Desarrollo, implementación y análisis de un modelo cinemático local de velocidades para Costa Rica basado en la integración y homogenización de datos de estaciones GNSS continuas

El primer procesamiento estricto realizado con el software científico Bernese y contemplando las más estrictas normas de cálculo recomendadas internacionalmente, permitió obtener un campo puntual de alta exactitud, basado en la integración y estandarización de los datos de una red GPS ubicada en Costa Rica. Este procesamiento contempló un total de 119 semanas de datos diarios, es decir unos 2,3 años, desde enero del año 2009 hasta abril del año 2011, para un total de 30 estaciones GPS, de las cuales 22 están ubicadas en el territorio nacional de Costa Rica y 8 internaciones pertenecientes a la red del Sistema Geocéntrico para las Américas (SIRGAS). Las denominadas soluciones semilibres generaron, semana a semana, una red GPS con una alta exactitud interna definida por medio de los vectores entre las estaciones y las coordenadas finales de la constelación satelital. La evaluación semanal dada por la repetibilidad de las soluciones brindó en promedio errores de 1,7 mm, 1,4 mm y 5,1 mm en las componentes [n e u], confirmando una alta consistencia en estas soluciones. Aunque las soluciones semilibres poseen una alta exactitud interna, las mismas no son utilizables para fines de análisis cinemático, pues carecen de un marco de referencia. En Latinoamérica, la densificación del Marco Internacional Terrestre de Referencia (ITRF), está representado por la red de estaciones de operación continua GNSS de SIRGAS, denominada como SIRGAS-CON. Por medio de las denominadas coordenadas semanales finales de las 8 estaciones consideradas como vínculo, se refirió cada una de las 119 soluciones al marco SIRGAS. La introducción del marco de referencia SIRGAS a las soluciones semilibres produce deformaciones en estas soluciones. Las deformaciones de las soluciones semilibres son producto de las cinemática de cada una de las placas en las que se ubican las estaciones de vínculo. Luego de efectuado el amarre semanal a las coordenadas SIRGAS, se hizo una estimación de los vectores de velocidad de cada una de las estaciones, incluyendo las de amarre, cuyos valores de velocidad se conocen con una alta exactitud. Para la determinación de las velocidades de las estaciones costarricenses, se programó una rutina en ambiente MatLab, basada en una ajuste por mínimos cuadrados. Los valores obtenidos en el marco de este proyecto en comparación con los valores oficiales, brindaron diferencias promedio del orden de los 0,06 cm/a, -0,08 cm/a y -0,10 cm/a respectivamente para las coordenadas [X Y Z]. De esta manera se logró determinar las coordenadas geocéntricas [X Y Z]T y sus variaciones temporales [vX vY vZ]T para el conjunto de 22 estaciones GPS de Costa Rica, dentro del datum IGS05, época de referencia 2010,5. Aunque se logró una alta exactitud en los vectores de coordenadas geocéntricas de las 22 estaciones, para algunas de las estaciones el cálculo de las velocidades no fue representativo debido al relativo corto tiempo (menos de un año) de archivos de datos. Bajo esta premisa, se excluyeron las ocho estaciones ubicadas al sur de país. Esto implicó hacer una estimación del campo local de velocidades con solamente veinte estaciones nacionales más tres estaciones en Panamá y una en Nicaragua. El algoritmo usado fue el denominado Colocación por Mínimos Cuadrados, el cual permite la estimación o interpolación de datos a partir de datos efectivamente conocidos, el cual fue programado mediante una rutina en ambiente MatLab. El campo resultante se estimó con una resolución de 30' X 30' y es altamente constante, con una velocidad resultante promedio de 2,58 cm/a en una dirección de 40,8° en dirección noreste. Este campo fue validado con base en los datos del modelo VEMOS2009, recomendado por SIRGAS. Las diferencias de velocidad promedio para las estaciones usadas como insumo para el cálculo del campo fueron del orden los +0,63 cm/a y +0,22 cm/a para los valores de velocidad en latitud y longitud, lo que supone una buena determinación de los valores de velocidad y de la estimación de la función de covarianza empírica, necesaria para la aplicación del método de colocación. Además, la grilla usada como base para la interpolación brindó diferencias del orden de -0,62 cm/a y -0,12 cm/a para latitud y longitud. Adicionalmente los resultados de este trabajo fueron usados como insumo para hacer una aproximación en la definición del límite del llamado Bloque de Panamá dentro del territorio nacional de Costa Rica. El cálculo de las