Milk production during the colostral period is not related to the later lactational performance in dairy cows

In dairy cows, milk yield increases rapidly after parturition until a peak at around wk 6 of lactation. However, the description of the shape of the lactation curve is commonly based on weekly average milk yields. For a more detailed analysis of the milk production curve from the very beginning of lactation including the colostral period and the effect of colostrum yield on further lactational performance, the first 10 milkings after parturition, daily milk yields from d 1 to 28 of lactation, and the cumulative milk production on d 100 to 305 of lactation were investigated in 17 primiparous and 39 multiparous cows milked twice daily. Milk yield at the first milking after parturition (colostrum) ranged from 1.3 to 20.7kg (Δ=19.4kg) in multiparous and from 1.8 to 10.9kg in primiparous animals (Δ=9.1kg). At the tenth milking, milk production ranged from 9.2 to 21.5kg (Δ=12.3kg) in multiparous and from 7.0 to 15.2kg (Δ=8.2kg) in primiparous animals. Immediately after parturition, daily milk production increased rapidly, but after approximately 1wk in lactation, the slope of the daily milk production curve flattened and continued more linear. A nonlinear regression equation was used to determine this timely change, which occurred earlier in primiparous (d 6.9±0.3) than in multiparous cows (d 8.2±0.2). The correlation between the amount of first colostrum and milk production during further lactation decreased already from 0.47 on d 5 to 0.32 on d 14. In multiparous cows, the correlation between total milk production of the previous 305d standard lactation and the amount of first colostrum was not significant (correlation=0.29), whereas the correlation with the daily production increased from 0.45 on d 5 to 0.69 on d 14. However, in primiparous animals, correlations between first-colostrum yield and daily milk yields up to d 28 of lactation were not significant, possibly due to the smaller sample size compared with multiparous animals. First-colostrum yield and cumulative milk production of 100, 200, and 305 lactation days were not significantly correlated in multiparous and primiparous cows. In conclusion, the milk production during the first few milkings is widely independent from the overall production level of a cow. Potentially, genetic selection toward lower milk yield during the very first days after parturition at a simultaneously high lactational performance may be a tool to ensure sufficient colostrum quality and to reduce the metabolic load around parturition.

Conformación de Superficies Reflectoras de Sistemas Dobles de Tipo Offset con Alimentadores descritos en Campo Próximo

This work discusses an iterative procedure of shaping offset dual-reflector antennas based on geometrical optics considering both far-field and near-field measurements of amplitude and phase from the feed horn. The surfaces synthesized will transform a known radiation field of a feed to a desired aperture distribution. This technique is applied for both circular and elliptical apertures and has the advantage to simplify the problem compared with existing techniques based on solving nonlinear differential equations. A MATLAB tool has been developed to implement the shaping algorithms. This procedure is applied for the design of a 1.1 m high-gain antenna for the ESA’s Solar Orbiter spacecraft. This antenna operating at X-band will manage high data rate and high efficiency communications with Earth stations.

Estudio y desarrollo de un preproceso basado en la difusión no lineal para la segmentación en imágenes

