P) en 2D. La microstructura y la composición obtenida mediante la simulación se comparan con los datos experimentales disponibles. Los resultados muestran el importante papel jugado por las diferencias en movilidad de difusión entre la fase austenita y martensita en la distibución de carbono en las aceros. Finalmente, un modelo multi-campo es propuesto mediante la incorporación del modelo de dislocación en grano-grueso al modelo desarrollado de Landau para incluir las diferencias morfológicas entre aceros y aleaciones con memoria de forma con la misma ruptura de simetría. La nucleación de dislocaciones, la formación de la martensita ’butterfly’, y la redistribución del carbono después del revenido son bien representadas en las simulaciones 2D del estudio de la evolución de la microstructura en aceros representativos. Con dicha simulación demostramos que incluyendo las dislocaciones obtenemos para dichos aceros, una buena comparación frente a los datos experimentales de la morfología de los bordes de macla, la existencia de austenita retenida dentro de la martensita, etc. Por tanto, basado en un modelo integral y en el desarrollo de códigos durante esta tesis, se ha creado una herramienta de modelización multiescala y multi-campo. Dicha herramienta acopla la termodinámica y la mecánica del continuo en la macroescala con la cinética de difusión y los modelos de campo de fase/Landau en la mesoescala, y también incluye los principios de la cristalografía y de la dinámica de red cristalina en la microescala. ABSTRACT Martensitic transformation (MT), in a narrow sense, is defined as the change of the crystal structure to form a coherent phase, or multi-variant domain structures out from a parent phase with the same composition, by small shuffles or co-operative movements of atoms. Over the past century, MTs have been discovered in different materials from steels to shape memory alloys, ceramics, and smart materials. They lead to remarkable properties such as high strength, shape memory/superelasticity effects or ferroic functionalities including piezoelectricity, electro- and magneto-striction, etc. Various theories/models have been developed, in synergy with development of solid state physics, to understand why MT can generate these rich microstructures and give rise to intriguing properties. Among the well-established theories, the Phenomenological Theory of Martensitic Crystallography (PTMC) is able to predict the habit plane and the orientation relationship between austenite and martensite. The re-interpretation of the PTMC theory within a continuum mechanics framework (CM-PTMC) explains the formation of the multivariant domain structures, while the Landau theory with inertial dynamics unravels the physical origins of precursors and other dynamic behaviors. The crystal lattice dynamics unveils the acoustic softening of the lattice strain waves leading to the weak first-order displacive transformation, etc. Though differing in statics or dynamics due to their origins in different branches of physics (e.g. continuum mechanics or crystal lattice dynamics), these theories should be inherently connected with each other and show certain elements in common within a unified perspective of physics. However, the physical connections and distinctions among the theories/models have not been addressed yet, although they are critical to further improving the models of MTs and to develop integrated models for more complex displacivediffusive coupled transformations. Therefore, this thesis started with two objectives. The first one was to reveal the physical connections and distinctions among the models of MT by means of detailed theoretical analyses and numerical simulations. The second objective was to expand the Landau model to be able to study MTs in polycrystals, in the case of displacive-diffusive coupled transformations, and in the presence of the dislocations. Starting with a comprehensive review, the physical kernels of the current models of MTs are presented. Their ability to predict MTs is clarified by means of theoretical analyses and simulations of the microstructure evolution of cubic-to-tetragonal and cubic-to-trigonal MTs in 3D. This analysis reveals that the Landau model with irreducible representation of the transformed strain is equivalent to the CM-PTMC theory and microelasticity model to predict the static features during MTs but provides better interpretation of the dynamic behaviors. However, the applications of the Landau model in structural materials are limited due its the complexity. Thus, the first result of this thesis is the development of a nonlinear Landau model with irreducible representation of strains and the inertial dynamics for polycrystals. The simulation demonstrates that the updated model is physically consistent with the CM-PTMC in statics, and also permits a prediction of a classical ’C shaped’ phase diagram of martensitic nucleation modes activated by the combination of quenching temperature and applied stress conditions interplaying with Landau transformation energy. Next, the Landau model of MT is further integrated with a quantitative diffusional transformation model to elucidate atomic relaxation and short range diffusion of elements during the MT in steel. The model for displacive-diffusive transformations includes the effects of grain boundary relaxation for heterogeneous nucleation and the spatio-temporal evolution of diffusion potentials and chemical mobility by means of coupling with a CALPHAD-type thermo-kinetic calculation engine and database. The model is applied to study for the microstructure evolution of polycrystalline carbon steels processed by the Quenching and Partitioning (Q&P) process in 2D. The simulated mixed microstructure and composition distribution are compared with available experimental data. The results show that the important role played by the differences in diffusion mobility between austenite and martensite to the partitioning in carbon steels. Finally, a multi-field model is proposed by incorporating the coarse-grained dislocation model to the developed Landau model to account for the morphological difference between steels and shape memory alloys with same symmetry breaking. The dislocation nucleation, the formation of the ’butterfly’ martensite, and the redistribution of carbon after tempering are well represented in the 2D simulations for the microstructure evolution of the representative steels. With the simulation, we demonstrate that the dislocations account for the experimental observation of rough twin boundaries, retained austenite within martensite, etc. in steels. Thus, based on the integrated model and the in-house codes developed in thesis, a preliminary multi-field, multiscale modeling tool is built up. The new tool couples thermodynamics and continuum mechanics at the macroscale with diffusion kinetics and phase field/Landau model at the mesoscale, and also includes the essentials of crystallography and crystal lattice dynamics at microscale.

