FRACTAL DIFFUSION IN AN ISOTROPOUS MEDIUM

Xuejuan Li, Qianni Liu, Abdulrahman Ali Alsolami and Xuange Geng
Additional contact information
Xuejuan Li: Department of Mathematics, School of Science, Xi ’an University of Architecture and Technology, Xi ’an, P. R. China
Qianni Liu: Department of Mathematics, School of Science, Xi ’an University of Architecture and Technology, Xi ’an, P. R. China
Abdulrahman Ali Alsolami: ��Department of Mathematics, Faculty of Science King Abdulaziz University, Jeddah, Saudi Arabia
Xuange Geng: Department of Mathematics, School of Science, Xi ’an University of Architecture and Technology, Xi ’an, P. R. China

FRACTALS (fractals), 2024, vol. 32, issue 06, 1-8

Abstract: This paper provides a comprehensive examination of fractal diffusion in an isotropic medium. This process has a fascinating temporal memory and an extremely high initial response, which are unquestionably characterized by the Caputo fractional derivative. Its spatio-symmetric property is described by the Riesz fractional derivative. To illustrate the diffusion mechanism, we present an example of a toxic gas leak in a subway station. The numerical results are extremely promising and challenging. They clearly indicate that a MEMS-based gas sensor can track a toxic gas leak immediately due to its extremely fast diffusion at the initial time. This is of great importance for public safety. Furthermore, the diffusion process is primarily contingent upon the density of the air, which we can easily control. The diffusion pattern in an isotropic medium exhibits fractal behavior, which is extremely helpful for designing an emergency system for evacuating people from the center of toxic gas leaks by changing air density or temperature. This paper presents a rigorous mathematical concept for monitoring systems and early warning systems for toxic gas leaks.

Keywords: Toxic Gas Leak; Emergency System Design; Fractal Diffusion; Numerical Method (search for similar items in EconPapers)
Date: 2024
References: Add references at CitEc
Citations:

Downloads: (external link)
http://www.worldscientific.com/doi/abs/10.1142/S0218348X24501238
Access to full text is restricted to subscribers

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wsi:fracta:v:32:y:2024:i:06:n:s0218348x24501238

Ordering information: This journal article can be ordered from

DOI: 10.1142/S0218348X24501238

Access Statistics for this article

FRACTALS (fractals) is currently edited by Tara Taylor

More articles in FRACTALS (fractals) from World Scientific Publishing Co. Pte. Ltd.
Bibliographic data for series maintained by Tai Tone Lim ().