En esta Tesis Doctoral se aborda la utilización de filtros de difusión no lineal para obtener imágenes constantes a trozos como paso previo al proceso de segmentación. En una primera parte se propone un formulación intrínseca para la ecuación de difusión no lineal que proporcione las condiciones de diseño necesarias sobre los filtros de difusión. A partir del marco teórico propuesto, se proporciona una nueva familia de difusividades; éstas son obtenidas a partir de técnicas de difusión no lineal relacionadas con los procesos de difusión regresivos. El objetivo es descomponer la imagen en regiones cerradas que sean homogéneas en sus niveles de grises sin contornos difusos. Asimismo, se prueba que la función de difusividad propuesta satisface las condiciones de un correcto planteamiento semi-discreto. Esto muestra que mediante el esquema semi-implícito habitualmente utilizado, realmente se hace un proceso de difusión no lineal directa, en lugar de difusión inversa, conectando con proceso de preservación de bordes. Bajo estas condiciones establecidas, se plantea un criterio de parada para el proceso de difusión, para obtener imágenes constantes a trozos con un bajo coste computacional. Una vez aplicado todo el proceso al caso unidimensional, se extienden los resultados teóricos, al caso de imágenes en 2D y 3D. Para el caso en 3D, se detalla el esquema numérico para el problema evolutivo no lineal, con condiciones de contorno Neumann homogéneas. Finalmente, se prueba el filtro propuesto para imágenes reales en 2D y 3D y se ilustran los resultados de la difusividad propuesta como método para obtener imágenes constantes a trozos. En el caso de imágenes 3D, se aborda la problemática del proceso previo a la segmentación del hígado, mediante imágenes reales provenientes de Tomografías Axiales Computarizadas (TAC). En ese caso, se obtienen resultados sobre la estimación de los parámetros de la función de difusividad propuesta. This Ph.D. Thesis deals with the case of using nonlinear diffusion filters to obtain piecewise constant images as a previous process for segmentation techniques. I have first shown an intrinsic formulation for the nonlinear diffusion equation to provide some design conditions on the diffusion filters. According to this theoretical framework, I have proposed a new family of diffusivities; they are obtained from nonlinear diffusion techniques and are related with backward diffusion. Their goal is to split the image in closed contours with a homogenized grey intensity inside and with no blurred edges. It has also proved that the proposed filters satisfy the well-posedness semi-discrete and full discrete scale-space requirements. This shows that by using semi-implicit schemes, a forward nonlinear diffusion equation is solved, instead of a backward nonlinear diffusion equation, connecting with an edgepreserving process. Under the conditions established for the diffusivity and using a stopping criterion I for the diffusion time, I have obtained piecewise constant images with a low computational effort. The whole process in the one-dimensional case is extended to the case where 2D and 3D theoretical results are applied to real images. For 3D, develops in detail the numerical scheme for nonlinear evolutionary problem with homogeneous Neumann boundary conditions. Finally, I have tested the proposed filter with real images for 2D and 3D and I have illustrated the effects of the proposed diffusivity function as a method to get piecewise constant images. For 3D I have developed a preprocess for liver segmentation with real images from CT (Computerized Tomography). In this case, I have obtained results on the estimation of the parameters of the given diffusivity function.

