Computing accumulation density of particles on a line with parabolic trajectories

In this paper, an ideal particle accumulation problem is studied, in which particles are emitted from a fixed point at the same emission velocity onto a plane with a negative y-intercept. Since particles acted on by gravity travel in space via parabolic trajectories, by studying such families of parabolas, the accumulation of particles on a plane can be deduced. An analytical equation, namely the accumulation density function, is subsequently established for representing particle accumulation on such a plane. This accumulation function provides a basis for simulating accumulation of materials on the surfaces in applications such as chemical vapor deposition and spray painting.