A new method to find the potential center of N-body systems

We present a new and fast method to nd the potential center of an N-body distribution. The method uses an iterative algorithm which exploits the fact that the gradient of the potential is null at its center: it uses a smoothing radius to avoid getting trapped in secondary minima. We have tested this method on several random realizations of King models (in which the numerical computation of this center is rather dicult, due to the constant density within their cores), and com- pared its performance and accuracy against a more straightforward, but computer intensive method, based on cartesian meshes of increasing spatial resolution. In all cases, both methods converged to the same center, within the mesh resolution, but the new method is two orders of magnitude faster. We have also tested the method with one astronomical problem: the evolu- tion of a 105 particle King model orbiting around a xed potential that represents our Galaxy. We used a spherical harmonics expansion N-body code, in which the potential center determination is crucial for the correct force computation. We compared this simulation with another one in which a method previously used to determine the expansion center is employed (White 1983). Our routine gives better results in energy conservation and mass loss.Fil: Aguilar, L. A.. Universidad Nacional Autonoma de Mexico. Instituto de Astronomia; MéxicoFil: Cruz, F.. Universidad Nacional Autonoma de Mexico. Instituto de Astronomia; MéxicoFil: Carpintero, Daniel Diego. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentin

LP-VIcode: a program to compute a suite of variational chaos indicators

An important point in analysing the dynamics of a given stellar or planetary system is the reliable identification of the chaotic or regular behaviour of its orbits. We introduce here the program LP-VIcode, a fully operational code which efficiently computes a suite of ten variational chaos indicators for dynamical systems in any number of dimensions. The user may choose to simultaneously compute any number of chaos indicators among the following: the Lyapunov Exponents, the Mean Exponential Growth factor of Nearby Orbits, the Slope Estimation of the largest Lyapunov Characteristic Exponent, the Smaller ALignment Index, the Generalized ALignment Index, the Fast Lyapunov Indicator, the Othogonal Fast Lyapunov Indicator, the dynamical Spectra of Stretching Numbers, the Spectral Distance, and the Relative Lyapunov Indicator. They are combined in an efficient way, allowing the sharing of differential equations whenever this is possible, and the individual stopping of their computation when any of them saturates.Comment: 26 pages, 9 black-and-white figures. Accepted for publication in Astronomy and Computing (Elsevier

On a possible origin for the lack of old star clusters in the Small Magellanic Cloud

We model the dynamical interaction between the Small and Large Magellanic Clouds and their corresponding stellar cluster populations. Our goal is to explore whether the lack of old clusters ($\gtrsim 7$ Gyr) in the Small Magellanic Cloud (SMC) can be the result of the capture of clusters by the Large Magellanic Cloud (LMC), as well as their ejection due to the tidal interaction between the two galaxies. For this purpose we perform a suite of numerical simulations probing a wide range of parameters for the orbit of the SMC about the LMC. We find that, for orbital eccentricities $e \geq 0.4$, approximately 15 per cent of the SMC clusters are captured by the LMC. In addition, another 20 to 50 per cent of its clusters are ejected into the intergalactic medium. In general, the clusters lost by the SMC are the less tightly bound cluster population. The final LMC cluster distribution shows a spatial segregation between clusters that originally belonged to the LMC and those that were captured from the SMC. Clusters that originally belonged to the SMC are more likely to be found in the outskirts of the LMC. Within this scenario it is possible to interpret the difference observed between the star field and cluster SMC Age-Metallicity Relationships for ages $\gtrsim 7$ Gyr.Comment: 5 pages, 3 figures, accepted for publication in MNRAS Letter

And yet it moves: The dangers of artificially fixing the Milky Way center of mass in the presence of a massive Large Magellanic Cloud

