Fractional structure «mixing - transport» as an open system
DOI:
https://doi.org/10.15587/1729-4061.2014.26199Keywords:
open system, fractional structure, Poincare recurrence time, fractality, visualization, exponent, interference, dynamics, Levy, Chirikov-TaylorAbstract
In the context of a research area “open systems physics”, fractional structure “mixing – transport” as an open system is proposed. The studies of power-law nonlocality and power-law memory, allowing to create mathematical methods, successfully used in transport (transfer) systems are considered.
Interaction paradigm of geoinformation space with fractional structure “mixing – transport” is proposed. It is shown that the interaction is crystallized into fractional structure “transport - mixing – transport”, formalization of which is presented as an open system model. It is noted that due to the complexity of the open system, the formation of various structures, such as Levy processes and random walks in fractal time is possible in it.
A base for understanding anomalous transport, adequate to Levy flights, is an association with superdiffusion processes, considered in transport theory.
It is noted that in describing the properties of systems with fractal structure, representations of Euclidean geometry cannot be used. There is a need to analyze these processes in terms of the fractional dimension geometry. Systems with fractal feature are characterized by effects such as memory, complex spatial mixing processes and self-organization.
Using the new research area - open systems physics, which integrates the fields such as synergy, dissipative structures, deterministic chaos, fractal concept introduces a new level of understanding in implementing complex tasks at interdisciplinary level.
A new vision of the open system, which is characterized by coherent Lagrangian structure (stable and unstable manifolds of fixed points and periodic orbits) and finite-time Lyapunov exponent is shown.
Based on the ideology of the nonlinear recursive analysis and the Poincare theory, visual images of Poincare fractional-order diagrams for the cases of the interference component influence in various frequency ranges are first acquired. Moreover, numerical characteristics of the fractional-order fractal dimension and the average Poincare recurrence time are obtained.
References
- Tarasov, V. E. (2012). The fractional oscillator as an open system. centr.eur.j.phys. De Gruyter Open Sp. z o.o., 10 (2), 382–389. doi:10.2478/s11534-012-0008-0
- Klimontovich, Y. L. (1996). Relative ordering criteria in open systems. Uspekhi Fizicheskikh Nauk. Uspekhi Fizicheskikh Nauk (UFN) Journal, 166 (11), 1231–1243 doi:10.3367/ufnr.0166.199611f.1231
- Tarasov, V. Ye. Avtoreferat dissertatsii (2011). Modeli teoreticheskoy fiziki s integro-differentsirovaniyem drobnogo poryadka. Na soiskaniye uchenoy ctepeni doktora fiziko-matematicheskikh nauk. Moskva.
- Tarasov, V. E. (2010). Fractional Dynamics of Open Quantum Systems. Fractional Dynamics. Springer Science + Business Media, 467–490. doi:10.1007/978-3-642-14003-7_20
- Zeleny, L. M., Milovanov, A. V. (2004). Fraktalnaya topologiya i strannaya kinetika: ot teorii perkolyatsii k problemam kosmicheskoy elektrodinamiki. Uspehi Fizicheskih Nauk, 174 (8), 810–850.
- Logunov, M. Yu., Butkovsky, L. Ya. (2008). Peremeshivaniye i lyapunovskiye pokazateli khaoticheskikh sistem.ZhTF, 78 (5), 1–8.
- Benkadda, S., Kassibrakis, S., White, R. B., Zaslavsky, G. M. (1996). Self-similarity and transport in the standard map, 1–28. doi:10.2172/304169
- Rossi, L., Turchetti, G., Vaienti, S. (2005). Poincaré recurrences as a tool to investigate the statistical properties of dynamical systems with integrable and mixing components. Journal of Physics: Conference Series, 7, 94–100. doi:10.1088/1742-6596/7/1/008
- Anishchenko, V. S., Astakhov, S. V. (2013). Teorija vozvratov Puankare i ejo prilozhenie k zadacham nelinejnoj fiziki. Uspekhi Fizicheskikh Nauk (UFN) Journal, 183 (10), 1009–1028. doi:10.3367/ufnr.0183.201310a.1009
- Vladimirsky, E. I. (2012). Vremena vozvrashcheniya Puankare pri vzaimodeystvii khaoticheskikh i stokhasticheskikh sistem. Eastern-European Journal of Enterprise Technologies, 6/4 (60), 4–8.
- Laskin, N., Lambadaris, I., Harmantzis, F. C., Devetsikiotis, M. (2002). Fractional Lévy motion and its application to network traffic modeling. Computer Networks, 40(3), 363–375. doi:10.1016/s1389-1286(02)00300-6
- Tarasov, V. E., Edelman, M. (2010). Fractional dissipative standard map. Chaos: An Interdisciplinary Journal of Nonlinear Science, 20 (2), 023–127. doi:10.1063/1.3443235
- Tagiyev, R. A., Vladimirsky, E. I. (2006). Matematicheskaya model integrirovannoy geoinformatsionnoy sistemy s prinyatiyem resheny po dannym aerokosmicheskikh izmereny. Izv. NAN Azerbaydzhana, XXVI (3), 146–151.
- Chukbar, K. V. (1995). Stokhastichesky perenos i drobnye proizvodnye. ZhETF, 108/5 (11), 1875–1884.
- Marquardt, T. (2006). Fractional Lévy processes with an application to long memory moving average processes. Bernoulli, 12 (6), 1099–1126. doi:10.3150/bj/1165269152
- Tarasov, V. E. (2013). Review of some promising fractional physical models. International Journal of Modern Physics B, 27 (09), 1330005. doi:10.1142/s0217979213300053
- Savin, A. V., Savin, D. V. (2013). The coexistence and evolution of attractor in the web map with weak dissipation. Arxiv: 1302.5361[nin CD], 1–6.
- Koshel, K. V., Prants, S. V. (2006). Khaoticheskaya advektsiya v okeane. Uspehi fizicheskih nauk, 176 (11), 1177–1205.
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