A method for determining the radius of an open cluster from stellar proper motions

We propose a method for calculating the radius of an open cluster in an objective way from an astrometric catalogue containing, at least, positions and proper motions. It uses the minimum spanning tree (hereinafter MST) in the proper motion space to discriminate cluster stars from field stars and it quantifies the strength of the cluster-field separation by means of a statistical parameter defined for the first time in this paper. This is done for a range of different sampling radii from where the cluster radius is obtained as the size at which the best cluster-field separation is achieved. The novelty of this strategy is that the cluster radius is obtained independently of how its stars are spatially distributed. We test the reliability and robustness of the method with both simulated and real data from a well-studied open cluster (NGC 188), and apply it to UCAC4 data for five other open clusters with different catalogued radius values. NGC 188, NGC 1647, NGC 6603 and Ruprecht 155 yielded unambiguous radius values of 15.2+/-1.8, 29.4+/-3.4, 4.2+/-1.7 and 7.0+/-0.3 arcmin, respectively. ASCC 19 and Collinder 471 showed more than one possible solution but it is not possible to know whether this is due to the involved uncertainties or to the presence of complex patterns in their proper motion distributions, something that could be inherent to the physical object or due to the way in which the catalogue was sampled.Comment: 12 pages including 14 figures and 1 table. Accepted for publication in MNRA

Nagel scaling and relaxation in the kinetic Ising model on a n-isotopic chain

The kinetic Ising model on a n-isotopic chain is considered in the framework of Glauber dynamics. The chain is composed of N segments with n sites, each one occupied by a different isotope. Due to the isotopic mass difference, the n spins in each segment have different relaxation times in the absence of the interactions, and consequently the dynamics of the system is governed by multiple relaxation mechanisms. The solution is obtained in closed form for arbitrary n, by reducing the problem to a set of n coupled equations, and it is shown rigorously that the critical exponent z is equal to 2. Explicit results are obtained numerically for any temperature and it is also shown that the dynamic susceptibility satisfies the new scaling (Nagel scaling) proposed for glass-forming liquids. This is in agreement with our recent results (L. L. Goncalves, M. Lopez de Haro, J. Taguena-Martinez and R. B. Stinchcombe, Phys. Rev. Lett. 84, 1507 (2000)), which relate this new scaling function to multiple relaxation processes.Comment: 4 pages, 2 figures, presented at Ising Centennial Colloquium, to be published in the Proceedings (Brazilian Journal of Physics.

From car to bike. Marketing and dialogue as a driver of change

The Paris Climate Agreement has sent a key message to the international community regarding the need to increase efforts to move towards a low-carbon economy and help slow climate change, while underpinning global long-term economic growth and sustainable development. COP 21 recognizes the social, economic and environmental value of voluntary mitigation actions and their co-benefits for adaptation, health and sustainable development. In this framework, the PTP Cycle project, running from 2013 to 2016 and funded by the European Commission through the Intelligent Energy Europe program, introduces a non-market approach through voluntary participation in the adoption of sustainable transport modes such as cycling, based on marketing to potential customers through Personalized Travel Plans. The medium-sized city of Burgos (Spain) and the cities of Ljubljana, Riga, Antwerp and London (boroughs of Haringey and Greenwich) developed a new policy instrument (Personalized Travel Plans) in order to increase bike patronage. Beyond potential savings of CO2, the results show that PTP as a form of Active Mobility Consultancy is a suitable instrument to influence modal shift to public transport, walking and cycling, and to address the challenges of climate change, while fostering sustainable transportation by changing mobility behaviour. These results, matching with the state-of-the-art of studies and pilot applications in other countries, allows deriving differentiated results for medium-size and large urban areas

Unitarity of the Leptonic Mixing Matrix

We determine the elements of the leptonic mixing matrix, without assuming unitarity, combining data from neutrino oscillation experiments and weak decays. To that end, we first develop a formalism for studying neutrino oscillations in vacuum and matter when the leptonic mixing matrix is not unitary. To be conservative, only three light neutrino species are considered, whose propagation is generically affected by non-unitary effects. Precision improvements within future facilities are discussed as well.Comment: Standard Model radiative corrections to the invisible Z width included. Some numerical results modified at the percent level. Updated with latest bounds on the rare tau decay. Physical conculsions unchange