A parallel implementation of 3D Zernike moment analysis

Zernike polynomials are a well known set of functions that find many applications in image or pattern characterization because they allow to construct shape descriptors that are invariant against translations, rotations or scale changes. The concepts behind them can be extended to higher dimension spaces, making them also fit to describe volumetric data. They have been less used than their properties might suggest due to their high computational cost. We present a parallel implementation of 3D Zernike moments analysis, written in C with CUDA extensions, which makes it practical to employ Zernike descriptors in interactive applications, yielding a performance of several frames per second in voxel datasets about 2003 in size. In our contribution, we describe the challenges of implementing 3D Zernike analysis in a general-purpose GPU. These include how to deal with numerical inaccuracies, due to the high precision demands of the algorithm, or how to deal with the high volume of input data so that it does not become a bottleneck for the system.

Bernstein polynomials in element-free Galerkin method

In the recent decades, meshless methods (MMs), like the element-free Galerkin method (EFGM), have been widely studied and interesting results have been reached when solving partial differential equations. However, such solutions show a problem around boundary conditions, where the accuracy is not adequately achieved. This is caused by the use of moving least squares or residual kernel particle method methods to obtain the shape functions needed in MM, since such methods are good enough in the inner of the integration domains, but not so accurate in boundaries. This way, Bernstein curves, which are a partition of unity themselves,can solve this problem with the same accuracy in the inner area of the domain and at their boundaries.

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.

Perfect imaging of three object points with only two analytic lens surfaces in two dimensions

In this work, a new two-dimensional analytic optics design method is presented that enables the coupling of three ray sets with two lens profiles. This method is particularly promising for optical systems designed for wide field of view and with clearly separated optical surfaces. However, this coupling can only be achieved if different ray sets will use different portions of the second lens profile. Based on a very basic example of a single thick lens, the Simultaneous Multiple Surfaces design method in two dimensions (SMS2D) will help to provide a better understanding of the practical implications on the design process by an increased lens thickness and a wider field of view. Fermat?s principle is used to deduce a set of functional differential equations fully describing the entire optical system. The transformation of these functional differential equations into an algebraic linear system of equations allows the successive calculation of the Taylor series coefficients up to an arbitrary order. The evaluation of the solution space reveals the wide range of possible lens configurations covered by this analytic design method. Ray tracing analysis for calculated 20th order Taylor polynomials demonstrate excellent performance and the versatility of this new analytical optics design concept.

Simplified Finite Element Assessment of Beams With and Without Shear Deformation

This paper presents a simplified finite element (FE) methodology for solving accurately beam models with (Timoshenko) and without (Bernoulli-Euler) shear deformation. Special emphasis is made on showing how it is possible to obtain the exact solution on the nodes and a good accuracy inside the element. The proposed simplifying concept, denominated as the equivalent distributed load (EDL) of any order, is based on the use of Legendre orthogonal polynomials to approximate the original or acting load for computing the results between the nodes. The 1-span beam examples show that this is a promising procedure that allows the aim of using either one FE and an EDL of slightly higher order or by using an slightly larger number of FEs leaving the EDL in the lowest possible order assumed by definition to be equal to 4 independently of how irregular the beam is loaded.

Modelling relativistic solitary wave interactions in over-dense plasmas: a perturbed nonlinear Schröndinger equation framework

We investigate the dynamics of localized solutions of the relativistic cold-fluid plasma model in the small but finite amplitude limit, for slightly overcritical plasma density. Adopting a multiple scale analysis, we derive a perturbed nonlinear Schrödinger equation that describes the evolution of the envelope of circularly polarized electromagnetic field. Retaining terms up to fifth order in the small perturbation parameter, we derive a self-consistent framework for the description of the plasma response in the presence of localized electromagnetic field. The formalism is applied to standing electromagnetic soliton interactions and the results are validated by simulations of the full cold-fluid model. To lowest order, a cubic nonlinear Schrödinger equation with a focusing nonlinearity is recovered. Classical quasiparticle theory is used to obtain analytical estimates for the collision time and minimum distance of approach between solitons. For larger soliton amplitudes the inclusion of the fifth-order terms is essential for a qualitatively correct description of soliton interactions. The defocusing quintic nonlinearity leads to inelastic soliton collisions, while bound states of solitons do not persist under perturbations in the initial phase or amplitude

