Percolation properties of an adsorbed polydisperse mixture of extended objects on a triangular lattice are studied by Monte Carlo simulations. The depositing objects of various shapes are formed by self-avoiding walks on the lattice. We study polydisperse mixtures in which the size ℓ of the shape making the mixture increases gradually with the number of components. This study examines the influence of the shape of the primary object defining a polydisperse mixture on its percolation and jamming properties. The dependence of the jamming density and percolation threshold on the number of components n making the mixture is analyzed. Determining the contribution of the individual components in the lattice covering allowed a better insight into the deposit structure of the n-component mixture at the percolation threshold. In addition, we studied mixtures of objects of various shapes but the same size.

Percolation model with nucleation and object growth is studied by Monte Carlo simulations on a triangular lattice with point-like impurities. Growing objects are needle-like objects and self-avoiding random walk chains. In each run through the system the lattice is initially randomly occupied by point-like impurities at given concentration ρimp . Then the seeds for the object growth are randomly distributed at given concentration ρ. The percolation properties and the jamming densities are compared for the two classes of growing objects on the basis of the results obtained for a wide range of densities ρ and ρimp up to the percolation threshold for the monomer deposition on a triangular lattice. Values of the percolation thresholds θp∗ have lower values for the needle-like objects than for the self-avoiding random walk chains. The difference is largest for the lowest values of ρ and ρimp , and ceases near the values of the site percolation threshold for monomers on the triangular lattice, ρp∗≃0.5 . Values of the jamming coverage θJ decrease with ρimp for given ρ. This effect is more prominent for the growing random walk chains.

The resistance drop with time in metallic granular materials has been the subject of research since the 19th century, but it is still not fully clarified. The wider application of granular materials in the industry has contributed to the increased interest in this phenomenon. The key parameters that are mainly examined are as follows: the influence of different packings, dimensions, and shapes of the granules, as well as the influence of the pressure, exerted on them. However, there is a limited number of papers that examine the temporal evolution of the resistance in these materials. In this report, we investigate how different packings of two-dimensional stainless steel beads (inox) as well as different currents injected into them affect the temporal evolution of resistance. We also examine the effect of the breaks in the current flow for the current varied between 0.2 and 8 mA for both inox beads as well as low-carbon steel cylinders. The results show the drop of resistance over time for all current values, which is more pronounced in earlier stages of the time evolution. Interruptions in current flow cause an immediate decrease of resistance in both materials.

Abstract An efficient method for evaluation of an optimal two-layer soil model from Wenner four-probe measuring method, which has been used during experimental investigations, is presented within this paper. A two-layer soil model is assumed, and this soil model is an adequate representation of nonhomogeneous soil for grounding system design. The application of optimization techniques is required to estimate the electrical parameters of the proposed soil model. In this paper, first the fast gradient-descent method to solve a given optimization problem is chosen, and then with the aim of faster calculation for accelerating the rate of convergence of an infinite sum, the application of Aitken’s δ2 method is proposed.

The percolation properties in anisotropic irreversible deposition of extended objects are studied by Monte Carlo simulations on a triangular lattice. Depositing objects of various shapes and sizes are made by directed self-avoiding walks on the lattice. Anisotropy is introduced by imposing unequal probabilities for placing the objects along different directions of the lattice. The degree of the anisotropy is characterized by the order parameter p  determining the probability for deposition in the chosen (horizontal) direction. For each of the other two directions adsorption occurs with probability . It is found that the percolation threshold increases with the degree of anisotropy, having the maximum values for fully oriented objects. Percolation properties of the elongated shapes, such as k-mers, are more affected by the presence of anisotropy than the compact ones. Percolation in anisotropic deposition was also studied for a lattice with point-like defects. For elongated shapes a slight decrease of the percolation threshold with the impurity concentration d can be observed. However, for these shapes, significantly increases with the degree of anisotropy. In the case when depositing objects are triangles, results are qualitatively different. The percolation threshold decreases with d, but is not affected by the presence of anisotropy.