A silviculture-oriented spatio-temporal model for germination in Pinus pinea L. in the Spanish Northern Plateau based on a direct seeding experiment

Natural regeneration in Pinus pinea stands commonly fails throughout the Spanish Northern Plateau under current intensive regeneration treatments. As a result, extensive direct seeding is commonly conducted to guarantee regeneration occurrence. In a period of rationalization of the resources devoted to forest management, this kind of techniques may become unaffordable. Given that the climatic and stand factors driving germination remain unknown, tools are required to understand the process and temper the use of direct seeding. In this study, the spatio-temporal pattern of germination of P. pinea was modelled with those purposes. The resulting findings will allow us to (1) determine the main ecological variables involved in germination in the species and (2) infer adequate silvicultural alternatives. The modelling approach focuses on covariates which are readily available to forest managers. A two-step nonlinear mixed model was fitted to predict germination occurrence and abundance in P. pinea under varying climatic, environmental and stand conditions, based on a germination data set covering a 5-year period. The results obtained reveal that the process is primarily driven by climate variables. Favourable conditions for germination commonly occur in fall although the optimum window is often narrow and may not occur at all in some years. At spatial level, it would appear that germination is facilitated by high stand densities, suggesting that current felling intensity should be reduced. In accordance with other studies on P. pinea dispersal, it seems that denser stands during the regeneration period will reduce the present dependence on direct seeding.

Nonlinear models for lateral dynamics of railway vehicles on bridges subject to wind action

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require threedimensional coupled vehicle-bridge models, wheree consideration of wheel to rail contact is a key aspect. Furthermore, an adequate evaluation of safety of rail traffic requires nonlinear models. A nonlinear coupled model is proposed here for vehicle-structure vertical and lateral dynamics. Vehicles are considered as fully three-dimensional multibody systems including gyroscopic terms and large rotation effects. The bridge structure is modeled by means of finite elements which may be of beam, shell or continuum type and may include geometric or material nonlinearities. The track geometry includes distributed track alignment irregularities. Both subsystems (bridge and vehicles) are described with coordinates in absolute reference frames, as opposed to alternative approaches which describe the multibody system with coordinates relative to the base bridge motion. The wheelrail contact employed is a semi-Hertzian model based on realistic wheel-rail profiles. It allows a detailed geometrical description of the contact patch under each wheel including multiple-point contact, flange contact and uplift. Normal and tangential stresses in each contact are integrated at each time-step to obtain the resultant contact forces. The models have been implemented within an existing finite element analysis software with multibody capabilities, Abaqus (Simulia Ltd., 2010). Further details of the model are presented in Antolín et al. (2012). Representative applications are presented for railway vehicles under lateral wind action on laterally compliant viaducts, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

Eigenstructure Assignment Based Controllers Applied to Flexible Spacecraft

The objective of this paper is to evaluate the behaviour of a controller designed using a parametric Eigenstructure Assignment method and to evaluate its suitability for use in flexible spacecraft. The challenge of this objective lies in obtaining a suitable controller that is specifically designated to alleviate the deflections and vibrations suffered by external appendages in flexible spacecraft while performing attitude manoeuvres. One of the main problems in these vehicles is the mechanical cross-coupling that exists between the rigid and flexible parts of the spacecraft. Spacecraft with fine attitude pointing requirements need precise control of the mechanical coupling to avoid undesired attitude misalignment. In designing an attitude controller, it is necessary to consider the possible vibration of the solar panels and how it may influence the performance of the rest of the vehicle. The nonlinear mathematical model of a flexible spacecraft is considered a close approximation to the real system. During the process of controller evaluation, the design process has also been taken into account as a factor in assessing the robustness of the system.

The Dynamics of High-Speed Railway Bridges: A Review of Design Issues and New Research for Lateral Dynamics

The dynamic effects of high-speed trains on viaducts are important issues for the design of the structures, as well as for the consideration of safe running conditions for the trains. In this work we start by reviewing the relevance of some basic design aspects. The significance of impact factor envelopes for moving loads is considered first. Resonance which may be achieved for high-speed trains requires dynamic analysis, for which some key aspects are discussed. The relevance of performing a longitudinal distribution of axle loads, the number of modes taken in analysis, and the consideration of vehicle-structure interaction are discussed with representative examples. The lateral dynamic effects of running trains on bridges is of importance for laterally compliant viaducts, such as some very tall structures erected in new high-speed lines. The relevance of this study is mainly for the safety of the traffic, considering both internal actions such as the hunting motion as well as external actions such as wind or earthquakes [1]. These studies require three-dimensional dynamic coupled vehicle-bridge models, and consideration of wheel to rail contact, a phenomenon which is complex and costly to model in detail. We describe here a fully nonlinear coupled model, described in absolute coordinates and incorporated into a commercial finite element framework [2]. The wheel-rail contact has been considered using a FastSim algorithm which provides a compromise between accuracy and computational cost, and captures the main nonlinear response of the contact interface. Two applications are presented, firstly to a vehicle subject to a strong wind gust traversing a bridge, showing the relevance of the nonlinear wheel-rail contact model as well as the dynamic interaction between bridge and vehicle. The second application is to a real HS viaduct with a long continuous deck and tall piers and high lateral compliance [3]. The results show the safety of the traffic as well as the importance of considering features such as track alignment irregularities.

Analysis of lateral dynamics of railway vehicles on viaducts with coupled models

The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require 3D coupled vehicle-bridge models, and consideration of wheel to rail contact, a phenomenon which is complex and costly to model in detail. We describe here a fully nonlinear coupled model, described in absolute coordinates and incorporated into a commercial finite element framework. Two applications are presented, firstly to a vehicle subject to a strong wind gust traversing a br idge, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle. The second application is to a real viaduct in a high-speed line, with a long continuous deck and tall piers with high lateral compliance. The results show the safety of the traffic as well as the relevance of considering the wind action and the nonlinear response.

Coupled models for the dynamics of bridges under high-speed rail traffic

The dynamic effects of high-speed trains on viaducts are important issues for the design of the structures, as well as for determining safe running conditions of trains. In this work we start by reviewing the relevance of some basic moving load models for the dynamic action of vertical traffic loads. The study of lateral dynamics of running trains on bridges is of importance mainly for the safety of the traffic, and may be relevant for laterally compliant bridges. These studies require 3D coupled vehicle-bridge models and consideration of wheel to rail contact. We describe here a fully nonlinear coupled model, formulated in absolute coordinates and incorporated into a commercial finite element framework. An application example is presented for a vehicle subject to a strong wind gust traversing a bridge, showing the relevance of the nonlinear wheel-rail contact model as well as the interaction between bridge and vehicle.