Nematodes as indicators of the effect of soil fumigants on soil functioning

Debido al futuro incierto de la mayor parte de los fumigantes edáficos usados actualmente en la Unión Europea, que pueden implicar riesgos para la salud humana/animal y el medio ambiente, es necesario desarrollar programas de manejo integrado para el control de plagas de cultivos. Estos programas se incluyen como obligatorios en el Reglamento (EC) No. 1107/2009. De acuerdo con este Reglamento, es obligatoria la evaluación del riesgo asociado al uso de productos fitosanitarios sobre los organismos edáficos no diana y sus funciones, además de llevar a cabo ensayos con diferentes especies indicadoras para obtener datos de toxicidad que puedan ser usados posteriormente en la evaluación de riesgo. Sin embargo, la baja representatividad de algunas de estas especies indicadoras en el área Mediterránea supone una gran limitación. En esta situación, el Panel Científico de Productos Fitosanitarios y sus Residuos de la Autoridad Europea en Seguridad Alimentaria (EFSA), ha señalado la necesidad de modificar los datos ecotoxicológicos requeridos para evaluar los efectos adversos de los productos fitosanitarios de una manera más integrada, incluyendo criterios funcionales y estructurales mediante organismos como bacterias, hongos, protozoos y nematodos. De este modo, la EFSA ha recomendado el uso de los nematodos en la evaluación de la funcionalidad y estructura del suelo. Los nematodos están globalmente distribuidos y son morfológicamente diversos; esto junto con su gran abundancia y diversidad de respuestas a las perturbaciones edáficas, los convierte en indicadores adecuados del estado del suelo. Puesto que los nematodos interaccionan con muchos otros organismos que participan en diferentes eslabones de la red trófica edáfica, jugando papeles importantes en procesos edáficos esenciales en los agroescosistemas, la diversidad de nematodos es, a menudo, usada como indicador biológico de los efectos de las prácticas agrícolas en el estado del suelo. En los últimos años, diferentes índices basados en la comunidad nematológica han facilitado la interpretación de datos complejos sobre la ecología del suelo. Los índices de la red trófica edáfica, basados en la abundancia de grupos funcionales definidos como grupos C-P y grupos tróficos, permiten la evaluación de la funcionalidad de la red trófica edáfica. Por otra parte, la dificultad en la identificación taxonómica de nematodos para explicar su uso limitado como indicadores ecológicos, es ampliamente discutida, y existe cierta controversia en cuanto a la eficacia de los diferentes métodos de identificación de nematodos. Se argumenta que la identificación morfológica es difícil y puede llevar mucho tiempo debido a la falta de expertos especializados, y se afirma que las técnicas moleculares pueden resolver algunas limitaciones de las técnicas morfológicas como la identificación de juveniles. Sin embargo, los métodos de identificación molecular tienen también limitaciones; la mayoría de las bases de datos de secuencias de ADN están fuertemente orientadas hacia los nematodos fitoparásitos, los cuales representan sólo una parte de la comunidad edáfica de nematodos, mientras que hay poca información disponible de nematodos de vida libre a pesar de representar la mayoría de los nematodos edáficos. Este trabajo se centra en el estudio de los efectos de fumigantes edáficos en la funcionalidad del suelo a través del uso de diferentes indicadores basados en la comunidad de nematodos, como los índices de la red trófica, índices de diversidad, abundancia de los taxones más relevantes etc. También se han analizado otros indicadores funcionales relacionados con la supresividad edáfica, el ciclo de nutrientes o la actividad de la microfauna del suelo. En el capítulo 1, la diversidad de nematodos estudiada en una explotación comercial de fresa y sus alrededores durante dos campañas consecutivas en el suroeste español, fue baja en los suelos fumigados con fumigantes químicos ambas campañas y, aunque se observó una recuperación a lo largo de la campaña en la zona tratada, los suelos fumigados mostraron una condición perturbada permanente. La comunidad de nematodos estuvo más asociada al ciclo de nutrientes en la zona sin cultivar que en los suelos cultivados, y se observó poca relación entre la biomasa de las plantas y la estructura de la comunidad de nematodos. Los surcos sin tratar dentro de la zona de cultivo funcionaron como reservorio tanto de nematodos fitoparásitos como beneficiosos; sin embargo estas diferencias entre los surcos y los lomos de cultivo no fueron suficientes para mantener la supresividad edáfica en los surcos. Los suelos tratados fueron menos supresivos que los suelos sin tratar, y se observaron correlaciones