Erratum to: “Nucleophilic addition of aromatic amide oximes to [2-B10H9NCC2H5]– anion”

Russian Journal of General Chemistry -     

Dynamics of an anharmonic oscillator with a periodic perturbation

We study the features of the stochastic dynamics of a Hamiltonian system with the potential x ²ⁿ subjected to an external monochromatic perturbation. Three regimes of stochastic diffusion, which differ in the value of the amplitude of the external perturbation, are detected. We demonstrate the possibility of chaotic regimes manifesting themselves in pendulum vibrations of the well of a water-moderated and-cooled nuclear power reactor as an application of the model being investigated. Finally, we propose a method of simple proportional control, which makes it possible to control the chaotic vibrations of the anharmonic oscillator. Zh. éksp. Teor. Fiz. 115, 361–377 (January 1999)     

Determnation of elasticity constants for microheterogeneous media

The foundations of the theory of stochastically heterogeneous solids were laid a long time ago by Voigt [1J, who developed a method for determining the macroscopic parameters of polycrystalline materials by averaging the appropriate crystallite parameters with respect to orientations. Lifshits and Rozentzveig [2] showed that it was necessary to consider the correlation properties of the field in computations of macroscopic parameters. They calculated the first corrections for the averaged elastic constants of polycrystallites for the case of cubic and hexagonal crystallites. Assuming a low degree of heterogeneity, these authors used an approximation which corresponds to the Born approximation in the theory of scattering [3]. This method and its modifications were subsequently used by several authors for the computation of macroscopic parameters of polycrystallites [4– 6] and of other microheterogeneous materials [8].Moreover, the assumption of a low degree of heterogeneity of the properties is very restrictive. It precludes use of the method in the case of macroscopically isotropic polycrystallites formed from essentially anisotropic crystallite stochastically glass reinforced plastics, and similar microheterogeneous materials. This rises the problem of developing procedures that could be applied in cases of a high degree of heterogeneity. This problem presents serious analytical difficulties, however. It is sufficient to point out that even computation of the second approximation (i.e., the one following the Born approximation) has not yet been completed. Analogous problems in the classical and quantum theories of scattering are also, as a rule, considered only in the Born approximation. More complicated methods (e.g., Feyman's method) make possible only partial summation of infinite sequences in which the result is obtained. A method analogous to that of a selfconsistent field in quantum mechanics [9,10] is promising; however, this method is approximate and the magnitude of its error has not yet been estimated.The possibility of accurate determination of mascroscopic parameters for certain classes of microheterogeneous media was demostrated in [11], in which a detailed analysis was presented of parameters forming a second order tensor and characterizing the distribution in the medium of a certain scalar value obeying an equation similar to the steady-state heat-conduction equation. Accurate formulas for macroscopic coefficients of thermal conductivity (diffusion) were derived for the case of a strongly anisotropic medium and for that of a medium with a high degree of transverse isotropy. We made a comparison with various approximate methods and evaluated their degree of error. This article describes an accurate method of computing macroscopic elastic constants for polycrystalline media with a high degree of anisotropy; for the case of polycrystals with a cubic structure [12] the error margin and range of application of approximate methods are estimated.     

The macroscopic coefficients of thermal conductivity and diffusion in microinhomogeneous solids

A method is given for calculating the macroscopic coefficients of thermal conductivity and diffusion for microinhomogeneous solids whose local coefficients of thermal conductivity (or diffusion) form an ergodic homogeneous stray field. In the case of marked isotropy of the field of the local coefficients, the calculations are taken to a conclusion. The final formulas for the structure are not much more complicated than the corresponding first-approximation formulas. The results of calculations for certain other cases are also given. The effect of anisotropy of the crystallites in polycrystalline material on the coefficients of thermal conductivity and diffusion is discussed.One of the main problems in the mechanics of microinhomogeneous bodies is the determination of the macroscopic constants from the corresponding microscopic characteristics. The assumption regarding the small inhomogeneity used by a number of authors [1, 2] is not applicable in the case of isotropic polycrystalline aggregates consisting of substantially anisotropic crystallites, stochastic reinforced media media, etc. The so-called self-consistent field method [3] opens up some interesting prospects, but this method is an approximate one and its errors have not yet been assessed. Nevertheless, by making certain fairly general assumptions about the correlation properties of the inhomogeneity, it is possible to obtain final accurate formulas for such macroscopic properties of the solids as the coefficients of thermal conductivity, diffusion, elasticity, and thermal expansion. Below we consider some of the simplest problems involved in determining the macroscopic constants which form a second-order tensor and which characterize the distribution of a certain scalar quantity in a microinhomogeneous body.     

On the motion of a mechanical system inside a rolling ball

We consider a mechanical system inside a rolling ball and show that if the constraints have spherical symmetry, the equations of motion have Lagrangian form. Without symmetry, this is not true.     

Methods of inertial gravimetry

The history and the current state of the art in inertial gravimetry in Russia are discussed as seen by the authors of this paper who witnessed the evolution of this new field of geophysics. Much attention is given to the information and algorithmic aspects of airborne gravimetry.     

Scattering and recoiling mapping of the Kr–Pt(1 1 1) system by SARIS

The technique of angle resolved mapping of scattering and recoiling imaging spectra (SARIS) combined with computer simulations is demonstrated to be a valuable tool for characterization of atomic collision events on surfaces. The energy distributions of scattered Kr and fast recoiled Pt atoms from a Pt(1 1 1) surface were measured as a function of exit angle. The use of a large area microchannel plate detector and time-of-flight techniques decreases the collection time and increases the number of detected trajectories above that of other designs. Classical ion trajectory simulations using the three-dimensional scattering and recoiling imaging code are used to simulate the kinematics of the scattering and recoiling particles. It is shown that SARIS mapping allows one to probe the kinematics of both scattered and recoiled particles, the probability for their occurrence in specific trajectories, their detection probabilities, and their threshold detection velocity. The measured and simulated energy distributions agree quantitatively if the detection efficiency is taken into account. The observed value of the threshold detection velocity for Pt atoms, ν^th=3.78(5)×10⁴ m/s, is in good agreement with previous studies.     

Thermoelasticity constants of polycrystals

Exact formulas are derived for the thermoelasticity constants of macroscopically homogeneous polycrystals. A method described earlier [1] is used as the basis. It is assumed that the local parameters form an ergodic homogeneous random field. No restriction is imposed on the degree of anisotropy of the crystals.