Abstract
The single-species annihilation reaction A + A → Ø is studied in the presence of a random velocity field generated by the stochastic Navier-Stokes equation. The renormalization group is used to analyze the combined influence of the density and velocity fluctuations on the long-time behavior of the system. The direct effect of velocity fluctuations on the reaction constant appears only from the two-loop order, therefore, all stable fixed points of the renormalization group and their regions of stability are calculated in the two-loop approximation in the two-parameter (ε, Δ) expansion. A renormalized integro-differential equation for the number density is put forward which takes into account the effect of density and velocity fluctuations at next-to-leading order. Solution of this equation in perturbation theory is calculated in a homogeneous system.
References
B. Derrida, V. Hakim, V. Pasquier, Phys. Rev. Lett. 75, 751 (1995)
R. Kroon, H. Fleurent, R. Sprik, Phys. Rev. E 47, 2462 (1993)
N.G. van Kampen, Stochastic processes in Physics and Chemistry (North-Holland Pub. Co., Amsterdam, 1984)
K. Kang, S. Redner, Phys. Rev. A 32, 435 (1985)
B.P. Lee, J. Phys. A 27, 2633 (1994)
J.L. Cardy, U.C. Tauber, Phys. Rev. Lett. 77, 4780 (1996)
C. Itzykson, J.-M. Drouffe, Statistical Field Theory (Cambridge University Press, Cambridge, 1991), Vol. 1
J.-M. Park, M.W. Deem, Phys. Rev. E 57, 3618 (1998)
W.J. Chung, M.W. Deem, Physica A 265, 486 (1999)
M.J.E. Richardson, J. Cardy, J. Phys. A 32, 4035 (1999)
M.W. Deem, J.-M. Park, Phys. Rev. E 58, 3223 (1998)
N. le Tran, J.-M. Park, M.W. Deem, J. Phys. A 32, 1407 (1999)
M. Hnatich, J. Honkonen, Phys. Rev. E 61, 3904 (2000)
U. Frisch, Turbulence: The Legacy of A.N. Kolmogorov (Cambridge University Press, Cambridge, 1995)
D. Forster, D.R. Nelson, M.J. Stephen, Phys. Rev. Lett. 36, 867 (1976)
D. Forster, D.R. Nelson, M.J. Stephen, Phys. Rev. A 16, 732 (1977)
L.T. Adzhemyan, A.N. Vasil’ev, Y.M. Pis’mak, Teor. Mat. Fiz. 57, 268 (1983)
M. Doi, J. Phys. A 9, 1465 (1976)
M. Doi, J. Phys. A 9, 1479 (1976)
L. Peliti, J. Phys. A 19, L365 (1986)
A.N. Vasil’ev, Functional Methods in Quantum Field Theory and Statistical Physics (Gordon and Breach, Amsterdam, 1998)
C. De Dominicis, P.C. Martin, Phys. Rev. A 19, 419 (1979)
A.N. Vasil’ev, The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (Chapman Hall/CRC, Boca Raton, 2004)
H.K. Janssen, Z. Phys. B 23, 377 (1976)
R. Bausch, H.K. Janssen, H. Wagner, Z. Phys. B 24, 113 (1976)
J. Zinn-Justin, Quantum Field Theory and Critical Phenomena (Oxford University Press, Oxford, 1989)
L.T. Adzhemyan, J. Honkonen, M.V. Kompaniets, A.N. Vasil’ev, Phys. Rev. E 71, 036305 (2005)
L.T. Adzhemyan, N.V. Antonov, A.N. Vasiliev, The Field Theoretic Renormalization Group in Fully Developed Turbulence (Gordon and Breach, Amsterdam, 1999)
L.T. Adzhemyan, N.V. Antonov, J. Honkonen, Phys. Rev. E 66, 036313 (2002)
M. Hnatich, J. Honkonen, D. Horvath, R. Semancik, Phys. Rev. E 59, 4112 (1999)
U.C. Täuber, M. Howard, B.P. Vollmayr-Lee, J. Phys. A 38, R79 (2005)
T. Tél, A. de Moura, C. Grebogi, G. Károlyi, Phys. Rep. 413, 91 (2005)
R. Benzi, M.H. Jensen, D.R. Nelson, P. Perlekar, S. Pigolotti, F. Toschi, Population dynamics in compressible flows, arXiv:1203.6319v1 [q-bio.PE] (2012)
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Hnatič, M., Honkonen, J. & Lučivjanský, T. Two-loop calculation of anomalous kinetics of the reaction A + A → Ø in randomly stirred fluid. Eur. Phys. J. B 86, 214 (2013). https://doi.org/10.1140/epjb/e2013-30982-9
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DOI: https://doi.org/10.1140/epjb/e2013-30982-9