Motivated by recent studies suggesting that the Large Magellanic Cloud (LMC) could be significantly more massive than previously thought, we explore whether the approximation of an inertial Galactocentric reference frame is still valid in the presence of such a massive LMC. We find that previous estimates of the LMC's orbital period and apocentric distance derived assuming a fixed Milky Way are significantly shortened for models where the Milky Way is allowed to move freely in response to the gravitational pull of the LMC. Holding other parameters fixed, the fraction of models favoring first infall is reduced. Due to this interaction, the Milky Way center of mass within the inner 50 kpc can be significantly displaced in phase-space in a very short period of time that ranges from 0.3 to 0.5 Gyr by as much as 30 kpc and 75 km/s. Furthermore, we show that the gravitational pull of the LMC and response of the Milky Way are likely to significantly affect the orbit and phase space distribution of tidal debris from the Sagittarius dwarf galaxy (Sgr). Such effects are larger than previous estimates based on the torque of the LMC alone. As a result, Sgr deposits debris in regions of the sky that are not aligned with the present-day Sgr orbital plane. In addition, we find that properly accounting for the movement of the Milky Way around its common center of mass with the LMC significantly modifies the angular distance between apocenters and tilts its orbital pole, alleviating tensions between previous models and observations. While these models are preliminary in nature, they highlight the central importance of accounting for the mutual gravitational interaction between the MW and LMC when modeling the kinematics of objects in the Milky Way and Local Group.Comment: Accepted for publication in ApJ; 16 pages, 11 figure

Consenso SECOT artrosis femorotibial medial.

Se presenta un consenso elaborado por SECOT sobre la actuación en la artrosis del compartimento medial de la rodilla para establecer criterios y recomendaciones clínicas orientadas a unificar criterios en su manejo, abordando los factores implicados en la patogenia de la artrosis femorotibial medial de rodilla, la utilidad de las técnicas diagnósticas por la imagen y la utilidad de la artroscopia. También se analizarán los tratamientos conservadores y el tratamiento quirúrgico. Los expertos consultados muestran consenso (acuerdo o desacuerdo)en el 65,85% de los ítems planteados, dejando 14 ítems donde no se encontró el consenso que se enmarcaron en la etiopatogenia de la artrosis, el valor de la RM en la patología degenerativa,la utilidad de los COX-2 y de los fármacos condroprotectores, así como sobre la técnica idónea de la osteotomía valguizante.© 2013 SECOT. Publicado por Elsevier España, S.L

A note on preservation of generalized fredholm spectra in berkani’s sense

In this paper, we study the relationships between the spectra derived from B-Fredholm theory corresponding to two given bounded linear operators. The main goal of this paper is to obtain sufficient conditions for which the spectra derived from B-Fredholm theory corresponding to two given operators are respectively the same. Among other results, we prove that B-Fredholm type spectral properties for an operator and its restriction are equivalent, as well as obtain conditions for which B-Fredholm type spectral properties corresponding to two given operators are the same. As application of our results, we obtain conditions for which the above mentioned spectra and the spectra derived from the classical Fredholm theory are the same

Integrated dual-wavelength AWG laser for sub-terahertz wave generation

We present a monolithically integrated ring dual-wavelength semiconductor laser in which both wavelengths (¿1 and ¿2) are generated and amplified by the same semiconductor optical amplifier (SOA). An arrayed waveguide grating (AWG) is used as intra-cavity filter to combine the two wavelengths. The use of a Mach-Zehnder construction allows equalizing actively the power of ¿1 and ¿2 and tuning their frequencies. An analytical model is exploited to investigate the influence of crosstalk on the functioning of the device and to identify a calibration strategy. The device has been fabricated using active/passive integration technology on a standardized photonic integration platform

