We present analytical magnetohydrodynamic (MHD) equilibria constructed through Euler potentials (EPs) under aligned force-free magnetic fields (FFMFs). Two classes of solutions are developed by introducing different functional dependencies for the governing free function, resulting in distinct velocity and magnetic field configurations. The equilibria capture key properties of coronal and prominence plasmas. Analysis of the figures shows how variations in the functional form influence the spatial distribution of kinetic energy, with quadratic and exponential profiles producing a stronger concentration near the lower boundary, which suggests enhanced flow stabilization. The squared velocity field highlights the importance of energy localization in determining equilibrium characteristics. These results extend earlier approaches to steady-state MHD equilibria and provide a theoretical framework for understanding plasma structuring in solar and astrophysical environments within an idealized incompressible MHD approximation.
In this study, the effect of viscous forces on magnetohydrodynamic (MHD) flow between two coaxial cylinders is investigated, where the inner cylinder undergoes linear axial stretching while the outer cylinder rotates with a constant angular velocity. A first-order slip boundary condition is imposed at the surface of the inner cylinder to account for the possibility of partial slip at the boundary. In addition, viscous dissipation is incorporated into the model to evaluate its contribution to the thermal behavior of the fluid. The governing partial differential equations for mass, momentum, and energy conservation are converted into a dimensionless system of ordinary differential equations by suitable transformations. The resultant equations are solved numerically with an efficient technique, specifically the Legendre Smooth Composite Pseudospectral Method. The influences of key parameters such as the curvature parameter, cylinder gap, magnetic parameter, and slip parameter are presented graphically, demonstrating that increasing the distance between the cylinders leads to higher fluid velocity and temperature levels. Furthermore, the results indicate the existence of a critical gap parameter at which the heat transfer rate reaches its minimum value. This observation provides useful physical insight for the optimal design of rotating cylindrical systems in engineering applications such as cooling devices, rotating machinery, and thermal energy transport systems.
A two-dimensional physical-mathematical model is proposed for analyzing the plane-deformed state of a nonferromagnetic plate under the action of a quasi-static electromagnetic field. Two-dimensional problems of electrodynamics, thermal conductivity, and thermoelasticity are formulated to find the determining functions, which are the tangential component of the magnetic field intensity vector, temperature, and components of the quasi-static stress tensor. To solve these problems, all determining functions are approximated by cubic polynomials in the thickness variable. This allows the initial two-dimensional problems for determining functions to be reduced to one-dimensional problems with respect to their integral characteristics. General solutions to problems for integral characteristics are obtained using a finite integral transform with respect to the transverse variable, as well as a Laplace integral transform with respect to the time variable. The change in time of the Fourier intensity of stresses in a lead plate under the action of a quasi-static electromagnetic field and their distribution across the plate cross-section at the moment of reaching maximum values are analyzed. The dependence of these quantities on the parameter characterizing surface and deep induction heating, as well as the conditions of convective heat transfer of the plate base and its side edges, is investigated.
The study looks at how fluids move and how heat is transferred in a channel that's not symmetrical, with walls that allow fluid to pass through, and it considers the effect of a heat source or sink. This channel is created by applying a wave train with varying amplitudes and phases on the channel walls. The channel walls are kept at different temperatures and have different reabsorption coefficients. The flow of a Jeffrey fluid is studied under the assumptions of long wavelength and low Reynolds number. Due to fluid absorption through two permeable walls, the flux is taken as a function in the longitudinal axis and the tangential velocity at the walls vanishes. Approximate solutions for governing equations of the non-linear modeled system are obtained by the perturbation technique up to the second order with small wave number delta which expresses the ratio of inlet width to wavelength which giving curvature effect. Some equations are solved using numerical integration. In addition, the effect of various physical parameters such as velocity profiles, streamlines, heat transfer, entropy generation, Bejan number, Nusselt number, normal force at the wall, and wall shear stress have been analyzed and presented through graphical illustrations. Channels with permeable and reabsorping walls may be an application on renal tubule flows.
