Z.M. Jakšić

Jamming and percolation in random sequential adsorption of extended objects on a triangular lattice with quenched impurities

Random sequential adsorption (RSA) on a triangular lattice with defects is studied by Monte Carlo simulations. The lattice is initially randomly covered by point-like impurities at a certain concentration p. The deposited objects are formed by self-avoiding random walks on the lattice. Jamming coverage and percolation threshold are determined for a wide range of impurity concentrations p for various object shapes. Rapidity of the approach to the jamming state is found to be independent on the impurity concentration. The jamming coverage decreases with the impurity concentration p and this decrease is more prominent for objects of larger size. For a certain defect concentration, decrease of the jamming coverage with the length of the walk making the object is found to obey an exponential law, . The results for RSA of polydisperse mixtures of objects of various sizes suggest that, in the presence of impurities, partial jamming coverage of small objects can have even larger values than in the case of an ideal lattice. Percolation in the presence of impurities is also studied and it is found that the percolation threshold is practically insensitive to the concentration of point defects p. Percolation can be reached at highest impurity concentrations with angled objects, and the critical defect concentration p c is lowest for the most compact objects.

Simulation Study of Granular Compaction Dynamics under Vertical Tapping

We study by numerical simulation the compaction dynamics of frictional hard disks in two dimensions, subjected to vertical shaking. 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 friction coefficient and coefficient of normal restitution. We find that the time evolution of the density is described by ρ(t)=ρ∞ − ρEα[−(t/τ)α], where Eα denotes the Mittag−Leffler function of order 0<α<1. The parameter τ is found to decay with tapping intensity Γ according to a power law τ ∝ Γ−γ , where parameter γ is almost independent of the material properties of grains. Also, an expression for the grain mobility during compaction process has been obtained.

Particle morphology effects in random sequential adsorption

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}.

Compaction of Anisotropic Granular Materials: Symmetry Effects

We perform numerical simulation of a lattice model for the compaction of a granular material based on the idea of reversible random sequential adsorption. Reversible random sequential adsorption of objects of various shapes on a two−dimensional triangular lattice is studied numerically by means of Monte Carlo simulations. The growth of the coverage ρ(t) above the jamming limit to its steady−state value ρ∞ is described by a pattern ρ (t) = ρ∞ − ρEβ[−(t/τ)β], where Eβ denotes the Mittag−Leffler function of order β ∈ (0, 1). For the first time, the parameter τ is found to decay with the desorption probability P− according to a power law τ = A P− −γ. Exponent γ is the same for all shapes, γ = 1.29 ± 0.01, but parameter A depends only on the order of symmetry axis of the shape. Finally, we present the possible relevance of the model to the compaction of granular objects of various shapes.