Abstract
The effect of turbulent mixing on the model of tricritical directed percolation is studied. The turbulent advecting velocity field is modeled by means of the Kraichnan’s rapid change ensemble. The non-equilibrium critical phenomena of one-component reaction-diffusion systems are investigated employing field theoretic renormalization group technique. We give a brief overview of the field-theoretic approach to the problem including renormalization group analysis. The renormalization procedure is performed in the framework of double (\(\varepsilon \), y)-expansion scheme, where the \(\varepsilon \) is the deviation from the upper critical dimension \(d_c = 3\) and the y is the exponent describing scaling behavior of velocity fluctuations. The corresponding asymptotic behavior is analyzed in leading order of perturbation theory.
12th CHAOS Conference Proceedings, 18–22 June 2019, Chania, Crete, Greece.
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References
U. Täuber, Critical Dynamics: a Field Theory Approach to Equilibrium and Non-Equilibrium Scaling Behavior (Cambridge University Press, New York, 2014)
H. Hinrichsen, Adv. Phys. 49(7), 815–958 (2000)
H.K. Janssen, U.C. Täuber, Ann. Phys. 315, 147 (2004)
H.K. Janssen, M. Müller, O. Stenull, Phys. Rev. E 70, 026114 (2004)
H.K. Janssen, J. Phys.: Condens. Matter 17, S1973–S1993 (2005)
S. Lübeck, J. Stat. Phys. 123(1), 193–221 (2005)
P. Grassberger, J. Stat. Mech. P01004, (2006)
N.V. Antonov, M. Hnatich, J. Honkonen, J. Phys. A: Math. Gen. 39, 7867 (2006)
N.V. Antonov, A.A. Ignatieva, J. Phys. A: Math. Gen. 39, 13593 (2006)
G. Falkovich, K. Gawȩdzki, M. Vergassola, Rev. Mod. Phys. 73, 913 (2001)
A.N. Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (Chapman & Hall/CRC, Boca Raton, 2004)
P. C. Martin, E. D. Siggia, H. A. Rose, Phys. Rev. A 8, 423 (1973); C. De Dominicis, J. Phys. (Paris), Colloq. 37, C1-247 (1976); H. K. Janssen, Z. Phys. B 23, 377 (1976); R. Bausch, H. K. Janssen, H. Wagner, ibid. 24, 113 (1976)
T. Ohtsuki, T. Keyes, Phys. Rev. A 35, 2697 (1987)
T. Ohtsuki, T. Keyes, Phys. Rev. A 36, 4434 (1987)
Acknowledgements
The work was supported by VEGA Grant No. 1/0345/17 of the Ministry of Education, Science, Research and Sport of the Slovak Republic and the grant of the Slovak Research and Development Agency under the contract No. APVV-16-0186.
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Hnatič, M., Lučivjanský, T., Mižišin, L. (2020). Tricritical Directed Percolation with Long-Range Spreading. In: Skiadas, C., Dimotikalis, Y. (eds) 12th Chaotic Modeling and Simulation International Conference. CHAOS 2019. Springer Proceedings in Complexity. Springer, Cham. https://doi.org/10.1007/978-3-030-39515-5_9
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