Detection of the diffusion nanoparticle in the turbulent flows using the random walk model

A probabilistic detection model is proposed to determine the location of random walk nanoparticles in the turbulent flows. This model maximises the benefits for the environmental, industrial and biological applications. In this paper, we present a generalised coordinated linear detection technique to find a one-dimensional random walk nanoparticle between two layers in turbulent flows. We have two sensors can start the searching process from any point rather than the origin. The initial position of the nanoparticle is a random variable that has a known probability distribution. More than showing the existence of a finite search plan, we derive some auxiliary results related to optimal search plan which minimises the expected value of the first meeting time between one of the sensors and the nanoparticle. A numerical example is provided to illustrate the effectiveness of this technique.