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Three‐dimensional advection–diffusion equation with steady state was evaluated from continuous point source taking the vertical and crosswind eddy diffusivities as power law of vertical height and downwind distance with constant wind speed to get the concentration in three dimensions. Separation of variables technique and Hankel transform were used to calculate this equation. The proposed analytical solution was compared with diffusion experiment of radioactive Iodine‐135 (I135) in unstable condition at Inshas, Cairo, Egypt. A good agreement achieved between calculated and observed concentration support our proposed model.

Natur The vertical fraction variation of eddy diffusivity was taken into consideration in the dispersion of pollutants from a point source. A power-law profile was used to describe the variation of wind speed and vertical eddy diffusivity with height above ground surface. The dry deposition of the diffusing particles at the ground surface is taken into account through the boundary conditions. The concentration of pollutants was derived assuming that the vertical diffusion is limited by an elevated inversion layer located at the top of the boundary layer "h". Also, the decay distance of a pollutant along the wind direction was estimated. The resulting analytical solutions have been applied on the emissions from Egypt's First Research Reactor at Inshas in unstable condition and Hanford diffusion experiment in stable condition. Comparisons between proposed and observed concentrations show a good agreement between the proposed and observed concentrations when α=0.81than other fractions and integer value. The results are discussed and presented in illustrative figures.

In this paper, we investigate the entanglement of the interaction of three modes of radiation field with moving and unmoving two-level atom. The time evolution of the von Neumann entropy, entropy squeezing and marginal atomic Wehrl entropy is investigated. The marginal atomic Wehrl entropy as squeezing indicator of the entanglement of the system is suggested. The results beacon the important roles played by both the atomic motion parameters in the evolution of entanglement, entropy squeezing and marginal atomic Wehrl entropy. Using special values of the photon number of transition and atomic motion parameter, the entanglement phenomena of sudden death and long living entanglenment can be appeared. The results show that there is atomic motion monotonic harmonization atomic Wehrl entropy (WE). It is illustrated that the amount of the above-mentioned phenomena can be tuned by controlling the evolved parameters appropriately.

In this  report, we solved the advection–diffusion equation under pollutants deposition on the ground surface, taking wind speed and vertical diffusion depend on the vertical height. Also, we estimated a simple diffusion model from point source in an urban atmosphere and the conservative material with downwind was evaluated. Then, we calculated the extreme ground-level concentration as a function of stack height and plume rise in two cases. Comparison between the proposed models and the emission from the Egyptian Atomic Research Reactor at Inshas had been done. Lastly, we discussed the results in this report.