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Updated: Jun 20, 2026
09:32
Cooling Rate Dependent Ellipsometry Measurements to Determine the Dynamics of Thin Glassy Films
Published on: January 26, 2016
Signature of glassy dynamics in dynamic mode decompositions
Zachary G Nicolaou1,2,3, Hangjun Cho4,5,6, Yuanzhao Zhang7
1University of Washington, Department of Applied Mathematics, Seattle, Washington 98195, USA.
Physical Review. E
|June 19, 2026
Summary
This study introduces a new data-driven method to analyze complex glassy dynamics. The dynamic mode decomposition reveals a spectral signature for detecting algebraic relaxation in disordered systems.
Area of Science:
- Physics
- Complex Systems
- Data Science
Background:
- Glasses exhibit complex dynamics with disordered low-energy states and slow relaxation.
- Far-from-equilibrium systems, like coupled oscillators, show anomalous algebraic relaxation.
- Disordered, high-dimensional systems are challenging for traditional theoretical analysis.
Purpose of the Study:
- To develop a data-driven method for characterizing glassy dynamics.
- To identify a model-agnostic signature for detecting algebraic relaxation.
- To analyze complex systems where traditional methods fall short.
Main Methods:
- Utilized dynamic mode decomposition (DMD), a data-driven spectral analysis technique.
- Approximated the Koopman spectrum to analyze system dynamics.
- Applied the method to both simple (1D ODE) and complex (coupled oscillators) systems.
Main Results:
- The gap between oscillatory and decaying modes in the Koopman spectrum vanishes during algebraic relaxation.
- This vanishing gap serves as a robust signature for glassy dynamics.
- Demonstrated the method's effectiveness on diverse examples.
Conclusions:
- Dynamic mode decomposition offers a powerful tool for analyzing complex glassy dynamics.
- The proposed spectral signature reliably detects algebraic relaxation.
- This data-driven approach advances the study of disordered and far-from-equilibrium systems.
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