Numerical Error Prediction and its applications in CFD using tau-estimation

Nowadays, Computational Fluid Dynamics (CFD) solvers are widely used within the industry to model fluid flow phenomenons. Several fluid flow model equations have been employed in the last decades to simulate and predict forces acting, for example, on different aircraft configurations. Computational time and accuracy are strongly dependent on the fluid flow model equation and the spatial dimension of the problem considered. While simple models based on perfect flows, like panel methods or potential flow models can be very fast to solve, they usually suffer from a poor accuracy in order to simulate real flows (transonic, viscous). On the other hand, more complex models such as the full Navier- Stokes equations provide high fidelity predictions but at a much higher computational cost. Thus, a good compromise between accuracy and computational time has to be fixed for engineering applications. A discretisation technique widely used within the industry is the so-called Finite Volume approach on unstructured meshes. This technique spatially discretises the flow motion equations onto a set of elements which form a mesh, a discrete representation of the continuous domain. Using this approach, for a given flow model equation, the accuracy and computational time mainly depend on the distribution of nodes forming the mesh. Therefore, a good compromise between accuracy and computational time might be obtained by carefully defining the mesh. However, defining an optimal mesh for complex flows and geometries requires a very high level expertize in fluid mechanics and numerical analysis, and in most cases a simple guess of regions of the computational domain which might affect the most the accuracy is impossible. Thus, it is desirable to have an automatized remeshing tool, which is more flexible with unstructured meshes than its structured counterpart. However, adaptive methods currently in use still have an opened question: how to efficiently drive the adaptation ? Pioneering sensors based on flow features generally suffer from a lack of reliability, so in the last decade more effort has been made in developing numerical error-based sensors, like for instance the adjoint-based adaptation sensors. While very efficient at adapting meshes for a given functional output, the latter method is very expensive as it requires to solve a dual set of equations and computes the sensor on an embedded mesh. Therefore, it would be desirable to develop a more affordable numerical error estimation method. The current work aims at estimating the truncation error, which arises when discretising a partial differential equation. These are the higher order terms neglected in the construction of the numerical scheme. The truncation error provides very useful information as it is strongly related to the flow model equation and its discretisation. On one hand, it is a very reliable measure of the quality of the mesh, therefore very useful in order to drive a mesh adaptation procedure. On the other hand, it is strongly linked to the flow model equation, so that a careful estimation actually gives information on how well a given equation is solved, which may be useful in the context of _ -extrapolation or zonal modelling. The following work is organized as follows: Chap. 1 contains a short review of mesh adaptation techniques as well as numerical error prediction. In the first section, Sec. 1.1, the basic refinement strategies are reviewed and the main contribution to structured and unstructured mesh adaptation are presented. Sec. 1.2 introduces the definitions of errors encountered when solving Computational Fluid Dynamics problems and reviews the most common approaches to predict them. Chap. 2 is devoted to the mathematical formulation of truncation error estimation in the context of finite volume methodology, as well as a complete verification procedure. Several features are studied, such as the influence of grid non-uniformities, non-linearity, boundary conditions and non-converged numerical solutions. This verification part has been submitted and accepted for publication in the Journal of Computational Physics. Chap. 3 presents a mesh adaptation algorithm based on truncation error estimates and compares the results to a feature-based and an adjoint-based sensor (in collaboration with Jorge Ponsín, INTA). Two- and three-dimensional cases relevant for validation in the aeronautical industry are considered. This part has been submitted and accepted in the AIAA Journal. An extension to Reynolds Averaged Navier- Stokes equations is also included, where _ -estimation-based mesh adaptation and _ -extrapolation are applied to viscous wing profiles. The latter has been submitted in the Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering. Keywords: mesh adaptation, numerical error prediction, finite volume Hoy en día, la Dinámica de Fluidos Computacional (CFD) es ampliamente utilizada dentro de la industria para obtener información sobre fenómenos fluidos. La Dinámica de Fluidos Computacional considera distintas modelizaciones de las ecuaciones fluidas (Potencial, Euler, Navier-Stokes, etc) para simular y predecir las fuerzas que actúan, por ejemplo, sobre una configuración de aeronave. El tiempo de cálculo y la precisión en la solución depende en gran