componentes del Polo de Euler por medio de una rutina programa en ambiente MatLab y aplicado a diferentes combinaciones de puntos no brindó mayores aportes a la definición física de este límite. La estrategia lo que confirmó fue simplemente la diferencia en la dirección de todos los vectores velocidad y no permitió reveló revelar con mayor detalle una ubicación de esta zona dentro del territorio nacional de Costa Rica. ABSTRACT The first strict processing performed with the Bernese scientific software and contemplating the highest standards internationally recommended calculation, yielded a precise field of high accuracy, based on the integration and standardization of data from a GPS network located in Costa Rica. This processing watched a total of 119 weeks of daily data, is about 2.3 years from January 2009 to April 2011, for a total of 30 GPS stations, of which 22 are located in the country of Costa Rica and 8 hospitalizations within the network of Geocentric System for the Americas (SIRGAS). The semi-free solutions generated, every week a GPS network with high internal accuracy defined by vectors between stations and the final coordinates of the satellite constellation. The weekly evaluation given by repeatability of the solutions provided in average errors of 1.7 mm 1.4 mm and 5.1 mm in the components [n e u], confirming a high consistency in these solutions. Although semi-free solutions have a high internal accuracy, they are not used for purposes of kinematic analysis, because they lack a reference frame. In Latin America, the densification of the International Terrestrial Reference Frame (ITRF), is represented by a network of continuously operating GNSS stations SIRGAS, known as SIRGAS-CON. Through weekly final coordinates of the 8 stations considered as a link, described each of the solutions to the frame 119 SIRGAS. The introduction of the frame SIRGAS to semi-free solutions generates deformations. The deformations of the semi-free solutions are products of the kinematics of each of the plates in which link stations are located. After SIRGAS weekly link to SIRGAS frame, an estimate of the velocity vectors of each of the stations was done. The velocity vectors for each SIRGAS stations are known with high accuracy. For this calculation routine in MatLab environment, based on a least squares fit was scheduled. The values obtained compared to the official values, gave average differences of the order of 0.06 cm/yr, -0.08 cm/yr and -0.10 cm/yr respectively for the coordinates [XYZ]. Thus was possible to determine the geocentric coordinates [XYZ]T and its temporal variations [vX vY vZ]T for the set of 22 GPS stations of Costa Rica, within IGS05 datum, reference epoch 2010.5. The high accuracy vector for geocentric coordinates was obtained, however for some stations the velocity vectors was not representative because of the relatively short time (less than one year) of data files. Under this premise, the eight stations located in the south of the country were excluded. This involved an estimate of the local velocity field with only twenty national stations plus three stations in Panama and Nicaragua. The algorithm used was Least Squares Collocation, which allows the estimation and interpolation of data from known data effectively. The algorithm was programmed with MatLab. The resulting field was estimated with a resolution of 30' X 30' and is highly consistent with a resulting average speed of 2.58 cm/y in a direction of 40.8° to the northeast. This field was validated based on the model data VEMOS2009 recommended by SIRGAS. The differences in average velocity for the stations used as input for the calculation of the field were of the order of +0.63 cm/yr, +0.22 cm/yr for the velocity values in latitude and longitude, which is a good determination velocity values and estimating the empirical covariance function necessary for implementing the method of application. Furthermore, the grid used as the basis for interpolation provided differences of about -0.62 cm/yr, -0.12 cm/yr to latitude and longitude. Additionally, the results of this investigation were used as input to an approach in defining the boundary of Panama called block within the country of Costa Rica. The calculation of the components of the Euler pole through a routine program in MatLab and applied to different combinations of points gave no further contributions to the physical definition of this limit. The strategy was simply confirming the difference in the direction of all the velocity vectors and not allowed to reveal more detail revealed a location of this area within the country of Costa Rica.

