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1

Mathematical modeling of random concentracion field and its second moments in semispace with erlangian distributions of layerd inclusions

Chernukha O., Bilushchak Y.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2016

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Vol. 20, No 3

295--334

EN

The processes of admixture diffusion in a two-phase stratified semispace with random disposition of syblayers are studied by the approach where internal random nonhomogeneities are considered as inner sources and the solution is found in the form of a Neumann series. The diffusion equations are formulated for one-connected regions of each phase and non-ideal contact conditions for the concentration on interphases are imposed. By the theory of generalized functions the contact problem is reduced to the equation of mass transfer in the whole body, which operator includes explicitly jump discontinuities of the concentration function and its derivatives. The obtained initial-boundary value problem of mass transfer is reduced to the equivalent integro-differentual equation. The solution is constructed in the form of a Neumann series and averaged over the ensemble of phase configurations with Erlangian and exponential distributions of inclusions. Dispersion and the two-point correlation function of the concentration field for diffusion are determined taking into account the probable distribution of inclusions, pair interaction of sublayers and the function of phase correlation. The dependence of the behavior of the averaged admixture concentration, field dispersion and the correlation function in the semispace with Erlangian and exponential distributions of inclusions on different medium characteristics is investigated and established.

2

Simulation of Diffusion Flows in Two-Phase Multilayered Stochastically Nonhomogeneous Bodies with Non-Uniform Distribution of Inclusions

Chaplya Y., Chernukha O., Davydok A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2015

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Vol. 19, No 3

321--351

EN

Admixture diffusion flows are investigated in two-phase randomly nonhomogeneous multilayered strips with non-uniform distributions of inclusions. Cases where the most probable disposition of layered inclusions is located near the body boundary on which the mass source acts in the neighborhood of another boundary and in the middle of the body are considered. The initial-boundary value problem is formulated for the function of random mass flow under conditions of a constant flow on the upper surface and zero concentration of the admixture on the lower surface. Calculation formulae are obtained for the diffusion flow averaged over the ensemble of phase configurations in the particular cases of beta-distribution at zero and nonzero initial concentrations. The dependences of the averaged admixture flows on medium characteristics are established. It is shown that if the admixture diffusion coefficient in inclusions is greater than in the matrix, consolidation of inclusions in the middle of the body leads to an increasing diffusion flow. Simulation of the averaged diffusion flows of the admixture in the multilayered strip is performed for different model variants of a probable disposition of phases in the body and their comparative analysis is carried out.

3

Mathematical Modeling of Random Diffusion Flows in Two-Phase Multilayered Stochastically Nonhomogeneous Bodies

Chaplya Y., Chernukha O., Davydok A.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

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2015

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Vol. 19, No 3

297--320

EN

An approach for studying stochastical diffusion flows of admixture particles in bodies of multiphase randomly nonhomogeneous structures is proposed, according to which initialboundary value problems of diffusion are formulated for flow functions and methods of solution construction are adapted for the formulated problems. By this approach the admixture diffusion flow is investigated in a two-phase multilayered strip for the uniform distribution of phases under conditions of constant flow on the upper surface and zero concentration of admixture on the lower surface. An integro-differential equation equivalent to the original initial-boundary value problem is constructed. Its solution is found in terms of the Neumann series. Calculation formulae are obtained for the diffusion flow averaged over the ensemble of phase configurations under both zero and constant nonzero initial concentrations. Software is developed, a dependence of averaged diffusion flows on the medium characteristics is studied and general regularities of this process are established.

4

Mathematical Modelling of Diffusive and Mechanical Processes in Bodies with Microstructure

Burak Y., Chaplya Y., Chernukha O., Owedyk J.

Computational Methods in Science and Technology

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2008

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Vol. 14, nr 2

87-95

EN

The continuum-thermodynamical approach is proposed for describing mechanical and diffusive processes in bodies with microstructure. Different physical states of admixture particles in a local body structure are taken into account. Features of a stresseddeformable state are discussed on an example of diffusive saturation of a layer in this case.

5

Double diffusivity from the distributed source on surface of a layer

Chaplia Y., Chernukha O.

Journal of Applied Computer Science

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2004

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Vol. 12, nr 2

45-64

EN

The solution has been obtained for the space problem of admixture diffusion by two ways allowing for mass transitions between the states under action of a constant circular source on a layer surface. This case has been compared with the solutions of the particular diffusion problems in a body with traps and diffusion in a medium with effective characteristics.

6

Admixture diffusion in a two-phase random nonhomogeneous stratified layer

Chaplia Y., Chernukha O.

Journal of Theoretical and Applied Mechanics

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2001

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Vol. 39 nr 4

929-946

EN

Vertical admixture diffusion has been considered in a layer with random nonhomogeneous two-phase stratified structure of material. Different phase diffusion coefficients and phase densities have been taken into account as well as jump discontinuities of the diffusion coefficient at interphase boundaries. Averaging the obtained expressions for the admixture concentration has been done over the ensemble of sublayer configurations with equally probable distribution, and two particular cases of beta-distribution of phases in the body.

PL

Dyfuzja substancji domieszkowej w dwufazowej warstwie losowo niejednorodnej. Rozważona jest jednowymiarowa (pionowa) dyfuzja substancji domieszkowej w warstwie tworzonej przez losowo-niejednorodny, dwufazowy materiał warstwowy.Przy konstruowaniu rozwiązań uwzględniono zarówno różnice współczynników dyfuzji i gęstości w różnych fazach, jak i nieciągłości współczynnika dyfuzji na granicach faz. Zgodnie z zaproponowanym podejściem przy rozwiązaniu zagadnienia brzegowego dyfuzji wpływ niejednorodności materiału sprowadzą się do rozpatrywania źródeł wewnętrznych masy, a same zagadnienie - do równania całkowego, które z koleji rozwiązano metodą rozwinięcia w szereg Neymana. Uśrednienieprzybliżonego rozwiązania po zbiorze konfiguracji faz, z których złożone jest ciało, wykonano dla równomiernego losowego rozkładu faz oraz dwóch szczegółowych przypadków rozkładu beta. Porównanie rozkładów uśrednionego pola koncentracji i koncentracji w jednorodnym ośrodku pokazało potrzebę wzięcia pod uwagę zarówno różnych dyfuzyjnych właściwości faz, jak i nieciągłości współczynnika dyfuzji na granicach faz w warunkach doskonałego kontaktu. Oprócz wyznaczono zależność uśrednionej koncentracji składnika domieszkowego od współczynników dyfuzji, gęstości i objętościowych udziału faz dla losowego rozkładu beta podwarstw.

7

Mechanoheterodiffusive processes in semispace under action of point source

Burak Y., Chaplia Y., Chernukha O.

Zeszyty Naukowe Katedry Mechaniki Stosowanej / Politechnika Śląska

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1999

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z. 10

41-46

EN

Mechanodiffusive phenomenon has been considered upon admixture diffusion from point source on surface into semispace. It was assumed that admixture particles migrate by two ways and transfer from one state to another. The problem has been solved by expansion in terms of the parameter of processes tie-up and application of integral transformations. Obtained results have been compared with found ones using effective characteristics.

PL

W artykule przedstawiono zjawiska mechanodyfuzyjne z dyfuzją inicjowaną źródłem punktowym na powierzchni półprzestrzeni. Założono, że cząsteczki migrują dwukierunkowo i przenoszą się z jednego stanu w drugi. Zagadnienie rozwiązano przez rozwinięcie parametrów procesów i zastosowanie przekształceii całkowych. Otrzymane wyniki zostały porównane z wynikami uzyskanymi za pomocą charakterystyk skutecznych.