Simulation study of random sequential adsorption of mixtures on a triangular lattice

Random sequential adsorption of binary mixtures of extended objects on a two-dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The depositing objects are formed by self-avoiding random walks on the lattice. We concentrate here on the influence of the symmetry properties of the shapes on the kinetics of the deposition processes in two-component mixtures. Approach to the jamming limit in the case of mixtures is found to be exponential, of the form: $\theta(t) \sim \theta_{jam}-\Delta\theta \exp (-t/\sigma),$ and the values of the parameter $\sigma$ are determined by the order of symmetry of the less symmetric object in the mixture. Depending on the local geometry of the objects making the mixture, jamming coverage of a mixture can be either greater than both single-component jamming coverages or it can be in between these values. Results of the simulations for various fractional concentrations of the objects in the mixture are also presented.Comment: 11 figures, 2 table

Reversible Random Sequential Adsorption of Dimers on a Triangular Lattice

We report on simulations of reversible random sequential adsorption of dimers on three different lattices: a one-dimensional lattice, a two-dimensional triangular lattice, and a two-dimensional triangular lattice with the nearest neighbors excluded. In addition to the adsorption of particles at a rate K+, we allow particles to leave the surface at a rate K-. The results from the one-dimensional lattice model agree with previous results for the continuous parking lot model. In particular, the long-time behavior is dominated by collective events involving two particles. We were able to directly confirm the importance of two-particle events in the simple two-dimensional triangular lattice. For the two-dimensional triangular lattice with the nearest neighbors excluded, the observed dynamics are consistent with this picture. The two-dimensional simulations were motivated by measurements of Ca++ binding to Langmuir monolayers. The two cases were chosen to model the effects of changing pH in the experimental system.Comment: 9 pages, 10 figure

Irreversible deposition of extended objects with diffusional relaxation on discrete substrates

Random sequential adsorption with diffusional relaxation of extended objects both on a one-dimensional and planar triangular lattice is studied numerically by means of Monte Carlo simulations. We focus our attention on the behavior of the coverage θ(t) as a function of time. Our results indicate that the lattice dimensionality plays an important role in the present model. For deposition of k-mers on 1D lattice with diffusional relaxation, we found that the growth of the coverage θ(t) above the jamming limit to the closest packing limit θCPL is described by the pattern θCPL - θ(t) ∝ Eβ[-(t/τ)β], where Eβ denotes the Mittag-Leffler function of order β ∈ (0,1). In the case of deposition of extended lattice shapes in 2D, we found that after the initial “jamming", a stretched exponential growth of the coverage θ(t) towards the closest packing limit θCPL occurs, i.e., θCPL - θ(t) ∝ exp[-(t/τ)β]. For both cases we observe that: (i) dependence of the relaxation time τ on the diffusion probability Pdif is consistent with a simple power-law, i.e., τ ∝ Pdif-δ; (ii) parameter β depends on the object size in 1D and on the particle shape in 2D

Structural Characterization and Statistical Properties of Two-Dimensional Granular Systems During the Compaction

We study the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking, by numerical simulation. Shaking is modeled by a series of vertical expansions of the disk packing, followed by dynamical recompression of the assembly under the action of gravity. The second phase of the shake cycle is based on an efficient event-driven molecular-dynamics algorithm. We analyze the compaction dynamics for various values of the friction coefficient and the coefficient of normal restitution. The granular organization at local level was studied by analyzing the shape factor ξ of the local volumes, associated with a natural way of subdividing the volume into local parts - the Voronoi partition. It gives a clear physical picture of the competition between less and more ordered domains of particles during the compaction. We calculate the distribution of the shape-factor for packings at different stages of the compaction process. We have also investigated a two-dimensional granular medium experimentally. We prepared the granular packings of metallic cylinders of diameters 4, 5, and 6 mm. The distributions of the shape-factor obtained numerically for various tapping intensities are consistent with our experimental results

Linear kinetic equation: long-time behavior of one-particle distribution function

We construct asymptotic (long-time) solution of the linear Boltzmann equation using the time-dependent perturbation theory generalized to non-Hermitian operators. We prove that for times much larger than the relaxation time τ0, t ≫τ0, one-particle distribution function separates into spatio-temporal and velocity dependent parts, and provide the explicit expression for the long-time solution of the linear Boltzmann equation. Our analysis does not assume that relative density gradients n^{-1}(\partial / \partial \mathaccent"017E{r}) n are small. It relates the hydrodynamic form of the one-particle distribution function to spectral properties of operators involved in linear Boltzmann equation

Percolation and jamming properties in particle shape-controlled seeded growth model

We consider the percolation model with nucleation and simultaneous growth of multiple finite clusters, taking the initial seed concentration $$\rho$$ as a tunable parameter. Growing objects expand with constant speed, filling the nodes of the triangular lattice according to rules that control their shape. As growing objects of predefined shape, we consider needle-like objects and “wrapping” objects whose size is gradually increased by wrapping the walks in several different ways, making triangles, rhombuses, and hexagons. Growing random walk chains are also analyzed as an example of objects whose shape is formed randomly during the growth. We compare the percolation properties and jamming densities of the systems of various growing shapes for a wide range of initial seed densities $$\rho < 0.5$$. To gain a basic insight into the structure of the jammed states, we consider the size distribution of deposited growing objects. The presence of the most numerous and the largest growing objects is recorded for the system in the jamming state. Our results suggest that at sufficiently low seed densities $$\rho$$, the way of the object growth has a substantial influence on the percolation threshold. This influence weakens with increasing $$\rho$$ and ceases near the value of the site percolation threshold for monomers on the triangular lattice, $$\rho _\text {p}^* = 0.5$$

Fractional kinetic model for granular compaction

We present an approach to granular compaction based on subordination of stochastic processes. In order to imitate, in a very simplified way, the compaction dynamics of granular material under tapping, we impose that particles switch stochastically between the two possible orientational states characterizing the average volumes of the grain in the presence of other grains. The main physical idea of our approach is that the interaction of grains with their environment is taken into account with the aid of the temporal subordination. Accordingly, we assume that the time intervals between the consecutive grain’s reorientations are governed by a certain waiting-time distribution ψ(t). It is demonstrated how the presence of the trapping events leads to the macroscopic observation of slow compaction dynamics, described by an exact fractional kinetic equation. We also perform numerical simulations to examine our analytical result. In addition, we reproduce the memory effects numerically by considering the response of the system to the abrupt change in the external excitation

Spatial distribution of metals in urban soil of Novi Sad, Serbia: GIS based approach

Metal concentrations in urban soils of Novi Sad, Serbia were measured and the pollution sources were identified using multivariate statistical methods. During July and August 2010, a total of 121 surface soil samples were collected across the central part of the city covering a surface area of 20 km(2) (4 km x 5 km). Concentrations of As, Co, Cr, Cu, Mn, Ni, Pb, and Zn were determined using the ICP-OES device. Pb concentration varied from 8.9 mg kg(-1) to 999,1 mg kg(-1) at the examined locations. A hierarchical cluster analysis was performed on the available data sets in order to identify associations among metals. GIS mapping technique was applied to produce geochemical maps showing the hot-spots of metal contamination. The elemental relationship in correlation matrix and the results of multivariate statistics supported a natural origin of As, Co, Cr, Mn, and Ni, while Cu, Pb, and Zn originated from anthropogenic inputs. Distribution patterns obtained using GIS mapping technique implied that traffic was the most important source of pollution