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Acta Physica Slovaca 66, No.2, 69 – 264 (2016) (195 pages)
ADVANCED FIELD-THEORETICAL METHODS IN STOCHASTIC DYNAMICS AND THEORY OF DEVELOPED TURBULENCE M. Hnatič1,2,3, J. Honkonen4, T. Lučivjanský1,5 1Faculty of Sciences, P. J. Safarik University, Park Angelinum 9, 041 54 Košice, Slovakia 2Institute of Experimental Physics SAS, Watsonova 47, 040 01 Košice, Slovakia 3BLTP, Joint Institute for Nuclear Research, Dubna, Russia 4Department of Military Technology, National Defence University, Helsinki, Finland 5Fakultät fur Physik, Universität Duisburg-Essen, D-47048 Duisburg, Germany Full text: ::pdf :: (Received 12 October 2016, accepted 24 October 2016) Abstract: Selected recent contributions involving fluctuating velocity fields to the rapidly developing domain of stochastic field theory are reviewed. Functional representations for solutions of stochastic differential equations and master equations are worked out in detail with an emphasis on multiplicative noise and the inherent ambiguity of the functional method. Application to stochastic models of isotropic turbulence of multi-parameter expansions in regulators of dimensional and analytic renormalization is surveyed. Effects of the choice of the renormalization scheme are investigated. Special attention is paid to the role and properties of the minimal subtraction scheme. Analysis of the consequences of symmetry breaking of isotropic turbulence with the use of the renormalization-group method is demonstrated by the effects due to helicity, strong and weak anisotropy. A careful description is given of the influence of turbulent advection on paradigmatic reaction-diffusion problems. PACS: 05.10.Cc, 05.10.Gg, 05.60.-k, 47.27.ef, 47.27.tb, 47.70.Fw, 64.60.ah Keywords: Stochastic dynamics, Doi formalism, Field-theoretic approach, Perturbative renormalization group, Fully developed turbulence, Processes in turbulent flows, Reaction-diffusion problems |
ISSN 1336-040X (online) ISSN 0323-0465 (printed) For authors: ActaStyle.cls |
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