Mathematical modelling of neural processes within the oculomotor system

It is presented a mathematical model of the oculomotor plant, based on experimental data in cats. The system that generates, from the neuronal processes at the motoneuron, the control signals to the eye muscles that moves the eye. In contrast with previous models, that base the eye movement related motoneuron behavior on a first order linear differential equation, non-linear effects are described: A dependency on the eye angular position of the model parameters.

Procedimiento De Amplificador De Envolvente De Señales Moduladas En RF Para Técnicas EER Y ET

An envelope amplifier for an EER (Envelope Elimination and Restoration) and ET (Envelope Tracking) techniques is shown in this paper. The amplifier is based on a high speed two phases buck converter and employs RF LDMOS technology for the switching stage. A DPWM (Digital Pulse With Modulation) signal is used to control the amplifier by means of a functions generator. Simulations and measurements on a circuit prototype are presented showing a good agreement. Up to 125W output peak power can be delivered over a 5Ω load resistor. About 80% efficiency has been obtained. And at the two tone test, the third order intermodulation products (IP3) remain below 45dBc over a 2MHz bandwidth.

Desarrollo de un modelo para la caracterización termoeconómica de ciclos combinados de turbinas de gas y de vapor en condiciones de carga variable

En la actualidad, el interés por las plantas de potencia de ciclo combinado de gas y vapor ha experimentado un notable aumento debido a su alto rendimiento, bajo coste de generación y rápida construcción. El objetivo fundamental de la tesis es profundizar en el conocimiento de esta tecnología, insuficientemente conocida hasta el momento debido al gran número de grados de libertad que existen en el diseño de este tipo de instalaciones. El estudio se realizó en varias fases. La primera consistió en analizar y estudiar las distintas tecnologías que se pueden emplear en este tipo de centrales, algunas muy recientes o en fase de investigación, como las turbinas de gas de geometría variable, las turbinas de gas refrigeradas con agua o vapor del ciclo de vapor o las calderas de paso único que trabajan con agua en condiciones supercríticas. Posteriormente se elaboraron los modelos matemáticos que permiten la simulación termodinámica de cada uno de los componentes que integran las plantas, tanto en el punto de diseño como a cargas parciales. Al mismo tiempo, se desarrolló una metodología novedosa que permite resolver el sistema de ecuaciones que resulta de la simulación de cualquier configuración posible de ciclo combinado. De esa forma se puede conocer el comportamiento de cualquier planta en cualquier punto de funcionamiento. Por último se desarrolló un modelo de atribución de costes para este tipo de centrales. Con dicho modelo, los estudios se pueden realizar no sólo desde un punto de vista termodinámico sino también termoeconómico, con lo que se pueden encontrar soluciones de compromiso entre rendimiento y coste, asignar costes de producción, determinar curvas de oferta, beneficios económicos de la planta y delimitar el rango de potencias donde la planta es rentable. El programa informático, desarrollado en paralelo con los modelos de simulación, se ha empleado para obtener resultados de forma intensiva. El estudio de los resultados permite profundizar ampliamente en el conocimiento de la tecnología y, así, desarrollar una metodología de diseño de este tipo de plantas bajo un criterio termoeconómico. ABSTRACT The growing energy demand and the need of shrinking costs have led to the design of high efficiency and quick installation power plants. The success of combined cycle gas turbine power plants lies on their high efficiency, low cost and short construction lead time. The main objective of the work is to study in detail this technology, which is not thoroughly known owing to the great number of degrees of freedom that exist in the design of this kind of power plants. The study is divided into three parts. Firstly, the different technologies and components that could be used in any configuration of a combined cycle gas turbine power plant are studied. Some of them could be of recent technology, such as the variable inlet guide vane compressors, the H-technology for gas turbine cooling or the once-through heat recovery steam generators, used with water at supercritical conditions. Secondly, a mathematical model has been developed to simulate at full and part load the components of the power plant. At the same time, a new methodology is proposed in order to solve the equation system resulting for any possible power plant configuration. Therefore, any combined cycle gas turbine could be simulated at any part load condition. Finally a themoeconomic model is proposed. This model allows studying the power plant not only from a thermodynamic point of view but also from a thermoeconomic one. Likewise, it allows determining the generating costs or the cash flow, thus achieving a trade off between efficiency and cost. Likewise, the model calculates the part load range where the power plant is profitable. Once the thermodynamic and thermoeconomic models are developed, they are intensively used in order to gain knowledge in the combined cycle gas turbine technology and, in this way, to propose a methodology aimed at the design of this kind of power plants from a thermoeconomic point of view.

