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Publications (99)
The different variants of two-stage random sequential adsorption (RSA) models for packing of disks and discorectangles on a two-dimensional (2D) surface were investigated. In the SD (sticks+disks) model, the discorectangles were first deposited and then the disks were added. In the DS (disks+sticks) model, the disks were first deposited and then di...
The different variants of two-stage random sequential adsorption (RSA) models for packing of disks and discorectangles on a two-dimensional (2D) surface were investigated. In the SD model, the discorectangles were first deposited and then the disks were added. In the DS model, the disks were first deposited and then discorectangles were added. At t...
The non-isothermal adsorption/desorption of gas in a cylindrical column filled with adsorbent particles has been considered theoretically. The model is based on Langmuir theory for equilibrium adsorption. Using the Heaviside operational method the analytical solutions for kinetics of changes of concentration of adsorbate in the inter- and intra-par...
The algorithm of the gradient procedure of identification of parameters of internal kinetics of systems of competitive diffusion for a heterogeneous catalytic nanoporous medium is presented. The results of designing and parallelizing a program implementing a Crank-Nicolson scheme using algebra-algorithmic specifications represented in a natural-lin...
The theoretical bases of mathematical modeling of nonisothermal competitive adsorption and desorption in nanoporous zeolite media for the extended Langmuir’s equilibrium are given. They most fully determine the mechanism of adsorption equilibrium for nanoporous particles media. The effective scheme of linearization of a nonlinear model is implement...
A two-dimensional Monte Carlo simulation of dead-end diafiltration of bidispersed particle suspensions was performed. The diafiltration process involves separation of components based on their size by using a permeable membrane. The continuous model was applied to study separation of mixture of disks with diameter d and D (D>d). It was assumed that...
Heterogeneous media consisting of thin layers of particles of forked porous structure with different physical-chemical properties are widely used in science-intensive technologies and priority sectors of industry, medicine, ecology, etc. Such layers are distributed systems of pores consisting of two main spaces: micro- and nanopores of particles an...
In the paper, the technologies for the high-performance intellectual nanoporous filtration systems based on the mathematical model of the two-level transport «filtration-consolidation» in the system of nanopores in two intraparticle spaces, which includes two subspaces of different-sized nanoporous particles are developed.
The results of the mathematical model of a capacitor development using a porous material of zeolite ZSM-5 as a medium holding a dielectric are presented. It is established, that the use of zeolite makes it possible to effectively retain the charge inside the capacitor and increase its capacity. The gradient of the charges concentration inside the c...
The technique is based on a hybrid model of the neuro-system (Brain cortex nodes and tremor-object), which describes on the basis of wave signal propagation the state and behavior of tremor-objects T, namely the segmental de-scription of 3D elements of trajectories of anormal neurological movements of the studied tremor-objects (limb of the hand) t...
The analytical theory of acoustic phonons arising in the layers of a nitride-based nanostructure, taking into account the presence of the piezoelectric effect, was developed. Proposed theory is based on the first obtained exact solutions of the system consisting of equation of motion for a semiconductor medium and Maxwell equation. The theory of th...
High-performance supercomputer computing technologies have been developed to model and identify the parameters of complex n-component competitive adsorption processes in nanoporous cybersystems with feedback. Using the Laplace transform and the Heaviside operating method with the decomposition of a nonlinear system with Langmuir-type adsorption equ...
The article considers the use an analytical and numerical approaches for finding solutions of mathematical model of diffusion mass transfer in the medium of particles of microporous structure. The special software developed based on both approaches and these software were used for computer simulation of pressures in particles and interparticle spac...
A basis for the mathematical modeling of non-isothermal gas competitive adsorption in a porous solid using Langmuir equilibrium is given. High-performance analytical solutions of considered adsorption models based on the Heaviside operating method and Landau’s decom- position and linearization approach of Langmuir equilibrium by expanding into a co...
High-performance methods and computer technologies for modeling of non-isothermal gas adsorption in nanoporous cyber-feedback systems based on the Heaviside operating method and Landau’s linearization approach to Langmuir’s nonlinear adsorption equilibrium using decomposition in a convergent series at the temperature transition point with subsequen...
The theory of the interaction of electrons with acoustic phonons in multilayer nitride-based AlN/GaN nanostructures was developed for the first time at $T\geqslant 0$ using the method of finite-temperature Green's functions and Dyson equation. Components of the Hamiltonian describing the system of electrons with acoustic phonons and the magnitudes...
