Propriedades críticas fora do equilíbrio e transição de fase em uma reação catalítica com efeito de volume excluído

Authors

  • Suzielli Mendonça Universidade de São Paulo - USP
  • Enzo Filippo Centenaro da Silva
  • Everaldo Arashiro

Keywords:

simulação computacional, expoentes críticos dinâmicos, modelo catalítico, probabilidade crítica

Abstract

We simulated a catalytic reaction model in a one-dimensional lattice, where big and small particles could be adsorbed in, obeying their own probabilities. The dynamic consisted of the adsorption of particles in the lattice, the reaction between them and the spontaneous desorption of the big-small particle pair. Then, the critical probability in which the phase transition took place from its absorbent to active state was obtained, as well as the dynamic critical exponents that characterized this transition. The values obtained with the simulations compared well with those known for the directed percolation universality class.

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References

Landau, D.P.; Binder, K. A Guide to Monte Carlo Simulations in Statistical Physics, 2nd ed.; Cambridge University Press: New York, USA, 2005.

Lobo, P. H. F.; Arashiro, E.; Silva, A. C.; Pinheiro, C. F. S. A smooth path to plot hydrogen atom via Monte Carlo method. Rev. Bras. Ens. Fis. 2019, 41, e20190073-2. https://doi.org/10.1590/1806-9126-RBEF-2019-0073

Keesen, F.; e Silva, A. C.; Arashiro, E.; Pinheiro, C. F. S. Simulations of populations of Sapajus robustus in a fragmented landscape. Ecol. Modell. 2017, 344, 38-47. https://doi.org/10.1016/j.ecolmodel.2016.11.003

Keesen, F.; e Silva, A. C.; Pinheiro, C. F. S.; Arashiro, E.; Ligeiro, Y.; de Viveiros Grelle, C. E. New applications of an old individual-based model for biological dynamics. Ecol. Modell. 2023, 476, 110234. https://doi.org/10.1016/j.ecolmodel.2022.110234

Lobo, P. H. F.; Mendonça, S. M.; Lazo, M. J.; Arashiro, E. Study of patterns of emerging clusters in a dynamic of chase and escape. Ci. e Nat. 2020, 42, 1-9. https://doi.org/10.5902/2179460X37562

Lourenço, G. M.; Keesen, F.; Fagundes, R.; Luna, P.; Silva, A. C.; Ribeiro, S. P.; Arashiro, E. Recruitment and entropy decrease during trail formation by foraging ants. Insect. Soc. 2020, 67, 59–69. https://doi.org/10.1007/s00040-019-00728-6

Ruziska, F. M.; Arashiro, E.; Tomé, T. Stochastic dynamics for two biological species and ecological niches. Physica A 2018, 489, 56-64. https://doi.org/10.1016/j.physa.2017.07.016

Mordechai, S. (Ed). Applications of Monte Carlo Method in Science and Engineering, 1st ed.; IntechOpen: London, England, 2011.

Shonkwiler, R. W. Finance with Monte Carlo, 1st ed.; Springer: New York, USA, 2013.

Carsey, T. M.; Harden, J. J. Monte Carlo simulation and resampling methods for social science. 1st ed.; Sage Publications: Los Angeles, USA, 2013.

Seco, J.; Verhaegen, F. (Eds.). Monte Carlo techniques in radiation therapy. 1st ed.; CRC Pres: Boca Raton, USA, 2013.

Arashiro, E.; Drugowich de Felício, J. R. Short-time critical dynamics of the Baxter-Wu model. Phys. Rev. E 2003, 67, 046123. https://doi.org/10.1103/PhysRevE.67.046123

Arashiro, E.; Drugowich de Felício, J. R.; Hansmann, U. H. Short-time dynamics of polypeptides. J. Chem. Phys. 2007, 126, 045107. https://doi.org/10.1063/1.2430709

Argolo, C.; Otaviano, H.; Gleria, I.; Arashiro, E.; Tome, T. Critical behavior and threshold of coexistence of a predator-prey stochastic model in a 2D lattice. Int J Bifurcat Chaos 2010, 20, 309-314. https://doi.org/10.1142/S0218127410025752

Fernandes, H. A.; Silva, R.; Santos, E. D.; Gomes, P. F.; Arashiro E. Alternative method to characterize continuous and discontinuous phase transitions in surface reaction models. Phys. Rev. E 2016, 94, 022129. https://doi.org/10.1103/PhysRevE.94.022129

Hua, D. Y.; Zhu, Y. J.; Ma, Y. Q. Critical exponents of the continuous phase transition in Ziff-Gulari-Barshad model. Int. J. Mod. Phys. B 2004, 18, 859-866. https://doi.org/10.1142/S0217979204024008

Da Costa, E. C.; Figueiredo, W. Catalysis with Competitive Reactions: Static and Dynamical Critical Behavior. Braz. J. Phys. 2003, 33, 487-500. https://doi.org/10.1590/S0103-97332003000300010

Ziff, R. M.; Gulari E.; Barshad, Y. Kinetic Phase Transitions in an Irreversible Surface-Reaction Model. Phys. Rev. Lett. 1986, 56, 2553. https://doi.org/10.1103/PhysRevLett.56.2553

Meakin, P.; Scalapino, D. J. Simple models for heterogeneous catalysis: Phase transition-like behavior in nonequilibrium systems. J. Chem. Phys. 1987, 87, 731-741. https://doi.org/10.1063/1.453570

Jensen, I.; Fogedby, H. C.; Dickman, R. Critical exponents for an irreversible surface reaction model, Phys. Rev. A 1990, 41, 3411(R). https://doi.org/10.1103/PhysRevA.41.3411

Huse, D. A. Remanent magnetization decay at the spin-glass critical point: A new dynamic critical exponent for nonequilibrium autocorrelations. Phys. Rev. B 1989, 40, 304. https://doi.org/10.1103/PhysRevB.40.304

Janssen, H.K.; Schaub, B.; Schmittmann, B. New universal short-time scaling behaviour of critical relaxation processes. Z. Physik B - Condensed Matter 1989, 73, 539–549. https://doi.org/10.1007/BF01319383

Hinrichsen, H. Non-equilibrium critical phenomena and phase transitions into absorbing states. Adv. Phys. 2000, 49, 815–958. https://doi.org/10.1080/00018730050198152

Da Silva, R.; Alves, N. A.; De Felício, J. R. D. Mixed initial conditions to estimate the dynamic critical exponent in short-time Monte Carlo simulation. Phys. Lett. A 2002, 298, 325-329. https://doi.org/10.1016/S0375-9601(02)00571-6

Park, H.; Köhler, J.; Kim I. M.; ben Avraham, D.; Redner, S., Excluded volume effects in heterogeneous catalysis: Reactions between “dollars” and “dimes”. J. Phys. A 1993, 26, 2071–2079.

Henkel, M.; Hinrichsen, H.; Lübeck, S. Non-equilibrium phase transitions, 1st ed.; Springer: Berlin, Germany, 2008.

Published

2023-01-31

How to Cite

Mendonça, S., Filippo Centenaro da Silva, E., & Arashiro, E. (2023). Propriedades críticas fora do equilíbrio e transição de fase em uma reação catalítica com efeito de volume excluído. Revista Interdisciplinar De Pesquisa Em Engenharia, 8(2), 8–17. Retrieved from https://periodicos.unb.br/index.php/ripe/article/view/46730