Vol. 10, No. 2 (2021): Regular Issue

Tower crane systems are commonly used at construction sites. The need to damp the swinging of the load presents a task requiring great skill for manual control. This has led earlier researchers to apply elaborate control strategies. In this paper, we propose the use of a 'pragmatic' paradigm to define a system that can move the load to the desired target with little or no swing. The essence of pragmatic control is gleaned from autopilot designs of half a century ago. The control is designed as a set of 'nested loops'. The error in an outer loop defines a demand value for the next inner loop, so for example the load position error defines a corrective velocity. In each case the demand is subjected to a limit. This is continued through each layer until the innermost loop, which might take the form of a velocity loop wrapped around a motor to give crisp velocity control. The dynamic model is derived as a state space representation. The proposed strategy was tested by MATLAB which showed that the strategy is successful and effective to control a tower crane system and suppress the load swing. Comparisons are made between the performance of this simples control strategy and that of the complex published alternatives.

In this paper we report on hyperchaos and multistability in a four-dimensional nonlinear dynamical system, namely a financial system modeled by a set of four first order ordinary differential equations, whose dynamical behavior is defined by five control parameters. An arbitrarily chosen cross-section of its five-dimensional parameter-space is used to prove numerically the occurrence of both phenomena, multistability and hyperchaos, in the system. Basins of attraction of periodic and chaotic attractors are presented, as well as some typical phase-space portraits.

The human~respiratory~and~cardiovascular~systems get affected from surrounding atmosphere. Systematic study of indoor and outdoor pollution is needed for better understanding of their global epidemiology. In this substantial body of research, a mathematical model for transmission of asthma in a variable size population under the effects of indoor smoke and outdoor air pollution is proposed. In addition, the reproduction number for the dynamical system is formulated which signifies the intensity of asthma exacerbation. The global and local stability of acquired equilibrium points is studied. The performance of the model is simulated numerically which illustrates how polluted environment effectively increases levels of aeroallergens and their effect on asthma exacerbation, and how such exposures can be meaningfully reduced.

In any business memory effect has great importance in inventory management as memory or past history cannot be ignored from the practical life of the inventory system. Many exogenous inventory parameters and factors at a given time depends not only their current values but also on the past histories. Thus an inventory management is a non Markovian process which can be tackled with memory dependent kernel of fractional derivatives. Another important factor of inventory management is deterioration of items which is directly related with memory effect as long memory of high rate of deterioration leads to poor impact on the business. Effect of long memory on deterioration of items have been studied in this paper using memory kernel of fractional derivatives. Fractional integration has been used to derive fractional order holding cost, deterioration cost, shortage cost and opportunity cost. Our analysis shows that for gradually increasing memory effect profit gradually increases. Our model is developed as a memory dependent inventory model.

In this paper, spatial patterns of a diffusive Tumor cell and immune cell model with sigmoid ratio-dependent functional response are investigated. The asymptotic stability behavior of the corresponding nonspatial model around the unique positive interior equilibrium point in homogeneous steady state is obtained. We have obtained the optimal condition under which the system loses stability and a Turing pattern occurs. Numerical simulations have been carried out in order to show the significant role of reaction-diffusion coefficients and other important parameters of the system. Various contour figures of spatial patterns through Turing instability are portrayed and analyzed in order to substantiate the applicability of the present model. The paper ends with an extended discussion of biological implications of the immune system.

This research article investigates the magnetohydrodynamic (MHD) three-dimensional flow of Maxwell nanofluid by considering convective surface boundary condition. Flow is generated because of a nonlinear stretching from the surface in lateral directions. Temperature and nanoparticles concentration distributions are studied via the Brownian movement and thermophoresis results. The governing partial differential equations are converted to the system of nonlinear ordinary differential equations through the use of suitable transformations then the obtained equations are solved numerically by applying RKF-45 method. The convergence of its solutions to the various existing parameters is verified through graphs sketched for temperature, velocity and nanoparticles concentration distributions.

Considering the pulse ansatz, we derive different classes of the modified complex Ginzburg-Landau (MCGL) equation and we use the Painleve truncated approach to construct the solitons solutions . We then present the importance of the saturation term. The solutions obtained by the combined methods are asymmetric- dark and bright solitons. Numerical simulations are performed to show how the wave propagates. The shape of solutions can be well controlled by adjusting the parameters of the system.

This work investigates the entropy generation in nanofluid flow in a sloping channel with Navier slip and asymmetric wall temperatures. The viscosity and thermal conductivity are assumed to be dependent on temperature. The equations governing the flow, temperature are nonlinear and are solved using Homotopy Analysis Method (HAM) after non-dimensionalisation. Comparisons with existing literature have been produced and are found to be in excellent agreement, for special case of the current formulation. The impact of pertinent flow and fluid parameters on entropy generation, Bejan number, Nusselt number and skin friction is addressed, developed and displayed graphically.

The present analysis consists of a mixed convection micropolar nanofluid flow in a porous medium-filled upright channel. The mathematical equations governing the flow consists of second order differential equations for the velocity, micropolarity and temperature. These equations have been solved utilizing the Homotopy Analysis Method (HAM). The series solution expression is thus obtained for the velocity, temperature and micro-rotation profiles. The value of the entropy generation and the irreversibility ratio are determined. The effect of specific flow parameters on the generation of entropy and irreversibility are displayed graphically and deliberated fervently.

Prey refuge and additional food provided to predator help in balancing the population in ecology. In this paper, we have analysed a fractional Holling Type-II predator-prey model with prey refuge and additional food to predator. Existence and uniqueness of solution is established with the help of existing theory of fractional calculus. Sufficient conditions for existence and stability of equilibrium points are derived. Effect of prey refuge and quality of additional food to predator on balancing the population is crucially analyzed. Theoretical results are supported by numerical simulations.

The present article evaluates the combined effects of magneto hydrodynamic and thermal radiation on channel flow of nanofluid with different shapes of nanoscale particles. In this paper Hamilton and Crosser's model is used to analyse the flow behavior and thermal diffusivity of nanofluids by considering different shape factors. The suitable non-dimensional variables imposed upon the governing equations which are restraining the flow and then they are transformed into a set of non-linear ordinary differential equations. Those equations have been solved by using the numerical scheme called Runge-Kutta-Fehlberg 45. The analysis of divergence in velocity and temperature profiles, for different fluid controlling parameters have been presented graphically and detailed discussion made on the results. The temperature of the fluid is maximum for the lamina shaped particle followed by column, tetrahedron, hexahedron and sphere shaped particles. Furthermore, a comprehensive discussion of the impacts of relevant parameters i.e., local nusselt number and local skin friction coefficient are also highlighted in graphs form.

The problem of feed-forward control of overhead crane system is discussed. By combining the Kalman's controllability theory and Hartman-Grobman theorem from the dynamical system theory, a linear, continuous state feedback-based feed-forward controller that stabilizes the crane system at the desired end position of payload is designed. The efficacy of proposed controller is demonstrated by comparing the simulation experiment results for overhead crane with/without time-varying length of hoisting/lowering rope.