Michael Kopp - Academia.edu (original) (raw)

Papers by Michael Kopp

In this paper, to demonstrate the chaotic behavior of a new 6D discrete system, the modern Matlab... more In this paper, to demonstrate the chaotic behavior of a new 6D discrete system, the modern Matlab-Simulink software environment was used. We have obtained a discrete 6D chaotic system by the Euler method from a continuous 6D system of dynamic equations. In the Matlab-Simulink environment, models for continuous and discrete 6D systems of equations were created, and the results were identical. To demonstrate the synchronization of two unidirectional connected continuous and discrete 6D systems, Simulink models were proposed. A discrete 6D system was applied for the chaotic masking of a narrow-band harmonic signal and image encryption. For visualizing and practical realization of the new chaotic discrete system we used Arduino Uno board and six light-emitting diodes (LEDs). The programming code and connecting technique are also shown. The program code was debugged into the free Arduino simulation environment such as Tinkercad. Compiling hex. file in the program software Arduino IDE ...

In this work, a new nonlinear dynamic (6D) system of equations is proposed that describes the pro... more In this work, a new nonlinear dynamic (6D) system of equations is proposed that describes the process of magnetic field generation. This system of equations is an alternative to the Rikitake dynamo system describing chaotic magnetic field reversals.The behavior of the new dynamical system is studied by analyzing the stability of equilibrium points. For fixed parameters of the 6D dynamical system, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the 6D dynamical system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. We have shown that an adaptive controller is used to stabilize the novel 6D chaotic system with unknown system parameters. An active control method is derived to achieve global chaotic synchronization of two identical novels 6D chaotic systems with unknown system parameters. Based on the results obtained in ...

In this work, a new nonlinear dynamic (6D) system of equations is proposed that describes the pro... more In this work, a new nonlinear dynamic (6D) system of equations is proposed that describes the process of magnetic field generation. This system of equations is an alternative to the Rikitake dynamo system describing chaotic magnetic field reversals. The behavior of the new dynamical system is studied by analyzing the stability of equilibrium points. For fixed parameters of the 6D dynamical system, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the 6D dynamical system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. We have shown that an adaptive controller is used to stabilize the novel 6D chaotic system with unknown system parameters. An active control method is derived to achieve global chaotic synchronization of two identical novels 6D chaotic systems with unknown system parameters. Based on the results obtained in Matlab-Simulink and LabVIEW models, a chaotic signal generator for the 6D chaotic system is implemented in the Multisim environment. The results of chaotic behavior simulation in the Multisim environment show similar behavior when comparing simulation results in Matlab-Simulink and LabVIEW models.

In this paper, Matlab-Simulink and LabView models are constructed for a new nonlinear dynamic sys... more In this paper, Matlab-Simulink and LabView models are constructed for a new nonlinear dynamic system of equations in an eight-dimensional (8D) phase space. For fixed parameters of the 8D dynamical system, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the 8D dynamical system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. We have shown that an adaptive controller is used to stabilize the novel 8D chaotic system with unknown system parameters. An active control method is derived to achieve global chaotic synchronization of two identical novel 8D chaotic systems with unknown system parameters. Based on the results obtained in Matlab-Simulink and LabView models, a chaotic signal generator for the 8D chaotic system is implemented in the Multisim environment. The results of chaotic behavior simulation in the Multisim environment show similar behavior when comparing simulation results in Matlab-Simulink and LabView models.

Functional Materials, 2020

The diffusive evolution has been studied of gas-filled pore has in a bounded particle in gas medi... more The diffusive evolution has been studied of gas-filled pore has in a bounded particle in gas media. The nonlinear equation set, describing the behaviour of gas-filled pore on bounded particle is obtained. Asymptotic modes are considered for evolution of small and large pores. Analytical solutions are obtained in asymptotic modes. The comparison is conducted of these solutions with results of numerical solution of complete equation set. The characteristic regularities of gas-filled pore behavior are found at arbitrary pore position relative to matrix particle center.

East European Journal of Physics, 2020

In this paper, we investigated a new large-scale instability that arises in an obliquely rotating... more In this paper, we investigated a new large-scale instability that arises in an obliquely rotating convective electrically conducting fluid in an external uniform magnetic field with a small-scale external force with zero helicity. This force excites small-scale velocity oscillations with a small Reynolds number. Using the method of multiscale asymptotic expansions, we obtain the nonlinear equations for vortex and magnetic disturbances in the third order of the Reynolds number. It is shown that the combined effects of the Coriolis force and the small external forces in a rotating conducting fluid possible large-scale instability. The linear stage of the magneto-vortex dynamo arising as a result of instabilities of -effect type is investigated. The mechanism of amplification of large-scale vortex disturbances due to the development of the hydrodynamic - effect taking into account the temperature stratification of the medium is studied. It was shown that a «weak» external magnetic fiel...

