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Phase transition of the one-dimensional coagulation-production process
1Research Institute for Technical Physics and Materials Science, H-1525 Budapest, P.O. Box 49, Hungary.
Summary
This study examines a one-dimensional coagulation-production model. It reveals a continuous phase transition at higher diffusion rates, aligning with previous exact solutions and simulations.
Area of Science:
- Statistical Physics
- Mathematical Modeling
- Chemical Kinetics
Background:
- An exact solution exists for a 1D coagulation-production process (2A-->A, AØA-->3A) with equal diffusion and coagulation rates.
- This model transitions to an inactive phase with a t(-1/2) density decay, irrespective of production rate.
Purpose of the Study:
- To investigate phase transitions in the 1D coagulation-production model beyond the exactly solved case.
- To compare predictions from cluster mean-field approximations and Monte Carlo simulations with the exact solution.
Main Methods:
- Utilizing cluster mean-field approximations.
- Performing Monte Carlo simulations.
- Comparing numerical results with an existing exact solution.
Main Results:
- Cluster mean-field approximations and Monte Carlo simulations predict a continuous phase transition for higher diffusion/coagulation rates.
- The universality of this phase transition matches that of the annihilation-fission model at low diffusions.
Conclusions:
- The study extends understanding of the 1D coagulation-production model, identifying a continuous phase transition under specific conditions.
- Numerical evidence supports the agreement in phase transition universality with related models, broadening insights into reaction-diffusion systems.