Percolation properties of two-component mixtures are studied by Monte Carlo simulations. Objects are deposited onto a substrate according to the random sequential adsorption model. Various shapes making the mixtures are made by self-avoiding walks on a triangular lattice. Percolation threshold for mixtures of objects covering the same number of sites is always lower than for the more compact object, and it can be even lower than for both components. Mixtures of percolating and non-percolating objects almost always percolate, but the percolation threshold is higher than for the percolating component. Adding a shape of high connectivity to a system of compact non-percolating objects, makes the deposit percolate. Lowest percolation thresholds are obtained for mixtures with elongated angled objects. Dependence of on the object length exhibits a minimum, so it could be estimated that the angled objects of length give the largest contribution to the percolation.

The properties of the random sequential adsorption of objects of various shapes on a two-dimensional triangular lattice are studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding lattice steps, whereby the size of the objects is gradually increased by wrapping the walks in several different ways. The aim of this work is to investigate the impact of the geometrical properties of the shapes on the jamming density θ_{J} and on the temporal evolution of the coverage fraction θ(t). Our results suggest that the order of symmetry axis of a shape exerts a decisive influence on adsorption kinetics near the jamming limit θ_{J}. The decay of probability for the insertion of a new particle onto a lattice is described in a broad range of the coverage θ by the product between the linear and the stretched exponential function for all examined objects. The corresponding fitting parameters are discussed within the context of the shape descriptors, such as rotational symmetry and the shape factor (parameter of nonsphericity) of the objects. Predictions following from our calculations suggest that the proposed fitting function for the insertion probability is consistent with the exponential approach of the coverage fraction θ(t) to the jamming limit θ_{J}.

In the preceding paper, Budinski-Petković et al (2016 J. Stat. Mech. 053101) studied jamming and percolation aspects of random sequential adsorption of extended shapes onto a triangular lattice initially covered with point-like impurities at various concentrations. Here we extend this analysis to needle-like impurities of various lengths . For a wide range of impurity concentrations p, percolation threshold θ∗ p is determined for k-mers, angled objects and triangles of two dierent sizes. For suciently large impurities, percolation threshold θ∗ p of all examined objects increases with concentration p, and this increase is more prominent for impurities of a larger length . We determine the critical concentrations of defects pc above which it is not possible to achieve percolation for a given object, for impurities of various lengths . It is found that the critical concentration pc of finite-size impurities decreases with the length of impurities. In the case of deposition of larger objects an exception occurs for point-like impurities when critical concentration pc of monomers is lower than pc for the dimer impurities. At relatively low concentrations p, the presence of small impurities (but not point-like) stimulates the percolation for larger depositing objects. I Lončarević et al The study of percolation with the presence of extended impurities Printed in the UK 093202 JSMTC6 © 2017 IOP Publishing Ltd and SISSA Medialab srl 2017 J. Stat. Mech.

Adsorption-desorption processes of polydisperse mixtures on a triangular lattice are studied by numerical simulations. Mixtures are composed of the shapes of different numbers of segments and rotational symmetries. Numerical simulations are performed to determine the influence of the number of mixture components and the length of the shapes making the mixture on the kinetics of the deposition process. We find that, above the jamming limit, the time evolution of the total coverage of a mixture can be described by the Mittag-Leffler function θ(t)=θ∞-ΔθE[-(t/τ)β] for all the mixtures we have examined. Our results show that the equilibrium coverage decreases with the number of components making the mixture and also with the desorption probability, via corresponding stretched exponential laws. For the mixtures of equal-sized objects, we propose a simple formula for predicting the value of the steady-state coverage fraction of a mixture from the values of the steady-state coverage fractions of pure component shapes.

We present a methodology to quantify the structural changes in the internal structure of granular packing. To this end, we use the Voronoї tessellation and a specific shape factor which is a clear indicator of the presence of different domains in the granular packing. Distributions of the shape factor in a 2D granular system of metallic disks are experimentally investigated. The analysis of disk packings at a “microscopic” level requires a precise measurement of grain positions. For this reason, we develop an accurate image processing technique based on the Standard Hough Transform. It is found that the properties of the probability distribution of the shape factor of the Voronoї cells are in accordance with the fact that the packings of monodisperse hard disks spontaneously assemble into the regions of local crystalline order.