A non-persistently transmitted-virus induces a pull?push strategy inits aphid vector to optimize transmission and spread

Plant viruses are known to modify the behaviour of their insect vectors, both directly and indirectly,generally adapting to each type of virus?vector relationship in a way that enhances transmissionefficiency. Here, we report results of three different studies showing how a virus transmitted in a non-persistent (NP) manner (Cucumber mosaic virus; CMV, Cucumovirus) can induce changes in its host plant,cucumber (Cucumis sativus cv. Marumba) that modifies the behaviour of its aphid vector (Aphis gossypiiGlover; Hemiptera: Aphididae) in a way that enhances virus transmission and spread non-viruliferousaphids changed their alighting, settling and probing behaviour activities over time when exposed toCMV-infected and mock-inoculated cucumber plants. Aphids exhibited no preference to migrate fromCMV-infected to mock-inoculated plants at short time intervals (1, 10 and 30 min after release), butshowed a clear shift in preference to migrate from CMV-infected to mock-inoculated plants 60 min afterrelease. Our free-choice preference assays showed that A. gossypii alates preferred CMV-infected overmock-inoculated plants at an early stage (30 min), but this behaviour was reverted at a later stage andaphids preferred to settle and reproduce on mock-inoculated plants. The electrical penetration graph(EPG) technique revealed a sharp change in aphid probing behaviour over time when exposed to CMV-infected plants. At the beginning (first 15 min) aphid vectors dramatically increased the number of shortsuperficial probes and intracellular punctures when exposed to CMV-infected plants. At a later stage (sec-ond hour of recording) aphids diminished their feeding on CMV-infected plants as indicated by much lesstime spent in phloem salivation and ingestion (E1 and E2). This particular probing behaviour includingan early increase in the number of short superficial probes and intracellular punctures followed by aphloem feeding deterrence is known to enhance the transmission efficiency of viruses transmitted in aNP manner. We conclude that CMV induces specific changes in a plant host that modify the alighting,settling and probing behaviour of its main vector A. gossypii, leading to optimum transmission and spreadof the virus. Our findings should be considered when modelling the spread of viruses transmitted in a NPmanner.

Efecto de la infección por virus persistentes y no persistentes sobre el comportamiento alimenticio, la preferencia, tasa de aterrizaje y asentamiento y la eficacia biológica de Aphis gossypii Glover

