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Estimates of threshold and strength of percolation clusters on square lattices with (1,π)-neighborhood
Computer Research and Modeling, 2014, v. 6, no. 3, pp. 405-414Views (last year): 4. Citations: 5 (RSCI).In this paper we consider statistical estimates of threshold and strength of percolation clusters on square lattices. The percolation threshold pc and the strength of percolation clusters P∞ for a square lattice with (1,π)-neighborhood depends not only on the lattice dimension, but also on the Minkowski exponent d. To estimate the strength of percolation clusters P∞ proposed a new method of averaging the relative frequencies of the target subset of lattice sites. The implementation of this method is based on the SPSL package, released under GNU GPL-3 using the free programming language R.
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Percolation modeling of hydraulic hysteresis in a porous media
Computer Research and Modeling, 2014, v. 6, no. 4, pp. 543-558Views (last year): 3. Citations: 1 (RSCI).In this paper we consider various models of hydraulic hysteresis in invasive mercury porosimetry. For simulating the hydraulic hysteresis is used isotropic site percolation on three-dimensional square lattices with $(1,\,\pi)$-neighborhood. The relationship between the percolation model parameters and invasive porosimetry data is studied phenomenologically. The implementation of the percolation model is based on libraries SPSL and SECP, released under license GNU GPL-3 using the free programming language R.
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Investigation of individual-based mechanisms of single-species population dynamics by logical deterministic cellular automata
Computer Research and Modeling, 2015, v. 7, no. 6, pp. 1279-1293Views (last year): 16. Citations: 3 (RSCI).Investigation of logical deterministic cellular automata models of population dynamics allows to reveal detailed individual-based mechanisms. The search for such mechanisms is important in connection with ecological problems caused by overexploitation of natural resources, environmental pollution and climate change. Classical models of population dynamics have the phenomenological nature, as they are “black boxes”. Phenomenological models fundamentally complicate research of detailed mechanisms of ecosystem functioning. We have investigated the role of fecundity and duration of resources regeneration in mechanisms of population growth using four models of ecosystem with one species. These models are logical deterministic cellular automata and are based on physical axiomatics of excitable medium with regeneration. We have modeled catastrophic death of population arising from increasing of resources regeneration duration. It has been shown that greater fecundity accelerates population extinction. The investigated mechanisms are important for understanding mechanisms of sustainability of ecosystems and biodiversity conservation. Prospects of the presented modeling approach as a method of transparent multilevel modeling of complex systems are discussed.
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International Interdisciplinary Conference "Mathematics. Computing. Education"