Volume 18, Issue 6 -

We compute the conservation laws for the Rosenau-Kortweg de Vries equation coupling with the Regularized Long-Wave equation using Noether’s approach through a remarkable method of increasing the order of the Rosenau-KdV-RLW equation. Furthermore, exact solutions for the Rosenau- KdV-RLW equation are acquired by employing the Kudryashov method.

This paper concentrates on the role of prostitutes in HIV/AIDS disease transmission among common population. In this communication, a nonlinear Susceptible-Infected-Treated-AIDS infected (SITA) model is developed to study the transmission dynamics of HIV/AIDS infection in three different classes. The behavior of the model is analyzed by the basic reproduction number R 0 and the results of the model are investigated by using stability theory of differential equations. Analysis of the model demonstrates that the disease-free equilibrium is locally stable for R0<1${R_0}\, \lt \,1$ and at R0>1,${R_0} \gt \,1, \,$ the endemic equilibrium is globally stable. Further, numerical simulation of the model is carried out.

The paper presents a numerical study of the discharged heat water effect on the aquatic environment from the thermal power plant by using two water discharged pipes. It is solved by the Navier–Stokes and temperature transport equations for an incompressible fluid in a stratified medium. The aim of this study is to improve the existing water discharge system to reduce the heat load on the reservoir-cooler of the thermal power plants operation (Ekibastuz SDPP-1). In this study thermal pollution to the reservoir-cooler using only two water discharged pipes as so using the existing one and building only one additional in the eastern part of the reservoir-cooler is numerically simulated. The numerical method is based on the projection method which was approximated by the finite volume method. The numerical solution of the equation system is divided into four stages. The algorithm is parallelized on a high-performance computer. The obtained numerical results of three-dimensional stratified turbulent flow for two water discharged pipes of the thermal power plant were compared with experimental data and with numerical results for one water discharged pipe. General thermal load in the reservoir-cooler decreases comparing one water discharged pipe and revealed qualitatively and quantitatively approximately the basic laws of hydrothermal processes occurring in the reservoir-cooler can be seen that from numerical simulations where two water discharged pipes were used.

In this article, we develop an accurate and efficient wavelet-based collocation method for solving both linear and nonlinear singularly perturbed boundary-value problems that arise in fluid mechanics. The properties of the Haar wavelet expansions together with operational matrix of integration are used to convert the underlying problems into systems of algebraic equations which can be efficiently solved by suitable solvers. The performance of the numerical scheme is assessed and tested on specific test problems and the comparisons are given with other methods existing in the recent literature. The numerical outcomes indicate that the method yields highly accurate results and is computationally more efficient than the existing ones.

The delay-dependent state estimation problem for Takagi-Sugeno fuzzy stochastic neural networks with time-varying delays is considered in this paper. We aim to design state estimators to estimate the network states such that the dynamics of the estimation error systems are guaranteed to be exponentially stable in the mean square. Both fuzzy-rule-independent and the fuzzy-rule-dependent state estimators are designed. Delay-dependent sufficient conditions are presented to guarantee the existence of the desired state estimators for the fuzzy stochastic neural networks. Finally, two numerical examples demonstrate that the proposed approaches are effective.

This paper is a contribution to a better understanding of heat transfer through porous channels used for mechanical sieving and filtration of liquids. The problem modeled by means of the Navier–Stokes equations and the energy equation is similar to a viscous flow between two uniformly permeable walls fixed at different temperatures. Thermal behaviors are determined through three branches denoted solutions of types I, II and III of a diagram of bifurcations presenting the values of the wall shear stress as the Reynolds number varies. We found that the distribution of temperature is similar through branches I and II where a large horizontal inflection area is observed as the Péclet number increases. This large horizontal inflection area inside the channel denotes the presence of thermal boundary layers which more precisely occur across branches I and II when the Péclet number approaches the value of 10. On the other hand, along branch III, thermal boundary layers do not exist and temperature presents a different behavior compared to those of branches I and II.

This paper presents the experimental investigation on synchronization of two Van der Pol oscillators with polynomial and delay unidirectional couplings. The intervals of coupling coefficients and delay leading to synchronization are determined experimentally using analog electronic circuits. Three cases are considered: autonomous Van der Pol oscillators, sinusoidally exited Van der Pol oscillators in the chaotic state and Van der Pol oscillators with two slowly sinusoidal excitations delivering periodic patterns of periodic pulses. It is found that the degree of the polynomial coupling reduces the intervals of coupling coefficients leading to synchronization and the delay affects the coupling intervals in a periodic way. The experimental results agree well with the results of the theoretical (mathematical and numerical) investigation.

The cart-pendulum system is a typical benchmark problem in the control field. It is a fully underactuated system having one control input for two degrees-of-freedom (DOFs) system. It has highly nonlinear structure, which can be used to validate different nonlinear and linear controllers and has wide range of real-time (realistic) applications like rockets propeller, tank missile launcher, self-balancing robot, stabilization of ships, design of earthquake resistant buildings, etc. In this work, modeling, simulation and real-time control of a cart-pendulum system is performed. The mathematical model of the system is developed using Euler-Lagrange approach. In order to achieve a more realistic model, the actuator dynamics is considered in the mathematical model. The main aim of this work is to investigate the performance of two different control strategies- first to swing-up the pendulum to near unstable equilibrium region and second to stabilize the pendulum at unstable equilibrium point. The swing-up problem is addressed by using energy controller in which cart is accelerated by providing a force to the cart with a AC servo motor with the help of timing pulley arrangement. The initial velocity of the cart is taken into account to confirm swing-up in the restricted track length. The cart displacement in the restricted track length is verified by simulation and experimental test-run. The regulation problem of stabilization of pendulum is addressed by developing the controller using Pole Placement Controller (PPC) and LQR Controller (LQRC). Both the control strategies are performed analytically and experimentally using the Googoltech Linear Inverted Pendulum (GLIP) setup. The analytical results, simulated in MATLAB and SIMULINK environment, are found in close agreement with the experimental results. In order to demonstrate the effect of both the stabilizing controllers on the performance of the system, comparison of the experimental results is reported in this work. It is demonstrated experimentally that LQR controller outperforms the Pole Placement controller, in terms of reduction in the oscillations of the inverted pendulum (56 %), as well as the magnitude of maximum control input (66.7 %). Further, robustness of the closed-loop system is investigated by providing external disturbances.

This paper is an attempt to compare the nonlinear chiroptical and non-reciprocity effects of bi-isotropic media. The nonlinearity used is of a Kerr type. Following the approach of Mezache–Benabdelaziz, recently new nonlinear effects are characterized in a bi-anisotropic medium, which is due to the magnetization vector under the influence of a strong electric field. We then use these results to present the solution of nonlinear Schrödinger equation in the general case of bi-isotropic (chiral and non-reciprocal). Numerical simulations were carried out, in order to confirm the effect of the nonlinear chiroptical and non-reciprocity on the propagation analysis.