Nanotube-based scanning rotational microscope

A scheme of the scanning rotational microscope is designed. This scheme is based on using carbon nanotubes simultaneously as a probe tip and as a bolt/nut pair which converts translational displacements of two piezo actuators into pure rotation of the probe tip. First-principles calculations of the interaction energy between movable and rotational parts of the microscope confirms the capability for its operation. The scanning rotational microscope with a chemically functionalized nanotube-based tip can be used to study how the interaction between individual molecules or a molecule and a surface depends on their relative orientation.Comment: 4 pages, 3 figure

Mathematical methods of market risk valuation in application to Russian stock market

This work is dedicated to comparative analysis and estimation of quantitative methods of risk valuation in application to Russian stock market, which include historical simulation, exponentially-weighted historical simulation, variance-covariance models with adaptive covariance matrix, variance-covariance models with exponentially-weighted adaptive covariance matrix, models based on GARCH(1,1), and Monte-Carlo Models. For the purpose of implementation of these models, algorithms of risk valuation have been developed on the basis of Value-at-Risk methodic as one of the most widely used and in accordance to RiskMetrics standards. Algorithms are implemented with usage of development environment of specialized decision support system software “Prognoz. Market risk†based on “Prognoz†analytical suite. The Decision support system mentioned above allows using different methods of risk measures calculation including standard and complex non-trivial methods. It also provides a capability to be individually tuned to better suit users’ requirements. For the purpose of backtesting of developed algorithms market risk measures were calculated using open data from Russian stock market (MICEX). For mentioned risk measures figures of quality and effectiveness were calculated, including average VaR exception value, average uncovered losses to VaR ratio, maximum loss to VaR ratio, average unused reserves, and multiplier to obtain coverage. Acquired results allowed distinguishing models which are insufficiently adequate if used in current situation on Russian stock market: models which use exponentially weighted historical simulation and some of models using variance-covariance approach. Other models can be taken as adequate with the significance level of 1% and 5%

Dislocations in stacking and commensurate-incommensurate phase transition in bilayer graphene and hexagonal boron nitride

Dislocations corresponding to a change of stacking in two-dimensional hexagonal bilayers, graphene and boron nitride, and associated with boundaries between commensurate domains are investigated using the two-chain Frenkel-Kontorova model on top of ab initio calculations. Structural transformations of bilayers in which the bottom layer is stretched and the upper one is left to relax freely are considered for gradually increased elongation of the bottom layer. Formation energies of dislocations, dislocation width and orientation of the boundary between commensurate domains are analyzed depending on the magnitude and direction of elongation. The second-order phase transition from the commensurate phase to the incommensurate one with multiple dislocations is predicted to take place at some critical elongation. The order parameter for this transition corresponds to the density of dislocations, which grows continuously upon increasing the elongation of the bottom layer above the critical value. In graphene and metastable boron nitride with the layers aligned in the same direction, where elementary dislocations are partial, this transition, however, is preceded by formation of the first dislocation at the elongation smaller than the critical one. The phase diagrams including this intermediate state are plotted in coordinates of the magnitude and direction of elongation of the bottom layer.Comment: 15 pages, 9 figure