Inhomogeneous Coupling in Two-Channel Asymmetric Simple Exclusion Processes

Asymmetric exclusion processes for particles moving on parallel channels with inhomogeneous coupling are investigated theoretically. Particles interact with hard-core exclusion and move in the same direction on both lattices, while transitions between the channels is allowed at one specific location in the bulk of the system. An approximate theoretical approach that describes the dynamics in the vertical link and horizontal lattice segments exactly but neglects the correlation between the horizontal and vertical transport is developed. It allows us to calculate stationary phase diagrams, particle currents and densities for symmetric and asymmetric transitions between the channels. It is shown that in the case of the symmetric coupling there are three stationary phases, similarly to the case of single-channel totally asymmetric exclusion processes with local inhomogeneity. However, the asymmetric coupling between the lattices lead to a very complex phase diagram with ten stationary-state regimes. Extensive Monte Carlo computer simulations generally support theoretical predictions, although simulated stationary-state properties slightly deviate from calculated in the mean-field approximation, suggesting the importance of correlations in the system. Dynamic properties and phase diagrams are discussed by analyzing constraints on the particle currents across the channels

Parallel Coupling of Symmetric and Asymmetric Exclusion Processes

A system consisting of two parallel coupled channels where particles in one of them follow the rules of totally asymmetric exclusion processes (TASEP) and in another one move as in symmetric simple exclusion processes (SSEP) is investigated theoretically. Particles interact with each other via hard-core exclusion potential, and in the asymmetric channel they can only hop in one direction, while on the symmetric lattice particles jump in both directions with equal probabilities. Inter-channel transitions are also allowed at every site of both lattices. Stationary state properties of the system are solved exactly in the limit of strong couplings between the channels. It is shown that strong symmetric couplings between totally asymmetric and symmetric channels lead to an effective partially asymmetric simple exclusion process (PASEP) and properties of both channels become almost identical. However, strong asymmetric couplings between symmetric and asymmetric channels yield an effective TASEP with nonzero particle flux in the asymmetric channel and zero flux on the symmetric lattice. For intermediate strength of couplings between the lattices a vertical cluster mean-field method is developed. This approximate approach treats exactly particle dynamics during the vertical transitions between the channels and it neglects the correlations along the channels. Our calculations show that in all cases there are three stationary phases defined by particle dynamics at entrances, at exits or in the bulk of the system, while phase boundaries depend on the strength and symmetry of couplings between the channels. Extensive Monte Carlo computer simulations strongly support our theoretical predictions.Comment: 16 page

ПРОБЛЕМИ ІДЕНТИЧНОСТІ Й ТРАДИЦІЇ У МОНУМЕНТАЛЬНОМУ ЖИВОПИСІ КИРИЛІВСЬКОЇ ЦЕРКВИ XII ТА XIX СТ. НА ПРИКЛАДІ АНГЕЛЬСЬКИХ ЧИНІВ. (Identity and Tradition Issues in Monumental Painting of XII and XIX Centuries of St. Cyril's Church by an Example of Angelic Ranks.)

Статтю присвячено осмисленню проблеми ідентичності та традиції у стінописі XII та ХІХст. Кирилівської церкви на прикладі зображення чинів небесної ієрархії. Аналізуються особливості, спільні та відмінні риси зображень ангельських чинів Кирилівської церкви XII та XIX cm. (The article is devoted to understanding the identity and tradition issues in murals ofXII and XIX centuries of St. Cyril's Church by an Example of celestial hierarchy ranks images. The author analyzes the characteristics, differences and similarities of angelic ranks images of St. Cyril's Church in the XII and XIX centuries.

Spontaneous Symmetry Breaking in Two-Channel Asymmetric Exclusion Processes with Narrow Entrances

Multi-particle non-equilibrium dynamics in two-channel asymmetric exclusion processes with narrow entrances is investigated theoretically. Particles move on two parallel lattices in opposite directions without changing them, while the channels are coupled only at the boundaries. A particle cannot enter the corresponding lane if the exit site of the other lane is occupied. Stationary phase diagrams, particle currents and densities are calculated in a mean-field approximation. It is shown that there are four stationary phases in the system, with two of them exhibiting spontaneous symmetry breaking phenomena. Extensive Monte Carlo computer simulations confirm qualitatively our predictions, although the phase boundaries and stationary properties deviate from the mean-field results. Computer simulations indicate that several dynamic and phase properties of the system have a strong size dependency, and one of the stationary phases predicted by the mean-field theory disappears in the thermodynamic limit.Comment: 13 page

Theoretical Investigation of Totally Asymmetric Exclusion Processes on Lattices with Junctions

Totally asymmetric simple exclusion processes on lattices with junctions, where particles interact with hard-core exclusion and move on parallel lattice branches that at the junction combine into a single lattice segment, are investigated. A simple approximate theory, that treats the correlations around the junction position in a mean-field fashion, is developed in order to calculate stationary particle currents, density profiles and a phase diagram. It is shown that there are three possible stationary phases depending on the state of each of the lattice branch. At first-order phase boundaries, where the density correlations are important, a modified phenomenological domain-wall theory, that accounts for correlations, is introduced. Extensive Monte Carlo computer simulations are performed to investigate the system, and it is found that they are in excellent agreement with theoretical predictions.Comment: 16 pages, 7 figure

