Growing Perfect Decagonal Quasicrystals by Local Rules

A local growth algorithm for a decagonal quasicrystal is presented. We show that a perfect Penrose tiling (PPT) layer can be grown on a decapod tiling layer by a three dimensional (3D) local rule growth. Once a PPT layer begins to form on the upper layer, successive 2D PPT layers can be added on top resulting in a perfect decagonal quasicrystalline structure in bulk with a point defect only on the bottom surface layer. Our growth rule shows that an ideal quasicrystal structure can be constructed by a local growth algorithm in 3D, contrary to the necessity of non-local information for a 2D PPT growth.Comment: 4pages, 2figure

Quantifying the complexity of random Boolean networks

We study two measures of the complexity of heterogeneous extended systems, taking random Boolean networks as prototypical cases. A measure defined by Shalizi et al. for cellular automata, based on a criterion for optimal statistical prediction [Shalizi et al., Phys. Rev. Lett. 93, 118701 (2004)], does not distinguish between the spatial inhomogeneity of the ordered phase and the dynamical inhomogeneity of the disordered phase. A modification in which complexities of individual nodes are calculated yields vanishing complexity values for networks in the ordered and critical regimes and for highly disordered networks, peaking somewhere in the disordered regime. Individual nodes with high complexity are the ones that pass the most information from the past to the future, a quantity that depends in a nontrivial way on both the Boolean function of a given node and its location within the network.Comment: 8 pages, 4 figure

Jamming Transition In Non-Spherical Particle Systems: Pentagons Versus Disks

We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient μ≈1. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, Znr, reaches 3, and the dependence of Znr on the packing fraction ϕ changes again when Znr reaches 4. (2) Though the packing fractions ϕc1 and ϕc2 at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of ϕc1 and ϕc2 for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution

Jamming Transition In Non-Spherical Particle Systems: Pentagons Versus Disks

We investigate the jamming transition in a quasi-2D granular material composed of regular pentagons or disks subjected to quasistatic uniaxial compression. We report six major findings based on experiments with monodisperse photoelastic particles with static friction coefficient μ≈1. (1) For both pentagons and disks, the onset of rigidity occurs when the average coordination number of non-rattlers, Znr, reaches 3, and the dependence of Znr on the packing fraction ϕ changes again when Znr reaches 4. (2) Though the packing fractions ϕc1 and ϕc2 at these transitions differ from run to run, for both shapes the data from all runs with different initial configurations collapses when plotted as a function of the non-rattler fraction. (3) The averaged values of ϕc1 and ϕc2 for pentagons are around 1% smaller than those for disks. (4) Both jammed pentagons and disks show Gamma distribution of the Voronoi cell area with same parameters. (5) The jammed pentagons have similar translational order for particle centers but slightly less orientational order for contacting pairs compared to jammed disks. (6) For jammed pentagons, the angle between edges at a face-to-vertex contact point shows a uniform distribution and the size of a cluster connected by face-to-face contacts shows a power-law distribution

A Ball in a Groove

We study the static equilibrium of an elastic sphere held in a rigid groove by gravity and frictional contacts, as determined by contact mechanics. As a function of the opening angle of the groove and the tilt of the groove with respect to the vertical, we identify two regimes of static equilibrium for the ball. In the first of these, at large opening angle or low tilt, the ball rolls at both contacts as it is loaded. This is an analog of the "elastic" regime in the mechanics of granular media. At smaller opening angles or larger tilts, the ball rolls at one contact and slides at the other as it is loaded, analogously with the "plastic" regime in the mechanics of granular media. In the elastic regime, the stress indeterminacy is resolved by the underlying kinetics of the ball response to loading.Comment: RevTeX 3.0, 4 pages, 2 eps figures included with eps

Intruder in a two-dimensional granular system: statics and dynamics of force networks in an experimental system experiencing stick-slip dynamics

In quasi-two-dimensional experiments with photoelastic particles confined to an annular region, an intruder constrained to move in a circular path halfway between the annular walls experiences stick-slip dynamics. We discuss the response of the granular medium to the driven intruder, focusing on the evolution of the force network during sticking periods. Because the available experimental data does not include precise information about individual contact forces, we use an approach developed in our previous work (Basak et al, J. Eng. Mechanics (2021)) based on networks constructed from measurements of the integrated strain magnitude on each particle. These networks are analyzed using topological measures based on persistence diagrams, revealing that force networks evolve smoothly but in a nontrivial manner throughout each sticking period, even though the intruder and granular particles are stationary. Characteristic features of persistence diagrams show identifiable changes as a slip is approaching, indicating the existence of slip precursors. Key features of the dynamics are similar for granular materials composed of disks or pentagons, but some details are consistently different. In particular, we find significantly larger fluctuations of the measures computed based on persistence diagrams, and therefore of the underlying networks, for systems of pentagonal particles

Force distributions in a triangular lattice of rigid bars

We study the uniformly weighted ensemble of force balanced configurations on a triangular network of nontensile contact forces. For periodic boundary conditions corresponding to isotropic compressive stress, we find that the probability distribution for single-contact forces decays faster than exponentially. This super-exponential decay persists in lattices diluted to the rigidity percolation threshold. On the other hand, for anisotropic imposed stresses, a broader tail emerges in the force distribution, becoming a pure exponential in the limit of infinite lattice size and infinitely strong anisotropy.Comment: 11 pages, 17 figures Minor text revisions; added references and acknowledgmen

Average stresses and force fluctuations in non-cohesive granular materials

A lattice model is presented for investigating the fluctuations in static granular materials under gravitationally induced stress. The model is similar in spirit to the scalar q-model of Coppersmith et al., but ensures balance of all components of forces and torques at each site. The geometric randomness in real granular materials is modeled by choosing random variables at each site, consistent with the assumption of cohesionless grains. Configurations of the model can be generated rapidly, allowing the statistical study of relatively large systems. For a 2D system with rough walls, the model generates configurations consistent with continuum theories for the average stresses (unlike the q-model) without requiring the assumption of a constitutive relation. For a 2D system with periodic boundary conditions, the model generates single-grain force distributions similar to those obtained from the q-model with a singular distribution of q's.Comment: 18 pages, 10 figures. Uses aps,epsfig,graphicx,floats,revte