medida de los modelos utilizados, así como de la dimensión espacial del problema considerado. Mientras que modelos simples basados en flujos perfectos, como modelos de flujos potenciales, se pueden resolver rápidamente, por lo general aducen de una baja precisión a la hora de simular flujos reales (viscosos, transónicos, etc). Por otro lado, modelos más complejos tales como el conjunto de ecuaciones de Navier-Stokes proporcionan predicciones de alta fidelidad, a expensas de un coste computacional mucho más elevado. Por lo tanto, en términos de aplicaciones de ingeniería se debe fijar un buen compromiso entre precisión y tiempo de cálculo. Una técnica de discretización ampliamente utilizada en la industria es el método de los Volúmenes Finitos en mallas no estructuradas. Esta técnica discretiza espacialmente las ecuaciones del movimiento del flujo sobre un conjunto de elementos que forman una malla, una representación discreta del dominio continuo. Utilizando este enfoque, para una ecuación de flujo dado, la precisión y el tiempo computacional dependen principalmente de la distribución de los nodos que forman la malla. Por consiguiente, un buen compromiso entre precisión y tiempo de cálculo se podría obtener definiendo cuidadosamente la malla, concentrando sus elementos en aquellas zonas donde sea estrictamente necesario. Sin embargo, la definición de una malla óptima para corrientes y geometrías complejas requiere un nivel muy alto de experiencia en la mecánica de fluidos y el análisis numérico, así como un conocimiento previo de la solución. Aspecto que en la mayoría de los casos no está disponible. Por tanto, es deseable tener una herramienta que permita adaptar los elementos de malla de forma automática, acorde a la solución fluida (remallado). Esta herramienta es generalmente más flexible en mallas no estructuradas que con su homóloga estructurada. No obstante, los métodos de adaptación actualmente en uso todavía dejan una pregunta abierta: cómo conducir de manera eficiente la adaptación. Sensores pioneros basados en las características del flujo en general, adolecen de una falta de fiabilidad, por lo que en la última década se han realizado grandes esfuerzos en el desarrollo numérico de sensores basados en el error, como por ejemplo los sensores basados en el adjunto. A pesar de ser muy eficientes en la adaptación de mallas para un determinado funcional, este último método resulta muy costoso, pues requiere resolver un doble conjunto de ecuaciones: la solución y su adjunta. Por tanto, es deseable desarrollar un método numérico de estimación de error más asequible. El presente trabajo tiene como objetivo estimar el error local de truncación, que aparece cuando se discretiza una ecuación en derivadas parciales. Estos son los términos de orden superior olvidados en la construcción del esquema numérico. El error de truncación proporciona una información muy útil sobre la solución: es una medida muy fiable de la calidad de la malla, obteniendo información que permite llevar a cabo un procedimiento de adaptación de malla. Está fuertemente relacionado al modelo matemático fluido, de modo que una estimación precisa garantiza la idoneidad de dicho modelo en un campo fluido, lo que puede ser útil en el contexto de modelado zonal. Por último, permite mejorar la precisión de la solución resolviendo un nuevo sistema donde el error local actúa como término fuente (_ -extrapolación). El presenta trabajo se organiza de la siguiente manera: Cap. 1 contiene una breve reseña de las técnicas de adaptación de malla, así como de los métodos de predicción de los errores numéricos. En la primera sección, Sec. 1.1, se examinan las estrategias básicas de refinamiento y se presenta la principal contribución a la adaptación de malla estructurada y no estructurada. Sec 1.2 introduce las definiciones de los errores encontrados en la resolución de problemas de Dinámica Computacional de Fluidos y se examinan los enfoques más comunes para predecirlos. Cap. 2 está dedicado a la formulación matemática de la estimación del error de truncación en el contexto de la metodología de Volúmenes Finitos, así como a un procedimiento de verificación completo. Se estudian varias características que influyen en su estimación: la influencia de la falta de uniformidad de la malla, el efecto de las no linealidades del modelo matemático, diferentes condiciones de contorno y soluciones numéricas no convergidas. Esta parte de verificación ha sido presentada y aceptada para su publicación en el Journal of Computational Physics. Cap. 3 presenta un algoritmo de adaptación de malla basado en la estimación del error de truncación y compara los resultados con sensores de featured-based y adjointbased (en colaboración con Jorge Ponsín del INTA). Se consideran casos en dos y tres dimensiones, relevantes para la validación en la industria aeronáutica. Este trabajo ha sido presentado y aceptado en el AIAA Journal. También se incluye una extensión de estos métodos a las ecuaciones RANS (Reynolds Average Navier- Stokes), en donde adaptación de malla basada en _ y _ -extrapolación son aplicados a perfiles con viscosidad de alas. Este último trabajo se ha presentado en los Actas de la Institución de Ingenieros Mecánicos, Parte G: Journal of Aerospace Engineering. Palabras clave: adaptación de malla, predicción del error numérico, volúmenes finitos

