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Evolution of Coagulation-Fragmentation Stochastic Processes Using Accurate Chemical Master Equation Approach
Farid Manuchehrfar1, Wei Tian1, Tom Chou2
1Department of Bioengineering, University of Illinois at Chicago (UIC), Chicago, Illinois, USA.
Communications in Information and Systems
|August 23, 2021
Summary
Coagulation and fragmentation (CF) is a fundamental process studied using the discrete Chemical Master Equation. Three-dimensional systems and higher attachment rates promote larger cluster formation.
Area of Science:
- Physical Chemistry
- Statistical Mechanics
- Complex Systems
Background:
- Coagulation and fragmentation (CF) describes particle aggregation and disaggregation.
- It is a ubiquitous stochastic process vital in physical and biological systems.
- CF often occurs in confined spaces with limited particle availability.
Purpose of the Study:
- To investigate the time-dependent behavior of coagulation and fragmentation (CF).
- To analyze the influence of dimensionality, attachment/detachment rates, and initial conditions on CF dynamics.
- To utilize the Accurate Chemical Master Equation (ACME) for dCME analysis.
Main Methods:
- Formulation of the CF process using the discrete Chemical Master Equation (dCME).
- Application of the Accurate Chemical Master Equation (ACME) method for time-dependent analysis.
- Comparative study of CF in one and three dimensions.
Main Results:
- Three-dimensional systems exhibit a higher propensity for forming large clusters compared to one-dimensional systems.
- The ratio of attachment to detachment rates significantly impacts system dynamics and steady-state.
- A clear relationship exists between initial conditions and the formation of large clusters.
Conclusions:
- Dimensionality is a critical factor influencing cluster size distribution in CF processes.
- Attachment and detachment rates dynamically control the evolution and equilibrium of the CF system.
- Initial conditions play a key role in determining the ultimate outcome of cluster formation.
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