Análisis de elementos de madera reforzados con materiales compuestos

Gran parte del patrimonio construido cuenta con edificios cuya estructura está compuesta por elementos de madera. El volumen económico que supone el mantenimiento y renovación de dicho patrimonio es considerable, por ello, es de especial interés el estudio de las diferentes técnicas de refuerzo aplicables a este tipo de estructuras. Las estructuras de madera han sido tradicionalmente reforzadas con piezas del mismo material, aumentando la sección de los elementos dañados, o con acero. La aparición de los materiales compuestos de polímeros reforzados con fibras, y su progresiva aplicación en obras de construcción, hizo que a principios de la década de los noventa se comenzara a aplicar este material en refuerzos de estructuras de madera (Puente de Sins, 1992). La madera es un material natural con una excelente relación entre sus características mecánicas y su peso. Con el uso de materiales compuestos como refuerzo ésta característica se mantiene. En cuanto a su modelo constitutivo, se admite un comportamiento elástico lineal a tracción paralela a la fibra hasta la rotura, mientras que a compresión, se considera un comportamiento lineal elástico inicial, seguido de un tramo plástico. En vigas de madera aserrada sometidas a flexión predomina el modo de fallo por tracción localizándose la fractura frecuentemente en el canto inferior. Los FRP tienen un comportamiento elástico lineal a tracción hasta la rotura y cuentan con excelentes propiedades mecánicas en relación a su peso y volumen. Si se refuerza la viga por el canto inferior se aumentará su capacidad de absorber tracciones y por tanto, es previsible que se produzca un incremento en la capacidad de carga, así como un aumento de ductilidad. En este trabajo se analizan los beneficios que aportan distintos sistemas de refuerzos de materiales compuestos. El objetivo es contribuir al conocimiento de esta técnica para la recuperación o aumento de las propiedades resistentes de elementos de madera sometidos a flexión. Se ha llevado a cabo un estudio basado en datos obtenidos experimentalmente mediante el ensayo a flexión de vigas de madera de pino silvestre reforzadas con materiales compuestos. Las fibras que componen los tejidos utilizados para la ejecución de los refuerzos son de basalto y de carbono. En el caso de los compuestos de fibra de basalto se aplican en distintos gramajes, y los de carbono en tejido unidireccional y bidireccional. Se analiza el comportamiento de las vigas según las variables de refuerzo aplicadas y se comparan con los resultados de vigas ensayadas sin reforzar. Además se comprueba el ajuste del modelo de cálculo no lineal aplicado para predecir la carga de rotura de cada viga reforzada. Con este trabajo queda demostrado el buen funcionamiento del FRP de fibra de basalto aplicado en el refuerzo de vigas de madera y de los tejidos de carbono bidireccionales con respecto a los unidireccionales. ABSTRACT Many of the buildings of the built heritage include a structure composed by timber elements. The economic volume involved in the maintenance and renewal of this built heritage is considerable, therefore, the study of the different reinforcement techniques applicable to this type of structure is of special interest. The wooden structures have traditionally been reinforced either with steel or with pieces of the same material, increasing the section of the damaged parts. The emergence of polymer composites reinforced with fibers, and their progressive use in construction, started to be applied as reinforcement in timber structures at the beginning of the nineties decade in the 20th century (Sins Bridge, 1992). Wood is a natural material with an excellent ratio between its mechanic characteristics and its weight. This feature is maintained with the use of composites as reinforcement. In terms of its constitutive model, linear elastic behavior parallel to the fiber up to fracture is admitted when subjected to tensile stress, while under compression, an initial linear elastic behavior, followed by a section plasticizing, is considered. In sawn timber beams subjected to bending, the predominant failure is mainly due to tensile stress; and frequently the fracture is located at the beam lower face. The FRP have a linear elastic behavior until fracture occurs, and have excellent mechanical properties in relation to their weight and volume. If the beam is reinforced by its lower face, its capacity to absorb tensile stresses will increase, and therefore, an increase in its carrying capacity is likely to be produced, as well as an increase in ductility. This work analyzes the benefits different reinforcement systems of composite materials provide, with the aim of contributing to the knowledge of this technique for recovering or increasing the strength properties of timber elements subjected to bending loads. It is a study based on data obtained experimentally using bending tests of pine timber beams reinforced with composite materials. Fibers used for the execution of the reinforcement are basalt and carbon. Basalt fiber composites are applied in different grammages, whereas with carbon composites, unidirectional and bidirectional fabrics are used. The behavior of the beams was analyzed regarding the reinforcement variables applied, and the results are compared with those of the tested beams without reinforcement. Furthermore it has been proved adjunting the nonlinear calculation model applied to predict the failure load of each reinforced beam. This work proves the good behavior of fiber reinforce plastic (FRP) with basalt fiber when applied to timber beams, and that of bidirectional carbon fabrics as opposed to the unidirectional ones.

Agricultural use of organic wastes as source of nitrogen and phosphorus: risks and opportunities

