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Conformal invariance of the probability density function for passive scalar fields (including arbitrary virus) in 2D turbulence: the proof of Polyakov conjecture

Grant number:21/09845-0
Support Opportunities:Research Grants - Visiting Researcher Grant - International
Start date: October 16, 2021
End date: April 06, 2023
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Alexandre Grichkov
Grantee:Alexandre Grichkov
Visiting researcher:Vladimir Grebenev
Visiting researcher institution: Siberian Branch of the Russian Academy of Sciences (SB RAS) , Russia
Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
City of the host institution:São Paulo
Associated research grant:18/23690-6 - Structures, representations, and applications of algebraic systems, AP.TEM

Abstract

Task 1: Symmetry analysis of the governing equation for the $n$-point PDF $f_n$ for passive scalar fields based on the direct method. Task 2: Conformal invariance of the probability measure. Task 3: The derivation of a Lie group of the symmetry transformations calculated. Task 4: The fine structure of a Lie algebra to classify the zero-isolines by the central charge. Then the effects of non-zero Gaussian white-in-time forcing and large-scale friction along flow surfaces will be included into the consideration. The method and calculations that worked out in (Grebenev, Wac\l{}awczyk and M Oberlack 2017, Wac\l{}awczyk, Grebenev and M Oberlack 2019, (Grebenev, Grishkov, Oberlack, Wac\l{}awczyk 2021) to find symmetries and calculate invariantsof LMN for 2D and 3D vorticity and velocity fields enable us to conclude that this work programme will be successfully completed. It will be published minimum two papers in higher-rank Journals. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (4)
(The scientific publications listed on this page originate from the Web of Science or SciELO databases. Their authors have cited FAPESP grant or fellowship project numbers awarded to Principal Investigators or Fellowship Recipients, whether or not they are among the authors. This information is collected automatically and retrieved directly from those bibliometric databases.)
GREBENEV, VLADIMIR; GRISHKOV, ALEXANDRE. SLE: differential invariants study. SAO PAULO JOURNAL OF MATHEMATICAL SCIENCES, v. 16, n. 2, p. 17-pg., . (21/09845-0)
GREBENEV, V. N.; GRISHKOV, A. N.; MEDVEDEV, S. B.. Symmetry transformations of the vortex field statistics in optical turbulence. THEORETICAL AND MATHEMATICAL PHYSICS, v. 217, n. 2, p. 11-pg., . (21/09845-0)
GREBENEV, V. N.; GRISHKOV, A. N.; OBERLACK, M.. Symmetry of the Lundgren-Monin-Novikov Equation for the Probability Distribution of the Vortex Field. DOKLADY PHYSICS, v. 68, n. 3, p. 5-pg., . (21/09845-0)