On Reducing the Collision Time Between a Nanosensor and a Randomly Moving Particle in the Fluid

The search model suggested in this study uses a unit-speed nanosensor to track the fluid's randomly linear flow particle, starting at the real line's origin. The nanosensor oscillates passing through the origin point (towards right and left) in the presence of a sequence of random points, and the particle's position is always changing with a random waiting time that varies with the Gaussian jump length. We may be able to consider the search distance as a function of a discounted effort-reward parameter (factor) because of this uncertainty. We demonstrate analytically how this parameter affects proving the existence of this model and reducing the expected value of the first collision time before the nanosensor returns a particle to the origin. To demonstrate the effectiveness of this model, a numerical example is provided.