Fractional Noether's Theorem with Classical and Riemann-Liouville Derivatives

We prove a Noether type symmetry theorem to fractional problems of the calculus of variations with classical and Riemann-Liouville derivatives. As result, we obtain constants of motion (in the classical sense) that are valid along the mixed classical/fractional Euler-Lagrange extremals. Both Lagrangian and Hamiltonian versions of the Noether theorem are obtained. Finally, we extend our Noether's theorem to more general problems of optimal control with classical and Riemann-Liouville derivatives.Comment: This is a preprint of a paper whose final and definite form will be published in: 51st IEEE Conference on Decision and Control, December 10-13, 2012, Maui, Hawaii, USA. Article Source/Identifier: PLZ-CDC12.1832.45c07804. Submitted 08-March-2012; accepted 17-July-2012. arXiv admin note: text overlap with arXiv:1001.450

On the White Dwarf distances to Galactic Globular Clusters

We analyze in detail various possible sources of systematic errors on the distances of globular clusters derived by fitting a local template DA white dwarf sequence to the cluster counterpart (the so-called WD-fitting technique). We find that the unknown thickness of the hydrogen layer of white dwarfs in clusters plays a non negligible role. For reasonable assumptions - supported by the few sparse available observational constraints - about the unknown mass and thickness of the hydrogen layer for the cluster white dwarfs, a realistic estimate of the systematic error on the distance is within +-0.10 mag. However, particular combinations of white dwarf masses and envelope thicknesses - which at present cannot be excluded a priori - could produce larger errors. Contamination of the cluster DA sequence by non-DA white dwarfs introduces a very small systematic error of about -0.03 mag in the Mv/(V-I) plane, but in the Mv/(B-V) plane the systematic error amounts to ~ +0.20 mag. Contamination by white dwarfs with helium cores should not influence appreciably the WD-fitting distances. Finally, we obtain a derivative D((m-M)v)/D(E(B-V))~ -5.5 for the WD-fitting distances, which is very similar to the dependence found when using the Main Sequence fitting technique.Comment: 12 pages, 11 figures A&A, accepted for publicatio

Axions and White Dwarfs

White dwarfs are almost completely degenerate objects that cannot obtain energy from the thermonuclear sources and their evolution is just a gravothermal process of cooling. The simplicity of these objects, the fact that the physical inputs necessary to understand them are well identified, although not always well understood, and the impressive observational background about white dwarfs make them the most well studied Galactic population. These characteristics allow to use them as laboratories to test new ideas of physics. In this contribution we discuss the robustness of the method and its application to the axion case.Comment: 4 pages, 1 figure, to appear in the Proceedings for the 6th Patras meeting on Axions, WIMPs and WISP