We numerically investigate the problem of the propagation of a shock in an horizontal non-loaded granular chain with a bead interaction force exponent varying from unity to large values. When $\alpha$ is close to unity we observed a cross-over between a nonlinearity-dominated regime and a solitonic one, the latest being the final steady state of the propagating wave. In the case of large values of $\alpha$ the deformation field given by the numerical simulations is completely different from the one obtained by analytical calculation. In the following we studied the interaction of these shock waves with a mass impurity placed in the bead chain. Two different physical pictures emerge whether we consider a light or a heavy impurity mass. The scatter of the shock wave with a light impurity yields damped oscillations of the impurity which then behave as a solitary wave source. Differently an heavy impurity is just shifted by the shock and the transmitted wave loses its solitonic character being fragmented into waves of decreasing amplitudes.Comment: 9 pages, 18 figures, Accepted in European Physical Journal

We numerically solve the propagation of a shock wave in a chain of elastic beads with no restoring forces under traction (no-tension elasticity). We find a sequence of peaks of decreasing amplitude and velocity. Analyzing the main peak at different times we confirm a recently proposed scaling law for its decay.

[1] The noise present in infrared satellite measurements of sea surface temperature (SST) hampers the use of surface quasi-geostrophic (SQG) equations to diagnose ocean dynamics at high resolutions. Here we propose a methodology to reduce the contribution of noise when diagnosing surface vorticity, divergence, and vertical velocity from SST able to retain the dynamics at scales of a few kilometers. It is based on the use of denoising techniques with curvelets as basis functions and the application of a selective low-pass filters to improve the reconstruction of surface upwelling/downwelling patterns. First, it is tested using direct numerical simulations of SQG turbulence and then applied to diagnose lowfrequency vertical velocity patterns from real MODIS (Moderate Resolution Imaging Spectroradiometer) images. The methodology here presented, which is not tied to the validity of SQG equations nor to the use of SST, is quite general and can be applied to a wide range of measurements and dynamical frameworks.Citation: Isern-Fontanet, J., and E. Hasco€ et (2014), Diagnosis of high-resolution upper ocean dynamics from noisy sea surface temperatures,

A granular column is subjected to a small amplitude impact on its top. For a generalized power-law contact force between neighboring grains, numerical simulations show that the propagation of the impulse wave is controlled by dispersion. This leads quantitatively to a power-law decrease of the amplitude of the wave with depth. We find numerically the dependence of this power-law exponent on the force-law exponent. An analytic expression for the decrease is then derived from a long-wave approximation.

By applying fractal electromagnetic force fields on a thin layer of brine, we generate steady quasi-two-dimensional laminar flows with multi-scale stagnation point topology. This topology is shown to control the evolution of pair separation (∆) statistics by imposing a turbulent-like locality based on the sizes and strain rates of hyperbolic stagnation points when the flows are fast enough, in which case ∆ 2 ∼ t γ is a good approximation with γ close to 3. Spatially multi-scale laminar flows with turbulent-like spectral and stirring properties are a new concept with potential applications in efficient and micro-fluidic mixing.