Agent-based Model of Oxidation Reactions of Ferrous Ions

Authors

  • A. L. Rivera Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México.; Centro de Ciencias de la Complejidad, Universidad Nacional Autónoma de México. Circuito Exterior S/N, Ciudad Universitaria, Coyoacán, 04510 Ciudad de México, México.
  • S. Ramos-Bernal Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México.
  • A. Negron-Mendoza Instituto de Ciencias Nucleares, Universidad Nacional Autónoma de México.

DOI:

https://doi.org/10.15415/jnp.2016.41015

Keywords:

Chemical reactions, radiation, kinetics of reactions, prey-predator model, Fricke-model

Abstract

Molecules in comets are formed through chemical oxidation reactions induced by radiation. Thesereactions can be simulated in laboratory experiments applying gamma radiation to samples at low temperatures. The kinetics of the induced reactions can be modeled by a system of coupled non-linear ordinary differential equations describing the mass balance of all of the species involved. However, finding a traditional solution to this system is difficult because of the large number of reactions involved, the need to solve all of the equations simultaneously, and the strong dependence on the initial conditions due to the non-linear character of the equations. For each species, the mass-balance equation includes all of the reaction rates leading to production (source terms) and to destruction (sink terms). In this sense, each equation is analogous to the prey-predator model, with the sink terms consider to be the “prey” and the source terms as the “predators”. Due to this, we can use an agent-based model to follow the kinetics of the chemical reactions. In this paper, we present a code in Python for an agent-based model of the chemical oxidation of ferrous ions (Fe2+) induced by gamma radiation and in the presence of molecular oxygen. We compare the results that this code produces for molar concentrations of Fe3+over time with those obtained in the laboratory.

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References

Ausloos, M., Dawid, H., &Merlone, U. Spatial interactions in agent-based modeling. InComplexity and Geographical Economics. Springer International Publishing, (pp. 353-377), (2015). http://dx.doi.org/10.1007/978-3-319-128054_14

Berryman, A.A. The origin and evolution of predator–prey theory. Ecology 75, 1530–1535, (1992). http://dx.doi.org/10.2307/1940005

Castillo, S. Negrón-Mendoza, A., Draganic, Z.D., Draganic, I.G. The radiolysis of aqueous solutions of malic acid. Radiation Physics and Chemistry, 26, 437443, (1985). http://dx.doi.org/10.1016/0146-5724(85)90232-8

Colín-García, M., Negrón-Mendoza, A., & Ramos-Bernal, S. Organic material formed from gamma irradiation of frozen HCN as a cometary ice analog: implication to the origin of life.InternationalJournal of Astrobiology, 9, 279-288, (2009). http://dx.doi.org/10.1089/ast.2006.0117

Cruz-Casta-eda, J., Negrón-Mendoza, A., Frías, D., Colín-García, M., Heredia, A., et al. Chemical evolution studies: The radiolysis and thermal decomposition of malonic acid. Journal ofRadioanalytical and NuclearChemistry, 304(1), 219225, (2015).

Draganic, Z.D., Negrón-Mendoza, A., Navarro-González, R.,Vujosevic, S.I. The presence of polymeric material in radiolyzed aqueous solution of ammonium bicarbonate. International Journal of Radiation Applications and Instrumentation. Part C. Radiation Physics and Chemistry, 30(4), 229-231, (1987). http://dx.doi.org/10.1016/1359-0197(87)90126-3

Ehrenfreund, P., &Charnley, S.B. Organic molecules in the interstellar medium, comets, and meteorites: A Voyage from Dark Clouds to the Early Earth. Annual Review of Astronomy and Astrophysics, 38, 427-483, (2000). http://dx.doi.org/10.1146/annurev.astro.38.1.427

Malchow, H. Motional instabilities in prey–predator systems. Journal of Theoretical Biology, 204(4), 639-647, (2000). http://dx.doi.org/10.1006/jtbi.2000.2074

Malchow, H., &Petrovskii, S.V. Dynamical stabilization of an unstable equilibrium in chemical and biological systems.Mathematical and Computer Modelling, 36(3), 307-319, (2002). http://dx.doi.org/10.1016/S0895-7177(02)00127-9

Negrón-Mendoza,A., Albarran, G., Ramos, S., & Chacon, E. Some aspects of laboratory cometary models.Journal of Biological Physics, 20(1-4), 71–76, (1995). http://dx.doi.org/10.1007/BF00700422

Negrón-Mendoza, A, &Ponnamperuma, C. Prebiotic formationof higher molecular weight compounds from the photolysisof aqueous acetic acid. Photochemistry and Photobiology, 36(5):595-597, (1982). http://dx.doi.org/10.1111/j.1751-1097.1982.tb04421.x

O’Donnell, J.H.O., & Sangster, D.F. Principles of Radiation Chemistry. Elsevier, New York, (1970).

Pal, D., &Mahapatra, G. S. Dynamic behavior of a predator–prey system of combined harvesting with interval-valued rate parameters. Nonlinear Dynamics, 83:2113–2123, (2016). http://dx.doi.org/10.1007/s11071-015-2469-3

Pascual, M. Diffusion-induced chaos in a spatialpredator-prey system. Proceedings of the RoyalSociety of London B, 251, 1-7, (1993). http://dx.doi.org/10.1098/rspb.1993.0001

Sánchez-Mejorada,G.,Frías, D., Negrón-Mendoza, A., & Ramos-Bernal, S. A comparison between experimental results and a mathematical model of the oxidation reactions induced by radiation of ferrous ions.Radiation Measurements, 43(2), 287–290, (2008). http://dx.doi.org/10.1016/j.radmeas.2007.11.038

Shampine, L.F. Numerical Solution of Ordinary Differential Equations. Academic Press, New York, (1994).

Zhdanov, V. P. Monte Carlo simulations of oscillations, chaos and pattern formation in heterogeneous catalytic reactions.Surface Science Reports, 45(7), 231-326, (2002). http://dx.doi.org/10.1016/S0167-5729(01)00023-1

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Published

2016-08-08

How to Cite

(1)
Rivera, A. L. .; Ramos-Bernal, S. .; Negron-Mendoza, A. . Agent-Based Model of Oxidation Reactions of Ferrous Ions. J. Nucl. Phy. Mat. Sci. Rad. A. 2016, 4, 149-157.

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