A Regular Perturbation Analysis Of The Non-Linear Contaminant Transport Equation with An Initial And Instantaneous Point Source.

In this research work, we provide a regular perturbation analysis of a non – linear equation arising in contaminant transport. The equation is characterised by advection, diffusion and absorption. Assuming the adsorption term is modelled by a Freundlich isotherm it can be non-linear in concentration and non-differentiable as the concentration approaches zero. We consider the approximation of this equation using a regular perturbation and thereby solving the resulting linear equations analytically

Viscous Dissipation Effect on Flow through a Horizontal Porous Channel with Constant Wall Temperature and a Periodic Pressure Gradient

The objective of this paper is to investigate the effects of viscous dissipation, constant wall temperature and a periodic pressure field on unsteady flow through a horizontal channel filled with porous material. The coupled nonlinear differential equations governing the flow were solved analytically using the usual method of separation variables and simple perturbation techniques. Effects of various parameters such as the Darcy, Reynolds, prandtl and Eckert numbers were also studied and visualized

Screening of Metal-Ion Intercalated Yttrium Carbide and Nitride MXenes for Energy Storage Applications via Density Functional Theory

Rechargeable batteries and energy storage devices play a major role in many facets of human endeavour due to their efficiency and portability. In this work, we investigated the suitability of single-layer intercalated Yttrium-based MXenes Y2CT2 (T= Li, Mg, Al) and Y2NLi2 as potential energy storage materials using the first principle calculation within the framework of the density functional theory approach. Upon intercalation, the lattice constants of the MXenes expand due to the size of the intercalating species and the electrostatic repulsion. We obtained the theoretical gravimetric capacities, open circuit voltages and adsorption energies. The obtained open circuit voltages for Y2CT2 (T= Li, Mg) and Y2NLi2 falls within the voltage window of 0 − 1.0V which has been found to eliminate dendrites formation caused by alkaline metals during the discharge-charge cycle. The adsorption energies indicate the stability of the intercalating ion on the MXenes surfaces except for Al cation. The results are consistent with other studies on similar MXene families in the existing literature. The work may aid the understanding of the electrochemical properties of 2D materials and we recommend Y2CLi2, Y2NLi2 , and Y2CMg2 for future investigation as potential materials for rechargeable batteries

Lattice Dynamics and thermodynamic Responses of XNbSn Half-Heusler Semiconductors: A First-Principles Approach

In this work, we have evaluated how CoNbSn, IrNbSn, and RhNbSn half Heusler alloys respond to temperature change and the accompanying lattice vibrations as a cubic crystal. There are reports in the literature for CoNbSn with which we compared our result; there are, however, no reports for the other two alloys except for their Debye temperature obtained via machine learning, and our results compare well. Considering that results in the literature for IrNbSn and RhNbSn are scanty, we first computed the alloys' structural and electronic properties to establish their structural stability using the density functional theory and generalised gradient approximation as implemented in the quantum espresso computational suite. We confirmed the equilibrium lattice structure by exploring the three possibilities for a half Heusler alloy and fitting the results to the state's Murnaghan equation. The negative formation energies obtained supports experimental simulation of the alloys. Results from the lattice dynamics and thermodynamic evaluation show that the alloys favour ionic bonding and are ductile. The Debye temperature positions IrNbSn to be the most promising material for thermoelectric application because it has the least Debye temperature; hence it is supposed to have the lowest thermal conductivity. The Dulong-Petit law is obeyed at high temperature as expected. The phonon dispersion and density of states show that the d orbitals of Co and Nb are the significant contributors to the dispersions at both the acoustic and optical modes of the alloys

The influence of external magnetic and Aharonov–Bohm flux fields on bound states of the Klein–Gordon and Schrodinger equations via the SWKB approach

We obtained the approximate two-dimensional bound states solutions of a Klein–Gordon particle moving in a quantum mechanical solvable potential under the influence of the external magnetic and Aharonov–Bohm flux fields. We utilized the supersymmetric WKB approach to obtain both the energy levels and normalized wave function in closed form. The proposed potential reduces to the screened Kratzer, Kratzer, Yukawa and Coulomb potential functions as special cases and admits the corresponding energy eigenvalues in both relativistic and non-relativistic regimes. When the external magnetic and Aharonov–Bohm flux fields were turned off, the relativistic, non-relativistic energies and ground state probability density overlap for the magnetic quantum numbers ($$m = - 1,1$$). The presence of the fields removes the degeneracy and shifts the energy levels of the Klein–Gordon particle. However, we found that the magnetic field strength has no effects on the maximum non-relativistic energy. Generally, the results are consistent with the works in existing literature where the authors utilized different forms of potential energy functions

Non-relativistic bound state solutions with

In this work, we studied the bound states and quantum theoretic-information measurements of an $$\alpha$$-deformed Kratzer-type potential with the Schrodinger equation. The ground state wave function in position-momentum spaces and the energy spectra equations for arbitrary quantum numbers are obtained in closed-form via the super-symmetric WKB method and Fourier transform. The obtained energy equation is bounded and reduces to the molecular Kratzer-type energy and the hydrogenic Coulomb’s energy upon proper adjustment of potential parameters. The wave function was used to obtain the Fisher, Shannon, Rényi and Tsallis theoretic-information measures numerically. Our results for the information measures obey the local Fisher inequality and the Bialynicki-Birula–Mycielski inequality. The Rényi and Tsallis entropies in position-momentum spaces were obtained for the index number $$q = 0.5$$ and $$q = 2$$ as a function of the potential parameter. The results of the theoretic-information quantities and probability densities revealed that the potential parameters strongly influence the localization and delocalization of the position of a nano particle

Information-theoretic measures and thermodynamic properties under magnetic and Aharonov–Bohm flux fields

We investigated the effects of external magnetic and Aharonov–Bohm flux fields on the thermodynamic properties, Fisher, Shannon and Rényi information-theoretic measures using the non-relativistic Schrödinger equation with a Varshni-type potential. We adopted the parametric Nikiforov–Uvarov approach to obtain the analytical bound states in closed form. The thermodynamic functions such as the free energy, specific heat capacity, vibrational entropy and mean energy were analyzed. Also, the results for the 2D Fisher's information-theoretic measure obey the inequality $$I\left(\rho \right)I\left(\gamma \right)\ge 16$$. The Rényi entropies sum applied to lithium hydride (LiH) diatomic molecule obeys the inequality $${R}_{2}\left(\rho \right)$$+$${R}_{2/3}\left(\gamma \right)\ge$$ 4.19926 for 2D system. Also, the global Shannon entropies sum inequality for the LiH molecule is verified. The applications of the external fields were found to strongly influence the splitting of the energy overlaps, the thermodynamic functions and the information-theoretic measures. The results may aid the understanding of the dynamics of quantum particles and molecules in external fields