Developing discontinuous Galerkin methods for the resolution of the incompressible Navier-Stokes equations

Informe de investigación elaborado a partir de una estancia en el Laboratorio de Diseño Computacional en Aeroespacial en el Massachusetts Institute of Technology (MIT), Estados Unidos, entre noviembre de 2006 y agosto de 2007. La aerodinámica es una rama de la dinámica de fluidos referida al estudio de los movimientos de los líquidos o gases, cuya meta principal es predecir las fuerzas aerodinámicas en un avión o cualquier tipo de vehículo, incluyendo los automóviles. Las ecuaciones de Navier-Stokes representan un estado dinámico del equilibrio de las fuerzas que actúan en cualquier región dada del fluido. Son uno de los sistemas de ecuaciones más útiles porque describen la física de una gran cantidad de fenómenos como corrientes del océano, flujos alrededor de una superficie de sustentación, etc. En el contexto de una tesis doctoral, se está estudiando un flujo viscoso e incompresible, solucionando las ecuaciones de Navier- Stokes incompresibles de una manera eficiente. Durante la estancia en el MIT, se ha utilizado un método de Galerkin discontinuo para solucionar las ecuaciones de Navier-Stokes incompresibles usando, o bien un parámetro de penalti para asegurar la continuidad de los flujos entre elementos, o bien un método de Galerkin discontinuo compacto. Ambos métodos han dado buenos resultados y varios ejemplos numéricos se han simulado para validar el buen comportamiento de los métodos desarrollados. También se han estudiado elementos particulares, los elementos de Raviart y Thomas, que se podrían utilizar en una formulación mixta para obtener un algoritmo eficiente para solucionar problemas numéricos complejos.

A model of the wind direction signature in the Stokes emission vector from the ocean surface at microwave frequencies

This paper presents a model of the Stokes emission vector from the ocean surface. The ocean surface is described as an ensemble of facets with Cox and Munk's (1954) Gram-Charlier slope distribution. The study discusses the impact of different up-wind and cross-wind rms slopes, skewness, peakedness, foam cover models and atmospheric effects on the azimuthal variation of the Stokes vector, as well as the limitations of the model. Simulation results compare favorably, both in mean value and azimuthal dependence, with SSM/I data at 53° incidence angle and with JPL's WINDRAD measurements at incidence angles from 30° to 65°, and at wind speeds from 2.5 to 11 m/s.

Simulación de fluidos inmiscibles con el Particle Finite Element Method (PFEM)

Proyecto de investigación realizado a partir de una estancia en el Centro Internacional de Métodos Computacionales en Ingeniería (CIMEC), Argentina, entre febrero y abril del 2007. La simulación numérica de problemas de mezclas mediante el Particle Finite Element Method (PFEM) es el marco de estudio de una futura tesis doctoral. Éste es un método desarrollado conjuntamente por el CIMEC y el Centre Internacional de Mètodos Numèrics en l'Enginyeria (CIMNE-UPC), basado en la resolución de las ecuaciones de Navier-Stokes en formulación Lagrangiana. El mallador ha sido implementado y desarrollado por Dr. Nestor Calvo, investigador del CIMEC. El desarrollo del módulo de cálculo corresponde al trabajo de tesis de la beneficiaria. La correcta interacción entre ambas partes es fundamental para obtener resultados válidos. En esta memoria se explican los principales aspectos del mallador que fueron modificados (criterios de refinamiento geométrico) y los cambios introducidos en el módulo de cálculo (librería PETSc, algoritmo predictor-corrector) durante la estancia en el CIMEC. Por último, se muestran los resultados obtenidos en un problema de dos fluidos inmiscibles con transferencia de calor.

Caraterización y uso de pantallas de cristal líquido para diferentes aplicaciones

Proyecto de investigación realizado a partir de una estancia en el Departamento de Física de la Universidad Autònoma de Barcelona entre octubre de 2007 y febrero del 2008. La investigación realizada se ha centrado en la caracterización y uso en diferentes aplicaciones de pantallas de cristal líquido por reflexión. Las fluctuaciones temporales de la modulación de estos dispositivos origina una despolarización parcial de la luz transmitida. Por ello para su caracterización se ha utilizado el formalismo de Mueller-Stokes. Se ha desarrollado un montaje experimental para la caracterización y se ha propuesto un modelo para predecir tanto su modulación en maplictud come en fase y polarización. También se ha estudiado la variación del comportamiento en función de la longitud de onda utilizada y del ángulo de incidencia. La respuesta de los sistemas ópticos en cuanto a su profundidad de enfoque y su resolución puede ser modificada mediante filtros de transmisión no uniforme. Hemos estudiado la capacidad de las pantallas de cristal líquido para implementar este tipo de filtros. Se han estudiado los efectos de diferentes tipos de filtros tanto teóricamente como experimentalmente. Se han diseñado sistemas ópticos telescópicos utilizando dos pantallas de cristal líquido. En estos sistemas se puede variar el aumento en tiempo real. Debido a la versatilidad que ofrecen las pantallas de cristal líquido se pueden implementar lentes cilíndricas con lo que se pueden variar los aumentos en cada una de las direcciones, formando así un procesador anamórfico programable. Por último se ha propuesto un procesador óptico de polarización. Las pantallas de cristal líquido cambian el estado de polarización de la luz incidente, lo que da lugar a la posibilidad de modular espacialmente el estado de polarización. Se han estudiado teóricamente y experimentalmente la propagación de estos haces.

