A new view of the Lindemann criterion

The Lindemann criterion is reformulated in terms of the average shear modulus $G_c$ of the melting crystal, indicating a critical melting shear strain which is necessary to form the many different inherent states of the liquid. In glass formers with covalent bonds, one has to distinguish between soft and hard degrees of freedom to reach agreement. The temperature dependence of the picosecond mean square displacements of liquid and crystal shows that there are two separate contributions to the divergence of the viscosity with decreasing temperature: the anharmonic increase of the shear modulus and a diverging correlation length .Comment: 4 pages, 3 figure

Nonextensive Thermostatistics and the HH-Theorem Revisited

In this paper we present a new derivation of the $H$-theorem and the corresponding collisional equilibrium velocity distributions, within the framework of Tsallis' nonextensive thermostatistics. Unlike previous works, in our derivation we do not assume any modification on the functional form of Boltzmann's original "molecular chaos hypothesis". Rather, we explicitly introduce into the collision scenario, the existence of statistical dependence between the molecules before the collision has taken place, through a conditional distribution $f(\vec{v}_2|\vec{v}_1)$. In this approach, different equilibrium scenarios emerge depending on the value of the nonextensive entropic parameter.Comment: 6 pages, 1 figure, to appear in Physica

Upper limits to the magnetic field in central stars of planetary nebulae

More than about twenty central stars of planetary nebulae (CSPN) have been observed spectropolarimetrically, yet no clear, unambiguous signal of the presence of a magnetic field in these objects has been found. We perform a statistical (Bayesian) analysis of all the available spectropolarimetric observations of CSPN to constrain the magnetic fields on these objects. Assuming that the stellar field is dipolar and that the dipole axis of the objects are oriented randomly (isotropically), we find that the dipole magnetic field strength is smaller than 400 G with 95% probability using all available observations. The analysis introduced allows integration of future observations to further constrain the parameters of the distribution, and it is general, so that it can be easily applied to other classes of magnetic objects. We propose several ways to improve the upper limits found here.Comment: 7 pages, 3 figures, accepted for publication in Ap

A search for magnetic fields on central stars in planetary nebulae

One of the possible mechanisms responsible for the panoply of shapes in planetary nebulae is the presence of magnetic fields that drive the ejection of ionized material during the proto-planetary nebula phase. Therefore, detecting magnetic fields in such objects is of key importance for understanding their dynamics. Still, magnetic fields have not been detected using polarimetry in the central stars of planetary nebulae. Circularly polarized light spectra have been obtained with the Focal Reducer and Low Dispersion Spectrograph at the Very Large Telescope of the European Southern Observatory and the Intermediate dispersion Spectrograph and Imaging System at the William Herschel Telescope. Nineteen planetary nebulae spanning very different morphology and evolutionary stages have been selected. Most of central stars have been observed at different rotation phases to point out evidence of magnetic variability. In this paper, we present the result of two observational campaigns aimed to detect and measure the magnetic field in the central stars of planetary nebulae on the basis of low resolution spectropolarimetry. In the limit of the adopted method, we can state that large scale fields of kG order are not hosted on the central star of planetary nebulae.Comment: Paper accepted to be published in Astronomy and Astrophysics on 20/01/201