In this paper, a solution of the dual-phase-lag heat conduction equation is presented. The considerations are related to the heat conduction in a homogeneous sphere. In our research, we assume that there is no heat exchange with the surroundings through the sphere's surface, but that it is heated by an internal heat source. The solution to the problem was derived analytically, but due to its complexity, numerical methods were used to determine the inverse Laplace transform, namely the Stefhest method. The considerations are summarized with numerical examples in which the influence of the Caputo derivative order on the temperature distribution in the considered sphere was investigated.
We investigate the asymptotic behavior of an eigenvalue problem arising in a multi-rod structure with clamped ends as the rod thickness tends to zero. For low-frequency modes, we prove convergence of the eigenvalues and eigenfunctions toward those of the classical flexural limit model. For higher-frequency modes, we introduce a spectral analysis framework and show that the associated eigenfunctions admit limit descriptions in terms of torsional and stretching vibrations, depending on the considered sequences.
A system of natural boundary conditions for second order differential operators of the Laplace type that act in the full bundle T*(2) of covariant two-tensors (bilinear forms) is constructed and investigated on a compact Riemannian manifold of dimension n >= 2 with the boundary. The system consists of 32, if n >= 2, and 16, if n = 2, boundary conditions. All of them are proved to be self-adjoint and elliptic. As a result, for each particular condition of the system, the operator has a discrete spectrum and there is an orthonormal basis in L-2(T*(2) ) composed of smooth sections satisfying this condition.
In the paper we give some properties of generalized, in the sense of Love, p-absolutely continuous functions defined on a compact interval I on the real line. Among others, we prove that the space of such functions equipped with Wiener's norm forms a Banach algebra. Moreover, we state the condition for the function space X(I) under which the generator of any corresponding composition operator mapping X(I) into C(I) is continuous. As a consequence, we get that the generator of any Nemytskij operator acting between the spaces of generalized p-absolutely continuous functions defined on I is continuous.
This work is conceived as a theoretical study. In this paper we consider the nonlinear differential equation of the second order, which is known in applications as the Thomas-Fermi equation. We deal with setting the conditions under which this equation exhibits singularity in (0, oo). In the available literature, the authors investigate the singularity of the above equation at point 0, using numerical solution methods. The investigated equation has a wide application in quantum mechanics. The Thomas-Fermi equation represents models of atomic ions with a finite charge cloud and an overall positive charge. The boundary of the charge cloud is defined by the condition y(x) = 0, where y(x) represents the charge density at a given point x. We illustrate the existence of singular solutions numerically with two examples. In addition, to its role in quantum mechanics, the equation also has potential applications in biochemistry. For example, if the atomic ions, e.g. sodium and chlorine ions penetrate the bacterium, they can cause the death of the bacterium.
The article aims to study the spectral properties of oscillating mechanical systems that comprise hysteretic components. The authors modelled the treated hysteretic systems as systems of nonlinear differential equations and used the MATLAB environment to obtain the respective numerical solutions. The results were then transformed into the frequency domains using the Fourier transform. The corresponding linear system used as a reference was processed in the same manner. The frequency domains were then analyzed and compared in order to investigate the influence of hysteresis on the treated systems. The obtained results show that the hysteretic components have a considerable impact on the natural frequencies of the studied systems. These varied according to the changes in stiffness that are a natural result of the hysteresis.
The article deals with the creation of a simulation model of a CNC production cell. Two variants of the model are presented, where one is with an operator and the second model is automated with a robotic manipulator. The robotic model of the CNC cell was also modified with a reduction in the number of CNC cantilevers. All models were simulated, and the obtained data are presented and compared in the article.
