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Modelling of transport processes: Theory and simulations
Ankita Gupta1, Bipasha Pal1, Akriti Jindal2
1Department of Mathematics, Indian Institute of Technology, Ropar Rupnagar-140001, Punjab, India.
Physicists study transport processes using the totally asymmetric simple exclusion process (TASEP) model. Parallel updates in TASEP introduce correlations, requiring advanced cluster mean-field theories for accurate analysis.
Area of Science:
- Statistical Mechanics
- Non-equilibrium Physics
Background:
- Transport processes are fundamental non-equilibrium systems studied by physicists.
- The totally asymmetric simple exclusion process (TASEP) is a key model for these systems.
- TASEP models exhibit different behaviors with open/periodic boundary conditions and sequential/parallel updates.
Purpose of the Study:
- To analyze the properties of TASEP in both transient and steady states.
- To investigate the impact of different updating rules (random sequential vs. parallel) on system dynamics.
- To explore the role of correlations induced by parallel updates.
Main Methods:
- Theoretical and numerical methods, including mean-field approaches.
- Monte Carlo simulations to implement both random sequential and parallel update rules.
- Development and application of cluster mean-field theory to account for correlations.
Main Results:
- Mean-field approaches, in their simplest form, align with random sequential updates by neglecting correlations.
- Parallel updates inherently introduce correlations into the TASEP model.
- Cluster mean-field theory provides a framework to handle the correlations arising from parallel updates.
Conclusions:
- Understanding correlations is crucial for accurately modeling TASEP dynamics, especially under parallel updates.
- The choice of updating rule significantly impacts system behavior and requires appropriate theoretical treatment.
- Advanced methods like cluster mean-field theory are necessary for systems with induced correlations.
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