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

Mathematical analysis of a model of chemotaxis arising from morphogenesis

We consider non-negative solution of a chemotaxis system with non constant chemotaxis sensitivity function X. This system appears as a limit case of a model formorphogenesis proposed by Bollenbach et al. (Phys. Rev. E. 75, 2007).Under suitable boundary conditions, modeling the presence of a morphogen source at x=0, we prove the existence of a global and bounded weak solution using an approximation by problems where diffusion is introduced in the ordinary differential equation. Moreover,we prove the convergence of the solution to the unique steady state provided that ? is small and ? is large enough. Numerical simulations both illustrate these results and give rise to further conjectures on the solution behavior that go beyond the rigorously proved statements.

On a mathematical model arising in MHD perturbed equilibrium for Stellarator devices. A numerical approach.

Abstract?We consider a mathematical model related to the stationary regime of a plasma of fusion nuclear, magnetically confined in a Stellarator device. Using the geometric properties of the fusion device, a suitable system of coordinates and averaging methods, the mathematical problem may be reduced to a two dimensional free boundary problem of nonlocal type, where the corresponding differential equation is of the Grad?Shafranov type. The current balance within each flux magnetic gives us the possibility to define the third covariant magnetic field component with respect to the averaged poloidal flux function. We present here some numerical experiences and we give some numerical approach for the averaged poloidal flux and for the third covariant magnetic field component.

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.

Linear Approach to the Orbiting Spacecraft Thermal Problem

A linear method is developed for solving the nonlinear differential equations of a lumped-parameter thermal model of a spacecraft moving in a closed orbit. This method, based on perturbation theory, is compared with heuristic linearizations of the same equations. The essential feature of the linear approach is that it provides a decomposition in thermal modes, like the decomposition of mechanical vibrations in normal modes. The stationary periodic solution of the linear equations can be alternately expressed as an explicit integral or as a Fourier series. This method is applied to a minimal thermal model of a satellite with ten isothermal parts (nodes), and the method is compared with direct numerical integration of the nonlinear equations. The computational complexity of this method is briefly studied for general thermal models of orbiting spacecraft, and it is concluded that it is certainly useful for reduced models and conceptual design but it can also be more efficient than the direct integration of the equations for large models. The results of the Fourier series computations for the ten-node satellite model show that the periodic solution at the second perturbative order is sufficiently accurate.

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.

Un método de diferencias finitas generalizadas para simular la actividad eléctrica de un tejido cardiaco

