Values Of Perturbation Parameters Research Articles

Analysis of stability of non-collinear equilibrium points: Application to Sun–Mars and Proxima Centauri systems

In the present work, we employ the modified elliptic restricted three-body problem by considering some additional perturbed forces such as: the radiation pressure, the primaries’ oblateness, and the effect of dust belt for studying the dynamical motion of the infinitesimal body. The semi-analytical solutions for the locations of non-collinear equilibrium points are obtained. The proposed model is applied to real astronomical systems. Thus, the Sun–Mars and the Proxima Centauri systems are used to estimate numerically and graphically the locations of these points in both systems at different values of perturbation parameters. In this context, the critical mass values are evaluated for both systems to analyze the stability motion of the infinitesimal body around the locations of equilibrium points and find the stability range of these locations. We demonstrate that the stability of non-collinear points in both systems depends on the parameter of mass ratio values of its own system. It is observed that the locations of these points and their stability will be affected significantly due to the changes in the values of perturbation parameters.

Fitted Tension Spline Method for Singularly Perturbed Time Delay Reaction Diffusion Problems

A uniformly convergent numerical method is presented for solving singularly perturbed time delay reaction-diffusion problems. Properties of the continuous solution are discussed. The Crank–Nicolson method is used for discretizing the temporal derivative, and an exponentially fitted tension spline method is applied for the spatial derivative. Using the comparison principle and solution bound, the stability of the method is analyzed. The proposed numerical method is second-order uniformly convergent. The theoretical analysis is supported by numerical test examples for various values of perturbation parameters and mesh size.

Accelerated Numerical Method for Singularly Perturbed Differential Difference Equations

In this paper, accelerated finite difference method for solving singularly perturbed delay reaction-diffusion equations is presented. First, the solution domain is discretized. Then, the derivatives in the given boundary value problem are replaced by finite difference approximations and the numerical scheme that provides algebraic systems of equations is obtained, which can easily be solved by Thomas algorithm. The consistency, stability and convergence of the method have been established. To increase the accuracy of our established scheme we used Richardson's extrapolation techniques. To validate the applicability of the proposed method, four model examples have been considered and solved for different values of perturbation parameters and mesh sizes. The numerical results have been presented in tables and graphs to illustrate; the present method approximates the exact solution very well. Moreover, the present method gives better accuracy than the existing numerical methods mentioned in the literature.

Diffusion and escape times in the open-leaky standard map.

We study the connection between transport phenomenon and escape rate statistics in two-dimensional standard map. For the purpose of having an open phase space, we let the momentum coordinate vary freely and restrict only angle with periodic boundary condition. We also define a pair of artificial holes placed symmetrically along the momentum axis where the particles might leave the system. As a consequence of the leaks the diffusion can be analyzed making use of only the ensemble of survived particles. We present how the diffusion coefficient depends on the size and position of the escape regions. Since the accelerator modes and, thus, the diffusion are strongly related to the system's control parameter, we also investigate effects of the perturbation strength. Numerical simulations show that the short-time escape statistics do not follow the well-known exponential decay especially for large values of perturbation parameters. The analysis of the escape direction also supports this picture as a significant amount of particles skip the leaks and leave the system just after a longtime excursion in the remote zones of the phase space.

Differential Transform Technique on the Effect of Baffle Convective Nanofluid Flow in Saturated Porous Channel

Simulations are shown for steady nanofluid saturated with porous medium in a vertical channel divided into two way by placing a thin baffle. Tiwari and Das model applied for continuity, momentum and energy equations are written using to define the nanofluid and non-Darcy model used for porous medium. The nonlinear equations are solved analytically using regular perturbation method and by semi analytical method using differential transform method. The validity of the solutions obtained by perturbation method and differential transform method are compared and found that they agree very well for small values of perturbation parameters. The numerical values of the velocity and temperature are shown graphically at different baffle positions for all the pertinent parameters. The Nusselt number for both regular and nanofluids are evaluated and tabulated.