Multi-microphone recordings (EigenMike32) inside a WFS system (Iosono) through Ambisonics techniques using Matlab

El audio multicanal ha avanzado a pasos agigantados en los últimos años, y no solo en las técnicas de reproducción, sino que en las de capitación también. Por eso en este proyecto se encuentran ambas cosas: un array microfónico, EigenMike32 de MH Acoustics, y un sistema de reproducción con tecnología Wave Field Synthesis, instalado Iosono en la Jade Höchscule Oldenburg. Para enlazar estos dos puntos de la cadena de audio se proponen dos tipos distintos de codificación: la reproducción de la toma horizontal del EigenMike32; y el 3er orden de Ambisonics (High Order Ambisonics, HOA), una técnica de codificación basada en Armónicos Esféricos mediante la cual se simula el campo acústico en vez de simular las distintas fuentes. Ambas se desarrollaron en el entorno Matlab y apoyadas por la colección de scripts de Isophonics llamada Spatial Audio Matlab Toolbox. Para probar éstas se llevaron a cabo una serie de test en los que se las comparó con las grabaciones realizadas a la vez con un Dummy Head, a la que se supone el método más aproximado a nuestro modo de escucha. Estas pruebas incluían otras grabaciones hechas con un Doble MS de Schoeps que se explican en el proyecto “Sally”. La forma de realizar éstas fue, una batería de 4 audios repetida 4 veces para cada una de las situaciones garbadas (una conversación, una clase, una calle y un comedor universitario). Los resultados fueron inesperados, ya que la codificación del tercer orden de HOA quedo por debajo de la valoración Buena, posiblemente debido a la introducción de material hecho para un array tridimensional dentro de uno de 2 dimensiones. Por el otro lado, la codificación que consistía en extraer los micrófonos del plano horizontal se mantuvo en el nivel de Buena en todas las situaciones. Se concluye que HOA debe seguir siendo probado con mayores conocimientos sobre Armónicos Esféricos; mientras que el otro codificador, mucho más sencillo, puede ser usado para situaciones sin mucha complejidad en cuanto a espacialidad. In the last years the multichannel audio has increased in leaps and bounds and not only in the playback techniques, but also in the recording ones. That is the reason of both things being in this project: a microphone array, EigenMike32 from MH Acoustics; and a playback system with Wave Field Synthesis technology, installed by Iosono in Jade Höchscule Oldenburg. To link these two points of the audio chain, 2 different kinds of codification are proposed: the reproduction of the EigenMike32´s horizontal take, and the Ambisonics´ third order (High Order Ambisonics, HOA), a codification technique based in Spherical Harmonics through which the acoustic field is simulated instead of the different sound sources. Both have been developed inside Matlab´s environment and supported by the Isophonics´ scripts collection called Spatial Audio Matlab Toolbox. To test these, a serial of tests were made in which they were compared with recordings made at the time by a Dummy Head, which is supposed to be the closest method to our hearing way. These tests included other recording and codifications made by a Double MS (DMS) from Schoeps which are explained in the project named “3D audio rendering through Ambisonics techniques: from multi-microphone recordings (DMS Schoeps) to a WFS system, through Matlab”. The way to perform the tests was, a collection made of 4 audios repeated 4 times for each recorded situation (a chat, a class, a street and college canteen or Mensa). The results were unexpected, because the HOA´s third order stood under the Well valuation, possibly caused by introducing material made for a tridimensional array inside one made only by 2 dimensions. On the other hand, the codification that consisted of extracting the horizontal plane microphones kept the Well valuation in all the situations. It is concluded that HOA should keep being tested with larger knowledge about Spherical Harmonics; while the other coder, quite simpler, can be used for situations without a lot of complexity with regards to spatiality.

