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Anomalous relaxation and self-organization in nonequilibrium processes
I Fatkullin1, K Kladko, I Mitkov
1Department of Mathematical Sciences, Rensselaer Polytechnic Institute, Troy, New York 12180, USA.
Summary
This study reveals dynamic self-organization in driven nonlinear systems, leading to universal stretched-exponential relaxation. Two distinct self-organization types, cooperative and anticooperative, dictate either fast or slow thermal relaxation dynamics.
Area of Science:
- Nonlinear dynamics
- Statistical physics
- Condensed matter physics
Background:
- Understanding thermal relaxation is crucial in many physical systems.
- Nonlinear elements and external driving can lead to complex emergent behaviors.
- Stretched-exponential relaxation is often associated with disordered or frustrated systems.
Purpose of the Study:
- To investigate thermal relaxation in ordered arrays of coupled nonlinear elements under external driving.
- To identify and characterize emergent self-organization phenomena.
- To explain the observed stretched-exponential relaxation without invoking disorder or frustration.
Main Methods:
- Modeling ordered arrays of coupled nonlinear elements.
- Applying external driving to the system.
- Analyzing the temporal dynamics of thermal relaxation.
- Investigating parameter dependencies of the relaxation process.
Main Results:
- The model exhibits dynamic self-organization.
- Relaxation follows a universal stretched-exponential form.
- Two types of self-organization, cooperative and anticooperative, were identified.
- Cooperative self-organization leads to fast relaxation, while anticooperative leads to slow relaxation.
Conclusions:
- Ordered nonlinear systems with external driving can exhibit dynamic self-organization and stretched-exponential relaxation.
- The observed behavior arises from cooperative and anticooperative self-organization, not disorder.
- A qualitative explanation for the stretched exponent's behavior across parameter ranges was provided.