Volume 16, Issue 2 -

In the present work, employing a one-dimensional model of a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution and stationary ions, we study the amplitude modulation of electron-acoustic waves by use of the conventional reductive perturbation method. Employing the field equations with fractional power type of nonlinearity, we obtained the nonlinear Schrödinger equation as the evolution equation of the same order of nonlinearity. Seeking a harmonic wave solution with progressive wave amplitude to the evolution equation it is found that the NLS equation with fractional power assumes envelope type of solitary waves.

We present a bidirectional coupling strategy to establish targeted linear generalized synchronization between two mismatched continuous chaotic dynamical systems. The strategy is based on Routh–Hurwitz stability criterion. Using the proposed coupling scheme we are able to achieve stable linear generalized synchronization between two mismatched chaotic dynamical systems. The coupling strategy is illustrated using the paradigmatic Lorenz, Rössler and Sprott systems.

The Thomas equation is studied to obtain new exact solutions. The wave transformation technique is applied to simplify the main form of the Thomas equation from partial differential equation (PDE) to an ordinary differential equation (ODE). The modified tanh and (G′/G$$G'/G$$)-expansion methods are used with the aid of Maple software to arrive at exact solutions for the Thomas equation. Many types of solutions are obtained.

In this paper, fractional coupled Schrödinger–Korteweg–de Vries equation (or Sch–KdV) equation with appropriate initial values has been solved by using a new novel method. The fractional derivatives are described in the Caputo sense. By using the present method, we can solve many linear and nonlinear coupled fractional differential equations. Basically, the present method originated from generalized Taylor’s formula [1]. The results reveal that the proposed method is very effective and simple for obtaining approximate solutions of fractional coupled Schrödinger–KdV equation. Numerical solutions are presented graphically to show the reliability and efficiency of the method. The method does not need linearization, weak nonlinearity assumptions or perturbation theory. The convergence of the method as applied to Sch–KdV is illustrated numerically as well as derived analytically. Moreover, the results are compared with those obtained by the Adomian decomposition method (ADM).

Our research focuses on the application of airlift contactors (ALRs) for the decontamination of CO 2 -containing gas streams, such as biogas. To assess the performance of ALRs during CO 2 absorption, a complex experimental programme was applied in a laboratory-scale rectangular pneumatic contactor, able to operate either as a bubble column or as an airlift reactor. Using the experimental data, a model based on artificial neural network (ANN) was developed. The algorithm for determining the optimal neural network model and for reactor optimization is clonal selection (CS) , belonging to artificial immune system class, which is a new computational intelligence paradigm based on the principles of the vertebrate immune system. To improve its capabilities and the probability for highly suitable models and input combinations, addressing maximum efficiency, a Back-Propagation (BK) algorithm – a supervised learning method based on the delta rule – is used as a local search procedure. It is applied in a greedy manner for the best antibody found in each generation. Since the highest affinity antibodies are cloned in the next generation, the effect of BK on the suitability of the individuals propagates into a large proportion of the population. In parallel with the BK hybridization of the basic CS–ANN combination, a series of normalization procedures are included for improving the overall results provided by the new algorithm called nCS-MBK (normalized Clonal Selection-Multilayer Perceptron Neural Network and Back-Propagation algorithm). The optimization allowed for achieving the optimal reactor configuration, which leads to a maximum amount of CO 2 dissolved in water.

In order to study the different backlash, gear damping ratio and random disturbance on dynamic behavior of gear transmission system, stochastic dynamic equations of the three-degree-of-freedom spur gear transmission system are established considering random disturbances of a low-frequency external excitation induced by torque fluctuation, gear damping ratio, gear backlash, excitation frequency and meshing stiffness. Using bifurcation diagram, phase diagram, time course diagram, Poincaré map and power spectrum of the system, the dynamic characteristics of the gear transmission system with different backlash under gear damping ratio changing, and the influence of the random disturbance of gear damping ratio on the bifurcation characteristic of system are analyzed. Numerical simulation shows that the gear transmission system will be from periodic motion with a noisy disturbance to chaotic-like motion by period-doubling bifurcation with decreasing gear damping ratio. In the small damping ratio range, the backlash has great effect on the motion characteristics. Random disturbance has an important effect on the bifurcation characteristics.

This communication addresses the chemical reaction effects in two-dimensional boundary layer flow of an upper convected Maxwell (UCM) fluid over a shrinking surface. Mathematical modeling has been performed and the adequate transformations have been utilized for the conversion of partial differential system into coupled nonlinear ordinary differential system. Numerical techniques namely shooting method combined with Runge–Kutta fourth order and Newton’s method are utilized for the construction of the solutions for the velocity and the concentration fields. Dual nature of solutions for both velocity and concentration field is displayed and discussed. It is noted that the range for suction is larger for the non-Newtonian fluid when compared with the Newtonian fluid. It is also observed that two solutions exist for different values of Deborah number.