Grassmannians Gr(N-1,N+1), closed differential N-1 forms and N-dimensional integrable systems

Integrable flows on the Grassmannians Gr(N-1,N+1) are defined by the requirement of closedness of the differential N-1 forms $\Omega_{N-1}$ of rank N-1 naturally associated with Gr(N-1,N+1). Gauge-invariant parts of these flows, given by the systems of the N-1 quasi-linear differential equations, describe coisotropic deformations of (N-1)-dimensional linear subspaces. For the class of solutions which are Laurent polynomials in one variable these systems coincide with N-dimensional integrable systems such as Liouville equation (N=2), dispersionless Kadomtsev-Petviashvili equation (N=3), dispersionless Toda equation (N=3), Plebanski second heavenly equation (N=4) and others. Gauge invariant part of the forms $\Omega_{N-1}$ provides us with the compact form of the corresponding hierarchies. Dual quasi-linear systems associated with the projectively dual Grassmannians Gr(2,N+1) are defined via the requirement of the closedness of the dual forms $\Omega_{N-1}^{\star}$. It is shown that at N=3 the self-dual quasi-linear system, which is associated with the harmonic (closed and co-closed) form $\Omega_{2}$, coincides with the Maxwell equations for orthogonal electric and magnetic fields.Comment: 26 pages, references adde

Chiral Skyrmionic matter in non-centrosymmetric magnets

Axisymmetric magnetic strings with a fixed sense of rotation and nanometer sizes (chiral magnetic vortices or Skyrmions) have been predicted to exist in a large group of non-centrosymmetric crystals more than two decades ago. Recently these extraordinary magnetic states have been directly observed in thin layers of cubic helimagnet (Fe,Co)Si. In this report we apply our earlier theoretical findings to review main properties of chiral Skyrmions, to elucidate their physical nature, and to analyse these recent experimental results on magnetic-field-driven evolution of Skyrmions and helicoids in chiral helimagnets.Comment: 13 pages, 7 figures, invited talk - JEMS-2010 ( 23-28 August, Krakow, Poland

A methodological approach to developing the model of correlation between economic development and environmental efficiency on the basis of company's non-financial reports

Having reviewed the most widely used international non-financial reporting standards, GRI was identified as the optimal standard for the Russian context. The environmental component of the GRI G4 guidelines and the contribution of each aspect to the overall sustainability picture were analysed. Over time, the value of biological resources increases, and therefore, a company’s economic development cannot continue in isolation. To determine the degree of harmony between economic development and ecological condition of the territories involved, new approaches and methods are required. Based on statistical methods, a model of correlation between economic development and environmental efficiency was developed that uses non-financial reporting data. The model can be used by oil and gas companies, and its general principles — by other industries. The results may interest stakeholders and serve as a platform for forecasting and making administrative decisions aimed at achieving harmony between economic development and environmental efficiency. The model was tested on the largest oil and gas Russian company “Surgutneftegaz” data. A positive correlation was shown between the two systems of its sustainable development: economy and ecology. The results obtained demonstrate the company’s strong commitment to conservation. Further research may yield more profound results, contributing to broader sustainable development

A Performance and Resource Consumption Assessment of Secure Multiparty Computation

In recent years, secure multiparty computation (SMC) advanced from a theoretical technique to a practically applicable technology. Several frameworks were proposed of which some are still actively developed. We perform a first comprehensive study of performance characteristics of SMC protocols using a promising implementation based on secret sharing, a common and state-of-the-art foundation. Therefor, we analyze its scalability with respect to environmental parameters as the number of peers, network properties -- namely transmission rate, packet loss, network latency -- and parallelization of computations as parameters and execution time, CPU cycles, memory consumption and amount of transmitted data as variables. Our insights on the resource consumption show that such a solution is practically applicable in intranet environments and -- with limitations -- in Internet settings

