Symmetries and exact solutions of KP equation with an arbitrary nonlinear term

The generalized KP (GKP) equations with an arbitrary nonlinear term model and characterize many nonlinear physical phenomena. The symmetries of GKP equation with an arbitrary nonlinear term are obtained. The condition that must satisfy for existence the symmetries group of GKP is derived and also the obtained symmetries are classified according to different forms of the nonlinear term. The resulting similarity reductions are studied by performing the bifurcation and the phase portrait of GKP and also the corresponding solitary wave solutions of GKP
equation are constructed.

Temperature fields in a channel partially filled with a porous material under local thermal non-equilibrium condition-an exact solution

This work examines analytically the forced convection in a channel partially filled with a porous material and subjected to constant wall heat flux. The Darcy–Brinkman–Forchheimer model is used to represent the fluid transport through the porous material. The local thermal non-equilibrium, two-equation model is further employed as the solid and fluid heat transport equations. Two fundamental models (models A and B) represent the thermal boundary conditions at the interface between the porous medium and the clear region. The governing equations of the problem are manipulated, and for each interface model, exact solutions, for the solid and fluid temperature fields, are developed. These solutions incorporate the porous material thickness, Biot number, fluid to solid thermal conductivity ratio and Darcy number as parameters. The results can be readily used to validate numerical simulations. They are, further, applicable to the analysis of enhanced heat transfer, using porous materials, in heat exchangers.

Screened Hybrid Exact Exchange Correction Scheme for Adsorption Energies on Perovskite Oxides

The bond formation between an oxide surface and oxygen, which is of importance for numerous surface reactions including catalytic reactions, is investigated within the framework of hybrid density functional theory that includes nonlocal Fock exchange. We show that there exists a linear correlation between the adsorption energies of oxygen on LaMO3 (M = Sc–Cu) surfaces obtained using a hybrid functional (e.g., Heyd–Scuseria–Ernzerhof) and those obtained using a semilocal density functional (e.g., Perdew–Burke–Ernzerhof) through the magnetic properties of the bulk phase as determined with a hybrid functional. The energetics of the spin-polarized surfaces follows the same trend as corresponding bulk systems, which can be treated at a much lower computational cost. The difference in adsorption energy due to magnetism is linearly correlated to the magnetization energy of bulk, that is, the energy difference between the spin-polarized and the non-spin-polarized solutions. Hence, one can estimate the correction ...