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In this study, we consider melting heat transfer and inclined magnetic field impacts on the flow of Carreau fluid past a stretched permeable sheet in a along with influences of variable thermal conductivity, diffusion-thermo, and thermal-diffusion. The problem is formulated as a system of nonlinear partial differential equations and using similarity transformations these are converted to non-linear ordinary differential equations. Numerical solutions of the problem are investigated via numerical algorithm by employing Runge–Kutta–Fehlberg fourth–fifth order scheme along with shooting method and the results are reported graphically for velocity, temperature, and concentration profiles. The velocity profile enhanced against the growing power law index, Weissenberg number, and melting parameter while it declines for magnetic parameter, angle of inclination, and porosity parameter. The temperature profile increases with modified Dufour parameter and Soret number while it diminishes for magnetic, thermal conductivity, and melting parameters. The concentration profile enhances for magnetic parameter while diminishes for modified Dufour parameter, Schmidt and Soret numbers. The numerical data is obtained for physical quantities of engineering interests against the various parameters. The skin friction results against the magnetic parameter are compared with previous published studies in the literature which validated the accuracy of our numerical findings.

We investigated two dimensional magnetohydrodynamic (MHD) stagnation point upper-convected Maxwell (UCM) fluid flow through a stretch sheet in a porous medium having the effects of heat generation/absorption and thermal stratification. Utilizing suitable similarity transformations, the governing partial differential equations (PDEs) of the fluid flow and heat transfer phenomena are converted to nonlinear dimensionless ordinary differential equations (ODEs). We numerically solved these nonlinear ODEs and compared our results of skin friction and Nusselt number with previous work which demonstrated accuracy of the presented solutions. We also illustrated the graphical behavior of dependent variables that is of the velocity and temperature fields versus the key parameters involved. It showed that velocity field decreases for Deborah number, porosity and magnetic parameters. The temperature of the fluid showed an increasing behavior for Deborah number, magnetic, porosity, and heat source/sink parameters while declining for thermal stratification and velocity ratio parameters.

A system of ordinary differential equations is considered, which arises in the modeling of genetic networks and artificial neural networks. Any point in phase space corresponds to a state of a network. Trajectories, which start at some initial point, represent future states. Any trajectory tends to an attractor, which can be a stable equilibrium, limit cycle or something else. It is of practical importance to answer the question of whether a trajectory exists which connects two points, or two regions of phase space. Some classical results in the theory of boundary value problems can provide an answer. Some problems cannot be answered and require the elaboration of new approaches. We consider both the classical approach and specific tasks which are related to the features of the system and the modeling object.

We developed a mathematical model to simulate the dynamics of background synaptic noise in non-neuronal cells. By employing the stochastic Ornstein–Uhlenbeck process, we represented excitatory synaptic conductance and integrated it into a whole-cell model to generate spontaneous and evoke cellular electrical activities. This single-cell model encompasses numerous biophysically detailed ion channels, depicted by a set of ordinary differential equations in Hodgkin–Huxley and Markov formalisms. Consequently, this approach effectively induced irregular spontaneous depolarizations (SDs) and spontaneous action potentials (sAPs), resembling electrical activity observed in vitro. The input resistance decreased significantly, while the firing rate of spontaneous action potentials increased. Moreover, alterations in the ability to reach the action potential threshold were observed. Background synaptic activity can modify the input/output characteristics of non-neuronal excitatory cells. Hence, suppressing these baseline activities could aid in identifying new pharmaceutical targets for various clinical diseases.

