Reduction in the Searching Time to Find a Brownian Nanoparticle in the Fluid

Alaa Awad Alzulaibani () and Mohamed Abd Allah El-Hadidy
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Alaa Awad Alzulaibani: Mathematics and Statistics Department, Faculty of Science, Taibah University, Yanbu, Saudi Arabia
Mohamed Abd Allah El-Hadidy: Mathematics and Statistics Department, Faculty of Science, Taibah University, Yanbu, Saudi Arabia†Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 01, 61-76

Abstract: This work studies the existence of a new search technique that uses two cooperative nanosensors to track a one-dimensional Brownian nanoparticle (target) in the fluid. This technique participates in the purification of impurities and contaminants from the fluid. In addition, it allows us to include the discounted effort-reward search as a parameter (factor) in the distance function. This parameter is based on past or observed data about the nanoparticle position at any time t. This will reduce the expected value of the first meeting time between one of the nanosensors and a nanoparticle. The searching process starts at the origin. More than finding the conditions that make this expected value finite, we calculate its approximate value. We present the effectiveness and applicability of this model by using an illustrative example.

Keywords: Discounted effort-reward search; cooperative search technique; Brownian motion (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500048

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