Intermittency, Diffusion and Generation in a Non-stationary Random Medium (original) (raw)
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Zeldovich Y., Molchanov S., Ruzmaikin A., Sokoloff D.
This classic survey considers passive scalar and vector transport processes in a random nonstationary medium, which are described by linear parabolic equations. Integration over random paths is used, along with the asymptotic behavior of the product of a large number of independent identically distributed random matrices. The most interesting effect is the appearance of concentrated structures (intermittency) of a smooth initial distribution of the transported quantity. The occurrence of intermittent distributions in the linear problem is due to the fact that the coefficients of the transport equation are stochastic. The intermittency shows itself in the rates of exponential growth of the successive moments (Lyapunov exponents) as the moment number increases. Moment equations are obtained for the scalar and vector, and are used to study temperature evolution and magnetic-field generation in a random fluid flow. These equations are differential in a medium with short time correlations and integral in the general case. The range of application of the diffusion description is analyzed. The behavior of the diffusion coefficients in the case of time reversal is examined. The properties of an individual realization of a scalar and vector are also explained, and a dynamo theorem is given on the exponential growth of the magnetic field in a random flow with renewal.
Publication based on the results of:
, Bowers G. M., Loganathan N. et al., Energy & Fuels 2021 Vol. 35 No. 20 P. 16515–16526
As global energy demand increases, natural gas recovery from source rocks is attracting considerable attention since recent development in shale extraction techniques has made the recovery process economically viable. Kerogens are thought to play an important role in gas recovery; however, the interactions between trapped shale gas and kerogens remain poorly understood due to the ...
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Ivchenko N., Lebedev V., Vergeles S. S., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2024 Vol. 110 No. 1 Article 015102
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 ...
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Privalov A., Vitaly V. Sinitsyn, Vogel M., The Journal of Physical Chemistry Letters 2023 Vol. 14 No. 30 P. 9335–9340
We use 1H and 17O NMR static field gradient diffusometry to measure self-diffusion coefficients of protons (DH) and oxygens (DO) in Nafion 212 with various hydration levels (λ = 4–18). For all samples and both nuclei, we obtain activation energies (Ea) of ≈0.19 eV. Analyzing the hydration-level dependence of DH and DO, we find DO/DH ≈ 1 at λ ≈ 18, resembling ...
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We investigate a stochastic model of the galactic dynamo in the planar approximation, assuming that turbulent diffusivity is a renewal process. For linear and nonlinear modifications of this model, numerical methods are applied to construct statistical moments and correlation tensors of the magnetic field. ...
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Akaliyski P., European Journal of Political Research 2019 Vol. 58 No. 2 P. 388–411
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This article is devoted to a preventing of harmful information spreading in social networks. Currently, social networks are widespread. Their popularity is growing every day. For this reason, they can be used not only by managers and marketers for the dissemination of advertising, product promotion, but also attackers for the dissemination of prohibited information. So it is necessary ...
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Yastrebinsky R. N., Bondarenko G.G., Pavlenko V. I. et al., Inorganic Materials: Applied Research 2021 Vol. 12 No. 5 P. 1206–1213
Diffusion-thermal phase transformations in modified titanium hydride containing a multi-barrier system of hydrogen traps are considered. Modification of titanium hydride was carried out by the method of layer-by-layer electrochemical precipitation of metallic titanium and copper from organic and inorganic solutions of their salts. The creation of a multilayer coating (Ti–Cu) on the surface of the titanium hydride by the ...
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In this paper the numerical simulation of surfactant dynamics in the topographically trapped long waves over a cylindrical shelf is described. Numerical modeling is based on the balance equation of the surface concentration. The dynamics of impurities was considered in the advection - diffusion - relaxation model. The comparison of different models of the shelf: ...
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A semiphenomenological model of the transport processes under the action of power energy sources is proposed. To explain the observed deviations of the linear system response to an external perturbation in the transport processes induced by intense energy fluxes, it is proposed to take into account the effect of inertia of the medium. The semiphenomenological ...
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Дещеня В. И., Kondratyuk N., Ланкин А. В. et al., Журнал физической химии 2022 Т. 96 № 3 С. 373–380
The temperature dependence of density is calculated for an aqueous solution of sucrose by the molecular dynamics method. The coefficients of viscosity and diffusion are also obtained in the 273–343 K range of temperatures. The hydrodynamic radius of a sucrose molecule in an aqueous solution is calculated. The obtained data are compared with the experimental ...