Una evolución del método de diferencias finitas ha sido el desarrollo del método de diferencias finitas generalizadas (MDFG) que se puede aplicar a mallas irregulares o nubes de puntos. En este método se emplea una expansión en serie de Taylor junto con una aproximación por mínimos cuadrados móviles (MCM). De ese modo, las fórmulas explícitas de diferencias para nubes irregulares de puntos se pueden obtener fácilmente usando el método de Cholesky. El MDFG-MCM es un método sin malla que emplea únicamente puntos. Una contribución de esta Tesis es la aplicación del MDFG-MCM al caso de la modelización de problemas anisótropos elípticos de conductividad eléctrica incluyendo el caso de tejidos reales cuando la dirección de las fibras no es fija, sino que varía a lo largo del tejido. En esta Tesis también se muestra la extensión del método de diferencias finitas generalizadas a la solución explícita de ecuaciones parabólicas anisótropas. El método explícito incluye la formulación de un límite de estabilidad para el caso de nubes irregulares de nodos que es fácilmente calculable. Además se presenta una nueva solución analítica para una ecuación parabólica anisótropa y el MDFG-MCM explícito se aplica al caso de problemas parabólicos anisótropos de conductividad eléctrica. La evidente dificultad de realizar mediciones directas en electrocardiología ha motivado un gran interés en la simulación numérica de modelos cardiacos. La contribución más importante de esta Tesis es la aplicación de un esquema explícito con el MDFG-MCM al caso de la modelización monodominio de problemas de conductividad eléctrica. En esta Tesis presentamos un algoritmo altamente eficiente, exacto y condicionalmente estable para resolver el modelo monodominio, que describe la actividad eléctrica del corazón. El modelo consiste en una ecuación en derivadas parciales parabólica anisótropa (EDP) que está acoplada con un sistema de ecuaciones diferenciales ordinarias (EDOs) que describen las reacciones electroquímicas en las células cardiacas. El sistema resultante es difícil de resolver numéricamente debido a su complejidad. Proponemos un método basado en una separación de operadores y un método sin malla para resolver la EDP junto a un método de Runge-Kutta para resolver el sistema de EDOs de la membrana y las corrientes iónicas. ABSTRACT An evolution of the method of finite differences has been the development of generalized finite difference (GFD) method that can be applied to irregular grids or clouds of points. In this method a Taylor series expansion is used together with a moving least squares (MLS) approximation. Then, the explicit difference formulae for irregular clouds of points can be easily obtained using a simple Cholesky method. The MLS-GFD is a mesh-free method using only points. A contribution of this Thesis is the application of the MLS-GFDM to the case of modelling elliptic anisotropic electrical conductivity problems including the case of real tissues when the fiber direction is not fixed, but varies throughout the tissue. In this Thesis the extension of the generalized finite difference method to the explicit solution of parabolic anisotropic equations is also given. The explicit method includes a stability limit formulated for the case of irregular clouds of nodes that can be easily calculated. Also a new analytical solution for homogeneous parabolic anisotropic equation has been presented and an explicit MLS- GFDM has been applied to the case of parabolic anisotropic electrical conductivity problems. The obvious difficulty of performing direct measurements in electrocardiology has motivated wide interest in the numerical simulation of cardiac models. The main contribution of this Thesis is the application of an explicit scheme based in the MLS-GFDM to the case of modelling monodomain electrical conductivity problems using operator splitting including the case of anisotropic real tissues. In this Thesis we present a highly efficient, accurate and conditionally stable algorithm to solve a monodomain model, which describes the electrical activity in the heart. The model consists of a parabolic anisotropic partial differential equation (PDE), which is coupled to systems of ordinary differential equations (ODEs) describing electrochemical reactions in the cardiac cells. The resulting system is challenging to solve numerically, because of its complexity. We propose a method based on operator splitting and a meshless method for solving the PDE together with a Runge-Kutta method for solving the system of ODE’s for the membrane and ionic currents.

Long wave theory for experimental devices with compressed/expanded surfactant monolayers

Surfactant monolayers are of interest in a variety of phenomena, including thin film dynamics and the formation and dynamics of foams. Measurement of surface properties has received a continuous attention and requires good theoretical models to extract the relevant physico- chemical information from experimental data. A common experimental set up consists in a shallow liquid layer whose free surface is slowly com- pressed/expanded in periodic fashion by moving two slightly immersed solid barriers, which varies the free surface area and thus the surfactant concentration. The simplest theory ignores the fluid dynamics in the bulk fluid, assuming spatially uniform surfactant concentration, which requires quite small forcing frequencies and provides reversible dynamics in the compression/expansion cycles. Sometimes, it is not clear whether depar- ture from reversibility is due to non-equilibrium effects or to the ignored fluid dynamics. Here we present a long wave theory that takes the fluid dynamics and the symmetries of the problem into account. In particular, the validity of the spatially-uniform-surfactant-concentration assumption is established and a nonlinear diffusion equation is derived. This allows for calculating spatially nonuniform monolayer dynamics and uncovering the physical mechanisms involved in the surfactant behavior. Also, this analysis can be considered a good means for extracting more relevant information from each experimental run.

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

Some consistent finite element formulations of 1-D beam models: a comparative study

A consistent Finite Element formulation was developed for four classical 1-D beam models. This formulation is based upon the solution of the homogeneous differential equation (or equations) associated with each model. Results such as the shape functions, stiffness matrices and consistent force vectors for the constant section beam were found. Some of these results were compared with the corresponding ones obtained by the standard Finite Element Method (i.e. using polynomial expansions for the field variables). Some of the difficulties reported in the literature concerning some of these models may be avoided by this technique and some numerical sensitivity analysis on this subject are presented.