The theory of the interaction of electrons with acoustic phonons in multilayer nitride-based AlN/GaN nanostructures was developed for the first time at T ≥ 0 using the method of finite-temperature Green's functions and Dyson equation. Components of the Hamiltonian describing the system of electrons with acoustic phonons and the magnitudes of the el...
The study of physical processes associated with acoustic phonons in nitride-based nanosystems is of great importance for the effective operation of modern nanoscale devices. In this paper, a consistent theory of acoustic phonons arising in multilayer nitride-based semiconductor resonant tunneling structures, that can function as a separate cascade...
Using the model of an elastic continuum, precise analytical solutions of the equations of motion are established and a theory of the spectrum and components of the displacement field of acoustic phonons is developed for a two-well resonant-tunneling nanostructure with AlN – quantum barriers and GaN∕AlxGa1−xN – quantum wells. For the experimentally...
Завдяки використанню сучасних комп’ютерних технологій, можна здійснити цифровий, послідовний та автоматизований підхід до діагностики стану здоров’я. Зокрема, у цій статті наводиться приклад застосування даних технологій до діагностики стану тремору. Будь-яке його відхилення щодо норми показує, що в людини може бути втома, надто збуджений емоційний...
In paper, using exact solutions of the stationary Schrödinger equation and the equation of motion for an elastic semiconductor medium, using the secondary quantization formalism, the theory of interaction of electrons with acoustic phonons in a multilayer arsenide-based AlAs/GaAlAs resonant tunneling structure is developed. Using the Matsubara Gree...
Розглядається задача моделювання неізотермічної адсорбції та десорбції в нанопористих цеоліт-системах для нелінійної адсорбційної рівноваги типу Ленґмюра. Пропонуються висопродуктивні методи операційного числення Гевісайда та перетворення Лапласа звикористанням схем лінеаризації на основі підходу Ландау щодорозкладу в ряд функції рівноваги Ленґмюра...
An experimental and theoretical study of the dehydration of natural gas using microporous silica beds for motor fuel technology in extreme winter climates is described. Analytical solutions to the problem of non-isothermal adsorption and desorption are based on Heaviside's operational method and Laplace integral transform, but the development of ca...
Using the elastic continuum model, exact analytical solutions for the equations of motion for the elastic medium of a multilayer resonant tunneling nanosystem describing the shear modes of acoustic phonons are obtained. The expressions describing the components of the stress tensor arising in the studied nanostructure and boundary conditions for th...
The mathematical model of adsorption and desorption of the main component of emissions of incomplete combustion products in nanoporous zeolite-medium for the cold start conditions is formulated. Using the method of Heveside's operating calculus, the model analytical solution, which provides high-speed modeling of concentration dependences in the ga...
The quantum mechanical theory of spectral parameters and dynamic conductivity of electrons, interacting with field of the created by them space charge in open flat resonance tunneling structure with a constant electric field in the model of rectangular potential wells and barriers has been developed. The influence of space charge on the conductivit...
The retrospective and limited identification problems in integrated form of the systems of filtration–consolidation in compressible media of microporous particles using the residual functional, taking into account the total liquid flow change on the observation surface are formulated. Highly productive methods of identification problems realization...
The identification problems of the model parameters of filtrationconsolidation in compressible media of micro-porous particles using residual functionals taking into account the total liquid flow changes on the observation surface are formulated. Highly productive methods of identification problems implementation based on the analytical solutions o...
In approximations of the effective mass and rectangular potential wells and potentials for the electron, by using solutions of the complete Schrödinger equation, was developed the theory of active dynamic conductivity of three barrier resonant tunnel structure in a weak electromagnetic field, taking into account the contribution of detector one- an...
Taking into account the previous experimental 12 results obtained by NMR, new procedures for identifying diffusion 13 coefficients for codiffusing benzene and hexane in intra-and 14 intercrystallite spaces of ZSM 5 zeolite were implemented, using 15 high-speed gradient methods and mathematical diffusion models, 16 as well as the NMR spectra of the...
Creation of highly efficient methods of identification by constructing low-cost analytical solutions to direct and conjugate problems is considered. Explicit expressions are constructed for residual functional gradients to identify the transfer parameters in nanoporous media with the known total mass distribution in the solid and gaseous phases of...
