### Article

## Structure of Current Sheets with Quasi-Adiabatic Dynamics of Particles in the Solar Wind

Within the self-consistent hybrid model based on the quasi-adiabatic approximation of the proton

dynamics, a fine structure of strong current sheets (SCSs) in the solar wind has been investigated, including

the heliospheric current sheet. The motion of electrons is fast and considered in the Boltzmann approximation.

The simulation results have been shown that the SCS profiles have a multiscale enclosed structure with

a narrow central current sheet that is enclosed in a wider sheet, similar to the heliospheric current sheet surrounded

by the plasma sheet. The features of the SCS structure are determined by the relative contributions

of the current of demagnetized protons in serpentine orbits and drift currents of electrons. The model predicts

and describes the properties of SCSs observed by spacecraft. It has been shown that the multiscale structure

of current sheets is an inherent intrinsic property of current sheets in the solar wind.

We investigate quasi-adiabatic dynamics of charged particles in strong current sheets (SCSs) in the solar wind, including the heliospheric current sheet (HCS), both theoretically and observationally. A self-consistent hybrid model of an SCS is developed in which ion dynamics is described at the quasi-adiabatic approximation, while the electrons are assumed to be magnetized, and their motion is described in the guiding center approximation. The model shows that the SCS profile is determined by the relative contribution of two currents: (i) the current supported by demagnetized protons that move along open quasi-adiabatic orbits, and (ii) the electron drift current. The simplest modeled SCS is found to be a multi-layered structure that consists of a thin current sheet embedded into a much thicker analog of a plasma sheet. This result is in good agreement with observations of SCSs at ∼1 au. The analysis of fine structure of different SCSs, including the HCS, shows that an SCS represents a narrow current layer (with a thickness of ∼104 km) embedded into a wider region of about 105 km, independently of the SCS origin. Therefore, multi-scale structuring is very likely an intrinsic feature of SCSs in the solar wind.

Numerous studies of the current sheets (CS) in the Earth’s magnetotail showed that quasi-adiabatic ion dynamics plays an important role in the formation of complicated multilayered current structures. In order to check whether the similar mechanisms operate in the Martian magnetotail, we analyzed 80 CS crossings using MAVEN measurements on the nightside of Mars at radial distances ~1.0–2.8RM. We found that CS structures experience similar dependence on the value of the normal component of the magnetic field at the neutral plane (BN) and on the ratio of the ion drift velocity outside the CS to the thermal velocity (VT/VD) as it was observed for the CSs in the Earth’s magnetotail. For the small values of BN, a thin and intense CS embedded in a thicker one is observed. The half-thickness L of this layer is ~30–100 km ≤ ρH+ (ρH+ is a gyroradius of thermal protons outside the CS). With the increase of BN, the L also increases up to several hundred kilometers (~ρO+, ρO2+), the current density decreases, and the embedding feature disappears. Our statistical analysis showed a good agreement between L values observed by MAVEN and the CS scaling obtained from the quasi-adiabatic model, if the plasma characteristics in Martian CSs are used as input parameters. Thus, we may conclude that in spite of the differences in magnetic topology, ion composition, and plasma thermal characteristics observed in the Earth’s and Martian magnetotails, similar quasi-adiabatic mechanisms contribute to the formation of the CSs in the magnetotails of both planets

In this work, we present for the first time the Lyman *α* intensities measured by Voyager 1/UVS in 2003–2014 (at 90–130 AU from the Sun). During this period Voyager 1 measured the Lyman *α* emission in the outer heliosphere at an almost fixed direction close to the upwind (i.e.“ toward the interstellar flow). The data show an unexpected behavior in 2003–2009: the ratio of observed intensity to the solar Lyman *α* flux is almost constant. Numerical modeling of these data is performed in the frame of a state-of-the-art self-consistent kinetic-MHD model of the heliospheric interface. The model results, for various interstellar parameters, predict a monotonic decrease of intensity not seen in the data. We propose two possible scenarios that explain the data qualitatively. The first is the formation of a dense layer of hydrogen atoms near the heliopause. Such a layer would provide an additional backscattered Doppler-shifted Lyman *α* emission, which is not absorbed inside the heliosphere and may be observed by Voyager. About 35 R of intensity from the layer is needed. The second scenario is an external nonheliospheric Lyman *α* component, which could be galactic or extragalactic. Our parametric study shows that ∼25 R of additional emission leads to a good qualitative agreement between the Voyager 1 data and the model results.

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.