An extensive adiabatic invariant for the Klein-Gordon model in the thermodynamic limit

We construct an extensive adiabatic invariant for a Klein-Gordon chain in the thermodynamic limit. In particular, given a fixed and sufficiently small value of the coupling constant $a$, the evolution of the adiabatic invariant is controlled up to times scaling as $\beta^{1/\sqrt{a}}$ for any large enough value of the inverse temperature $\beta$. The time scale becomes a stretched exponential if the coupling constant is allowed to vanish jointly with the specific energy. The adiabatic invariance is exhibited by showing that the variance along the dynamics, i.e. calculated with respect to time averages, is much smaller than the corresponding variance over the whole phase space, i.e. calculated with the Gibbs measure, for a set of initial data of large measure. All the perturbative constructions and the subsequent estimates are consistent with the extensive nature of the system.Comment: 60 pages. Minor corrections with respect to the first version. To appear in Annales Henri Poincar\'

Dynamic and Transparent Analysis of Commodity Production Systems

We propose a framework that provides a programming interface to perform complex dynamic system-level analyses of deployed production systems. By leveraging hardware support for virtualization available nowadays on all commodity machines, our framework is completely transparent to the system under analysis and it guarantees isolation of the analysis tools running on its top. Thus, the internals of the kernel of the running system needs not to be modified and the whole platform runs unaware of the framework. Moreover, errors in the analysis tools do not affect the running system and the framework. This is accomplished by installing a minimalistic virtual machine monitor and migrating the system, as it runs, into a virtual machine. In order to demonstrate the potentials of our framework we developed an interactive kernel debugger, nicknamed HyperDbg. HyperDbg can be used to debug any critical kernel component, and even to single step the execution of exception and interrupt handlers.Comment: 10 pages, To appear in the 25th IEEE/ACM International Conference on Automated Software Engineering, Antwerp, Belgium, 20-24 September 201

FPU phenomenon for generic initial data

The well known FPU phenomenon (lack of attainment of equipartition of the mode--energies at low energies, for some exceptional initial data) suggests that the FPU model does not have the mixing property at low energies. We give numerical indications that this is actually the case. This we show by computing orbits for sets of initial data of full measure, sampled out from the microcanonical ensemble by standard Montecarlo techniques. Mixing is tested by looking at the decay of the autocorrelations of the mode--energies, and it is found that the high--frequency modes have autocorrelations that tend instead to positive values. Indications are given that such a nonmixing property survives in the thermodynamic limit. It is left as an open problem whether mixing obtains within time--scales much longer than the presently available ones

Tail resonances of FPU q-breathers and their impact on the pathway to equipartition

Upon initial excitation of a few normal modes the energy distribution among all modes of a nonlinear atomic chain (the Fermi-Pasta-Ulam model) exhibits exponential localization on large time scales. At the same time resonant anomalies (peaks) are observed in its weakly excited tail for long times preceding equipartition. We observe a similar resonant tail structure also for exact time-periodic Lyapunov orbits, coined q-breathers due to their exponential localization in modal space. We give a simple explanation for this structure in terms of superharmonic resonances. The resonance analysis agrees very well with numerical results and has predictive power. We extend a previously developed perturbation method, based essentially on a Poincare-Lindstedt scheme, in order to account for these resonances, and in order to treat more general model cases, including truncated Toda potentials. Our results give qualitative and semiquantitative account for the superharmonic resonances of q-breathers and natural packets

The Impacts of Airport Centrality in the EU Network and Inter- Airport Competition on Airport Efficiency

In this paper we study the relationship between airport efficiency and two factors: an airport’s centrality in the EU network, and the intensity of competition from alternative airports in the same catchment area. We apply a two-stage econometric model based on the Simar & Wilson (2007) bootstrap procedure to a balanced sample of 57 European airports. We also design and compute our own measures of airport centrality and competition. The results show that efficiency is positively related to centrality in the European network, as measured by a weighted sum of minimal paths passing through the airport in question. The intensity of competition between airports also has a positive effect on efficiency. Our analysis suggests that air transportation policies should focus on increasing competition within important catchment areas (e.g., by investing in infrastructure facilitating access to alternative airports) and enhancing the connectivity of the EU network (e.g., by subsidizing new point-to-point connections between airports with capacity to spare).air transportation, efficiency, network centrality, inter – airports competition.