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Analysis of particle settlement characteristics in a one-dimensional deterministic model

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  • S. E. Velázquez-Pérez

    (Departamento Físico-Matemáticas, Universidad Autónoma de San Luis Potosí, Niño Artillero s/n. Zona Universitaria Poniente, San Luis Potosí 78290, Mexico2Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Av. Parque Chapultepec 1570, Privadas del Pedregal, San Luis Potosí 78295, Mexico)

  • H. E. Gilardi-Velázquez

    (Facultad de Ingeniería, Universidad Panamericana, Josemaría Escrivá de Balaguer 101, Aguascalientes, Aguascalientes 20296, Mexico)

  • E. Campos-Cantón

    (Division of Control and Dynamical Systems, Instituto Potosino de Investigación Científica y Tecnológica, Camino a la Presa San Jos 2055, Col. Lomas 4 Sección, San Luis Potosí, San Luis Potosí 78216, Mexico)

Abstract

In this paper, we investigate how particles settle in a one-dimensional deterministic model. We leverage a model for deterministic Brownian motion and introduce boundary conditions to simulate particle settling. By adjusting parameters in the Jerk equation, we explore how different diffusion, and the size of the settling space affect the particles’ behavior. We analyze how these parameters influence the settling time and its relationship to the dispersion medium. Additionally, we examine statistical properties as follows: the average settling time, the probability distributions for mean displacement, and how the probability distribution of settling times changes with the size of the space.

Suggested Citation

  • S. E. Velázquez-Pérez & H. E. Gilardi-Velázquez & E. Campos-Cantón, 2025. "Analysis of particle settlement characteristics in a one-dimensional deterministic model," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 36(11), pages 1-19, November.
    • Handle: RePEc:wsi:ijmpcx:v:36:y:2025:i:11:n:s012918312550024x
    DOI: 10.1142/S012918312550024X
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