Effect of small-scale bernstein turbulence on low-frequency plasma waves in the preflare solar chromosphere

The studied region is a part of the current circuit of a magnetic loop in a solar active region in the altitude range of 1400–2500 km above the photosphere. At the earliest stage of development of a flare process, the magnetic field of the loop was assumed to be stationary and uniform in the interval corresponding to weak fields (the so-called deca-hectogauss fields). The conditions for emergence and development of instability of the second harmonic of Bernstein modes in this previously unexamined region were determined. This instability (and low-frequency instabilities emerging later) was assumed to be caused by the sub-Dreicer electric field of the loop, while pair Coulomb collisions were considered to be the major factor hindering its development. The obtained extremely low instability thresholds point to the possibility of subsequent emergence of low-frequency instabilities (and plasma waves corresponding to them) with much higher threshold values against the background of saturated Bernstein turbulence. The frequency of electron scattering by turbulence pulsations in this scenario normally exceeds the frequency of pair Coulomb (primarily ion–electron) collisions. Both the quasistatic sub-Dreicer field in the loop and the weak spatial inhomogeneity of plasma temperature and density were taken into account in the process of derivation and analysis of the dispersion relation for low-frequency waves. It was demonstrated that the solutions of the obtained dispersion relation in the cases of prevalent pair Coulomb collisions and dominant electron momentum losses at pulsations of saturated Bernstein turbulence are morphologically similar and differ only in the boundary values of perturbation parameters. In both cases, these solutions correspond to the two wave families, namely, kinetic Alfven waves and kinetic ion acoustic waves. These waves have their own electric fields and may play the important role in the process of preflare acceleration of energetic electrons.

The effect of nonlinear damping on vibrational resonance and chaotic behavior of a beam fixed at its two ends and prestressed

This research work is based on the study of the dynamic of one-degree-of freedom nonlinear oscillator representing a built-in clamped–clamped prestressed beam model with a nonlinear damping. First of all, we model this moving structure where we regard the perturbations as a combination of both low-frequency force and high-frequency force. Then, we analyze the occurrence of vibrational resonance, where the response consists of a slow motion and a fast motion respectively with low and high frequencies. Through this, we obtain an approximate analytical expression of the response amplitude and we determine the values of the low frequency and the amplitude of the high-frequency force at which vibrational resonance occurs. The theoretical predictions are found to be in good agreement with numerical results. Moreover, for fixed parameters values of the system, as the nonlinear damping vary, we found appearance and the disappearance of resonance with or without cross-well motion. Secondly, we study the chaotic dynamic of the beam. In this case, critical values of perturbation parameters for the onset of the chaotic motion are specified using Melnikov’s method. Hence, the global dynamical changes of the system have been examined by plotting phase portrait, bifurcation diagram and their corresponding Lyapunov exponent.

Data-informed influence analysis

The likelihood-based influence analysis methodology introduced in Cook (1986) uses a parameterised space of local perturbations of a base model.It is frequently the case that such perturbation schemes involve more parameters of interest and perturbation parameters than there are observations, and hence the perturbation space is often explored rather than estimated, where exploration means discovering the effect on inference of putatively choosing values of perturbation parameters. This paper considers the question of what can be learned about the perturbation parameters through the data. It extends Cook's methodology to take account of information available in the data regarding the perturbations, the general philosophy of the approach being that of learn what you can and explore what you cannot learn. Both local and global analyses are possible, as indicated by the data, while the eigenvector sign indeterminacy of local analysis is removed. Numerical examples are given and further developments are briefly indicated.

Energy levels of a two-dimensional anharmonic oscillator: Hill determinant approach

The energy levels of the Schrodinger equation for the potentialx 2+y 2+λ[a xxx4+2a xyx2 y 2+a yyy4] are calculated using Hill determinant approach for several eigenstates and over a wide range of values of perturbation parameters. The obtained numerical results agree with those previously reported by other methods.