positivas entre la supresividad edáfica y la estructura de la red trófica edáfica y la diversidad de nematodos. En el capítulo 2, se evaluaron los efectos de dos pesticidas orgánicos con efecto nematicida y dos nematicidas convencionales sobre las propiedades físico químicas del suelo, la diversidad de nematodos y la biomasa de las plantas en condiciones experimentales en dos tipos de suelo: suelos agrícolas poco diversos y suelos provenientes de una zona de vegetación natural muy diversos. El mayor efecto se observó en el tratamiento con neem, el cual indujo un gran incremento en el número de dauerlarvas en los suelos pobres en nutrientes, mientras que el mismo tratamiento indujo un incremento de poblaciones de nematodos bacterívoros, más estables y menos oportunistas, en los suelos del pinar ricos en materia orgánica. En el capítulo 3, se comparó la eficacia de métodos moleculares (TRFLP, Terminal Restriction Fragment Length Polymorphism) y morfológicos (microscopía de alta resolución) para la identificación de diferentes comunidades denematodos de España e Irlanda. Se compararon estadísticamente las diferencias y similitudes en la diversidad de nematodos, otros indicadores ecológicos y de la red trófica edáfica. Las identificaciones mediante el uso de TRFLP sólo detectó un porcentaje de los taxones presentes en las muestras de suelo identificadas morfológicamente, y los nematodos omnívoros y predadores no fueron detectados molecularmente en nuestro estudio. Los índices calculados en base a los nematodos micróboros mostraron más similitud cuando se identificaron morfológica y molecularmente que los índices basados en grupos tróficos más altos. Nuestros resultados muestran que, al menos con la técnica usada en este estudio, la identificación morfológica de nematodos es una herramienta fiable y más precisa que la identificación molecular, puesto que en general se obtiene una mayor resolución en la identificación de nematodos. En el capítulo 4, se estudiaron también los efectos de los nematicidas químicos sobre la comunidad de nematodos y la biomasa de las plantas en condiciones experimentales de campo, donde se aplicaron en una rotación de cultivo judía-col durante un ciclo de cultivo. Se aplicaron dos tipos de enmiendas orgánicas con el objetivo de mitigar el efecto negativo de los productos fitosanitarios sobre la diversidad edáfica. El efecto de los nematicidas sobre las propiedades del suelo y sobre la comunidad de nematodos fue más agudo que el efecto de las enmiendas. La incorporación de los restos de cosecha al final del ciclo de cultivo de la judía tuvo un gran efecto sobre la comunidad de nematodos, y aunque el número total de nematodos incrementó al final del experimento, se observó una condición perturbada permanente de la red trófica edáfica a lo largo del experimento. ABSTRACT Due to the uncertain future of the soil fumigants most commonly used in the EU, that might involve risks for human/animal health and the environment, there is a need to develop new integrated pest management programs, included as mandatory in the Regulation (EC) No. 1107/2009, to control crop diseases. According to this Regulation, evaluating the risk associated to the use of the plant production products (PPP) on non-target soil fauna and their function, and developing assays with different indicator species to obtain toxicity data to be used in the risk evaluation is mandatory. However, the low representativeness of some of these indicator species in the Mediterranean area is a relevant limitation. In this situation, the Scientific Panel of Plant Protection Products and their Residues of the European Food Safety Authority (EFSA) has pointed out the necessity of modifying the ecotoxicological data set required to evaluate non-target effects of PPP in a more integrated way, including structural and functional endpoints with organism such as bacteria, fungi, protists and nematodes. Thus, EFSA has recommended the use of nematodes in the assessment of the functional and structural features of the soil. Nematodes are globally distributed and morphologically diverse, and due to their high abundance and diversity of responses to soil disturbance, they are suitable indicators of the soil condition. Since nematodes interact with many other organisms as participants in several links of the soil food web, playing important roles in essential soil processes in agroecosystems, nematode diversity is often used as a biological indicator of the effects of agricultural practices on soil condition. In the last years, various indices based on soil nematode assemblages, have facilitated the interpretation of complex soil ecological data. Soil food web indices based on the abundances of functional guilds defined by C-P groups and trophic groups, permit