Evolution and breakup of viscous rotating drops

We study the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity $Omega$ or constant angular momentum L surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. The analysis is carried out by combining asymptotic analysis and full numerical simulation by means of the boundary element method. We pay special attention to the stability/instability of equilibrium shapes and the possible formation of singularities representing a change in the topology of the fluid domain. When the evolution is at constant $Omega$, depending on its value, drops can take the form of a flat film whose thickness goes to zero in finite time or an elongated filament that extends indefinitely. When evolution takes place at constant L and axial symmetry is imposed, thin films surrounded by a toroidal rim can develop, but the film thickness does not vanish in finite time. When axial symmetry is not imposed and L is sufficiently large, drops break axial symmetry and, depending on the value of L, reach an equilibrium configuration with a 2-fold symmetry or break up into several drops with a 2- or 3-fold symmetry. The mechanism of breakup is also described

Numerical simulation of the evolution of viscous rotating drops

In this contribution we simulate numerically the evolution of a viscous fluid drop rotating about a fixed axis at constant angular velocity ? or constant angular momentum L, surrounded by another viscous fluid. The problem is considered in the limit of large Ekman number and small Reynolds number. In the lecture we will describe the numerical method we have used to solve the PDE system that describes the evolution of the drop (3D boundary element method). We will also present the results we have obtained, paying special attention to the stability/instability of the equilibrium shapes.

Efficient methodologies for system matrix modelling in iterative image reconstruction for rotating high-resolution PET

A fully 3D iterative image reconstruction algorithm has been developed for high-resolution PET cameras composed of pixelated scintillator crystal arrays and rotating planar detectors, based on the ordered subsets approach. The associated system matrix is precalculated with Monte Carlo methods that incorporate physical effects not included in analytical models, such as positron range effects and interaction of the incident gammas with the scintillator material. Custom Monte Carlo methodologies have been developed and optimized for modelling of system matrices for fast iterative image reconstruction adapted to specific scanner geometries, without redundant calculations. According to the methodology proposed here, only one-eighth of the voxels within two central transaxial slices need to be modelled in detail. The rest of the system matrix elements can be obtained with the aid of axial symmetries and redundancies, as well as in-plane symmetries within transaxial slices. Sparse matrix techniques for the non-zero system matrix elements are employed, allowing for fast execution of the image reconstruction process. This 3D image reconstruction scheme has been compared in terms of image quality to a 2D fast implementation of the OSEM algorithm combined with Fourier rebinning approaches. This work confirms the superiority of fully 3D OSEM in terms of spatial resolution, contrast recovery and noise reduction as compared to conventional 2D approaches based on rebinning schemes. At the same time it demonstrates that fully 3D methodologies can be efficiently applied to the image reconstruction problem for high-resolution rotational PET cameras by applying accurate pre-calculated system models and taking advantage of the system's symmetries.

Hexagonal patterns in a model for rotating convection

We study a model equation that mimics convection under rotation in a fluid with temperature- dependent properties (non-Boussinesq (NB)), high Prandtl number and idealized boundary conditions. It is based on a model equation proposed by Segel [1965] by adding rotation terms that lead to a Kuppers-Lortz instability [Kuppers & Lortz, 1969] and can develop into oscillating hexagons. We perform a weakly nonlinear analysis to find out explicitly the coefficients in the amplitude equation as functions of the rotation rate. These equations describe hexagons and os- cillating hexagons quite well, and include the Busse?Heikes (BH) model [Busse & Heikes, 1980] as a particular case. The sideband instabilities as well as short wavelength instabilities of such hexagonal patterns are discussed and the threshold for oscillating hexagons is determined.

Defect chaos and bursts: Hexagonal rotating convection and the complex Ginzburg-Landau equation

We employ numerical computations of the full Navier-Stokes equations to investigate non-Boussinesq convection in a rotating system using water as the working fluid. We identify two regimes. For weak non- Boussinesq effects the Hopf bifurcation from steady to oscillating (whirling) hexagons is supercritical and typical states exhibit defect chaos that is systematically described by the cubic complex Ginzburg-Landau equation. For stronger non-Boussinesq effects the Hopf bifurcation becomes subcritical and the oscil- lations exhibit localized chaotic bursting, which is modeled by a quintic complex Ginzburg-Landau equation.

Frozen orbits for scientific missions using rotating tethers

We derive a semi-analytic formulation that permits to study the long-term dynamics of fast-rotating inert tethers around planetary satellites. Since space tethers are extensive bodies they generate non-keplerian gravitational forces which depend solely on their mass geometry and attitude, that can be exploited for controlling science orbits. We conclude that rotating tethers modify the geometry of frozen orbits, allowing for lower eccentricity frozen orbits for a wide range of orbital inclination, where the length of the tether becomes a new parameter that the mission analyst may use to shape frozen orbits to tighter operational constraints.

