Promoting or Suppressing Transition to Weak Turbulence in Porous Media Convection via Feedback Control

2011 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Porous Media ◽  
Feedback Control ◽  
Transition Point ◽  
Initial Conditions ◽  
Practical Significance ◽  
Weak Turbulence ◽  
Simple Transformation ◽  
Transition To Chaos ◽  
Main Effect ◽  
Transformation Of Variables

A method of using feedback control to promote or suppress the transition to chaos in porous media convection is demonstrated in this paper. Feedback control is used in the present paper to provide a comparison between an analytical expression for the transition point to chaos and numerical results. In addition it is shown that such a feedback control can be applied as an excellent practical means for controlling (suppressing or promoting) chaos by using a Magyari transformation. The latter shows that the controlled model can be transformed into the uncontrolled one via a simple transformation of variables implying that the main effect the feedback control has on the solution is equivalent to altering the initial conditions. The theoretical and practical significance of such an equivalent alteration of the initial conditions is presented and discussed.

Heat Transfer Regimes and Hysteresis in Porous Media Convection

2000 ◽  
Vol 123 (1) ◽  
pp. 145-156 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Heat Transfer ◽  
Heat Flux ◽  
Porous Media ◽  
Nusselt Number ◽  
Transition Point ◽  
Initial Conditions ◽  
Turbulent Convection ◽  
Practical Significance ◽  
Lorenz Equations ◽  
Adomian’S Decomposition Method

Results of an investigation of different heat transfer regimes in porous media convection are presented by using a truncated Galerkin representation of the governing equations that yields the familiar Lorenz equations for the variation of the amplitude in the time domain. The solution to this system is obtained analytically by using a weak non-linear analysis and computationally by using Adomian’s decomposition method. Expressions for the averaged Nusselt number are derived for steady, periodic, as well as weak-turbulent (temporal-chaotic) convection. The phenomenon of Hysteresis in the transition from steady to weak-turbulent convection, and backwards, is particularly investigated, identifying analytically its mechanism, which is confirmed by the computational results. While the post-transient chaotic solution in terms of the dependent variables is very sensitive to the initial conditions, the affinity of the averaged values of these variables to initial conditions is very weak. Therefore, long-term predictability of these averaged variables, and in particular the Nusselt number, becomes possible, a result of substantial practical significance. Actually, the only impact that the transition to chaos causes on the predicted results in terms of the averaged heat flux is a minor loss of accuracy. Therefore, the predictability of the results in the sense of the averaged heat flux is not significantly affected by the transition from steady to weak-turbulent convection. The transition point is shown to be very sensitive to a particular scaling of the equations, which leads the solution to an invariant value of steady-state for sub-transitional conditions, a result that affects the transition point in some cases.

Analytical Prediction of the Transition to Chaos in Porous Media Natural Convection

2008 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Stability Analysis ◽  
Analytical Solution ◽  
Linear Stability Analysis ◽  
Transition Point ◽  
Analytical Prediction ◽  
Linear Solution ◽  
Transition To Chaos ◽  
Validity Condition

The failure of the linear stability analysis to predict accurately the transition point from steady to chaotic solutions in porous media natural convection motivates this study. A weak non-linear solution to the problem is shown to produce an accurate analytical expression for the transition point as long as the validity condition and consequent accuracy of the latter solution is fulfilled. The analytical results are compared to accurate computational solutions showing an excellent fit within the validity domain of the analytical solution.

Computer simulation of optical radiation scattering by aerosol media

2020 ◽  
Vol 86 (8) ◽  
pp. 43-48
Author(s):  
V. V. Semenov
Keyword(s):  
Finite Element Method ◽  
Computer Simulation ◽  
Finite Element ◽  
Optical Radiation ◽  
Light Transmission ◽  
Initial Conditions ◽  
Practical Significance ◽  
The Finite Element Method ◽  
Dispersed Medium ◽  
Element Method

Development of the technologies simulating optical processes in an arbitrary dispersed medium is one of the important directions in the field of optical instrumentation and can provide computer simulation of the processes instead of using expensive equipment in physical experiments. The goal of the study is simulation of scattering of optical radiation by aerosol media using the finite element method to show a practical significance of the results of virtual experiments. We used the following initial conditions of the model: radius of a spherical particle of distilled water is 1 μm, wavelength of the incident optical radiation is 0.6328 μm, air is a medium surrounding the particle. An algorithm for implementation of the model by the finite element method is proposed. A subprogram has been developed which automates a virtual experiment for a group of particles to form their random arrangement in the model and possibility of changing their geometric shape and size within predetermined intervals. Model dependences of the radiation intensity on the scattering angle for single particle and groups of particles are presented. Simulation of the light transmission through a dispersed medium provides development of a given photosensor design and determination of the minimum number of photodetectors when measuring the parameters of the medium under study via analysis of the indicatrix of scattering by a group of particles.

scholarly journals Effect of Nonlinear Dissipation on the Basin Boundaries of a Driven Two-Well Modified Rayleigh–Duffing Oscillator

2015 ◽  
Vol 25 (02) ◽  
pp. 1550024 ◽  
Author(s):  
C. H. Miwadinou ◽  
A. V. Monwanou ◽  
J. B. Chabi Orou
Keyword(s):  
Initial Conditions ◽  
Duffing Oscillator ◽  
Excitation Amplitude ◽  
Nonlinear Damping ◽  
Homoclinic Bifurcation ◽  
Nonlinear Dissipation ◽  
Transition To Chaos ◽  
Melnikov Criterion ◽  
Quadratic Nonlinearities ◽  
Basin Boundaries

This paper considers the effect of nonlinear dissipation on the basin boundaries of a driven two-well modified Rayleigh–Duffing oscillator where pure cubic, unpure cubic, pure quadratic and unpure quadratic nonlinearities are considered. By analyzing the potential, an analytic expression is found for the homoclinic orbit. The Melnikov criterion is used to examine a global homoclinic bifurcation and transition to chaos. Unpure quadratic parameter and parametric excitation amplitude effects are found on the critical Melnikov amplitude μ cr . Finally, the phase space of initial conditions is carefully examined in order to analyze the effect of the nonlinear damping, and particularly how the basin boundaries become fractalized.

