[ Laboratory | <= S.B.Vrhovac ]
My research interests include:
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Abstract: We study the relaxation process in a two-dimensional lattice gas model, based on the concept of geometrical frustration. In this model the particles are $k$-mers which can both randomly translate and rotate on the planar triangular lattice. In the absence of rotation, the diffusion of hard-core particles in crossed single-file systems is investigated. We monitor, for different densities, several quantities: mean square displacement, the self-part of the van~Hove correlation function, and the self intermediate scattering function. We observe a considerable slowing down of diffusion on a long-time scale when suppressing the rotational motion of $k$-mers; our system is subdiffusive at intermediate times between the initial transient and the long-time diffusive regime. We show that the self-part of the van~Hove correlation function exhibits, as a function of particle displacement, a stretched exponential decay at intermediate times. The self intermediate scattering function (SISF), displaying slower than exponential relaxation, suggests the existence of heterogeneous dynamics. For each value of density, the SISF is well described by the Kohlrausch-Williams-Watts law; the characteristic timescale $\tau(q_n)$ is found to decrease with the wave vector $q_n$ according to a simple power-law. Furthermore, the slowing down of the dynamics with density $\rho_0$ is consistent with the scaling law $1/{\tau(q_n;\rho_0)} \propto (\rho_c - \rho_0)^{\varkappa}$, with the same exponent $\varkappa=3.34\pm0.12$ for all wave vectors $q_n$. The density $\rho_c$ is approximately equal to the closest packing limit, $\theta_{CPL} \lessapprox 1$, for dimers on the two-dimensional triangular lattice. The self-diffusion coefficient $D_s$ scale with the same power-law exponent and critical density.
Abstract: In a preceding paper, \v{S}\'{c}epanovi\'{c} \emph{et al.} [Phys. Rev. E \textbf{84}, 031109 (2011)] studied the diffusive motion of a $k$-mers on the planar triangular lattice. Among other features of this system, we observed that the suppression of rotational motion results in a subdiffusive dynamics on intermediate length and time scales. We also confirmed that systems of this kind generally exhibit heterogeneous dynamics. Here we extend this analysis to objects of various shapes that can be made by self-avoiding random walks on a triangular lattice. We start by studying the percolation properties of random sequential adsorption of extended objects on a triangular lattice. We find that for various objects of the same length, the threshold $\rho_p^*$ of more compact shapes exceeds the $\rho_p^*$ of elongated ones. At the lower densities of $\rho_p^*$, the long-time decay of self-intermediate scattering function (SISF) is characterized by the Kohlrausch-Williams-Watts law. It is found that near the percolation threshold $\rho_p^*$, the decay of SISF to zero occurs via the power-law for sufficiently low wave-vectors. Our results establish that power-law divergence of the relaxation time $\tau$ as a function of density $\rho$ occurs at a shape-dependent critical density $\rho_c$ above the percolation threshold $\rho_p^*$. In the case of $k$-mers, the critical density $\rho_c$ cannot be distinguished from the closest packing limit $\rho_{CPL} \lessapprox 1$. For other objects, the critical density $\rho_c$ is usually below the jamming limit $\rho_{jam}$.
Abstract: 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.
Abstract: We present an analysis of the USA stock market using a simple fractal function. Financial bubbles preceding the 1987, 2000 and 2007 crashes are investigated using the Besicov- itch–Ursell fractal function. Fits show a good agreement with the S&P 500 data when a complete financial growth is considered, starting at the threshold of the abrupt growth and ending at the peak. Moving the final time of the fitting interval towards earlier dates causes growing discrepancy between two curves. On the basis of a detailed analysis of the finan- cial index behavior we propose a method for identifying the stage of the current financial growth and estimating the time in which the index value is going to reach the maximum.
Abstract: We study a stochastic lattice model describing the dynamics of a group chasing and escaping between two species in an environment that contains obstacles. The Monte Carlo simulations are carried out on a two-dimensional square lattice. Obstacles are represented by non-overlapping lattice shapes that are randomly placed on the lattice. The model includes smart pursuit (chasers to targets) and evasion (targets from chasers). Both species can affect their movement by visual perception within their finite sighting range $\sigma$.We concentrate here on the role that density and shape of the obstacles plays in the time evolution of the number of targets, $N_T(t)$. Temporal evolution of the number of targets $N_T(t)$ is found to be stretched-exponential, of the form $N_T(t) = N_T(0) - \delta N_T(\infty) \left(1 - \exp[-(t/\tau)^{\beta}]\right)$, regardless of whether the obstacles are present or not. The characteristic timescale $\tau$ is found to decrease with the initial density of targets $\rho_0^T$ according to a power-law, i.e., $\tau\propto (\rho_0^T)^{-\gamma}$. Furthermore, temporal dependences of the number of targets $N_T (t)$ are compared for various combinations of chasers and targets with different sighting ranges, $\sigma=1,\;2$, in order to analyze the relationship between the ability of species and the capture dynamics in the presence of obstacles.
Abstract: This paper examines the influence of environmental perturbations on dynamical regimes of model ecosystems. We study a stochastic lattice model describing the dynamics of a group chasing and escaping between predators and prey. The model includes smart pursuit (predators to prey) and evasion (prey from predators). Both species can affect their movement by visual perception within their finite sighting range. Non-conservative processes that change the number of individuals within the population, such as breeding and physiological dying, are implemented in the model. The model contains five parameters that control the breeding and physiological dying of predators and prey: the birth and two death rates of predators and two parameters characterizing the birth and death of prey. We study the response of our model of group chase and escape to sudden perturbations in values of parameters that characterize the non-conservative processes. Temporal dependencies of the number of predators and prey are compared for various perturbation events with different abrupt changes of probabilities affecting the non-conservative processes.
Abstract: In order to understand how a heterogeneous habitat affects the population dynamics of the predator-prey system, a spatially explicit lattice model consisting of predators, prey, and obstacles are constructed. The model includes smart pursuit (predators to prey) and evasion (prey from predators). Both species can affect their movement by visual perception within their finite sighting range. Non-conservative processes that change the number of individuals within the population, such as breeding and physiological dying, are implemented in the model. Obstacles are represented by non-overlapping lattice shapes that are randomly placed on the lattice. In the absence of obstacles, numerical simulations revealed regular, coherent oscillations with a nearly constant predator-prey phase difference. Numerical simulations have shown that changing the probabilities for non-conservative processes can increase or decrease the period of coherent oscillations in species abundances and change the relative lag between coherent components. When we introduced obstacles into the model, we observed random transitions between coherent and non-coherent oscillating regimes. In a non-coherent regime, predator and prey abundances continued to oscillate, but without a well-defined phase relationship. Our model suggests that stochasticity introduced by density fluctuations of obstacles is responsible for the reversible shift from coherent to non-coherent oscillations.
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