Resumen En el presente trabajo, utilizando una generalización del potencial de Miyamoto-Nagai, se ajustan las curvas de rotación observadas de tres galaxias espirales a las velocidades circulares analíticas. Los datos observacionales se tomaron de un conjunto de imágenes de línea de 21 centímetros (o línea HI) obtenidos con el Westerbork Synthesis Radio Telescope (WSRT), para tres galaxias particulares en el grupo de la Ursa Major: NGC 3726, NGC 3877 y NGC 4010. Seguidamente, se analiza la dinámica del sistema en términos del método de secciones de Potincaré, encontrando que para valores grandes del momento angular de la partícula de prueba o valores bajos su energía total, la dinámica es principalmente regular, mientras que en los casos opuestos, la dinámica es principalmente caótica. Nuestro modelo abre la posibilidad de encontrar orbitas´ caóticas acotadas para estrellas presentes en esas galaxias particulares. © 2019. Acad. Colomb. Cienc. Ex. Fis. Nat.

Abstract In the present paper, using a generalization of the Miyamoto and Nagai potential we adjusted the observed rotation curves of three specific spiral galaxies to the analytical circular velocities. The observational data have been taken from a 21 cm-line synthesis imaging survey using the Westerbork Synthesis Radio Telescope, for three particular galaxies in the Ursa Major cluster: NGC 3726, NGC 3877 and NGC 4010. Accordingly, the dynamics of the system is analyzed in terms of the Poincaré sections method, finding that for larger values of the angular momentum of the test particle or lower values its total energy the dynamics is mainly regular, while on the opposite cases, the dynamics is mainly chaotic. Our toy model opens the possibility to find chaotic bounded orbits for stars in those particular galaxies.© 2019. Acad. Colomb. Cienc. Ex. Fis. Nat.

Resumen Presentamos modelos de masa de disco máximo para un conjunto de galaxias espirales del Cluster Ursa Major. Los modelos se obtienen por medio del método de Hunter y las soluciones particulares se eligen de tal manera que las velocidades circulares se ajustan muy exactamente a las curvas de rotación observadas de algunas galaxias espirales específicas. Bajo la hipótesis del disco máximo, suponemos que la masa del disco es lo más grande posible, en consonancia con la curva de rotación de la galaxia. Por lo tanto, la contribución de la masa del halo de la materia oscura se considera insignificante en las partes internas de las espirales. Los modelos reproducen la estructura general de las curvas de rotación en la mayoría de las galaxias, proporcionando buenos ajustes para calcular la masa total de estas galaxias obteniendo valores del orden de 1010 M ☉. Basados en el criterio de estabilidad vertical presentado por Vieira and Ramos-Caro (2016), encontramos que todas las galaxias analizadas presentan un comportamiento verticalmente estable. Por otro lado, a partir del análisis de la frecuencia epicíclica se observa que todos los modelos presentaron mayormente un comportamiento estable radial excepto en el borde del disco.

Abstract Maximum disc mass models for a set of spiral galaxies from the Ursa Major Cluster are presented. We construct the models using the Hunther method and the particular solutions are chosen in such a way that the circular velocities are adjusted very accurately to the observed rotation curves of some specific spiral galaxies. Under the maximum disc hypothesis, we consider that the rotation curves of the analyzed galaxies can be modeled with only the contribution of the disc. This implies that it is not necessary to consider the contribution ot the dark matter halo in the inner part of the spiral. In this way, the models reproduce the global behavior of the rotation curves in the great majority of galaxies. Producing good adjustments to calculate the total mass of these galaxies, and yielding values of the order of 1O10 M ☉. Based on the vertical stability criterion presented by Viera & Ramos-caro (2016), we find that all the galaxies analyzed present a vertically stable behavior. On the other hand, from the analysis of the epicyclic frequency we find that all the models exhibit mainly a radial stable behaviour except at the edge of the disc.

