Internal states of model isotropic granular packings. II. Compression and pressure cycles

This is the second paper of a series of three investigating, by numerical means, the geometric and mechanical properties of spherical bead packings under isotropic stresses. We study the effects of varying the applied pressure P (from 1 or 10 kPa up to 100 MPa in the case of glass beads) on several types of configurations assembled by different procedures, as reported in the preceding paper. As functions of P, we monitor changes in solid fraction \Phi, coordination number z, proportion of rattlers (grains carrying no force) x0, the distribution of normal forces, the level of friction mobilization, and the distribution of near neighbor distances. Assuming the contact law does not involve material plasticity or damage, \Phi is found to vary very nearly reversibly with P in an isotropic compression cycle, but all other quantities, due to the frictional hysteresis of contact forces, change irreversibly. In particular, initial low P states with high coordination numbers lose many contacts in a compression cycle, and end up with values of z and x0 close to those of the most poorly coordinated initial configurations. Proportional load variations which do not entail notable configuration changes can therefore nevertheless significantly affect contact networks of granular packings in quasistatic conditions.Comment: Published in Physical Review E 12 page

Incremental response of granular materials: DEM results

We systematically investigate the incremental response of various equilibrium states of dense 2D model granular materials, along the biaxial compression path (\sigma 11 < \sigma 22, \sigma 12 = 0). Stress increments are applied in arbitrary directions in 3- dimensional stress space (\sigma 11, \sigma 22, \sigma 12). In states with stable contact networks we compute the stiffness matrix and the elastic moduli, and separate elastic and irreversible strains in the range in which the latter are homogeneous functions of degree one of stress increments. Without principal stress axis rotation, the response abides by elastoplasticity with a Mohr-Coulomb criterion and a non-associated flow rule. However a nonelastic shear strain is also observed for increments of \sigma 12, and shear and in-plane responses couple. This behavior correlates to the distribution of friction mobilization and sliding at contacts.Comment: 4 page

How granular materials deform in quasistatic conditions

Based on numerical simulations of quasistatic deformation of model granular materials, two rheological regimes are distinguished, according to whether macroscopic strains merely reflect microscopic material strains within the grains in their contact regions (type I strains), or result from instabilities and contact network rearrangements at the microscopic level (type II strains). We discuss the occurrence of regimes I and II in simulations of model materials made of disks (2D) or spheres (3D). The transition from regime I to regime II in monotonic tests such as triaxial compression is different from both the elastic limit and from the yield threshold. The distinction between both types of response is shown to be crucial for the sensitivity to contact-level mechanics, the relevant variables and scales to be considered in micromechanical approaches, the energy balance and the possible occurrence of macroscopic instabilitie

Charge density wave in graphene: magnetic-field-induced Peierls instability

We suggest that a magnetic-field-induced Peierls instability accounts for the recent experiment of Zhang et al. in which unexpected quantum Hall plateaus were observed at high magnetic fields in graphene on a substrate. This Peierls instability leads to an out-of-plane lattice distortion resulting in a charge density wave (CDW) on sublattices A and B of the graphene honeycomb lattice. We also discuss alternative microscopic scenarios proposed in the literature and leading to a similar CDW ground state in graphene.Comment: Proceeding of the "graphene conference" (25 September - 01 October 2006) held in Dresde

Criticality in multicomponent spherical models : results and cautions

To enable the study of criticality in multicomponent fluids, the standard spherical model is generalized to describe an \ns-species hard core lattice gas. On introducing \ns spherical constraints, the free energy may be expressed generally in terms of an \ns\times\ns matrix describing the species interactions. For binary systems, thermodynamic properties have simple expressions, while all the pair correlation functions are combinations of just two eigenmodes. When only hard-core and short-range overall attractive interactions are present, a choice of variables relates the behavior to that of one-component systems. Criticality occurs on a locus terminating a coexistence surface; however, except at some special points, an unexpected ``demagnetization effect'' suppresses the normal divergence of susceptibilities at criticality and distorts two-phase coexistence. This effect, unphysical for fluids, arises from a general lack of symmetry and from the vectorial and multicomponent character of the spherical model. Its origin can be understood via a mean-field treatment of an XY spin system below criticality.Comment: 4 figure

Is the luxury industry really a financier’s dream ?

Although modest in terms of sales, compared to most other sectors, luxury does get a high share of investors', financial analysts’ and media attention. Why would this sector receive a share of attention much bigger than its actual weight? Is it because of its glamourous image, or the incredible prices attached to its products, now displayed in all the media for mass desire? Are the financiers dreaming too?luxury brands; sales; investment; performance; profitability; finance;

Landau levels in quasicrystals

Two-dimensional tight-binding models for quasicrystals made of plaquettes with commensurate areas are considered. Their energy spectrum is computed as a function of an applied perpendicular magnetic field. Landau levels are found to emerge near band edges in the zero-field limit. Their existence is related to an effective zero-field dispersion relation valid in the continuum limit. For quasicrystals studied here, an underlying periodic crystal exists and provides a natural interpretation to this dispersion relation. In addition to the slope (effective mass) of Landau levels, we also study their width as a function of the magnetic flux per plaquette and identify two fundamental broadening mechanisms: (i) tunneling between closed cyclotron orbits and (ii) individual energy displacement of states within a Landau level. Interestingly, the typical broadening of the Landau levels is found to behave algebraically with the magnetic field with a nonuniversal exponent.Comment: 14 pages, 9 figure