El nitrógeno (N) y el fósforo (P) son nutrientes esenciales en la producción de cultivos. El desarrollo de los fertilizantes de síntesis durante el siglo XX permitió una intensificación de la agricultura y un aumento de las producciones pero a su vez el gran input de nutrientes ha resultado en algunos casos en sistemas poco eficientes incrementando las pérdidas de estos nutrientes al medio ambiente. En el caso del P, este problema se agrava debido a la escasez de reservas de roca fosfórica necesaria para la fabricación de fertilizantes fosfatados. La utilización de residuos orgánicos en agricultura como fuente de N y P es una buena opción de manejo que permite valorizar la gran cantidad de residuos que se generan. Sin embargo, es importante conocer los procesos que se producen en el suelo tras la aplicación de los mismos, ya que influyen en la disponibilidad de nutrientes que pueden ser utilizados por el cultivo así como en las pérdidas de nutrientes de los agrosistemas que pueden ocasionar problemas de contaminación. Aunque la dinámica del N en el suelo ha sido más estudiada que la del P, los problemas importantes de contaminación por nitratos en zonas vulnerables hacen necesaria la evaluación de aquellas prácticas de manejo que pudieran agravar esta situación, y en el caso de los residuos orgánicos, la evaluación de la respuesta agronómica y medioambiental de la aplicación de materiales con un alto contenido en N (como los residuos procedentes de la industria vinícola y alcoholera). En cuanto al P, debido a la mayor complejidad de su ciclo y de las reacciones que ocurren en el suelo, hay un mayor desconocimiento de los factores que influyen en su dinámica en los sistemas suelo-planta, lo que supone nuevas oportunidades de estudio en la evaluación del uso agrícola de los residuos orgánicos. Teniendo en cuenta los conocimientos previos sobre cada nutriente así como las necesidades específicas en el estudio de los mismos, en esta Tesis se han evaluado: (1) el efecto de la aplicación de residuos procedentes de la industria vinícola y alcoholera en la dinámica del N desde el punto de vista agronómico y medioambiental en una zona vulnerable a la contaminación por nitratos; y (2) los factores que influyen en la disponibilidad de P en el suelo tras la aplicación de residuos orgánicos. Para ello se han llevado a cabo incubaciones de laboratorio así como ensayos de campo que permitieran evaluar la dinámica de estos nutrientes en condiciones reales. Las incubaciones de suelo en condiciones controladas de humedad y temperatura para determinar el N mineralizado se utilizan habitualmente para estimar la disponibilidad de N para el cultivo así como el riesgo medioambiental. Por ello se llevó a cabo una incubación en laboratorio para conocer la velocidad de mineralización de N de un compost obtenido a partir de residuos de la industria vinícola y alcoholera, ampliamente distribuida en Castilla-La Mancha, región con problemas importantes de contaminación de acuíferos por nitratos. Se probaron tres dosis crecientes de compost correspondientes a 230, 460 y 690 kg de N total por hectárea que se mezclaron con un suelo franco arcillo arenoso de la zona. La evolución del N mineral en el suelo a lo largo del tiempo se ajustó a un modelo de regresión no lineal, obteniendo valores bajos de N potencialmente mineralizable y bajas contantes de mineralización, lo que indica que se trata de un material resistente a la mineralización y con una lenta liberación de N en el suelo, mineralizándose tan solo 1.61, 1.33 y 1.21% del N total aplicado con cada dosis creciente de compost (para un periodo de seis meses). Por otra parte, la mineralización de N tras la aplicación de este material también se evaluó en condiciones de campo, mediante la elaboración de un balance de N durante dos ciclos de cultivo (2011 y 2012) de melón bajo riego por goteo, cultivo y manejo agrícola muy característicos de la zona de estudio. Las constantes de mineralización obtenidas en el laboratorio se ajustaron a las temperaturas reales en campo para predecir el N mineralizado en campo durante el ciclo de cultivo del melón, sin embargo este modelo generalmente sobreestimaba el N mineralizado observado en campo, por la influencia de otros factores no tenidos en cuenta para obtener esta predicción, como el N acumulado en el suelo, el efecto de la planta o las fluctuaciones de temperatura y humedad. Tanto el ajuste de los datos del laboratorio al modelo de mineralización como las predicciones del mismo fueron mejores cuando se consideraba el efecto de la mezcla suelo-compost que cuando se aislaba el N mineralizado del compost, mostrando la importancia del efecto del suelo en la mineralización del N procedente de residuos orgánicos. Dado que esta zona de estudio ha sido declarada vulnerable a la contaminación por nitratos y cuenta con diferentes unidades hidrológicas protegidas, en el mismo ensayo de campo con melón bajo riego por goteo se evaluó el riesgo de contaminación por nitratos tras la aplicación de diferentes dosis de compost bajo dos regímenes de riego, riego ajustado a las necesidades del cultivo (90 ó 100% de la evapotranspiración del cultivo (ETc)) o riego excedentario (120% ETc). A lo largo del ciclo de cultivo se estimó semanalmente el drenaje mediante la realización de un balance hídrico, así como se tomaron muestras de la solución de suelo y se determinó su concentración de nitratos. Para evaluar el riesgo de contaminación de las aguas subterráneas asociado con estas prácticas, se utilizaron algunos índices medioambientales para determinar la variación en la calidad del agua potable (Índice de Impacto (II)) y en la concentración de nitratos del acuífero (Índice de Impacto Ambiental (EII)). Para combinar parámetros medioambientales con parámetros de producción, se calculó la eficiencia de manejo. Se observó que la aplicación de compost bajo un régimen de riego ajustado no aumentaba el riesgo de contaminación de las aguas subterráneas incluso con la aplicación de la dosis más alta. Sin embargo, la aplicación de grandes cantidades de compost combinada con un riego excedentario supuso un incremento en el N lixiviado a lo largo del ciclo de cultivo, mientras que no se obtuvieron mayores producciones con respecto al riego ajustado. La aplicación de residuos de la industria vinícola y alcoholera como fuente de P fue evaluada en suelos calizos caracterizados por una alta capacidad de retención de P, lo cual en algunos casos limita la disponibilidad de este nutriente. Para ello se llevó a cabo otro ensayo de incubación con dos suelos de diferente textura, con diferente contenido de carbonato cálcico, hierro y con dos niveles de P disponible; a los que se aplicaron diferentes materiales procedentes de estas industrias (con y sin compostaje previo) aportando diferentes cantidades de P. A lo largo del tiempo se analizó el P disponible del suelo (P Olsen) así como el pH y el carbono orgánico disuelto. Al final de la incubación, con el fin de estudiar los cambios producidos por los diferentes residuos en el estado del P del suelo se llevó a cabo un fraccionamiento del P inorgánico del suelo, el cual se separó en P soluble y débilmente enlazado (NaOH-NaCl-P), P soluble en reductores u ocluido en los óxidos de Fe (CBD-P) y P poco soluble precipitado como Ca-P (HCl-P); y se determinó la capacidad de retención de P así como el grado de saturación de este elemento en el suelo. En este ensayo se observó que, dada la naturaleza caliza de los suelos, la influencia de la cantidad de P aplicado con los residuos en el P disponible sólo se producía al comienzo del periodo de incubación, mientras que al final del ensayo