Articles
http://nur.nu.edu.kz:80/handle/123456789/4174
2020-06-05T03:27:46ZDead-Core Solutions to Simple Catalytic Reaction Problems in Chemical Engineering
http://nur.nu.edu.kz:80/handle/123456789/4777
Dead-Core Solutions to Simple Catalytic Reaction Problems in Chemical Engineering
Sabit, F.; Shakipov, Mansur; Skrzypacz, Piotr; Golman, Boris
The catalytic chemical reaction is usually carried out in a pellet where the catalyst is distributed throughout its porous structure. The selectivity, yield and productivity of the catalytic reactor often depend on the rates of chemical reactions and the rates of diffusion of species involved in the reactions in the pellet porous space. In such systems, the fast reaction can lead to the consumption of reactants close to the external pellet surface and creation of the dead core where no reaction occurs.
This will result in an inefficient use of expensive catalyst. In the discussed simplified diffusion-reaction problems a nonlinear reaction term is of power-law type with a small positive reaction exponent. Such reaction term represents the kinetics of catalytic reaction accompanied by a strong adsorption of the reactant. The ways to calculate the exact solutions possessing dead cores are presented. It was also proved analytically that the exact solution of the nonlinear two-point boundary value problem satisfies physical a-priori bounds. Furthermore, the approximate solutions were obtained using the orthogonal collocation method for pellets of planar, spherical and cylindrical geometries. Numerical results confirmed that the length of the dead core increases for the more active catalysts due to the larger values of the reaction rate constant. The dead core length also depends on the pellet geometry.
2019-02-20T00:00:00ZWeighted L^{p}-Hardy and L^{p}-Rellich inequalities with boundary terms on stratified Lie groups
http://nur.nu.edu.kz:80/handle/123456789/4776
Weighted L^{p}-Hardy and L^{p}-Rellich inequalities with boundary terms on stratified Lie groups
Ruzhansky, Michael; Sabitbek, Bolys; Suragan, Durvudkhan
In this paper, generalised weighted Lp-Hardy, Lp-Caffarelli–Kohn–Nirenberg, and Lp-Rellich inequalities with boundary terms are obtained on stratified Lie groups. As consequences, most of the Hardy type inequalities and Heisenberg–Pauli–Weyl type uncertainty principles on stratified groups are recovered. Moreover, a weighted L2-Rellich type inequality with the boundary term is obtained.
2018-06-29T00:00:00ZAdaptive numerical homogenization for upscaling single phase flow and transport
http://nur.nu.edu.kz:80/handle/123456789/4762
Adaptive numerical homogenization for upscaling single phase flow and transport
Amanbek, Yerlan; Singh, Gurpreet; Wheeler, Mary F.; Duijn, Hansvan
We propose an adaptive multiscale method to improve the efficiency and the accuracy of numerical computations by combining numerical homogenization and domain decomposition for modeling flow and transport. Our approach focuses on minimizing the use of fine scale properties associated with advection and diffusion/dispersion. Here a fine scale flow and transport problem is solved in subdomains defined by a transient region where spatial changes in transported species concentrations are large while a coarse scale problem is solved in the remaining subdomains. Away from the transient region, effective macroscopic properties are obtained using local numerical homogenization. An Enhanced Velocity Mixed Finite Element Method (EVMFEM) as a domain decomposition scheme is used to couple these coarse and fine subdomains [1]. Specifically, homogenization is employed here only when coarse and fine scale problems can be decoupled to extract temporal invariants in the form of effective parameters. In this paper, a number of numerical tests are presented for demonstrating the capabilities of this adaptive numerical homogenization approach in upscaling flow and transport in heterogeneous porous medium.
2019-03-05T00:00:00ZSoliton surface associated with the WDVV equation for n = 3 case
http://nur.nu.edu.kz:80/handle/123456789/4669
Soliton surface associated with the WDVV equation for n = 3 case
Zhadyranova, A.A.; Myrzakul, Zhanbota
his paper describes the soliton surfaces approach to the Witten-Dijkgraaf-E.Verlinde-H. Verlinde (WDVV) equation. We constructed the surface associated with the WDVV equations using Sym-Tafel formula, which gives a connection between the classical geometry of manifolds immersed in R m and the theory of solitons. The so-called Sym-Tafel formula simplifies the explicit reconstruction of the surface from the knowledge of its fundamental forms, unifies various integrable nonlinearities and enables one to apply powerful methods of the soliton theory to geometrical problems. The soliton surfaces approach is very useful in construction of the so-called integrable geometries. Indeed, any class of soliton surfaces is integrable. Geometrical objects associated with soliton surfaces (tangent vectors, normal vectors, foliations by curves etc.) usually can be identified with solutions to some nonlinear models (spins, chiral models, strings, vortices etc.) [1], [2]. We consider the geometry of surfaces immersed in Euclidean spaces. Such soliton surfaces for the WDVV equation for n = 3 case with an antidiagonal metric η11 = 0 are considered, and first and second fundamental forms of soliton surfaces are found for this case. Also, we study an area of surfaces for the WDVV equation for n = 3 case with an antidiagonal metric η11 = 0.
2019-11-01T00:00:00ZClassifying equivalence relations in the Ershov hierarchy
http://nur.nu.edu.kz:80/handle/123456789/4660
Classifying equivalence relations in the Ershov hierarchy
Mustafa, Manat; Bazhenov, Nikolay; Mauro, Luca San; Sorbi, Andrea; Yamaleev, Mars
Computably enumerable equivalence relations (ceers) received a lot of attention in the literature. The standard tool to classify ceers is provided by the computable reducibility ⩽c. This gives rise to a rich degree structure. In this paper, we lift the study of c-degrees to the Δ02 case. In doing so, we rely on the Ershov hierarchy. For any notation a for a non-zero computable ordinal, we prove several algebraic properties of the degree structure induced by ⩽c on the Σ−1a∖Π−1a equivalence relations. A special focus of our work is on the (non)existence of infima and suprema of c-degrees.
2020-02-13T00:00:00ZExistence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids
http://nur.nu.edu.kz:80/handle/123456789/4645
Existence of self-similar solutions of the two-dimensional Navier–Stokes equation for non-Newtonian fluids
Wei, Dongming; Al-Ashhab, Samer
The reduced problem of the Navier–Stokes and the continuity equations, in two-dimensional Cartesian coordinates with Eulerian description, for incompressible non-Newtonian fluids, is considered. The Ladyzhenskaya model, with a non-linear velocity dependent stress tensor is adopted, and leads to the governing equation of interest. The reduction is based on a self-similar transformation as demonstrated in existing literature, for two spatial variables and one time variable, resulting in an ODE defined on a semi-infinite domain. In our search for classical solutions, existence and uniqueness will be determined depending on the signs of two parameters with physical interpretation in the equation. Illustrations are included to highlight some of the main results.
2019-04-20T00:00:00Z