Resumo Apresentamos modelos de massa de disco máximo para um conjunto de galáxias espirais do Cluster Ursa Major. Os modelos são obtidos por meio do método Hunter e as soluções particulares são escolhidas de tal forma que as velocidades circulares são ajustadas com muita precisão às curvas de rotação observadas de algumas galáxias espirais específicas. Sob a hipótese de disco máximo, supomos que a massa do disco é tão grande quanto possível, consistente com a curva de rotação da galáxia. A contribuição de massa do halo da matéria escura é, portanto, assumida como insignificante nas partes internas das espirais. Os modelos reproduzem a estrutura geral das curvas de rotação na maioria das galáxias, proporcionando bons ajustes para calcular a massa total dessas galáxias obtendo valores da ordem de 1010 M ☉. Com base no critério de estabilidade vertical apresentado por Vieira and Ramos-Caro (2016), descobrimos que todas as galáxias analisadas apresentam um comportamento verticalmente estável. Por outro lado, a partir da análise da frequência epicíclica, descobrimos que todos os modelos apresentaram principalmente um comportamento estável radial, exceto na borda do disco.

Resumen Movimiento regular y caótico de partículas de prueba en campos gravitacionales axialmente simétricos debido a cuerpos con deformación cuadrupolar y octupolar es estudiado usando superficies de sección de Poincaré. Encontramos que la inclusión del término octupolar induce una distorsión en las curvas KAM correspondiente a trayectorias regulares, así como un aumento en la caoticidad. El hecho de que la activación del momento octupolar incremente la caoticidad y lleve a la aparición de regiones inestables, puede ser visto aún en el caso correspondiente a deformación oblata, la cual comúnmente presenta movimiento regular. Así, los resultados aquí obtenidos son la generalización, para el caso de gravedad Newtoniana, de los obtenidos previamente por Heiss, W. D., Nazmitdinov, R. G. & Radu, S. (1994) y Li, J. (1998) para osciladores armónicos.

Abstract Regular and chaotic test particle motion in axially symmetric gravitational fields due to bodies with quadrupolar and octupolar deformation are studied using Poincaré surfaces of section. We find that inclusion of the octupolar term induces a distortion in the KAM curves corresponding to regular trajectories, as well as an increasing in chaoticity. The fact the switching on of the octupolar moment it increases chaoticity and leads to the apparition of spindle torus, can be seen even in the case corresponding to oblate deformation, which commonly presents regular motion. Thus, the results here obtained are the generalization, for the case of Newtonian gravity, of those previously obtained by Heiss, W. D., Nazmitdinov R. G. & Radu, S. (1994) and Li, J. (1998) for harmonic oscillators.

Resumen Uno de los criterios más importantes para la caracterización de modelos galácticos o discos de acreción astrofísicamente relevantes, es el análisis de la estabilidad de dichos modelos. En este trabajo, se realiza un análisis de la estabilidad de discos delgados estáticos relativistas con simetría axial, mediante la introducción de una perturbación de primer orden en el tensor de energía-impulso del fluido. El formalismo se aplica a tres modelos construidos con el método de desplazamiento-corte-reflexión (DCR), previamente considerados en la literatura (Ujevic and Letelier, 2004), pero modificando el criterio de masa, es decir, usando la masa de Komar en lugar de la masa total superficial. Bajo estas condiciones, se encuentra que los valores de masa total son independientes de los parámetros del método DCR, lo que permite elegir la condición de frontera para el radio de corte que tome el valor máximo y a la vez permita una perturbación apreciable y bien comportada en el disco. Como resultado general, se encuentra que para la mayoría de modos de oscilación, la masa de Komar es más apropiada para definir el radio de corte.

Abstract The study on the stability of relativistic disks is one of the most important criteria for the characterization of astrophysically relevant galactic or accretion disks models. In this paper, we perform an analysis of the stability of static axisymmetric relativistic thin disks, by introducing a first-order perturbation into the energy-momentum tensor of the fluid. The formalism is applied to three particular models built with the aid of the displace-cut-reflect (DCR) method, and previously considered in literature (Ujevic and Letelier, 2004), but modifying the mass criteria, i.e., using the Komar mass instead of the total surface mass. Under this conditions, it is found that the total mass values are independent of the parameters of the DCR-method, which let us choose the boundary condition for the cutoff radius, such that it takes the maximum value that allows an appreciable and well-behaved perturbation on the disk. As a general result, we found that the Komar mass is more appropriate to define the cutoff radius.