Evidence for a disaggregation of the universe.

Combining the kinematical definitions of the two dimensionless parameters, the deceleration q(x) and the Hubble t 0 H(x), we get a differential equation (where x=t/t 0 is the age of the universe relative to its present value t 0). First integration gives the function H(x). The present values of the Hubble parameter H(1) [approximately t 0 H(1)≈1], and the deceleration parameter [approximately q(1)≈−0.5], determine the function H(x). A second integration gives the cosmological scale factor a(x). Differentiation of a(x) gives the speed of expansion of the universe. The evolution of the universe that results from our approach is: an initial extremely fast exponential expansion (inflation), followed by an almost linear expansion (first decelerated, and later accelerated). For the future, at approximately t≈3t 0 there is a final exponential expansion, a second inflation that produces a disaggregation of the universe to infinity. We find the necessary and sufficient conditions for this disaggregation to occur. The precise value of the final age is given only with one parameter: the present value of the deceleration parameter [q(1)≈−0.5]. This emerging picture of the history of the universe represents an important challenge, an opportunity for the immediate research on the Universe. These conclusions have been elaborated without the use of any particular cosmological model of the universe

Adams methods: implementation as predictor-corrector methods

In this paper, Adams explicit and implicit formulas are obtained in a simple way and a relationship between them is established, allowing for their joint implementation as predictor-corrector methods. It is shown the purposefulness, from a didactic point of view, of Excel spreadsheets for calculations and for the orderly presentation of results in the application of Adams methods to solving initial value problems in ordinary differential equations.

Low-dimensional modeling of streaks in a wedge flow boundary layer

This paper is concerned with the low dimensional structure of optimal streaks in a wedge flow boundary layer, which have been recently shown to consist of a unique (up to a constant factor) three-dimensional streamwise evolving mode, known as the most unstable streaky mode. Optimal streaks exhibit a still unexplored/unexploited approximate self-similarity (not associated with the boundary layer self-similarity), namely the streamwise velocity re-scaled with their maximum remains almost independent of both the spanwise wavenumber and the streamwise coordinate; the remaining two velocity components instead do not satisfy this property. The approximate self-similar behavior is analyzed here and exploited to further simplify the description of optimal streaks. In particular, it is shown that streaks can be approximately described in terms of the streamwise evolution of the scalar amplitudes of just three one-dimensional modes, providing the wall normal profiles of the streamwise velocity and two combinations of the cross flow velocity components; the scalar amplitudes obey a singular system of three ordinary differential equations (involving only two degrees of freedom), which approximates well the streamwise evolution of the general streaks.

Single optical surface imaging designs with unconstrained object to image mapping

In this work, novel imaging designs with a single optical surface (either refractive or reflective) are presented. In some of these designs, both object and image shapes are given but mapping from object to image is obtained as a result of the design. In other designs, not only the mapping is obtained in the design process, but also the shape of the object is found. In the examples considered, the image is virtual and located at infinity and is seen from known pupil, which can emulate a human eye. In the first introductory part, 2D designs have been done using three different design methods: a SMS design, a compound Cartesian oval surface, and a differential equation method for the limit case of small pupil. At the point-size pupil limit, it is proven that these three methods coincide. In the second part, previous 2D designs are extended to 3D by rotation and the astigmatism of the image has been studied. As an advanced variation, the differential equation method is used to provide the freedom to control the tangential rays and sagittal rays simultaneously. As a result, designs without astigmatism (at the small pupil limit) on a curved object surface have been obtained. Finally, this anastigmatic differential equation method has been extended to 3D for the general case, in which freeform surfaces are designed.

Hard transition to chaotic dynamics in Alfven wave fronts

The derivative nonlinear Schrodinger DNLS equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model equal dampings of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase, no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic relaxation oscillations that are absent for zero growth rate. This hard transition in phase-space behavior occurs for left-hand LH polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable, with damping less than about unstable wave frequency 2/4 x ion cyclotron frequency. The structural stability of the transition was explored by going into a fully 3-wave model different dampings of daughter waves,four-dimensional flow; both models differ in significant phase-space features but keep common features essential for the transition.

