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## Passive scalar transport by a non-Gaussian turbulent flow in the Batchelor regime

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 2017. Vol. 96. No. 1. P. 013117-1-013117-8.

We analyze passive scalar advection by a turbulent flow in the Batchelor regime. No restrictions on the velocity statistics of the flow are assumed. The properties of the scalar are derived from the statistical properties of velocity; analytic expressions for the moments of scalar density are obtained. We show that the scalar statistics can differ significantly from that obtained in the frames of the Kraichnan model.

Ilyin A., Zybin K., Сирота В. А., EPL 2018 Vol. 121 P. 34002-p1-34002-p6

Statistical moments of magnetic ﬁeld in a viscous range of turbulence are calculated for arbitrary initial conditions. It is shown that the evolution of magnetic ﬁeld in the case of ﬁnite initial distribution in a linear velocity ﬁeld consists of two or three consecutive regimes: exponential growth is followed by exponential decay. This solves the ...

Added: October 30, 2019

Ilyin A., Kopyev A. V., Sirota V. A. et al., Physics of Fluids 2021 Vol. 33 No. 7 P. 075105-1-075105-10

Kinematic dynamo in incompressible isotropic turbulent flows with high magnetic Prandtl number is considered. The approach interpreting an arbitrary magnetic field distribution as a superposition of localized perturbations (blobs) is developed. We derive a general relation between stochastic properties of an isolated blob and a stochastically homogenous distribution of magnetic field advected by the same ...

Added: July 20, 2021

Ilyin A., Zybin K., Сирота В. А., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2017 Vol. 96 P. 013117-1-013117-8

WeanalyzepassivescalaradvectionbyaturbulentﬂowintheBatchelorregime.Norestrictionsonthevelocity statistics of the ﬂow are assumed. The properties of the scalar are derived from the statistical properties of velocity; analytic expressions for the moments of scalar density are obtained. We show that the scalar statistics can differ signiﬁcantly from that obtained in the frames of the Kraichnan model. ...

Added: October 30, 2019

Kopiev A. V., Zybin K., Journal of Turbulence 2018 Vol. 19 No. 9 P. 717-730

On the grounds of Kolmogorov's 4/5 law analytical relations for triple two-point correlations of velocity and velocity gradients in homogeneous isotropic incompressible turbulence are derived. The corresponding correlation tensor can be expressed in terms of dissipation ε, the second-order longitudinal velocity structure function and one more scalar function of distance between the points. However, some ...

Added: February 21, 2019

Zybin K., Ilyin A., Сирота В. А. et al., EPL 2020 Vol. 132 P. 24001

Evolution of a stochastically homogeneous magnetic field advected by an incompressible turbulent flow with large magnetic Prandtl numbers is considered at scales smaller than the Kolmogorov viscous scale. It is shown that, despite the unlimited growth of the magnetic field, its feedback on the fluid's dynamics remains negligibly small. ...

Added: December 23, 2020

Ilyin A., Sirota V., Zybin K., Journal of Statistical Physics 2016 Vol. 163 No. 4 P. 765-783

A functional method for calculating averages of the time-ordered exponential of a continuous isotropic random N×NN×N matrix process is presented. The process is not assumed to be Gaussian. In particular, the Lyapunov exponents and higher correlation functions of the T-exponent are derived from the statistical properties of the process. The approach may be of use ...

Added: October 30, 2019

Ilyin A., Zybin K., Сирота В. А., Physica Scripta 2019 Vol. 94 P. 064001

Statistical properties of a statistically homogeneous random magnetic ﬁeld in a viscous diffusive ﬂuid are derived from the evolution of a single blob of the magnetic ﬁeld. It is shown that, although the magnetic ﬁeld of a single blob decreases in time, the volume occupied by the magnetic ﬁeld and its energy increase; this is ...

Added: October 30, 2019

Jabir J. M., Martinez K., Bossy M., / Cornell University. Series arXiv "math". 2021.

We present the construction of an original stochastic model for the instantaneous turbulent kinetic energy at a given point of a flow, and we validate estimator methods on this model with observational data examples. Motivated by the need for wind energy industry of acquiring relevant statistical information of air motion at a local place, we ...

Added: January 30, 2021

Ilyin A., Kopyev A. V., Sirota V. A. et al., Physics of Fluids 2020 Vol. 32 No. 12 P. 125114

We consider fluctuations of magnetic field excited by external force and advected by isotropic turbulent flow. It appears that non-Gaussian velocity gradient statistics and finite region of pumping force provide the existence of stationary solution. The mean-square magnetic field is calculated for arbitrary velocity gradient statistics. An estimate for possible feedback of magnetic field on ...

Added: December 16, 2020

Lebedev V., Vergeles S. S., / Cornell University. Series Physics "arxiv.org". 2023.

Chaotic variations in flow speed up mixing of scalar fields via intensified stirring. This paper addresses the statistical properties of a passive scalar field mixing in a regular shear flow with random fluctuations against its background. We consider two-dimensional flow with shear component dominating over smooth fluctuations. Such flow is supposed to model passive scalar ...

Added: December 28, 2023

Doludenko A., Fortova S., Kolokolov I. et al., Physics of Fluids 2021 Vol. 33 No. 011704 P. 1-6

We investigate the coherent vortex produced by two-dimensional turbulence excited in a finite box. We establish analytically the mean velocity
profile of the vortex for the case where the bottom friction is negligible and express its characteristics via the parameters of pumping. Our
theoretical predictions are verified and confirmed by direct numerical simulations in the framework of ...

Added: January 20, 2021

Ilyin A., Zybin K., Сирота В. А., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2019 Vol. 99 No. 5 P. 052220-1-052220-6

The impact of turbulent advection in reaction-diffusion systems is investigated for the viscous range of scales. We show that the population size can increase exponentially even in systems with density saturation, at the expense of exponential propagation of the reaction front. Exact expressions for scaling exponents of the density and population size are calculated in ...

Added: October 30, 2019

191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90

It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...

Added: September 23, 2016

Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624

Added: February 27, 2013

Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013

Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...

Added: February 5, 2014

Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70

A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...

Added: July 19, 2014

Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83

We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...

Added: November 1, 2019

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Sinelshchikov D., Кудряшов Н. А., Theoretical and Mathematical Physics 2018 Vol. 196 No. 2 P. 1230-1240

We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...

Added: February 9, 2019

Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189

The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...

Added: January 28, 2020

Kolokolov I., Lebedev V., Sizov G. A., Journal of Experimental and Theoretical Physics 2011 Vol. 140 No. 2 P. 387-400

We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field ...

Added: February 2, 2017

ООО Фирма "Элист", 2014

В книге представлены тезисы докладов I тура XV Всероссийской научно-технической конференции и школы молодых ученых, аспирантов и студентов. ...

Added: October 17, 2014

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020

Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45

Added: October 17, 2014