The ethical sphere of the culture

Статья посвящена этической сфере и ее проявлению в художественной культуре на продуктивном, содержательном, языковом, морфологическом и функциональном уровнях.Ethical sphere and its manifestations on the productive, content, language, morphological and functional levels of the culture

Hall resistivity of granular metals

We calculate the Hall conductivity \sig_{xy} and resistivity $\rho_{xy}$ of a granular system at large tunneling conductance $g_{T}\gg 1$. We show that in the absence of Coulomb interaction the Hall resistivity depends neither on the tunneling conductance nor on the intragrain disorder and is given by the classical formula $\rho_{xy}=H/(n^* e c)$, where $n^*$ differs from the carrier density $n$ inside the grains by a numerical coefficient determined by the shape of the grains. The Coulomb interaction gives rise to logarithmic in temperature $T$ correction to $\rho_{xy}$ in the range \Ga \lesssim T \lesssim \min(g_T E_c,\ETh), where \Ga is the tunneling escape rate, $E_c$ is the charging energy and \ETh is the Thouless energy of the grain.Comment: 4 pages, 1 figur

Research on optical properties of fishnet metamaterials with fractal-structured unit cell

В настоящей работе исследовались сетчатые метаматериалы с разработанной гео-метрией единичной ячейки на основе ковра Серпинского. Были обнаружены поло-сы отрицательного показателя преломления в ближнем ИК и видимом диапазоне. Наблюдалось линейное смещение спектральных особенностей в длинноволновую область с увеличением порядка фрактального разбиения. Обсуждались перспекти-вы применения рассмотренных метаматериалов в оптических устройствах – фильтрах, линзах, модуляторах и т. д., а также высокочувствительных датчиках давления, биологических и химических сенсорах с возможностью дистанционного помехоустойчивого считывания показаний.Fishnet metamaterials with proposed Sierpinski carpet geometry of unit cell were studied in this work. The spectral bands with negative refractive index were discovered in near-IR and visible regions. The linear red shift of spectral features was observed with the in-creasing partition order of fractal. We discussed the possible applications of analyzed metamaterials in optical devices (filters, lenses, modulators etc.), high-sensitive pressure meters, biomedical and chemical sensors capable of remote jam-resistant data acquisition.Программа развития УрФУ на 2013 год (п.1.2.2.3

Plasmonic nanostructures with local temporal response: a platform for time-varying photonics

This work is devoted to the development of an approach for implementation and designing time-varying media. A mechanism based on the use of plasmonic nanostructures with a reduced plasmon lifetime is proposed. It is shown that such nanostructures can be used to enhance the strength and speed of modulation of the refractive index ofnonlinear media. This is achieved through decreasing of the spectral dispersion of the real permittivity. Plasmonic materials with peculiar optical properties, such as flatdispersion in the near-infrared range, were synthesized. For this purpose, we prepared TiON thin films and performed thermal post-treatment for fine-tuning permittivity of TiON. It has been shown that the proposed materials allow one to achieve an ultrashort plasmon lifetime on the order of 0.1 fs, which is an order of magnitude shorter than in the case of traditional plasmonic materials

Subexponential estimations in Shirshov's height theorem (in English)

In 1993 E. I. Zelmanov asked the following question in Dniester Notebook: "Suppose that F_{2, m} is a 2-generated associative ring with the identity x^m=0. Is it true, that the nilpotency degree of F_{2, m} has exponential growth?" We show that the nilpotency degree of l-generated associative algebra with the identity x^d=0 is smaller than Psi(d,d,l), where Psi(n,d,l)=2^{18} l (nd)^{3 log_3 (nd)+13}d^2. We give the definitive answer to E. I. Zelmanov by this result. It is the consequence of one fact, which is based on combinatorics of words. Let l, n and d>n be positive integers. Then all the words over alphabet of cardinality l which length is greater than Psi(n,d,l) are either n-divided or contain d-th power of subword, where a word W is n-divided, if it can be represented in the following form W=W_0 W_1...W_n such that W_1 >' W_2>'...>'W_n. The symbol >' means lexicographical order here. A. I. Shirshov proved that the set of non n-divided words over alphabet of cardinality l has bounded height h over the set Y consisting of all the words of degree <n. Original Shirshov's estimation was just recursive, in 1982 double exponent was obtained by A.G.Kolotov and in 1993 A.Ya.Belov obtained exponential estimation. We show, that h<Phi(n,l), where Phi(n,l) = 2^{87} n^{12 log_3 n + 48} l. Our proof uses Latyshev idea of Dilworth theorem application.Comment: 21 pages, Russian version of the article is located at the link arXiv:1101.4909; Sbornik: Mathematics, 203:4 (2012), 534 -- 55

Coulomb interaction and magnetic catalysis in the quantum Hall effect in graphene