Reduced three-wave model to study the hard transition to chaotic dynamics in Alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear, cubic coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. In a reduced three-wave model (equal damping of daughter waves, three-dimensional flow for two wave amplitudes and one relative phase), no matter how small the growth rate of the unstable wave there exists a parametric domain with the flow exhibiting chaotic dynamics that is absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralelling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable.

Fully 3-wave model to study the hard transition to chaotic dynamics in alfven wave-fronts

The derivative nonlinear Schrödinger (DNLS) equation, describing propagation of circularly polarized Alfven waves of finite amplitude in a cold plasma, is truncated to explore the coherent, weakly nonlinear coupling of three waves near resonance, one wave being linearly unstable and the other waves damped. No matter how small the growth rate of the unstable wave, the four-dimensional flow for the three wave amplitudes and a relative phase, with both resistive damping and linear Landau damping, exhibits chaotic relaxation oscillations that are absent for zero growth-rate. This hard transition in phase-space behavior occurs for left-hand (LH) polarized waves, paralleling the known fact that only LH time-harmonic solutions of the DNLS equation are modulationally unstable. The parameter domain developing chaos is much broader than the corresponding domain in a reduced 3-wave model that assumes equal dampings of the daughter waves

Comparison of particle dispersion obtained with simple stochastic models and les in pipe flow

A hybrid Eulerian-Lagrangian approach is employed to simulate heavy particle dispersion in turbulent pipe flow. The mean flow is provided by the Eulerian simulations developed by mean of JetCode, whereas the fluid fluctuations seen by particles are prescribed by a stochastic differential equation based on normalized Langevin. The statistics of particle velocity are compared to LES data which contain detailed statistics of velocity for particles with diameter equal to 20.4 µm. The model is in good agreement with the LES data for axial mean velocity whereas rms of axial and radial velocities should be adjusted.

On the generative equations of fractal self-similarity in granular media and the related PSD models

The physical appearance of granular media suggests the existence of geometrical scale invariance. The paper discuss how this physico-empirical property can be mathematically encoded leading to different generative models: a smooth one encoded by a differential equation and another encoded by an equation coming from a measure theoretical property.

Simulación numérica computacional de fenómenos dinámicos

En este proyecto se trata la simulación numérica de un fenómeno dinámico, basado en el comportamiento de una onda transmitida a lo largo de una cuerda elástica de un instrumento musical, cuyos extremos se encuentran anclados. El fenómeno físico, se desarrolla utilizando una ecuación en derivadas parciales hiperbólicas con variables espacial y temporal, acompañada por unas condiciones de contorno tipo Dirichlet en los extremos y por más condiciones iniciales que dan comienzo al proceso. Posteriormente se han generado algoritmos para el método numérico empleado (Diferencias finitas centrales y progresivas) y la programación del problema aproximado con su consistencia, estabilidad y convergencia, obteniéndose unos resultados acordes con la solución analítica del problema matemático. La programación y salida de resultados se ha realizado con Visual Studio 8.0. y la programación de objetos con Visual Basic .Net In this project the topic is the numerical simulation of a dynamic phenomenon, based on the behavior of a transmitted wave along an elastic string of a musical instrument, whose ends are anchored. The physical phenomenon is developed using a hyperbolic partial differential equation with spatial and temporal variables, accompanied by a Dirichlet boundary conditions at the ends and more initial conditions that start the process. Subsequently generated algorithms for the numerical method used (central and forward finite differences) and the programming of the approximate problem with consistency, stability and convergence, yielding results in line with the analytical solution of the mathematical problem. Programming and output results has been made with Visual Studio 8.0. and object programming with Visual Basic. Net

On a comparison method to reaction-diffusion systems and its applications to chemotaxis

In this paper we consider a general system of reaction-diffusion equations and introduce a comparison method to obtain qualitative properties of its solutions. The comparison method is applied to study the stability of homogeneous steady states and the asymptotic behavior of the solutions of different systems with a chemotactic term. The theoretical results obtained are slightly modified to be applied to the problems where the systems are coupled in the differentiated terms and / or contain nonlocal terms. We obtain results concerning the global stability of the steady states by comparison with solutions of Ordinary Differential Equations.