Approximate Analytical Model for the Squeeze-Film Lubrication of the Human Ankle Joint with Synovial Fluid Filtrated by Articular Cartilage

The aim of this article is to propose an analytical approximate squeeze-film lubrication model of the human ankle joint for a quick assessment of the synovial pressure field and the load carrying due to the squeeze motion. The model starts from the theory of boosted lubrication for the human articular joints lubrication (Walker et al., Rheum Dis 27:512–520, 1968; Maroudas, Lubrication and wear in joints. Sector, London, 1969) and takes into account the fluid transport across the articular cartilage using Darcy’s equation to depict the synovial fluid motion through a porous cartilage matrix. The human ankle joint is assumed to be cylindrical enabling motion in the sagittal plane only. The proposed model is based on a modified Reynolds equation; its integration allows to obtain a quick assessment on the synovial pressure field showing a good agreement with those obtained numerically (Hlavacek, J Biomech 33:1415–1422, 2000). The analytical integration allows the closed form description of the synovial fluid film force and the calculation of the unsteady gap thickness.

X-parameters based analytical design of non-linear microwave circuits Application to oscillator design

Resumen El diseño clásico de circuitos de microondas se basa fundamentalmente en el uso de los parámetros s, debido a su capacidad para caracterizar de forma exitosa el comportamiento de cualquier circuito lineal. La relación existente entre los parámetros s con los sistemas de medida actuales y con las herramientas de simulación lineal han facilitado su éxito y su uso extensivo tanto en el diseño como en la caracterización de circuitos y subsistemas de microondas. Sin embargo, a pesar de la gran aceptación de los parámetros s en la comunidad de microondas, el principal inconveniente de esta formulación reside en su limitación para predecir el comportamiento de sistemas no lineales reales. En la actualidad, uno de los principales retos de los diseñadores de microondas es el desarrollo de un contexto análogo que permita integrar tanto el modelado no lineal, como los sistemas de medidas de gran señal y los entornos de simulación no lineal, con el objetivo de extender las capacidades de los parámetros s a regímenes de operación en gran señal y por tanto, obtener una infraestructura que permita tanto la caracterización como el diseño de circuitos no lineales de forma fiable y eficiente. De acuerdo a esta filosofía, en los últimos años se han desarrollado diferentes propuestas como los parámetros X, de Agilent Technologies, o el modelo de Cardiff que tratan de proporcionar esta plataforma común en el ámbito de gran señal. Dentro de este contexto, uno de los objetivos de la presente Tesis es el análisis de la viabilidad del uso de los parámetros X en el diseño y simulación de osciladores para transceptores de microondas. Otro aspecto relevante en el análisis y diseño de circuitos lineales de microondas es la disposición de métodos analíticos sencillos, basados en los parámetros s del transistor, que permitan la obtención directa y rápida de las impedancias de carga y fuente necesarias para cumplir las especificaciones de diseño requeridas en cuanto a ganancia, potencia de salida, eficiencia o adaptación de entrada y salida, así como la determinación analítica de parámetros de diseño clave como el factor de estabilidad o los contornos de ganancia de potencia. Por lo tanto, el desarrollo de una formulación de diseño analítico, basada en los parámetros X y similar a la existente en pequeña señal, permitiría su uso en aplicaciones no lineales y supone un nuevo reto que se va a afrontar en este trabajo. Por tanto, el principal objetivo de la presente Tesis consistiría en la elaboración de una metodología analítica basada en el uso de los parámetros X para el diseño de circuitos no lineales que jugaría un papel similar al que juegan los parámetros s en el diseño de circuitos lineales de microondas. Dichos métodos de diseño analíticos permitirían una mejora significativa en los actuales procedimientos de diseño disponibles en gran señal, así como una reducción considerable en el tiempo de diseño, lo que permitiría la obtención de técnicas mucho más eficientes. Abstract In linear world, classical microwave circuit design relies on the s-parameters due to its capability to successfully characterize the behavior of any linear circuit. Thus the direct use of s-parameters in measurement systems and in linear simulation analysis tools, has facilitated its extensive use and success in the design and characterization of microwave circuits and subsystems. Nevertheless, despite the great success of s-parameters in the microwave community, the main drawback of this formulation is its limitation in the behavior prediction of real non-linear systems. Nowadays, the challenge of microwave designers is the development of an analogue framework that allows to integrate non-linear modeling, large-signal measurement hardware and non-linear simulation environment in order to extend s-parameters capabilities to non-linear regimen and thus, provide the infrastructure for non-linear design and test in a reliable and efficient way. Recently, different attempts with the aim to provide this common platform have been introduced, as the Cardiff approach and the Agilent X-parameters. Hence, this Thesis aims to demonstrate the X-parameter capability to provide this non-linear design and test framework in CAD-based oscillator context. Furthermore, the classical analysis and design of linear microwave transistorbased circuits is based on the development of simple analytical approaches, involving the transistor s-parameters, that are able to quickly provide an analytical solution for the input/output transistor loading conditions as well as analytically determine fundamental parameters as the stability factor, the power gain contours or the input/ output match. Hence, the development of similar analytical design tools that are able to extend s-parameters capabilities in small-signal design to non-linear ap- v plications means a new challenge that is going to be faced in the present work. Therefore, the development of an analytical design framework, based on loadindependent X-parameters, constitutes the core of this Thesis. These analytical nonlinear design approaches would enable to significantly improve current large-signal design processes as well as dramatically decrease the required design time and thus, obtain more efficient approaches.

