Dislocation model of a nanotwin

We propose a dislocation model of a nanotwin, which is used to calculate the stress fields in the nanotwin. We consider the role of these stresses in the process of interdislocation interaction and nanotwin growth.     

Accuracy analysis of airborne gravimeter calibration using repeated flight paths

Some possible errors in determining the gravity anomalies are discussed. Such errors may be caused by an inaccurate calibration of the gravimeter used in an airborne survey system. An approach based on wavelet decompositions is proposed for its additional calibration with the use of flight data obtained during repeated flights.     

Parametric oscillations and stability of systems with large modulation coefficient

We study parametric oscillations of linear systems with one degree of freedom for large values of the modulation coefficient. We use the classical analytic Lyapunov-Poincaré perturbation methods and an original numerically-analytic method of accelerated convergence to construct periodic solutions and the corresponding eigenvalues. We find the boundaries of stability and instability domains. We use specific models to illustrate the main properties of parametric oscillations of systems with singular character of the perturbation dependence on the modulation coefficient. We consider periodic boundary value problems for the modified Mathieu equation and the Kochin equation modeling crankshaft torsional vibrations and show that there are significant differences between weakly and essentially perturbed periodicmotions both for the lowest and arbitrary oscillation modes. We also describe the unusual properties of the boundaries in the domain of the system determining parameters.     

A quality criterion for visual tracking during nystagmus

The aim of this study is to construct a quantitative characteristic for the degree of gaze stabilization on a visual target with consideration of physiological constraints. A quality criterion for visual tracking during optokinetic vestibulocervical nystagmus is proposed. The index of imaginary tracking during rotation in the dark allows one to speak of a difference in the image stabilization quality between a healthy person and a patient. Experimental nystagmus data are used to calculate the quality index of visual tracking and the index of imaginary tracking.     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

Application of the wavelet transform for a channel flow in a mixed convection phenomenon

The aim of this paper is to investigate laminar-turbulent transition in a mixed convection phenomenon occurring in a horizontal rectangular duct. Indeed, laminar-turbulent transition is well known in the case of forced convection but the presence of secondary flow induced by natural convection on this transition is not well highlighted. In this study, we will not be concerned by determining a critical threshold value of a Reynolds number of transition but only to estimate the degree of turbulence in the transition regime, i.e. weak turbulence in the case of a mixed convection phenomenon. This is possible thanks to the application of the wavelet transform. The calculation of the Hölder exponent, associated with the maximum value of the singularity spectrum for various experimental conditions allows the degree of turbulence to be measured. The variation of the Hölder exponent versus heat flux and Reynolds number enables us to show that there are two ways to go towards turbulence: thermal by increasing heat flux and hydrodynamic by increasing fluid velocity.     

Chlorination of aromatic substrates catalyzed by the phthalocyanine complexes

The chlorination of benzene, toluene, and o-xylene with molecular chlorine in the presence of the phthalocyanine complexes of different structures was studied. The transformations of the catalysts during the reaction were investigated. Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1644–1647, August, 2008.