### Article

## Current sheets in planetary magnetospheres

In this article we aim to highlight the problems related to the structure and stability of the

comparatively thin current sheets that were relatively recently discovered by space missions in

the magnetospheres of the Earth and planets, as well as in the solar wind. These magnetoplasma

structures are universal in collisionless cosmic plasmas and can play a key role in the processes

of storage and release of energy in the space environment. The development of a self-consistent

theory for these sheets in the Earth’s magnetosphere, where they were first discovered, has a long

and dramatic history. Solution of the problem of the thin current sheet structure and stability

become possible in the framework of a kinetic quasi-adiabatic approach required to explain their

embedding and metastability properties. It was found that the structure and stability of current

structures are completely determined by the nonlinear dynamics of plasma particles. Theoretical

models have been developed to predict many properties of these structures and interpret many

experimental observations in planetary magnetospheres and the heliosphere.

This paper describes modeling of spacecraft charging dynamics which is used in COULOMB-2 code in the case of spacecraft surface complex shape. The modeling of spacecraft charging is carried out via numerically solving the system of differential equations for time variations of local electric charge on every discrete element of the spacecraft surface. The presented computation results are obtained for spacecraft charging in hot magnetosphere plasma for several spacecraft design elements in a time interval of 20–10 000 s. The results are compared with the similar ones obtained with the NASCAP-2k and MUSCAT codes, and a good consistency was found.

Increasing the temporal resolution and instant coverage of velocity space of space plasma measurements is one of the key issues for experimentalists. Today, the top‐hat plasma analyzer appears to be the favorite solution due to its relative simplicity and the possibility to extend its application by adding a mass‐analysis section and an electrostatic angular scanner. Similarly, great success has been achieved in MMS mission using such multiple top‐hat analyzers to achieve unprecedented temporal resolution. An instantaneous angular coverage of charged particles measurements is an alternative approach to pursuing the goal of high time resolution. This was done with 4‐D Fast Omnidirectional Nonscanning Energy Mass Analyzer and, to a lesser extent, by DYMIO instruments for Mars‐96 and with the Fast Imaging Plasma Spectrometer instrument for MErcury Surface, Space ENvironment, GEochemistry, and Ranging mission. In this paper we describe, along with precursors, a plasma analyzer with a 2*π* electrostatic mirror that was developed originally for the Phobos‐Soil mission with a follow‐up in the frame of the BepiColombo mission and is under development for future Russian missions. Different versions of instrument are discussed along with their advantages and drawbacks

The content of the model of evolution of complex systems developed by Sergey P. Kurdyumov is under consideration in the article. Some key ideas, which were put forward by him, constitute nowadays a foundation for development of a methodology for studying complex self-developing systems of different nature. The model is based on four concepts: the relationship of space and time, complexity and its nature, nonlinearity, blow-up regimes. Self-organization and rapid, avalanche-like growth of complexity, evolutionary cycles and regimes switching occur as a necessary mechanism for maintaining “life” of complex structures. The methodology allows us to understand the nonlinear dynamics of evolutionary processes in systems of very different nature and to show the possibility of controlling them and creating the desired futures. Special attention is paid to considering possible applications of this model for understanding the dynamics of complex social, demographic and geopolitical systems.

The evolutionary model elaborated by Sergei P. Kurdyumov is considered in the article. Some key ideas put forward by him constitute a basis for development of the methodology of sudy of complex selforganizing systems, called also synergetics. Four important theoretical notions form a fundament of this evolutionary model: connection between space and time, complexity and its nature, blow-up regimes, in which self-organization and rapid, avalanche-like growth of complexity occur, evolutionary cycles and switching of different regimes as a necessary mechanism for maintenance of “life” of complex structures. The methodology allows to understand the nature of innovative shifts in nature and society and to show a possibility of management of innovative processes and of construction of desirable future. Some approaches for possible application of this model for understanding of dynamics of complex social, demographic and geopolitical system are discussed.

The work is devoted to fundamental aspects of the classical molecular dynamics method, which was developed half a century ago as a means of solving computational problems in statistical physics and has now become one of the most important numerical methods in the theory of condensed state. At the same time, the molecular dynamics method based on solving the equations of motion for a multiparticle system proved to be directly related to the basic concepts of classical statistical physics, in particular, to the problem of the occurrence of irreversibility. This paper analyzes the dynamic and stochastic properties of molecular dynamics systems connected with the local instability of trajectories and the errors of the numerical integration. The probabilistic nature of classical statistics is discussed. We propose a concept explaining the finite dynamic memory time and the emergence of irreversibility in real systems.

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.

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