Dynamical analysis for cylindrical geometry in non-minimally coupled f(R,T) gravity

2021 ◽  
Author(s):  
M. Z. Bhatti ◽  
Z. Yousaf ◽  
M. Yousaf
Keyword(s):  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Momentum Tensor ◽  
Dynamical Analysis ◽  
Dynamical Equations ◽  
Physical Constraints ◽  
Cylindrical System ◽  
Modified Gravity Theory ◽  
The Stability ◽  
Tensor Formula

This paper aims to investigate the stability constraints under the influence of particular modified gravity theory [Formula: see text], i.e. [Formula: see text] gravity in which the Lagrangian is a varying function of [Formula: see text] and trace of energy momentum tensor ([Formula: see text]). We examine stable behavior for compact cylindrical star having anisotropic symmetric configuration. We establish dynamical equations as well as equations of continuity in the background of this particular non-minimal coupled [Formula: see text]. We utilize perturbation technique which will be applied on geometrical as well as material physical quantities to constitute collapse equation. We continue this significant investigation to understand the dynamical behavior of considered cylindrical system under non-minimal coupled [Formula: see text] functional, i.e. [Formula: see text]. This gravitational function gives compatible findings only for [Formula: see text], also [Formula: see text] and [Formula: see text] considered in this astrophysical model as coupling entity. This model contains [Formula: see text] which is constant entity, having the values of order of the effective Ricci scalar [Formula: see text]. Furthermore, we impose some physical constraints to determine and maintain the stability criteria by establishing the expression of adiabatic index, i.e. [Formula: see text] for cylindrical anisotropic configuration, in Newtonian [Formula: see text] and post-Newtonian ([Formula: see text]) eras.

Dynamics of shearing viscous fluids in f(R,T) gravity

2017 ◽  
Vol 27 (01) ◽  
pp. 1750181 ◽  
Author(s):  
Hina Azmat ◽  
M. Zubair ◽  
Ifra Noureen
Keyword(s):  
Cylindrical Symmetry ◽  
Dynamical Analysis ◽  
Index Formula ◽  
Anisotropic Fluid ◽  
Perturbation Approach ◽  
Field Equations ◽  
Dynamical Equations ◽  
Cylindrical System ◽  
Pressure Anisotropy ◽  
The Stability

In this paper, we have analyzed the dynamical stability of shearing viscous anisotropic fluid with cylindrical symmetry in [Formula: see text] theory. We have chosen two viable [Formula: see text] models for dynamical analysis, and explored their nature and role for stable stellar configuration. Modified field equations and corresponding dynamical equations have been constructed, perturbation approach is adopted to deal with complexity of these equations. With the help of perturbed dynamical equations, the evolution equation has been established to analyze the role of shear viscosity and pressure anisotropy on dynamics of cylindrical system. The adiabatic index [Formula: see text] is used to investigate the instabilities appearing in Newtonian (N) and post-Newtonian (pN) approximations. Some conditions are found for material variables that are required to meet the stability criterion. We compare the outcomes of our analysis with the results of various models available in literature to reach at more comprehensive conclusion.

Impact of f(R,T) gravity in evolution of charged viscous fluids

2021 ◽  
Vol 30 (04) ◽  
pp. 2150027
Author(s):  
I. Noureen ◽  
Usman-ul-Haq ◽  
S. A. Mardan
Keyword(s):  
Stability Analysis ◽  
Energy Momentum Tensor ◽  
Momentum Tensor ◽  
Viscous Fluids ◽  
Fluid Distribution ◽  
Perturbation Scheme ◽  
Field Equations ◽  
Dynamical Equations ◽  
Stability Of Stars ◽  
The Stability

In this work, the evolution of spherically symmetric charged anisotropic viscous fluids is discussed in framework of [Formula: see text] gravity. In order to conduct the analysis, modified Einstein Maxwell field equations are constructed. Nonzero divergence of modified energy momentum tensor is taken that implicates dynamical equations. The perturbation scheme is applied to dynamical equations for stability analysis. The stability analysis is carried out in Newtonian and post-Newtonian limits. It is observed that charge, fluid distribution, electromagnetic field, viscosity and mass of the celestial objects greatly affect the collapsing process as well as stability of stars.

scholarly journals Fixed Point Root-Finding Methods of Fourth-Order of Convergence

Symmetry ◽  
2019 ◽  
Vol 11 (6) ◽  
pp. 769 ◽  
Author(s):  
Alicia Cordero ◽  
Lucía Guasp ◽  
Juan R. Torregrosa
Keyword(s):  
Weight Function ◽  
Dynamical Behavior ◽  
Nonlinear Problems ◽  
Dynamical Analysis ◽  
Function Technique ◽  
Weight Functions ◽  
Good Tool ◽  
Quadratic Polynomials ◽  
Root Finding ◽  
The Stability

In this manuscript, by using the weight-function technique, a new class of iterative methods for solving nonlinear problems is constructed, which includes many known schemes that can be obtained by choosing different weight functions. This weight function, depending on two different evaluations of the derivative, is the unique difference between the two steps of each method, which is unusual. As it is proven that all the members of the class are optimal methods in the sense of Kung-Traub’s conjecture, the dynamical analysis is a good tool to determine the best elements of the family in terms of stability. Therefore, the dynamical behavior of this class on quadratic polynomials is studied in this work. We analyze the stability of the presented family from the multipliers of the fixed points and critical points, along with their associated parameter planes. In addition, this study enables us to select the members of the class with good stability properties.

