Theoretical and Mathematical Physics最新文献

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.

In the presence of dark energy, Bianchi type V space–time and its cosmological model are examined in Lyra geometry. A hybrid nature of the scale factor (a=sqrt[m]{t^ne^{xi t}}) and the power-law expansion (H=la^{-n}) are analyzed to derive an exact solution characterizing a universe transitioning from an early decelerating stage to the present accelerating phase. The derived cosmological model is investigated under different admissible values of (n). An equation that represents a special case of the Raychaudhuri equation for timelike geodesic is also established. Several geometrical and physical characteristics of the model are analyzed and illustrated with graphical representation.

We study the thermal performance and chemical reactive flow of a hybrid nanofluid over a stretching sheet heat generation. Titanium oxide (TiO(_{2})) and silicon dioxide (SiO(_{2})) combine to form a hybrid nanofluid, which is an improper fluid with water, Eg((50,{:},50)) as a general fluid. Using a suitable similarity variable, the constitutive partial differential equations are converted into a system of connected nonlinear ordinary differential equations. The resulting equations are then solved numerically using the efficient finite element analysis method with the help of Mathematica 10.4 software and, for better results, with the Neural Network Levenberg–Marquardt method in MATLAB R2017b. The present study can be useful in precision engineering and nanotechnology tasks such as developing microfluidic devices and biomedical apparatuses where nanofluid flow control is crucial. The model assists in understanding fluid dynamics for complex cooling systems, particularly in industries where efficient heat transfer is essential, such as electronics and aerospace. Surface tension plays a major role in determining the uniformity and quality of thin films, and therefore it can also be advantageous in coating technologies and material processing. Our results reveal that increasing the volume fraction parameters (phi_1) and (phi_2) results in a thicker thermal boundary layer in both steady and unsteady states. Higher values of (phi_1) and (phi_2) enhance the (phi_1) velocity profile while reducing the (phi_2) velocity profile for both steady and unsteady states of TiO(_2)/SiO(_2)–water/Eg((50,{:},50)) hybrid nanofluid. The results show that thermal conductivity performance of the hybrid nanofluid model is efficient compared with a single nanofluid.

We study the three-species system in which the species of the first kind

is neutral to the species of the third kind

and ammensal to the species of the second kind.

We give an analytic analysis of the model. A collection of first-order nonlinear ordinary differential equations characterizes the model. The stability criteria of the interior equilibrium state are discussed. Additionally, an exact solution of the perturbed equations is determined. A stochastic process is used to illustrate the model stability. MatLab is used to do numerical simulation to support the analytic conclusions.

We investigate the effects of Joule combustion, Hall current, and thermal dispersion on an unstable MHD free convection heat and mass transfer revolving flow of a dense, indestructible, and electrically conducting second-grade fluid that is passing through an exponential plate embedded in a porous medium. This flow was realized in the context of a heat source and viscous dissipation. By the perturbation approach, it is possible to obtain an accurate analytic solution of the governing equations for the fluid velocity, fluid temperature, and species concentration. This solution is obtained while taking the proper initial and boundary conditions into consideration. With the assistance of the MATLAB program, graphical representations are provided for the numerical values of the main and secondary fluid velocities, the temperature of the fluid, and the concentration of the species. The shear stresses, the Nusselt number, and the Sherwood number are calculated analytically, rendered computationally in a tabular style, and discussed with regard to the most important factors with the purpose of satisfying engineering curiosity. The results reveal that an increase in the Hall current parameter enhances the primary velocity while reducing the secondary velocity. Additionally, the thermal diffusion parameter increases the species concentration, while the Schmidt number reduces it due to lower mass diffusivity. These findings have practical applications in industrial processes involving magnetohydrodynamic systems, such as cooling systems for rotating machinery, and in geophysical fluid dynamics for analyzing flows in porous media under thermal and magnetic influences.