Dynamic Boundaries in Asymmetric Exclusion Processes

We investigate the dynamics of a one-dimensional asymmetric exclusion process with Langmuir kinetics and a fluctuating wall. At the left boundary, particles are injected onto the lattice; from there, the particles hop to the right. Along the lattice, particles can adsorb or desorb, and the right boundary is defined by a wall particle. The confining wall particle has intrinsic forward and backward hopping, a net leftward drift, and cannot desorb. Performing Monte Carlo simulations and using a moving-frame finite segment approach coupled to mean field theory, we find the parameter regimes in which the wall acquires a steady state position. In other regimes, the wall will either drift to the left and fall off the lattice at the injection site, or drift indefinitely to the right. Our results are discussed in the context of non-equilibrium phases of the system, fluctuating boundary layers, and particle densities in the lab frame versus the frame of the fluctuating wall.Comment: 13 page

Balance network of asymmetric simple exclusion process

We investigate a balance network of the asymmetric simple exclusion process (ASEP). Subsystems consisting of ASEPs are connected by bidirectional links with each other, which results in balance between every pair of subsystems. The network includes some specific important cases discussed in earlier works such as the ASEP with the Langmuir kinetics, multiple lanes and finite reservoirs. Probability distributions of particles in the steady state are exactly given in factorized forms according to their balance properties. Although the system has nonequilibrium parts, the expressions are well described in a framework of statistical mechanics based on equilibrium states. Moreover, the overall argument does not depend on the network structures, and the knowledge obtained in this work is applicable to a broad range of problems

The development of blockchain technology in Russia : outlook and trends

Purpose: The article addresses the issue of new scientific decisions shaping with respect to the study of problems, current trends and perspectives of blockchain technology usage in the Russian Federation. Design/methodology/approach: To achieve the objectives of this study the increasing interest to blockchain technology in Russia was discussed. Findings: The article determined main problems in blockchain technology which includes gaps in legislative regulation; the existence of a considerable number of projects that are undergoing the development stage and that have not proved own economic feasibility yet; incomplete understanding of the blockchain spheres’ implementation by state officials, society and business representatives as well as expected outcomes according to the amount and time of their receiving; disputes on cryptocurrencies turnover in the country’s territory and their influence in the national economy. Practical implications: The study has demonstrated the interest growth mainly by businesses to the usage of blockchain technology in order to improve own competitiveness and to obtain additional benefits, including the form of their profits. Originality/value: The research has also determined the area of further key studies in blockchain technology usage in Russia and the world.peer-reviewe

Fatty oil accumulation in vegetable soybean seeds and its thin-layer chromatography

Received: February 23rd, 2021 ; Accepted: May 5th, 2021 ; Published: May 20th, 2021 ; Correspondence: [email protected] paper studies the accumulation of crude oil (triacylglycerides, monoacylglycerides, diacylglycerides, free fatty acids, phospholipids, tocopherols, pigments, sterols, waxes) in soybean vegetable samples. Samples were taken from two groups: grown in an experimental field and in protected ground of the Federal Scientific Center for Vegetable Growing in the Moscow Region. Both groups were observed in the phase of technical ripeness and in the phase of complete biological ripeness (finally ripe seeds). Soxhlet method as arbitration in analysis was used as suitable for the extraction of lipophilic substances. It was determined that the fat content in the technical ripeness phase in most soybean samples averaged 10.5%. In the phase of biological ripeness, the highest accumulation of fatty oil was observed in Hidaka and Nordic (17.6%). The oil content in vegetable forms of soybeans was consistently lower than that of grain varieties: in the phases of technical and biological ripeness by 55.6% and 22.0% (in relative values) respectively. Thus, he accumulation of oil in seeds is determined mainly genetically. The refractive index of vegetable and oil soybean was established equal on average 1.4755. According to this finding the soybean oil can be classified as semi-drying. Thin layer chromatography (TLC) was used to study the lipophilic components of soybean fatty oil. It was found experimentally that the best separation of the components is achieved using an eluent system: carbon tetrachloride: chloroform in a 2: 3 ratio. It was found that the main fatsoluble compounds are the following (in order of increasing Rf in the chromatogram): phospholipids, monoacylglycerides, triacylglycerides, tocopherols, fatty acid esters. As a finding of the research vegetable soybean cultivated at 55 °N in both technical and biological ripeness phases significantly accumulate crude oil in the seeds. This crude oil contained ω-6, ω-3, phospholipids, and vitamin E

Two-Channel Totally Asymmetric Simple Exclusion Processes

Totally asymmetric simple exclusion processes, consisting of two coupled parallel lattice chains with particles interacting with hard-core exclusion and moving along the channels and between them, are considered. In the limit of strong coupling between the channels, the particle currents, density profiles and a phase diagram are calculated exactly by mapping the system into an effective one-channel totally asymmetric exclusion model. For intermediate couplings, a simple approximate theory, that describes the particle dynamics in vertical clusters of two corresponding parallel sites exactly and neglects the correlations between different vertical clusters, is developed. It is found that, similarly to the case of one-channel totally asymmetric simple exclusion processes, there are three stationary state phases, although the phase boundaries and stationary properties strongly depend on inter-channel coupling. An extensive computer Monte Carlo simulations fully support the theoretical predictions.Comment: 13 pages, 10 figure