Destruction of the family of steady states in the planar problem of Darcy convection

The natural convection of incompressible fluid in a porous medium causes for some boundary conditions a strong non-uniqueness in the form of a continuous family of steady states. We are interested in the situation when these boundary conditions are violated. The resulting destruction of the family of steady states is studied via computer experiments based on a mimetic finite-difference approach. Convection in a rectangular enclosure is considered under different perturbations of boundary conditions (heat sources, infiltration). Two scenario of the family of equilibria are found: the transformation to a limit cycle and the formation of isolated convective patterns.Comment: 12 pages, 6 figure

Staggered grids discretization in three-dimensional Darcy convection

We consider three-dimensional convection of an incompressible fluid saturated in a parallelepiped with a porous medium. A mimetic finite-difference scheme for the Darcy convection problem in the primitive variables is developed. It consists of staggered nonuniform grids with five types of nodes, differencing and averaging operators on a two-nodes stencil. The nonlinear terms are approximated using special schemes. Two problems with different boundary conditions are considered to study scenarios of instability of the state of rest. Branching off of a continuous family of steady states was detected for the problem with zero heat fluxes on two opposite lateral planes.Comment: 20 pages, 9 figure

Planar inviscid flows in a channel of finite length : washout, trapping and self-oscillations of vorticity

The paper addresses the nonlinear dynamics of planar inviscid incompressible flows in the straight channel of a finite length. Our attention is focused on the effects of boundary conditions on vorticity dynamics. The renowned Yudovich's boundary conditions (YBC) are the normal component of velocity given at all boundaries, while vorticity is prescribed at an inlet only. The YBC are fully justified mathematically: the well posedness of the problem is proven. In this paper we study general nonlinear properties of channel flows with YBC. There are 10 main results in this paper: (i) the trapping phenomenon of a point vortex has been discovered, explained and generalized to continuously distributed vorticity such as vortex patches and harmonic perturbations; (ii) the conditions sufficient for decreasing Arnold's and enstrophy functionals have been found, these conditions lead us to the washout property of channel flows; (iii) we have shown that only YBC provide the decrease of Arnold's functional; (iv) three criteria of nonlinear stability of steady channel flows have been formulated and proven; (v) the counterbalance between the washout and trapping has been recognized as the main factor in the dynamics of vorticity; (vi) a physical analogy between the properties of inviscid channel flows with YBC, viscous flows and dissipative dynamical systems has been proposed; (vii) this analogy allows us to formulate two major conjectures (C1 and C2) which are related to the relaxation of arbitrary initial data to C1: steady flows, and C2: steady, self-oscillating or chaotic flows; (viii) a sufficient condition for the complete washout of fluid particles has been established; (ix) the nonlinear asymptotic stability of selected steady flows is proven and the related thresholds have been evaluated; (x) computational solutions that clarify C1 and C2 and discover three qualitatively different scenarios of flow relaxation have been obtained

Numerical analysis of ideal fluid flows through plane duct of finite length

The results of numerical study of the non-stationary problem in which the governing equations are the 2D Euler equations are presented. On the boundary of the duct the normal velocity is prescribed everywhere and the vorticity is given on the inflow parts. The variant of vortex particles-in-cells method is proposed and is used for PDE approximation. Firstly we have studied dynamics of different types of initial vorticity patches for classical flows (uniform, Couette and Poiseuille flows). We have found that for sufficiently big perturbations of initial vorticity a new stable separated flows (which are consist of a trough flow zone and a recirculation zone) can be realized. We present a number of examples of separated flows with different structure. Investigation of vorticity behavior in time and structures of stable separated flows are also presented

Phase separation in a chaotic flow

The phase separation between two immiscible liquids advected by a bidimensional velocity field is investigated numerically by solving the corresponding Cahn-Hilliard equation. We study how the spinodal decomposition process depends on the presence -or absence- of Lagrangian chaos. A fully chaotic flow, in particular, limits the growth of domains and for unequal volume fractions of the liquids, a characteristic exponential distribution of droplet sizes is obtained. The limiting domain size results from a balance between chaotic mixing and spinodal decomposition, measured in terms of Lyapunov exponent and diffusivity constant, respectively.Comment: Minor changes - Version accepted for publication - Physical Review Letter

ПРОТОЧНО-ИНЖЕКЦИОННОЕ ОПРЕДЕЛЕНИЕ ВАЛИНА ПЬЕЗОКВАРЦЕВЫМ СЕНСОРОМ, МОДИФИЦИРОВАННЫМ ПОЛИМЕРОМ С МОЛЕКУЛЯРНЫМИ ОТПЕЧАТКАМИ А.Н.Зяблов, С.И.Говорухин, О.В. Дуванова, В.Ф. Селеменев, Ань Тьен Нгуен