On the identification of Ti-Ta-Nb-oxides in “wiikites” from Karelia

Purpose. With respect to the nature of Ti-Ta-Nb-oxides, which are included in the mineral associations that have historically gone by the now outdated name of “wiikites”, there is no unanimity of opinion. The main difficulty in identifying them is associated with the complexity of their chemical composition, their metamict structure and the substantial changes in their initial mineral form due to the effects of natural weathering. The aim of this work is the development of methodology to identify Ti-Ta-Nb-oxides corresponding to the mineral formulas AB2O6 and A2B2O7. Methods. The methodology developed in the work includes two experimental approaches: 1) electron probe microanalysis of phases revealed through use of the SEM-BSE method. Based on the resulting data, a hypothesis about the nature of the Ti-Ta-Nb-oxides in a number of wiikite samples is proposed. 2) XRD analysis of those phases that are formed in the course of thermal annealing of samples from 200 to 1000°C. Based on the resulting data here, the previous hypotheses are either accepted or rejected for each sample. Findings. Using this methodology, three “wiikite” samples were analyzed (the experimental codes were Wk-2, Wk-3 and Wk-7). The Ti-Ta-Nb-oxides in two of these wiikites (Wk-2 and Wk-3) were preliminarily determined to be hydroxyyttropyrochlore and hydroxycalciobetafite, respectively. In the third sample (Wk-7), the Ti-Ta-Nb-oxide was classified as polycrase. The results of XRD phase analysis of the annealed samples were compatible with the primary hypotheses that hydroxycalciobetafite and polycrase were the initial minerals in “wiikites” 3 and 7, respectively. Originality. The paper considers the issue of the chemical conditions necessary for the recovery of the original Ti-Ta-Nb-oxide during recrystallization of the metamict structures. This is a problem that has not been substantively addressed in the literature. Also for the first time experimentally proved the existence of the polycrase in “wiikites”. Practical implications. Completed work expands our knowledge of the mineral composition of the granitic pegmatites of the Baltic shield and the possibility of their use both for research purposes and for needs of national economy.Мета. Розробка методології ідентифікації Ti-Ta-Nb-оксидів складного хімічного складу з метаміктною структурою, що відповідають мінеральним формулами АВ2О6 та А2В2О7. Методика. Для розробки методології ідентифікації у роботі використано два експериментальних підходи: 1) рентген-спектральний мікроаналіз фаз, виявлених методом скануючої електронної мікроскопії зразків у назад відображених електронах. На основі отриманих результатів висунута гіпотеза щодо природи Ti-Ta-Nb-оксидів. 2) рентген-дифракційний аналіз фаз, що утворюються в процесі термічного відпалу зразків від 200 до 1000°С. На основі отриманих результатів для кожного зразка первинна гіпотеза приймалася або відкидалася. Результати. З використанням даної методики були вивчені три зразки “віікітів” (шифри зразків: Wk-2, Wk-3 і Wk-7). Наявність Ti-Ta-Nb-оксидів попередньо визначено e двох зразках (Wk-2 і Wk-3) відповідно, як гідроксііттропірохлор та гідроксікальціобетафіт. У третьому зразку (Wk-7) Ti-Ta-Nb діагностований як полікраз. Результати рентген-дифракційного аналізу відпалених зразків підтвердили гіпотези про те, що початковими мінералами у Wk-3 і Wk-7 були гідроксікальціобетафіт і полікраз відповідно. Наукова новизна. Визначено хімічні умови, необхідні для утворення початкового Тi-Ta-Nb під час рекристалізації метаміктної структури, що раніше не розглядалось у відповідній тематичній науковій літературі. Вперше експериментально виявлено присутність у “віікітах” полікраза. Практична значимість. Отримані результати розширюють й доповнюють знання щодо мінерального складу гранітних пегматитів Балтійського щита та надають можливість їх використання в дослідницьких цілях і потребах народного господарства.Цель. Разработка методологии идентификации Ti-Ta-Nb-оксидов сложного химического состава с метамиктной структурой, соответствующих минеральным формулам АВ2О6 и А2В2О7. Методика. Для разработки методологии идентификации в работе использовано два экспериментальных подхода: 1) рентген-спектральный микроанализ фаз, выявленных методом сканирующей электронной микроскопии образцов в обратно отраженных электронах. На основе полученных результатов выдвинута гипотеза о природе Ti-Ta-Nb-оксидов. 2) рентген-дифракционный анализ фаз, образующихся в процессе термического отжига образцов от 200 до 1000°С. На основе полученных результатов для каждого образца первоначальная гипотеза принималась или отвергалась. Результаты. С использованием данной методики были изучены три образца “виикитов” (шифры образцов: Wk-2, Wk-3 и Wk-7). Наличие Ti-Ta-Nb-оксидов предварительно определено в двух образцах (Wk-2 и Wk-3) соответственно, как гидроксииттропирохлор и гидроксикальциобетафит. В третьем образце (Wk-7) Ti-Ta-Nb диагностирован как поликраз. Результаты рентген-дифракционного анализа отожженных образцов подтвердили гипотезы о том, что первоначальными минералами в Wk-3 и Wk-7 были гидроксикальциобетафит и поликраз соответственно. Научная новизна. Определены химические условия, необходимые для образования первоначального Тi-Ta-Nb во время рекристаллизации метамиктной структуры, что ранее не рассматривалось в соответствующих тематических научных литературе. Впервые экспериментально выявлено присутствие в “виикитах” поликраза. Практическая значимость. Полученные результаты расширяют и дополняют знания о минеральном составе гранитных пегматитов Балтийского щита и дают возможности их использования в исследовательских целях и нуждах народного хозяйства.The study was conducted using equipment of the Center of X-ray Diffraction Studies and the Center for Microscopy and Microanalysis of the Research Park at Saint Petersburg State University, as well as the analytical laboratory of OJSC MMC Norilsk Nickel in Saint Petersburg

Spin-flop transition in uniaxial antiferromagnets: magnetic phases, reorientation effects, multidomain states

The classical spin-flop is the field-driven first-order reorientation transition in easy-axis antiferromagnets. A comprehensive phenomenological theory of easy-axis antiferromagnets displaying spin-flops is developed. It is shown how the hierarchy of magnetic coupling strengths in these antiferromagnets causes a strongly pronounced two-scale character in their magnetic phase structure. In contrast to the major part of the magnetic phase diagram, these antiferromagnets near the spin-flop region are described by an effective model akin to uniaxial ferromagnets. For a consistent theoretical description both higher-order anisotropy contributions and dipolar stray-fields have to be taken into account near the spin-flop. In particular, thermodynamically stable multidomain states exist in the spin-flop region, owing to the phase coexistence at this first-order transition. For this region, equilibrium spin-configurations and parameters of the multidomain states are derived as functions of the external magnetic field. The components of the magnetic susceptibility tensor are calculated for homogeneous and multidomain states in the vicinity of the spin-flop. The remarkable anomalies in these measurable quantities provide an efficient method to investigate magnetic states and to determine materials parameters in bulk and confined antiferromagnets, as well as in nanoscale synthetic antiferromagnets. The method is demonstrated for experimental data on the magnetic properties near the spin-flop region in the orthorhombic layered antiferromagnet (C_2H_5NH_3)_2CuCl_4.Comment: (15 pages, 12 figures; 2nd version: improved notation and figures, correction of various typos