Phase formation and dielectric properties of MgFe2O4 nanoparticles synthesized by hydrothermal technique.

In the recent development of energy storage devices, the scientific study has demonstrated a significant interest in the applications of the magnesium iron oxide (MgFe2O4) nanoparticles. In this work, we present synthesized novel MgFe2O4 nanoparticles at different molarities (0.1-0.5 M), via hydrothermal technique. An X-ray Diffractometer was used to study the phase analysis of the prepared samples at different molarities. A pure cubic phase of the MgFe2O4 is observed at molar concentrations of 0.3 M and 0.4 M. However, the mixed phases consisting of (MgFe2O4 + Î³-Fe2O3) were also observed at 0.1 M, 0.2 M, and 0.5 M. The pure cubic MgFe2O4 nanoparticles depict the large value of crystallite size, 19.5 nm, and the lowest dislocation density and strain. The vibrating Sample Magnetometer shows the ferromagnetic nature of the pure MgFe2O4 with a high saturation magnetization. The value of saturation magnetization surged from 36.88 emu/g to 55.2 emu/g at 0.4 M concentration. The dielectric response of the materials as a function of applied frequency was studied thoroughly by using an Impedance Analyzer. The highest value of dielectric constant and low tangent loss was also reported at 0.4 M. Cole-Cole plots are the affirmation of the contribution of both grains and grain boundaries in the charge mechanism. These distinctive features make the synthesized material an excellent choice for future spintronics and energy storage devices.

A novel simulation-based analysis of a stochastic HIV model with the time delay using high order spectral collocation technique.

The economic impact of Human Immunodeficiency Virus (HIV) goes beyond individual levels and it has a significant influence on communities and nations worldwide. Studying the transmission patterns in HIV dynamics is crucial for understanding the tracking behavior and informing policymakers about the possible control of this viral infection. Various approaches have been adopted to explore how the virus interacts with the immune system. Models involving differential equations with delays have become prevalent across various scientific and technical domains over the past few decades. In this study, we present a novel mathematical model comprising a system of delay differential equations to describe the dynamics of intramural HIV infection. The model characterizes three distinct cell sub-populations and the HIV virus. By incorporating time delay between the viral entry into target cells and the subsequent production of new virions, our model provides a comprehensive understanding of the infection process. Our study focuses on investigating the stability of two crucial equilibrium states the infection-free and endemic equilibriums. To analyze the infection-free equilibrium, we utilize the LaSalle invariance principle. Further, we prove that if reproduction is less than unity, the disease free equilibrium is locally and globally asymptotically stable. To ensure numerical accuracy and preservation of essential properties from the continuous mathematical model, we use a spectral scheme having a higher-order accuracy. This scheme effectively captures the underlying dynamics and enables efficient numerical simulations.

Mathematical modeling and control of lung cancer with IL2 cytokine and anti-PD-L1 inhibitor effects for low immune individuals.

Mathematical formulations are crucial in understanding the dynamics of disease spread within a community. The aim of this work is to examine that the Lung Cancer detection and treatment by introducing IL2 and anti-PD-L1 inhibitor for low immune individuals. Mathematical model is developed with the created hypothesis to increase immune system by antibody cell's and Fractal-Fractional operator (FFO) is used to turn the model into a fractional order model. A newly developed system TCDIL2Z is examined both qualitatively and quantitatively in order to determine its stable position. The boundedness, positivity and uniqueness of the developed system are examined to ensure reliable bounded findings, which are essential properties of epidemic models. The global derivative is demonstrated to verify the positivity with linear growth and Lipschitz conditions are employed to identify the rate of effects in each sub-compartment. The system is investigated for global stability using Lyapunov first derivative functions to assess the overall impact of IL2 and anti-PD-L1 inhibitor for low immune individuals. Fractal fractional operator is used to derive reliable solution using Mittag-Leffler kernel. In fractal-fractional operators, fractal represents the dimensions of the spread of the disease and fractional represents the fractional ordered derivative operator. We use combine operators to see real behavior of spread as well as control of lung cancer with different dimensions and continuous monitoring. Simulations are conducted to observe the symptomatic and asymptomatic effects of Lung Cancer disease to verify the relationship of IL2, anti-PD-L1 inhibitor and immune system. Also identify the real situation of the control for lung cancer disease after detection and treatment by introducing IL2 cytokine and anti-PD-L1 inhibitor which helps to generate anti-cancer cells of the patients. Such type of investigation will be useful to investigate the spread of disease as well as helpful in developing control strategies from our justified outcomes.

Unsteady mhd flow of tangent hyperbolic liquid past a vertical porous plate plate.

The analysis in this communication addresses the unsteady MHD flow of tangent hyperbolic liquid through a vertical plate. The model on mass and heat transport is set up with Joule heating, heat generation, viscous dissipation, thermal radiation, chemical reaction and Soret-Dufour in the form of partial differential equations (PDEs). The PDEs are simplified into a dimensionless PDEs by utilizing a suitable quantities. The simplified equations are solved by utilizing the spectral relaxation method (SRM). The outcomes shows that increase in the Weissenberg and the magnetic field degenerates the velocity profile. The thermal radiation is found to elevate the velocity and temperature profiles as its values increases. The impact of Soret and Dufour on the flow is found to alternate each other. The computational outcomes for concentration, temperature and velocity are illustrated graphically for all encountered flow parameters. The present outcomes are compared with previous outcomes and are found to correlate.

Solitary wave behavior of (2+1)-dimensional Chaffee-Infante equation.

The behavior of gas diffusion in a homogeneous medium is described by the (2+1)-dimensional Chaffee-Infante equation. In this work, the solitary wave behavior of the (2+1)-dimensional Chaffee-Infante equation is studied with the help of extended sinh-Gordon equation expansion technique. Bright, dark, periodic, kink, anti-kink and singular traveling wave patterns are observed for suitable choice of parameters. The 3D graphs, 2D plots and contour plots are included to understand the dynamics of the obtained solutions. The obtained results depict that the extended sinh-Gordon equation expansion technique provides an efficient tool for solving other equations that occur in different branches of science and technology.