Conceptual design of the beryllium rotating target for the ESS-Bilbao facility

The ESS-Bilbao facility, hosted by the University of the Basque Country (UPV/EHU), envisages the operation of a high-current proton accelerator delivering beams with energies up to 50 MeV. The time-averaged proton current will be 2.25 mA, delivered by 1.5 ms proton pulses with a repetition rate of 20 Hz. This beam will feed a neutron source based upon the Be (p,n) reaction, which will enable the provision of relevant neutron experimentation capabilities. The neutron source baseline concept consists in a rotating beryllium target cooled by water. The target structure will comprise a rotatable disk made of 6061-T6 aluminium alloy holding 20 beryllium plates. Heat dissipation from the target relies upon a distribution of coolant-flow channels. The practical implementation of such a concept is here described with emphasis put on the beryllium plates thermo-mechanical optimization, the chosen coolant distribution system as well as the mechanical behavior of the assembly.

On the harmonic analysis of cup anemometer rotation speed: A principle to monitor performance and maintenance status of rotating meteorological sensors

The calibration results of one anemometer equipped with several rotors, varying their size, were analyzed. In each case, the 30-pulses pert turn output signal of the anemometer was studied using Fourier series decomposition and correlated with the anemometer factor (i.e., the anemometer transfer function). Also, a 3-cup analytical model was correlated to the data resulting from the wind tunnel measurements. Results indicate good correlation between the post-processed output signal and the working condition of the cup anemometer. This correlation was also reflected in the results from the proposed analytical model. With the present work the possibility of remotely checking cup anemometer status, indicating the presence of anomalies and, therefore, a decrease on the wind sensor reliability is revealed.

Long-term dynamics of fast rotating tethers around planetary satellites

We derive a semi-analytic formulation that enables the study of the long-term dynamics of fast-rotating inert tethers around planetary satellites. These equations take into account the coupling between the translational and rotational motion, which has a non-negligible impact on the dynamics, as the orbital motion of the tether center of mass strongly depends on the tether plane of rotation and its spin rate, and vice-versa. We use these governing equations to explore the effects of this coupling on the dynamics, the lifetime of frozen orbits and the precession of the plane of rotation of the tether.

Stability analysis of a free falling pararotor

The pararotor is a decelerator device based on the autorotation of a rotating wing. When it is dropped, it generates an aerodynamic force parallel to the main motion direction, acting as a decelerating force. In this paper, the rotational motion equations are shown for the vertical flight without any lateral wind component and some simplifying assumptions are introduced to obtain analytic solutions of the motion. First, the equilibrium state is obtained as a function of the main parameters. Then the equilibrium stability is analyzed. The motion stability depends on two nondimensional parameters, which contain geometric, inertia, and aerodynamic characteristics of the device. Based on these two parameters a stability diagram can be defined. Some stability regions with different types of stability trajectories (nodes, spirals, focuses) can be identified for spinning motion around axes close to the major, minor, and intermediate principal axes. It is found that the blades contribute to stability in a case of spin around the intermediate principal inertia axis, which is otherwise unstable. Subsequently, the equations for determining the angles of nutation and spin of the body are obtained, thus defining the orientation of the body for a stationary motion and the parameters on which that position depends.

WCSPH viscosity diffusion processes in vortex flows

The aim of this paper is to clarify the role played by the most commonly used viscous terms in simulating viscous laminar flows using the weakly compressible approach in the context of smooth particle hydrodynamics (WCSPH). To achieve this, Takeda et al. (Prog. Theor. Phys. 1994; 92(5):939–960), Morris et al. (J. Comput. Phys. 1997; 136:214–226) and Monaghan–Cleary–Gingold's (Appl. Math. Model. 1998; 22(12):981–993; Monthly Notices of the Royal Astronomical Society 2005; 365:199–213) viscous terms will be analysed, discussing their origins, structures and conservation properties. Their performance will be monitored with canonical flows of which related viscosity phenomena are well understood, and in which boundary effects are not relevant. Following the validation process of three previously published examples, two vortex flows of engineering importance have been studied. First, an isolated Lamb–Oseen vortex evolution where viscous effects are dominant and second, a pair of co-rotating vortices in which viscous effects are combined with transport phenomena. The corresponding SPH solutions have been compared to finite-element numerical solutions. The SPH viscosity model's behaviour in modelling the viscosity related effects for these canonical flows is adequate

