Mathematical modeling of non-isothermal adsorption mass transfer in nanoporous catalysts

Розглянуто математичну модель неізотермічного адсорбційного масопереносу в пласті мікропористого каналізатора з урахуванням впливу температурної складової. Побудовано аналітичний розв’язок запропонованої моделі з використанням інтегральних перетворень Фур’є та Лапласа. Проведено числове моделювання зміни концентрації адсорбтиву в пласті мікропористого середовища на різних стадіях процесу при різних значеннях температуриThe mathematical model of non-isothermal adsorption mass transfer in micro- and nanopores of intraparticle and interparticle spaces catalytic media, which considers effect of temperature during adsorption process, has been considered. The paper is based on the results of previously proposed bi-porous model and takes into account dependence of diffusion and flow temperature changes of environment on concentration profiles of adsorbed components in interparticle space of micro- and nano poreus of crystallites, which is a limiting factor of adsorption process. Mathematical model consists of a system of three partial differential equations, the first equation describing material balance in the interparticle space (gas phase), the second equation describing diffusion heat balance in the media and the third equation is a internal kinetic equation, which establishes connection between gas and solid phases based on the Langmuir-Hinshelwood balance equation. Solution of non-isothermal mass transfer adsorption model is built with the Laplace’s and Fourier’s integral transformations. Obtained analytical solution of model has the advantage over numerical solution due to a significant reduction in the number of iterations that is crucial for use gradients methods of identification to solve problems of kinetic parameters determination from experimental distributions. Numerical model of concentration profiles in micropores particles at different values of temperature as a function of layer thickness coordinate for different moments from the beginning of the adsorption process has been presented. Having analyzed the graphs we see that the concentrations of benzene in the middle of nanopore particles of adsorbent increases from the middle to the edge, and the value depends on the temperature. Thus for different temperatures, characteristics of concentration profiles are the same

HIGH-PERFORMANCE MODELING, IDENTIFICATION AND ANALYSIS OF HETEROGENEOUS ABNORMAL NEUROLOGICAL MOVEMENT’S PARAMETERS BASED ON COGNITIVE NEURO FEEDBACK-INFLUENCES

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) taking into account the matrix of cogni-tive influences of groups of cortex neuro-nodes. The rapid analytical solution of the model as a vector function that describes the 3D elements of the trajectories at each movements segment are constructed using the hybrid integral Fourier’s transformations and hybrid spectral function. The main element of the solution is the adaptive infuences matrix  that determines the state parameters of the action of certain groups of brain neuro- cortex. Models and methods of multivariable identification are being developed to investigate their neuro-feedback, which suggest  high-speed parallel computations on multicore computers. This model-ing technology consider as a scientific basis for designing inelidgence information systems of the quality medical diagnostic i of critical neurological diseases.Key words: Computer simulation, Software system, High-performance compu-ting, Tremor diseases, Modeling of objects and processes, Multi-parameter iden-tification

Mathematical modeling of dynamic processes of diffusion masstransfer in heterogeneous halflimited flat magnetic mediums

Методом інтеґральних перетворень Фур’є з n-точками спряження побудовано математичну модель процесів дифузійного переносу в багатошарових магнітних напівобмежених середовищах. Знайдено точний розв`язок такої задачі шляхом побудови головних розв`язків – фундаментальних функцій Коші і Гріна. Досліджено умови їх збіжності. Здійснено моделювання дифузійного пeреносу та проведено адекватність моделі за результатами натуpних експериментів.Mathematical model of diffusion mathtransfer in multilayer magnetic halflimited medium with use of n-conjuction points Fouirer transformation has been built. The analitycal olution of such problem according to Couchy and Green function has been found for the first time. The conditions of convergence. Mathematical modeling of diffusion masstransfer and adequacy check has been done

Mathematical modeling and optimal control of electro-diffusion masstransfer systems

З використаннм методів варіаційного числення, інтегрального перетворення Фур’є та методу Коші розв’язано спряжену та пряму задачу оптимального керування йонопереносом з урахуванням інтеґрального критерію мінімізації енерґовитрат. Виконано числове моделювання оптимальних розподілів струму та густин електричних зарядів.With use of variations calculus methods, integral Fourier transform and Coushy method was solved direct and dual problems of optimum control of iontrasnfer with consider of intergral test of energy consumption minimum. Computational modeling of electric current and charges density distributions has been done

Modeling of chrome diffusion transfer processes in multicomposite oxide nanofilms

Побудовано математичну модель дифузійного переносу в багатокомпозитних оксидних наноплівках. За результатами експериментальних досліджень вмісту хрому в зразках, створених за технологією виробництва супертонкого волокна, отримано розподіли коефіцієнтів дифузії хрому. Змодельовано кінетику процесу дифузії у вигляді розподілів вмісту хрому в зразку для різних технологічних зрізів та часових тривалостей формування мультишару наноплівки.This paper deals with a problem of mathematical modeling of diffusive transport in multilayer mediums. The aim is to analyze and to model the diffusion transfer of chromium (Cr) in the mineral fibers on the basis of the proposed mathematical model of multicomposite medium. Multycomposite medium with established uniform layers n and n +1- th layer, whose thickness is much greater than the previous ones is analysed. The proposed mathematical model is based on the account of component interdiffusion between adjacent layers of n-layer medium. To find a solution of the problem Fourier integral transformations were consistently applied. For numerical simulation results of experimental studies on chromium distribution in feeders operated for 20 and 30 days in the production of super-thin basalt fibers (STBF) were used. Having applied the approaches of optimal control theory of distributed systems for analysis of experimental distributions, the diffusion coefficients of chromium (Cr) in a medium layers were obtained. Examples of numerical modeling of the distribution of chromium in production of STBF are provided. These concentration distributions are constructed for different time points of forming process of multicomposite nanofilms. For ease of analysis of diffusion transfer kinetics, distributions are given for the five time points, that correspond to conditionally stages of protective layer formation from the beginning (0.25T) to the end (1T). While analyzing the results it is worth stressing the almost complete coincidence of model chromium distribution curve with corresponding experimental distributions. The maximum deviation between these two concentrations for the period of multycomposite completion are less than 3%, which tesifies the reliability of the proposed model. These spatially distributed chromium concentration distributions for various technological sections of oxide nanofilms and time durations of multiconposite nanofils formation process allow to analyse of the kinetics of multilayer formation, that can be applied for the process operations improvement and new nanomaterials properties study