A family of analytical potential-density pairs for flat galaxies with spheroidal halos is presented. The potential are obtained by means of the sum of two independent terms: a potential associated with a thin disc and a potential associated with a spheroidal halo, which are expressed as appropriated superpositions of products of Legendre functions, in such a way that the model implies a linear relationship between the masses of the thin disc and the spheroidal halo. By taking a particular case for the halo potential, we found that the circular velocity obtained can be adjusted very accurately to the observed rotation curves of some specific galaxies, so that the models are stable against radial and vertical perturbations. Two particular models for the galaxies NGC4389 and UGC6969 are obtained by adjusting the circular velocity with data of the observed rotation curve of some galaxies of the Ursa Mayor Cluster, as reported in Verheijen and Sancisi (2001). The values of the halo mass and the disc mass for these two galaxies are computed obtaining a very narrow interval of values for these quantities. Furthermore, the values of obtained masses are in perfect agreement with the expected order of magnitude and with the relative order of magnitude between the halo mass and the disc mass.

Se presenta la derivación de funciones de distribución para los primeros cuatro miembros de una familia de discos, obtenida previamente en González and Reina (2006), la cual representa a una familia de modelos de galaxias axialmente simétricas de radio finito y con densidad superficial de masa bien comportada. Para ello, se emplean varios enfoques desarrollados a partir del par potencial-densidad y, utilizando esencialmente el método introducido por Kalnajs (1976), se obtienen algunas funciones de distribución que dependen de la integral de Jacobi. Ahora, ya que este método exige que la densidad de masa se pueda expresar adecuadamente como una función del potencial gravitacional, sólo es posible hacer esto para los primeros cuatro discos de la familia. También encontramos otro tipo de funciones de distribución, comenzando con la parte par de las funciones de distribución anteriores y utilizando el principio de máxima entropía con el fin de encontrar la parte impar y por lo tanto una nueva función de distribución, como fue señalado por Dejonghe (1986). El resultado es una amplia variedad de estados de equilibrio correspondiente a varios modelos auto-consistentes de galaxias planas finitas.

We present the derivation of distribution functions for the first four members of a family of disks, previously obtained in González and Reina (2006), which represent a family of axially symmetric galaxy models with finite radius and well-behaved surface mass density. In order to do this, we employ several approaches that have been developed starting from the potential-density pair and, essentially using the method introduced by Kalnajs (1976), we obtain some distribution functions that depend on the Jacobi integral. Now, as this method demands that the mass density can be properly expressed as a function of the gravitational potential, we can do this only for the first four disks of the family. We also find another kind of distribution functions by starting with the even part of the previous distribution functions and using the maximum entropy principle in order to find the odd part and so a new distribution function, as it was pointed out by Dejonghe (1986). The result is a wide variety of equilibrium states corresponding to several self-consistent finite flat galaxy models.

Se presenta una nueva familia de discos gruesos newtonianos estables a partir del método de desplazamiento, corte, llenado y reflexión construidos en (González & Letelier, 2004; Vogt & Letelier, 2005). Soluciones de la ecuación de Laplace en coordenadas cilíndricas son consideradas, éstas representarán el campo gravitacional de objetos con momentos multipolares externos solamente. Se definen y calculan las cantidades físicas en el plano del disco, tales como, la frecuencia epicíclica, kapa, la frecuencia vertical, ny, y la velocidad circular, ípsilonc de las partículas. Además, se determina la densidad superficial de masa, sigma, la densidad del disco grueso, rho, y el criterio de estabilidad de los discos gruesos a través del momentum angular o el criterio de Rayleigh (Rayleigh, 1917; Landau, 1987). Finalmente, se representan las propiedades físicas para algunos parámetros considerando sólo hasta el término cuadrupolar en la expansión multipolar del potencial gravitacional.

We present a new family of stable thick discs from known displace, cut, fill and reflect method (González & Letelier, 2004; Vogt & Letelier, 2005) is presented. Solutions of the Laplace equation in cylindrical coordinates are considered, these one represent the gravitational field of objects with only external multipole moments. The physical quantities in the plane of the disk, are defined and calculated such as, the epicyclic frequency, kappa, the vertical frequency, nu, and the circular velocity, upsilonc of particles. The surface density, sigma, density of thick disk, rho, and stability of thick disks through of specific angular momentum or Rayleigh criterion (Rayleigh, 1917), and (Landau, 1987) were calculated. Finally, the physical properties are shown for only some parameters considering only until quadrupolar term in the expasion gravitational potential multipolar

Resumen. En este trabajo se presenta un estudio de las geodésicas temporales y nulas en el disco delgado relativista y newtoniano de Bonnor-Sackfield. Se analiza el movimiento de las partículas de prueba en el plano ecuatorial, tanto para el modelo newtoniano del disco delgado como para el disco relativista correspondiente. La naturaleza de las órbitas posibles se estudia por medio de un análisis cualitativo del potencial efectivo, y numéricamente mediante la solución de la ecuación de movimiento de las trayectorias ecuatorial radial y no radial: Se analiza la existencia de órbitas estables, circulares inestables y estables marginalmente, tanto para el caso newtoniano, como el relativista. Se presentan ejemplos de los resultados numéricos obtenidos con algunos valores de los parámetros simples.