evaluating soil food web functioning. On the other hand, the difficulty of nematode taxonomical identification is commonly argued to explain their limited used as ecological indicators, and there is a certain controversy in terms of the efficacy of various nematode identification methods. It is argued that the morphological identification is difficult and time consuming due to the lack of specialist knowledge, and it is claimed that molecular techniques can solve some limitations of morphological techniques such as the identification of juveniles. Nevertheless, molecular identification methods are limited too, since most of the DNA-based databases are strongly oriented towards plant-parasitic nematodes that represent only a fraction of the soil nematode community, while there is little information available on free-living nematodes, which represent most soil nematodes. This work focuses on the study of the effects of soil fumigants on soil functioning through the use of different indicators based on soil nematode community as soil food web indices, diversity indices, the abundance of more relevant taxa etc. Other functional indicators related to soil suppressiveness, nutrient cycling, or the activity of soil microfauna have been also studied. In chapter 1, nematode diversity assessed in a commercial strawberry farm and its surroundings for two consecutive growing seasons in southern Spain, was low in fumigated soils with chemical pesticides throughout both seasons and, although yearly recovery occurred within the treated fields, fumigated soils showed a permanent perturbed condition. The nematode community was more closely associated to nutrient cycling in the non-cropped than in the cropped soils, and the link between plant biomass and nematode community structure was weak. Non-treated furrows within the treated fields were a reservoir of both beneficial and plant-parasitic nematodes, but such difference between furrows and beds was not enough to maintain more suppressive soil assemblages in the furrows. Treated soils were less suppressive than unmanaged soils, and there was a positive and significant correlation between soil suppressiveness and soil food web structure and diversity. In chapter 2, the effects of two organic pesticides with nematicide effect and two chemical nematicides on soil physicalchemical properties, soil nematode diversity and plant biomass in experimental conditions were assessed in two types of soils: low diversity soils from an agricultural farm, and high diversity soils from a natural vegetation area. The larger effect was observed on the neem treatment, which induced a large boost of dauer juveniles in the nutrient-depleted soil, while the same treatment induced the increase of more stable, less opportunistic, populations of generalist bacterivore nematodes in the pine forest soil, rich in organic matter. In chapter 3, comparison of the efficiency of molecular (TRFLP, Terminal Restriction Fragment Length Polymorphism) and morphological (microscopy at high magnification) identification methods was carried out in different nematode communities from five sites of different land uses in Spain and Ireland. Differences and similarities on nematode diversity and other ecological and soil food web indices assessed by both methods, were statistically compared. Molecular identification with TRFLP only detected a percentage of the taxa present in the soil samples identified morphologically, and omnivores and predators were not detected molecularly in our study. Indices involving microbial feeding nematodes were more similar between identification methods than indices involving higher trophic links. Our results show that, at least with the technique used in this study, identifying nematodes morphologically is a reliable and more precise identification tool than molecular identification, since a higher taxonomic resolution is in general obtained compared to TRFLP. In chapter 4, the effect of chemical nematicides on nematode community descriptors and plant biomass was also studied in field conditions in an experimental area in which dazomet and dimethyl disulfide was applied in a bean-cabbage rotation system for a single season. Organic amendments were incorporated into the soil with the aim of mitigate the negative effect of the pesticides on soil diversity. The effect of the nematicides was much more noticeable than the effect of the amendments on soil properties and nematode community descriptors. The incorporation of bean crop residues into the soil at the end of bean crop cycle affected soil nematode community descriptors to a great extent, and although total number of nematodes increased at the end of the experiment, a permanent perturbed soil food web condition was observed along the experiment.