Evaluation of a PET Prototype Using LYSO:Ce Monolithic Detector Block

We have analyzed the performance of a PET demonstrator formed by two sectors of four monolithic detector blocks placed face-to-face. Both front-end and read-out electronics have been evaluated by means of coincidence measurements using a rotating 22Na source placed at the center of the sectors in order to emulate the behavior of a complete full ring. A continuous training method based on neural network (NN) algorithms has been carried out to determine the entrance points over the surface of the detectors. Reconstructed images from 1 MBq 22Na point source and 22Na Derenzo phantom have been obtained using both filtered back projection (FBP) analytic methods and the OSEM 3D iterative algorithm available in the STIR software package [1]. Preliminary data on image reconstruction from a 22Na point source with Ø = 0.25 mm show spatial resolutions from 1.7 to 2.1 mm FWHM in the transverse plane. The results confirm the viability of this design for the development of a full-ring brain PET scanner compatible with magnetic resonance imaging for human studies.

Projector Model for Efficient List-Mode Reconstruction in PET Scanners with Parallel Planar Detectors

We have developed a new projector model specifically tailored for fast list-mode tomographic reconstructions in Positron emission tomography (PET) scanners with parallel planar detectors. The model provides an accurate estimation of the probability distribution of coincidence events defined by pairs of scintillating crystals. This distribution is parameterized with 2D elliptical Gaussian functions defined in planes perpendicular to the main axis of the tube of response (TOR). The parameters of these Gaussian functions have been obtained by fitting Monte Carlo simulations that include positron range, acolinearity of gamma rays, as well as detector attenuation and scatter effects. The proposed model has been applied efficiently to list-mode reconstruction algorithms. Evaluation with Monte Carlo simulations over a rotating high resolution PET scanner indicates that this model allows to obtain better recovery to noise ratio in OSEM (ordered-subsets, expectation-maximization) reconstruction, if compared to list-mode reconstruction with symmetric circular Gaussian TOR model, and histogram-based OSEM with precalculated system matrix using Monte Carlo simulated models and symmetries.

The PSE-3D instability analysis methodology for flows depending strongly on two and weakly on the third spatial dimension

The present contribution discusses the development of a PSE-3D instability analysis algorithm, in which a matrix forming and storing approach is followed. Alternatively to the typically used in stability calculations spectral methods, new stable high-order finitedifference-based numerical schemes for spatial discretization 1 are employed. Attention is paid to the issue of efficiency, which is critical for the success of the overall algorithm. To this end, use is made of a parallelizable sparse matrix linear algebra package which takes advantage of the sparsity offered by the finite-difference scheme and, as expected, is shown to perform substantially more efficiently than when spectral collocation methods are used. The building blocks of the algorithm have been implemented and extensively validated, focusing on classic PSE analysis of instability on the flow-plate boundary layer, temporal and spatial BiGlobal EVP solutions (the latter necessary for the initialization of the PSE-3D), as well as standard PSE in a cylindrical coordinates using the nonparallel Batchelor vortex basic flow model, such that comparisons between PSE and PSE-3D be possible; excellent agreement is shown in all aforementioned comparisons. Finally, the linear PSE-3D instability analysis is applied to a fully three-dimensional flow composed of a counter-rotating pair of nonparallel Batchelor vortices.

El injerto en pepino corto tipo español (Cucumis sativus L.) recomencaciones para su empleo en la zona central española

