The weakly dissipative version of the Kolmogorov-Arnold-Moser theory and practical calculations

Богданов, Р. И.; Богданов, М. Р.

doi:10.1134/s0965542508030093

Cited by 3 publications

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“…When the parameters of the model are varied and the temperature on the boundary of the effective zone is increased, temperature fluctuations may be observed in the effective zone. This will lead to structuring of the counterflow along the radius of the effective channel, and agrees with data acquired in [5,[10][11][12]. Thus, the magnitude of the reduction in operating effectiveness is, of course, required in the recalculation that makes it possible to evaluate the operating effectiveness of the packing in a selected regime.…”

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confidence: 52%

Modeling the vertical flow of a gaseous mixture with solid inclusions in a cylindrical pipe

et al. 2011

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Reduction of experimental data obtained in fluidization and film regimes is required in the building of adequate models representing the feed of a gaseous mixture with solid inclusions into a liquid counterflow within a vessel. Reduction to a small-dimensional model permitting effective computer implementation is performed, proceeding from equations of the conservation of the radial moment of solid particles and the conservation of energy with the inclusion of laws governing the conservation of axial moments of the gas and solid particles. Results of numerical calculations within the framework of the refined model simulating MEA cleaning in a counterflow column make it possible to draw a conclusion concerning the potential for optimization of geometric characteristics of the vessel employed. Temperature fluctuations in the effective zone, i.e., structuring of the counterflow along the radius of the effective channel, may be observed when the parameters of the model are varied and the temperature on the boundary of the column is increased. Among other things, the results of the study permit assessment of the reduction in operational effectiveness of the packing in a selected regime.Reduction of experimental data obtained in fluidization and film regimes when a gaseous mixture with solid inclusion is fed into a counterflow with a liquid in a vessel is required for the development of adequate models. Reduction to a small-dimensional model that permits effective computer realization is performed below, proceeding from equations of the conservation of the radial moment of solid particles and conservation of energy with inclusion of laws governing the axial moments of the gas and solid particles. Results of numerical analyses within the framework of the refined model simulating MEA cleaning in a counterflow column enable us to conclude the potential for optimization of the geometric characteristics of the vessel under investigation. Temperature fluctuations in the effective zone, i.e., structuring of the counterflow along the radius of the effective channel, may be observed when the parameters of the model are varied and the temperature is increased on the boundary of the column. Among other things, these considerations make it possible to evaluate the reduction in operating effectiveness of the packing for a selected regime. To test the model described in [1], we examined MEA cleaning in a counterflow column. Basic equations of the model of a vertical flow of a gaseous mixture with solid inclusions in a cylindrical pipe are presented in dimensionless coordinates with consideration of particle-particle interaction and interaction of the particles with the surrounding medium, and the forces that develop as a result of particle collisions. The model includes equations of the conservation of the axial

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Modeling the vertical flow of a gaseous mixture with solid inclusions in a cylindrical pipe

et al. 2011

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“…The simplest example studied in sufficient detail to date is associated with Bogdanov-Takens bifurcation discovered in the 1970s [12,13,[24][25][26][27][28][29][30][31][32][33][34]. This bifurca tion occurs in the case of the degeneracy of dynamic systems in continuous time, dependent on two param eters.…”

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Direct measurement theory, Ito-Stratonovich theory, and weakly dissipative Kolmogorov-Arnold-Moser theory

Богданов

Kuzin

2012

J. Synch. Investig.

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The direct measurement theory studies linear functionals as applied to the problems of quantum mechanics in addition to considering quadratic functionals on the space of wave functions, well established since the beginning of the 20th century. The theory is based on the time invariance principle of an appropriate space for linear functionals. In this case, it turns out that the second order Schrödinger equation is factorized: factors "respect" the effect of one of two groups, i.e., the group of inertial gas motion or the nonlinear group. In the weakly dissipative Kolmogorov-Arnold-Moser (KAM) theory, the former group is of extraordinary interest in connection with the formation of caustic curves which, in turn, cause the appearance of advanced and delayed potentials, which makes it possible to estimate anew the ideas of Ito-Stratonovich in the theory of stochastic processes.

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Methods of evaluation and scale of functional spaces

Богданов

2013

J Math Sci

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The weakly dissipative version of the Kolmogorov-Arnold-Moser theory and practical calculations

Cited by 3 publications

References 10 publications

Modeling the vertical flow of a gaseous mixture with solid inclusions in a cylindrical pipe

Modeling the vertical flow of a gaseous mixture with solid inclusions in a cylindrical pipe

Direct measurement theory, Ito-Stratonovich theory, and weakly dissipative Kolmogorov-Arnold-Moser theory

Methods of evaluation and scale of functional spaces

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