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Published on: February 28, 2016
Multifrequency phase locking and hyperplane structures in particle orientation
1Kansai University, Graduate School of Science and Engineering, Osaka 564-8680, Japan.
Physical Review. E
|February 20, 2026
Summary
Flakelike particles in fluid flows align into anisotropic states through nonlinear phase locking. This phenomenon, driven by multifrequency forcing, reveals universal synchronization principles applicable across diverse scientific fields.
Area of Science:
- Fluid dynamics
- Nonlinear dynamics
- Complex systems
Background:
- Flakelike particles in fluid flows show complex orientation dynamics sensitive to shear and vorticity.
- Understanding the transition from isotropic to anisotropic orientation is crucial.
Purpose of the Study:
- Investigate conditions for isotropic-to-anisotropic orientation evolution in flakelike particles.
- Model particle orientation as a nonlinear phase oscillator under multifrequency forcing.
Main Methods:
- Applied Fourier decomposition to time-dependent velocity gradients.
- Formulated phase-locking phenomena as hyperplanes in multidimensional frequency space.
- Conducted numerical simulations to observe locking hyperplanes.
Main Results:
- Identified resonance conditions and phase-locking phenomena.
- Confirmed emergence, collision, and persistence of locking hyperplanes.
- Demonstrated structural correspondence to Arnold tongues and devil's staircases.
Conclusions:
- Developed a framework for quantitatively predicting anisotropic orientation alignment.
- Unified particle aggregation with externally driven synchronization phenomena.
- Provided a generalized theoretical basis for multifrequency locking in nonlinear systems.
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