En el complejo de plagas que atacan a los principales cultivos hortícolas protegidos, destacan principalmente los Hemípteros, y dentro de estos los pulgones, dada su importancia como vectores de virus que provocan considerables daños y pérdidas económicas. Debido a que la dispersión de la mayoría de los virus de plantas puede ser eficaz con densidades bajas de vectores y su control es muy complicado al no existir métodos curativos para su control, es necesario generar nuevos conocimientos sobre las interacciones virus-vector con el fin de desarrollar nuevas y eficaces estrategias de control. Por ello, el objetivo general de esta Tesis ha sido conocer el efecto de la infección viral (directo-mediado por la presencia del virus en el vector- e indirecto-mediado por las alteraciones físico-químicas que se originan en la planta como consecuencia de la infección viral-) sobre el comportamiento y eficacia biológica del vector Aphis gossypii Glover y sus posibles repercusiones en la epidemiología de virosis de transmisión no persistente (Cucumber mosaic virus, CMV, Cucumovirus) y persistente (Cucurbit aphid-borne yellows virus, CABYV, Polerovirus). El primer objetivo de esta Tesis Doctoral, se centró en el estudio del efecto indirecto del virus de transmisión no persistente CMV sobre el comportamiento alimenticio y la preferencia del pulgón A. gossypii en el cultivo de pepino. Los ensayos de despegue y aterrizaje mostraron que los pulgones que fueron liberados en las plantas de pepino infectadas con CMV tuvieron una mayor propensión en migrar hacia las plantas no infectadas (60, 120 y 180 minutos después de la liberación) que aquellos que fueron sometidos al tratamiento contrario (planta no infectada hacia planta infectada con CMV). El estudio de preferencia y asentamiento mostró que el vector A. gossypii prefiere asentarse en plantas infectadas con CMV en una etapa temprana de evaluación (30 minutos después de la liberación). Sin embargo, este comportamiento se revirtió en una etapa posterior (4 y 48 horas después de la liberación), donde los pulgones se asentaron más en las plantas no infectadas. A través de la técnica de Gráficos de Penetración Eléctrica (EPG) se observó un efecto indirecto del virus CMV, revelado por un cambio brusco en el comportamiento de prueba del pulgón a lo largo del tiempo, cuando éstos fueron expuestos a las plantas infectadas con CMV. Los primeros 15 minutos de registro EPG mostraron que los pulgones hicieron un número mayor de punciones intracelulares (potencial drops - pds) y pruebas en las plantas infectadas con CMV que en las plantas no infectadas. Por otra parte, la duración de la primera prueba fue más corta y la duración total de las pds por insecto fue mucho más larga en las plantas infectadas con CMV. Se observaron diferencias significativas en el tiempo transcurrido desde el final de la última pd hasta el final de la prueba, siendo ese tiempo más corto para los pulgones que estaban alimentándose en plantas infectadas con CMV. En la segunda hora de registro los pulgones rechazaron las plantas infectadas con CMV como fuente de alimento, permaneciendo menos tiempo en las fases de prueba en floema (fase de salivación – E1 y fase de ingestión del floema – E2). El comportamiento alimenticio observado sobre las plantas infectadas con CMV favorece la adquisición y posterior transmisión de los virus de transmisión no persistente, los cuales son adquiridos e inoculados durante la realización de pruebas intracelulares en las primeras pruebas de corta duración. En el segundo objetivo de la Tesis se evaluó el efecto directo e indirecto del virus de transmisión persistente CABYV en el comportamiento alimenticio y preferencia del pulgón A. gossypii en cultivo de pepino, especie susceptible al virus, y algodón, especie inmune al virus. No se observó un efecto directo del virus relevante en el comportamiento alimenticio del vector, ya que los resultados obtenidos a nivel floemático en plantas de pepino no se observaron en plantas de algodón, inmune al virus CABYV. Esto sugiere que los resultados obtenidos en pepino, pueden deberse a un “posible efecto indirecto” originado por la infección de las plantas susceptibles al virus durante la realización del ensayo, lo que indirectamente puede modificar el comportamiento del pulgón durante la fase de evaluación. Sin embargo, el virus CABYV modificó indirectamente el comportamiento alimenticio de su vector a través de cambios en la planta infectada. Los pulgones tardaron menos tiempo en llegar al floema, realizaron un mayor número de pruebas floemáticas y permanecieron durante más tiempo en actividades floemáticas en plantas infectadas con CABYV. El comportamiento observado sobre las plantas infectadas con CABYV favorece la adquisición de virus persistentes, los cuales son adquiridos durante la alimentación sostenida en floema. El estudio de preferencia y asentamiento de A. gossypii mostró que los pulgones virulíferos prefieren asentarse en plantas no infectadas a corto y largo plazo de evaluación (2, 4 y 48 horas después de la liberación). Los ensayos de despegue y aterrizaje mostraron que los pulgones virulíferos que fueron liberados en las plantas de pepino infectadas con CABYV tuvieron una mayor propensión en migrar hacia las plantas no infectadas (3, 6, 24 y 48 horas después de la liberación) que aquellos que fueron sometidos al tratamiento contrario (planta no infectada hacia planta infectada con CABYV). Sin embargo, los pulgones no virulíferos no mostraron preferencia por plantas de pepino no infectadas o infectadas con CABYV en ninguno de los ensayos (preferencia o despegue) o periodos evaluados (corto y largo plazo). Los resultados indican que el virus CABYV es capaz de modificar indirectamente el comportamiento alimenticio de su vector a través de cambios en la planta infectada, favoreciendo su adquisición por su principal vector, A. gossypii. Una vez que los pulgones tienen capacidad de transmitir el virus (virulíferos) se produce un cambio en su comportamiento prefiriendo asentarse sobre plantas no infectadas optimizándose así la dispersión viral. El tercer objetivo de la Tesis, fue evaluar los efectos directos e indirectos del virus CABYV así como los efectos indirectos del virus CMV en la eficacia biológica del vector A. gossypii. Los