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## Calculation of viscosities of branched alkanes from 0.1 to 1000 MPa by molecular dynamics methods using COMPASS force field

Shear viscosity is one of the key subjects of molecular modeling studies since this quality is used in the development of lubricants. In this paper, we use molecular dynamics methods to predict viscosity dependence on pressure up to 1000 MPa for 2,2,4-trimethylhexane. The COMPASS class II force field is used to determine atomic interactions in the model. The shear viscosity is calculated using Green-Kubo and Müller-Plathe methods. To achieve the convergence of the Green-Kubo integral, the time decomposition method is used. The approach is validated by 2,2,4-trimethylpentane for which experimental data are available. The calculated 2,2,4-trimethylhexane viscosity coefficient dependence is fit by Tait-like equation and does not show super-Arrhenius behavior. The Tait fit matches the experiment produced by Scott Bair for the pressures up to 500 MPa within the accuracy of the methods.

Strong interaction among charge carriers can make them move like viscous fluid. Here we explore alternating current (AC) effects in viscous electronics. In the Ohmic case, incompressible current distribution in a sample adjusts fast to a time-dependent voltage on the electrodes, while in the viscous case, momentum diffusion makes for retardation and for the possibility of propagating slow shear waves. We focus on specific geometries that showcase interesting aspects of such waves: current parallel to a one-dimensional defect and current applied across a long strip. We find that the phase velocity of the wave propagating along the strip respectively increases/decreases with the frequency for no-slip/no-stress boundary conditions. This is so because when the frequency or strip width goes to zero (alternatively, viscosity go to infinity), the wavelength of the current pattern tends to infinity in the no-stress case and to a finite value in a general case. We also show that for DC current across a strip with no-stress boundary, there only one pair of vortices, while there is an infinite vortex chain for all other types of boundary conditions.

We present a study of viscosities of methane, n-butane and their mixtures by the non-equilibrium molecular dynamics simulations and derivation of semiempirical volume-based mixing rules. The Batchinski equation $\eta = C / (V - b)$ is used to describe the viscosities of pure components, with parameters fitted to reproduce molecular dynamics results. Cubic root, Arrhenius and Batchinski mixing rules are tested for mixtures. The viscosities of pure components used in mixing equations are expressed as functions of volume of component rather than pressure. This allows to apply the mixing rules to metastable and stable liquids, dense supercritical fluids and solutions of gas in liquid. To obtain volumes of components in mixture, molecular dynamics method is used. The mixing rules predictions are compared against direct non-equilibrium molecular dynamics calculations of mixture viscosities. The best agreement with the molecular dynamics data is found when Batchinski mixing is used. The proposed viscosity model predictions are in agreement with the experimental data on viscosities of methane-butane mixtures. The model can be used for the interpretation and interpolation of the experimental data on viscosities of liquids, which is demonstrated on the example of methane + propane system.

Molecular modelling is used to calculate transport properties and to study relaxation of liquid n-triacontane (C30H62). The problem is important in connection with the behavior of liquid isolators in a pre-breakdown state. Two all-atom models and a united-atom model are used. Shear viscosity is calculated using the Green–Kubo formula. The force fields are compared with each other using the following criteria: the required time for one molecular dynamics step, the compliance of the main physical and transport properties with experimental values. The problem of the system equilibration is considered. The united-atom potential is used to model the n-triacontane liquid with an initial directional orientation. The time of relaxation to the disordered state, when all molecules orientations are randomized, are obtained. The influence of the molecules orientations on the shear viscosity value and the shear viscosity relaxation are treated.

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.