Title: On the existence of the tracking model for N-dimensional Brownian particle in the fluid

Authors: Mohamed Abd Allah El-Hadidy; Alaa Awad Alzulaibani

Addresses: Mathematics Department, Faculty of Science, Tanta University, Tanta, Egypt; Mathematics and Statistics Department, Faculty of Science, Taibah University, Yanbu, Saudi Arabia ' Mathematics and Statistics Department, Faculty of Science, Taibah University, Yanbu, Saudi Arabia

Abstract: In this work, an existential study of the tracking technique of N-dimensional Brownian particle in the fluid has been discussed. A set of nano-robot sensors start the tracking process from the origin of N-dimensional space. Besides giving the conditions which present the finiteness of the expected value of the first meeting time between one of the nano-robot sensors and the particle, we provide the computational expected value of this time.

Keywords: probabilistic methods; statistical physics; mathematical analysis; N-dimensional Brownian motion; purify impurities.

DOI: 10.1504/IJMOR.2023.133715

International Journal of Mathematics in Operational Research, 2023 Vol.26 No.1, pp.59 - 95

Received: 03 May 2022
Accepted: 28 Jun 2022
Published online: 02 Oct 2023 *

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