Existence of Tracking Brownian Nanoparticle Technique with Reducing its First Collision Time with One of the Nanosensors in the Interactive Medium

Abstract

This study discusses the existence of tracking N-dimensional Brownian nanoparticle in an interactive medium, where this tracking is based on Brownian motion analysis. A group of N nanosensors begin the tracking process at the origin of N dimensional space, where the nanosensors serve an important role in detecting and monitoring this nanoparticle. Each nanosensor oscillates as it passes through the origin of its planer surface (to the right and left) in the presence of a succession of random points on each axis. The space's plans cross on a real line, with the origin (0,0,...,0). Because of this uncertainty, we may be able to calculate the overall distance in each tracking step as a function of a discounted effort-reward parameter. We show analytically how this parameter influences demonstrating the existence of this model and lowering the computationally expected value of the first collision time between a nanosensor and a nanoparticle.