Micro/nano structural elements are utilized in various branches of engineering practice as parts of MEMS/NEMS sensors and actuators. Therefore, it is necessary to investigate the mechanical behaviour of such structures in the micro/nano scales. It is well known that strain-gradients can induce polarization even in non-piezoelectric solids, and this effect is called as direct flexoelectricity. Besides the direct flexoelectric effect, there exist the converse flexoelectric effect, wherein an applied electric field gradient induces mechanical strains. The paper aims to derive the formulation for bending of flexoelectric FGM micro/nano plates taking into account the assumptions of the Kirchhoff-Love plate bending theory. We shall investigate the influence of the gradation parameters on the static responses of the flexoelectric micro/nano plates. The functional gradation of material coefficients complies with rule of mixture. For the numerical solution of complex boundary value problems, the moving finite element approximation technique is applied for spatial variations of field variables. Several numerical experiments are presented for illustration of multi-physical effects in the bending of flexoelectric FGM plates.
Long-term exposure to high levels of PM10 and PM2.5 represents a serious health risk and causes significant environmental damage. Therefore, it is necessary to monitor and predict the concentrations of air pollutants to implement both short-term and long-term actions to prevent health-risky situations. This study aims to determine the optimal probability distribution for modeling PM10 and PM2.5 concentrations in the city of Tren & ccaron;& iacute;n, Slovakia. The dataset, comprising daily average concentrations of PM10 and PM2.5 measured from January 1, 2017, to December 31, 2024, was fitted with the lognormal, gamma, log-logistic, Weibull, and exponentiated Weibull distributions. The exponentiated Weibull probability distribution has not previously been applied to such a dataset. To identify the best-fitting distribution, five performance indicators were employed: the root mean squared error, the coefficient of determination, the prediction accuracy, the Kolmogorov-Smirnov and Anderson-Darling tests. The Weibull distribution generally exhibited the worst performance. In contrast, the exponentiated Weibull distribution consistently ranked among the top three best distributions.
This study presents the application of a general regression neural network to model the effects of carbon black type and content on the mixing dynamics of rubber blends. The neural network model, trained on data from 16 tests (four carbon black types with contents of 45-60 phr), accurately reconstructs the torque and temperature profiles during blend mixing. Model optimization was performed using 10-fold cross-validation. The simulation results (average R2 approximate to 1 and RMSE approximate to 10-4) confirm the practical applicability of the presented model for predicting the time evolution of nonlinear processes in complex technological applications.
In recent decades the application of a micro/nano electromechanical system for sophisticated energy harvesting devices have increased in popularity. In order to design such a sophisticated devices, it is necessary to know the mechanical behavior of such a structures at micro/nano scale under various thermal conditions. The thermal conductivity at nano scale can be reduced significantly at nanoscales. If the size of the nanostructure is smaller than the phonon mean free path, they are scattered on interfaces and thermal conductivity is reduced. It is known that piezoelectric materials convert mechanical energy into the electrical energy. This electro mechanical coupling is even more pronounced at nano scale where the flexoelectric effect is present. Flexoelectricity is size dependent and requires strain gradients in order convert mechanical energy in to electrical. The micro/nano electromechanical systems work in a different multiphysical environment, therefore, in order to ensure the structural integrity of these sophisticated devices it is necessary to have numerical models that take into account size dependency and electro-thermo-mechanical interaction. The nonlocal higher order heat conduction equation with incorporated size effects will be considered. The new mathematical model will be established based on the generalized heat conduction model and strain gradient elasticity theory with one microstructural length scale parameter. The interaction of thermal mechanical and electrical fields and the influence of the size effect will be numerically modeled.
This paper considers the boundary value problem concerning the natural vibrations of a single-rod column, in which two stiffness discontinuities occur at a given position. The column is subjected to a load of a follower force directed towards the negative pole. The load is generated by loading heads made of circular elements. The stiffness discontinuities of the column rod were modeled using rotational springs with a given stiffness. The boundary value problem of column stability was formulated based on the principle of minimum potential energy. In the case of stability tests, the static stability criterion was used to determine the critical load. Based on the mathematical model, numerical calculations were performed regarding the stability problem. Based on the calculations, the critical force of the system was determined. Numerical calculations were performed for various values of the system parameters, which include: the stiffness value of the rotational springs defining the stiffness discontinuities of the column rod, the location of the stiffness discontinuities along the rod, the parameters of the loading system, including the radii of the loading heads and the length of the bolt connecting the head of the loading system with the column rod.
