Stability domains for time-delay feedback control with latency

We generalize a known analytical method for determining the stability of periodic orbits controlled by time-delay feedback methods when latencies associated with the generation and injection of the feedback signal cannot be ignored. We discuss the case of extended time-delay autosynchronization (ETDAS) and show that nontrivial qualitative features of the domain of control observed in experiments can be explained by taking into account the effects of both the unstable eigenmode and a single stable eigenmode in the Floquet theory.Comment: 9 pages, 6 figures; Submitted to Physical Review

Anisotropy in granular media: classical elasticity and directed force chain network

A general approach is presented for understanding the stress response function in anisotropic granular layers in two dimensions. The formalism accommodates both classical anisotropic elasticity theory and linear theories of anisotropic directed force chain networks. Perhaps surprisingly, two-peak response functions can occur even for classical, anisotropic elastic materials, such as triangular networks of springs with different stiffnesses. In such cases, the peak widths grow linearly with the height of the layer, contrary to the diffusive spreading found in `stress-only' hyperbolic models. In principle, directed force chain networks can exhibit the two-peak, diffusively spreading response function of hyperbolic models, but all models in a particular class studied here are found to be in the elliptic regime.Comment: 34 pages, 17 figures (eps), submitted to PRE, figures amended, partially to compare better to recent exp. wor

Vector lattice model for stresses in granular materials

A vector lattice model for stresses in granular materials is proposed. A two dimensional pile built by pouring from a point is constructed numerically according to this model. Remarkably, the pile violates the Mohr Coulomb stability criterion for granular matter, probably because of the inherent anisotropy of such poured piles. The numerical results are also compared to the earlier continuum FPA model and the (scalar) lattice $q$-model

Modelling quasicrystals at positive temperature

We consider a two-dimensional lattice model of equilibrium statistical mechanics, using nearest neighbor interactions based on the matching conditions for an aperiodic set of 16 Wang tiles. This model has uncountably many ground state configurations, all of which are nonperiodic. The question addressed in this paper is whether nonperiodicity persists at low but positive temperature. We present arguments, mostly numerical, that this is indeed the case. In particular, we define an appropriate order parameter, prove that it is identically zero at high temperatures, and show by Monte Carlo simulation that it is nonzero at low temperatures

Defensive alliances in spatial models of cyclical population interactions

As a generalization of the 3-strategy Rock-Scissors-Paper game dynamics in space, cyclical interaction models of six mutating species are studied on a square lattice, in which each species is supposed to have two dominant, two subordinated and a neutral interacting partner. Depending on their interaction topologies, these systems can be classified into four (isomorphic) groups exhibiting significantly different behaviors as a function of mutation rate. On three out of four cases three (or four) species form defensive alliances which maintain themselves in a self-organizing polydomain structure via cyclic invasions. Varying the mutation rate this mechanism results in an ordering phenomenon analogous to that of magnetic Ising model.Comment: 4 pages, 3 figure

Critical States in a Dissipative Sandpile Model

A directed dissipative sandpile model is studied in the two-dimension. Numerical results indicate that the long time steady states of this model are critical when grains are dropped only at the top or, everywhere. The critical behaviour is mean-field like. We discuss the role of infinite avalanches of dissipative models in periodic systems in determining the critical behaviour of same models in open systems.Comment: 4 pages (Revtex), 5 ps figures (included

Scaling in a Nonconservative Earthquake Model of Self-Organised Criticality

We numerically investigate the Olami-Feder-Christensen model for earthquakes in order to characterise its scaling behaviour. We show that ordinary finite size scaling in the model is violated due to global, system wide events. Nevertheless we find that subsystems of linear dimension small compared to the overall system size obey finite (subsystem) size scaling, with universal critical coefficients, for the earthquake events localised within the subsystem. We provide evidence, moreover, that large earthquakes responsible for breaking finite size scaling are initiated predominantly near the boundary.Comment: 6 pages, 6 figures, to be published in Phys. Rev. E; references sorted correctl

Statistics of the contact network in frictional and frictionless granular packings

Simulated granular packings with different particle friction coefficient mu are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces P(f) are computed and compared with existing experimental data. Here f equivalent to F/F-bar is the contact force F normalized by the average value F-bar. P(f) exhibits exponential-like decay at large forces, a plateau/peak near f = 1, with additional features at forces smaller than the average that depend on mu. Computations of the force-force spatial distribution function and the contact point radial distribution function indicate that correlations between forces are only weakly dependent on friction and decay rapidly beyond approximately three particle diameters. Distributions of the particle-particle contact angles show that the contact network is not isotropic and only weakly dependent on friction. High force-bearing structures, or force chains, do not play a dominant role in these three dimensional, unloaded packings.Comment: 11 pages, 13 figures, submitted to PR

Properties of layer-by-layer vector stochastic models of force fluctuations in granular materials

We attempt to describe the stress distributions of granular packings using lattice-based layer-by-layer stochastic models that satisfy the constraints of force and torque balance and non-tensile forces at each site. The inherent asymmetry in the layer-by-layer approach appears to lead to an asymmetric force distribution, in disagreement with both experiments and general symmetry considerations. The vertical force component probability distribution is robust and in agreement with predictions of the scalar q model while the distribution of horizontal force components is qualitatively different and depends on the details of implementation.Comment: 18 pages, 12 figures (with subfigures), 1 table. Uses revtex, epsfig,subfigure, and cite. Submitted to PRE. Plots have been bitmapped. High-resolution version is available. Email [email protected] or download from http://rainbow.uchicago.edu/~mbnguyen/research/vm.htm

Stress response inside perturbed particle assemblies

The effect of structural disorder on the stress response inside three dimensional particle assemblies is studied using computer simulations of frictionless sphere packings. Upon applying a localised, perturbative force within the packings, the resulting {\it Green's} function response is mapped inside the different assemblies, thus providing an explicit view as to how the imposed perturbation is transmitted through the packing. In weakly disordered arrays, the resulting transmission of forces is of the double-peak variety, but with peak widths scaling linearly with distance from the source of the perturbation. This behaviour is consistent with an anisotropic elasticity response profile. Increasing the disorder distorts the response function until a single-peak response is obtained for fully disordered packings consistent with an isotropic description.Comment: 8 pages, 7 figure captions To appear in Granular Matte