Energy dissipation and dispersion effects in granular media

Abstract

The strong interactions between particles will make the energy within the granular materials propagate through the network of contacts and be partly dissipated. Establishing a model that can clearly classify the dissipation and dispersion effects is crucial for the understanding of the global behaviors in the granular materials. For particles with rate-independent material, the dissipation effects come from the local plastic deformation and can be constrained at the energy level by using energetic restitution coefficients. On the other hand, the dispersion effects should depend on the intrinsic nature of the interaction law between two particles. In terms of a bistiffness compliant contact model that obeys the energetical constraint defined by the energetic coefficients, our recent work related to the issue of multiple impacts indicates that the propagation of energy during collisions can be represented by a distributing law. In particular, this law shows that the dispersion effects are dominated by the relative contact stiffness and the relative potential energy stored at the contact points. In this paper, we will apply our theory to the investigation of the wave behavior in granular chain systems. The comparisons between our numerical results and the experimental ones by Falcon, [Eur. Phys. J. B 5, 111 (1998)] for a column of beads colliding against a wall show very good agreement and confirm some conclusions proposed by Falcon Other numerical results associated with the case of several particles impacting a chain, and the collisions between two so-called solitary waves in a Hertzian type chain are also presented.

Collective modes and the speed of sound in the Fulde-Ferrell-Larkin-Ovchinnikov state

“…From this pair of equations, it is straightforward to solve for G 11 and G 41 . In a similar manner, we find the Green's functions G 14 and G 44 .…”

“…We find the interesting result that the the anisotropic pairing of the FFLO state leads to an anisotropy in the speed of sound in the system. Furthermore, we study a quasi-1D optical lattice in which the tunneling in two directions of a three-dimensional (3D) lattice is restricted, as it has been recently suggested that a quasi-1D geometry would provide optimal conditions for the formation of the FFLO state [38][39][40][41][42].…”

Impact–contact dynamics in a disc–ball system

“…For the rough contacts, Coulomb friction law specifies that the tangential and normal components of the contact forces should satisfy the following relationship characterized by two coefficients: 20) where μ i > 0 and μ s i > μ i are the slip and stick friction coefficients at contact point i, respectively. If v τ i = 0, the force of friction F τ i opposes motion and has magnitude μ i F n i .…”

Nesting and lifetime effects in the FFLO state of quasi-one-dimensional imbalanced Fermi gases

“…Both models are exactly solvable (or integrable) and their energy spectra and thermodynamical properties can be calculated exactly using the Bethe ansatz and numerical methods [28]. The Yang-Gaudin model does not include inter-tube couplings and eventually it will be necessary to consider these [30,33] to fully describe the experiments.…”

“…The majority of the recent literature on 1D spin-imbalanced Fermi gases considers the simplest possible system that exhibits FFLO-type pairing namely, the YangGaudin model or its lattice version, the Hubbard model with attractive interactions [28,29,30,31,32]. Both models are exactly solvable (or integrable) and their energy spectra and thermodynamical properties can be calculated exactly using the Bethe ansatz and numerical methods [28].…”