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## Magnetohydrodynamic Modeling of the Solar Wind Key Parameters and Current Sheets in the Heliosphere: Radial and Solar Cycle Evolution

We develop an axisymmetric numerical MHD model that allows us to investigate the spatial characteristics of the interplanetary magnetic field (IMF) and key solar wind plasma parameters from 20 to 400 solar radii over all heliolatitudes. The study is aimed at an analysis of the evolution of the spatial structure of the heliosphere through the solar cycle. We consider various combinations of the relative input of the quadrupole and dipole harmonics of the solar magnetic field to imitate the solar cycle. Self-consistent solutions for the IMF, electric current, solar wind speed, density, thermal pressure, and temperature in the solar wind are obtained. The spatial evolution of the IMF and properties of quasi-stationary current sheets (QCSs) are analyzed during different phases of the solar cycle. It is shown that a classic low-latitude heliospheric current sheet is formed in the solar wind as a part of the system of longitudinal and latitudinal electric currents symmetric in the northern and southern hemispheres only during solar minimum. While the quadrupole magnetic field increases, the second QCS appears. The model successfully describes a smooth transition from the state of the fast solar wind at high heliolatitudes and the slow solar wind at low heliolatitudes at solar minimum to the solar wind speed of the same values in a wide range of heliolatitudes at solar maximum. It reproduces the actively debated phenomenon of the south–north asymmetry of the IMF in the heliosphere and shows the distribution of thermal plasma parameters consistent with observations.

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.

The correlation tensors of magnetic field in a two-dimensional chaotic flow of conducting fluid are studied. It is shown that there is a stage of resistive evolution where the field correlators grow exponentially with time. The two-and four-point field correlation tensors are computed explicitly in this stage in the framework of Batchelor–Kraichnan–Kazantsev model. They demonstrate strong temporal intermittency of the field fluctuations and high level of non-Gaussianity in spatial field distribution

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 ability of phase mixing to provide eﬃcient damping of Alfvén waves even in weakly dissipative plasmas made it a popular mechanismforexplainingthesolarcoronalheating.Initiallyitwasstudiedintheequilibriumconﬁgurationswiththestraightmagnetic ﬁeldlinesandtheAlfvénspeedonlyvaryinginthedirectionperpendiculartothemagneticﬁeld.LatertheanalysisoftheAlfvénwave phase mixing was extended in various directions. In particular it was studied in two-dimensional planar magnetic plasma equilibria. Analytical investigation was carried out under the assumption that the wavelength is much smaller than the characteristic scale of the background quantity variation. This assumption enabled using the Wentzel, Kramers, and Brillouin (WKB) method. When it is not satisﬁed the study was only carried out numerically. In general, even the wave propagation in a one-dimensional inhomogeneous equilibrium can be only studied numerically. However there is one important exception, so-called non-reﬂective equilibria. In these equilibria the wave equation with the variable phase speed reduces to the Klein-Gordon equation with constant coeﬃcients. In this paper we apply the theory of non-reﬂective wave propagation to studying the Alfvén wave phase mixing in two-dimensional planar magnetic plasma equilibria. Using curvilinear coordinates we reduce the equation describing the Alfvén wave phase mixing to the equationthatbecomesaone-dimensionalwaveequationintheabsenceofdissipation.Thisequationisfurtherreducedtotheequation which is the one-dimensional Klein-Gordon equation in the absence of dissipation. Then we show that this equation has constant coeﬃcients when a particular relation between the plasma density and magnetic ﬁeld magnitude is satisﬁed. Using the derived Klein- Gordon-type equation we study the phase mixing in various non-reﬂective equilibria. We emphasise that our analysis is valid even when the wavelength is comparable with the characteristic scale of the background quantity variation. In particular, we study the Alfvén wave damping due to phase mixing in an equilibrium with constant plasma density and exponentially divergent magnetic ﬁeld lines. We conﬁrm the result previously obtained in the WKB approximation that there is enhanced Alfvén wave damping in this equilibrium with the damping length proportional to ln(Re), where Re is the Reynolds number. Our theoretical results are applied to heating of coronal plumes. We show that, in spite of enhanced damping, Alfvén waves with periods of the order of one minute can be eﬃciently damped in the lower corona, at the height about 200 Mm, only if the shear viscosity is increased by about 6 orders of magnitude in comparison with its value given by the classical plasma theory. We believe that such increase of the shear viscosity can be provided by the turbulence.

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.

The Handbook of CO₂ in Power Systems' objective is to include the state-of-the-art developments that occurred in power systems taking CO₂ emission into account. The book includes power systems operation modeling with CO₂ emissions considerations, CO₂ market mechanism modeling, CO₂ regulation policy modeling, carbon price forecasting, and carbon capture modeling. For each of the subjects, at least one article authored by a world specialist on the specific domain is included.