Could cell membranes produce acoustic streaming? Making the case for synechococcus self-propulsion

Sir James Lighthill proposed in 1992 that acoustic streaming occurs in the inner ear, as part of the cochlear amplifier mechanism. Here we hypothesize that some of the most ancient organisms use acoustic streaming not only for self-propulsion but also to enhance their nutrient uptake. We focus on a motile strain of Synechococcus, a yanobacteria whose mechanism for self-propulsion is not known. Molecular motors could work like piezoelectric transducers acting on the crystalline structure surrounding the outer cell membrane. Our calculations show that a traveling surface acoustic wave (SAW)could account for the observed velocities. These SAW waves will also produce a non-negligible Stokes layer surrounding the cell: motion within this region being essentially chaotic. Therefore, an AS mechanism would be biologically advantageous, enhancing localized diffusion processes and consequently, chemical reactions. We believe that acoustic streaming, produced by nanometer scale membrane vibrations could be widespread in cell biology. Other possible instances are yeast cells and erythrocytes. Flows generated by acoustic streaming may also be produced by silica coated diatoms along their raphe. We note that microelectromechanical (MEMS) acoustic streaming devices were first introduced in the 1990’s. Nature may have preceded this invention by 2.7 Gyr.

Contact melting of a three-dimensional phase change material on a flat substrate

In this paper a model is developed to describe the three dimensional contact melting process of a cuboid on a heated surface. The mathematical description involves two heat equations (one in the solid and one in the melt), the Navier-Stokes equations for the flow in the melt, a Stefan condition at the phase change interface and a force balance between the weight of the solid and the countering pressure in the melt. In the solid an optimised heat balance integral method is used to approximate the temperature. In the liquid the small aspect ratio allows the Navier-Stokes and heat equations to be simplified considerably so that the liquid pressure may be determined using an igenfunction expansion and finally the problem is reduced to solving three first order ordinary differential equations. Results are presented showing the evolution of the melting process. Further reductions to the system are made to provide simple guidelines concerning the process. Comparison of the solutions with experimental data on the melting of n-octadecane shows excellent agreement.

Solució global per la gestió de dades d'empleat mitjançant J2ME/J2EE.

Aquest treball final de carrera es basa en l'anàlisi, disseny i implementació d'una solució per comunicar un empleat i la seva empresa per tal de gestionar informació i dades de l'empleat com poden ser: la nòmina, el full d'hores, el full de despeses i la consulta i sol·licitud de vacances.

Influence of average size and interface passivation on the spectral emission of Si nanocrystals embedded in SiO2

The correlation between the structural (average size and density) and optoelectronic properties [band gap and photoluminescence (PL)] of Si nanocrystals embedded in SiO2 is among the essential factors in understanding their emission mechanism. This correlation has been difficult to establish in the past due to the lack of reliable methods for measuring the size distribution of nanocrystals from electron microscopy, mainly because of the insufficient contrast between Si and SiO2. With this aim, we have recently developed a successful method for imaging Si nanocrystals in SiO2 matrices. This is done by using high-resolution electron microscopy in conjunction with conventional electron microscopy in dark field conditions. Then, by varying the time of annealing in a large time scale we have been able to track the nucleation, pure growth, and ripening stages of the nanocrystal population. The nucleation and pure growth stages are almost completed after a few minutes of annealing time at 1100°C in N2 and afterward the ensemble undergoes an asymptotic ripening process. In contrast, the PL intensity steadily increases and reaches saturation after 3-4 h of annealing at 1100°C. Forming gas postannealing considerably enhances the PL intensity but only for samples annealed previously in less time than that needed for PL saturation. The effects of forming gas are reversible and do not modify the spectral shape of the PL emission. The PL intensity shows at all times an inverse correlation with the amount of Pb paramagnetic centers at the Si-SiO2 nanocrystal-matrix interfaces, which have been measured by electron spin resonance. Consequently, the Pb centers or other centers associated with them are interfacial nonradiative channels for recombination and the emission yield largely depends on the interface passivation. We have correlated as well the average size of the nanocrystals with their optical band gap and PL emission energy. The band gap and emission energy shift to the blue as the nanocrystal size shrinks, in agreement with models based on quantum confinement. As a main result, we have found that the Stokes shift is independent of the average size of nanocrystals and has a constant value of 0.26±0.03 eV, which is almost twice the energy of the Si¿O vibration. This finding suggests that among the possible channels for radiative recombination, the dominant one for Si nanocrystals embedded in SiO2 is a fundamental transition spatially located at the Si¿SiO2 interface with the assistance of a local Si-O vibration.

