Geometric phase for nonlinear oscillators from perturbative renormalization group

We formulate a renormalization group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous models with time-independent parameters, as well as nonautonomous models with slowly varying parameters. We show that the renormalization group equations for the nonautonomous case can be used to determine the geometric phase acquired by the oscillator during the change of its parameters. We illustrate the obtained results by applying them to the Van der Pol, and Van der Pol-Duffing models.Comment: 12 pages, 2 figure

Original scientific article Administrative-legal Status of a Voluntary Squad During Martial Law

The subject of the research is social relations that arise in the course of the activities of voluntary squads during martial law, including the possibility of their involvement by law enforcement and other bodies in the performance of state tasks to ensure public order and national security. The purpose of the work is to determine the theoretical and applied problems of legal regulation of the administrativelegal status of a voluntary squad during the period of martial law. When writing the article, formal-legal, historical-and comparative-legal, logical methods were used. The relevance of the topic is associated with the lack of a clear and even mechanism for the creation and functioning of voluntary squads precisely during the period of martial law. At the legislative level, their competence (powers, forms and acts of responding to violations of laws by individuals and legal entities) in the process of ensuring public order in the controlled territory is not defined. The fact of the absence of a single terminological series in the formation of the legal basis for the activities of voluntary squads is stated. The main part of the article substantiates the conclusion that such voluntary public organizations, taking into account their basic characteristics, should be referred to in regulatory legal acts, regardless of the direction of their action, as a “voluntary people's squad”. A comparative analysis of the legal status of a voluntary squad and volunteer formations is presented. It is concluded that they do not correlate as general and private, voluntary formation, due to the specifics of the goals of education, functioning and financing, is not a kind of voluntary squads. The conclusion is substantiated that voluntary squads should be actively used by law enforcement agencies to ensure the strengthening of public order during martial law. The question is raised about the need to specify in the normative legal acts the administrative and legal status of voluntary squads precisely in the period of martial law. Proposals are made on the mechanism of legal regulation of the powers of voluntary teams and the social and legal protection of combatants when they perform state tasks under these conditions

Administrative and Legal Framework for Citizens’ Participation in the Maintenance of Public Order in Russia and Finland

The article provides a comparative analysis of administrative legal norms of the Russian Federation and Finland that regulate the participation of citizens in the protection of public order. The relevance of the chosen topic is determined by the fact that the human rights activities of law enforcement agencies, their importance in the fieldof public law enforcement, personal and public security is often unproductive, especially in the context of the global economic crisis, in which the functioning of law enforcement agencies alone is obviously not enough to protect human rights and freedoms and maintain public law and order. It is known that public tension in the state, including in Russia and Finland, increases sharply in emergency situations: during man-made disasters, epidemics, social crises, and terrorist activities. In such situations, the existence of public organizations whose activities guarantee the protection of public order and the elimination of negative consequences of emergency situations is extremely necessary. The Author considers the concept of public order, reveals its essence and content. The definition of the term “protection of public order” is formulated. It defines the legal regulation of citizens’ participation in public order protection in the Russian Federation and Finland. Common and similar features of such regulation are highlighted. The main legal acts regulating the participation of citizens in the protection of public order in Russia and Finland are analyzed in detail. According to the Author, strict centralization, as well as the lack of proper interaction of law enforcement agencies with society, is one of the key problems of enforcement and protection of public order in the law enforcement system of Russia and Finland. The issue of voluntary national teams functioning both in Russia and Finland is being considered. Attention is drawn to their specific features. In the end, the author concludes that at present, both for Russia and Finland, the issue of protecting citizens who take part in the protection of public order is a difficult one. It can be stated that in comparison with the Russian Federation, Finland provides a much smaller amount of guarantees for the protection of citizens who participate in the protection of public order

Studies of concentration and temperature dependencies of precipitation kinetics in iron-copper alloys using kinetic monte carlo and stochastic statistical simulations

The earlier-developed ab initio model and the kinetic Monte Carlo method (KMCM) are used to simulate precipitation in a number of iron-copper alloys with different copper concentrations x and temperatures T. The same simulations are also made using the improved version of the earlier-suggested stochastic statistical method (SSM). The results obtained enable us to make a number of general conclusions about the dependencies of the decomposition kinetics in Fe-Cu alloys on x and T. We also show that the SSM describes the precipitation kinetics in a fair agreement with the KMCM, and employing the SSM in conjunction with the KMCM enables us to extend the KMC simulations to the longer evolution times. The results of simulations seem to agree with available experimental data for Fe-Cu alloys within statistical errors of simulations and the scatter of experimental results. Comparison of results of simulations to experiments for some multicomponent Fe-Cu-based alloys enables us to make certain conclusions about the influence of alloying elements in these alloys on the precipitation kinetics at different stages of evolution.Comment: 18 pages, 17 postscript figures, LaTe

Registration of terahertz irradiation with silicon carbide nanostructures

The response to external terahertz (THz) irradiation from the silicon carbide nanostructures prepared by the method of substitution of atoms on silicon is investigated. The kinetic dependence of the longitudinal voltage is recorded at room temperature by varying the drain-source current in the device structure performed in a Hall geometry. In the frameworks of proposed model based on the quantum Faraday effect the incident radiation results in the appearance of a generated current in the edge channels with a change in the number of magnetic flux quanta and in the appearance of features in the kinetic dependence of the longitudinal voltage. The generation of intrinsic terahertz irradiation inside the silicon carbide nanostructures is also revealed by the electrically-detected electron paramagnetic resonance (EDEPR) measured the longitudinal voltage as a function of the magnetic field value.Comment: 11 pages, 6 figure