The long-term cyclotron dynamics of relativistic wave packets: spontaneous collapse and revival

In this work we study the effects of collapse and revival as well as {\it Zitterbewegung} (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some level $n_0$ of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and visualized. Our computations demonstrate that due to dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the positive energy only) loses the spatial localization so that the evolution can no longer be described classically. However, at the half-revival time $t=T_R/2$ its reshaping takes place firstly. The behavior of the wave packet containing the states of both energy bands (with $E_n>0$ and $E_n<0$) is more complicated. At short times of a few classical periods such packet splits into two parts which rotate with cyclotron frequency in the opposite directions and meet each other every one-half of the cyclotron period. At these moments their wave functions have significant overlap that leads to ZB. At the time of fractional revival each of two sub-packets is decomposed into few packets-fractions. However, at $t=T_R$ each of the two sub-packets (with positive or negative energy) restores at various points of the cyclotron orbit, that makes it impossible reshaping of initial wave packet entirely unlike the wave packet which consists of states with energies $E_n>0$ only. Obtained results can be useful for the description of electromagnetic radiation and absorption in relativistic plasma on astrophysics objects, where super high magnetic field has the value of the order $10^8-10^9$T, as well as for interpretation of experiments with trapped ions

Graphene superlattice with periodically modulated Dirac gap

Graphene-based superlattice (SL) formed by a periodic gap modulation is studied theoretically using a Dirac-type Hamiltonian. Analyzing the dispersion relation we have found that new Dirac points arise in the electronic spectrum under certain conditions. As a result, the gap between conduction and valence minibands disappears. The expressions for the position of these Dirac points in ${\bf k}$-space and threshold value of the potential for their emergence were obtained. At some parameters of the system, we have revealed interface states which form the top of the valence miniband.Comment: 5 pages, 4 figures, accepted to Physical Review

Space-time evolution of Dirac wave packets

In this work we study the dynamics of free 3D relativistic Gaussian wave packets with different spin polarization. We analyze the connection between the symmetry of initial state and the dynamical characteristics of moving particle. The corresponding solutions of Dirac equation having different types of symmetry were evaluated analytically and numerically and after that the electron probability densities, as well as, the spin densities were visualized. The average values of velocity of the packet center and the average spin were calculated analytically, and the parameters of transient Zitterbewegung in different directions were obtained. These results can be useful for the interpretation of future experiments with trapped ions.Comment: 10 pages, 7 figure

Critical fields for vortex expulsion from narrow superconducting strips

We calculate the critical magnetic fields for vortex expulsion for an infinitely long superconducting strip, using the Ginzburg-Landau formalism. Two critical fields can be defined associated with the disappearance of either the energetic stability or metastability of vortices in the center of the strip for decreasing magnetic fields. We compare the theoretical predictions for the critical fields in the London formalism with ours and with recently published experimental results. As expected, for narrow strips our results reproduce better the experimental findings.Comment: 5 pages, 5 figure

Composition Peculiarities of the Main Iconostasis of the Church of St John the Warrior in Yakimanka Street

Поступила в редакцию 02.02.2018. Принята к печати 18.04.2018.Submitted on 02 February, 2018. Accepted on 18 April, 2018.Статья посвящена истории трансформации композиции барочного иконостаса, созданного в начале XVIII в. мастерами-иконописцами круга Оружейной палаты Московского Кремля для церкви Трех Святителей, стоявшей у Красных ворот в Москве до 1928 г. По результатам научно-исследовательской работы и архивных поисков, на основании анализа и сопоставления документов и архивных фотографий, а также описей XVIII, XIX и XX вв. и других документов, сохранившихся в архиве церкви святого мученика Иоанна Воина, выявлены даты передачи главного иконостаса со всеми находившимися в нем иконами, некоторых других икон, книг и церковной утвари, принадлежавших приходской общине Трехсвятительского храма, в Музейный фонд, церкви Иоанна Воина на Я киманке, церкви Петра и Павла на Басманной улице, в музей XVIII в. и другие музеи Москвы и Московской области. Были уточнены даты создания иконостаса, отражены основные моменты изменения композиции главного храмового иконостаса, выявлены утраченные ярусы и выдвинуто редположение о том, какие именно иконы их составляли. Предпринята попытка определить авторство икон, составляющих ряды иконостаса и не имеющих авторской подписи. На основании архивных находок, проделанной научно-исследовательской работы, анализа текстов архивных документов и фотографий выполнена схема-реконструкция главного иконостаса церкви Трех Святителей, что стояла у Красных ворот, до его разборки и перевозки в храм Иоанна Воина на Я киманке. Прояснены авторский замысел и композиционное решение, а также определены хронологические рамки и высказано предположение о причинах, повлекших перемещения рядов и икон иконостаса и связанное с этим изменение размера иконостаса и его композиции.This article considers the history of the composition transformation of the baroque iconostasis created in the early 18th century by Moscow icon painters of the Armoury of the Moscow Kremlin for the Church of the Three Holy Hierarchs located by the Red Gate in Moscow until 1928. Referring to the results of research work and archival search, analysis and comparison of documents and archival photographs, as well as inventories of the 18th, 19th, and 20th centuries and other documents that are still kept in the archive of St John the Warrior’s Church, the author determines the date when the main iconostasis and all the icons it contained, some other icons, books and church plate belonging to the parish of the Church of the Three Holy Hierarchs were transferred to the Museum Fund, the Church of St John the Warrior in Yakimanka Street, the Church of SS Peter and Paul in Basmannaya Street, and the Museum of the 18th Century and other museums of Moscow and Moscow Region. The article makes an attempt to determine the period in which the iconostasis was created, reflecting the main issues connected with the change in the composition of the main iconostasis, revealing the missing parts and putting forward a hypothesis about the icons that could have made part of the iconostasis. Additionally, the author tries to attribute the icons which make part of the iconostasis but do not have a signature. Referring to archival findings and research carried out, and analysis of archival documents and photographs, the author reconstructs the main iconostasis of the Church of the Three Holy Hierarchs by the Red Gate before the iconostasis was disassembled and taken to the Church of St John the Warrior in Yakimanka Street. The article clarifies the author’s concept and composition of the iconostasis, and attempts to establish the period of its creation and the reasons that led to the transfer of the icons and the resulting change of its size and composition

