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## Earth's Magnetotail as the Reservoir of Accelerated Single‐ and Multicharged Oxygen Ions Replenishing Radiation Belts

Acceleration of single‐ and multi‐charged oxygen ions in the perturbed Earth's magnetotail is investigated as the possible source of energetic heavy ions in the ring current. The numerical model is developed that allows evaluating the acceleration of oxygen ions O+‐O+8 in two possible scenarios of characteristic perturbations: (A) passage of multiple dipolarization fronts in the magnetotail; (B) passage of fronts followed by electromagnetic turbulence. It is shown that acceleration processes depend on particle charges as well as characteristic time scales of induced electric field variations. Maximum energies gained by oxygen ions correlate with values of their charges. Our simulations show that all kinds of single‐ and multiply charged heavy particles can be efficiently accelerated during multiple dipolarizations processes of the type (A) from initial energies 12 keV to maximum energies about several MeV. The gain of energies of heavy ions under the (B) scenario of magnetospheric perturbations is about 10% higher than in (A) scenario. The shapes of obtained in the model energy spectra were shown to be in agreement with experimental spectra in the range of L‐shells corresponding to ring/radiation belts. Therefore we conclude that the Earth's magnetotail can play the role of the depot where oxygen ions of both ionospheric and solar wind origin can be effectively accelerated during magnetic substorms to energies about several MeV and then populate the ring current and radiation belts of the Earth.

We introduce a new asymptotic invariant of magnetic fields, namely, the quadratic (and polynomial) helicity. We construct a higher asymptotic invariant of a magnetic field. We also discuss various problems that can be solved by using the magnetic helicity invariant.

The possibility of long-term operation of the equipment on satellites is closely related to the dynamics of the electron fluxes of the Earth’s external radiation belt (SRW), an increase in radiation loads can lead to disruption of the operation of electronic systems: the appearance of surface currents and the appearance of spontaneous electric discharges. The structure of the electron flow of the SRWS is formed under the influence of a number of competing processes of transportation, acceleration and particle loss that occur inside the magnetosphere and at its boundaries under the influence of the solar wind (NE). Significant variations in the SREP electron flux associated with the restructuring of the structure of the SV fluxes cause significant changes in the structure of the energy spectra of the SRPS electrons, which leads to a change in radiation dose loads for spacecraft equipment. The paper analyzes the dynamics of the energy spectra of the SCL electrons for the period of the minimum solar activity of the 23rd solar cycle in 2007 and in 2009 and shows the effect of two different sources of SW on the formation of the flows of SCW electrons, high-speed and slow SW flows.

The generalized Wiedemann-Franz law for a nonisothermal quasi-neutral plasma with developedion-acoustic turbulence and Coulomb collisions has been proven. The results obtained are used to explain the anomalously low thermal conductivity in the chromosphere-corona transition region of the solar atmosphere. Model temperature distributions in the lower corona and the transition region that correspond to well-known experimental data have been determined. The results obtained are useful for explaining the abrupt change in turbulent-plasma temperature at distances smaller than the particle mean free path.

The system of equations for average velocity and Reynolds stresses are examined supposing the smallness of diffusive, relaxation and viscous processes. Such turbulent state is named ideal. It is shown that the spectrum of turbulence has the form of spectrum of absolutely black body.

Within the framework of model calculations the possibility of occurrence of the ion-acoustic oscillation instability in a plasma without current and particle fluxes, but with an anisotropic distribution function, which corresponds to heat flux is shown. The model distribution function was selected taking into account the medium conditions. The increment of ion-acoustic oscillation is investigated as functional of the distribution function parameters. The threshold condition for the anisotropic part of the distribution function, under which the build-up of ion-acoustic oscillation with the wave vector opposite to the heat flux begins is studied. The critical heat flux, which corresponds to the threshold of ion-acoustic instability, is determined. For the solar conditions, the critical heat flux proved to be close to the heat flux from the corona into the chromosphere on the boundary of the transition region. The estimations show that outside of active regions and even in active regions with weaker magnetic fields ion-acoustic turbulence can be responsible for the formation of the sharp temperature jump. The generalized Wiedemann-Franz law for a non-isothermic quasi-neutral plasma with developed ion-acoustic turbulence is discussed. This law determines the relationship between electrical and thermal conductivities in a plasma with well-developed ion-acoustic turbulence. The anomalously low thermal conductivity responsible to the formation of high temperature gradients in the zone of the temperature jump is explained. The results are used to explain some properties of stellar atmosphere transition regions.

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.