Jurnal Diferensial

Solution of Direct and Inverse Dynamic Problem for the Previously Disturbed Dynamical Systems

2024-06-04T12:39:58+00:00

The paper deals with developing backgrounds to study and design the controllers for a wide class of dynamical systems that can be found in various branches of human life. We offer to use the known approach based on the solution of direct and inverse dynamic problems. This approach us to define system motions by external signals that are given to it as well as define these signals by known motion trajectories. Since the used approach operates with the transfer functions apparatus we offer to generalize these functions by taking into account the system's non-zero initial state while performing the Laplace-Carson's transformation. Such an approach gives us the possibility to consider the generalized transfer function as some matrix differential operator that defines free and perturbed system motions. We study this operator in our paper and show the patterns of its determination and implementation. Our study allows us to supplement the definition of direct and inverse dynamic problems and consider the last one as the problem with several solutions that define the control signal, external efforts, and initial conditions. We use them to define the generalized direct and inverse transfer functions.

Coupled Effects of Magnetohydrodynamics and Nanoparticles on Nonlinear Stretching Wedge Flow with Multiple Slips and Non-Uniform Heating

2024-06-04T13:01:57+00:00

This study investigates the complex interplay between magnetohydrodynamics (MHD), nanoparticle behavior, and fluid flow characteristics in the context of a nonlinear stretching wedge with multiple slips and non-uniform heating. The flow is driven by a water-based fluid containing nano-sized particles of aluminum oxide and copper $\left( Al_2O_3-Cu/H_2O\right)$ . The governing equations of the problem are derived and then solved using appropriate numerical techniques. The effects of various parameters such as the magnetic field strength, nanoparticle volume fraction, wedge angle, slip parameters, and non-uniform heat source are thoroughly analyzed. Results reveal significant alterations in the flow behavior due to the presence of nanoparticles and the applied magnetic field. The interaction between the fluid flow and magnetic field induces a substantial change in velocity and temperature distributions along the wedge surface. Moreover, the slip effects and non-uniform heat source further modify the flow characteristics. This investigation provides valuable insights into the coupled effects of MHD, nanoparticles, and slip conditions on the flow dynamics and thermal behavior in nonlinear stretching wedge configurations. Such insights are crucial for understanding and optimizing processes involving fluid flow and heat transfer in engineering applications, particularly those utilizing nano-fluids and magnetic fields.

Dynamics of COVID-19 Incorporating Preventive Measures and Treatment

2024-06-04T13:33:46+00:00

The surge of Coronavirus disease (COVID-19) was felt all over the world greatly after it was declared a pandemic in the year 2020. After 3 years in 2023, the disease passed the pandemic phase
and entered an endemic phase. But that didn’t reduce the global threat of the disease as the disease continues to still claim lives daily. In this work, we examined the dynamics of the coronavirus
disease from a mathematical view using a deterministic SEIAISQVRIP LP model. This consists of
investigating the disease-free and endemic equilibria, basic reproduction number and stability. The
local stability of the disease-free equilibrium was determined by solving the Jacobian matrix of the
system of the system of differential equations while the basic reproduction number was calculated
using the next generation matrix method. Numerical simulations to determine the active factor(s) in
the transmission, preventive and possible elimination of the disease were carried out using a computational software called Maple. It was revealed that over time when all modalities are out into place the rate of recovery increases and as the rate of the pathogen virus death increases, the pathogen virus gradually fades from the environment.