Study of social tension based on electronic social networks big data

The article presents a methodology for assessing the level of social tension according to the data of electronic social networks. The calculation of the level of social tension according to the specified method is carried out automatically using software tools and requires the participation of the researcher only at the level of an analytical conclusion. An approach to identifying the dissatisfaction of the population at the level of the simplest actions of social network accounts has been described in detail. The necessity of identifying certain spheres of public life for the identification of population discontent has been substantiated, the indicated spheres have been highlighted and described. An indicator has been developed that makes it possible to calculate the level of social tension within each of the identified spheres of public life, taking into account the level of negative messages (posts and comments) and the discussion of each topic. A generalising indicator of the level of social tension has been developed, combining individual indicators of tension by topic. The calculation of the generalising indicator makes it possible to identify the level of social tension in a region or other territorial entity and track its dynamics in any perspective, including retrospectively.The proposed methodology for assessing social tension based on data from electronic social networks differs significantly from existing sociological and statistical approaches. Its main advantage lies in the minimal time lag between the dynamics of social tension, reflected in the social network, and its identification, which expands the possibilities of a prompt response to the growth of negative moods in society. Another difference of the proposed approach is the possibility of multiple repetitions of calculations with minimal, in contrast to the sociological method, the cost of additional resources for each subsequent iteration of the calculation of the indicator value

Geometry-induced reduction of the critical current in superconducting nanowires

Reduction of the critical current in narrow superconducting NbN lines with sharp and rounded bends with respect to the critical current in straight lines was studied at different temperatures. We compare our experimental results with the reduction expected in the framework of the London model and the Ginsburg-Landau model. We have experimentally found that the reduction is significantly less than either model predicts. We also show that in our NbN lines the bends mostly contribute to the reduction of the critical current at temperatures well below the superconducting transition temperature

Anomalies of Density, Stresses, and the Gravitational Field in the Interior of Mars

We determined the possible compensation depths for relief harmonics of different degrees and orders. The relief is shown to be completely compensated within the depth range of 0 to 1400 km. The lateral distributions of compensation masses are determined at these depths and the maps are constructed. The possible nonisostatic vertical stresses in the crust and mantle of Mars are estimated to be 64 MPa in compression and 20 MPa in tension. The relief anomalies of the Tharsis volcanic plateau and symmetric feature in the eastern hemisphere could have arisen and been maintained dynamically due to two plumes in the mantle substance that are enriched with fluids. The plumes that originate at the core of Mars can arise and be maintained by the anomalies of the inner gravitational field achieving +800 mGal in the region of plume formation, - 1200 mGal above the lower mantle-core transition layer, and -1400 mGal at the crust.Comment: 9 pages, 5 figure

Influense of various forms of iron on growth of Chlorella vulgaris Beijer culture

A comparative study of the toxic effect of magnetic nanoparticles of iron oxide (MNPs) and ions of bivalent and trivalent iron in the composition of sulfates on the growth of an intensive culture of Chlorella vulgaris Beijer is provided. The high sensitivity of the introduced biotest is shown for the case of a standard toxicant (potassium dichromate). Using the probit-analysis, and semi-extincting specific growth rate of EC50 culture concentrations were established in four-day experiments, which amounted to 1.3 ± 0.2 mg/l for potassium dichromate, 0.8 ± 0.1 mg/l for ferrous iron, 2.0 ± 0.2 mg/l for trivalent 1 and for MNPs iron oxide - 13 ± 1 mg / l. The probit analysis features and the significantly lower semi-suppressing specific growth rate of the culture in experiments with MNPs compared with ionic iron suggests a possible manifestation of other forms of exposure that are not related to the mechanism of chemical intoxication. © Published under licence by IOP Publishing Ltd.Russian Science Foundation, RSF: 18-19-00090In part this research was supported by the Russian Science Foundation (grant number 18-19-00090). We would like to thank I.N. Egorova, O.M. Samatov, A.M. Murzakaev and I.V. Beketov for very special support

The Formation of Indicator Framework for Effective Assessment of Investment Attractiveness of the Region

Despite the in-depth study of many theoretical aspects of investment activities and assessment of investment attractiveness, today the impact of the investment policy on the development of an effective strategy and the formation of favorable investment climate is not properly reflected in the contemporary research. At the same time unstable situation in socio-economic development of Russia requires new approaches to the problem of investment activity. In this regard, the article provides indicator framework to assess properly the investment attractiveness of the region's economy relating to foreign direct investment in the current context. At that, the proposed indicator framework is based on a number of principles, which allow achieving the objective assessment of investment attractiveness of regions and feasibility of the concerned indicators. Keywords: foreign direct investment, investment activity, investment climate, assessment of investment attractiveness, region's economy. JEL Classifications: F21; F51; H77; O2