resultados obtenidos en los ensayos realizados con el virus persistente CABYV indican que el virus parece no modificar directamente ni indirectamente la eficacia biológica del vector en plantas de pepino o algodón, no observándose diferencias estadísticas en ninguno de los parámetros poblacionales evaluados (tiempo de desarrollo, tasa intrínseca de crecimiento, tiempo generacional medio, tasa media de crecimiento relativo y ninfas totales). En cuanto a los ensayos realizados con el virus no persistente, CMV, los resultados muestran un efecto indirecto del virus sobre la biología del vector. Así resultó que tanto la tasa intrínseca de crecimiento natural (rm) como la tasa media de crecimiento relativo (RGR) fueron más altas para pulgones crecidos sobre plantas infectadas con CMV que sobre plantas no infectadas, favoreciendo la reproducción y crecimiento poblacional del vector sobre plantas infectadas con CMV. Los resultados obtenidos en la presente Tesis, ofrecen un ejemplo de como los virus de plantas pueden manipular directa e indirectamente a su vector, maximizando así su dispersión entre las plantas. Esos nuevos conocimientos generados tienen implicaciones importantes en la transmisión, dispersión y en la epidemiología de los virus y deben ser considerados para diseñar o ajustar los modelos de simulación existentes y patrones de dispersión que describen las epidemias de estos virus. ABSTRACT The main objective of this Thesis has been to understand the effect of the viral infection (direct-mediated by the presence of the virus in the vector and indirect mediated by the chemical and physical changes originated in the plant as a consequence of the viral infection) on the behaviour and biological efficacy of the vector Aphis gossypii Glover and its consequences in the epidemiology of two viral diseases, one with non-persistent transmission (Cucumber mosaic virus, CMV, Cucumovirus) and another with persistent transmission (Cucurbit aphid-borne yellows virus, CABYV, Polerovirus). The first objective of this Thesis was the study of the indirect effect of the nonpersistent virus CMV on the feeding behaviour and preference of the aphid A. gossypii in cucumber plants. The results of the alighting and settling behaviour studies showed that aphids exhibited no preference to migrate from CMV-infected to mock-inoculated plants at short time intervals (1, 10 and 30 min after release), but showed a clear shift in preference to migrate from CMV-infected to mock-inoculated plants 60 min after release. Our free-choice preference assays showed that A. gossypii alates preferred CMV-infected over mockinoculated plants at an early stage (30 min), but this behaviour was reverted at a later stage and aphids preferred to settle and reproduce on mock-inoculated plants. The electrical penetration graph (EPG) technique revealed a sharp change in aphid probing behaviour over time when exposed to CMV-infected plants. At the beginning (first 15 min) aphid vectors dramatically increased the number of short superficial probes and intracellular punctures when exposed to CMV-infected plants. At a later stage (second hour of recording) aphids diminished their feeding on CMV-infected plants as indicated by much less time spent in phloem salivation and ingestion (E1 and E2). This particular probing behaviour including an early increase in the number of short superficial probes and intracellular punctures followed by a phloem feeding deterrence is known to enhance the transmission efficiency of viruses transmitted in a NP manner. We conclude that CMV induces specific changes in a plant host that modify the alighting, settling and probing behaviour of its main vector A. gossypii, leading to optimum transmission and spread of the virus. The second objective of this work was to evaluate the effects that the persistently aphid transmitted Cucurbit aphid-borne yellows virus (CABYV) can induce directly and indirectly on the alighting, settling and probing behaviour activities of the cotton aphid A. gossypii. Only minor direct changes on aphid feeding behaviour was observed due to CABYV when viruliferous aphids fed on mock-inoculated plants. However, the feeding behaviour of non-viruliferous aphids was very different on CABYV-infected than on mockinoculated plants. Non-viruliferous aphids spent longer time feeding from the phloem when plants were infected by CABYV than on mock-inoculated plants, suggesting that CABYV indirectly manipulates aphid feeding behaviour through its shared host plant in order to favour viral acquisition. The vector alighting and settling preference was compared between nonviruliferous and viruliferous aphids. Viruliferous aphids showed a clear preference for mockinoculated over CABYV-infected plants at short and long time, while such behaviour was not observed for non-viruliferous aphids. Overall, our results indicate that CABYV induces changes in its host plant that modifies aphid feeding behaviour in a way that virus acquisition from infected plants is enhanced. Once the aphids become viruliferous they prefer to settle on healthy plants, leading to optimize the transmission and spread of the virus. The third objective was to evaluate the direct and indirect effects of CABYV and indirect effects of the CMV on the A. gossypii fitness. Obtained results for the persistent virus CABYV showed that the virus did not modify the vector fitness in cucumber or cotton plants. None of the evaluated variables was statistically significant (development time (d), intrinsic growth rate (rm), mean relative growth rate (RGR) and total number of nymphs). On the other hand, data obtained for the non-persistent virus (CMV) showed an indirect effect of the virus on the vector fitness. Thus, the rm and RGR were higher for aphids grown on CMV-infected plants compared to aphids grown on mock-inoculated plants. Overall, the obtained results are clear examples of how plant viruses could manipulate directly and indirectly vector behaviour to optimize its own dispersion. These results are important for a better understanding of transmission, dispersion and epidemiology of plant viruses transmitted by vectors. This information could be also considered to design or adjust simulation models and dispersion patterns that describe plant virus epidemics.

