Dispersion in optical fibers and timing for particle identification

In the framework of the TOF Wall laser calibration system of the HARP experiment, a study of time dispersion properties of mono-mode and multi-mode optical fibers in the green band (532 nm) has been carried out. Dispersion less than 4 ps/m has been obtained with $\approx$10 $\mu$m core diameter fibers.Comment: 2 pages, 1 .ps figure, moriond.sty included. Talk given at the XXXVIIth Rencontres de Moriond on Electroweak Interactions and Unified Theories, Les Arcs, France, 9-16 Mar 200

Long time stability of small amplitude Breathers in a mixed FPU-KG model

In the limit of small couplings in the nearest neighbor interaction, and small total energy, we apply the resonant normal form result of a previous paper of ours to a finite but arbitrarily large mixed Fermi-Pasta-Ulam Klein-Gordon chain, i.e. with both linear and nonlinear terms in both the on-site and interaction potential, with periodic boundary conditions. An existence and orbital stability result for Breathers of such a normal form, which turns out to be a generalized discrete Nonlinear Schr\"odinger model with exponentially decaying all neighbor interactions, is first proved. Exploiting such a result as an intermediate step, a long time stability theorem for the true Breathers of the KG and FPU-KG models, in the anti-continuous limit, is proven.Comment: Substantial revision in the presentation. Stability time scale slightly modifie

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\'

Approximation of small-amplitude weakly coupled oscillators with discrete nonlinear Schrodinger equations

Small-amplitude weakly coupled oscillators of the Klein-Gordon lattices are approximated by equations of the discrete nonlinear Schrodinger type. We show how to justify this approximation by two methods, which have been very popular in the recent literature. The first method relies on a priori energy estimates and multi-scale decompositions. The second method is based on a resonant normal form theorem. We show that although the two methods are different in the implementation, they produce equivalent results as the end product. We also discuss applications of the discrete nonlinear Schrodinger equation in the context of existence and stability of breathers of the Klein--Gordon lattice

Existence and continuous approximation of small amplitude breathers in 1D and 2D Klein--Gordon lattices

We construct small amplitude breathers in 1D and 2D Klein--Gordon infinite lattices. We also show that the breathers are well approximated by the ground state of the nonlinear Schroedinger equation. The result is obtained by exploiting the relation between the Klein Gordon lattice and the discrete Non Linear Schroedinger lattice. The proof is based on a Lyapunov-Schmidt decomposition and continuum approximation techniques introduced in [7], actually using its main result as an important lemma

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