COMPLEX DYNAMICAL ANALYSIS OF A COUPLED NETWORK FROM INNATE IMMUNE RESPONSES

2013 ◽  
Vol 23 (11) ◽  
pp. 1350180 ◽  
Author(s):  
JINYING TAN ◽  
XIUFEN ZOU
Keyword(s):  
Immune Responses ◽  
Negative Feedback ◽  
Equilibrium Points ◽  
Dynamical Behavior ◽  
Innate Immune ◽  
Dynamical Analysis ◽  
Innate Immune Responses ◽  
Dynamical Behaviors ◽  
Positive And Negative Feedback ◽  
The Stability

In this paper, we investigate the complex dynamical behaviors of a biological network that is derived from innate immune responses and that couples positive and negative feedback loops. The stability conditions of the non-negative equilibrium points (EPs) of the system are obtained, using the theory of dynamical systems, and we deduce that no more than three stable EPs exist in this system. Through bifurcation analysis and numerical simulations, we find that the system presents rich dynamical behaviors, such as monostability, bistability and oscillations. These results reveal how positive and negative feedback cooperatively regulate the dynamical behavior of the system.

scholarly journals Dynamical Analysis of an Interleaved Single Inductor TITO Switching Regulator

2009 ◽  
Vol 2009 ◽  
pp. 1-19 ◽  
Author(s):  
Abdelali El Aroudi ◽  
Vanessa Moreno-Font ◽  
Luis Benadero
Keyword(s):  
Chaotic Behavior ◽  
Piecewise Linear ◽  
Dynamical Behavior ◽  
Current Mode ◽  
Operating Conditions ◽  
Dynamical Analysis ◽  
Time Intervals ◽  
Switching Regulator ◽  
Duty Cycles ◽  
The Stability

We study the dynamical behavior of a single inductor two inputs two outputs (SITITO) power electronics DC-DC converter under a current mode control in a PWM interleaved scheme. This system is able to regulate two, generally one positive and one negative, voltages (outputs). The regulation of the outputs is carried out by the modulation of two time intervals within a switching cycle. The value of the regulated voltages is related to both duty cycles (inputs). The stability of the whole nonlinear system is therefore studied without any decoupling. Under certain operating conditions, the dynamical behavior of the system can be modeled by a piecewise linear (PWL) map, which is used to investigate the stability in the parameter space and to detect possible subharmonic oscillations and chaotic behavior. These results are confirmed by numerical one dimensional and two-dimensional bifurcation diagrams and some experimental measurements from a laboratory prototype.

scholarly journals Performance Analysis of a Peak-Current Mode Control with Compensation Ramp for a Boost-Flyback Power Converter

2016 ◽  
Vol 2016 ◽  
pp. 1-14 ◽  
Author(s):  
Juan-Guillermo Muñoz ◽  
Guillermo Gallo ◽  
Gustavo Osorio ◽  
Fabiola Angulo
Keyword(s):  
Closed Loop ◽  
Power Converters ◽  
Monodromy Matrix ◽  
Current Mode ◽  
Power Converter ◽  
Dynamical Analysis ◽  
Dynamical Equations ◽  
Peak Current ◽  
Operation Conditions ◽  
The Stability

High voltage gain power converters are very important in photovoltaic applications mainly due to the low output voltage of photovoltaic arrays. This kind of power converters includes three or more semiconductor devices and four or more energy storage elements, making the dynamical analysis of the controlled system more difficult. In this paper, the boost-flyback power converter is controlled by peak-current mode with compensation ramp. The closed-loop analysis is performed to guarantee operation conditions such that a period-1 orbit is attained. The converter is considered as a piecewise linear system, and the closed-loop stability is determined by using the monodromy matrix, obtained by the composition of the saltation matrixes with the solutions of the dynamical equations in the linear intervals. The largest eigenvalue of the monodromy matrix gives the stability of the period-1 orbit, and a deep analysis using bifurcation diagrams let us reach a conclusion about the loss of the stability, which is experimentally verified. To avoid overcompensation effects, the minimum value required by the compensation ramp is obtained, and the minimum and maximum values of the load resistance are found too. The system has a good transient response under disturbances in the load and in the input voltage.

scholarly journals Dynamical analysis of a giving up smoking model with time delay

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Zizhen Zhang ◽  
Ruibin Wei ◽  
Wanjun Xia
Keyword(s):  
Hopf Bifurcation ◽  
Time Delay ◽  
Local Stability ◽  
Center Manifold ◽  
Dynamical Behavior ◽  
Sufficient Conditions ◽  
Dynamical Analysis ◽  
Normal Form Theory ◽  
Center Manifold Theorem ◽  
Form Theory