El injerto en hortalizas es uno de los temas de más actualidad en el panorama hortícola, no solo español, sino occidental, y recalcamos occidental, pues en muchos países que no corresponden a ese ámbito, sobre todo asiáticos: Japón, Corea, China, Filipinas, etc., esta es una técnica que cuenta con una gran difusión desde hace décadas, siendo, por ejemplo en Japón, la mayoría de sus cultivos de cucurbitáceas y solanáceas realizados con planta injertada. A finales de los noventa quedó claro que el empleo de bromuro de metilo tenía una fecha de caducidad y que las zonas que tenían una fuerte dependencia de este desinfectante de suelo debían de buscar alternativas a un plazo lo más corto posible, con un punto añadido sobre etapas anteriores, debían ser alternativas lo más respetuosas posible con el medio ambiente y que no incrementaran, de forma importante, los costes de producción. En la zona centro y concretamente en los invernaderos de la Comunidad de Madrid y zonas cercanas de Toledo y Guadalajara el pepino era y es el cultivo predominante, los horticultores empleaban el bromuro de metilo de forma sistemática para desinfectar sus suelos y la desaparición de este producto les planteaba una gran incertidumbre, lo que llevó a que desde diferentes instancias se buscaran diferentes alternativas. Tras analizar las posibilidades que se podían implementar y conocido el buen resultado que había dado el injerto en sandía en Almería, se decidió acometer los trabajos que conforman esta Tesis Doctoral, planteando en la zona, diferentes ensayos con la idea de conocer, si el injerto en pepino, con los cultivares empleados habitualmente, podía ser una alternativa real para los horticultores, tanto de Madrid, como los de las zonas cercanas de Toledo y Guadalajara. Se pretendía conocer sobre todo las repercusiones agronómicas y si esta técnica podría emplearse en solitario o era necesario complementarla con otras alternativas: desinfectantes químicos, solarización, biofumigación e incluso desinfección con vapor de agua. Los ensayos fueron realizados de forma secuencial entre el año 1999 y el 2011, comprobándose en primer lugar que el empleo de portainjertos híbridos de calabaza era posible con los cultivares de pepino corto tipo español, mayoritariamente empleados en los últimos años del siglo XX y primeros del XXI, fundamentalmente: Serena. Tras los primeros ensayos, Shintoza parecía el portainjerto híbrido de calabaza (Cucurbita maxima x C. moschata) con mejores perspectivas de empleo, pues presentaba la ventaja adicional de ser bien conocido por los semilleros que producen planta injertada al ser, en esos momentos, el portainjerto más empleado en sandía, lo que garantizaba por su lado, su empleo en pepino, y que los horticultores pudiesen disponer de planta injertada. Más adelante los trabajos se encaminaron hacia la determinación de la densidad y tipo de poda más adecuado para la planta injertada, realizándose múltiples ensayos en esta dirección, que culminaron con la conclusión de que el extravigor que los portainjertos conferían a las plantas permitía conducir estas a dos o más brazos (se suelen emplear dos, por mejor adaptación a los trabajos de manejo de la planta por parte de los agricultores), con lo que se podría disminuir la densidad de planta y por tanto ahorrar en este capítulo, cosa que preocupaba y preocupa a los agricultores. Se llegó a determinar que es posible reducir la densidad de plantación en alrededor de un 25%, estando la densidad de brazos más adecuada entre 3 y 3.5 br•m-2. Tras las primeras decisiones tomadas sobre el portainjerto y la densidad más adecuada, se continuó con el estudio de adaptación de estas propuestas a los nuevos cultivares que las empresas de semillas iban proponiendo y los agricultores adoptando. Estas acciones se complementaron con la introducción de nuevos portainjertos susceptibles de sustituir a Shintoza o rotar con él para cambiar de sistema radicular, lo que es conveniente cuando se emplean, como es el caso, portainjertos que no son resistentes a nematodos, principalmente de la especie Meloidogyne incognita, el mayor problema en la zona, debido al suelo. Cultivares como Trópico, en un primer momento, y Urano y Motril más recientemente, se adaptaron muy bien a esta técnica. Entre los portainjertos que mostraron buena adaptación a la técnica de injerto y suficientemente buena compatibilidad con la mayoría de los cultivares ensayados destacan: RS-841, Strongtosa y Camel. Azman también mostró un comportamiento relevante, pero este portainjerto no podrá ser empleado, al ser recientemente retirado del mercado por la empresa que lo obtuvo y comercializó Aunque no era el objetivo principal de esta Tesis Doctoral, se ha comprobado que puede ser interesante combinar el empleo del injerto con otras técnicas alternativas al bromuro de metilo para superar los problemas debidos a enfermedades del suelo o nematodos, pero debe seguirse trabajando pues este es un tema en continua evolución, tanto si se trata de desinfectantes, a la mayoría de los cuales les está siendo retirado el permiso para su comercialización, como de otros métodos como la biofumigación o el empleo de vapor de agua. Queda muy claro que el injerto puede considerarse entre los métodos respetuosos con el medio ambiente, si no el que más, en lo que alternativas al bromuro de metilo se refiere. También en otro momento, se comprobó que con plantas injertadas es posible reducir el aporte de nutrientes, sobre todo nitrógeno, lo que además de un ahorro supone una mejora más desde el punto de vista medioambiental. En definitiva, queda demostrado que es factible el empleo del injerto en pepino corto tipo español, que las selecciones de los híbridos entre Cucurbita maxima y C. moschata que habitualmente se están empleando en sandía son también de aplicación en estos pepinos y que su empleo puede llevarnos a producciones suficientemente remuneradoras, alargándose en muchos casos el ciclo y no modificando, de forma