Theory summary. Hard Probes 2012

I provide a summary of the theoretical talks in Hard Probes 2012 together with some personal thoughts about the present and the future of the field.Comment: 8 pages. Proceedings of the conference Hard Probes 2012 - Sardinia - Italy - May 27 -June 1 2012 --- Comments welcom

Small clique number graphs with three trivial critical ideals

The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. In this article we provide a set of minimal forbidden graphs for the set of graphs with at most three trivial critical ideals. Then we use these forbidden graphs to characterize the graphs with at most three trivial critical ideals and clique number equal to 2 and 3.Comment: 33 pages, 3 figure

Capture of field stars by giant interstellar clouds: the formation of moving stellar groups

In the solar neighbourhood, there are moving groups of stars with similar ages and others of stars with heterogeneous ages as the field stars. To explain these facts, we have constructed a simple model of three phases. Phase A: a giant interstellar cloud is uniformly accelerated (or decelerated) with respect to the field stars during a relatively short period of time (10 Myr) and the cloud's mass is uniformly increased; phase B: the acceleration (or deceleration) and mass accretion of the cloud cease. The star formation spreads throughout the cloud, giving origin to stellar groups of similar ages; and phase C: the cloud loses all its gaseous component at a constant rate and in parallel is uniformly decelerated (or accelerated) until reaching the initial velocity of phase A (case 1) or the velocity of the gas cloud remains constant (case 2). Both cases give equivalent results. The system equations for the star motions governed by a time-dependent gravitational potential of the giant cloud and referred to a coordinate system co-moving with the cloud have been solved analytically. We have assumed a homogeneous spheroidal cloud of fixed semi-major axis a=300 pc and of an initial density of 7 at cm^{-3}, with a density increment of 100 per cent and a cloud's velocity variation of 30 km s^{-1}, from the beginning to the end of Phase A. The result is that about 4 per cent of the field stars that are passing within the volume of the cloud at the beginning of phase A is captured. The Sun itself could have been captured by the same cloud that originated the moving groups of the solar neighbourhood.Comment: 13 pages, 15 figure