Yaroslav Bazaikin

• D. Sc.
• Professor (Associate) at Jan Evangelista Purkyně University in Ústí nad Labem

The sintering process is widely used in modern industry because it allows for obtaining materials with predefined properties. Chemical or physical techniques can measure these properties. Besides the cost of such methods, it is worth noting that some techniques destroy samples, which causes difficulties in measuring the parameters’ evolution. Compu...

In this article, we propose an original algorithm for numerical simulation of the conjugated reactive transport. The algorithm is essentially oriented toward the use of GPUs. We simulate the CO2 chemosorption by soda-lime sorbent, assuming a multi-scale process. Macropore space supports both advective and diffusive transport of the reactive species...

The sintering simulation is an actual problem in computational mathematics since computer simulation allows performing much more experiments than can be performed using chemical or physical techniques, especially in the case of studying the material’s intrinsic structure. The most perspective approach for the sintering simulation is a phase-field m...

The paper presents a numerical algorithm for conjugated reactive transport at two spatial scales, in application to C02 chemosorption. Transport at the macroporous scale (intergranular space) is supported by both the fluid flow and diffusion. At the microporous scale diffusion is assumed as the only transport mechanism. The mathematical model used...

The paper presents a numerical algorithm for simulation of the reactive transport at the pore scale. The algorithm allows simulating pore space evolution, porosity, absolute permeability, and form factor changes due to core matrix dissolution or precipitation. We also, introduce the topological measure; the persistence diagrams of independent cycle...

Computer simulation of the sintering process makes it possible to study the internal properties of the sample, the measurement of which by chemical or physical methods can be difficult and expensive. The interest in studying the properties of yttrium oxide is caused by the fact that it can be used to deactivate sorbents from calcium oxide, which ar...

The paper deals with a modified Godbillon-Vey class defined by Losik for codimension-one foliations. This characteristic class takes values in the cohomology of the second order frame bundle over the leaf space of the foliation. The definition of the Reeb foliation depends upon two real functions satisfying certain conditions. All these foliations...

We present an algorithm for the pore-scale simulation of the reactive transport in a 3D case. The algorithm is designed to facilitate the observation of pore space changes caused by chemical fluid-solid interaction. Additionally, the algorithm allows estimation of the main macroscopic properties evolution of the porous material, such as permeabilit...

The paper presents a finite-difference algorithm for reactive transport simulation at the pore scale in 3D. We simulate the matrix dissolution and crystal precipitation due to heterogeneous reactions, acquired at the fluid-solid interface. The fluid flow and the reactive transport are computed using finite difference method on a regular rectangular...

The paper presents an original algorithm for reducing three-dimensional digital images to improve the computing performance of persistence diagrams. These diagrams represent changes in pore space topology during essential or artificial changes in the structure of porous materials. The algorithm has linear complexity because during reduction, each v...

The paper presents an original algorithm for reducing three-dimensional digital images to improve persistence diagrams computing performance. These diagrams represent topology changes in digital rocks pore space. The algorithm has linear complexity because removing the voxel is based on the structure of its neighborhood. We illustrate that the algo...

The article describes the application of the digital image reduction algorithm to speed up the calculation of persistent diagrams that describe changes in the topology of the pore space of the rock matrix during the dissolution process. The dependence of the efficiency of the reduction algorithm on the properties of the rock sample and the value of...

In the current study, the volume-sintering model was implemented for the simulation of sorption/desorption and textural evolution of the set of CaO-based sorbents with broad differences in porous structure. The porous structure of the materials was modeled with the dense random packing of spheres using the Lubachevsky–Stillinger compression algorit...

Following Losik’s approach to Gelfand’s formal geometry, certain characteristic classes for codimension-one foliations coming from the Gelfand-Fuchs cohomology are considered. Sufficient conditions for nontriviality in terms of dynamical properties of generators of the holonomy groups are found. The nontriviality for the Reeb foliations is shown; t...

Chaotic foliations generalize Devaney’s concept of chaos for dynamical systems. The property of a foliation to be chaotic is transversal, i.e, depends on the structure of the leaf space of the foliation. The transversal structure of a Cartan foliation is modeled on a Cartan manifold. The problem of investigating chaotic Cartan foliations is reduced...

Mathematical model for macromolecule catalytic conversion in a flow reactor includes four interconnected numerical calculations of different scales for the following phenomena: effect of increasing the concentration of coke grains and their size (nanometers, scale of coke particles) on porosity, tortuosity, and specific area of the catalyst computi...

In this paper, we present an algorithm for the numerical simulation of reactive transport at the pore scale to facilitate observation of pore space and rock matrix evolution. Moreover, simulation at the pore scale opens up the possibility of estimating changes in the transport properties of rocks, such as permeability and tortuosity. To quantitativ...

The definition of the Reeb foliation depends upon two real functions satisfying certain conditions. All these foliations are pairwise homeomorphic and have trivial Godbillon-Vey class. We construct explicit examples of the Reeb foliations that are not diffeomorphic. For this purpose we show that a modified Godbillon-Vey class defined by Losik is no...

Texture evolution of alumina hydrotreating catalyst was theoretically modeled using geometrical characteristics calculated via Monte-Carlo methods and methods of the graph theory. In the prescribed model deactivation was specified by monotonic increase of alumina grain radius, which imitated deposition of coke and metal species onto the pore surfac...

