Theoretical and Mathematical Physics最新文献

We investigate the complex dynamics of narrow-band wave fields described by the viscous Benjamin–Ono equation, a model of significant relevance in hydrodynamics. Through detailed numerical simulations, we analyze the role of Reynolds viscosity in shaping statistical moments, energy spectra, and the occurrence of extreme internal wave events. In particular, we show that freak waves of moderate amplitude can occur in viscous fluids.

We show the existence and uniqueness of the solution with a moving internal transition layer in the initial boundary-value problem for the singularly perturbed parabolic reaction–diffusion equation in the case of a balance between reaction and diffusion. Using the Vasil’eva method of boundary functions, we construct an asymptotic approximation of the solution of the front form. We prove the existence and uniqueness theorem using the asymptotic method of Nefedov’s differential inequalities. The obtained results can be used to develop effective numerical algorithms for solving hard problems appearing in the theory of nonlinear heat conduction and in population dynamics.

We consider the abstract linear parabolic equation with a nonlocal-in-time condition for an integral-type solution in a separable Hilbert space. The problem is solved approximately using the semidiscrete Galerkin method. Under conditions of weak solvability for the problem, we establish error estimates for an approximate solution. Under additional assumptions on the smoothness of the solution of the exact problem, we also obtain the convergence rate that is exact in the order of approximation for projection subspaces of finite-element type.

The Kantorovich–Galerkin method is extended to solve a wider range of problems related to oscillations of mechanical systems with moving boundaries. We take bending rigidity, environmental resistance, and foundation rigidity into account. The main attention is paid to studying the resonance characteristics of the solutions obtained. Quadrature expressions for the amplitudes of dynamical modes of different orders are derived. As an illustration, the problem of forced oscillations of a string with a uniformly moving boundary is considered. The error of the Kantorovich–Galerkin method is estimated depending on the velocity of the boundaries.

The purpose of this study is to investigate the influence that heat radiation has on the flow of a three-dimensional, viscous, electrically conducting, incompressible, upper-convicted Maxwell nanofluid over a bidirectional stretching surface. Additionally, aspects such as magnetic fields, porous media, thermophoresis, and Brownian motion are taken into consideration. Nonlinear radiative heat transmission is included in the energy equation in the Rosseland approximation version of the equation. For the purpose of resolving the ordinary differential equations that are formed from the reduction of the main governing nonlinear partial differential equations by similarity transformations, the “bvp4c” solver by MATLAB is used. The skin-friction, heat transfer rates, and mass transfer coefficients are analyzed numerically, and visual representations are used to demonstrate the impacts of a large number of important components on the velocity, temperature, and concentration profiles. The numerical findings of the study have been evaluated, and it has been determined that they are substantially in accord with the results available in the literature.

We present a comparative evaluation of heat and mass transfer in nanofluids incorporating a banana leaf nanofiber (BLF) and carbon nanofibers (CNFs) with water as the base fluid. We made a novel attempt that by using BLF we can enhance the thermal conductivity even though CNFs have high thermal properties. We calculate the Nusselt number, Sherwood number, and skin friction coefficient to examine the influence of these nanoparticles. The BLF, an organic and sustainable option, contrasts with CNFs, which offers exceptional thermal enhancement. The equations governing the flow are solved using finite element methods. While both nanofluids improve heat and mass transfer, CNFs demonstrate superior thermal properties, whereas BLF offers an environmentally friendly and cost-effective alternative. The study expands on the use of nanofluids in heat exchangers, cooling systems, thermal management of electronics, and sustainable engineering solutions.

We analyze the magnetohydrodinamic flow through porous media in a coaxial circular duct. The exact governing equations of motion and the magnetic field equations are solved to obtain the velocity and the magnetic and the shear stress on the boundary. This behavior is discussed computationally for different values of the governing parameters.

We explore the impact of the aligned magnetic field, buoyant force, and thermal radiation on the unsteady MHD-free convection of momentum and energy transmission in a viscous, incompressible, electrically conducting water-based Cu and TiO(_2) Jeffrey nanofluid. We consider radiation absorption and thermo diffusion. The flow occurs along permeable objects with isothermal inclined plates, with Cu and TiO(_2) in water being the focus. Analytic solutions for the governing equations of fluid velocity, temperature, and species concentration are derived using the perturbation method, considering initial and boundary conditions. Results for shear stress and the heat and mass transfer rates at the plate are presented graphically, along with tables for various flow characteristics.

We investigate an unsteady magnetohydrodynamic temperature and mass transfer of a hybrid tiny fluid mixed convection transfer of fluids through permeable material over a stretching sheet. The influence of thermal radiation and activation energy is also taken into consideration. In order to create hybrid nanoparticles, nanoparticles of titanium oxide (TiO(_2)) and nanoparticles of alumina (Al(_2)O(_3)) are mixed, and the base fluid is used as water. The set of discrete differential equations with nonlinear behavior that govern the fluid flow is transformed into a set of ordinary differential equations by the use of a similarity transformation and nondimensional variables. These equations are solved numerically by employing the Runge–Kutta fourth-order method in conjunction with various firing techniques. The consequences of a large number of interconnected factors, such as the magnetic field factors, the Prandtl number, the buoyancy factors, the unsteady factors, thermal radiation, the rate of chemical reaction, and the energy of activation are plotted and analyzed in relation to the velocity, temperature, and concentration profiles. The study reveals that increasing the magnetic field reduces fluid velocity, while higher activation energy and chemical reaction rates decrease concentration. Thermal radiation enhances temperature profiles, and the Prandtl number inversely affects the temperature.

We use a three-compartment model to examine the concentration of moxalactam activity. A set of three non-linear ordinary differential equations characterizes the model. The system of equations is solved using the Laplace transform and the Eigenvalue methods. After (40) patients with abdominal sepsis received an intravenous dose of moxalactam (2.0)g, the plasma concentrations were assessed over an (8)-hour period. The method of residuals is used to calculate the transfer coefficients from moxalactam concentrations, and MATLAB is used to plot the variation of moxalactam concentration-time curves. Excretion from the central and tissue compartments is taken into account in this model.