Shear-induced rigidity of frictional particles: Analysis of emergent order in stress space

Solids are distinguished from fluids by their ability to resist shear. In traditional solids, the resistance to shear is associated with the emergence of broken translational symmetry as exhibited by a non-uniform density pattern, which results from either minimizing the energy cost or maximizing the entropy or both. In this work, we focus on a class of systems, where this paradigm is challenged. We show that shear-driven jamming in dry granular materials is a collective process controlled solely by the constraints of mechanical equilibrium. We argue that these constraints lead to a broken translational symmetry in a dual space that encodes the statistics of contact forces and the topology of the contact network. The shear-jamming transition is marked by the appearance of this broken symmetry. We extend our earlier work, by comparing and contrasting real space measures of rheology with those obtained from the dual space. We investigate the structure and behavior of the dual space as the system evolves through the rigidity transition in two different shear protocols. We analyze the robustness of the shear-jamming scenario with respect to protocol and packing fraction, and demonstrate that it is possible to define a protocol-independent order parameter in this dual space, which signals the onset of rigidity.Comment: 14 pages, 17 figure

Fluctuations in Shear-Jammed States: A Statistical Ensemble Approach

Granular matter exists out of thermal equilibrium, i.e. it is athermal. While conventional equilibrium statistical mechanics is not useful for characterizing granular materials, the idea of constructing a statistical ensemble analogous to its equilibrium counterpart to describe static granular matter was proposed by Edwards and Oakshott more than two decades ago. Recent years have seen several implementations of this idea. One of these is the stress ensemble, which is based on properties of the force moment tensor, and applies to frictional and frictionless grains. We demonstrate the full utility of this statistical framework in shear jammed (SJ) experimental states [1,2], a special class of granular solids created by pure shear, which is a strictly non-equilbrium protocol for creating solids. We demonstrate that the stress ensemble provides an excellent quantitative description of fluctuations in experimental SJ states. We show that the stress fluctuations are controlled by a single tensorial quantity: the angoricity of the system, which is a direct analog of the thermodynamic temperature. SJ states exhibit significant correlations in local stresses and are thus inherently different from density-driven, isotropically jammed (IJ) states.Comment: 6 pages, 4 figure

Joint Source-Channel Coding of JPEG 2000 Image Transmission Over Two-Way Multi-Relay Networks

In this paper, we develop a two-way multi-relay scheme for JPEG 2000 image transmission. We adopt a modified time-division broadcast (TDBC) cooperative protocol, and derive its power allocation and relay selection under a fairness constraint. The symbol error probability of the optimal system configuration is then derived. After that, a joint source-channel coding (JSCC) problem is formulated to find the optimal number of JPEG 2000 quality layers for the image and the number of channel coding packets for each JPEG 2000 codeblock that can minimize the reconstructed image distortion for the two users, subject to a rate constraint. Two fast algorithms based on dynamic programming (DP) and branch and bound (BB) are then developed. Simulation demonstrates that the proposed JSCC scheme achieves better performance and lower complexity than other similar transmission systems