el incremento en el P disponible del suelo se igualaba independientemente del P aplicado con cada residuo, aumentando el P retenido en la fracción menos soluble con el aumento del P aplicado. Por el contrario, la aplicación de materiales orgánicos menos estabilizados y con un menor contenido en P, produjo un aumento en las formas de P más lábiles debido a una disolución del P retenido en la fracción menos lábil, lo cual demostró la influencia de la materia orgánica en los procesos que controlan el P disponible en el suelo. La aplicación de residuos aumentó el grado de saturación de P de los suelos, sin embargo los valores obtenidos no superaron los límites establecidos que indican un riesgo de contaminación de las aguas. La influencia de la aplicación de residuos orgánicos en las formas de P inorgánico y orgánico del suelo se estudió además en un suelo ácido de textura areno francosa tras la aplicación en campo a largo plazo de estiércol vacuno y de compost obtenido a partir de biorresiduos, así como la aplicación combinada de compost y un fertilizante mineral (superfosfato tripe), en una rotación de cultivos. En muestras de suelo recogidas 14 años después del establecimiento del experimento en campo, se determinó el P soluble y disponible, la capacidad de adsorción de P, el grado de saturación de P así como diferentes actividades enzimáticas (actividad deshidrogenasa, fosfatasa ácida y fosfatasa alcalina). Las diferentes formas de P orgánico en el suelo se estudiaron mediante una técnica de adición de enzimas con diferentes substratos específicos a extractos de suelo de NaOH-EDTA, midiendo el P hidrolizado durante un periodo de incubación por colorimetría. Las enzimas utilizadas fueron la fosfatasa ácida, la nucleasa y la fitasa las cuales permitieron identificar monoésteres hidrolizables (monoester-like P), diésteres (DNA-like P) e inositol hexaquifosfato (Ins6P-like P). La aplicación a largo plazo de residuos orgánicos aumentó el P disponible del suelo proporcionalmente al P aplicado con cada tipo de fertilización, suponiendo un mayor riesgo de pérdidas de P dado el alto grado de saturación de este suelo. La aplicación de residuos orgánicos aumentó el P orgánico del suelo resistente a la hidrólisis enzimática, sin embargo no influyó en las diferentes formas de P hidrolizable por las enzimas en comparación con las observadas en el suelo sin enmendar. Además, las diferentes formas de P orgánico aplicadas con los residuos orgánicos no se correspondieron con las analizadas en el suelo lo cual demostró que éstas son el resultado de diferentes procesos en el suelo mediados por las plantas, los microorganismos u otros procesos abióticos. En este estudio se encontró una correlación entre el Ins6P-like P y la actividad microbiana (actividad deshidrogenasa) del suelo, lo cual refuerza esta afirmación. Por último, la aplicación de residuos orgánicos como fuente de N y P en la agricultura se evaluó agronómicamente en un escenario real. Se estableció un experimento de campo para evaluar el compost procedente de residuos de bodegas y alcoholeras en el mismo cultivo de melón utilizado en el estudio de la mineralización y lixiviación de N. En este experimento se estudió la aplicación de tres dosis de compost: 1, 2 y 3 kg de compost por metro lineal de plantación correspondientes a 7, 13 y 20 t de compost por hectárea respectivamente; y se estudió el efecto sobre el crecimiento de las plantas, la acumulación de N y P en la planta, así como la producción y calidad del cultivo. La aplicación del compost produjo un ligero incremento en la biomasa vegetal acompañado por una mejora significativa de la producción con respecto a las parcelas no enmendadas, obteniéndose la máxima producción con la aplicación de 2 kg de compost por metro lineal. Aunque los efectos potenciales del N y P fueron parcialmente enmascarados por otras entradas de estos nutrientes en el sistema (alta concentración de nitratos en el agua de riego y ácido fosfórico suministrado por fertirrigación), se observó una mayor acumulación de P uno de los años de estudio que resultó en un aumento en el número de frutos en las parcelas enmendadas. Además, la mayor acumulación de N y P disponible en el suelo al final del ciclo de cultivo indicó el potencial uso de estos materiales como fuente de estos nutrientes. ABSTRACT Nitrogen (N) and phosphorus (P) are essential nutrients in crop production. The development of synthetic fertilizers during the 20th century allowed an intensification of the agriculture increasing crop yields but in turn the great input of nutrients has resulted in some cases in inefficient systems with higher losses to the environment. Regarding P, the scarcity of phosphate rock reserves necessary for the production of phosphate fertilizers aggravates this problem. The use of organic wastes in agriculture as a source of N and P is a good option of management that allows to value the large amount of wastes generated. However, it is important to understand the processes occurring in the soil after application of these materials, as they affect the availability of nutrients that can be used by the crop and the nutrient losses from agricultural systems that can cause problems of contamination. Although soil N dynamic has been more studied than P, the important concern of nitrate pollution in Nitrate Vulnerable Zones requires the evaluation of those management practices that could aggravate this situation, and in the case of organic wastes, the evaluation of the agronomic and environmental response after application of materials with a high N content (such as wastes from winery and distillery industries). On the other hand, due to the complexity of soil P cycle and the reactions that occur in soil, there is less knowledge about the factors that can influence its dynamics in the soil-plant system, which means new opportunities of study regarding the evaluation of the agricultural use of organic wastes. Taking into account the previous knowledge of each nutrient and the specific needs of study, in this Thesis we have evaluated: (1) the effect of the application of wastes from the winery and distillery industries on N dynamics from the agronomic and environmental viewpoint in a vulnerable zone; and (2) the factors that influence P availability in soils after the application of organic wastes. With this purposes, incubations were carried out in laboratory conditions as well as field trials that allow to assess the dynamic of these nutrients in real conditions. Soil incubations under controlled moisture and temperature conditions to determine N mineralization are commonly used to estimate N availability for crops together with the environmental risk. Therefore, a laboratory incubation was conducted in order to determine the N mineralization rate of a compost made from wastes generated in the winery and distillery industries, widely distributed in Castilla-La Mancha, a region with significant problems of aquifers contamination by nitrates. Three increasing doses of compost corresponding to 230, 460 and 690 kg of total N per hectare were mixed with a sandy clay loam soil collected in this area. The evolution of mineral N in soil over time was adjusted to a nonlinear regression model, obtaining low values of potentially mineralizable N and low constants of mineralization, indicating that it is a material resistant to mineralization with a slow release of N, with only 1.61, 1.33 and 1.21% of total N applied being mineralized with each increasing dose of compost (for a period of six months). Furthermore, N mineralization after the application of this material was also evaluated in field conditions