Dynamic exponent in Extremal models of Pinning

The depinning transition of a front moving in a time-independent random potential is studied. The temporal development of the overall roughness w(L,t) of an initially flat front, $w(t)\propto t^\beta$, is the classical means to have access to the dynamic exponent. However, in the case of front propagation in quenched disorder via extremal dynamics, we show that the initial increase in front roughness implies an extra dependence over the system size which comes from the fact that the activity is essentially localized in a narrow region of space. We propose an analytic expression for the $\beta$ exponent and confirm this for different models (crack front propagation, Edwards-Wilkinson model in a quenched noise, ...).Comment: RevTex, 3 figures .ep

Rheological properties vs Local Dynamics in model disordered materials at Low Temperature

We study the rheological response at low temperature of a sheared model disordered material as a function of the bond rigidity. We find that the flow curves follow a Herschel-Bulkley law, whatever is the bond rigidity, with an exponent close to 0.5. Interestingly, the apparent viscosity can be related to a single relevant time scale $t_{rel}$, suggesting a strong connection between the local dynamics and the global mechanical behaviour. We propose a model based on the competition between the nucleation and the avalanche-like propagation of spatial strain heterogeneities. This model can explain the Herschel-Bulkley exponent on the basis of the size dependence of the heterogeneities on the shear rate.Comment: 9 pages, 7 figure

The non dissipative damping of the Rabi oscillations as a "which-path" information

Rabi oscillations may be viewed as an interference phenomenon due to a coherent superposition of different quantum paths, like in the Young's two-slit experiment. The inclusion of the atomic external variables causes a non dissipative damping of the Rabi oscillations. More generally, the atomic translational dynamics induces damping in the correlation functions which describe non classical behaviors of the field and internal atomic variables, leading to the separability of these two subsystems. We discuss on the possibility of interpreting this intrinsic decoherence as a "which-way" information effect and we apply to this case a quantitative analysis of the complementarity relation as introduced by Englert [Phys. Rev. Lett. \textbf{77}, 2154 (1996)].Comment: 5 pages, 2 figure

Particle displacements in the elastic deformation of amorphous materials: local fluctuations vs. non-affine field

We study the local disorder in the deformation of amorphous materials by decomposing the particle displacements into a continuous, inhomogeneous field and the corresponding fluctuations. We compare these fields to the commonly used non-affine displacements in an elastically deformed 2D Lennard-Jones glass. Unlike the non-affine field, the fluctuations are very localized, and exhibit a much smaller (and system size independent) correlation length, on the order of a particle diameter, supporting the applicability of the notion of local "defects" to such materials. We propose a scalar "noise" field to characterize the fluctuations, as an additional field for extended continuum models, e.g., to describe the localized irreversible events observed during plastic deformation.Comment: Minor corrections to match the published versio

Risque-Pays et Investissements Directs Etrangers au Benin

The purpose of this paper is to analyze the impact of country risk on the entry of foreign direct investment into Benin For this purpose at least one variable of each country risk component political risk economic risk and financial risk has been taken into account in the model From the Hendry-based Error Correction Model ECM over the period from 1980 to 2015 the results from the econometric estimation suggest that FDI inflow is positively explained by the rate of economic growth and the rate while foreign debt and corruption do not favor the growth of FDI in Benin For the country to become a pole of attractiveness of FDI it is imperative to clean up the institutional framework in the field of political right to undertake economic reforms and to work for a real financial independence to ensure its solvency and self-financin

Collective Behavior of Asperities in Dry Friction at Small Velocities

We investigate a simple model of dry friction based on extremal dynamics of asperities. At small velocities, correlations develop between the asperities, whose range becomes infinite in the limit of infinitely slow driving, where the system is self-organized critical. This collective phenomenon leads to effective aging of the asperities and results in velocity dependence of the friction force in the form $F\sim 1- \exp(-1/v)$.Comment: 7 pages, 8 figures, revtex, submitted to Phys. Rev.

Inhomogeneous elastic response of silica glass

Using large scale molecular dynamics simulations we investigate the properties of the {\em non-affine} displacement field induced by macroscopic uniaxial deformation of amorphous silica,a strong glass according to Angell's classification. We demonstrate the existence of a length scale $\xi$ characterizing the correlations of this field (corresponding to a volume of about 1000 atoms), and compare its structure to the one observed in a standard fragile model glass. The "Boson-peak'' anomaly of the density of states can be traced back in both cases to elastic inhomogeneities on wavelengths smaller than $\xi$, where classical continuum elasticity becomes simply unapplicable