Analytical properties of horizontal visibility graphs in the Feigenbaum scenario

Time series are proficiently converted into graphs via the horizontal visibility (HV) algorithm, which prompts interest in its capability for capturing the nature of different classes of series in a network context. We have recently shown [B. Luque et al., PLoS ONE 6, 9 (2011)] that dynamical systems can be studied from a novel perspective via the use of this method. Specifically, the period-doubling and band-splitting attractor cascades that characterize unimodal maps transform into families of graphs that turn out to be independent of map nonlinearity or other particulars. Here, we provide an in depth description of the HV treatment of the Feigenbaum scenario, together with analytical derivations that relate to the degree distributions, mean distances, clustering coefficients, etc., associated to the bifurcation cascades and their accumulation points. We describe how the resultant families of graphs can be framed into a renormalization group scheme in which fixed-point graphs reveal their scaling properties. These fixed points are then re-derived from an entropy optimization process defined for the graph sets, confirming a suggested connection between renormalization group and entropy optimization. Finally, we provide analytical and numerical results for the graph entropy and show that it emulates the Lyapunov exponent of the map independently of its sign.

An analytical model for simulating the bond of prestressed concrete during the prestressed force release

A bond analytical model is proposed in this paper. The model is capable of reproducing the bond stress developed between the steel and concrete, in precast prestressed elements, during the entire process of prestressing force release. The bond stress developed in the transmission zone, where the bond stress is not constant, is also obtained. The steel and concrete stresses as well as the slip between both materials can be also estimated by means of the relation established in the model between these parameters and the bond stress. The model is validated with the results of a series of tests, considering different steel indentation depths and concrete covers and it is extended to evaluate the transmission length. This has been checked by comparing the transmission length predicted by the model and one measured experimentally in two series of tests.

Hybrid behavioral-analytical loss model for a high frequency and low load DC/DC buck converter

This work presents a behavioral-analytical hybrid loss model for a buck converter. The model has been designed for a wide operating frequency range up to 4MHz and a low power range (below 20W). It is focused on the switching losses obtained in the power MOSFETs. Main advantages of the model are the fast calculation time (below 8.5 seconds) and a good accuracy, which makes this model suitable for the optimization process of the losses in the design of a converter. It has been validated by simulation and experimentally with one GaN power transistor and three Si MOSFETs. Results show good agreement between measurements and the model

Hierarchical boundary elements

In this paper we show the possibility of applying adaptive procedures as an alternative to the well-known philosophy of standard Boundary Elements. The three characteristic steps of adaptive procedures, i.e. hierarchical shape functions families, indicator criteria, and a posteriori estimation, can be defined in order to govern an automatic refinement and stopping of the solution process. A computer program to treat potential problems, called QUEIMADA, has been developed to show the capabilities of the new idea.

An analytical model for simulating the bond of prestressed concrete during the prestressed force release

A bond analytical model is proposed in this paper. The model is capable of reproducing the bond stress developed between the steel and concrete, in precast prestressed elements, during the entire process of prestressing force release. The bond stress developed in the transmission zone, where the bond stress is not constant, is also obtained. The steel and concrete stresses as well as the slip between both materials can be also estimated by means of the relation established in the model between these parameters and the bond stress. The model is validated with the results of a series of tests, considering different steel indentation depths and concrete covers and it is extended to evaluate the transmission length. This has been checked by comparing the transmission length predicted by the model and one measured experimentally in two series of tests.

New method for analytical photovoltaic parameter extraction

Correct modeling of the equivalent circuits regarding solar cell and panels is today an essential tool for power optimization. However, the parameter extraction of those circuits is still a quite difficult task that normally requires both experimental data and calculation procedures, generally not available to the normal user. This paper presents a new analytical method that easily calculates the equivalent circuit parameters from the data that manufacturers usually provide. The analytical approximation is based on a new methodology, since methods developed until now to obtain the aforementioned equivalent circuit parameters from manufacturer's data have always been numerical or heuristic. Results from the present method are as accurate as the ones resulting from other more complex (numerical) existing methods in terms of calculation process and resources.

Design of a Semi-analytical Method to Describe Plasma-Wall Interactions

Electric probes are objects immersed in the plasma with sharp boundaries which collect of emit charged particles. Consequently, the nearby plasma evolves under abrupt imposed and/or naturally emerging conditions. There could be localized currents, different time scales for plasma species evolution, charge separation and absorbing-emitting walls. The traditional numerical schemes based on differences often transform these disparate boundary conditions into computational singularities. This is the case of models using advection-diffusion differential equations with source-sink terms (also called Fokker-Planck equations). These equations are used in both, fluid and kinetic descriptions, to obtain the distribution functions or the density for each plasma species close to the boundaries. We present a resolution method grounded on an integral advancing scheme by using approximate Green's functions, also called short-time propagators. All the integrals, as a path integration process, are numerically calculated, what states a robust grid-free computational integral method, which is unconditionally stable for any time step. Hence, the sharp boundary conditions, as the current emission from a wall, can be treated during the short-time regime providing solutions that works as if they were known for each time step analytically. The form of the propagator (typically a multivariate Gaussian) is not unique and it can be adjusted during the advancing scheme to preserve the conserved quantities of the problem. The effects of the electric or magnetic fields can be incorporated into the iterative algorithm. The method allows smooth transitions of the evolving solutions even when abrupt discontinuities are present. In this work it is proposed a procedure to incorporate, for the very first time, the boundary conditions in the numerical integral scheme. This numerical scheme is applied to model the plasma bulk interaction with a charge-emitting electrode, dealing with fluid diffusion equations combined with Poisson equation self-consistently. It has been checked the stability of this computational method under any number of iterations, even for advancing in time electrons and ions having different time scales. This work establishes the basis to deal in future work with problems related to plasma thrusters or emissive probes in electromagnetic fields.

