Asymptotics of the solutions of the stochastic lattice wave equation

We consider the long time limit theorems for the solutions of a discrete wave equation with a weak stochastic forcing. The multiplicative noise conserves the energy and the momentum. We obtain a time-inhomogeneous Ornstein-Uhlenbeck equation for the limit wave function that holds both for square integrable and statistically homogeneous initial data. The limit is understood in the point-wise sense in the former case, and in the weak sense in the latter. On the other hand, the weak limit for square integrable initial data is deterministic

Long time, large scale limit of the Wigner transform for a system of linear oscillators in one dimension

We consider the long time, large scale behavior of the Wigner transform W_\eps(t,x,k) of the wave function corresponding to a discrete wave equation on a 1-d integer lattice, with a weak multiplicative noise. This model has been introduced in Basile, Bernardin, and Olla to describe a system of interacting linear oscillators with a weak noise that conserves locally the kinetic energy and the momentum. The kinetic limit for the Wigner transform has been shown in Basile, Olla, and Spohn. In the present paper we prove that in the unpinned case there exists $\gamma_0>0$ such that for any $\gamma\in(0,\gamma_0]$ the weak limit of W_\eps(t/\eps^{3/2\gamma},x/\eps^{\gamma},k), as \eps\ll1, satisfies a one dimensional fractional heat equation $\partial_t W(t,x)=-\hat c(-\partial_x^2)^{3/4}W(t,x)$ with $\hat c>0$. In the pinned case an analogous result can be claimed for W_\eps(t/\eps^{2\gamma},x/\eps^{\gamma},k) but the limit satisfies then the usual heat equation

Thermal conductivity in harmonic lattices with random collisions

We review recent rigorous mathematical results about the macroscopic behaviour of harmonic chains with the dynamics perturbed by a random exchange of velocities between nearest neighbor particles. The random exchange models the effects of nonlinearities of anharmonic chains and the resulting dynamics have similar macroscopic behaviour. In particular there is a superdiffusion of energy for unpinned acoustic chains. The corresponding evolution of the temperature profile is governed by a fractional heat equation. In non-acoustic chains we have normal diffusivity, even if momentum is conserved.Comment: Review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Superdiffusion of energy in Hamiltonian systems perturbed by a conservative noise

We review some recent results on the anomalous diffusion of energy in systems of 1D coupled oscillators and we revisit the role of momentum conservation.Comment: Proceedings of the conference PSPDE 2012 https://sites.google.com/site/meetingpspde

The new servo-spill power converter of the CERN SPS machine

The so-called servo-spill system of the SPS machine requires a very specific power converter to be used as the power actuator of the system. Due to this particular function, the main performance required, for this power converter, is an unusual large signal current bandwidth of up to 1.5 kHz. The procurement is based on a similar industrial product using switch mode technology. This paper describes the main power part as well as the control approach chosen to fulfil the specific requirements of this power converter. Final operational results are also presented

Coulomb-Volkov approach of ionization by extreme ultraviolet laser pulses in the subfemtosecond regime

In conditions where the interaction betweeen an atom and a short high-frequency extreme ultraviolet laser pulse is a perturbation, we show that a simple theoretical approach, based on Coulomb-Volkov-type states, can make reliable predictions for ionization. To avoid any additional approximation, we consider here a standard case : the ionization of hydrogen atoms initially in their ground state. For any field parameter, we show that the method provides accurate energy spectra of ejected electrons, including many above threshold ionization peaks, as long as the two following conditions are simultaneously fulfilled : (i) the photon energy is greater than or equal to the ionization potential ; (ii) the ionization process is not saturated. Thus, ionization of atoms or molecules by the high order harmonic laser pulses which are generated at present may be addressed through this Coulomb-Volkov treatment.Comment: 19 pages including 5 figures and figure caption

The impact of two-dimensional elastic disk

The impact of a two-dimensional elastic disk with a wall is numerically studied. It is clarified that the coefficient of restitution (COR) decreases with the impact velocity. The result is not consistent with the recent quasi-static theory of inelastic collisions even for very slow impact. The abrupt drop of COR is found due to the plastic deformation of the disk, which is assisted by the initial internal motion.(to be published in J. Phys. Soc. Jpn.)Comment: 6 Pages,2 figure

Destabilizing Taylor-Couette flow with suction

We consider the effect of radial fluid injection and suction on Taylor-Couette flow. Injection at the outer cylinder and suction at the inner cylinder generally results in a linearly unstable steady spiralling flow, even for cylindrical shears that are linearly stable in the absence of a radial flux. We study nonlinear aspects of the unstable motions with the energy stability method. Our results, though specialized, may have implications for drag reduction by suction, accretion in astrophysical disks, and perhaps even in the flow in the earth's polar vortex.Comment: 34 pages, 9 figure

LCC analysis for glued laminated timber components exposed in external

The aim of the experimentation is to characterize the performances of glued laminated timber components exposed to atmospheric agents, in the light of the concept of Life Cycle Cost, particularly emphasized in the Italian new legislation on public works. In fact, it could be seen that the design of the construction details and the initial characteristics of glue laminated timber components, require a particular attention to avoid errors that may undermine the possibility to perform the structural functions for which, above all, this material it is dedicated. The experimentation consisted of a series of tests aimed to identify the performance of glued laminated timber beams taken in site, after a work executed some years ago on a theatre built in Roman era, and to compare them with similarly manufactured new elements. The tests performed were thermography, ultrasound, Wood-Pecker penetrometer, mechanical characterization. The results will be used to begin setting limits and conditions for outdoor use of glue laminated timber, and assume a reliable life cycle, and consequently identify the most appropriate maintenance strategy for the LCC