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## Prediction of viscosity-density dependence of liquid methane+n-butane+n-pentane mixtures using the molecular dynamics method and empirical correlations

We present a study of viscosities of *n*-pentane and binary and ternary methane–*n*-butane–*n*-pentane mixtures in liquid state at the temperature 360 K by the non-equilibrium molecular dynamics simulations with a modified fully flexible version of the all-atom TraPPE-EH force field. The Batchinski correlation is used to describe the viscosities of pure *n*-pentane. The calculated viscosity-density dependence for liquid *n*-pentane is in agreement with the experimental data. We show that the viscosity-volume dependencies of liquid binary and ternary mixtures can be fitted by the Batchinski's equation as well, and the coefficients for the mixtures are obtained by linear mixing of the coefficients for pure components. The model can be used for the interpretation and interpolation of the experimental data on viscosities of hydrocarbon liquids. The Batchinski-like behavior of viscosity of liquid mixtures in some density range can be used as a test for more complex correlations, which we show by comparing the hard sphere correlation and the expanded fluid correlation for hydrocarbons.

Within the framework of the Lagrangian approach a method for describing a wave packet on the surface of an infinitely deep, viscous fluid is developed. The case, in which the inverse Reynolds number is of the order of the wave steepness squared is analyzed. The expressions for fluid particle trajectories are determined, accurate to the third power of the steepness. The conditions, under which the packet envelope evolution is described by the nonlinear Schrödinger equation with a dissipative term linear in the amplitude, are determined. The rule, in accordance with which the term of this type can be correctly added in the evolutionary equation of an arbitrary order is formulated.

Proof-of-concept results are presented on the application of molecular modeling and simulation to the gas extraction problems. Both hydrocarbon mixtures and gas hydrates in porous media are considered.

Standing surface waves in a viscous infinite-depth fluid are studied. The solution of the problem is obtained in the linear and quadratic approximations. The case of long, as compared with the boundary layer thickness, waves is analyzed in detail. The trajectories of fluid particles are determined and an expression for the vorticity is derived.

In the XXI century the Arctic region is a matter of huge interest of many parties, including not only countries, but also large companies and international organisations. Fragile environment, influence of climate change, technological progress, rich resource base and unresolved border

disputes guarantee attention to the territory. However, even considering those variables, we believe that system analysis is more relevant, giving an opportunity to see the whole picture instead of fragments and local issues. The main question posed in this work is how to find balance between common and specific, general and individual in the Arctic, and the authors believe they succeeded in solving this problem. We believe that understanding of the Arctic is only possible when taking into consideration its history, geography, environment, legal issues and economic prospects. In other words, the only approach possible needs to cover all the regional issues and analyze these important factors, which is provided by the new institutional economics, through the union of fundamental and applied science.

The comparison methodology for the use of integrated indicators of economic efficiency of projects for the development of hydrocarbon reserves in the formation of the resource base in a planned and a market economy in Russia. Case studies expert decision-making showed that economic sections of existing regulations in the field of subsurface hydrocarbons need to be revised. The universal criterion of economic justification of rational variants of development of hydrocarbon reserves as the development of facilities, and on the field as a whole, which provides consensus interests of the state and subsoil user. Project performance indicators provides a clear economic characteristics of such concepts as "selective development" and " hard to recover reserves"

A model for organizing cargo transportation between two node stations connected by a railway line which contains a certain number of intermediate stations is considered. The movement of cargo is in one direction. Such a situation may occur, for example, if one of the node stations is located in a region which produce raw material for manufacturing industry located in another region, and there is another node station. The organization of freight traﬃc is performed by means of a number of technologies. These technologies determine the rules for taking on cargo at the initial node station, the rules of interaction between neighboring stations, as well as the rule of distribution of cargo to the ﬁnal node stations. The process of cargo transportation is followed by the set rule of control. For such a model, one must determine possible modes of cargo transportation and describe their properties. This model is described by a ﬁnite-dimensional system of diﬀerential equations with nonlocal linear restrictions. The class of the solution satisfying nonlocal linear restrictions is extremely narrow. It results in the need for the “correct” extension of solutions of a system of diﬀerential equations to a class of quasi-solutions having the distinctive feature of gaps in a countable number of points. It was possible numerically using the Runge–Kutta method of the fourth order to build these quasi-solutions and determine their rate of growth. Let us note that in the technical plan the main complexity consisted in obtaining quasi-solutions satisfying the nonlocal linear restrictions. Furthermore, we investigated the dependence of quasi-solutions and, in particular, sizes of gaps (jumps) of solutions on a number of parameters of the model characterizing a rule of control, technologies for transportation of cargo and intensity of giving of cargo on a node station.

Event logs collected by modern information and technical systems usually contain enough data for automated process models discovery. A variety of algorithms was developed for process models discovery, conformance checking, log to model alignment, comparison of process models, etc., nevertheless a quick analysis of ad-hoc selected parts of a journal still have not get a full-fledged implementation. This paper describes an ROLAP-based method of multidimensional event logs storage for process mining. The result of the analysis of the journal is visualized as directed graph representing the union of all possible event sequences, ranked by their occurrence probability. Our implementation allows the analyst to discover process models for sublogs defined by ad-hoc selection of criteria and value of occurrence probability

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.