Abstract. A study of timelike and null equatorial geodesics in the Bonnor- Sackfield relativistic thin disk is presented. The motion of test particles in the equatorial plane is analyzed, both for the newtonian thin disk model as for the corresponding relativistic disk. The nature of the possible orbits is studied by means of a qualitative analysis of the effective potential and by numerically solving the motion equation for radial and non-radial equatorial trajectories. The existence of stable, unstable and marginally stable circular orbits is analyzed, both for the newtonian and relativistic case. Examples of the numerical results, obtained with some simple values of the parameters, are presented.

Two families of exact simple solutions of Einstein field equations for inhomogeneous stiff cosmologies are presented. The method to obtain the solutions is based on the introduction of auxiliary functions in order to cast the Einstein equations in such a way that can be explicitly integrated. Although the equations are mathematically equivalent to the equations obtained when the source of matter is a scalar field, it is worth to mention that the source that we consider is not a scalar field but a perfect fluid with a stiff equation of state. The obtained solutions are expressed in terms of simple functions of the used coordinates and two families of particular solutions are considered. The geometrical and kinematical properties of the solutions are then analyzed and the parameters are restricted in order to have a physically acceptable behavior. The two particular solutions are of the Petrov type I, the first one being regular everywhere whereas the second one presents a big-bang singularity. Now, for a particular value of one of the parameters, the second particular solution is a vacuum solution of the Bianchi I type that reduces to the Kasner solution.

This paper describes the design and installation of an automated experimental device applied to a parallel co-current hot air dryer to perform drying studies in the field of food engineering. The development of this work was divided into two main activities: (i) design of the automation system and (ii) validation of automatically collected data. A device capable of collecting and registering real time data and images from drying processes, and transmitting them through Internet was obtained. The data processed by the automatic device was statistically validated. It is concluded that the proposed automation device is feasible, reliable and attractive for the users, facilitating the teaching-learning process in an important area of Food Engineering.

El presente trabajo describe el diseño y montaje de un dispositivo experimental para la automatización de un secador de aire caliente con flujo paralelo en co-corriente para realizar estudios de secado. El desarrollo del trabajo se dividió en dos actividades principales: (i) diseño del sistema de automatización y (ii) la validación de los datos entregados por el equipo. Se obtuvo un dispositivo capaz de registrar las variables del proceso de secado y de la imagen de la muestra deshidratada en tiempo real, como así mismo transmitir dicha información a través de Internet. Los datos procesados por el sistema automático comparados con experiencias manuales tradicionales (no automatizadas) se validaron estadísticamente. Se concluye finalmente que la propuesta es viable, fiable y atractiva para el usuario por lo que facilita el proceso de enseñanza-aprendizaje en un área de especial importancia en Ingeniería de Alimentos.

A detailed study is presented of the counterrotating model (CRM) for electrovacuum stationary axially symmetric relativistic thin disks of infinite extension without radial stress, in the case when the eigenvalues of the energy-momentum tensor of the disk are real quantities, so that there is not heat flow. We find a general constraint over the counterrotating tangential velocities needed to cast the surface energy-momentum tensor of the disk as the superposition of two counterrotating charged dust fluids. We then show that, in some cases, this constraint can be satisfied if we take the two counterrotating tangential velocities as equal and opposite or by taking the two counterrotating streams as circulating along electro-geodesics. However, we show that, in general, it is not possible to take the two counterrotating fluids as circulating along electro-geodesics nor take the two counterrotating tangential velocities as equal and opposite. A simple family of models of counterrotating charged disks based on the Kerr-Newman solution are considered where we obtain some disks with a CRM well behaved. We also show that the disks constructed from the Kerr-Newman solution can be interpreted, for all the values of parameters, as a matter distribution with currents and purely azimuthal pressure without heat flow. The models are constructed using the well-known "displace, cut and reflect" method extended to solutions of vacuum Einstein-Maxwell equations. We obtain, in all the cases, counterrotating Kerr-Newman disks that are in agreement with all the energy conditions.