EDROMO: An accurate propagator for elliptical orbits in the perturbed two-body problem

EDROMO is a special perturbation method for the propagation of elliptical orbits in the perturbed two-body problem. The state vector consists of a time-element and seven spatial elements, and the independent variable is a generalized eccentric anomaly introduced through a Sundman time transformation. The key role in the derivation of the method is played by an intermediate reference frame which enjoys the property of remaining fixed in space as long as perturbations are absent. Three elements of EDROMO characterize the dynamics in the orbital frame and its orientation with respect to the intermediate frame, and the Euler parameters associated to the intermediate frame represent the other four spatial elements. The performance of EDromo has been analyzed by considering some typical problems in astrodynamics. In almost all our tests the method is the best among other popular formulations based on elements.

Global Stability Analysis of a Compressible Turbulent Flow around a High-Lift Configuration

The purpose of this work is to analyze a complex high lift configuration for which significant regions of separated flow are present. Current state of the art methods have some diffculty to predict the origin and the progression of this separated flow when increasing the angle of attack. The mechanisms responsible for the maximum lift limit on multi-element wing con?gurations are not clear; this stability analysis could help to understand the physics behind the phenomenon and to find a relation between the flow separation and the instability onset. The methodology presented herein consists in the computation of a steady base flow solution based on a finite volume discretization and a proposal of the solution for a generalized eigenvalue problem corresponding to the perturbed and linearized problem. The eigenvalue problem has been solved with the Arnoldi iterative method, one of the Krylov subspace projection methods. The described methodology was applied to the NACA0012 test case in subsonic and in transonic conditions and, finally, for the first time to the authors knowledge, on an industrial multi-component geometry, such as the A310 airfoil, in order to identify low frequency instabilities related to the separation. One important conclusion is that for all the analyzed geometries, one unstable mode related to flow separation appears for an angle of attack greater than the one correspondent to the maximum lift coe?cient condition. Finally, an adjoint study was carried out in order to evaluate the receptivity and the structural sensitivity of the geometries, giving an indication of the domain region that could be modified resulting in the biggest change of the flowfield.

Direct and adjoint global stability analysis of turbulent transonic flows over a NACA0012 profile

In this work, various turbulent solutions of the two-dimensional (2D) and three-dimensional compressible Reynolds averaged Navier?Stokes equations are analyzed using global stability theory. This analysis is motivated by the onset of flow unsteadiness (Hopf bifurcation) for transonic buffet conditions where moderately high Reynolds numbers and compressible effects must be considered. The buffet phenomenon involves a complex interaction between the separated flow and a shock wave. The efficient numerical methodology presented in this paper predicts the critical parameters, namely, the angle of attack and Mach and Reynolds numbers beyond which the onset of flow unsteadiness appears. The geometry, a NACA0012 profile, and flow parameters selected reproduce situations of practical interest for aeronautical applications. The numerical computation is performed in three steps. First, a steady baseflow solution is obtained; second, the Jacobian matrix for the RANS equations based on a finite volume discretization is computed; and finally, the generalized eigenvalue problem is derived when the baseflow is linearly perturbed. The methodology is validated predicting the 2D Hopf bifurcation for a circular cylinder under laminar flow condition. This benchmark shows good agreement with the previous published computations and experimental data. In the transonic buffet case, the baseflow is computed using the Spalart?Allmaras turbulence model and represents a mean flow where the high frequency content and length scales of the order of the shear-layer thickness have been averaged. The lower frequency content is assumed to be decoupled from the high frequencies, thus allowing a stability analysis to be performed on the low frequency range. In addition, results of the corresponding adjoint problem and the sensitivity map are provided for the first time for the buffet problem. Finally, an extruded three-dimensional geometry of the NACA0012 airfoil, where all velocity components are considered, was also analyzed as a Triglobal stability case, and the outcoming results were compared to the previous 2D limited model, confirming that the buffet onset is well detected.