apreciable, la calidad. Queda también demostrado que aunque los portainjertos no sean resistentes a nematodos, su extravigor les hace desarrollarse, desde el punto de vista productivo, suficientemente, llegando por tanto, a “convivir” con ese problema. Al no ser resistentes los portainjertos, y permanecer e incluso agravarse el problema de nematodos es conveniente poder contar con diferentes portainjertos que nos permitan rotar entre ellos y utilizar diferentes sistemas radiculares que harán menos fácil el parasitismo de los nematodos, como recomiendan los nematólogos que se haga. ABSTRACT Vegetable grafting is one of the most current practices in horticulture, not only in Spain, but also in other Western and Asian countries, such as Japan, South Korea, China, the Philippines, etc. This is a decades-old, widespread technique: In fact, most cucurbit and solanaceous crops in Japan and Korea are grafted. At the end of the 1990s, it was clear that methyl bromide had an expiry date. Consequently, the areas strongly dependant on this soil disinfectant had to look for alternatives as quickly as possible. Besides, these had to be as environmentally friendly as possible and should not increase production costs significantly. The cucumber has been and still is the most important crop in greenhouses of the Comunidad de Madrid and in areas near Toledo and Guadalajara. Cucumber growers used methyl bromide systematically to disinfect the soil. The banning of this chemical product brought about uncertainty, which encouraged the search for different alternatives. After analyzing the different possibilities and taking into account the good results of watermelon grafting in Almería, it was decided to carry out the works that make up this doctoral thesis. Different trials were made in order to know if the cultivars used in cucumber grafting might be a real alternative for farmers, not only in Madrid, but also in the areas near Toledo and Guadalajara. The main aim was to assess the agronomic repercussions and whether that technique could be used alone, or if other complementary alternatives, such as chemical disinfectants, solarisation, biofumigation, or even steam disinfection, were necessary. Trials were carried out sequentially from 1999 to 2011. It was observed that the use of pumpkin hybrid rootstocks could be applied to cultivars of Spanish short cucumbers, mainly grown in the late 20th and early 21st centuries eg Serena. After the early trials, Shintoza (Cucurbita maxima x C. moschata), a pumpkin hybrid rootstock, seemed to be the best option, as it had the additional advantage of being well known by nurseries growing grafting plants. Bearing this in mind, Shintoza was then the hybrid rootstock to be used in cucumbers and consequently growers could have grafted plants at their disposal. Later on, research was focused on density and the most adequate type of pruning, by carrying out several trials. These experiments showed that, the extra vigour the rootstocks gave to the plants, allowed them to have two or three stems, (normally nurserymen use two, as it is easier for them to manage the plants). These findings would lead to the lessening the density of the plant and thus reduce costs, something which worried and still worries farmers. It was stated that it would be possible to reduce the density of the plants by about 25%, the optimum density of the stems ranging from 3 to 3.5 stem-m-2. Once decisions were taken both on the rootstock and the appropriate density, we went on to study how to apply these proposals to the new cultivars which the seed companies were proposing and the farmers were applying. These measures were complemented with the introduction of new rootstocks capable of replacing Shintoza, or rotating with it in order to change the root system. This is particularly necessary when rootstocks, non-resistant to nematodes, mainly of the species Meloidogyne incognita, are used. This is the main problem due to the soil of that area. Cultivars such as Trópico, at first, and Urano and Motril, more recently, adapted quite well to this technique. Among the rootstocks which adapted well to grafting and which were compatible with most tested cultivars, were, in particular, RS-841 Strongtosa and Camel. The behaviour of Azman was worth studying, but this rootstock was removed from the market by the company which had bought and commercialized it. Although not the main purpose of the research, it was observed that combining grafting with other alternatives to methyl bromide in order to overcome problems due to soil diseases or nematodes may be worthwhile. However, further research is needed, as this topic is in constant evolution, not only when we come to disinfectants, most of which are being affected by the removal of the permit for commercialization, but also when we refer to other techniques such as biofumigation or the use of steam. Results also showed that grafted plants may reduce the amount of fertilizers, particularly nitrogen, used: This means both saving money and the protection of the environment. We may conclude by saying that grafting Spanish short cucumbers is feasible, that the selections of the hybrids between Cucurbita maxima and C. moschata, habitually used in watermelon grafting, can also be applied to these cucumbers. It can also be concluded that the use of these grafting techniques may lead to profitable yields, by lengthening the growing cycle in many cases and by maintaining the quality to a large extent. Although these rootstocks are not resistant to nematodes, the results showed that their extra vigour enables them to develop in terms of production, and thus they cope with this problem. Since these rootstocks are not resistant to nematodes and the problem with these nematodes may even worsen, it is recommended that different types of rootstocks should be available to enable both the rotation and the use of different root systems, which will encourage the parasitism of nematodes.