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Inverse cascade avalanche model with limit cycle exhibiting period doubling, intermittency, and self-similarity
1Department of Physics, University of Warwick, Coventry CV4 7AL, United Kingdom.
Summary
A novel sandpile algorithm models transport in confined systems. It simulates fluid flow dynamics, dissipating energy via avalanches and exhibiting complex emergent behaviors like limit cycles and random walks.
Area of Science:
- Computational Physics
- Complex Systems Modeling
Background:
- Transport phenomena in driven dissipative systems are complex.
- Modeling fluid flow dynamics requires sophisticated algorithms.
Purpose of the Study:
- To present a one-dimensional avalanche sandpile algorithm for transport simulation.
- To investigate emergent dynamics in driven dissipative confinement systems.
Main Methods:
- Developed a conservative, nonlocal, and linear redistribution rule mimicking fluid flow.
- Introduced a 'fluidization' parameter L(f) to define the operational length scale.
- Analyzed limiting cases (L(f)=1 and L(f)=N) and intermediate values.
Main Results:
- The algorithm conserves mass and dissipates potential energy through avalanches.
- Emergent dynamics include limit cycles with period-doubling, intermittency, and random walks.
- Analytical solutions were obtained for specific fluidization parameter values.
Conclusions:
- The sandpile algorithm effectively models transport and energy dissipation in confined systems.
- The system exhibits rich emergent dynamics dependent on the fluidization parameter.
- This model provides insights into complex behaviors in driven dissipative systems.
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