The dynamics of symmetry breaking responsible for lifting the degeneracy of the Landau levels in the integer quantum Hall effect in graphene is studied in a low-energy model with the Coulomb interaction. The gap equation for Dirac quasiparticles is analyzed for both the lowest and higher Landau levels, taking into account the Landau levels mixing. It is shown that the characteristic feature of the long-range Coulomb interaction is the decrease of the gap parameters with increasing the Landau level index $n$ ("running" gaps). The renormalization (running) of the Fermi velocity as a function of $n$ is also studied. The solutions of the gap equation reproduce correctly the experimentally observed integer quantum Hall plateaus in graphene in strong magnetic fields.Comment: 22 pages, 5 figures; Final version published in the Proceedings of the 2010 Nobel Symposium on Graphene and Quantum Matte

Enhancement of Superconductivity in Disordered Films by Parallel Magnetic Field

We show that the superconducting transition temperature T_c(H) of a very thin highly disordered film with strong spin-orbital scattering can be increased by parallel magnetic field H. This effect is due to polarization of magnetic impurity spins which reduces the full exchange scattering rate of electrons; the largest effect is predicted for spin-1/2 impurities. Moreover, for some range of magnetic impurity concentrations the phenomenon of {\it superconductivity induced by magnetic field} is predicted: superconducting transition temperature T_c(H) is found to be nonzero in the range of magnetic fields $0 < H^* <= H <= H_c$.Comment: 4 pages, 2 figure

Распределение пористости неконсолидированной части киля торосов

An ice ridge is a special case of granular medium with a wide range of fractions. It represents a chaotic piling-up of blocks occurring under the action of gravity in the sail and due to the Archimedes force in the keel. An important characteristic of the internal structure of ice ridges is their porosity. Scientists from different countries have been dealing with this problem. First-year ice ridges are taken into consideration in Arctic and subarctic marine structural design, and the calculation of ice loads includes ridge porosity and strength, as well as other parameters. The aim of the present work is to discern the regularities of porosity distribution in the unconsolidated part of the keel with depth. Ice ridge porosity is identified by means of processing thermodrilling records. In this paper, porosity is interpreted as a step function equal to zero if there is ice at the point (x, y, z), and to one if there is no ice at the point (x, y, z). The author applies the model of compaction of the bulk medium under the influence of gravity, and, particularly for the keel, due to the Archimedes force. A zero depth corresponds to the lower surface of the keel, so each individual porosity distribution of the unconsolidated part of the keel at the drilling point must be shifted down until the maximum keel draft depth is reached in the region under consideration. After alignment, the step curves are averaged. The distance is measured up, starting from the depth of the maximum keel draft. The curve of the averaged porosity can be divided into segments reflecting the characteristic features of the distribution. According to the graphs, average porosity decreases exponentially. Ice ridges of several geographical regions are considered, and in each region is divided into groups by years of research. On the whole, 17 depth-wise distributions of the average porosity are obtained for seven regions. Each distribution was approximated according to the model, taking into account the average density of water and ice in the region. For each distribution, the values of compactibility and porosity at the zero depth, i. e. at the lower edge of the keel, were obtained; the second value only has mathematical sense. It is more convenient to consider the maximum value of the average porosity, which is taken as the initial porosity. With a probability of 90 %, the initial porosity is within the range of 0.450 ± 0.125. As the distance from the keel edge increases, the porosity curves converge to a fairly narrow range of values. At a distance of 12–14 m, this range is 0.07…0.12. The second parameter characterizing the porosity distribution in the unconsolidated part of the keel is compactibility. The steepness of the exponent approximating the average porosity curve depends on it, too. Compactibility is most affected by the strength of the ridged ice as well as the ice thickness. From the literature on the physical properties of ice it is known that as the temperature of ice increases, its strength decreases, and its plasticity increases. Thus, it can be concluded that compactibility is determined by the ice crystal structure as well the ice average temperature at the time of ridging — the warmer the ice, the higher the compactibility of the ice blocks in the keel.Целью настоящей работы было исследование распределения пористости в торосах, т. к. эта информация может быть востребована при проведении расчетов ледовых нагрузок от воздействия торосов на гидротехнические сооружения. Пористость торосов определяется в результате обработки записей скорости термобурения. Рассмотрена неконсолидированная часть киля тороса как сыпучая среда и ее уплотнение под действием силы Архимеда. Распределения пористости неконсолидированной части киля в точках бурения выравнены и осреднены. Отсчет расстояния производится вверх, начиная от глубины максимальной осадки киля. Выявлено, что пористость экспоненциально убывает с расстоянием от края киля, а скорость убывания определяется начальной пористостью (на нижнем краю киля) и уплотняемостью битого льда киля. С вероятностью 90 % начальная пористость лежит в интервале 0,450 ± 0,125. С ростом расстояния от края киля кривые пористости, построенные для разных исследований, сходятся к довольно узкому диапазону значений. На расстоянии 12–14 м этот диапазон составляет 0,07…0,12. Обосновывается вывод, что уплотняемость киля в процессе торошения определяется прочностью торосящегося льда, которая, в свою очередь, определяется кристаллическим строением и средней температурой льда в момент торошения — чем теплее лед, тем уплотняемость выше