The current research aims to examine the impact of a tangent hyperbolic fluid flow confined by a stretching sheet with the existence of variable thermal conductivity, mixed convection, and magneto hydrodynamics. A mathematical model is developed in the form of partial differential equations (PDEs) and then converted into ordinary differential equations by using self-felicitous transformations. The technique of BVP4C (MATLAB package) has been used to simplify these ordinary differential equations. The numerical solution of skin friction, mixed convection, Nusselt number, and velocity and temperature profiles for different values of the involved parameters is indicated through tables and graphs. It can be noticed that the velocity profile decreases when the Hartmann number increases. The effect of Weissenberg number, inclined angle, and power law index for velocity profiles is also identical to the Hartmann number. The temperature profile decays due to an increment in the Prandtl number. Skin friction and the Nusselt number have also been explained. The physical reasoning for growth or decay of these parameters has been discussed in detail.

Symmetries are crucial to the investigation of nonlinear physical processes, particularly the evaluation of a differential problem in the real world. This study focuses on the investigation of the Kadomtsev–Petviashvili $\left(\mathrm{KP}\right)$ model within a (3+1)-dimensional domain, governing the behavior of wave propagation in a medium characterized by both nonlinearity and dispersion. The inquiry employs two distinct analytical techniques to derive multiple soliton solutions and multiple solitary wave solutions. These methods include the modified Sardar sub-equation technique and the Darboux transformation $\left(\mathrm{DT}\right)$. The modified Sardar sub-equation technique is used to obtain multiple soliton solutions, while the $\mathrm{DT}$ is introduced to develop two bright and two dark soliton solutions. These solutions are presented alongside their corresponding constraint conditions and illustrated through 3-D, 2-D, and contour plots to physically portray the derived solutions. The results demonstrate that the employed analytical techniques are useful and have not yet been explored in the context of the analyzed models. The proposed methodologies are valuable and can be applied to additional nonlinear evolutionary models employed to describe nonlinear physical models within the domain of nonlinear science.

Modeling and design of on-chip interconnect, the interconnection between the components is becoming the fundamental roadblock in achieving high-speed integrated circuits. The scaling of interconnect in nanometer regime had shifted the paradime from device-dominated to interconnect-dominated design methodology. Driven by the expanding complexity of on-chip interconnects, a passivity preserving model order reduction (MOR) is essential for designing and estimating the performance for reliable operation of the integrated circuit. In this work, we developed a new frequency selective reduce norm spectral zero (RNSZ) projection method, which dynamically selects interpolation points using spectral zeros of the system. The proposed reduce-norm scheme can guarantee stability and passivity, while creating the reduced models, which are fairly accurate across selected narrow range of frequencies. The reduced order results indicate preservation of passivity and greater accuracy than the other model order reduction methods.

This paper presents the sensitivity analysis of an epidemiological model, SEIR, describing the transmission of Hepatitis B Virus. The classical sensitivities, the system sensitivity and the sensitivity norms of the model have been found. The sensitivities show that the susceptible individuals are majorly affected by the birth rate, contact rate, the rate at which the exposed individuals become infected and the fraction of the infected individuals in the population. System sensitivity describes the sensitivity of the whole model output with respect to all the parameters. The results of the classical sensitivities of the parameters are in agreement with the results given by the system sensitivities. The contact rate, beta has the largest sensitivity norm and the exposed infected fraction of the population, t(1) has the least sensitivity norm. The qualitative and the quantitative sensitivity studies of the SEIR model reaffirm each other.