A new model describing the evolution of sorptive and textural properties of a CaO-based sorbent during repetitive sorption/regeneration cycles has been developed. The proposed model considers the morphology of nascent monodisperse CaO and the sintering of sorbent grains upon the assumption of the surface mass-transfer mechanism. In addition, the ob...

Following Losik, for a codimension one foliation $\mathcal{F}$ on a smooth manifold $M$, two characteristic classes as elements of the cohomology $H^3(S(M/\mathcal{F})/\text{O}(1))$ and $H^2(S(M/\mathcal{F})/\text{GL}(1,\mathbb{R}))$, where $S(M/\mathcal{F})$ is the bundle of frames of infinite order over the leaf space $M/\mathcal{F}$, are conside...

Evolution of alumina catalyst texture during macromolecule conversion with an emphasis on heavy oil hydroprocessing was theoretically estimated using geometrical characteristics of the porous media that were in turn calculated via Monte-Carlo methods and methods of the graph theory. Two types of alumina texture have been modeled: unimodal mesoporou...

In order to study the effect of the micro-CT scan resolution and size on the accuracy of up-scaled digital rock property estimation of core samples Bentheimer sandstone images with the resolution varying from 0.9 μm to 24 μm are used. We statistically show that the correlation length of the pore-to-matrix distribution can be reliably determined for...

Due to the apparatus restrictions the resolution of the micro-CT scans of rock samples and the size of the 3D image are strictly connected. Thus improve in the resolution giving more detailed representation of the rock structure reduce the size of the sample, so that it goes below the representative volume for the estimation of a particular propert...

The evolution of sorptive and textural properties of CaO-based sorbents during repetitive sorption/regeneration cycles has been mathematically simulated. The proposed model takes into account the morphology of nascent CaO, sorbent sintering physics and CO2 sorption kinetics. The results show that the model is in good agreement with the experimental...

Complete Riemannian metrics with holonomy group G 2 on manifolds obtained by deformation of cones over S 3 × S 3 are constructed.

We discuss the study of topological characteristics of random fields that are used for numerical simulation of oil and gas reservoirs and numerical algorithms (see arXiv:1302.3669), for computing such characteristics, for which we demonstrate results of their applications.

We present an algorithm for computing the main topological characteristics of three-dimensional bodies. The algorithm is based on a discretization of Morse theory and uses discrete analogs of smooth functions with only nondegenerate (Morse) and the simplest degenerate critical points.

Complete Riemannian metrics with holonomy group $G_2$ are constructed on the manifolds obtained by deformations of cones over $S^3 \times S^3$.

A system of differential equations with 5 unknowns is fully investigated; this system is equivalent to the existence of a parallel Spin(7)-structure on a cone over a 3-Sasakian manifold. A continuous one-parameter family of solutions to this system is explicitly constructed; it corresponds to metrics with a special holonomy group, SU(4), which gene...

Causal properties of Lorentzian symmetric spaces are investigated in the paper. The global hyperbolicity of the Cahen--Wallach Lorentzian symmetric spaces is proved. Comment: 9 pages

We construct Riemannian metrics of positive Ricci curvature on some moment-angle manifolds. In particular, we construct a nonformal moment-angle Riemannian manifold of positive Ricci curvature. Keywordspositive Ricci curvature–moment-angle manifold–quasitoric manifold

We completely explore the system of ODE's which is equivalent to the existence of a parallel $Spin(7)$-structure on the cone over a 7-dimensional 3-Sasakian manifold. The one-dimensional family of solutions of this system is constructed. The solutions of this family correspond to metrics with holonomy SU(4) which generalize the Calabi metrics. Comm...

We prove that each special Lorentzian holonomy group (with the exception of those including the isotropy groups of K\"ahler symmetric spaces with rank greater than one) can be realized as the holonomy group of a globally hyperbolic Lorentzian manifold. Comment: 17 pages

We prove that each special Lorentzian holonomy group (with the exception of those including the isotropy groups of Kähler symmetric spaces) can be realized as the holonomy group of a globally hyperbolic Lorentzian manifold.

We construct metrics with the holonomy group SU(2) on the tangent bundles of weighted complex projective lines and give a geometric description of the moduli space of special Kahler metrics on a K3-surface in the neighborhood of the flat orbifold $T^4/Z_3$.

We complete the study of the existence of Riemannian metrics with Spin(7) holonomy that smoothly resolve standard cone metrics on noncompact manifolds and orbifolds related to 7-dimensional 3-Sasakian spaces.

We construct complete noncompact Riemannian metrics with G 2-holonomy on noncompact orbifolds that are ℝ3-bundles with the twistor space as a spherical fiber.

We prove that there is a T 2-invariant Riemannian metric of positive Ricci curvature on every four-dimensional simply connected T 2-manifold.

We construct some complete Spin(7)-holonomy Riemannian metrics on the noncompact orbifolds that are ℝ4-bundles with an arbitrary 3-Sasakian spherical fiber M. We prove the existence of the smooth metrics for M = S 7 and M = SU(3)/U(1) which were found earlier only numerically.

We construct metrics with the holonomy group SU(2) on the tangent bundles of weighted complex projective lines. We give a geometric description of a neighborhood of the moduli space of special Kahler metrics on a K3-surface.

We construct a family of four-dimensional smooth Ricci-flat Riemann orbifolds of cohomogeneity two which possess the structure of complex line bundles.

An infinite family of pairwise nonhomeomorphic 13-dimensional positively curved manifolds is constructed