Fractional structure «mixing - transport» as an open system - Владимирский, Эдуард Иосифович; Исмайлов, Бахрам Исрафил оглы (Eastern-European Journal of Enterprise Technologies, 2014)
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.