by carrying out a N balance during two growing seasons (2011 and 2012) of a melon crop under drip irrigation, a crop and management very characteristic of the area of study. The mineralization constants obtained in the laboratory were adjusted to the actual temperatures observed in the field to predict N mineralized during each growing season, however, this model generally overestimated the N mineralization observed in the field, because of the influence of other factors not taken into account for this prediction, as N accumulated in soil, the plant effect or the fluctuations of temperature and moisture. The fitting of the laboratory data to the model as well as the predictions of N mineralized in the field were better when considering N mineralized from the soil-compost mixture rather than when N mineralized from compost was isolated, underlining the important role of the soil on N mineralization from organic wastes. Since the area of study was declared vulnerable to nitrate pollution and is situated between different protected hydrological units, the risk of nitrate pollution after application of different doses compost was evaluated in the same field trial with melon under two irrigation regimes, irrigation adjusted to the crop needs (90 or 100% of the crop evapotranspiration (ETc)) or excedentary irrigation (120% ETc). Drainage was estimated weekly throughout the growing season by conducting a water balance, samples of the soil solution were taken and the concentration of nitrates was determined. To assess the risk of groundwater contamination associated with these practices, some environmental indices were used to determine the variation in the quality of drinking water (Impact Index (II)) and the nitrates concentration in the groundwater (Environmental Impact Index (EII)). To combine environmental parameters together with yield parameters, the Management Efficiency was calculated. It was observed that the application of compost under irrigation adjusted to the plant needs did not represent a higher risk of groundwater contamination even with the application of the highest doses. However, the application of large amounts of compost combined with an irrigation surplus represented an increase of N leaching during the growing season compared with the unamended plots, while no additional yield with respect to the adjusted irrigation strategy is obtained. The application of wastes derived from the winery and distillery industry as source of P was evaluated in calcareous soils characterized by a high P retention capacity, which in some cases limits the availability of this nutrient. Another incubation experiment was carried out using two soils with different texture, different calcium carbonate and iron contents and two levels of available P; to which different materials from these industries (with and without composting) were applied providing different amounts of P. Soil available P (Olsen P), pH and dissolved organic carbon were analyzed along time. At the end of the incubation, in order to study the changes in soil P status caused by the different residues, a fractionation of soil inorganic P was carried out, which was separated into soluble and weakly bound P (NaOH-NaCl- P), reductant soluble P or occluded in Fe oxides (CBD-P) and P precipitated as poorly soluble Ca-P (HCl-P); and the P retention capacity and degree of P saturation were determined as well. Given the calcareous nature of the soils, the influence of the amount of P applied with the organic wastes in soil available P only occurred at the beginning of the incubation period, while at the end of the trial the increase in soil available P equalled independently of the amount of P applied with each residue, increasing the P retained in the least soluble fraction when increasing P applied. Conversely, the application of less stabilized materials with a lower content of P resulted in an increase in the most labile P forms due to dissolution of P retained in the less labile fraction, demonstrating the influence of organic matter addition on soil P processes that control P availability in soil. As expected, the application of organic wastes increased the degree of P saturation in the soils, however the values obtained did not exceed the limits considered to pose a risk of water pollution. The influence of the application of organic wastes on inorganic and organic soil P forms was also studied in an acid loamy sand soil after long-term field application of cattle manure and biowaste compost and the combined application of compost and mineral fertilizer (triple superphosphate) in a crop rotation. Soil samples were collected 14 years after the establishment of the field experiment, and analyzed for soluble and available P, P sorption capacity, degree of P saturation and enzymatic activities (dehydrogenase, acid phosphatase and alkaline phosphatase). The different forms of organic P in soil were determined by using an enzyme addition technique, based on adding enzymes with different substrate specificities to NaOH-EDTA soil extracts, measuring the hydrolyzed P colorimetrically after an incubation period. The enzymes used were acid phosphatase, nuclease and phytase which allowed to identify hydrolyzable monoesters (monoester-like P) diesters (DNA-like P) and inositol hexakisphosphate (Ins6P-like P). The long-term application of organic wastes increased soil available P proportionally to the P applied with each type of fertilizer, assuming a higher risk of P losses given the high degree of P saturation of this soil. The application of organic wastes increased soil organic P resistant to enzymatic hydrolysis, but no influence was observed regarding the different forms of enzyme hydrolyzable organic P compared to those observed in the non-amended soil. Furthermore, the different forms of organic P applied with the organic wastes did not correspond to those analyzed in the soil which showed that these forms in soil are a result of multifaceted P turnover processes in soil affected by plants, microorganisms and abiotic factors. In this study, a correlation between Ins6P-like P and the microbial activity (dehydrogenase activity) of soil was found, which reinforces this claim. Finally, the application of organic wastes as a source of N and P in agriculture was evaluated agronomically in a real field scenario. A field experiment was established to evaluate the application of compost made from wine-distillery wastes in the same melon crop used in the experiments of N mineralization and leaching. In this experiment the application of three doses of compost were studied: 1 , 2 and 3 kg of compost per linear meter of plantation corresponding to 7, 13 and 20 tonnes of compost per hectare respectively; and the effect on plant growth, N and P accumulation in the plant as well as crop yield and quality was studied. The application of compost produced a slight increase in plant biomass accompanied by a significant improvement in crop yield with respect to the unamended plots, obtaining the maximum yield with the application of 2 kg of compost per linear meter. Although the potential effects of N and P were partially masked by other inputs of these nutrients in the system (high concentration of nitrates in the irrigation water and phosphoric acid supplied by fertigation), an effect of P was observed the first year of study resulting in a greater plant P accumulation and in an increase in the number of fruits in the amended plots. In addition, the higher accumulation of available N and P in the topsoil at the end of the growing season indicated the potential use of this material as source of these nutrients.