The model parameter identification competitive diffusion in nanoporous particles media with solvability justification of direct and conjugate boundary problems are implemented. The exact analytical solutions these problems by operational method Heaviside are received. The explicit expressions of functional gradients residual for the transfer parame...
The new methodology of mathematical modeling and investigation of equilibrium masstransfer for the multicompound heterogeneous media of nanopores structures are created. The exact analytical and numerical solutions of the adsorption masstransfer models using the inegral transformations of Fourier and of Bessel, the Heviside operatinal calculus, the...
The study of the co-diffusion of several gases through a microporous solid and of the resulting instantaneous distribution (out of equilibrium) of the adsorbed phases is particularly important in many fields, such as gas separation, heterogeneous catalysis, etc. Solutions to the direct and inverse problems are based on Heaviside’s operational metho...
The study of the co-diffusion of gases through a
microporous solid and the resulting instantaneous
distribution (out of equilibrium) of the adsorbed phases is
particularly important in many fields, such as gas separation,
heterogeneous catalysis, etc. Classical 1H NMR imaging is
the best technique for the visualisation of these processes,
but it re...
A physical model of solid–liquid expression from liquid containing plant materials is presented in one-dimensional (1-D) formulation. The layer of sliced cellular material is conceptualized as a double porosity system with extraparticle and intraparticle networks for liquid flow. Filtration-consolidation equations with corresponding initial and bou...
Physical model of solid-liquid expression from liquid containing plant materials is presented in one-dimensional formulation. The layer of sliced cellular material is conceptualized as a double porosity system with extraparticle and intraparticle networks for liquid flowing. The filtration-consolidation equations with corresponding initial and boun...
A new NMR imaging technique is used for following the co-diffusion and co-adsorption of benzene
and hexane in a ZSM5 zeolite bed used as examples. Contrary to the classical 1H NMR imaging, the
“Slice Selection Procedure” gives a signal characteristic of each adsorbed gas. It can therefore
provide directly, at every moment and at every level of the...
This technique is used to follow the co-diffusion and coadsorption
of benzene and hexane in a ZSM5 zeolite bed used
as examples. Since it gives a signal characteristic of each
adsorbed gas, it can therefore provide directly, at every moment
and at every level of the bed, the distribution of several gases
competing in diffusion and adsorption, and t...
A new NMR imaging technique is used for following the co-diffusion and co-adsorption of benzene
and hexane in a ZSM5 zeolite bed used as examples. Contrary to the classical 1H NMR imaging, the
“Slice Selection Procedure” gives a signal characteristic of each adsorbed gas. It can therefore
provide directly, at every moment and at every level of the...
The study of the co-diffusion of several gases through a microporous solid and the resulting instantaneous distribution (out of equilibrium) of the adsorbed phases is particularly important in many fields, such as gas separation and heterogeneous catalysis. Classical 1H NMR imaging is a good technique for the visualization of these processes but, s...
ANALYTIC AND NUMERICAL SOLUTIONS COMPARISON FOR LIQUID FLOWING FROM POROUS PARTICLES DURING PRESSING OF BIOLOGICAL MATERIALS PROBLEM
M. PETRYK1, E. VOROBIEV2, D. MYKHALYK1
1-Laboratoire de Modélisation Mathématique de Transfert de Masse en Milieux Hétérogènes et Nanopores, Université d’Etat Ivan PULU’Y de Ternopil, 56, rue Ruska, 46001, Ternopil,...
Consideration has been given to identification of the diffusion parameters in nanoporous components under conditions of their variability in time and under assumption of their constancy on small time intervals.
The identification of diffusion parameters of a two-component solution in heterogeneous nanoporous materials is analyzed. The gradient of the residual functional is obtained based on optimal control theory. The results of numerical experiments are presented.
On the basis of theory of optimal control we constructed explicit expressions of gradients of functional-discrepancies for identification by gradient methods of parameters of diffusion problems of one-component substance in nanoporous medium. Results of identification of diffusion coefficient for nanoporous components are adduced.
We construct nonlinear mathematical model of mass transfer of "filtration−consolidation" type in medium of moisture saturated particles of microporous structure with application of linearization methods and the Fourier and Laplace integral transforms. Numerical modeling is performed and distribution of pressures in micropores of interparticle space...
