### Article

## Acceleration and particle transport in collisionless plasma in the process of dipolarization and nonstationary turbulence

In this paper, the particle acceleration processes around magnetotail dipolarization fronts (DFs) were reviewed. We summarize the spacecraft observations (including Cluster, THEMIS, MMS) and numerical simulations (including MHD, test-particle, hybrid, LSK, PIC) of these processes. Specifically, we (1) introduce the properties of DFs at MHD scale, ion scale, and electron scale, (2) review the properties of suprathermal electrons with particular focus on the pitch-angle distributions, (3) define the particle-acceleration process and distinguish it from the particle-heating process, (4) identify the particle-acceleration process from spacecraft measurements of energy fluxes, and (5) quantify the acceleration efficiency and compare it with other processes in the magnetosphere (e.g., magnetic reconnection and radiation-belt acceleration processes). We focus on both the acceleration of electrons and ions (including light ions and heavy ions). Regarding electron acceleration, we introduce Fermi, betatron, and non-adiabatic acceleration mechanisms; regarding ion acceleration, we present Fermi, betatron, reflection, resonance, and non-adiabatic acceleration mechanisms. We also discuss the unsolved problems and open questions relevant to this topic, and suggest directions for future studies.

The method of equivalent systems is used to simulate resonator slow-wave structures of beamplasma devices. A collisionless plasma is considered as a filler for the drift channel. The adequacy of the model is shown by comparing the calculation results with known experimental data. The dispersion characteristics of slow-wave systems are analyzed. The structure of the high-frequency unit of a beam-plasma traveling wave tube is developed, and the parameters of the tube are evaluated using the VEGA code.

Magnetic field dipolarizations are often observed in the magnetotail during substorms. These generally include three temporal scales: (1) actual dipolarization when the normal magnetic field changes during several minutes from minimum to maximum level; (2) sharp Bz bursts (pulses) interpreted as the passage of multiple dipolarization fronts with characteristic time scales < 1 min, and (3) bursts of electric and magnetic fluctuations with frequencies up to electron gyrofrequency occurring at the smallest time scales (≤ 1 s). We present a numerical model where the contributions of the above processes (1)-(3) in particle acceleration are analyzed. It is shown that these processes have a resonant character at different temporal scales. While O+ ions are more likely accelerated due to the mechanism (1), H+ ions (and to some extent electrons) are effectively accelerated due to the second mechanism. High-frequency electric and magnetic fluctuations accompanying magnetic dipolarization as in (3) are also found to efficiently accelerate electrons.

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.

Let G be a semisimple algebraic group whose decomposition into the product of simple components does not contain simple groups of type A, and P⊆G be a parabolic subgroup. Extending the results of Popov [7], we enumerate all triples (G, P, n) such that (a) there exists an open G-orbit on the multiple flag variety G/P × G/P × . . . × G/P (n factors), (b) the number of G-orbits on the multiple flag variety is finite.

I give the explicit formula for the (set-theoretical) system of Resultants of m+1 homogeneous polynomials in n+1 variables