Volume 79, Issue 12

This paper explores in detail the integrable Akbota equation, a Heisenberg ferromagnet-type problem that is essential to the study of surface and curve geometry. A variety of soliton families are represented by the generalized solitonic wave profiles that are produced using the improved modified Sardar sub-equation technique, which is renowned for its accuracy and dependability. There has never been a study that used this technique before the current one. As a result, the solitonic wave structures have kink, dark, brilliant, king-singular, dark-singular, dark-bright, exponential, trigonometric, and rational solitonic structures, among other characteristics. In order to check the energy conservation, the Hamiltonian function is created and energy level demonstrated. The sensitivity analysis is also presented at various initial conditions. The graphical representation is also depicted along with the appropriate parametric values.

This study examines the stability of double-diffusive convection in a Kuvshiniski viscoelastic nanofluid, in which the fluid is affected by two fields (such as temperature and salinity) that influence its density. The classical Fick’s law, which assumes an immediate response of temperature to the heat flux gradient, is not entirely correct because it suggests an instantaneous reaction at all points, which is not entirely accurate since information propagates at a finite speed. This shortcoming of Fick’s law leads us to consider the Maxwell–Cattaneo effect (MC effect). Thus, our research focuses on Maxwell–Cattaneo double-diffusive convection in a horizontal layer of a porous medium saturated with viscoelastic nanofluid. Here, the fluid’s small dimensions result in its relaxation time being comparable to its thermal diffusion time, necessitating the use of the Maxwell–Cattaneo relationship. The behavior of viscoelastic nanofluids is described by a constitutive equation of the Kuvshiniski kind, and for the porous medium, Brinkman–Darcy model is considered. The nanofluid model includes the effects of Brownian diffusion and thermophoresis, with the assumption that the flux of the nanoparticle volume fraction is zero at the isothermal boundaries. The framework of linear and nonlinear stability theory leads the analysis. By applying linear stability theory with the help of normal mode technique, the conditions for the occurrence of both stationary and oscillatory convective motions are found in terms of a critical thermal Rayleigh number. The Kuvshiniski viscoelastic fluid exhibits Newtonian behavior in a state of stationary convection. We have discussed two cases for oscillatory convection that are when (i) Maxwell–Cattaneo coefficient for temperature ( C T ) = 0 and (ii) Maxwell–Cattaneo coefficient for salinity ( C C ) = 0. Convective heat and mass transfers are determined using a weakly nonlinear stability analysis. The effects of various factors on oscillatory and stationary states as well as the mass and heat transport are depicted graphically. It is found that with increase in the value of Kuvshiniski parameter F , thermal Rayleigh number Ra also increases for both cases C T = 0 and C C = 0. Ra drops with increasing values of modified diffusivity ratio N A and thermosolutal Lewis number Ls for both stationary as well as oscillatory convection. With increase in the value of Darcy number Da, an interesting pattern can be seen. For stationary convection, Ra increases with Da, but it has reverse effect on oscillatory convection (for both the cases). Streamlines, isotherms, and isohalines are also examined.

This paper presents essential findings on the reducible equations introduced by Courant and Friedrichs in their seminal work, Supersonic Flow and Shock Waves. In this paper, we discuss the presence of simple waves in a 2-D magnetohydrodynamic system with an anti-van der Waals-modified Chaplygin gas. Following the approach of Hu and Sheng (characteristic decomposition of the 2 × 2 quasilinear strictly hyperbolic systems). Appl. Math. Lett. 25(3), 262–267 (2012), and (simple waves and characteristic decompositions of quasilinear hyperbolic systems in two independent variables). Math. Methods Appl. Sci. 38(8), 1494–1505 (2015) for the characteristic decomposition of a strictly hyperbolic system, we establish the existence of simple waves for a non-reducible system. This extends Courant and Friedrichs’s fundamental finding, which was initially proposed for reducible system (R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, New York, Interscience Publishers, Inc, 1948, p. 464). These results enhance our understanding of simple wave behaviour in magnetohydrodynamic systems with modified Chaplygin gas, expanding the applicability of Courant and Friedrichs’s theoretical framework.

The Choi representation of completely positive trace preserving (CPTP) maps, i.e. quantum channels is often used in the context of quantum information and computation as it is easy to work with. It is a correspondence between CPTP maps and quantum states also termed as the Choi–Jamiołkowski isomorphism. It is especially useful if a parametrization of the set of CPTP maps is needed in order to consider a general map or optimize over the set of these. Here we provide a brief introduction to this topic, focusing on certain useful calculational techniques which are presented in full detail.

This research assesses the thermophysical and ultrasonic characteristics of the intermetallic compound Ni 3 Ti, which has a hexagonal crystalline structure. The selected material exhibits many noteworthy characteristics, including the shape memory effect, a high melting point, extremely elastic qualities, etc. The Lennard-Jones potential model has been used to calculate the higher-order elastic constants. The mechanical properties of the material, which provide details regarding its stability and intrinsic qualities, are computed using the second-order elastic constants. Additionally, we have computed the thermal conductivity at 300 K, specific heat, ultrasonic velocities, and Debye temperature. Ultimately, the ultrasonic attenuation is determined using all of the available parameters. The obtained results agree with the data available in the literature.