Lock-free Parallel Dynamic Programming

We show a method for parallelizing top down dynamic programs in a straightforward way by a careful choice of a lock-free shared hash table implementation and randomization of the order in which the dynamic program computes its subproblems. This generic approach is applied to dynamic programs for knapsack, shortest paths, and RNA structure alignment, as well as to a state-of-the-art solution for minimizing the máximum number of open stacks. Experimental results are provided on three different modern multicore architectures which show that this parallelization is effective and reasonably scalable. In particular, we obtain over 10 times speedup for 32 threads on the open stacks problem.

F2TE3: A Transparent semi-monocoque VIP Envelope

This article examines a new lightweight, slim, high energy efficient, light-transmitting, self-supporting envelope system, providing for seamless, free-form designs for use in architectural projects. The system exploits vacuum insulation panel technology. The research was based on envelope components already existing on the market and patents and prototypes built by independent laboratories, especially components implemented with silica gel insulation, as this is the most effective transparent thermal insulation there is today. The tests run on these materials revealed that there is not one that has all the features required of the new envelope model, although some do have properties that could be exploited to generate this envelope, namely, the vacuum chamber of vacuum insulation panels, the use of monolithic aerogel as insulation in some prototypes, and reinforced polyester barriers. These three design components have been combined and tested to design a new, variable geometry, energy-saving envelope system that also solves many of the problems that other studies ascribe to the use of vacuum insulation panels.

F2TE3: A Transparent semi-monocoque VIP Envelope

This article examines a new lightweight, slim, high energy efficient, light-transmitting, selfsupporting envelope system, providing for seamless, free-form designs for use in architectural projects. The system exploits vacuum insulation panel technology. The research was based on envelope components already existing on the market and patents and prototypes built by independent laboratories, especially components implemented with silica gel insulation, as this is the most effective transparent thermal insulation there is today.

