Non-equilibrium Statistical Mechanics of Anharmonic Crystals with Self-consistent Stochastic Reservoirs

We consider a d-dimensional crystal with an arbitrary harmonic interaction and an anharmonic on-site potential, with stochastic Langevin heat bath at each site. We develop an integral formalism for the correlation functions that is suitable for the study of their relaxation (time decay) as well as their behavior in space. Furthermore, in a perturbative analysis, for the one-dimensional system with weak coupling between the sites and small quartic anharmonicity, we investigate the steady state and show that the Fourier's law holds. We also obtain an expression for the thermal conductivity (for arbitrary next-neighbor interactions) and give the temperature profile in the steady state

Nonequilibrium dynamics of a stochastic model of anomalous heat transport: numerical analysis

We study heat transport in a chain of harmonic oscillators with random elastic collisions between nearest-neighbours. The equations of motion of the covariance matrix are numerically solved for free and fixed boundary conditions. In the thermodynamic limit, the shape of the temperature profile and the value of the stationary heat flux depend on the choice of boundary conditions. For free boundary conditions, they also depend on the coupling strength with the heat baths. Moreover, we find a strong violation of local equilibrium at the chain edges that determine two boundary layers of size $\sqrt{N}$ (where $N$ is the chain length), that are characterized by a different scaling behaviour from the bulk. Finally, we investigate the relaxation towards the stationary state, finding two long time scales: the first corresponds to the relaxation of the hydrodynamic modes; the second is a manifestation of the finiteness of the system.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica

Thermodynamic entropy production fluctuation in a two dimensional shear flow model

We investigate fluctuations in the momentum flux across a surface perpendicular to the velocity gradient in a stationary shear flow maintained by either thermostated deterministic or by stochastic boundary conditions. In the deterministic system the Gallavotti-Cohen (GC)relation for the probability of large deviations, which holds for the phase space volume contraction giving the Gibbs ensemble entropy production, never seems to hold for the flux which gives the hydrodynamic entropy production. In the stochastic case the GC relation is found to hold for the total flux, as predicted by extensions of the GC theorem but not for the flux across part of the surface. The latter appear to satisfy a modified GC relation. Similar results are obtained for the heat flux in a steady state produced by stochastic boundaries at different temperatures.Comment: 9 postscript figure

The October 2000 flooding in Valle d'Aosta (Italy): Event description and land planning measures for the risk mitigation

On October 13-16th, 2000 heavy rainfalls in the Northwestern Italian Alps caused huge flooding and landslides with significant damages to houses and infrastructures and several life losses. In this paper a description of the main events that affected Valle d’Aosta’s region and the subsequent land planning measures adopted for the risk mitigation are presented. After a first meteorological and hydrological framing, based on the data of the regional monitoring system (that pointed out rainfalls up to 236 mm in 24 h also in high‐altitude zones, because of the rise of the isotherm 0°C around 3000 m above sea level), the main effects of the event (extensive flooding, landslides, soil slips and debris flows) in the regional catchment of the Dora Baltea river are described. Through aerial and direct surveys those effects have been transferred into a thematic cartography within two months from the event, in order to have detailed elements for the technical, administrative and political land planning decisions, and, on this basis, a new regional directive containing detailed measures for the hydro‐geological risk mitigation and land safety has been adopted. © 2003 by Taylor nad Francis Group, LLC

Thermal conductivity of the Toda lattice with conservative noise

We study the thermal conductivity of the one dimensional Toda lattice perturbed by a stochastic dynamics preserving energy and momentum. The strength of the stochastic noise is controlled by a parameter $\gamma$. We show that heat transport is anomalous, and that the thermal conductivity diverges with the length $n$ of the chain according to $\kappa(n) \sim n^\alpha$, with $0 < \alpha \leq 1/2$. In particular, the ballistic heat conduction of the unperturbed Toda chain is destroyed. Besides, the exponent $\alpha$ of the divergence depends on $\gamma$