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Kinetics of a migration-driven aggregation process with birth and death.
1Department of Physics, Wenzhou Normal College, Wenzhou 325027, China. linzhenquan@yahoo.com.cn
Summary
This study introduces an aggregation model with migration and birth-death processes. The model predicts scaling laws for aggregate size distribution, applicable to city populations and wealth distribution.
Area of Science:
- Mathematical Modeling
- Statistical Physics
- Complex Systems
Background:
- Aggregation phenomena are prevalent in natural and social systems.
- Understanding the dynamics of aggregate size distribution is crucial for various scientific fields.
- Existing models may not fully capture the interplay of migration and demographic processes.
Purpose of the Study:
- To develop and analyze a novel irreversible aggregation model.
- To investigate the influence of migration, birth, and death rates on aggregate evolution.
- To determine the long-time asymptotic behavior of aggregate size distribution.
Main Methods:
- Mean-field theory application.
- Development of scaling theory.
- Analysis of birth-death processes with size-dependent rates and symmetric migration kernels.
Main Results:
- The model conserves total mass when birth and death rates are equal (J(1)=J(2)).
- Total mass grows exponentially when birth rates exceed death rates (J1>J2).
- Aggregate size distribution follows a scaling law for upsilon<=2 in the long term.
Conclusions:
- The proposed model offers a robust framework for studying irreversible aggregation.
- The findings provide insights into the evolution of distributions in systems like city populations and wealth.
- The scaling law behavior is a key characteristic for upsilon<=2, indicating predictable long-term dynamics.