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Event-driven power-law relaxation in weak turbulence
Ludovico Silvestri1, Leone Fronzoni, Paolo Grigolini
1Dipartimento di Fisica "E. Fermi," Università di Pisa and INFM CRS-SOFT, Largo Pontecorvo 3, 56127 Pisa, Italy.
Physical Review Letters
|March 5, 2009
Summary
This study reveals weak turbulence in liquid crystals exhibits a 1/f noise spectrum. The system
Area of Science:
- Soft Matter Physics
- Nonlinear Dynamics
- Complex Systems
Background:
- Turbulence in liquid crystals is influenced by external electric fields.
- Understanding spectral properties of weak turbulence is crucial for complex systems.
- Non-Poissonian events and coherent structures are hypothesized drivers of system complexity.
Purpose of the Study:
- To characterize the spectral properties of weak turbulence in liquid crystals under an electric field.
- To investigate the theoretical underpinnings of system complexity driven by critical events.
- To validate theoretical predictions through experimental observation of system relaxation.
Main Methods:
- Experimental characterization of spectral properties (1/f noise spectrum S(f) proportional to 1/f^eta) in liquid crystals.
- Theoretical modeling of system complexity using the density of crucial events (psi(tau)).
- Experimental observation of system relaxation to equilibrium after abrupt voltage changes.
Main Results:
- A 1/f noise spectrum with exponent eta (0
- The exponent eta was theoretically linked to crucial event statistics (eta=3-micro).
- Experimental relaxation dynamics confirmed theoretical predictions and showed violations of linear response theory.
Conclusions:
- Weak turbulence in liquid crystals displays scale-invariant behavior governed by critical events.
- The theoretical framework successfully explains the observed spectral properties and system dynamics.
- The findings challenge conventional linear response theory in complex systems.
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