A study on the existence of a cooperative search method with reducing the first metting time between one of several nano-sensors and a Brownian particle

The coordinated search method for a one-dimensional Brownian particle in the fluid is investigated in this paper. This technique helps to remove pollutants and impurities from the fluid. To locate a Brownian particle that moves along one of n disjoint real lines, we have 2n cooperative nano-sensors coordinate their efforts such that each line contains two of them. All of these nano-sensors begin their searches at the origin. Because of random travelled distances right and left of the origin, we have a random sequence of distances on each line. Due to this uncertainty, we are able to integrate the discounted effort-reward search as a parameter in the distance function. By doing this, the expected value of the first meeting time between one of the nano-sensors and a Brownian particle will be reduced. We determine the approximate value of this expected value in addition to identifying the conditions under which it is finite. We use an example to illustrate the usefulness and application of this model.