La memoria en el proceso creativo de Juan Muñoz = Memory in the creative process of Juan Muñoz

Esta tesis integra un estudio reflexivo sobre la relación de dependencia entre la creación y la memoria a través del análisis de la última obra del escultor Juan Muñoz: Double Bind (Tate Modern, Londres, 2001). Desde esta posición es obligado replantear el análisis de la obra, lo que hace necesario su estudio cubriendo el mayor espectro posible de información accesible más allá de la obra en sí, para aproximarse a la convergencia entre memoria y creación. La perspectiva de análisis propuesta abre camino a nuevas consideraciones so¬bre la relevancia del conocimiento en el desarrollo del proceso creativo. Este análisis no debe tan sólo suponer una aportación al conocimiento del trabajo de Juan Muñoz. Debe también desprenderse de él la innegable participación y necesaria lectura del pasado en el presente. La amnesia de los tiempos pasados impide completar el atlas de imágenes en las que se apoya la creación impidiendo el conocimiento del origen de las fuentes de inspi¬ración y las bases de la creación de una determinada obra. Este hecho limita y distorsiona sus posibles interpretaciones. Pretendo un acercamiento al entendimiento de la forma de mirar y de crear a través del tiempo que es memoria. La memoria tiene un cometido de crucial importancia para la actividad mental y juega un papel fundamental en la conducta y en la creación. La obra es el resultado de la búsqueda de una idea que exprese algo que el creador no puede ex¬presar de otra manera. Es la necesidad de expresar las ideas mediante un lenguaje que se desarrolla en el tiempo y en el espacio, reflejo del ser que responde al pensamiento. Es una forma de experiencia donde subyacen las sendas del pasado y donde se plantea el futuro. Sólo el creador accede a la obra desde dentro, el observador llega a ella desde el exterior y mediante su propia subjetividad. Las obras son formas de experiencia de sus autores, comunicar el mensaje de dicha experiencia supone por tanto interpretar. Persiguiendo la necesidad de saber y entender, pretender explicar el sentido de una cosa implica una apreciación intencionada asociada al entendimiento del intérprete. Las obras son produc¬tos que portan un mensaje y que contienen en su estructura las trazas del tiempo vivido por su creador. Si se quiere adquirir un acercamiento que represente la posición de un autor, será necesario no solo mirar a través de ella, si no introducirse en el contexto de su historia. Mirar hacia atrás, hacia la profundidad del presente para tener conciencia del pensamiento presente y futuro. Recorrer de este modo la instalación Double Bind de Juan Muñoz proporciona una síntesis de sus preocupaciones e intereses a la vez que aporta un conocimiento no necesariamente inmediato, pero relevante y trascendente de la obra, su creador y la historia. ABSTRACT This thesis comprises a reflective study of the dependence relationship between creation and memory through the analysis of the latest work by the sculptor Juan Muñoz: Double Bind (Tate Modern, London, 2001). From this position, it is mandatory to rethink the analysis of the work, making it necessary to cover the widest possible range of information available beyond the work itself, in order to obtain a closer view of the convergence between memory and creation. The proposed analytical approach opens up new considerations on the relevance of knowledge during the development of the creative process. This analysis should not only make a contribution to the knowledge of the work of Juan Muñoz. It should also infer the undeniable involvement and the necessary reading of the past in the present. Amnesia regarding past makes it impossible to complete the atlas of images on which the creation is based, blocking knowledge of the origin of the sources of inspiration and the basis for the creation of a specific work. This fact limits and distorts its possible interpretations. My intention is an approach to how to understand memory as the way of looking and creating over time. Memory has a crucial role to mental activity and plays a key role in behaviour and creation. The work is the result of finding an idea that expresses something that the creator can not express otherwise. It is the need to express ideas by means of a language that develops throughout time and space, a reflection of the being that responds to the thought. It is a way of experience underlying the paths of the past and where the future is set out. Only the creator can access the work from the inside. The observer sees it from the outside and in accordance with his/her own subjectivity. The works form a part of the experience of their authors, thus implying the interpretation of the message of their experience being passed on. The pursuit of knowledge and understanding, and trying to explain the meaning of something implies a deliberate appreciation associated with the understanding of the interpreter. The works are products bearing a message and containing in their structure traces of the time lived by their creator. If one wants to come close to what the author’s posture represents, it will not only be necessary to penetrate it, but also to introduce oneself into the context of its history. Take a look back, towards the depth of the present in order to become aware of present and future thinking. To go across the installation of Double Bind by Juan Muñoz in this way offers a synthesis of his concerns and interests while also providing a not necessarily immediate knowledge, but one which is relevant and important to the work, its creator and history.

Numerical and analytical study of an atherosclerosis inflammatory disease model

We study a reaction–diffusion mathematical model for the evolution of atherosclerosis as an inflammation process by combining analytical tools with computer-intensive numerical calculations. The computational work involved the calculation of more than sixty thousand solutions of the full reaction–diffusion system and lead to the complete characterisation of the ωω-limit for every initial condition. Qualitative properties of the solution are rigorously proved, some of them hinted at by the numerical study