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Aggregation-Fragmentation of Clusters in the Framework of gTASEP with Attraction Interaction

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Abstract

This article provides summary of some of our results, concerning a model of aggregation and fragmentation of clusters of particles obeying the stochastic discrete-time discrete-space kinetics of the generalized Totally Asymmetric Simple Exclusion Process (gTASEP) with open boundaries. The model in essence is the ordinary TASEP with backward ordered sequential update with special kinematic interaction added, i.e., it has a second modified hopping probability \(~{{p}_{m}}\) for particles in a cluster in addition to the standard hopping probability \(p\). We consider separately the two cases of attraction interaction (\(p\) < \(~{{p}_{m}}\)): (1) the limiting case of irreversible aggregation (\({{p}_{m}}\) = 1); and (2) the generic case of attraction, when \(~p\) < \(~{{p}_{m}}\) < 1 (then aggregation and fragmentation of clusters is allowed). We put special emphasis on the use of random walk theory in the study of gTASEP. It is applied to study the inter-cluster gaps time evolution, which helps to assess the properties of the nonequilibrium stationary phases of the system and the phase transitions between them. Theoretical conclusions are in agreement with the Monte Carlo simulations.

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ACKNOWLEDGMENTS

The authors gratefully acknowledge joint work and fruitful discussions with their late colleagues and coauthors, Prof. V.B. Priezzhev and Prof. J.G. Brankov. Many results presented here are obtained in collaboration with them. This article is based on the presentation given at Memorial seminar dedicated to Vyacheslav Priezzhev. The authors very much appreciate the invitation and the support provided by the organizing committee of the Memorial seminar. Partial financial supports by the Bulgarian MES through Grant no. D01-221/03.12.2018 for NCDSC—part of the Bulgarian National Roadmap on RIs, and by the Plenipotentiary Representative of the Bulgarian Government at the Joint Institute for Nuclear Research, Dubna, through grant no. 01-3-1137-2019/2023 also are thankfully acknowledged.

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  1. Institute of Mechanics, Bulgarian Academy of Sciences, 1113, Sofia, Bulgaria

    N. Zh. Bunzarova & N. C. Pesheva

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Bunzarova, N.Z., Pesheva, N.C. Aggregation-Fragmentation of Clusters in the Framework of gTASEP with Attraction Interaction. Phys. Part. Nuclei 52, 169–184 (2021). https://doi.org/10.1134/S1063779621020027

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