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Symmetry Breaking in Stochastic Dynamics and Turbulence

by 1,2,3,*,†, 4,† and 1,†
Faculty of Science, Šafárik University, Moyzesova 16, 040 01 Košice, Slovakia
Bogolyubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia
Department of Military Technology, National Defence University, 00861 Helsinki, Finland
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2019, 11(10), 1193;
Received: 19 August 2019 / Revised: 6 September 2019 / Accepted: 13 September 2019 / Published: 23 September 2019
(This article belongs to the Special Issue Symmetry and Mesoscopic Physics)
Symmetries play paramount roles in dynamics of physical systems. All theories of quantum physics and microworld including the fundamental Standard Model are constructed on the basis of symmetry principles. In classical physics, the importance and weight of these principles are the same as in quantum physics: dynamics of complex nonlinear statistical systems is straightforwardly dictated by their symmetry or its breaking, as we demonstrate on the example of developed (magneto)hydrodynamic turbulence and the related theoretical models. To simplify the problem, unbounded models are commonly used. However, turbulence is a mesoscopic phenomenon and the size of the system must be taken into account. It turns out that influence of outer length of turbulence is significant and can lead to intermittency. More precisely, we analyze the connection of phenomena such as behavior of statistical correlations of observable quantities, anomalous scaling, and generation of magnetic field by hydrodynamic fluctuations with symmetries such as Galilean symmetry, isotropy, spatial parity and their violation and finite size of the system. View Full-Text
Keywords: stochastic dynamics; symmetry breaking; field-theoretic renormalization group stochastic dynamics; symmetry breaking; field-theoretic renormalization group
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MDPI and ACS Style

Hnatič, M.; Honkonen, J.; Lučivjanský, T. Symmetry Breaking in Stochastic Dynamics and Turbulence. Symmetry 2019, 11, 1193.

AMA Style

Hnatič M, Honkonen J, Lučivjanský T. Symmetry Breaking in Stochastic Dynamics and Turbulence. Symmetry. 2019; 11(10):1193.

Chicago/Turabian Style

Hnatič, Michal, Juha Honkonen, and Tomáš Lučivjanský. 2019. "Symmetry Breaking in Stochastic Dynamics and Turbulence" Symmetry 11, no. 10: 1193.

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