Global Stability Analysis of Turbulent Transonic Flows on Airfoil geometries

La aparición de inestabilidades en un flujo es un problema importante que puede afectar a algunas aplicaciones aerodinámicas. De hecho existen diferentes tipos de fenómenos no-estacionarios que actualmente son tema de investigación; casos como la separación a altos ángulos de ataque o el buffet transónico son dos ejemplos de cierta relevancia. El análisis de estabilidad global permite identificar la aparición de dichas condiciones inestables, proporcionando información importante sobre la región donde la inestabilidad es dominante y sobre la frecuencia del fenómeno inestable. La metodología empleada es capaz de calcular un flujo base promediado mediante una discretización con volúmenes finitos y posteriormente la solución de un problema de autovalores asociado a la linealización que aparece al perturbar el flujo base. El cálculo numérico se puede dividir en tres pasos: primero se calcula una solución estacionaria para las ecuaciones RANS, luego se extrae la matriz del Jacobiano que representa el problema linealizado y finalmente se deriva y se resuelve el problema de autovalores generalizado mediante el método iterativo de Arnoldi. Como primer caso de validación, la técnica descrita ha sido aplicada a un cilindro circular en condiciones laminares para detectar el principio de las oscilaciones de los vórtices de von Karman, y se han comparado los resultados con experimentos y cálculos anteriores. La parte más importante del estudio se centra en el análisis de flujos compresibles en régimen turbulento. La predicción de la aparición y la progresión de flujo separado a altos ángulos de ataque se han estudiado en el perfil NACA0012 en condiciones tanto subsónicas como supersónicas y en una sección del ala del A310 en condiciones de despegue. Para todas las geometrías analizadas, se ha podido observar que la separación gradual genera la aparición de un modo inestable específico para altos ángulos de ataque siempre mayores que el ángulo asociado al máximo coeficiente de sustentación. Además, se ha estudiado el problema adjunto para obtener información sobre la zona donde una fuerza externa provoca el máximo cambio en el campo fluido. El estudio se ha completado calculando el mapa de sensibilidad estructural y localizando el centro de la inestabilidad. En el presente trabajo de tesis se ha analizado otro importante fenómeno: el buffet transónico. En condiciones transónicas, la interacción entre la onda de choque y la capa límite genera una oscilación de la posición de la onda de choque y, por consiguiente, de las fuerzas aerodinámicas. El conocimiento de las condiciones críticas y su origen puede ayudar a evitar la oscilación causada por estas fuerzas. Las condiciones para las cuales comienza la inestabilidad han sido calculadas y comparadas con trabajos anteriores. Por otra parte, los resultados del correspondiente problema adjunto y el mapa de sensibilidad se han obtenido por primera vez para el buffet, indicando la región del dominio que sera necesario modificar para crear el mayor cambio en las propiedades del campo fluido. Dado el gran consumo de memoria requerido para los casos 3D, se ha realizado un estudio sobre la reducción del domino con la finalidad de reducirlo a la región donde está localizada la inestabilidad. La eficacia de dicha reducción de dominio ha sido evaluada investigando el cambio en la dimensión de la matriz del Jacobiano, no resultando muy eficiente en términos del consumo de memoria. Dado que el buffet es un problema en general tridimensional, el análisis TriGlobal de una geometría 3D podría considerarse el auténtico reto futuro. Como aproximación al problema, un primer estudio se ha realizado empleando una geometría tridimensional extruida del NACA00f2. El cálculo del flujo 3D y, por primera vez en casos tridimensionales compresibles y turbulentos, el análisis de estabilidad TriGlobal, se han llevado a cabo. La comparación de los resultados obtenidos con los resultados del anterior modelo 2D, ha permitido, primero, verificar la exactitud del cálculo 2D realizado anteriormente y también ha proporcionado una estimación del consumo de memoria requerido para el caso 3D. ABSTRACT Flow unsteadiness is an important problem in aerodynamic applications. In fact, there are several types of unsteady phenomena that are still at the cutting edge of research in the field; separation at high angles of attack and transonic buffet are two important examples. Global Stability Analysis can identify the unstable onset conditions, providing important information about the instability location in the domain and the frequency of the unstable phenomenon. The methodology computes a base flow averaged state based on a finite volume discretization and a solution for a generalized eigenvalue problem corresponding to the perturbed linearized equations. The numerical computation is then performed in three steps: first, a steady solution for the RANS equation is computed; second, the Jacobian matrix that represents the linearized problem is obtained; and finally, the generalized eigenvalue problem is derived and solved with an Arnoldi iterative method. As a first validation test, the technique has been applied on a laminar circular cylinder in order to detect the von Karman vortex shedding onset, comparing the results with experiments and with previous calculations. The main part of the study focusses on turbulent and compressible cases. The prediction of the origin and progression of separated flows at high angles of attack has been studied on the NACA0012 airfoil at subsonic and transonic conditions and for the A310 airfoil in take-off configuration. For all the analyzed geometries, it has been found that gradual separation generates the appearance of one specific unstable mode for angles of attack always greater than the ones related to the maximum lift coefficient. In addition, the adjoint problem has been studied to suggest the location of an external force that results in the largest change to the flow field. From the direct and the adjoint analysis the structural sensitivity map has been computed and the core of the instability has been located. The other important phenomenon analyzed in this work is the transonic buffet. In transonic conditions, the interaction between the shock wave and the boundary layer leads to an oscillation of the shock location and, consequently, of the aerodynamic forces. Knowing the critical operational conditions and its origin can be helpful in preventing such fluctuating forces. The instability onset has then been computed and compared with the literature. Moreover, results of the corresponding adjoint problem and a sensitivity map have been provided for the first time for the buffet problem, indicating the region that must be modified to create the biggest change in flow field properties. Because of the large memory consumption required when a 3D case is approached, a domain reduction study has been carried out with the aim of limiting the domain size to the region where the instability is located. The effectiveness of the domain reduction has been evaluated by investigating the change in the Jacobian matrix size, not being very efficient in terms of memory consumption. Since buffet is a three-dimensional problem, TriGlobal stability analysis can be seen as a future challenge. To approximate the problem, a first study has been carried out on an extruded three-dimensional geometry of the NACA0012 airfoil. The 3D flow computation and the TriGlobal stability analysis have been performed for the first time on a compressible and turbulent 3D case. The results have been compared with a 2D model, confirming that the buffet onset evaluated in the 2D case is well detected. Moreover, the computation has given an indication about the memory consumption for a 3D case.

