Banamali Roy

Solution of the Duffing–van der Pol oscillator equation by a differential transform method

In this paper, we have tried to implement a relatively new exact series method of solution, known as the differential transform method, for solving one of the widely studied and challenging equations in nonlinear dynamics, the Duffing–van der Pol oscillator equation. Chandrasekar et al (2004 J. Phys. A 37 4527) showed that the force-free Duffing–van der Pol oscillator is completely integrable for a specific parametric choice, and they derived a general solution for this parametric choice. The results of this paper are in sufficient agreement with those of Chandrasekar et al.

The role of negative ions on the Jeans instability in a complex plasma in the presence of nonthermal positive ions

The role of negative ions on Jeans instability in the presence of nonthermal positive ions has been investigated in this paper. Electrons and negative ions are considered Boltzmann-distributed, while the positive ions follow nonthermal velocity distribution. A negatively charged dust component is modeled by continuity and momentum equations. The linear dispersion relation shows that the presence of negative ions reduces the critical value of the nonthermal parameter acr, which consequently increases the unstable region and hence pronounces the Jeans instability. The growth rate of this Jeans instability decreases with the increasing negative ion temperature.

Effect of secondary electron emission on the Jeans instability in a dusty plasma

In this paper the effect of secondary electron emission on Jeans instability in a dusty plasma has been investigated. Due to secondary electron emission, dust grains may have two stable equilibrium states out of which one is negative and the other is positive. Here both cases have been considered separately. It has been shown that secondary electron emission enhances Jeans instability when equilibrium dust charge is negative. It has also been shown that growth rate of Jeans instability reduces with increasing secondary electron emission when equilibrium dust charge is positive.

Effect of secondary electron emission on the propagation of dust acoustic waves in a dusty plasma

The effect of secondary electron emission on dust acoustic wave (DA) propagation has been investigated based on orbit motion limited theory of dust grain charging. The emitted secondaries are assumed to have the same temperature as that of the ambient plasma electrons so that the plasma effectively consists of three components: the ions, electrons, and the variable charge dusts. Together with the effect of secondary emission, the effect of ion and electron capture and ionization of neutral atoms and recombination have been included in the ion and electron fluid equations. Small amplitude perturbation is considered about a charge neutral steady state. It is seen that if the dust charge is positive there may occur under certain conditions zero frequency exponentially growing perturbation about the equilibrium. The possibility of the occurrence of such purely growing mode in a dusty plasma was not noted earlier. The frequency and damping decrement of DA waves in dusty plasmas with negatively charged dust and...

Jean's instability in a drifting dusty plasma in the presence of secondary electron emission

In this paper, we have studied the effect of dust drift on Jeans instability in a complex plasma in the presence of secondary electron emission from dust grains. The drift motion of dust grains is shown to be responsible for the excitation of dust-ion-acoustic Jeans mode (DIAJ), which grows with oscillation at a frequency depending exclusively on the dust drift. This oscillation of the growing DIAJ mode develops due to energy loss of the wave to the dust grains and the ions when the drift velocity is nearly equal to the phase velocity of the wave.

Jeans instability in a complex plasma in the presence of negative ions

General fluid dispersion relations for the Jeans instability in a complex plasma have been derived in two cases. (i) Electrons, positive ions and negative ions are all Boltzmann distributed and dust grains are cold and inertial. (ii) Electrons are Boltzmann distributed, positive ions and negative ions are inertial and dust grains are streaming. In both cases grain charge fluctuations are considered. Both the dispersion relations show that presence of negative ions reduces the threshold of the Jeans instability in the complex plasma system. The streaming motion of dust grains is responsible for the development of an unstable mode which is not purely growing.

Propagation of dust acoustic waves in a complex plasma with negative ions

The role of negative ions on dust acoustic wave (DAW) propagation has been investigated based on orbit motion limited (OML) theory of dust grain charging. The complex plasma being assumed as composed of Boltzmannian electrons, positive ions, negative ions and variable charge dust grains. It is found that the presence of low temperature negative ions reduces both the frequency and damping of the dust acoustic waves implying that lower frequency dust acoustic waves propagate in a complex plasma with low temperature negative ions for longer time interval.

SOLUTION OF HIGHER-ORDER ABEL EQUATIONS BY DIFFERENTIAL TRANSFORM METHOD

In this paper, the second-, third- and fourth-order Abel equations are solved. The differential transform method (DTM) is used to compute approximate solutions of the nonlinear ordinary Abel differential equations. The results are compared with the results obtained by the classical Runge–Kutta (RK4) method. Figures are presented to show the reliability and simplicity of the method.

Effect of Streaming Negative Ions on Dust Acoustic Wave Propagation in Complex Plasma

The role of streaming negative ions on the dust acoustic wave (DAW) propagation has been investigated based on orbit motion limited (OML) theory of dust grain charging. The complex plasma being assumed as composed of Boltzmanian electrons, inertial positive ions, streaming negative ions and the variable charge dust grains. Dust charge is assumed to be fluctuating. It is found that the dust acoustic wave becomes unstable when ratio of the thermal velocity with the streaming velocity of negative ions crosses some threshold value.

Jeans instability in the background of secondary electron emission in a complex plasma

In this paper, the effect of secondary electron emission on the Jeans instability in a dusty plasma has been investigated. Owing to secondary electron emission, dust grains may have two stable equilibrium states one of which is negative and the other is positive. In this paper, the case of positive dust grains is reported. Positively charged dust grains attract lighter electrons and repel heavier ions, which resist charge condensation by restricting dust-mass enhancement. As secondary electron emission increases, the dust grains acquire more positive charge and acquire more electrons and repel more heavier ions; this increases the threshold of the Jeans instability. It has been shown that the growth rate of the Jeans instability decreases with increasing secondary electron emission when the equilibrium dust charge is positive.