Statistical Dynamical Systems of Flaky Particles Suspended in a Two-Dimensional Incompressible Fluid and Their Neural Network Modeling

Arai, Isshin; Tomoaki Itano; Masako Sugihara-Seki

doi:10.51094/jxiv.1195

##article.authors##

Arai, Isshin Graduate School of Sience and Engineering, Kansai University https://orcid.org/0009-0007-5615-7233
Tomoaki Itano Department of Pure and Applied Physics, Faculty of Engineering Science, Kansai University
Masako Sugihara-Seki Department of Pure and Applied Physics, Faculty of Engineering Science, Kansai University

DOI:

https://doi.org/10.51094/jxiv.1195

キーワード:

fluid dynamics、 nonlinear dynamics、 flow visualization、 neural network

抄録

In optical visualization experiments using flakey particles, the relationship between the resulting brightness patterns and the flow field is complex, and numerous studies have been conducted to explore this connection, for example G. Gauthier, P. Gondret, and M. Rabaud, Physics of Fluids, vol.10, no.9, pp.2147-2154, 1998. We present a dynamical system model for the orientation distribution of flakey particles floating in an incompressible Newtonian fluid. Optical flow visualization using flakey particles is closely related to the orientation dyanmics described by multiple points moving on a unit sphere, which is goverened under the shear history experienced by an infinitesimal flakey particle drifting in the flow.

Although these points move individually on the unit sphere according to the flow field, quantitatively evaluating the time-dependent flow information obtained via visualization is generally challenging.

To address this difficulty, we project the set of points on the unit sphere into a three-dimensional space determined by the particle trajectories so that we can gain insight into flow-visualization experiments. Additionally, we employ a simple neural network model to characterize the dynamics, which are not necessarily closed, in this three-dimensional space. Our approach provides a new perspective for understanding the relationship between distribution states and their governing principles, offering potential applications not only in fluid dynamics but also in visualization techniques and data-driven modeling in related fields.

利益相反に関する開示

All authors have no conflicts of interest related to this study.

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