### Article

## Thin current sheets of sub‐ion scales observed by MAVEN in the Martian magnetotail.

Current sheets (CSs) play a crucial role in the storage and conversion of magnetic energy in

planetary magnetotails. Using high‐resolution magnetic field data from MAVEN spacecraft, we report

the existence of super thin current sheets (STCSs) in the Martian magnetotail. The typical half‐thickness of

the STCSs is ~5 km, and it is much less than the gyroradius of thermal protons (ρp). The STCSs are

embedded into a thicker sheet with L ≥ ρp forming a multiscale current configuration. The formation of

STCS does not depend on ion composition, but it is controlled by the small value of the normal component of

the magnetic field at the neutral plane (BN). A number of the observed multiscale CSs are located in the

parametric map close to the tearing‐unstable domain, and thus, the inner STCS can provide an additional

free energy to excite ion tearing mode in the Martian magnetotailThin Current Sheets

The Earth’s magnetosphere is an open dynamic system permanently interacting with the solar wind, i.e., the plasma flow from the Sun. Some plasma processes in the magnetosphere are of spontaneous explosive character, while others develop rather slowly as compared to the characteristic times of plasma particle motion in it. The large-scale current sheet in the magnetotail can be in an almost equilibrium state both in quiet periods and during geomagnetic perturbations, and its variations can be considered quasistatic. Thus, under some conditions, the magnetotail current sheet can be described as an equilibrium plasma system. Its state depends on various parameters, in particular, on those determining the dynamics of charged particles. Knowing the main governing parameters, one can study the structure and properties of the current sheet equilibrium. This work is devoted to the self-consistent modeling of the equilibrium thin current sheet (TCS) of the Earth’s magnetotail, the thickness of which is comparable with the ion gyroradius. The main objective of this work is to examine how the TCS structure depends on the parameters characterizing the particle dynamics and magnetic field geometry. A numerical hybrid self-consistent TCS model in which the tension of magnetic field lines is counterbalanced by the inertia of ions moving through the sheet is constructed. The ion dynamics is considered in the quasi-adiabatic approximation, while the electron motion, in the conductive fluid approximation. Depending on the values of the adiabaticity parameter κ (which determines the character of plasma particle motion) and the dimensionless normal component of the magnetic field , the following two scenarios are considered: (A) the adiabaticity parameter is proportional to the particle energy and = const and (B) the particle energy is fixed and the adiabaticity parameter is proportional to . The structure of the current sheet and particle dynamics in it are studied as functions of the parameters κ and . It is shown that, in scenario A, the current sheet thickness decreases with increasing adiabaticity parameter due to a decrease in the ion gyroradius. Accordingly, the radius of curvature of magnetic field lines decreases, which leads to an increase in the contribution of electron drift currents near the neutral plane z = 0. Numerical simulations demonstrate that current equilibria can exist if the adiabaticity parameter lies in the range . At κ ~ 0.7, the contribution of electron drift currents to the total current density is much larger than the contribution of ions and the ion motion becomes chaotic. At larger values of the adiabaticity parameter, no equilibrium solutions were found in the framework of the given one-dimensional model. Therefore, the value κ = 0.7 corresponds to the upper applicability limit of the quasi-adiabatic model of the current sheet. In scenario B, an increase in the parameter κ leads to the appearance of a large number of quasi-trapped ions in the current sheet, due to which the current sheet thickens and the amplitude of the current density decreases. As a result, equilibrium solutions exist in a much narrower range of the adiabaticity parameter, . Consequences of the existence of parametric boundaries of equilibrium solutions for the TCS under actual geomagnetic conditions are discussed.

We outline the history and development of the theory of thin current sheets in a collisionless space plasma from the early ideas of V L Ginzburg and S I Syrovatskii to the present day. We review the key achievements of the quasi- adiabatic theory, which provided insight into the fine structure of thin current sheets and enabled a comparison with experi- ment. This comparison showed the quasi-adiabatic approach to be more effective than the classical MHD approximation. With the development of the quasi-adiabatic theory in the last two decades, the existence of a number of new thin current sheet features, such as multi-scaling, metastability, and em- bedding, has been predicted and subsequently confirmed in situ; the role of individual particle populations in the forma- tion of the current sheet fine structure has also been investi- gated. The role of nonadiabatic effects in accelerating plasma beamlets interacting with current sheets is examined. Asym- metry mechanisms in thin current sheets in the presence of a magnetic shear component are described. A study is carried out of current sheet self-organization processes leading to the formation of a shear magnetic component consistent with currents flowing in the plasma. It is demonstrated that the ongoing development of the theory of thin current structures is a logical continuation of Syrovatskii's and Ginzburg's ideas on cosmic rays and reconnected current sheets in the solar corona.

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.