Phase Transition as an Emergent Phenomenon Analysed by Violation of Structural Invariant (M, BM)
Abstract
When modeling complex systems, we usually encounter the following difficulties: partiality, large amounts of data and uncertainty of conclusions. The most common approach used for modeling is the physical approach, sometimes reinforced by statistical procedures. If we assume emergences in the complex system, a physical approach is not appropriate at all. Instead, we build here the approach of structural invariants. In this paper, we show that another plane can be built above the plane of physical description, which is responsible for violation of structural invariants. Main attention is concentrated (in this article) on the invariant matroid and bases of matroid (M, BM) in combination with Ramsey graph theory. In addition, the article introduces a calculus that describes the emergent phenomena using two quantities - the power of the emergent phenomenon and the complexity of the structure of the considered complex system. We show the application of the method for modeling phase transition in chemistry.
References
Bila, J. The detection of emergent situations by structural invariants. In Proceedings of 17th International Conference on Soft Computing - MENDEL 2011 (2011), R. Matousek, Ed., VUT Press, pp. 534-539.
Bila, J. Modeling of complex systems by means of partial algebras. In Proc. of Interdisciplinary Symposium of Complex Systems (2014), A. Sanayei, I. Zelinka, and O. Rossler, Eds., Springer: Heidelberg, Germany, pp. 89-100.
Bila, J. Emergent phenomena in complex systems and their detection. International Journal of Enhanced Research in Science Technology and Engineering 6 (2017), 40-53.
Bila, J. Emergent phenomena in complex systems. Advances in Intelligent Systems and Computing 837 (2019), 262-270.
Bila, J., and Novak, M. Detection of emergent situations in complex systems by structural invariant (MB, M). MENDEL 23 (2017), 163-170.
Bila, J., Rodriguez, R., and Novak, M. Emergent phenomena in natural complex systems. MENDEL 25 (2019), 103-110.
Blaha, P., Schwarz, K., Madses, G., Kvasnicka, D., and Luitz, J., 2001. wien2k, An Augmented plane wave - Local Orbitals. Program for Calculating Crystal Properties.
Draper, P., Meade, P., Reece, M., and Shih, D. Implication of a 125 gev higgs for the mssm and low-scale susy breaking. Physical Review D 85 (2012), Article ID 095007.
Hohenberg, P., and Kohn, W. Inhomogeneous electron gas. Physical Review 136 (1964), Article ID B864.
Holland, T. Foundations for the modeling and simulation of emergent behavior systems. In Engineering Emergence: Modeling and Simulation Approach (2018), L. Rainey and M. Jamshidi, Eds., CRS Press /Taylor and Francis: Boca Raton, USA, pp. 217-258.
Johnson, J., and Padilla, J. Ontology of emergence. In Engineering Emergence: Modeling and Simulation Approach (2018), L. Rainey and M. Jamshidi, Eds., CRS Press /Taylor and Francis: Boca Raton, USA, pp. 185-198.
Kotyrba, M., Volna, E., and Bujok, P. Unconventional modeling of complex system via cellular automata and differential evolution. Swarm and Evolutionary Computation 25 (2015), 52-62.
Laughlin, R. A Different Universe (Reinventing Physics from the Bottom Down). Basic Books, New York, USA, 2006.
Oxley, J. Matroid Theory. Oxford Science Publications, Oxford, UK, 2001.
Ramsey, F. On a problem of formal logic. Proceedings of the London Mathematical Society 30 (1930), 264-286.
Reshak, A., Alahmed, Z., and Bila, J. Phase transition in BaThO3 from Pbnm to Ibmm turn the fundamentals energy band gap from indirect to direct. Journal of Alloys and Compounds 771 (2019), 607-613.
Reshak, A., Alahmed, Z., Bila, J., and et al. Exploration of the electronic structure of monoclinic alpha-Eu2(MoO4)(3): DFT-based study and X-ray photoelectron spectroscopy. The Journal of Physical Chemistry C 120 (2016), 10559-10568.
Saaty, T. Exploring the inference between hierarchies, multiple objectives and fuzzy sets. Fuzzy Sets and Systems 1 (1978), 57-68.
Siegenfeld, A., and Bar-Yam, Y. An introduction to complex systems science and its applications. Complexity (2020), Article ID 6105872.
Weinstein, W. Ramsey Number. A Wolfram Web Resource: https://mathworld.wolfram.com/RamseyNumber.html.
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