A nonlinear mathematical model of two-component competitive diffusion in bounded nanoporous media of spherical particles is proposed. The solvability of the linearized system of boundary-value problems, built with the use of a small parameter method, is grounded. By the methods of the Heaviside operational calculus and Cauchy fundamental matrices t...
A nonlinear mathematical model of two-component competitive diffusion in bounded nanoporous media of spherical particles is proposed. The solvability of the linearized system of boundary-value problems, built with the use of a small parameter method, is grounded. By the methods of the Heaviside operational calculus and Cauchy fundamental matrices t...
We proposed nonlinear mathematical model of two-component competitive diffusion in bounded nanoporous media of spherical particles. Exact analytical solutions of this model were constructed with application of the Heaviside operational calculus and the Cauchy fundamental matrixes. We conduct numerical modeling and analysis of dynamics of variation...
The analytical solution of the equations of gas diffusion in a heterogeneous zeolite bed is presented. The problem is handled by assuming that the bed consists of a large number of very thin layers of solid, perpendicular to the direction of propagation of the gas. Mass transfer by diffusion in such a material is determined by a system of different...
The problem of mass transfer during the pressing is conceptualized as a doble-porosity flowing in two volumes: 1) in a porous medium of sliced particles and 2) in the extra particles network. An inter porosity flowing occurs between these two porous volumes. The mathematical model includes the system of two differential equations of consolidation w...
The solution of the problem of multilevel mass transfer system in heterogeneous media of nanoporous particles was constructed by methods of the Laplace integral transform and the Cauchy fundamental functions. We perform numerical analysis of mass transfer in heterogeneous and nanoporous catalytic zeolite bed, and verify model for adequacy with solv...
The solution of the problem of multilevel mass transfer system in heterogeneous media of nanoporous particles was constructed by methods of the Laplace integral transform and the Cauchy fundamental functions. We perform numerical analysis of mass transfer in heterogeneous and nanoporous catalytic zeolite bed, and verify model for adequacy with solv...
The problem of mass transfer during the removal of the liquid from expressed biological particles is presented in one-dimensional formulation. The biological material is conceptualized as a double-porosity. When this material undergoes a pressing, the liquid flows in two volumes: (1) in a porous medium of sliced particles and (2) in the extrapartic...
We present the analytical solution of the equations of gas diffusion in a heterogeneous
zeolite bed. The problem is handled by assuming that the bed consists of a large number of very
thin layers of solid, perpendicular to the direction of propagation of the gas. Mass transfer by
diffusion in such a material is determined by a system of differentia...
Study of benzene diffusion and molecular transport in beds of zeolite crystallity
An exact analytical solution is obtained to describe mass transfer in symmetric heterogeneous and nanoporous media with a
system of n-interface interactions. The Laplace integral transform and Cauchy fundamental functions are used. A solvability
theorem is proved. New recurrence algorithms and computational procedures are developed to form influenc...
An exact analytical solution is obtained to describe mass transfer in symmetric heterogeneous and nanoporous media with a system of n-interface interactions. The Laplace integral transform and Cauchy fundamental functions are used. A solvability theorem is proved. New recurrence algorithms and computational procedures are developed to form influenc...
We present the analytical solution of the equations of gas diffusion in a heterogeneous zeolite bed. The problem is handled by assuming that the bed consists of a large number of very thin layers of solid, perpendicular to the direction of propagation of the gas. Mass transfer by diffusion in such a material is determined by a system of differentia...
The problem of mass transfer for diffusion and adsorption in non-regular disperse and porous multilayer media with no stationary
regimes of mass exchange processes on the mass exchanged surfaces, which is described by systems of differential equations
with boundary conditions and contact conditions, is introduced. The exact analytical solution of t...
The problem of mass transfer during the pressing of liquid containing biological particles is presented in the one-dimensional formulation. The liquid flowing during pressing is conceptualized as a double-porosity flowing in two volumes. The mathematical model includes two differential equations of consolidation withinitial and boundary conditions....
The experimental and the theoretical study of adsorption end desorption of water vapour in micro porous beds of base of silica gel for of gases system of draying are presented. Experimental and modeling distributions of concentrations of moisture and temperatures for inlet and outlet of the adsorber for cyclic stages of drying and regeneration rece...
