Quasi-stationary distributions for the Domany-Kinzel stochastic cellular automaton

We construct the {\it quasi-stationary} (QS) probability distribution for the Domany-Kinzel stochastic cellular automaton (DKCA), a discrete-time Markov process with an absorbing state. QS distributions are derived at both the one- and two-site levels. We characterize the distribuitions by their mean, and various moment ratios, and analyze the lifetime of the QS state, and the relaxation time to attain this state. Of particular interest are the scaling properties of the QS state along the critical line separating the active and absorbing phases. These exhibit a high degree of similarity to the contact process and the Malthus-Verhulst process (the closest continuous-time analogs of the DKCA), which extends to the scaling form of the QS distribution.Comment: 15 pages, 9 figures, submited to PR

Phase diagram of a probabilistic cellular automaton with three-site interactions

We study a (1+1) dimensional probabilistic cellular automaton that is closely related to the Domany-Kinzel (DKCA), but in which the update of a given site depends on the state of {\it three} sites at the previous time step. Thus, compared with the DKCA, there is an additional parameter, $p_3$, representing the probability for a site to be active at time $t$, given that its nearest neighbors and itself were active at time $t-1$. We study phase transitions and critical behavior for the activity {\it and} for damage spreading, using one- and two-site mean-field approximations, and simulations, for $p_3=0$ and $p_3=1$. We find evidence for a line of tricritical points in the ($p_1, p_2, p_3$) parameter space, obtained using a mean-field approximation at pair level. To construct the phase diagram in simulations we employ the growth-exponent method in an interface representation. For $p_3 =0$, the phase diagram is similar to the DKCA, but the damage spreading transition exhibits a reentrant phase. For $p_3=1$, the growth-exponent method reproduces the two absorbing states, first and second-order phase transitions, bicritical point, and damage spreading transition recently identified by Bagnoli {\it et al.} [Phys. Rev. E{\bf 63}, 046116 (2001)].Comment: 15 pages, 7 figures, submited to PR

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

The Influence of the Degree of Heterogeneity on the Elastic Properties of Random Sphere Packings

The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher elastic properties than their more homogeneous counterparts at equal volume fraction. In this paper, packings of spherical particles are used as model structures to computationally investigate the elastic properties of coagulated particle gels as a function of their degree of heterogeneity. The discrete element model comprises a linear elastic contact law, particle bonding and damping. The simulation parameters were calibrated using a homogeneous and a heterogeneous microstructure originating from earlier Brownian dynamics simulations. A systematic study of the elastic properties as a function of the degree of heterogeneity was performed using two sets of microstructures obtained from Brownian dynamics simulation and from the void expansion method. Both sets cover a broad and to a large extent overlapping range of degrees of heterogeneity. The simulations have shown that the elastic properties as a function of the degree of heterogeneity are independent of the structure generation algorithm and that the relation between the shear modulus and the degree of heterogeneity can be well described by a power law. This suggests the presence of a critical degree of heterogeneity and, therefore, a phase transition between a phase with finite and one with zero elastic properties.Comment: 8 pages, 6 figures; Granular Matter (published online: 11. February 2012

Noise effects on one-Pauli channels

PACS. 05.40.-a Fluctuation phenomena, random processes, noise, and Brownian motion - 03.67.Hk Quantum communication,

Growth exponent in the Domany-Kinzel cellular automaton

PACS. 05.10.-a Computational methods in statistical physics and nonlinear dynamics – 02.50.-r Probability theory, stochastic processes, and statistics,

Jamming transition evinced by Voronoi Tesselation

We calculated the Voronoi tessellation (VT) of simulations of two-dimensional granular system disturbed by an intruder. The intruder is kept fixed within a rectangular box containing certain amount of grains. Making the box to move against the intruder we calculated the VT for several instants of this movement, analyzing geometrical properties of the Voronoi polygons in function of time. The dependence of stationary values of the polygon areas and number of sides in function of the packing fraction (ϕ) of the granular media has shown that the system displays a possible jamming transition at critical point ϕc ≈ 80:5%

Segregation in arch formation

We report new segregation phenomena in the clogging arches formed during the discharge of granular piles. Results from molecular dynamics simulations show segregation effects with respect to both size and density ratios used in piles built with bidisperse mixtures of grains. The clogging arch is preferentially constituted of large grains when size bidisperse piles were discharged, whereas for density bidisperse mixtures there is a predominance of light grains in the arch for large orifice widths but, for small widths, an inversion in the preference is observed, with a slightly higher incidence of heavy grains forming the arches. We present arguments based on the reverse buoyancy effect and the statistics collected for the avalanche size distributions to explain how these effects can be understood as a crossover between two different segregation mechanisms acting independently at small and large orifice width limits

Experimental evidence of granulence

We present an experimental study of velocity fluctuations in quasistatic flow of a 2D granular material deformed in a shear apparatus named 1γ2ε [1]. Radjaï and Roux [2] revealed systematic similarities between velocity fluctuations observed in discrete element simulations of quasistatic flow of granular material and turbulent flows in fluids. The character of these velocity fluctuations - named granulence by [2] - manifests as a non-Gaussian broadening of the probability density function of the fluctuations as the length of the analyzed shear-window is decreased, and exhibits some space and time scaling. The experiments presented are simple shear tests on granular samples composed of about 2000 wooden rods. The kinematics of the rod centers was followed by means of 2D Particle Image Tracking (PIT) technique applied to a sequence of 24 Mpixels digital pictures acquired throughout the duration of the loading at a frequency of 0.08 image/s. This analysis confirms the existence of granulence features in a real experimental test, which is comparable to that previously observed in numerical simulations of [2]. The experimental results obtained open up a new avenue for further studies on fluctuations in granular materials