A new method to find the potential center of <i>N</i>-body systems

We present a new and fast method to nd the potential center of an N-body distribution. The method uses an iterative algorithm which exploits the fact that the gradient of the potential is null at its center: it uses a smoothing radius to avoid getting trapped in secondary minima. We have tested this method on several random realizations of King models (in which the numerical computation of this center is rather dicult, due to the constant density within their cores), and compared its performance and accuracy against a more straightforward, but computer intensive method, based on cartesian meshes of increasing spatial resolution. In all cases, both methods converged to the same center, within the mesh resolution, but the new method is two orders of magnitude faster. We have also tested the method with one astronomical problem: the evolution of a 105 particle King model orbiting around a xed potential that represents our Galaxy. We used a spherical harmonics expansion N-body code, in which the potential center determination is crucial for the correct force computation. We compared this simulation with another one in which a method previously used to determine the expansion center is employed (White 1983). Our routine gives better results in energy conservation and mass loss.Se presenta un método rápido para encontrar el centro del potencial de una distribución de N-cuerpos. El método usa un algoritmo iterativo que aprovecha el hecho de que el gradiente del potencial es nulo en su centro; emplea asimismo un radio de suavizado para evitar quedar atrapado en mínimos locales. Se ha probado el método con modelos de King (cuyos núcleos, de densidad relativamente constante, hacen particularmente difícil la determinación numérica de este centro), y se ha comparado su eficiencia y precisión con un método más directo, aunque de cálculo intensivo, basado en mallas cartesianas de resolución espacial creciente. En todos los casos, ambos métodos convergen al mismo centro dentro de la resolución de la malla, aunque el método iterativo es dos órdenes de magnitud más rápido. Utilizamos este método en un problema astronómico: la evolución de un modelo de King de 105 partículas, en órbita alrededor de un potencial fijo representativo de nuestra Galaxia. Se utilizó un código de N-cuerpos con expansión en armónicos esféricos, en el que la determinación del centro del potencial es esencial para un cálculo correcto de las fuerzas. Se comparó esta simulación con el mismo código pero con un método empleado anteriormente para determinar el centro de expansión (White 1983). Con nuestra rutina se obtienen mejores resultados en la conservación de energía y de la masa.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

A new method to find the potential center of <i>N</i>-body systems

We present a new and fast method to nd the potential center of an N-body distribution. The method uses an iterative algorithm which exploits the fact that the gradient of the potential is null at its center: it uses a smoothing radius to avoid getting trapped in secondary minima. We have tested this method on several random realizations of King models (in which the numerical computation of this center is rather dicult, due to the constant density within their cores), and compared its performance and accuracy against a more straightforward, but computer intensive method, based on cartesian meshes of increasing spatial resolution. In all cases, both methods converged to the same center, within the mesh resolution, but the new method is two orders of magnitude faster. We have also tested the method with one astronomical problem: the evolution of a 105 particle King model orbiting around a xed potential that represents our Galaxy. We used a spherical harmonics expansion N-body code, in which the potential center determination is crucial for the correct force computation. We compared this simulation with another one in which a method previously used to determine the expansion center is employed (White 1983). Our routine gives better results in energy conservation and mass loss.Se presenta un método rápido para encontrar el centro del potencial de una distribución de N-cuerpos. El método usa un algoritmo iterativo que aprovecha el hecho de que el gradiente del potencial es nulo en su centro; emplea asimismo un radio de suavizado para evitar quedar atrapado en mínimos locales. Se ha probado el método con modelos de King (cuyos núcleos, de densidad relativamente constante, hacen particularmente difícil la determinación numérica de este centro), y se ha comparado su eficiencia y precisión con un método más directo, aunque de cálculo intensivo, basado en mallas cartesianas de resolución espacial creciente. En todos los casos, ambos métodos convergen al mismo centro dentro de la resolución de la malla, aunque el método iterativo es dos órdenes de magnitud más rápido. Utilizamos este método en un problema astronómico: la evolución de un modelo de King de 105 partículas, en órbita alrededor de un potencial fijo representativo de nuestra Galaxia. Se utilizó un código de N-cuerpos con expansión en armónicos esféricos, en el que la determinación del centro del potencial es esencial para un cálculo correcto de las fuerzas. Se comparó esta simulación con el mismo código pero con un método empleado anteriormente para determinar el centro de expansión (White 1983). Con nuestra rutina se obtienen mejores resultados en la conservación de energía y de la masa.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

On the hereditary character of new strong variations of weyl type theorems

Berkani and Kachad [18], [19], and Sanabria et al. [32], introduced and studied strong variations of Weyl type Theorems. In this paper, we study the behavior of these strong variations of Weyl type theorems for an operator T on a proper closed and Tinvariant subspace W ⊆ X such that T n (X) ⊆ W for some n ≥ 1, where T ∈ L(X) and X is an infinite-dimensional complex Banach space. The main purpose of this paper is to prove that for these subspaces (which generalize the case T n (X) closed for some n ≥ 0), these strong variations of Weyl type theorems are preserved from T to its restriction on W and vice-versa. As consequence of our results, we give sufficient conditions for which these strong variations of Weyl type Theorems are equivalent for two given operators. Also, some applications to multiplication operators acting on the boundary variation space BV [0, 1] are given