Estudio de la respuesta dinámica transversal de viaductos altos de líneas de ferrocarril de alta velocidad bajo la acción de cargas de uso

Es conocido que las dimensiones de los puentes de ferrocarril han ido cambiando debido a las estrictas condiciones de trazado impuestas en las líneas de alta velocidad. Además, la creciente preocupación de la sociedad por cuidar y proteger el medio ambiente, reflejado en la correspondiente normativa, ha generado nuevos condicionantes en el diseño de estas infraestructuras. En concreto, se ha limitado el movimiento de grandes volúmenes de terreno particularmente en los espacios protegidos. Por estas razones, hoy en día se proyectan y construyen puentes de ferrocarril más altos y más largos en todo el mundo. En España se han construido varios viaductos de pilas altas para líneas de alta velocidad. Ejemplos de estas infraestructuras son el Viaducto O’Eixo y el Viaducto de Barbantiño, situados en la línea de alta velocidad Madrid-Galicia, Estos viaductos altos se caracterizan por tener una mayor flexibilidad lateral y una frecuencia fundamental de oscilación baja, de hasta 0.2 Hz. La respuesta dinámica de este tipo de estructura puede aumentar como consecuencia de la aproximación entre la frecuencias propias de la misma y las de excitación debidas al paso del tren y a la acción del viento. Por lo tanto, estas estructuras pueden presentar problemas a la hora de cumplir con las limitaciones impuestas en las normas de diseño de puentes de ferrocarril, y otras, para garantizar la seguridad del tráfico y el confort de los viajeros. La respuesta dinámica lateral de viaductos de pilas altas no ha sido suficientemente estudiada en la literatura científica. Se pueden intuir varios de los motivos para explicar esta carencia. El primero es la relativamente reciente aparición de este tipo de viaductos asociados al desarrollo de la alta velocidad. Por otro lado, se hace necesario, para estudiar este tema, construir nuevos modelos numéricos adecuados para el estudio de la interacción dinámica lateral del puente y del tren. La interacción entre el puente y un tren viajando sobre él es un problema dinámico no lineal, dependiente del tiempo y de acoplamiento entre los dos subsistemas que intervienen (vehículo y puente). Los dos subsistemas, que pueden ser modelados como estructuras elásticas, interaccionan el uno con el otro a través de las fuerzas de contacto, que tiene una marcada naturaleza no lineal por el rozamiento entre rueda y carril, y por la geometría de los perfiles de estos dos elementos en contacto. En esta tesis, se desarrolla la formulación completa de un modelo no lineal de interacción tren-vía-puente-viento que reproduce adecuadamente las fuerzas laterales de contacto rueda-carril, fuerzas que van a tener una gran influencia en los índices de seguridad del tráfico. Este modelo se ha validado a partir de casos resueltos en la literatura científica, y de medidas experimentales tomadas en eventos dinámicos ocurridos en los viaductos de Arroyo de Valle y Arroyo de las Piedras. Puentes altos que han estado monitorizados en servicio durante dos años. En los estudios realizados en este trabajo, se cuantifican, empleando el modelo construido, los niveles de seguridad del tráfico y de confort de los pasajeros de trenes ligeros de alta velocidad, como el tren articulado AVE S-100, que viajan sobre viaductos altos sometidos, o no, a fuertes vientos laterales racheados. Finalmente, se ha obtenido el grado de mejora de la seguridad del tráfico y del confort de los viajeros, cuando se emplean pantallas anti-viento en el tablero y amortiguadores de masa sintonizados en la cabeza de las pilas de un viaducto alto. Resultando, el uso simultaneo de estos dos dispositivos (pantallas y amortiguadores de masa), en puentes altos de líneas de alta velocidad, una opción a considerar en la construcción de estas estructuras para elevar significativamente el nivel de servicio de las mismas. It is known that dimensions of railway bridges have been changing due to the strict high-speed lines layout parameters. Moreover, the growing concern of society to take care of and protect the environment, reflected in the corresponding regulations, has created new environment requirements for the design of these infrastructures. Particularly, the mentioned regulations do not allow designers to move far from terrain to build these railway lines. Due to all these reasons, longer and higher railway bridges are being designed and built around the world. In Spain, several high pier railway viaducts have been built for high speed lines. Barbantiño Viaduct and Eixo Viaduct, belonging to the Madrid-Galicia high speed line, are examples of this kind of structures. These high viaducts have great lateral flexibility and a low fundamental vibration frequency of down to 0.2 Hz. The dynamic response of high speed railway bridges may increase because of the approximation between the natural viaduct frequencies and the excitation ones due to the train travel and the wind action. Therefore, this bridge response could not satisfy the serviceability limits states, for traffic safety and for passenger comfort, considered by the design standards of high speed bridges. It is difficult to find papers in the scientific literature about the lateral response of high-speed trains travel over long viaducts with high piers. Several reasons could explain this issue. On one hand, the construction of this kind of viaduct is relatively recent and it is associated to the development of the high speed railway. On the other hand, in order to study the dynamic lateral interaction between the train and the high bridge, it is necessary to build new numerical and complex models. The interaction between the bridge-track subsystem and the vehicle subsystem travelling over the bridge is a coupling, nonlinear and time dependent problem. Both subsystems, train and bridge, which can be modelled as elastic structures, interact each other through the contact forces. These forces have a strong nonlinear nature due to the friction and the geometry of rail and wheel profiles. In this thesis, the full formulation of a train-track-bridge-wind nonlinear interaction model is developed. This model can reproduce properly the lateral contact wheel-rail forces, which have a great influence on traffic safety indices. The validation of the model built has been reached through interaction solved cases found in the scientific literature and experimental measures taken in dynamic events which happened at Arroyo de las Piedras and Arroyo del Valle Viaducts. These high bridges have been controlled during two years of service by means of structural health monitoring. In the studies carried out for this thesis, the levels of traffic safety and passenger comfort are quantified using the interaction model built, in the cases of high speed and light trains, as AVE S-100, travelling over high pier bridges and with or without lateral turbulent winds acting. Finally, the improvement rate of the traffic safety and passenger comfort has been obtained, when wind barriers are used at the bridge deck and tuned mass dampers are installed at the pier heads of a high viaduct. The installation of both devices, wind barriers and tuned mass damper, at the same time, turned out to be a good option to be considered in the design of high pier railway viaducts, to improve significantly the serviceability level of this kind of structures.

