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Universal power-law and partial condensation in aggregation-chipping processes.
Hiroshi Yamamoto1, Toshiya Ohtsuki
1Center for Natural Sciences, Kitasato University, 1-15-1, Kitasato, Minami-ku, Sagamihara 252-0373, Japan. hyamamot@kitasato-u.ac.jp
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 28, 2010
Summary
In aggregation-chipping processes, a universal power-law distribution emerges above a critical average cluster size. This phenomenon, observed in cluster dynamics, indicates a stable system behavior with finite-sized chipped units.
Area of Science:
- Statistical Physics
- Complex Systems
Background:
- Investigating cluster dynamics in aggregation-chipping processes is crucial for understanding complex systems.
- Previous studies have explored aggregation and chipping phenomena separately.
Purpose of the Study:
- To analyze the asymptotic behavior of cluster size distribution functions in simultaneous aggregation-chipping processes.
- To identify conditions leading to universal power-law distributions and partial condensation.
Main Methods:
- Numerical simulations were employed to observe system behavior.
- The z-transform technique was utilized for detailed analysis, particularly for L=2.
- Analytical calculations determined the critical average cluster size threshold.
Main Results:
- A universal power-law distribution with an exponent of -5/2 was observed above a critical average cluster size threshold (
c). - The system exhibits partial condensation, with one dominant cluster coexisting with the power-law distribution.
- The critical threshold
c increases monotonically with the maximum chipped unit size (L).
Conclusions:
- The asymptotic power-law distribution is universal under conditions of finite-sized chipped units.
- The findings provide insights into the statistical behavior of systems undergoing simultaneous aggregation and fragmentation.
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