Random sequential adsorption (RSA) is a broadly used model for irreversible deposition on substrates. Over the last decades, a huge number of works have been published concerning this topic. Here we give a brief review of the results for irreversible deposition on two-dimensional discrete substrates. Depositing objects are randomly and sequentially adsorbed onto the substrate, and they are not allowed to overlap, so the jamming coverage θ j a m is less than in close packing. The kinetics of the process is described by the time-dependence of the coverage fraction θ ( t ) , and for the discrete substrates, this dependence was found to be of the form: θ ( t ) = θ j a m − A e − t / σ . Another topic of interest is the percolation of the deposit that can occur at a certain coverage. The coverage of the surface is increased through the RSA process up to the percolation threshold when a cluster that extends through the whole system appears. A percolating cluster arises in the system when the opposite edges are connected via some path of nearest neighbor sites occupied by the particles. Studying percolation is of great interest due to its relevance to conductivity in composite materials, flow through porous media, polymerization, the properties of nanomaterials, etc.

A percolation model with nucleation and object growth is studied by Monte Carlo simulations on a triangular lattice with finite-size impurities. The growing objects are needle-like objects and self-avoiding random walk chains. Results are obtained for three different shapes of impurities covering three lattice sites—needle-like, angled and triangular. In each run through the system, the lattice is initially randomly occupied by impurities of a specified shape at a given concentration ρ imp . Then, the seeds for the object growth are randomly distributed at a given concentration ρ. The percolation and jamming properties of the growing objects are compared for the three different impurity shapes. For all the impurity shapes, the percolation thresholds θ p ∗ have lower values in the growing needle-like objects than in the growing self-avoiding random walk chains. In the presence of needle-like and angled impurities, the percolation threshold increases with the impurity concentration for a fixed seed density. The percolation thresholds have the highest values in the needle-like impurities, and somewhat lower values in the angled impurities. On the other hand, in the presence of the triangular impurities, the percolation threshold decreases with the concentration of impurities.

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.