The missing baryon problem represents a longstanding challenge in cosmology, highlighting a discrepancy between the amount of baryonic matter predicted by cosmological models and the amount directly observed in the universe. While observations of the cosmic microwave background and Big Bang nucleosynthesis accurately constrain the baryon density of the early universe, only a fraction of this baryonic matter is accounted for in stars, galaxies, and hot gas within galaxy clusters today. Recent advances suggest that much of the missing baryonic matter resides in the warm–hot intergalactic medium (WHIM), a diffuse, filamentary gas with temperatures of (10^5)–(10^7) K. Detecting the WHIM has been challenging due to its low density and weak emissions. However, breakthroughs in observational techniques, such as X-ray and UV spectroscopy, along with cosmological simulations, have provided compelling evidence for its presence. This review synthesizes the latest theoretical and observational efforts to locate the missing baryons, emphasizing the role of the WHIM, novel detection strategies, and their implications for understanding large-scale cosmic structure and galaxy formation. Future missions promise to refine these findings, bringing us closer to resolving this fundamental issue in astrophysics.

We explore the Friedmann–Robertson–Walker cosmological model within the context of Lyra geometry, with a particular focus on the deceleration parameter expressed in terms of the Hubble parameter, (q = - frac{Rddot{R}}{dot{R^{2}}} = - Bigl( frac{dot{H} + H^{2}}{H^{2}} Bigr) = b (mathrm{const})), and the equation of state in the form (P = gammarho). The Lyra geometry, an extension of Riemannian geometry, introduces a gauge function that modifies the conventional metric, potentially offering novel insights into cosmological phenomena. We investigate the impact of this geometry on the dynamics of the universe by analyzing the behavior of the deceleration parameter, which indicates the rate of change of the universe’s expansion. Our findings demonstrate that the incorporation of Lyra geometry significantly influences the deceleration parameter, suggesting new possibilities for understanding cosmic acceleration and the transition from deceleration to acceleration phases. This work enhances our understanding of the universe’s evolution and provides a platform for future research into alternative geometric frameworks in cosmology.

Microfluidic technologies have emerged as transformative diagnostic tools in health care, significantly accelerating diagnostic processes and enhancing patient outcomes. This article explores the principles of fluid dynamics in microfluidic systems, particularly at low Reynolds numbers, and their practical applications. Traditional microfluidic devices often rely on additional hardware for liquid handling, increasing costs, complicating maintenance, and limited accessibility in low-resource settings. To address these challenges, the study introduces a mechanically pulsating heat exchanger utilizing microfluidic technologies, which incorporates internal walls within the flow channel. This innovative design alters the flow patterns of liquid and vapor plugs, significantly improving thermal efficiency in heat pipes. The article highlights the role of flow patterns in preventing blockages and their utility in generating emulsion droplets, blending substances, and separating components through periodic mass flow fluctuations. Furthermore, the advantages of pulsatile flow in microfluidic systems are examined. Unlike steady flows, pulsatile flows offer unique benefits, such as simulating physiological conditions, enhancing cell culture environments, and automating bioassays. These capabilities make pulsatile flows invaluable for advancing biomedical research and diagnostic technologies. However, realizing their full potential requires deeper physics-based insights and further research. This work underscores the promise of microfluidic systems in health care and beyond, paving the way for cost-effective, efficient, and accessible diagnostic solutions.

In the framework of magnetic fields, thermophoresis, porous media, and Brownian motion, this study examines the rotation and Hall current effects on an electrically conductive, viscous, incompressible, non-Newtonian Eyring–Powell fluid, including nanofluid particles, across a stretched sheet. The governing nonlinear partial differential equations (PDEs) in this work are converted into ordinary differential equations (ODEs) using appropriate similarity transformations. This system of ODEs is then numerically solved using the MATLAB bvp4c solver. Effects of numerous crucial factors on the velocity, temperature, and concentration profiles are shown in graphs. Furthermore, the stretched sheet mass transfer rate, heat transfer rate, and skin-friction coefficient are calculated and shown in tables. The published results and the present findings are compared in a tabular analysis.

The renowned Indian mathematician Srinivasa Ramanujan introduced a significant summation in 1918, known as the Unitary Ramanujan Sum (C^*_N(L)). In recent years, this sum has garnered considerable attention in the fields of signal and image processing. In this paper, we focus on the application of the Unitary Ramanujan Sum to power systems. A line-to-ground fault is simulated in the MATLAB platform with an IEEE (9)-bus system and the results are presented for the validation of the Unitary Ramanujan Sum application.