Purpose—This study aims to perform an in-depth analysis of double-diffusive natural convection (DDNC) in an irregularly shaped porous cavity. We investigate the convective heat transfer process induced by the lower wall treated as a heat source while the side walls of the enclosure are maintained at a lower temperature and concentration, and the remaining wall is adiabatic. Various factors, such as the Rayleigh number, Darcy effects, Hartmann number, Lewis number and effects of magnetic inclination are evaluated for their influence on flow dynamics and heat distribution. Design/methodology/approach—After validating the results, the FEM (finite element method) is used to simulate the flow pattern, temperature variations, and concentration by solving the nonlinear partial differential equations with the modified Rayleigh number (104 ≤ Ra ≤ 107), Darcy number (10−4 ≤ Da ≤ 10−1), Lewis number (0.1≤Le≤10), and Hartmann number 0≤Ha≤40 as the dimensionless operating parameters. Findings—The finding shows that the patterns of convection and the shape of the isotherms within porous enclosures are notably affected by the angle of the applied magnetic field. This study enhances our understanding of how double-diffusive natural convection (DDNC) operates in these enclosures, which helps improve heating and cooling technologies in various engineering fields. Research limitations/implications—Numerical and experimental extensions of the present study make it possible to investigate differences in thermal performance as a result of various curvatures, orientations, boundary conditions, and the use of three-dimensional analysis and other working fluids. Practical implications—The geometry configurations used in this study have wide-ranging applications in engineering fields, such as in heat exchangers, crystallization, microelectronics, energy storage, mixing, food processing, and biomedical systems. Originality/value—This study shows how an inclined magnetic field affects double-diffusive natural convection (DDNC) within a porous system featuring an irregularly shaped cavity, considering various multiphysical conditions.

In this article, we introduce a flexible and reliable technique to simulate and optimize the characteristics of a Dynamic Electrical Vehicle (DEV). The DEV model is a discrete event-based modeling technique used in electrical vehicle research to improve the effectiveness and performance of various electrical vehicles (EVs) components. Here, the DEVS model is applied to EV research in several ways, including battery management optimization, evaluation of power train design and control strategy, and driver behavior analysis. The essential power train elements, including the battery, motor, generator, internal combustion engine, and power electronics are included in the mathematical model for the dynamic electric vehicle. The model is derived using the conservation of energy principle. The model includes mathematical equations for the electrical power output, battery charge level, motor torque, motor power output, generator power output, internal combustion engine torque, mechanical power delivered to the generator, and the efficiencies of the power electronics, motor, generator, and engine. The model is examined by using a numerical method called the Runge–Kutta Method of order 4 for dynamic electric vehicle’s performance under various driving states for maximum effectiveness and performance. It is revealed that the DEV model provides a systematic method to simulate and optimize the behavior of complex EV systems.

This paper introduces a new 3D chaotic attractor in a gene regulatory network. The proposed model has eighteen parameters. Formulas for characteristic numbers of critical points for three-dimensional systems were considered. We show that the three equilibrium points of the new chaotic 3D system are unstable and deduce that the three-dimensional system exhibits chaotic behavior. The possible outcomes of this 3D model were compared with the results of the Chua circuit. The bifurcation structures of the proposed 3D system are investigated numerically, showing periodic solutions and chaotic solutions. Lyapunov exponents and Kaplan-Yorke dimension are calculated. For calculations, the Wolfram Mathematica is used.

The question of targeted control over trajectories of systems of differential equations encountered in the theory of genetic and neural networks is considered. Examples are given of transferring trajectories corresponding to network states from the basin of attraction of one attractor to the basin of attraction of the target attractor. This article considers a system of ordinary differential equations that arises in the theory of gene networks. Each trajectory describes the current and future states of the network. The question of the possibility of reorienting a given trajectory from the initial state to the assigned attractor is considered. This implies an only partial control of the network. The difficulty lies in the selection of parameters, the change of which leads to the goal. Similar problems arise when modeling the response of the body’s gene networks to serious diseases (e.g., leukemia). Solving such problems is the first step in the process of applying mathematical methods in medicine and pharmacology.

The responsibilities of a teacher are diverse and intricate. Societal shifts, political developments, and rapid technological progress have added further layers of complexity to teachers' daily tasks. The current research endeavors to analyze how teachers, with varying levels of experience and backgrounds, adapt to these changes in education and perceive opportunities for further development. The aim of the article is to study Latvian teachers' perspectives on education in Latvia and identify areas for improvement. To reach the aim, focus group discussion was conducted involving six teachers from diverse backgrounds. Through content analysis, the study identified the primary challenges facing the current education process in Latvia: 1) prolonged, ineffective educational reforms; 2) challenges in rural education; 3) inappropriate teacher training; 4) the need for adaptive teaching methods; 5) the importance of cooperation among teachers and with parents. Addressing these areas could lead to significant improvements in the Latvian education system. The analysis sheds light on several issues within education, including the dynamics of teacher-pupil roles, the quality of educational outcomes, and pupil attitudes.