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Николаев В.Г., Личность. Культура. Общество 2016 Т. XVIII № 1-2 С. 274–290
В статье даются обзор и анализ состояния переводной литературы в российской социологии 1990-х – 2000-х годов. В качестве теоретической рамки используется хьюзианский подход с двойной перспективой – экологической и символической. На экологическом уровне выделяются ключевые институциональные влияния, определявшие развитие научного перевода и состав переводной литературы в рассматриваемый период. На символическом уровне рассматриваются типовые символические трансформации, ...
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For the field u(x, t) governed by the Burgers equation with a thermal noise, short-time asymptotics of multipoint correlators are obtained. Their exponential parts are independent of the correlator number. This means that they are determined by a single rare fluctuation and exhibit the intermittency phenomenon ...
Added: February 25, 2017
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Glazov M., Physical Review B: Condensed Matter and Materials Physics 2019 Vol. 100 P. 034703-1–034703-13
We study theoretically the nonequilibrium exciton transport in monolayer transition metal dichalcogenides. We consider the situation where excitons interact with nonequilibrium phonons, e.g., under the conditions of localized excitation where a “hot spot” is formed. We develop the theory of the exciton drag by the phonons and analyze in detail the regimes of diffusive propagation ...
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Asymmetric membrane materials based on MK-40 membranes modified with a thin layer of perfluorinated ion exchangers MF-4SK with embedded polyaniline were obtained. The diffusion characteristics of the obtained composites are investigated. An abnormal asymmetry of ion transport in a neutral medium was detected. The diffusion coefficients of individual cations for membranes with mixed cation composition ...
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Antropov A., Stegailov V., Journal of Nuclear Materials 2023 Vol. 573 Article 154123
The influence of helium pressure on the mechanisms of diffusion of the He-filled nanobubbles in fcc Al is investigated by the classical molecular dynamics. It is shown that at pressures <20 kbar gas suppresses self-diffusion, while the concentration of adatoms, rather than their mobility, plays a key role. However, as the pressure increases to values at which ...
Added: February 1, 2023
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In this work, we study the applicability of the equilibrium molecular dynamics methods for the prediction of both static and dynamic properties of sucrose aqueous solution for various concentrations and temperatures. The OPLS-AA force field with 1.14*CM1A charge corrections is used to describe the interactions in the model. We analyze the prediction power of the model against ...
Added: August 9, 2022
Ivchenko N., Vergeles S. S., Журнал экспериментальной и теоретической физики 2023 Т. 163 № 5 С. 724–733
We study statistical properties of the passive scalar advection in a 2D flow that consist of a steady-state shear flow and a relatively weak smooth random component taking into account the effects of finite weak diffusion. The model is closely related to the dynamics of passive scalar transfer inside coherent vortices emerging as a result ...
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Galitskaya E., Privalov A., Weigler M. et al., Journal of Membrane Science 2020 Vol. 596 Article 117691
It is established that the values of the coefficients of self-diffusion of water in proton-exchange membranes at a fixed temperature and the amount of moisture content depend on the method of membrane manufacture, the length of the side chain (diameter of channels), but within the experimental error do not depend on the thickness of the ...
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Our analysis allows us to talk about two waves of the echo of the Arab spring in Western Europe. The first wave was observed in 2011 and was expressed in the explosive growth of mainly peaceful protests. Taking into account the data on the direct impact of the events of the Arab Spring on the ...
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Novikov S.V., Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 2018 Vol. 98 No. 1 P. 012128-1– 012128-8
We demonstrate that the Einstein relation for the diffusion of a particle in the random-energy landscape with the Gaussian density of states is an exclusive one-dimensional property and does not hold in higher dimensions. We also consider the analytical properties of the particle velocity and diffusivity for the limit of weak driving force and establish a connection between ...
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Glazov M., Physical Review Letters 2020 Vol. 124 P. 166802
We study theoretically weak localization of excitons in atomically thin transition metal dichalcogenides. The constructive interference of excitonic de Broglie waves on the trajectories forming closed loops results in a decrease of the exciton diffusion coefficient. We calculate the interference contribution to the diffusion coefficient for the experimentally relevant situation of exciton scattering by acoustic ...
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In this study we investigate impurity dynamics in media with random characteristics for different physical assumptions. We first discuss possible models for diffusion in porous media on the small scale. Then we describe some random processes, which are able to represent the disorder in such a medium. After that, we recall the definition of a ...
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Logvinova K. V., Kozyrev O., European Journal of Scientific Research 2010 Vol. 45 No. 3 P. 383–390
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Added: January 9, 2013