Experimental and Analytical Study of Masonry Infill Reinforced Concrete Frames Retrofitted with Steel Braces

In the present work a seismic retrofitting technique is proposed for masonry infilled reinforced concrete frames based on the replacement of infill panels by K-bracing with vertical shear link. The performance of this technique is evaluated through experimental tests. A simplified numerical model for structural damage evaluation is also formulated according to the notions and principles of continuum damage mechanics. The proposed model is calibrated with the experimental results. The experimental results have shown an excellent energy dissipation capacity with the proposed technique. Likewise, the numerical predictions with the proposed model are in good agreement with experimental results.

Analytical solution to the one-dimensional non-uniform absorption of solar radiation in uncoated and coated single glass panes

The analytical solution to the one-dimensional absorption–conduction heat transfer problem inside a single glass pane is presented, which correctly takes into account all the relevant physical phenomena: the appearance of multiple reflections, the spectral distribution of solar radiation, the spectral dependence of optical properties, the presence of possible coatings, the non-uniform nature of radiation absorption, and the diffusion of heat by conduction across the glass pane. Additionally to the well established and known direct absorptance αe, the derived solution introduces a new spectral quantity called direct absorptance moment βe, that indicates where in the glass pane is the absorption of radiation actually taking place. The theoretical and numerical comparison of the derived solution with existing approximate thermal models for the absorption–conduction problem reveals that the latter ones work best for low-absorbing uncoated single glass panes, something not necessarily fulfilled by modern glazings.

Analytical evaluation of uncertainty on active antenna arrays

An analytical method for evaluating the uncertainty of the performance of active antenna arrays in the whole spatial spectrum is presented. Since array processing algorithms based on spatial reference are widely used to track moving targets, it is essential to be aware of the impact of the uncertainty sources on the antenna response. Furthermore, the estimation of the direction of arrival (DOA) depends on the array uncertainty. The aim of the uncertainties analysis is to provide an exhaustive characterization of the behavior of the active antenna array associated with its main uncertainty sources. The result of this analysis helps to select the proper calibration technique to be implemented. An illustrative example for a triangular antenna array used for satellite tracking is presented showing the suitability of the proposed method to carry out an efficient characterization of an active antenna array.

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.

