The non-Newtonian liquid scheme is created to address the limitations of the classical (Newtonian) scheme in terms of accurately reflecting real-world fluid flow behavior in industrial applications and improving operational efficiency. The Reiner–Philippoff model, one of the many extant models, modeling non-Newtonian fluids, is of concern because it only captures a few features in some circumstances. Thus, this study aims to investigate the theoretical aspects of Cattaneo–Christov for heat diffusion fusion of Reiner–Philippoff liquid stream in the presence of Darcy–Forchheimer media. Furthermore, the procedure of heat transport is taken out in the occurrence of nonlinear heat radiative, viscous dissipation and Ohmic heating. The partial derivatives of nonlinear differential equations are changed into similarity equations of a certain form by using appropriate similarity transformations. Furthermore, the Runge–Kutta–Fehlberg method with shooting approach is utilized to solve the dimensionless model. The influence of pertinent fluid flow parameters is illustrated graphically. The further engineering curiosity of a local Nusselt number is illustrated and analyzed. It is found that velocity curve is boosted with the augmenting scales of Reiner–Philippoff liquid parameter and Forchheimer number. Further, it is analyzed that increasing the thermal relaxation parameter and Eckert number reduces the heat transport rate at the surface.

In this work, we are concerned with generating solutions of a class of Convection–Diffusion–Reaction (CDR) equation from the solutions of another CDR equation through the Darboux transformations. The method is elucidated by cases with certain types of the reaction coefficients. We have also discussed briefly supersymmetric pairs of CDR equations connected through similarity solutions.

One of the interesting topics of recent research is the study of the Weibel electromagnetic instability growth rate in the interaction of high-intensity lasers with the dense plasma of fusion fuel pellets. In this paper, the effect of stresses caused by laser ponderomotive force on the growth rate of Weibel instability in the nonlinear phase is investigated. The growth of the nonlinear phase of Weibel instability growth rate, which is the saturation phase of Weibel instability, in the presence of stress leads to viscosity turbulence. The results show that the coefficient of reduction of fuel viscosity in the presence of the stress flow is about 0.0014 due to the anomalous transfer mechanism caused by the nonlinear growth of the Weibel instability.

Molecular dynamics method was employed to establish the model of three-dimensional cross-linked polystyrene (PS) formed by divinylbenzene (DVB) and PS chains. Density, radial distribution function, free volume fraction, mean square displacement of systems with different cross-linking degrees (DVB contents of 0%, 3.8%, 7.1% and 11.1%) were studied, as well as macroscopic properties such as glass transition temperature, elastic mechanical properties, uniaxial tensile deformation. The results showed that cross-linking algorithm proposed was feasible for constructing cross-linked PS. With the increase of cross-linking degree, cross-linked PS became denser, and glass transition temperature increased, indicating an increase of heat resistance. Compared with uncross-linked PS, elastic modulus of three cross-linked systems increased by 19.26%, 29.56% and 40.19%; bulk modulus increased by 2.9%, 20.98% and 44.03%; and shear modulus increased by 21.05%, 29.82% and 42.98%. Tensile stress-strain curves showed that network structure formed by adding DVB improved yield stress and tensile resistance of PS.

In this work, we investigate a theoretical study of the stationary entanglement of an optomechanical system by adding a Kerr medium in the cavity where the mechanical resonator is perturbatively connected to an auxiliary qubit. The degree of entanglement between the cavity field and the mechanical system is measured by using the logarithmic negativity. We show that optomechanical entanglement is decreased by Kerr interaction due to photon blockage enhanced by mirror–qubit coupling, we also show that this enhancement is influenced by the temperature. In addition, we find that, in the presence of the mirror–qubit coupling, entanglement can arise with far weaker optomechanical coupling. The proposed scheme shows that the presence of the mirror–qubit coupling and Kerr medium is an effective control for an optomechanical system.

In the frame of a time-dependent oscillator model, the field induced by the coupling between the atomic electric dipole and an external X-ray laser field is investigated. The aim of the paper is to asses if in the resonant case (the frequency of the incoming field matches the frequency of the atom’s collective dipole oscillation) the damped collective oscillation induced by the external time-varying electric field can produce a significant amplification of the total electric field at the nucleus position.