AbstractIn this paper, we are concerned with a delayed smoking model in which the population is divided into five classes. Sufficient conditions guaranteeing the local stability and existence of Hopf bifurcation for the model are established by taking the time delay as a bifurcation parameter and employing the Routh–Hurwitz criteria. Furthermore, direction and stability of the Hopf bifurcation are investigated by applying the center manifold theorem and normal form theory. Finally, computer simulations are implemented to support the analytic results and to analyze the effects of some parameters on the dynamical behavior of the model.

scholarly journals Nonlinear Dynamics and Stability Analysis of a Three-Cell Flying Capacitor DC-DC Converter

2021 ◽  
Vol 11 (4) ◽  
pp. 1395
Author(s):  
Abdelali El Aroudi ◽  
Natalia Cañas-Estrada ◽  
Mohamed Debbat ◽  
Mohamed Al-Numay
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Monodromy Matrix ◽  
Dynamical Behavior ◽  
Period Doubling ◽  
Simple Expression ◽  
Buck Converter ◽  
State Variables ◽  
Bifurcation Phenomena ◽  
The Stability

This paper presents a study of the nonlinear dynamic behavior a flying capacitor four-level three-cell DC-DC buck converter. Its stability analysis is performed and its stability boundaries is determined in the multi-dimensional paramertic space. First, the switched model of the converter is presented. Then, a discrete-time controller for the converter is proposed. The controller is is responsible for both balancing the flying capacitor voltages from one hand and for output current regulation. Simulation results from the switched model of the converter under the proposed controller are presented. The results show that the system may undergo bifurcation phenomena and period doubling route to chaos when some system parameters are varied. One-dimensional bifurcation diagrams are computed and used to explore the possible dynamical behavior of the system. By using Floquet theory and Filippov method to derive the monodromy matrix, the bifurcation behavior observed in the converter is accurately predicted. Based on justified and realistic approximations of the system state variables waveforms, simple and accurate expressions for these steady-state values and the monodromy matrix are derived and validated. The simple expression of the steady-state operation and the monodromy matrix allow to analytically predict the onset of instability in the system and the stability region in the parametric space is determined. Numerical simulations from the exact switched model validate the theoretical predictions.

The Static and Dynamic Behavior of MEMS Arches Under Electrostatic Actuation

2009 ◽  
Author(s):  
Hassen M. Ouakad ◽  
Mohammad I. Younis ◽  
Fadi M. Alsaleem ◽  
Ronald Miles ◽  
Weili Cui
Keyword(s):  
Multiple Scales ◽  
Perturbation Technique ◽  
Dynamical Behavior ◽  
Primary Resonance ◽  
Reduced Order Model ◽  
Harmonic Load ◽  
Order Model ◽  
Reduced Order ◽  
Electrostatically Actuated ◽  
Model Equations

In this paper, we investigate theoretically and experimentally the static and dynamic behaviors of electrostatically actuated clamped-clamped micromachined arches when excited by a DC load superimposed to an AC harmonic load. A Galerkin based reduced-order model is used to discretize the distributed-parameter model of the considered shallow arch. The natural frequencies of the arch are calculated for various values of DC voltages and initial rises of the arch. The forced vibration response of the arch to a combined DC and AC harmonic load is determined when excited near its fundamental natural frequency. For small DC and AC loads, a perturbation technique (the method of multiple scales) is also used. For large DC and AC, the reduced-order model equations are integrated numerically with time to get the arch dynamic response. The results show various nonlinear scenarios of transitions to snap-through and dynamic pull-in. The effect of rise is shown to have significant effect on the dynamical behavior of the MEMS arch. Experimental work is conducted to test polysilicon curved microbeam when excited by DC and AC loads. Experimental results on primary resonance and dynamic pull-in are shown and compared with the theoretical results.

Stability of Shear-Thickening Liquids Between Rotating Cylinders

2010 ◽  
Author(s):  
Nariman Ashrafi ◽  
Habib Karimi Haghighi
Keyword(s):  
Couette Flow ◽  
Dynamical Behavior ◽  
Shear Thickening ◽  
Shear Thinning ◽  
Taylor Vortex ◽  
Shear Dependent Viscosity ◽  
Shear Thinning Fluids ◽  
Shear Thickening Fluids ◽  
The Stability ◽  
Dependent Viscosity

The effects of nonlinearities on the stability are explored for shear thickening fluids in the narrow-gap limit of the Taylor-Couette flow. It is assumed that shear-thickening fluids behave exactly as opposite of shear thinning ones. A dynamical system is obtained from the conservation of mass and momentum equations which include nonlinear terms in velocity components due to the shear-dependent viscosity. It is found that the critical Taylor number, corresponding to the loss of stability of Couette flow becomes higher as the shear-thickening effects increases. Similar to the shear thinning case, the Taylor vortex structure emerges in the shear thickening flow, however they quickly disappear thus bringing the flow back to the purely azimuthal flow. Naturally, one expects shear thickening fluids to result in inverse dynamical behavior of shear thinning fluids. This study proves that this is not the case for every point on the bifurcation diagram.

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