New methods for the estimation of Takagi-Sugeno model based extended Kalman filter and its applications to optimal control for nonlinear systems

This paper describes new approaches to improve the local and global approximation (matching) and modeling capability of Takagi–Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy and fast convergence. The main problem encountered is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the application of the T-S method because this type of membership function has been widely used during the last 2 decades in the stability, controller design of fuzzy systems and is popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S identification method with optimized performance in approximating nonlinear functions. We propose a noniterative method through weighting of parameters approach and an iterative algorithm by applying the extended Kalman filter, based on the same idea of parameters’ weighting. We show that the Kalman filter is an effective tool in the identification of T-S fuzzy model. A fuzzy controller based linear quadratic regulator is proposed in order to show the effectiveness of the estimation method developed here in control applications. An illustrative example of an inverted pendulum is chosen to evaluate the robustness and remarkable performance of the proposed method locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity, and generality of the algorithm. An illustrative example is chosen to evaluate the robustness. In this paper, we prove that these algorithms converge very fast, thereby making them very practical to use.

A new approach to fuzzy estimation of Takagi-Sugeno model and its applications to optimal control for nonlinear systems

An efficient approach is presented to improve the local and global approximation and modelling capability of Takagi-Sugeno (T-S) fuzzy model. The main aim is obtaining high function approximation accuracy. The main problem is that T-S identification method cannot be applied when the membership functions are overlapped by pairs. This restricts the use of the T-S method because this type of membership function has been widely used during the last two decades in the stability, controller design and are popular in industrial control applications. The approach developed here can be considered as a generalized version of T-S method with optimized performance in approximating nonlinear functions. A simple approach with few computational effort, based on the well known parameters' weighting method is suggested for tuning T-S parameters to improve the choice of the performance index and minimize it. A global fuzzy controller (FC) based Linear Quadratic Regulator (LQR) is proposed in order to show the effectiveness of the estimation method developed here in control applications. Illustrative examples of an inverted pendulum and Van der Pol system are chosen to evaluate the robustness and remarkable performance of the proposed method and the high accuracy obtained in approximating nonlinear and unstable systems locally and globally in comparison with the original T-S model. Simulation results indicate the potential, simplicity and generality of the algorithm.

Type-I intermittency with discontinuous reinjection probability density in a truncation model of the derivative nonlinear Schrödinger equation

In previous papers, the type-I intermittent phenomenon with continuous reinjection probability density (RPD) has been extensively studied. However, in this paper type-I intermittency considering discontinuous RPD function in one-dimensional maps is analyzed. To carry out the present study the analytic approximation presented by del Río and Elaskar (Int. J. Bifurc. Chaos 20:1185-1191, 2010) and Elaskar et al. (Physica A. 390:2759-2768, 2011) is extended to consider discontinuous RPD functions. The results of this analysis show that the characteristic relation only depends on the position of the lower bound of reinjection (LBR), therefore for the LBR below the tangent point the relation {Mathematical expression}, where {Mathematical expression} is the control parameter, remains robust regardless the form of the RPD, although the average of the laminar phases {Mathematical expression} can change. Finally, the study of discontinuous RPD for type-I intermittency which occurs in a three-wave truncation model for the derivative nonlinear Schrodinger equation is presented. In all tests the theoretical results properly verify the numerical data

Nonlinear analysis of a simple model of temperature evolution in a satellite

We analyze a simple model of the heat transfer to and from a small satellite orbiting round a solar system planet. Our approach considers the satellite isothermal, with external heat input from the environment and from internal energy dissipation, and output to the environment as black-body radiation. The resulting nonlinear ordinary differential equation for the satellite’s temperature is analyzed by qualitative, perturbation and numerical methods, which prove that the temperature approaches a periodic pattern (attracting limit cycle). This approach can occur in two ways, according to the values of the parameters: (i) a slow decay towards the limit cycle over a time longer than the period, or (ii) a fast decay towards the limit cycle over a time shorter than the period. In the first case, an exactly soluble average equation is valid. We discuss the consequences of our model for the thermal stability of satellites.

Column Generation Algorithms for Nonlinear Optimization II: Numerical Investigations

García et al. present a class of column generation (CG) algorithms for nonlinear programs. Its main motivation from a theoretical viewpoint is that under some circumstances, finite convergence can be achieved, in much the same way as for the classic simplicial decomposition method; the main practical motivation is that within the class there are certain nonlinear column generation problems that can accelerate the convergence of a solution approach which generates a sequence of feasible points. This algorithm can, for example, accelerate simplicial decomposition schemes by making the subproblems nonlinear. This paper complements the theoretical study on the asymptotic and finite convergence of these methods given in [1] with an experimental study focused on their computational efficiency. Three types of numerical experiments are conducted. The first group of test problems has been designed to study the parameters involved in these methods. The second group has been designed to investigate the role and the computation of the prolongation of the generated columns to the relative boundary. The last one has been designed to carry out a more complete investigation of the difference in computational efficiency between linear and nonlinear column generation approaches. In order to carry out this investigation, we consider two types of test problems: the first one is the nonlinear, capacitated single-commodity network flow problem of which several large-scale instances with varied degrees of nonlinearity and total capacity are constructed and investigated, and the second one is a combined traffic assignment model