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

Abstract

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.

Keywords:

• Uncertainty
• probabilistic methods
• collision time
• search theory
• discounted effort-reward parameter

Mathematics Subject Classification:

• 46N30
• 90B40

Author contributions

Mohamed A. El-Hadidy did the investigation, methodology, conceptualization, resources and methodology. Alaa A. Alzulaibani did the formal analysis, validation, writing-original draft preparation and visualization. Faten S. Alamri did the validation, writing-original draft preparation and visualization. All authors reviewed the article.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The data used to support the findings of this study are included within the article.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

This research was funded by Princess Nourah bint Abdulrahman University and Researchers Supporting Project number (PNURSP2024R346), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.