Average balance equations, scale dependence, and energy cascade for granular materials

A new averaging method linking discrete to continuum variables of granular materials is developed and used to derive average balance equations. Its novelty lies in the choice of the decomposition between mean values and fluctuations of properties which takes into account the effect of gradients. Thanks to a local homogeneity hypothesis, whose validity is discussed, simplified balance equations are obtained. This original approach solves the problem of dependence of some variables on the size of the averaging domain obtained in previous approaches which can lead to huge relative errors (several hundred percentages). It also clearly separates affine and nonaffine fields in the balance equations. The resulting energy cascade picture is discussed, with a particular focus on unidirectional steady and fully developed flows for which it appears that the contact terms are dissipated locally unlike the kinetic terms which contribute to a nonlocal balance. Application of the method is demonstrated in the determination of the macroscopic properties such as volume fraction, velocity, stress, and energy of a simple shear flow, where the discrete results are generated by means of discrete particle simulation.Comment: Accepted forpublication in Physical Review

Experiments and DEM Simulations of Granular Ratcheting

In this work we studied the effect of cyclic loading on a granular packing by means of numerical simulations and experiments. A confined packing of glass beads was prepared and one of the walls was moved cyclically with a prescribed amplitude of the order of the particle diameter. Different amplitudes were tested, and their effect on the free surface evolution, the force transmitted to the moving wall and the displacement patterns in the material was characterized. Discrete numerical simulations were also carried out with the specific purpose of evaluating the effect of the particle shape on the dynamics of the system. The displacement amplitude of the moving wall was shown to increase the maximum force experienced at the end of the compressive phase of the wall movement; the angularity of the particles had a similar effect. Force-wall displacement curves displayed a peculiar hysteretic behavior. The evolution of the system towards an asymptotic state was shown to be faster for spheres than for angular particles; the latter displayed an interesting long-time evolution of the force-displacement paths which deserves deeper investigations

Generation Engineering of Heralded Narrowband Colour Entangled States

Efficient heralded generation of entanglement together with its manipulation is of great importance for quantum communications. In addition, states generated with bandwidths naturally compatible with atomic transitions allow a more efficient mapping of light into matter which is an essential requirement for long distance quantum communications. Here we propose a scheme where the indistinguishability between two spontaneous four-wave mixing processes is engineered to herald generation of single-photon frequency-bin entangled states, i.e., single-photons shared by two distinct frequency modes. We show that entanglement can be optimised together with the generation probability, while maintaining absorption negligible. Besides, the scheme illustrated for cold rubidium atoms is versatile and can be implemented in several other physical systems

Condition for equivalence of q-deformed and anharmonic oscillators

The equivalence between the q-deformed harmonic oscillator and a specific anharmonic oscillator model, by which some new insight into the problem of the physical meaning of the parameter q can be attained, are discussed

Radiation 'damping' in atomic photonic crystals

The force exerted on a material by an incident beam of light is dependent upon the material's velocity in the laboratory frame of reference. This velocity dependence is known to be diffcult to measure, as it is proportional to the incident optical power multiplied by the ratio of the material velocity to the speed of light. Here we show that this typically tiny effect is greatly amplified in multilayer systems composed of resonantly absorbing atoms (e.g. optically trapped 87Rb), which may exhibit ultra-narrow photonic band gaps. The amplification of the effect is shown to be three orders of magnitude greater than previous estimates for conventional photonic-band-gap materials, and significant for material velocities of a few ms/s.Comment: 5 pages, 3 figure