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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Alaa Awad Alzulaibani & Mohamed Abd Allah El-Hadidy, 2025. "Reduction in the Searching Time to Find a Brownian Nanoparticle in the Fluid," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 21(01), pages 61-76, March.
    • Handle: RePEc:wsi:nmncxx:v:21:y:2025:i:01:n:s1793005725500048
    DOI: 10.1142/S1793005725500048
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