Buckling instability of web plastifying dampers: analytical and numerical approach

This paper describes a numerical study on the instability of a brace-type seismic damper based on the out of plane yielding of the web of wide-flange steel sections (Web Plastifying Damper, WPD)The damper is intended to be installed in a framed structure as a standard diagonal brace. Under lateral forces, the damper is subjected to high axial forces, therefore its buckling instability is a matter of concern. Several finite element models representing WPDs with different axial stiffness and various geometries of their components were developed and analyzed taking into account both material and geometrical nonlinearities. The influence of several parameters defining the WPD in the load-displacement curve was examined. Furthermore, a simplified model to predict the buckling load is proposed.

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

Accurate analytical approximation of asteroid deflection with constant tangential thrust

We present analytical formulas to estimate the variation of achieved deflection for an Earth-impacting asteroid following a continuous tangential low-thrust deflection strategy. Relatively simple analytical expressions are obtained with the aid of asymptotic theory and the use of Peláez orbital elements set, an approach that is particularly suitable to the asteroid deflection problem and is not limited to small eccentricities. The accuracy of the proposed formulas is evaluated numerically showing negligible error for both early and late deflection campaigns. The results will be of aid in planning future low-thrust asteroid deflection missions

Analytical Calculation of Stall-inception and Surge Points for an Axial-flow Compresor Rotor

Recently, a theoretical criterion to calculate the stability of an axial-flow compressor rotor has been presented in the scientific literature. This theoretical criterion was used for determining the locus of the stability line over the rotor map and for predicting the post-stall evolution of the constant-speed line of a rotor. The main objective of this paper is to improve the predictions of such a model. To do that, the paper proposes a different characterization of the characteristic azimuthal length and a calculation of the ratio of specific heats based on a polytropic exponent. Thanks to these new values, the model predicts two bifurcation points in the behaviour of the flow: the inception point of the instability and the surge point. Experimental data from a pure axial compressor are used to validate the model showing that the prediction of the flow coefficient at the surge point has an error inferior to 5%. For the rotor studied, the paper provides a quantitative and qualitative description of the inception of the instability and of the mechanism involved in the instable region of the compressor map. The paper also discusses the role of rotor efficiency in the position of the bifurcations and gives a sensitivity analysis of its position. Finally, it presents a discussion about how the model can explain the different behaviours exhibited by the same rotor when the flow coefficient is reduced

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.

Empirical and analytical study of instabilities in hybrid optical bistable systems

As it is well known from the work by Gibbs et al., optical turbulence and periodic oscillations are easily seen in hybrid optical bistable devices when a delay is added to the feedback. Such effects, as it was pointed out by Gibbs, may be used to convert cw laser power into a train of light pulses.

Explicit Expressions for Solar Panel Equivalent Circuit Parameters Based on Analytical Formulation and the Lambert W-Function

Due to the high dependence of photovoltaic energy efficiency on environmental conditions (temperature, irradiation...), it is quite important to perform some analysis focusing on the characteristics of photovoltaic devices in order to optimize energy production, even for small-scale users. The use of equivalent circuits is the preferred option to analyze solar cells/panels performance. However, the aforementioned small-scale users rarely have the equipment or expertise to perform large testing/calculation campaigns, the only information available for them being the manufacturer datasheet. The solution to this problem is the development of new and simple methods to define equivalent circuits able to reproduce the behavior of the panel for any working condition, from a very small amount of information. In the present work a direct and completely explicit method to extract solar cell parameters from the manufacturer datasheet is presented and tested. This method is based on analytical formulation which includes the use of the Lambert W-function to turn the series resistor equation explicit. The presented method is used to analyze commercial solar panel performance (i.e., the current-voltage–I-V–curve) at different levels of irradiation and temperature. The analysis performed is based only on the information included in the manufacturer’s datasheet.

On the analytical approach for modeling photovoltaic systems behavior

The 1-diode/2-resistors electric circuit equivalent to a photovoltaic system is analyzed. The equations at particular points of the I–V curve are studied considering the maximum number of terms. The maximum power point as a boundary condition is given special attention. A new analytical method is developed based on a reduced amount of information, consisting in the normal manufacturer data. Results indicate that this new method is faster than numerical methods and has similar (or better) accuracy than other existing methods, numerical or analytical.