East European Journal of Physics, 2019

Journal of Experimental and Theoretical Physics, 2018

ЖУРНАЛ ЭКСПЕРИМЕНТАЛЬНОЙ И ТЕОРЕТИЧЕСКОЙ ФИЗИКИ, 2018

Open Journal of Fluid Dynamics, 2015

In this paper, we find a new large scale instability in rotating flow forced turbulence. The turb... more In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain the nonlinear stage of the instability and the generation vortex kinks.

Issue 2 2020, 2020

In this paper we studied the weakly nonlinear stage of stationary convective instability in a non... more In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear non-autonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.

Open Journal of Fluid Dynamics, 2015

In this paper, we find a new large scale instability which appears in obliquely rotating flow wit... more In this paper, we find a new large scale instability which appears in obliquely rotating flow with the small scale turbulence, generated by external force with small Reynolds number. The external force has no helicity. The theory is based on the rigorous method of multi-scale asymptotic expansion. Nonlinear equations for instability are obtained in the third order of the perturbation theory. In this article, we explain in detail the nonlinear stage of the instability and we find the nonlinear periodic vortices and the vortex kinks of Beltrami type.

The diffusive evolution has been studied of gas-filled pore has in a bounded particle in gas medi... more The diffusive evolution has been studied of gas-filled pore has in a bounded particle
in gas media. The nonlinear equation set, describing the behaviour of gas-filled pore on
bounded particle is obtained. Asymptotic modes are considered for evolution of small
and large pores. Analytical solutions are obtained in asymptotic modes. The comparison
is conducted of these solutions with results of numerical solution of complete equation
set. The characteristic regularities of gas-filled pore behavior are found at arbitrary pore
position relative to matrix particle center.

Поступила в редакцию 1 октября 2019 г., после переработки 27 ноября 2019 г. Принята к публикации ... more Поступила в редакцию 1 октября 2019 г., после переработки 27 ноября 2019 г. Принята к публикации 28 ноября 2019 г.

Journal of Experimental and Theoretical Physics, 2018

We study the stability of a convective flow in a nonuniformly rotating plasma layer in an axially... more We study the stability of a convective flow in a nonuniformly rotating plasma layer in an axially uniform magnetic field. The stationary and oscillating regimes of magnetic convection are considered depending on the angular velocity profile (Rossby number Ro) of the electroconducting medium. Using the Galerkin method for describing the weakly nonlinear stage of evolution of convection, we have obtained a nonlinear dynamic system of Lorentz-type equations. Numerical analysis of these equations has revealed the chaotic behavior of convective flows. The criteria for the emergence of chaotic flows are obtained depending on parameters of convection (Rayleigh number Ra), magnetic field (Chandrasekhar number Q), and rotation (Taylor number Ta) for the Rayleigh (Ro =-1) and Kepler (Ro =-3/4) angular velocity profiles of the medium.

