COMPUTER SIMULATION OF SELF-ORGANIZATION OF CLUSTER SYSTEMS: DEPENDENCE OF STRUCTURE OF GENESIS AND CONTROL PARAMETERS
Kryvchenko Yuri , Odesa National Academy of Food Technologies, Odesa, Ukraine
Urgency of the research. Percolation methods show high efficiency in the study of matter, genesis and evolution of connected regions in materials. In such problems, the cluster system of the physical body and its impact on the object as a whole are studied. The study of the structure and properties of percolation clusters will make it possible to investigate and predict the behavior of objects (solids) under various environmental conditions, the genesis of their formations in time.
Target setting. The practical investigation of cluster systems in solids is associated with the complexity and labor intensity of the experiments. The main problems are that to obtain reliable information about the structure and properties it is necessary to synthesize clusters with a wide range of parameters and create a reliable system for their diagnostics.
Actual scientific researches and issues analysis. The article reviews recent publications in Ukrainian and foreign journals, including experimental and theoretical papers containing studies of self-organizing criticality.
Uninvestigated parts of general matters defining. In the above studies, the possibilities of describing the processes of generation and evolution of cluster systems in solids are expanding; there is a hypothesis that allows significantly increase the number of variants of cluster formation.
The research objective. To conduct simulation of cluster formation with interacting elements using the Monte Carlo method. To determine the dependence of the parameters of self-organizing percolation systems on the degree of self-organization, the correlation length, the generation rate of the system, and other parameters. To get analytical expressions for dependencies and relative error values.
The statement of basic materials. To solve the problems associated with the practical study of cluster systems, a software complex for modeling cluster formation has been developed, in which the cluster-cluster and cluster-particle interactions are simulated. In the model, a multidimensional percolation problem is solved. As an algorithm for the growth of clusters, a path to increase sequentially a given number of particles is used.
Conclusions. Computer calculations carried out, in particular, by the Monte Carlo method, give the most reliable predictions of the properties of percolation systems. Analytic expressions are obtained for the dependences of the power of an infinite cluster, its radius, the degree of anisotropy and lacunarity from the aggregation distance, on the number of particles generated at each iteration, and on the number of acts of interaction between the elements of the cluster system, and also the first three dimensions of the Renyi spectrum are calculated.
self-organizing criticality; percolation problems with self-organization; cluster structure; interaction of particles; cluster formation; computer modelling.
1. Feder, J. (1988). Fractals. New York: Plenum Press [in English].
2. Mandelbrot, B. (1982). The Fractal Geometry of Nature. San Francisco: W.H. Freeman and Co [in English].
3. Bak, P. (1998). Life laws. Nature, 391, 652-653 [in English].
4. Bak, P., Tang, C., Wiesenfeld, K. (1987). Self-organized criticality: an explanation of 1/f noice. Physical Review Letters, 59, 381–384 [in English].
5. Bak, P., Tang, C., Wiesenfeld, K. (1988). Self-organized criticality. Physical Review, A38, 367–374 [in English].
6. Zelenyi, L., Milovanov A. (2004). Fractal topology and strange kinetics: from percolation theory to problems in cosmic electrodynamics. Phys. Usp., 47, 749–788 [in English].
7. Zosimov, V., Tarasov, D. (1997). Dynamic fractal structure of emulsions, caused by the motion and interaction of particles. The numerical model. Journal of Experimental and Theoretical Physics, 84, 725–730 [in English].
8. Herega, A., Drik, N.G., Ugolnikov, A.P. (2012). Hybrid ramified Sierpinski carpet: percolation transition, critical exponents, and force field. Physics-Uspekhi, 55, 519–521 [in English].
9. Sokolov, I. M. (1986). Dimensionalities and Other Geometrical Critical Exponents in Percolation Theory. Sov. Phys. Usp., 29, 924–945 [in English].
10. Herega, A. (2018). The Selected Models of the Mesostructure of Composites: Percolation, Clusters, and Force Fields. Heidelberg: Springer [in English].
11. Herega, A., Sukhanov, V., Vyrovoy, V. (2016). Multicentric genesis of material structure: Development of the percolation model and some applications. AIP Conference Proceedings, 20–72 [in English].
12. Alencar, A. M., Andrade, J. S. Jr., Lucena, L. S. (1997). Self-organized percolation. Physical Review, E56, 2379–2383 [in English].
13. Chubynsky, M. V., Brière, M.-A., Mousseau, N. (2006). Self-organization with equilibration: A model for the intermediate phase in rigidity percolation. Physical Review, E74 [in English].
14. Sheinman, M., Sharma, A., Alvarado, J., Koenderink, G. H., MacKintosh, F. C. (2015). Anomalous discontinuity at the percolation critical point of active gels. Physical Review Letters, 114 [in English].