F²TE³: A Transparent semi-monocoque VIP Envelope

This article examines a new lightweight, slim, high energy efficient, light-transmitting, self-supporting envelope system, providing for seamless, free-form designs for use in architectural projects. The system exploits vacuum insulation panel technology. The research was based on envelope components already existing on the market and patents and prototypes built by independent laboratories, especially components implemented with silica gel insulation, as this is the most effective transparent thermal insulation there is today. The tests run on these materials revealed that there is not one that has all the features required of the new envelope model, although some do have properties that could be exploited to generate this envelope, namely, the vacuum chamber of vacuum insulation panels, the use of monolithic aerogel as insulation in some prototypes, and reinforced polyester barriers. These three design components have been combined and tested to design a new, variable geometry, energy-saving envelope system that also solves many of the problems that other studies ascribe to the use of vacuum insulation panels.

Evaluating social choice techniques into intelligent environments by agent based social simulation

The primary hypothesis stated by this paper is that the use of social choice theory in Ambient Intelligence systems can improve significantly users satisfaction when accessing shared resources. A research methodology based on agent based social simulations is employed to support this hypothesis and to evaluate these benefits. The result is a six-fold contribution summarized as follows. Firstly, several considerable differences between this application case and the most prominent social choice application, political elections, have been found and described. Secondly, given these differences, a number of metrics to evaluate different voting systems in this scope have been proposed and formalized. Thirdly, given the presented application and the metrics proposed, the performance of a number of well known electoral systems is compared. Fourthly, as a result of the performance study, a novel voting algorithm capable of obtaining the best balance between the metrics reviewed is introduced. Fifthly, to improve the social welfare in the experiments, the voting methods are combined with cluster analysis techniques. Finally, the article is complemented by a free and open-source tool, VoteSim, which ensures not only the reproducibility of the experimental results presented, but also allows the interested reader to adapt the case study presented to different environments.

On the Use of Matrix-Free Shift-Invert Strategies For Global Flow Instability Analysis

A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrix-free framework. Validations and comparisons to the classical exponential method have been performed in three different cases: (i) stenotic flow, (ii) backward-facing step and (iii) lid-driven swirling flow. Results show that this new approach speeds up the required Krylov subspace iterations and has the capability of converging to specific parts of the global spectrum. It is shown that, although the exponential method remains the method of choice if leading eigenvalues are sought, the performance of the present method could be dramatically improved with the use of a preconditioner. In addition, as opposed to other methods, this strategy can be directly applied to any time-stepper, regardless of the temporal or spatial discretization of the latter.

Design of a Semi-analytical Method to Describe Plasma-Wall Interactions

Electric probes are objects immersed in the plasma with sharp boundaries which collect of emit charged particles. Consequently, the nearby plasma evolves under abrupt imposed and/or naturally emerging conditions. There could be localized currents, different time scales for plasma species evolution, charge separation and absorbing-emitting walls. The traditional numerical schemes based on differences often transform these disparate boundary conditions into computational singularities. This is the case of models using advection-diffusion differential equations with source-sink terms (also called Fokker-Planck equations). These equations are used in both, fluid and kinetic descriptions, to obtain the distribution functions or the density for each plasma species close to the boundaries. We present a resolution method grounded on an integral advancing scheme by using approximate Green's functions, also called short-time propagators. All the integrals, as a path integration process, are numerically calculated, what states a robust grid-free computational integral method, which is unconditionally stable for any time step. Hence, the sharp boundary conditions, as the current emission from a wall, can be treated during the short-time regime providing solutions that works as if they were known for each time step analytically. The form of the propagator (typically a multivariate Gaussian) is not unique and it can be adjusted during the advancing scheme to preserve the conserved quantities of the problem. The effects of the electric or magnetic fields can be incorporated into the iterative algorithm. The method allows smooth transitions of the evolving solutions even when abrupt discontinuities are present. In this work it is proposed a procedure to incorporate, for the very first time, the boundary conditions in the numerical integral scheme. This numerical scheme is applied to model the plasma bulk interaction with a charge-emitting electrode, dealing with fluid diffusion equations combined with Poisson equation self-consistently. It has been checked the stability of this computational method under any number of iterations, even for advancing in time electrons and ions having different time scales. This work establishes the basis to deal in future work with problems related to plasma thrusters or emissive probes in electromagnetic fields.