Different solutions of the diffusion equation and its applications

Abstract

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.

Fractional Diffusion Equation under Singular and Non-Singular Kernel and Its Stability

“…A classical manner to derive the diffusion equation is by considering the mass conservation principle and Fick's law of diffusion [2]. This equation has a wide variety of applications in different fields such as physics [3,4], epidemiology [5], rumor propagation [6], chemistry [7], the economy [8], and many others [9][10][11][12][13][14]. In physics, this equation is used, for example, to describe the heat, particles, mass diffusion in space [15], and the physics in semiconductors [16].…”