A mathematical model to study the dynamics of carbon capture in forest plantations

Fast-growing forest plantations play an important role in reducing global warming and have great potential for carbon capture. In this study, we aimed to model the dynamics of carbon capture in fast-growing plantations. A mathematical model is proposed consisting of a tridimensional nonlinear system. The variables involved are the amount of living biomass, the intrinsic growth of biomass, and the burned area by forestry fire. The environmental humidity is also considered, assumed as a parameter by simplicity. The solutions of the model are approximated numerically by the Runge-Kutta fourth-order method. Once the equilibria of the model have been obtained and its local stability determined, the analysis of the model reveals that the living biomass, as well as the stored carbon, decreases in each harvest cycle as a consequence of the negative effects of fire on soil properties. Furthermore, the model shows that the maximum area burned is attained always after the maximum volume of biomass is obtained. Numerical simulations show that the model solutions are reasonable for the growth dynamics of a plantation, from a theoretical perspective. The mathematical results suggest that a suitable optimal management strategy to avoid biomass losses in the successive regeneration cycles of the plantation is the prevention of fires together with soil fertilization, applied to fast-growing plantations.

The Impact of Media Coverage and Curfew on the Outbreak of Coronavirus Disease 2019 Model: Stability and Bifurcation

In this study, the spreading of the pandemic coronavirus disease (COVID-19) is formulated mathematically. The objective of this study is to stop or slow the spread of COVID-19. In fact, to stop the spread of COVID-19, the vaccine of the disease is needed. However, in the absence of the vaccine, people must have to obey curfew and social distancing and follow the media alert coverage rule. In order to maintain these alternative factors, we must obey the modeling rule. Therefore, the impact of curfew, media alert coverage, and social distance between the individuals on the outbreak of disease is considered. Five ordinary differential equations of the first-order are used to represent the model. The solution properties of the system are discussed. The equilibria and the basic reproduction number are computed. The local and global stabilities are studied. The occurrence of local bifurcation near the disease-free equilibrium point is investigated. Numerical simulation is carried out in applying the model to the sample of the Iraqi population through solving the model using the Runge–Kutta fourth-order method with the help of Matlab. It is observed that the complete application of the curfew and social distance makes the basic reproduction number less than one and hence prevents the outbreak of disease. However, increasing the media alert coverage does not prevent the outbreak of disease completely, instead of that it reduces the spread, which means the disease is under control, by reducing the basic reproduction number and making it an approachable one.

STEADY MHD SLIP FLOW OVER A PERMEABLE STRETCHING CYLINDER WITH THERMAL RADIATION

Aim of the paper is to investigate the effects of thermal radiation and velocity slip on steady MHD slip flow of viscous incompressible electrically conducting fluid over a permeable stretching cylinder saturated in porous medium in the presence of external magnetic field. The governing nonlinear partial differential equations are transformed into ordinary differential equations by suitable similarity transformation and solved numerically using Runge-Kutta fourth order method with shooting technique. Effect of various physical parameters on fluid velocity, temperature, skin –friction coefficient and Nusselt number are presented through graphs and discussed numerically.

Mathematical Modelling of Transient Processes in an Asynchronous Drive with a Long Shaft Including Cardan Joints

Beginning with the classic methods, a mathematical model of an electromechanical system is developed that consists of a deep bar cage induction motor that, via a complex motion transmission with distributed mechanical parameters, drives a working machine, loading the drive system with a constant torque. The electromagnetic field theory serves to create the motor model, which allows addressing the displacement of current in the rotor cage bars. Ordinary and partial differential equations are used to describe the electromechanical processes of energy conversion in the motor. The complex transmission of the drive motion consists of a long shaft with variable geometry cardan joints mounted on its ends. Non-linear electromechanical differential equations are presented as a system of ordinary differential equations combined with a mixed problem of Dirichlet first-type and Poincaré third-type boundary conditions. This system of equations is integrated by discretising partial derivatives by means of the straight-line methods and successive integration as a function of time using the Runge–Kutta fourth-order method. Starting from there, complicated transient processes in the drive system are analysed. Results of computer simulations are presented in the graphic form, which is analysed.

