The evolution of Giant Molecular Filaments

In recent years there has been a growing interest in studying giant molecular filaments (GMFs), which are extremely elongated (> 100pc in length) giant molecular clouds (GMCs). They are often seen as inter-arm features in external spiral galaxies, but have been tentatively associated with spiral arms when viewed in the Milky Way. In this paper, we study the time evolution of GMFs in a high-resolution section of a spiral galaxy simulation, and their link with spiral arm GMCs and star formation, over a period of 11Myrs. The GMFs generally survive the inter-arm passage, although they are subject to a number of processes (e.g. star formation, stellar feedback and differential rotation) which can break the giant filamentary structure into smaller sections. The GMFs are not gravitationally bound clouds as a whole, but are, to some extent, confined by external pressure. Once they reach the spiral arms, the GMFs tend to evolve into more substructured spiral arm GMCs, suggesting that GMFs may be precursors to arm GMCs. Here, they become incorporated into the more complex and almost continuum molecular medium that makes up the gaseous spiral arm. Instead of retaining a clear filamentary shape, their shapes are distorted both by their climb up the spiral potential and their interaction with the gas within the spiral arm. The GMFs do tend to become aligned with the spiral arms just before they enter them (when they reach the minimum of the spiral potential), which could account for the observations of GMFs in the Milky Way.Comment: 15 pages, 11 figures, MNRAS accepte

A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator

In [1,2] we have developed a method (we call it the S-function method) that is successful in treating certain classes of rational second order ordinary differential equations (rational 2ODEs) that are particularly `resistant' to canonical Lie methods and to Darbouxian approaches. In this present paper, we generalize the S-function method making it capable of dealing with a class of elementary 2ODEs presenting elementary functions. Then, we apply this method to a Duffing-Van der Pol forced oscillator, obtaining an entire class of first integrals

Solving 1ODEs with functions

Here we present a new approach to deal with first order ordinary differential equations (1ODEs), presenting functions. This method is an alternative to the one we have presented in [1]. In [2], we have establish the theoretical background to deal, in the extended Prelle-Singer approach context, with systems of 1ODEs. In this present paper, we will apply these results in order to produce a method that is more efficient in a great number of cases. Directly, the solving of 1ODEs is applicable to any problem presenting parameters to which the rate of change is related to the parameter itself. Apart from that, the solving of 1ODEs can be a part of larger mathematical processes vital to dealing with many problems.Comment: 31 page

Explaining Jupiter's magnetic field and equatorial jet dynamics

Spacecraft data reveal a very Earth-like Jovian magnetic field. This is surprising since numerical simulations have shown that the vastly different interiors of terrestrial and gas planets can strongly affect the internal dynamo process. Here we present the first numerical dynamo that manages to match the structure and strength of the observed magnetic field by embracing the newest models for Jupiter's interior. Simulated dynamo action primarily occurs in the deep high electrical conductivity region while zonal flows are dynamically constrained to a strong equatorial jet in the outer envelope of low conductivity. Our model reproduces the structure and strength of the observed global magnetic field and predicts that secondary dynamo action associated to the equatorial jet produces banded magnetic features likely observable by the Juno mission. Secular variation in our model scales to about 2000 nT per year and should also be observable during the one year nominal mission duration.Comment: 7 pages, 4 figures, accepted for publication in Geophysical Research Letter