Flow-injection determination methods of analysis are gaining their popularity due to vast production of pure amino-acids and their quality control. This report describes methods of valine determination in aqueous solutions using a flow-injection system with piezoelectric sensor on the basis of molecular imprinted polymers (MIP) as a detector. To produce MIP polyamide acid was synthesized at 453 K directly on the surface of the sensor. The tamplate was removed without destruction of polymeric coating. Modified sensors MIP-Val were fit into a cell of original design. The speed of the eluent flow through the cell was 0.9 ml/min. The volume of the injected sample was 100 uL.The experimental part proved the ability of piezoelectric sensor modified with molecular imprinted polymer to determine valine in binary mixtures with glutamic acid. Detection limit of valine was 10-5 mol/L. The obtained data showed selectivity of piezoelectric sensor modified with (MIP) only to valine. Imprinting factor for the sensor modified with MIP-Val, IF =3.2Keywords: valine, glutamic acid, piezoelectric sensor, molecular imprinted polymers (MIPs), flowing-injection analysis. (Russian)DOI: http://dx.doi.org/10.15826/analitika.2014.18.4.010 *A.N. Zyablov, *S.I. Govorukhin, *O.V. Duvanova, *V.F. Selemenev, **Nguen An' T'en * Voronezh State University, Voronezh, Russian Federation**Ho Chi Minh City University of Pedagogy, Ho Chi Minh City, Viet Nam REFERENCES1. Kel'ner R., Merme Zh.-M., Otto M., Vidmer G.M. Analiticheskaia khimiia. Problemy i podkhody [Analytical Chemistry. Issues and Approaches], Moscow, Mir: AST, 2004. Vol. 1. 608 p. (in Russian).2. Evgen'ev M.I., Garmonov S.Iu., Shakirova L.Sh. [Flow injection analysis of drugs]. Zhurn. analit. khimii [J. of Anal. Chem], 2001, vol. 56, no. 4, pp. 355-366 (in Russian).3. Gendrikson O.D., Zherdev A.V., Dzantiev B.B. [Molecularly imprinted polymers and their use in the biological assay]. Uspekhi biologicheskoi khimii [Success of biological chemistry], 2006, vol. 46, pp. 149-192 (in Russian).4. Ziablov A.N., Kalach A.V., Zhibrova Iu.A., Selemenev V.F., D'iakonova O.V. [Determination glycine piezosensor aqueous solutions modified with a molecularly imprinted polymer]. Zhurn. analit. khimii [J. of Anal. Chem], 2010, vol. 65, no. 1, pp. 93-95 (in Russian).5. Zhibrova Iu.A., Ziablov A.N., Shcheglova N.A., Krasnikova O.P., Selemenev V.F. [Molecularly imprinted polymers for piezoelectric sensors Message 1. Analysis of pharmaceutical preparations containing glycine]. Sorbtsionnye i khromatograficheskie protsessy [Sorption and chromatographic processes], 2008, vol. 8, no. 4, pp. 686-688 (in Russian).6. Ziablov A. N., Monicheva T.S., Selemenev V.F. [Detection of amino acids in the preparation of "BCAA" piezoelectric sensor modified with molecularly imprinted polymers]. Analitika i kontrol' [Analitics and control], 2012, vol. 16, no. 4, pp. 406-409 (in Russian).7. Ziablov A.N., Nikitskaia L.M., Zhibrova Iu.A., Kalach A.V., Selemenev V.F. P'ezosensor na osnove polimerov s molekuliarnym otpechatkom aminokislot [Piezosensor based on Molecularly imprinted polymers of amino acids]. Patent RF. no 2010142819/28, 2011 (in Russian).8. Bykov V.A., Krylov I.A., Manakov M.N. Mikrobiologicheskoe proizvodstvo biologicheski aktivnykh veshchestv i preparatov [Microbiological production of bioactive substances and drugs]. Moscow, High school, 1987. 143 p. (in Russian).9. Cormack P. A. G., Elorza A. Z. [Molecularly imprinted polymers: synthesis and characterization]. Journal of Chromatography B, 2004, vol. 804, no. 1, pp. 173-182.10. Dmitrienko S.G., Irkha V.V., Kuznetsova L. Iu, Zolotov Iu. A. [Use of molecularly imprinted polymers in separation processes and concentration of organic compounds]. Zhurn. analit. khimii [J. of Anal. Chem.], 2004, vol. 59, no. 9, pp. 902-913.Предложен способ определения валина в водных растворах с применением проточно-инжекционной системы, имеющей в качестве детектора пьезоэлектрический сенсор на основе полимера с молекулярными отпечатками (ПМО-Val). Диапазон определяемых концентраций валина составляет 10–1–10–6 М, экспериментально установленный предел обнаружения - 10–5 М. Выявлены рабочие условия проточно-инжекционного определения валина в смесях с глутаминовой кислотой. Оценена способность пьезоэлектрического сенсора на основе полимера с молекулярными отпечатками к распознаванию валина в бинарных смесях с глутаминовой кислотой. Импринтинг-фактор для сенсора, модифицированного ПМО-Val, IF = 3.2. Рекомендуемый способ анализа характеризуется экспрессностью, небольшим расходом проб и реагентов, возможностью автоматизации измерений.Ключевые слова: валин, глутаминовая кислота, пьезоэлектрический сенсор, полимеры с молекулярными отпечатками, проточно-инжекционный анализ. DOI: http://dx.doi.org/10.15826/analitika.2014.18.4.010 ЛИТЕРАТУРА1.Аналитическая химия. Проблемы и подходы: в 2 т. / ред.: Р. Кельнер [и др.]; пер. с англ.: А.Г. Борзенко [и др.] под ред. Ю.А. Золотова. М.: Мир: АСТ, 2004. Т.1. 608 с.2. Евгеньев М.И., Гармонов С.Ю., Шакирова Л.Ш. Проточно-инжекционный анализ лекарственных веществ // Журн. аналит. химии. 2001. Т. 56, № 4. С. 355-366.3. Гендриксон О.Д., Жердев А.В., Дзантиев Б.Б. Молекулярно-импринтированные полимеры и их применение в биологическом анализе // Успехи биологической химии. 2006. Т. 46. С. 149-192.4. Определение глицина в водных растворах пьезосенсором, модифицированным полимером с молекулярным отпечатком / А.Н. Зяблов [и др.] // Журн. аналит. химии. 2010. Т. 65, № 1. С. 93-95.5. Полимеры с молекулярными отпечатками для пьезокварцевых сенсоров Сообщение 1. Анализ лекарственных препаратов, содержащих глицин / Ю.А. Жиброва [и др.] // Сорбционные и хроматографические процессы. 2008. Т. 8, Вып. 4. С. 686-688.6. Зяблов А. Н., Моничева Т.С., Селеменев В.Ф. Детектирование аминокислот в препарате "ВСАА" пьезокварцевыми сенсорами, модифицированными полимерами с молекулярными отпечатками // Аналитика и контроль. 2012. Т. 16, № 4. С. 406-409.7. Пат. 102264 Российская Федерация, МПК(51) G01N27/12. Пьезосенсор на основе полимеров с молекулярным отпечатком аминокислот / А.Н. Зяблов [и др.] (РФ). № 2010142819/28; заявл. 19.10.2010; опубл. 20.02.2011, Бюл. № 5. 5 с. 8. Микробиологическое производство биологически активных веществ и препаратов / В.А. Быков [и др]. М.: Высш. шк., 1987. 143 с.9. 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Identification and dynamics prediction of a plane vortex structure based on a mathematical model of a point vortices system