Implementation of the variation of the luni-solar acceleration into GLONASS orbit calculus

In the differential equation system describes the motion of GLONASS satellites (rus. Globalnaya Navigazionnaya Sputnikovaya Sistema, or Global Navigation Satellite System ), the acceleration caused by the luni-solar traction is often taken as a constant during the period of the integration. In this work-study, we assume that the acceleration due to the luni-solar traction is not constant but varies linearly during the period of integration following this assumption; the linear functions in the three axes of the luni-solar acceleration are computed for an interval of 30 min and then implemented into the differential equations. The use of the numerical integration of Runge-Kutta fourth-order is recommended in the GLONASS-ICD (Interface Control Document) to solve for the differential equation system in order to get an orbit solution. The computation of the position and velocity of a GLONASS satellite in this study is performed by using the Runge-Kutta fourth-order method in forward and backward integration, with initial conditions provided in the broadcast ephemerides file.

Effects of Isoperimetric Constraint for Reducing HSV-2 Infection Using Optimal Control Strategy

Optimal control is helpful for testing and comparing different vaccination strategies of a certain disease. Genital herpes is one of the most prevalent sexually-transmitted diseases globally. In this paper, we have proposed an optimal control problem applied to HSV-2 model after introducing the constraint and state variables. Optimal control problem is formulated based on ordinary differential equation and isoperimetric constraint in the vaccine supply is also included. Mathematical analysis such as the characterization of optimal control using Pontryagin’s maximum principle is studied. Generally optimal control theory is used for finding the optimal way for implementing the strategies, minimizing the number of infectious and latent individuals and keeping the cost of implementation as low as possible. Here the optimality system is derived and solved numerically using a Runge-Kutta fourth order method and this is an iterative method. Using numerical simulation we observe that how the optimal vaccination schedule is altered by imposing isoperimetric constraint. Finally, on applying the isoperimetric constraint on the optimal control problem of HSV-2 epidemic model, we observe that optimal vaccination schedule with isoperimetric constraint indicates successful short-term control of the disease. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 62-68

A Comparative Study on Classical Fourth Order and Butcher Sixth Order Runge-Kutta Methods with Initial and Boundary Value Problems

In this paper, it is discussed about Runge-Kutta fourth-order method and Butcher Sixth order Runge-Kutta method for approximating a numerical solution of higher-order initial value and boundary value ordinary differential equations. The proposed methods are most efficient and extolled practically for solving these problems arising indifferent sector of science and engineering. Also, the shooting method is applied to convert the boundary value problems to initial value problems. Illustrative examples are provided to verify the accuracy of the numerical outcome and compared the approximated result with the exact result. The approximated results are found in good agreement with the result of the exact solution and firstly converge to more accuracy in the solution when step size is very small. Finally, the error with different step sizes is analyzed and compared to these two methods.

A Comparative Study on Classical Fourth Order and Butcher Sixth Order Runge-Kutta Methods with Initial and Boundary Value Problems

In this paper, it is discussed about Runge-Kutta fourth-order method and Butcher Sixth order Runge-Kutta method for approximating a numerical solution of higher-order initial value and boundary value ordinary differential equations. The proposed methods are most efficient and extolled practically for solving these problems arising indifferent sector of science and engineering. Also, the shooting method is applied to convert the boundary value problems to initial value problems. Illustrative examples are provided to verify the accuracy of the numerical outcome and compared the approximated result with the exact result. The approximated results are found in good agreement with the result of the exact solution and firstly converge to more accuracy in the solution when step size is very small. Finally, the error with different step sizes is analyzed and compared to these two methods.

Entropy Analysis of the Nonlinear Convective Flow of a Jeffrey Fluid over an Inclined Sheet with Variable Electrical Conductivity and Thermal Conductivity

A steady two-dimensional nonlinear convective flow of a viscous, incompressible, electrically conducting, and non-Newtonian Jeffrey fluid over an inclined stretching sheet with convective boundary conditions and entropy generation is studied under the influence of transverse magnetic field, electrical conductivity and thermal conductivity. The thermal conductivity and electrical conductivity are temperature dependent functions. The governing continuity, momentum and energy equations are transformed to ordinary differential equations (ODEs) using appropriate similarity variables. The resulting coupled ODEs and the corresponding boundary conditions, are solved numerically using Runge-Kutta fourth order method and shooting technique. The velocity, entropy generation rate, temperature and Bejan distributions are presented graphically and discussed. The numerical values of the skin-friction and Nusselt number are obtained and also discussed for various thermophysical parameters through a Table. Furthermore, a comparison with earlier work done with limiting case was carried out and found to be in excellent agreement.