Browsing by Author "Dujak, Dijana"

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    Anomalous tracer diffusion in the presence of extended obstacles on a triangular lattice
    Lončarević, Ivana; Dujak, Dijana; Jakšić, Zorica; Karač, Aleksandar; Budinski-Petković, Ljuba; Vrhovac, Slobodan
    Proteins diffuse to their sites of action within cells in a crowded, strongly interacting environment of nucleic acids and other macromolecules. An interesting question is how the highly crowded environment of biological cells affects the dynamic properties of passively diffusing particles. The Lorentz model is a generic model covering many of the aspects of transport in a heterogeneous environment. We investigate biologically relevant situations of immobile obstacles of various shapes and sizes. The Monte Carlo simulations for the diffusion of a tracer particle are carried out on a two-dimensional triangular lattice. Obstacles are represented by non-overlapping lattice shapes that are randomly placed on the lattice. Our simulation results indicate that the mean-square displacement displays anomalous transport for all obstacle shapes, which extends to infinite times at the corresponding percolation thresholds. In the vicinity of this critical density the diffusion coefficient vanishes according to a power law, with the same conductivity exponent for all obstacle shapes. At the fixed density of obstacles, we observe that the diffusion coefficient is higher for the smaller obstacles if the object size is defined as the highest projection of the object on one of the six directions on the triangular lattice. The dynamic exponent, which describes the anomalous transport at the critical density, is the same for all the obstacle shapes. Here we show that the values of critical exponents estimated for all disordered environments do not depend on the microscopic details of the present model, such as obstacle shape, and agree with the predicted values for the underlying percolation problem. We also provide the evidence for a divergent non-Gaussian parameter close to the percolation transition for all obstacle shapes.
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    Percolation and jamming properties in particle shape-controlled seeded growth model
    Dujak, Dijana; Karač, Aleksandar; Budinski-Petković, Ljuba; Jakšić, Zorica; Vrhovac, Slobodan
    We consider the percolation model with nucleation and simultaneous growth of multiple finite clusters, taking the initial seed concentration ρ 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 ρ< 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 ρ, the way of the object growth has a substantial influence on the percolation threshold. This influence weakens with increasing ρ and ceases near the value of the site percolation threshold for monomers on the triangular lattice, ρp∗=0.5.
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    Percolation in irreversible deposition on a triangular lattice: Effects of anisotropy
    Lončarević, Ivana; Budinski-Petković, Ljuba; Dujak, Dijana; Karač, Aleksandar; Jakšić, Zorica; Vrhovac, Slobodan
    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 creases 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.
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    Percolation in random sequential adsorption of mixtures on a triangular lattice
    Dujak, Dijana; Karač, Aleksandar; Budinski-Petković, Ljuba; Lončarević, Ivana; Jakšić, Zorica; Vrhovac, Slobodan
    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 θp for mixtures of objects covering the same number of sites is always lower than θp for the more compact object, and it can be even lower than θp for both components. Mixtures of percolating and non-percolating objects almost always percolate, but the percolation threshold is higher than θp for the percolating component. Adding a shape of high connectivity to a system of compact nonpercolating objects, makes the deposit percolate. Lowest percolation thresholds are obtained for mixtures with elongated angled objects. Dependence of θp on the object length exhibits a minimum, so it could be estimated that the angled objects of length 6 ≤ ℓ ≤ 10 give the largest contribution to the percolation.
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    The Study of Percolation with the Presence of Extended Impurities
    Lončarević, Ivana; Budinski-Petković, Ljuba; Dujak, Dijana; Karač, Aleksandar; Jakšić, Zorica; Vrhovac, Slobodan
    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 ℓ. For a wide range of impurity concentrations p, percolation threshold θp∗ is determined for k-mers, angled objects and triangles of two different sizes. For sufficiently large impurities, percolation threshold θp∗ of all examined objects increases with concentration p, and this increase is more prominent for impurities of a larger length ℓ. We determine the critical concentrations of pc∗ defects above which it is not possible to achieve percolation for a given object, for impurities of various lengths ℓ. It is found that the critical concentration pc∗ of finite-size impurities decreases with the length ℓ 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.