Discretized integral hydrodynamics

Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid. In the appropriate limit, these become the usual conservation laws of mass, momentum, and energy. We also discuss the special cases of the Navier-Stokes equations for viscous flow and the Fourier law for thermal conduction in the presence of hydrodynamic fluctuations. By means of a discretization procedure, we show how the integral equations can give rise to the so-called particle dynamics of smoothed particle hydrodynamics and dissipative particle dynamics.

Aportaciones al conocimiento taxonomico de Verbascum blattaria L. y V. virgatum Stok.

Se estudia la variabilidad de los caracteres utilizados tradicionalmente en la taxonomía de los afínes Verbascum blattaria L. y V. virgatum Stokes, sobre la base de materiales procedentes de la Península Ibérica. El estudio comparado de ambas entidades ha comportado la creación de un nuevo taxon: V. virgatum Stokes subsp. dertosense Benedí and Rovira, restringido por ahora a las montañas tarraconenses de los Ports de Beseit (Horta de Sant Joan, Tarragona).

Ras-association domain of sorting nexin 27 is critical for regulating expression of GIRK potassium channels

G protein-gated inwardly rectifying potassium (GIRK) channels play an important role in regulating neuronal excitability. Sorting nexin 27b (SNX27b), which reduces surface expression of GIRK channels through a PDZ domain interaction, contains a putative Ras-association (RA) domain with unknown function. Deleting the RA domain in SNX27b (SNX27b-DRA) prevents the down-regulation of GIRK2c/GIRK3 channels. Similarly, a point mutation (K305A) in the RA domain disrupts regulation of GIRK2c/GIRK3 channels and reduces H-Ras binding in vitro. Finally, the dominant-negative H-Ras (S17N) occludes the SNX27b-dependent decrease in surface expression of GIRK2c/GIRK3 channels. Thus, the presence of a functional RA domain and the interaction with Ras-like G proteins comprise a novel mechanism for modulating SNX27b control of GIRK channel surface expression and cellular excitability.

Synthesis of highly focused fields with circular polarization at any transverse plane

We develop a method for generating focused vector beams with circular polarization at any transverse plane. Based on the Richards-Wolf vector model, we derive analytical expressions to describe the propagation of these set of beams near the focal area. Since the polarization and the amplitude of the input beam are not uniform, an interferometric system capable of generating spatially-variant polarized beams has to be used. In particular, this wavefront is manipulated by means of spatial light modulators displaying computer generated holograms and subsequently focused using a high numerical aperture objective lens. Experimental results using a NA=0.85 system are provided: irradiance and Stokes images of the focused field at different planes near the focal plane are presented and compared with those obtained by numerical simulation.

The Coordinated Radio and Infrared Survey for High-mass Star Formation. II. Source Catalog

The CORNISH project is the highest resolution radio continuum survey of the Galactic plane to date. It is the 5 GHz radio continuum part of a series of multi-wavelength surveys that focus on the northern GLIMPSE region (10° < l < 65°), observed by the Spitzer satellite in the mid-infrared. Observations with the Very Large Array in B and BnA configurations have yielded a 1.''5 resolution Stokes I map with a root mean square noise level better than 0.4 mJy beam 1. Here we describe the data-processing methods and data characteristics, and present a new, uniform catalog of compact radio emission. This includes an implementation of automatic deconvolution that provides much more reliable imaging than standard CLEANing. A rigorous investigation of the noise characteristics and reliability of source detection has been carried out. We show that the survey is optimized to detect emission on size scales up to 14'' and for unresolved sources the catalog is more than 90% complete at a flux density of 3.9 mJy. We have detected 3062 sources above a 7σ detection limit and present their ensemble properties. The catalog is highly reliable away from regions containing poorly sampled extended emission, which comprise less than 2% of the survey area. Imaging problems have been mitigated by down-weighting the shortest spacings and potential artifacts flagged via a rigorous manual inspection with reference to the Spitzer infrared data. We present images of the most common source types found: H II regions, planetary nebulae, and radio galaxies. The CORNISH data and catalog are available online at http://cornish.leeds.ac.uk.

Transient shear banding in time-dependent fluids

We study the dynamics of shear-band formation and evolution using a simple rheological model. The description couples the local structure and viscosity to the applied shear stress. We consider in detail the Couette geometry, where the model is solved iteratively with the Navier-Stokes equation to obtain the time evolution of the local velocity and viscosity fields. It is found that the underlying reason for dynamic effects is the nonhomogeneous shear distribution, which is amplified due to a positive feedback between the flow field and the viscosity response of the shear thinning fluid. This offers a simple explanation for the recent observations of transient shear banding in time-dependent fluids. Extensions to more complicated rheological systems are considered.

Optical Encryption using Photon-Counting Polarimetric Imaging

We present a polarimetric-based optical encoder for image encryption and verification. A system for generating random polarized vector keys based on a Mach-Zehnder configuration combined with translucent liquid crystal displays in each path of the interferometer is developed. Polarization information of the encrypted signal is retrieved by taking advantage of the information provided by the Stokes parameters. Moreover, photon-counting model is used in the encryption process which provides data sparseness and nonlinear transformation to enhance security. An authorized user with access to the polarization keys and the optical design variables can retrieve and validate the photon-counting plain-text. Optical experimental results demonstrate the feasibility of the encryption method.