Analytical Prediction of the Transition to Chaos in Lorenz System

2008 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Stability Analysis ◽  
Analytical Solution ◽  
Linear Stability Analysis ◽  
Transition Point ◽  
Lorenz System ◽  
Analytical Prediction ◽  
Lorenz Equations ◽  
Linear Solution ◽  
Transition To Chaos ◽  
Validity Condition

The failure of the linear stability analysis to predict accurately the transition point from steady to chaotic solutions in Lorenz equations motivates this study. A weak non-linear solution to the problem is shown to produce an accurate analytical expression for the transition point as long as the validity condition and consequent accuracy of the latter solution is fulfilled. The analytical results are compared to accurate computational solutions showing an excellent fit within the validity domain of the analytical solution.

Allometric Weight–Length Regression Model

1969 ◽  
Vol 26 (1) ◽  
pp. 123-131 ◽  
Author(s):  
L. V. Pienaar ◽  
J. A. Thomson
Keyword(s):  
Regression Model ◽  
Nonlinear Model ◽  
Nonlinear Estimation ◽  
Multiplicative Model ◽  
The Other ◽  
Practical Significance ◽  
Sample Problem ◽  
Length Relationship ◽  
The Common ◽  
Transformation Of Variables

Two methods of fitting the allometric weight–length relationship are described, one involving the common logarithmic transformation of variables in a multiplicative model and the other assuming an additive nonlinear model and general nonlinear estimation procedures. Differences in the assumptions involved in the two methods are emphasized and the practical significance of the different methods is demonstrated with the aid of a sample problem. A number of procedures are suggested to compensate for possibly unjustified assumptions.

Weak Turbulence in Small Prandtl Number Convection in Porous Media

2010 ◽  
Author(s):  
Peter Vadasz
Keyword(s):  
Porous Media ◽  
Stability Analysis ◽  
Prandtl Number ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Weak Turbulence ◽  
Numerical Computations ◽  
Prandtl Numbers ◽  
Convection In Porous Media

The dynamics of weak turbulence in small Prandtl number convection in porous media is substantially distinct than the corresponding dynamics for moderate and large Prandtl numbers. Linear stability analysis is performed and its results compared with numerical computations to reveal the underlying phenomena.

Position Control of an Underactuated Planar 2R Manipulator

2001 ◽  
Author(s):  
José A. Rosas-Flores ◽  
Jaime Alvarez-Gallegos ◽  
Rafael Castro-Linares
Keyword(s):  
Feedback Control ◽  
Optimization Algorithm ◽  
Position Control ◽  
Initial Conditions ◽  
Error Modeling ◽  
Underactuated System

Abstract In this paper the problem of regulation of an underactuated planar 2R manipulator is solved by tracking appropriate planned trajectories. A class of parametric trajectories is propossed to reach a desired configuration. The parameters of the trajectories are found by using an optimization algorithm. Besides, a feedback control is proposed to regulate the manipulator under error modeling and small desviations on the initial conditions. By using simulations, it is illustrated that if the coordinates of the underactuated system track the planned trajectories then the system reaches the desired configuration.

CONCEPTUAL PROVISIONS OF THE STATE POLICY OF ENSURING THE ECONOMIC SECURITY OF UKRAINE IN THE CONDITIONS OF MODERN THREATS AND DIGITALIZATION

2021 ◽  
Vol 298 (5 Part 1) ◽  
pp. 280-286
Author(s):  
Olga GARAFONOVA ◽  
◽  
Liydmyla POLISHCHUK ◽  
Liudmyla DYKHNYCH ◽  
Inna YASHCHENKO ◽  
...  
Keyword(s):  
National Economy ◽  
State Policy ◽  
Structural Changes ◽  
Initial Conditions ◽  
Positive Impact ◽  
Economic Security ◽  
The State ◽  
Practical Significance ◽  
External Threats ◽  
The Impact

The article focuses on the relevance of identification and typology of modern risks and threats to the economic security of Ukraine. According to the nature of modern risks and threats, they are classified as hybrid. The hybrid nature of modern threats to Ukraine’s economic security necessitates the application of new approaches to the formation and implementation of state policy to ensure the economic security of Ukraine’s national economy. It is shown that the economic security of the state is a complex dynamic system that requires constant monitoring and management of resilience to internal and external threats in order to ensure a positive impact on socio-economic development, improve macroeconomic development, ensure quality and necessary structural changes and institutional reforms. formation of the system of competitiveness of the national economy. Under such conditions, the general goal of state policy should be to improve Ukraine’s economic security system, ensure a higher level of its resistance to the impact of hybrid risks and threats, factors and conditions of globalization and the world order. The elements of the state policy of economic security of Ukraine are determined, namely – the initial conditions, the purpose of state policy, goals and principles of policy, directions of formation of the system of counteraction to security threats, financial-resource and organizational-managerial support. The practical significance of the research results is that the immaturity of the integral system of economic security of the state is identified, which is due to the imperfection of the institutional environment, the imbalance of its structure, the predominance of the role of informal institutions over formal ones. The scientific novelty of the study is to substantiate the conceptual provisions of state policy to ensure the economic security of the state in the face of non-standard hybrid risks and threats.

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