Bivariate Krawtchouk polynomials: Inversion and connection problems with the NAVIMA algorithm

In this paper we present a recurrent procedure to solve an inversion problem for monic bivariate Krawtchouk polynomials written in vector column form, giving its solution explicitly. As a by-product, a general connection problem between two vector column of monic bivariate Krawtchouk families is also explicitly solved. Moreover, in the non monic case and also for Krawtchouk families, several expansion formulas are given, but for polynomials written in scalar form.

A model of ocular dominance column development by competition for trophic factor

Recent experimental evidence has shown that application of certain neurotrophic factors (NTs) to the developing primary visual cortex prevents the development of ocular dominance (OD) columns. One interpretation of this result is that afferents from the lateral geniculate nucleus compete for postsynaptic trophic factor in an activity-dependent manner. Application of excess trophic factor eliminates this competition, thereby preventing OD column formation. We present a model of OD column development, incorporating Hebbian synaptic modification and activity-driven competition for NT, which accounts for both normal OD column development as well as the prevention of that development when competition is removed. In the “control” situation, when available NT is below a critical amount, OD columns form normally. These columns form without weight normalization procedures and in the presence of positive inter-eye correlations. In the “experimental” case, OD column development is prevented in a local neighborhood in which excess NT has been added. Our model proposes a biologically plausible mechanism for competition between neural populations that is motivated by several pieces of experimental data, thereby accounting for both normal and experimentally perturbed conditions.

Perturbed dentate gyrus function in serotonin 5-HT2C receptor mutant mice

Serotonin systems have been implicated in the regulation of hippocampal function. Serotonin 5-HT2C receptors are widely expressed throughout the hippocampal formation, and these receptors have been proposed to modulate synaptic plasticity in the visual cortex. To assess the contribution of 5-HT2C receptors to the serotonergic regulation of hippocampal function, mice with a targeted 5-HT2C-receptor gene mutation were examined. An examination of long-term potentiation at each of four principal regions of the hippocampal formation revealed a selective impairment restricted to medial perforant path–dentate gyrus synapses of mutant mice. This deficit was accompanied by abnormal performance in behavioral assays associated with dentate gyrus function. 5-HT2C receptor mutants exhibited abnormal performance in the Morris water maze assay of spatial learning and reduced aversion to a novel environment. These deficits were selective and were not associated with a generalized learning deficit or with an impairment in the discrimination of spatial context. These results indicate that a genetic perturbation of serotonin receptor function can modulate dentate gyrus plasticity and that plasticity in this structure may contribute to neural mechanisms underlying hippocampus-dependent behaviors.

On the classification of binary shifts of finite commutant index

We provide a complete classification up to conjugacy of the binary shifts of finite commutant index on the hyperfinite II1, factor. There is a natural correspondence between the conjugacy classes of these shifts and polynomials over GF(2) satisfying a certain duality condition.