Abstract:
Abstract: This work studies the
active control of chemical oscillations governed by a forced modified Van der
Pol-Duffing oscillator. We considered the dynamics of nonlinear chemical
systems subjected to an external sinusoidal excitation. The approximative
solution to the first order of the modified Van der Pol-Duffing oscillator is
found using the Lindstedt’s perturbation method. The harmonic balance method is
used to find the amplitudes of the oscillatory states of the system under
control. The effects of the constraint parameterand the control
parameterof the modelon the amplitude of oscillations are
presented. The effects of the active control on the behaviors of the model are
analyzed and it appears that with the appropriate selection of the coupling
parameter, the chaotic behavior of the model has given way to periodic
movements. Numerical simulations are used to validate and complete the
analytical results obtained.

We consider f(R,T) theory of gravity, where R is the curvature scalar and T is the trace of the energy momentum tensor. Attention is attached to the special case, f(R,T)=R+2f(T) and two expressions are assumed for the function f(T),(a_{1}T^{n}+b_{1})/(a_{2}T^{n}+b_{2}) and a_{3}In^{q}(b_{
}

Abstract:
This paper analyses the effects of small injection/suction Reynolds number, Hartmann parameter, permeability parameter and wave number on a viscous incompressible electrically conducting fluid flow in a parallel porous plates forming a channel. The plates of the channel are parallel with the same constant temperature and subjected to a small injection/suction. The upper plate is allowed to move in flow direction and the lower plate is kept at rest. A uniform magnetic field is applied perpendicularly to the plates. The main objective of the paper is to study the effect of the above parameters on temporal linear stability analysis of the flow with a new approach based on modified Orr-Sommerfeld equation. It is obtained that the permeability parameter, the Hartmann parameter and the wave number contribute to the linear temporal stability while the small injection/suction Reynolds number has a negligible effect on the stability.

Abstract:
The rotating Rayleigh-Bénard convection in the presence of helical force is modeled by a four mode Lorenz model. This model is extended to study how this force affects the onset of Küppers-Lortz (KL) instability. We observed that when S < 3, the critical Taylor number and the critical angle for the onset of KL instability decrease as helical force intensity S increases. This influence of helical force is similar to that obtained in rotating fluid layer under periodic modulation of the rotation rate (Bhattacharjee, 1990). In the range 3 S 14.9246, the system exhibits the reentrant behavior of rolls demonstrating the constructive and destructive role of rotation in the KL instability apparition. In this case, we observed that the application of this force allows the KL instability for small values of Taylor number. In addition, it has been found that there exists a threshold (14.9246) in the magnitude of the helical force that allows suppressing the KL instability in the system for any value of Taylor number.

Abstract:
We investigate particle production in an expanding universe under the assumption that the Lagrangian contains the Einstein term $R$ plus a modified gravity term of the form $R^\alpha$, where $\alpha$ is a constant. Dark fluid is considered as the main content of the universe and the big rip singularity appears. Quantum effects due to particle creation is analysed near the singularity and we find that for $\alpha\in ]1/2, 1[$, quantum effects are dominant and the big rip may be avoided whereas for $\alpha\in J$ the dark fluid is dominant and the singularity remains. The Cardy-Verlinde formula is also introduced and its equivalence with the total entropy of the universe is checked. It is found that this can always occur in Einstein gravity while in f(R) gravity, it holds only for $\alpha=\frac{n+1}{2n+6}$, $n$ being the space dimension, corresponding to the situation in which the big rip cannot be avoided.

Abstract:
We investigate inviscid instability in an electrically conducting fluid affected by a parallel magnetic field. The case of low magnetic Reynolds number in Poiseuille flow is considered. When the magnetic field is sufficiently strong, for a flow with low hydrodynamic Reynolds number, it is already known that the neutral disturbances are three-dimensional. Our investigation shows that at high hydrodynamic Reynolds number(inviscid flow), the effect of the strength of the magnetic field on the fastest growing perturbations is limited to a decrease of their oblique angle i.e. angle between the direction of the wave propagation and the basic flow. The waveform remains unchanged. The detailed analysis of the linear instability provided by the eigenvalue problem shows that the magnetic field has a stabilizing effect on the electrically conducting fluid flow. We find also that at least, the unstability appears if the main flow possesses an inflexion point with a suitable condition between the velocity of the basic flow and the complex stability parameter according to Rayleigh's inflexion point theorem.

Abstract:
For applications regarding transition prediction, wing design and control of boundary layers, the fundamental understanding of disturbance growth in the flat plate boundary layer is an important issue. In the present work we investigate the stability of boundary layer in Poiseuille flow. We normalize pressure and time by inertial and viscous effects. The disturbances are taken to be periodic in the spanwise direction and time. We present a set of linear governing equations for the parabolic evolution of wavelike disturbances. Then, we derive the so-called modified Orr-Sommerfeld equation that can be applied in the layer. Contrary to what one might think of, we find that Squire’s theorem is not applicable for the boundary layer. We find also that normalization by inertial or viscous effects leads to the same order of stability or instability. For the 2-D disturbances flow, we find the same critical Reynolds number for our two normalizations. This value coincides with the one we know for neutral stability of the known Orr-Sommerfeld equation. We notice also that for all over values of k in the case , correspond the same values of at whatever the normalization. We therefore conclude that in the boundary layer with 2-D disturbances, we have the same neutral stability curve whatever the normalization. We find also that for a flow with high hydrodynamic Reynolds number, the neutral disturbances in the boundary layer are two dimensional. At last, we find that transition from stability to instability or the opposite can occur according to the Reynolds number and the wave number.

Abstract:
This paper considers effect of nonlinear dissipation on the basin boundaries of a driven two-well Modified Rayleigh-Duffing Oscillator where pure and unpure quadratic and cubic 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 in the case of our oscillator. It is found the effects of unpure quadratic parameter and amplitude of parametric excitation on the critical Melnikov amplitude $\mu_{cr}$. Finally, we examine carefully the phase space of initial conditions in order to analyze the effect of the nonlinear damping, and particular how the basin boundaries become fractalized.

Abstract:
In this paper the equation of forced Van der Pol generalized oscillator is examined with renormalization group method. A brief recall of the renormalization group technique is done. We have applied this method to the equation of forced Van der Pol generalized oscillator to search for its asymptotic solution and its renormalization group equation. The analysis of the numerical simulation graph is done; the method's efficiency is pointed out.

Abstract:
We investigate the effect of small suction Reynolds number and permeability parameter on the stability of Poiseuille fluid flow in a porous medium between two parallel horizontal stationary porous plates . We have shown that the perturbed flow is governed by an equation named modified Orr-Sommerfeld equation. We find also that the normalization of the wall-normal velocity with characteristic small suction (or small injection) velocity is important for a perfect command of porous medium fluid flow stability analysis. The stabilizing effect of the parameters in general and small suction Reynolds number and permeability parameters in particular on the linear stability are found.