Numerical analysis of the one-mode solutions in the Fermi-Pasta-Ulam system

The stability of the one-mode nonlinear solutions of the Fermi-Pasta-Ulam - $\beta$ system is numerically investigated. No external perturbation is considered for the one-mode exact analytical solutions, the only perturbation being that introduced by computational errors in numerical integration of motion equations. The threshold energy for the excitation of the other normal modes and the dynamics of this excitation are studied as a function of the parameter $\mu$ characterizing the nonlinearity, the energy density $\epsilon$ and the number N of particles of the system. The achieved results confirm in part previous results, obtained with a linear analysis of the problem of the stability, and clarify the dynamics by which the one-mode exchanges energy with the other modes with increasing energy density. In a range of energy density near the threshold value and for various values of the number of particles N, the nonlinear one-mode exchanges energy with the other linear modes for a very short time, immediately recovering all its initial energy. This sort of recurrence is very similar to Fermi recurrences, even if in the Fermi recurrences the energy of the initially excited mode changes continuously and only periodically recovers its initial value. A tentative explanation of this intermittent behaviour, in terms of Floquet's theorem, is proposed.Comment: 37 pages, 41 figure

Euclidean distance geometry and applications

Euclidean distance geometry is the study of Euclidean geometry based on the concept of distance. This is useful in several applications where the input data consists of an incomplete set of distances, and the output is a set of points in Euclidean space that realizes the given distances. We survey some of the theory of Euclidean distance geometry and some of the most important applications: molecular conformation, localization of sensor networks and statics.Comment: 64 pages, 21 figure

The Student City. Strategic Planning for Student Communities in EU Cities

Students are the citizens and the high-skilled working class of tomorrow. They keep cities lively and diverse. They are the main consumers of cultural and recreational facilities. They have a distinct expenditure pattern that in some cases is crucial to support the economy of whole cities or specific neighborhoods. Increased international students' mobility is a major vector of socio-economic integration between regions of Europe. However, the conditions for a full integration of student communities in local communities are not always met. Students are still an "invisible population", with little space in local policy, no decision power, and an ambiguous role in social development. The importance of human capital as a determinant of the competitiveness of cities demands pro-active, integral city policies targeting this community. Whereas education programs are generally carried out at the national or regional level, they often neglect the "urban" dimension of the issue, forgetting that human capital is highly mobile, and that it needs to be attracted, welcomed and managed locally. A new EURICUR study intends to contribute to the elaboration of a framework for comprehensive strategic action aiming at the integration of student communities in urban development. To this aim, the essential characteristics of the relationship of students with host communities in European cities have been analysed, as well as the role of higher education institutions and other actors in building the "student-friendly" city. This framework has been tested in nine European cities: Rotterdam, Utrecht and Eindhoven (NL), München (D), Lyon and Lille (F), Venice (I), Birmingham (GB) and Helsinki (SF). A wide typology of situations and problems has been found, with some common points that are clear indications for policymakers. To name a few, the importance that firms today attach to flexible, locally-oriented education curricula, which puts increased pressure on HEIs to work together with local governments in the definition of their supply; and the importance of diverse, versatile student communities in building the creative city, which underscores the role of campus planning but also solicits a socially responsible attitude of firms in enhancing the quality of education facilities.

Memory effects in a Markov chain dephasing channel

We study a dephasing channel with memory, modelled by a Markov chain. We show that even weak memory effects have a detrimental impact on the performance of quantum error correcting schemes designed for uncorrelated errors. We also discuss an alternative scheme that takes advantage of memory effects to protect quantum information.Comment: 5 pages, 1 figure, NIC@QS proceeding