Generalized diffusion equation with nonlocality of space-time. Memory function modelling

Kostrobij, P.; Markovych, B. M.; Токарчук, М. В.

doi:10.5488/cmp.23.23003

Cited by 3 publications

(1 citation statement)

References 77 publications

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“…For numerical implementations of mathematical models of heat and mass transfer with phase transitions, two main approaches are used. The first approach uses methods with the phase boundary detection at each time span [9]. For the second approach, end-to-end calculation methods are used, in particular, using the generalized formulation of the classical Stefan problem [10,11].…”

Section: Introductionmentioning

confidence: 99%

Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

Sokolovskyy¹,

Boretska²,

Gayvas³

et al. 2021

Math. Model. Comput.

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The article deals with constructing and implementing mathematical models of non-isothermal moisture transfer during drying of anisotropic capillary-porous materials, in particular wood, taking into account the movement of the evaporation zone for non-steady drying schedules, as well as to the development of effective analytical and numerical methods for their implementation. An analytical-numerical method for the determination of non-isothermal moisture transfer under non-steady schedules of the drying process has been developed, taking into account the dynamics of the phase transition boundary change. Calculation relationships are established for determining the phase transition temperature taking into account transport gradients and time for which the relative saturation reaches the boundaries of the phase transition.

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Section: Introductionmentioning

confidence: 99%

Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

Sokolovskyy¹,

Boretska²,

Gayvas³

et al. 2021

Math. Model. Comput.

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Generalized diffusion equation with nonlocality of space-time: Analytical and numerical analysis

Kostrobij

Токарчук

Markovych

et al. 2021

Journal of Mathematical Physics

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We present a general approach for obtaining the generalized transport equations for weakly nonequilibrium processes with fractional derivatives by using the Liouville equation with fractional derivatives for a system of classical particles and the Zubarev nonequilibrium statistical operator method. A generalized diffusion equation for a system of classical particles in fractional derivatives is obtained for weakly nonequilibrium processes. Based on the non-Markov diffusion equation, taking into account the spatial nonlocality and modeling the generalized coefficient of particle diffusion Dαα′(r,r′;t,t′)=W(t,t′)D̄αα′(r,r′) using fractional calculus, the generalized Cattaneo–Maxwell-type diffusion equation in fractional time and space derivatives is obtained. In the case of a constant diffusion coefficient, analytical and numerical studies of the frequency spectrum for the Cattaneo–Maxwell diffusion equation in fractional time and space derivatives are performed. Numerical calculations of the phase and group velocities with a change in values of characteristic relaxation time, diffusion coefficient, and indices of temporal ξ and spatial α nonlocality are carried out.

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Microscopic theory of the influence of dipole superparamagnetics (type <beta-CD<FeSO_4>>) on current flow in semiconductor layered structures (type GaSe, InSe)

Kostrobij¹,

Ivashchyshyn²,

Markovych³

et al. 2020

Math. Model. Comput.

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A statistical approach to description of the charge carrier transfer processes in hybrid nanostructures taking into account electromagnetic fields is proposed using the method of the nonequilibrium statistical operator Zubarev. Generalized transfer equations are obtained, which describe non-Markov processes of charge transfer in the system taking into account magnetic and polarization processes under the influence of external and induced internal electromagnetic fields. Weakly nonequilibrium charge transfer processes in nanostructures are considered, and a nonequilibrium statistical operator is obtained, by means of which the magneto-diffusion transfer equations for electrons in layered nanostructures are obtained. A generalized Cattaneo-type diffusion equation in time fractional derivatives is obtained for electrons with a characteristic relaxation time and a generalized model is proposed that takes into account the complexity of relaxation electro-magnetic diffusion processes for electrons in layered nanostructures.

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Generalized diffusion equation with nonlocality of space-time. Memory function modelling

Cited by 3 publications

References 77 publications

Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

Mathematical modeling of convection drying process of wood taking into account the boundary of phase transitions

Generalized diffusion equation with nonlocality of space-time: Analytical and numerical analysis

Microscopic theory of the influence of dipole superparamagnetics (type <beta-CD<FeSO_4>>) on current flow in semiconductor layered structures (type GaSe, InSe)

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