Drastic fall-off of the thermal conductivity for disordered lattices in the limit of weak anharmonic interactions

We study the thermal conductivity, at fixed positive temperature, of a disordered lattice of harmonic oscillators, weakly coupled to each other through anharmonic potentials. The interaction is controlled by a small parameter $\epsilon > 0$. We rigorously show, in two slightly different setups, that the conductivity has a non-perturbative origin. This means that it decays to zero faster than any polynomial in $\epsilon$ as $\epsilon\rightarrow 0$. It is then argued that this result extends to a disordered chain studied by Dhar and Lebowitz, and to a classical spins chain recently investigated by Oganesyan, Pal and Huse.Comment: 21 page

Groundwater resources in the main ethiopian rift valley: An overview for a sustainable development

In arid and semi-arid areas, human health and economic development depend on water availability, which can be greatly compromised by droughts. In some cases, the presence of natural contaminants may additionally reduce the availability of good quality water. This research analyzed the water resources and hydrochemical characteristics in a rural area of the central Main Ethiopian Rift Valley, particularly in the districts of Shashemene, Arsi Negelle, and Siraro. The study was developed using a census of the main water points (springs and wells) in the area and the sampling and physico-chemical analysis of the water, with particular regard to the fluoride concentration. In many cases, fluoride content exceeded the drinking water limits set by the World Health Organization, even in the absence of anthropogenic contamination. Two different aquifers were recognized: A shallow aquifer related to the eastern escarpment and highlands, and a deep aquifer in the lowland areas of the rift valley on the basis of compositional changes from Ca–Mg/HCO3 to Na–HCO3. The distribution of fluoride, as well as pH and EC values, showed a decrease from the center of the lowlands to the eastern highlands, with similar values closely aligned along an NNE/SSW trend. All these data contribute to creating awareness among and sharing information on the risks with rural communities and local governments to support the adequate use of the available water resources and to plan appropriate interventions to increase access to fresh water, aimed at the sustainable human and rural local development of the region

Nonequilibrium dynamics of a stochastic model of anomalous heat transport

We study the dynamics of covariances in a chain of harmonic oscillators with conservative noise in contact with two stochastic Langevin heat baths. The noise amounts to random collisions between nearest-neighbour oscillators that exchange their momenta. In a recent paper, [S Lepri et al. J. Phys. A: Math. Theor. 42 (2009) 025001], we have studied the stationary state of this system with fixed boundary conditions, finding analytical exact expressions for the temperature profile and the heat current in the thermodynamic (continuum) limit. In this paper we extend the analysis to the evolution of the covariance matrix and to generic boundary conditions. Our main purpose is to construct a hydrodynamic description of the relaxation to the stationary state, starting from the exact equations governing the evolution of the correlation matrix. We identify and adiabatically eliminate the fast variables, arriving at a continuity equation for the temperature profile T(y,t), complemented by an ordinary equation that accounts for the evolution in the bulk. Altogether, we find that the evolution of T(y,t) is the result of fractional diffusion.Comment: Submitted to Journal of Physics A, Mathematical and Theoretica

Geostructural and geomechanical study of the piastrone quarry (Seravezza, Italy) supported by photogrammetry to assess failure mode

The use of non-contact-techniques for rock mass characterization has been growing significantly over the last decade. However, their application to stability assessment of ornamental stone has not yet received much attention from researchers. This study utilizes rock mass data both in terms of slope orientations and degree of fracturing obtained from a point cloud, a set of three-dimensional (3D) points representing a rock mass surface, to (1) investigate the influence of geostructures at different scales and (2) assess quarry stability by determining areas susceptible to different failure types. Multi-resolution point clouds are obtained through several photogrammetric survey techniques to identify important structural elements of the site. By integrating orientation data of discontinuity planes, obtained with a traditional survey, and of traces, outlined on point clouds, several joint sets were identified. Kinematic tests revealed various potential failure modes of the rock slope. Moreover, an analysis of the influence of the discontinuity strength determined by the presence of rock bridges was carried out. The study revealed that the strength of the quarry face is governed by the presence of rock bridges that act to improve the stability condition of the rock fronts

Anomalous thermal conductivity and local temperature distribution on harmonic Fibonacci chains

The harmonic Fibonacci chain, which is one of a quasiperiodic chain constructed with a recursion relation, has a singular continuous frequency-spectrum and critical eigenstates. The validity of the Fourier law is examined for the harmonic Fibonacci chain with stochastic heat baths at both ends by investigating the system size N dependence of the heat current J and the local temperature distribution. It is shown that J asymptotically behaves as (ln N)^{-1} and the local temperature strongly oscillates along the chain. These results indicate that the Fourier law does not hold on the harmonic Fibonacci chain. Furthermore the local temperature exhibits two different distribution according to the generation of the Fibonacci chain, i.e., the local temperature distribution does not have a definite form in the thermodynamic limit. The relations between N-dependence of J and the frequency-spectrum, and between the local temperature and critical eigenstates are discussed.Comment: 10 pages, 4 figures, submitted to J. Phys.: Cond. Ma

Third Order Renormalization Group applied to the attractive one-dimensional Fermi Gas

We consider a Callan-Symanzik and a Wilson Renormalization Group approach to the infrared problem for interacting fermions in one dimension with backscattering. We compute the third order (two-loop) approximation of the beta function using both methods and compare it with the well known multiplicative Gell-Mann Low approach. We point out a previously unnoticed qualitative dependence of the third order fixed point on an arbitrary dimensionless parameter, which strongly suggest the spurious nature of the fixed point.Comment: 16 pages, Revised version, added comment

Heat Conduction in One-Dimensional chain of Hard Discs with Substrate Potential

Heat conduction of one-dimensional chain of equivalent rigid particles in the field of external on-site potential is considered. Zero diameters of the particles correspond to exactly integrable case with divergent heat conduction coefficient. By means of simple analytical model it is demonstrated that for any nonzero particle size the integrability is violated and the heat conduction coefficient converges. The result of the analytical computation is verified by means of numerical simulation in a plausible diapason of parameters and good agreement is observedComment: 14 pages, 7 figure