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Active diffusion model and dynamic structure factor of self-propelled particles in a three parameters fluctuating Mittag-Leffler fluid

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  • Rodríguez, R.F.
  • Gomez-Solano, J.R.
  • Fujioka, J.

Abstract

In this work, we generalize a hydrodynamical model we have proposed in previous work to calculate analytically the time-dependent diffusion coefficient, and the light scattering structure factor of a dilute suspension of active particles self-propelling through a fluctuating linear, viscoelastic fluid. This generalization considers that the internal additive fluctuations acting on this active suspension are modeled by a three-parameter Mittag-Leffler function. We describe the dynamics of the fluctuations in terms of a generalized Langevin equation. Using a generalized Stokes-Einstein relation, we describe the behavior of the particle’s frequency-dependent diffusion coefficient and the Rayleigh component of the light scattering structure, for more general viscoelasticity than Maxwell’s exponential behavior. The behavior of these properties of the suspended particles as a function of the parameters characterizing the time-memory and the internal noise correlation is analyzed.

Suggested Citation

  • Rodríguez, R.F. & Gomez-Solano, J.R. & Fujioka, J., 2025. "Active diffusion model and dynamic structure factor of self-propelled particles in a three parameters fluctuating Mittag-Leffler fluid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 662(C).
    • Handle: RePEc:eee:phsmap:v:662:y:2025:i:c:s0378437125000639
    DOI: 10.1016/j.physa.2025.130411
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    References listed on IDEAS

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    1. Camacho, J.F. & Híjar, H. & Rodríguez, R.F., 2005. "Hydrodynamic correlation functions for a nematic liquid crystal in a stationary state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 348(C), pages 252-276.
    2. Liemert, André & Sandev, Trifce & Kantz, Holger, 2017. "Generalized Langevin equation with tempered memory kernel," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 466(C), pages 356-369.
    3. Gomez-Solano, Juan Ruben, 2024. "Energy fluctuations of a Brownian particle freely moving in a liquid," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 646(C).
    4. Rodríguez, R.F. & Fujioka, J. & Salinas-Rodríguez, E., 2021. "Nonequilibrium fractional correlation functions and fluctuation–dissipation in linear viscoelasticity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 583(C).
    5. R. F. Rodríguez & H. Híjar, 2006. "Long-range order and dynamic structure factor of a nematic under a thermal gradient," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 50(1), pages 105-110, March.
    6. Trifce Sandev, 2017. "Generalized Langevin Equation and the Prabhakar Derivative," Mathematics, MDPI, vol. 5(4), pages 1-11, November.
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