Average amplitudes analysis for a phenomenological model under hydrodynamic interactions with periodic perturbation and multiplicative trichotomous noise

Lini Qiu, Guitian He (), Yun Peng, Huijun Lv and Yujie Tang
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Lini Qiu: Center for Applied Mathematics of Guangxi Minzu University
Guitian He: Center for Applied Mathematics of Guangxi Minzu University
Yun Peng: Center for Applied Mathematics of Guangxi Minzu University
Huijun Lv: Center for Applied Mathematics of Guangxi Minzu University
Yujie Tang: Center for Applied Mathematics of Guangxi Minzu University

The European Physical Journal B: Condensed Matter and Complex Systems, 2023, vol. 96, issue 4, 1-20

Abstract: Abstract From a statistical mechanics perspective, to describe the dynamics of a tracer, a phenomenological model has been established by a generalized Langevin equation (GLE) which includes a Basset force, a periodic perturbation force, a Stokes force, an external force and a thermal noise. Using the generalized Shapiro-Loginov formula, the iterative expressions of the first moments of the system are obtained. The time series of the first moments have been extensively investigated. By analyzing the time series of the first moments of the system with different system parameters, the irregular responses of the curves are revealed and tend to be stable for a long time. Significantly, the dynamics of average amplitudes of the first moments, influenced by various system parameters, have also been addressed in detail. Especially, the monotonic and non-monotonic properties of the average amplitudes of the first moments versus the memory exponent $$\alpha $$ α are discussed.

Date: 2023
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DOI: 10.1140/epjb/s10051-023-00511-4

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