Improved linear response for stochastically driven systems

The recently developed short-time linear response algorithm, which predicts the average response of a nonlinear chaotic system with forcing and dissipation to small external perturbation, generally yields high precision of the response prediction, although suffers from numerical instability for long response times due to positive Lyapunov exponents. However, in the case of stochastically driven dynamics, one typically resorts to the classical fluctuation-dissipation formula, which has the drawback of explicitly requiring the probability density of the statistical state together with its derivative for computation, which might not be available with sufficient precision in the case of complex dynamics (usually a Gaussian approximation is used). Here we adapt the short-time linear response formula for stochastically driven dynamics, and observe that, for short and moderate response times before numerical instability develops, it is generally superior to the classical formula with Gaussian approximation for both the additive and multiplicative stochastic forcing. Additionally, a suitable blending with classical formula for longer response times eliminates numerical instability and provides an improved response prediction even for long response times

Design of construction materials for fast neutron molten salt reactors with closed nuclear fuel cycle

Согласно дорожной карте мирового развития атомной энергетики жидкосолевой реактор с пристанционным уран-ториевым ядерно-топливным циклом является одним из шести инновационных реакторных конструкций. Для развития концепции солевого ядерного реактора и ее реализации необходимо осуществить подбор стойких конструкционных материалов в урансодержащих солевых расплавах. Объектами исследования выбраны коррозионностойкие аустенитные сплавы на основе никеля и стали на основе железа. Исследования осуществлены при 750 °С в электролите NaCl–KCl–UCl3 и NaCl–KCl–UCl4 с содержанием урана 1 и 6 мас.%. Определены скорости коррозии исследуемых материалов в расплаве после 30 часов выдержки. Показано, что все исследуемые материалы, за исключением суперсплава Hastelloy N, подвергаются структурным изменениям и, как следствие, межкристаллитной коррозии. По границам зерен у большинства никелевых сплавов в процессе выдержки образуются избыточные интерметаллические мю-фазы, а у аустенитных сталей 12Х18Н10Т и 03Х17Н14М3 – карбиды хрома, что приводит к образованию микрогальванопар и последующему растворению их анодных зон. Сделаны выводы о применимости материалов в расплавах и их перспективах использования.According to the technology roadmap for Generation IV nuclear energy systems molten salt reactors (MSR) with on-site uranium-thorium nuclear fuel cycle is one of six innovative reactor types. Practical realization of MSR relies on construction materials stable in uranium- and thorium-containing salt melts. Corrosion-resistant alloys based on nickel and steels based on iron were chosen for the present study. Corrosion tests were performed in NaCl–KCl–UCl3, NaCl–KCl–UCl4 (1, 6 wt. % uranium) melts at 750 °С. The corrosion rates of the studied materials were determined after 30 h of exposure in the melt. It was shown, that all studied materials, except Hastelloy N super alloy, were subjected to structural changes and, as a consequence, to intergranular corrosion. Excessive intermetallic mu-phases were formed along the grain boundaries in nickel based alloys, and chromium carbides in 12Kh18N10T and 03Kh17N14M3 austenitic steels. The formation of excessive phases leads to the appearance of microgalvanic pairs with subsequent dissolution of their anodic zones. Conclusions about possibility and prospects of application of studied materials in melts were made.Программа развития УрФУ на 2013 год (п.2.1.2.1

On a graded q-differential algebra

Given a unital associatve graded algebra we construct the graded q-differential algebra by means of a graded q-commutator, where q is a primitive N-th root of unity. The N-th power (N>1) of the differential of this graded q-differential algebra is equal to zero. We use our approach to construct the graded q-differential algebra in the case of a reduced quantum plane which can be endowed with a structure of a graded algebra. We consider the differential d satisfying d to power N equals zero as an analog of an exterior differential and study the first order differential calculus induced by this differential.Comment: 6 pages, submitted to the Proceedings of the "International Conference on High Energy and Mathematical Physics", Morocco, Marrakech, April 200