EAST EUROPEAN JOURNAL OF PHYSICS, 2019

In this paper the stability of the non-uniformly rotating cylindrical plasma in the axial uniform... more In this paper the stability of the non-uniformly rotating cylindrical plasma in the axial uniform magnetic field with the vertical temperature gradient is investigated. In the approximation of geometrical optics a dispersion equation for small axisymmetric perturbations is obtained with the effects of viscosity, ohmic and heat conductive dissipation taken into account. The stability criteria for azimuthal plasma flows are obtained in the presence of the vertical temperature gradient and the constant magnetic field. The Rayleigh-Benard problem for stationary convection in the non-uniformly rotating layer of the electrically conducting fluid in the axial uniform magnetic field is considered. In the linear theory of stationary convection the critical value of the Rayleigh number с Ra subject to the profile of the inhomogeneous rotation (Rossby number Ro) is obtained. It is shown that the negative values of the Rossby number < 0 Ro have a destabilizing effect, since the critical Rayleigh number с Ra becomes smaller, than in the case of the uniform rotation = 0 Ro , or of the rotation with positive Rossby numbers > 0 Ro. To describe the nonlinear convective phenomena the local Cartesian coordinate system was used, where the inhomogeneous rotation of the fluid layer was represented as the rotation with a constant angular velocity 0 Ω  and azimuthal shear 0 () U x  with linear dependence on the coordinate x. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number a nonlinear Ginzburg-Landau equation was obtaned. This equation describes the evolution of the finite amplitude of perturbations by utilizing the solution of the Ginzburg-Landau equation. It is shown that the weakly nonlinear convection based on the equations of the six-mode (6) D Lorentz model transforms into the identical Ginzburg-Landau equation. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various profiles of the angular velocity of the rotation of electrically conductive fluid. Досліджується стійкість циліндричної плазми, що неоднорідно обертається в аксіальному однорідному магнітному полі з вертикальним градієнтом температури. У наближенні геометричної оптики отримано дисперсійне рівняння для малих осесиметричних збурень з урахуванням ефектів в'язкості, омічної та теплопровідної дисипації. Знайдено критерії стійкості азимутальних течій плазми при наявності вертикального градієнта температури і постійного магнітного поля. Розглянуто задачу Релея-Бенара для стаціонарної конвекції в шарі електропровідної рідини, що неоднорідно обертається в аксіальному магнітному полі. У лінійній теорії стаціонарної конвекції отримано критичне значення числа Релея с Ra в залежності від профілю неоднорідного обертання (числа Росбі Ro). Показано, що негативні значення числа Росбі < 0 Ro надають дестабілізуючий ефект, оскільки критичне число Релея с Ra стає меншим, ніж у разі однорідного обертання = 0 Ro або обертання з позитивними числами Росбі > 0 Ro. Для опису нелінійних конвективних явищ використовувалася локальна декартова система координат, в якій неоднорідне обертання шару рідини представляється у вигляді обертання з постійною кутовою швидкістю 0 Ω  і азимутальним широм 0 () U x  , профіль швидкості якого є локально лінійним. В результаті застосування методу теорії збурень за малим параметром надкритичності стаціонарного числа Релея отримано нелінійне рівняння типу Гінзбурга-Ландау, що описує еволюцію кінцевої амплітуди збурень. Показано, що розглянута слабонелінійна

In this paper we studied the weakly nonlinear stage of stationary convective instability in a non... more In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear nonautonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.

In this work, a new nonlinear dynamic (6D) system of equations is proposed that describes the pro... more In this work, a new nonlinear dynamic (6D) system of equations is proposed that describes the process of magnetic field generation. This system of equations is an alternative to the Rikitake dynamo system describing chaotic magnetic field reversals. The behavior of the new dynamical system is studied by analyzing the stability of equilibrium points. For fixed parameters of the 6D dynamical system, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the 6D dynamical system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. We have shown that an adaptive controller is used to stabilize the novel 6D chaotic system with unknown system parameters. An active control method is derived to achieve global chaotic synchronization of two identical novels 6D chaotic systems with unknown system parameters. Based on the results obtained in Matlab-Simulink and LabVIEW models, a chaotic signal generator for the 6D chaotic system is implemented in the Multisim environment. The results of chaotic behavior simulation in the Multisim environment show similar behavior when comparing simulation results in Matlab-Simulink and LabVIEW models.

Functional Materials, 2020

East European Journal of Physics, 2020

East European Journal of Physics, 2019

Journal of Experimental and Theoretical Physics, 2018

ЖУРНАЛ ЭКСПЕРИМЕНТАЛЬНОЙ И ТЕОРЕТИЧЕСКОЙ ФИЗИКИ, 2018

Open Journal of Fluid Dynamics, 2015

Issue 2 2020, 2020

Open Journal of Fluid Dynamics, 2015

The diffusive evolution has been studied of gas-filled pore has in a bounded particle in gas medi... more The diffusive evolution has been studied of gas-filled pore has in a bounded particle
in gas media. The nonlinear equation set, describing the behaviour of gas-filled pore on
bounded particle is obtained. Asymptotic modes are considered for evolution of small
and large pores. Analytical solutions are obtained in asymptotic modes. The comparison
is conducted of these solutions with results of numerical solution of complete equation
set. The characteristic regularities of gas-filled pore behavior are found at arbitrary pore
position relative to matrix particle center.

Journal of Experimental and Theoretical Physics, 2018

EAST EUROPEAN JOURNAL OF PHYSICS, 2019

In this paper we studied the weakly nonlinear stage of stationary convective instability in a non... more In this paper we studied the weakly nonlinear stage of stationary convective instability in a nonuniformly rotating layer of an electrically conductive fluid in an axial uniform magnetic field under the influence of: a) temperature modulation of the layer boundaries; b) gravitational modulation; c) modulation of the magnetic field; d) modulation of the angular velocity of rotation. As a result of applying the method of perturbation theory for the small parameter of supercriticality of the stationary Rayleigh number nonlinear nonautonomous Ginzburg-Landau equations for the above types of modulation were obtaned. By utilizing the solution of the Ginzburg-Landau equation, we determined the dynamics of unsteady heat transfer for various types of modulation of external fields and for different profiles of the angular velocity of the rotation of electrically conductive fluid.