Soret and Dufour effects on mixed convection unsteady MHD boundary layer flow over stretching sheet in porous medium with chemically reactive species

This paper studies the thermal-diffusion and diffusion thermo-effects in the hydro-magnetic unsteady flow by a mixed convection boundary layer past an imperme- able vertical stretching sheet in a porous medium in the presence of chemical reaction. The velocity of t^he stretching surface, the surface temperature, and the concentration are assumed to vary linearly with the distance along the surface. The governing partial differential equations are transformed into self-similar unsteady equations using similarity transformations .and solved numerically by the Runge-Kutta fourth order scheme in as- sociation with the shooting method for the whole transient domain from the initial state to the final steady state flow. Numerical results for the velocity, the temperature, the concentration, the skin friction, and the Nusselt and Sherwood numbers are shown graph- ically for various flow parameters. The results reveal that there is a smooth transition of flow from unsteady state to the final steady state. A special case of our results is in good agreement with an earlier published work.

Laser, Universe and Arrow of Time

We have presented a comparison between the universe and the Laser. In many ways, the physics of laser and the universe are analogous. The root of the analogy is the fact that both laser and early universe depend completely on the quantum nature. We have also presented a simple analogous example of the growth of a flower at successive stages of development and shown how the arrow of time may be represented in these cases.

Investigation of proton structure function F_(2)^(p)at HERA in light of an analytical solution to the Balitsky–Kovchegov equation

In this paper,the proton structure function F_(2)^(p)(x,Q^(2))at small-x is investigated using an analytical solution to the Balitsky–Kovchegov(BK)equation.In the context of the color dipole description of deep inelastic scattering(DIS),the structure function F_(2)^(p)(x,Q^(2))is computed by applying the analytical expression for the scattering amplitude N(k,Y)derived from the BK solution.At transverse momentum k and total rapidity Y,the scattering amplitude N(k,Y)represents the propagation of the quark-antiquark dipole in the color dipole description of DIS.Using the BK solution we extracted the integrated gluon density xg(x,Q^(2))and then compared our theoretical estimation with the LHAPDF global data fits,NNPDF3.1sx and CT18.Finally,we have investigated the behavior of F_(2)^(p)(x,Q^(2))in the kinematic region of 10^(-5)≤x≤10^(-2)and 2.5 GeV^(2)≤Q^(2)≤60 GeV^(2).Our predicted results for F_(2)^(p)(x,Q^(2))within the specified kinematic region are in good agreement with the recent high-precision data for F_(2)^(p)(x,Q^(2))from HERA(H1 Collaboration)and the LHAPDF global parametrization group NNPDF3.1sx.

Phase structures and critical behavior of rational non-linear electrodynamics Anti de Sitter black holes in Rastall gravity

This research paper presents a black hole solution with a rational nonlinear electrodynamics source within the Rastall gravity framework.The paper analyzes the thermodynamic properties of the solution in normal phase space and explores its critical behavior.The phase structure is examined using the extended first law of thermodynamics,with the cosmological constantΛserving as pressure P.The isotherms exhibit van der Waals behavior at small values of horizon r_(+).The paper also investigates the Gibbs free energy behavior and finds two critical points with two pressures where the re-entrant phase transition occurs and disappears.We also explore the prevalent microstructure of black holes in Ruppeiner geometry,uncovering significant deviations in the nature of particle interactions from conventional practice.Moreover,the thermodynamic geometry is analyzed using the Ruppeiner formalism,with the normalized Ricci scalar indicating possible point-phase transitions of the heat capacity,and the normalized extrinsic curvature having the same sign as the normalized Ricci scalar.The three-phase transitions of the heat capacity are those that we find for the normalized Ruppeiner curvatures.Thus,there is an absolute correspondence.