The aim of the article is developing and analyse an algorithmic method for solution finding of one inverse problem of 2d vortex fluid dynamics. It is identification and prediction of the flow structure evolution of the based on the data on fluid velocity vectors in a set of reference points. Theoretical analysis of convergence and adequacy of the method is difficult due to the ill-posedness typical of inverse problems, these issues studied experimentally. Methods. The proposed method uses a mathematical model of a point vortex dynamics system for identification and prediction flow structures. The parameters of the model system are found by minimising the functional that evaluates the closeness of the original and model vectors fields at the reference points. The prediction of the vortex structure dynamics is based on the solution of the Cauchy problem for a system of ordinary differential equations with the parameters found in the first stage. Results. As a result of the calculations, we found it out: the algorithm converges to the desired minimum from a wide range of initial approximations; the algorithm converges in all cases when the identified structure consists of sufficiently distant vortices; the forecast of the development of the current gives good results with a steady flow; if the above conditions are violated, the part of successful calculations decreases, false identification and an erroneous forecast may occur; with the convergence of the method, the coordinates and circulation of the eddies of the model system are close to the characteristics of the eddies of the test configurations; the structures of the streamlines of the flows are topologically equivalent; convergence depends more on location than on the number of vectors used for identification. Conclusion. An algorithm for solving the problem of identifying and the evolution forecast of a 2d vortex flow structure is proposed when the fluid velocity vectors in a finite set of reference points are known. The method showed its high efficiency when using from 40 to 200 reference points. The results of the study make it possible to recommend the proposed algorithm for identifying flat vortex structures, which consist of vortices separated from each other