A nonlinear Lagrangian particle model for grains assemblies including grain relative rotations

International audienceWe formulate a discrete Lagrangian model for a set of interacting grains, which is purely elastic. The considered degrees of freedom for each grain include placement of barycenter and rotation. Further, we limit the study to the case of planar systems. A representative grain radius is introduced to express the deformation energy to be associated to relative displacements and rotations of interacting grains. We distinguish inter‐grains elongation/compression energy from inter‐grains shear and rotations energies, and we consider an exact finite kinematics in which grain rotations are independent of grain displacements. The equilibrium configurations of the grain assembly are calculated by minimization of deformation energy for selected imposed displacements and rotations at the boundaries. Behaviours of grain assemblies arranged in regular patterns, without and with defects, and similar mechanical properties are simulated. The values of shear, rotation, and compression elastic moduli are varied to investigate the shapes and thicknesses of the layers where deformation energy, relative displacement, and rotations are concentrated. It is found that these concentration bands are close to the boundaries and in correspondence of grain voids. The obtained results question the possibility of introducing a first gradient continuum models for granular media and justify the development of both numerical and theoretical methods for including frictional, plasticity, and damage phenomena in the proposed model

Observation of the Gamma-Ray Binary HESS J0632+057 with the HESS, MAGIC, and VERITAS Telescopes

The results of gamma-ray observations of the binary system HESS J0632 + 057 collected during 450 hr over 15 yr, between 2004 and 2019, are presented. Data taken with the atmospheric Cherenkov telescopes H.E.S.S., MAGIC, and VERITAS at energies above 350 GeV were used together with observations at X-ray energies obtained with Swift-XRT, Chandra, XMM-Newton, NuSTAR, and Suzaku. Some of these observations were accompanied by measurements of the H alpha emission line. A significant detection of the modulation of the very high-energy gamma-ray fluxes with a period of 316.7 +/- 4.4 days is reported, consistent with the period of 317.3 +/- 0.7 days obtained with a refined analysis of X-ray data. The analysis of data from four orbital cycles with dense observational coverage reveals short-timescale variability, with flux-decay timescales of less than 20 days at very high energies. Flux variations observed over a timescale of several years indicate orbit-to-orbit variability. The analysis confirms the previously reported correlation of X-ray and gamma-ray emission from the system at very high significance, but cannot find any correlation of optical H alpha parameters with fluxes at X-ray or gamma-ray energies in simultaneous observations. The key finding is that the emission of HESS J0632 + 057 in the X-ray and gamma-ray energy bands is highly variable on different timescales. The ratio of gamma-ray to X-ray flux shows the equality or even dominance of the gamma-ray energy range. This wealth of new data is interpreted taking into account the insufficient knowledge of the ephemeris of the system, and discussed in the context of results reported on other gamma-ray binary systems