Improvement of accuracy of interferometric measurement of wedge angle of plates

A method is proposed for improving the accuracy of measuring the wedge angle of transparent plates using a lateral-shear holographic interferometer. Consecutive processing of a pair of interferograms with doubled number of interference fringes leads to reduction of the observational error by a factor of two compared to traditional interferometric methods. Data on the experimental validation of the method are presented.     

Distribution of zeros of the partition function of the lattice gases of fisher and of temperley

The distributions of zeros of the partition function of lattice gas models of Fisher (at some temperature) and of Temperley are obtained. The former is a closed loop crossing the real axis and the latter is a part of the negative real axis.     

Calculation of energy characteristics of adsorption of metals

Within the framework of the electron density functional, a technique is developed for calculation of the adsorption energy and variation in the electron work function for metal substrates due to metal atom adsorption. The corrections to the local density approximation, which are associated with non-uniformity of the electron density in the subsurface region and discontinuous ion charge distribution over the crystal lattice sites, are included into consideration. It is shown that adsorption of alkali metal atoms results in lower electron work function, while that of transition metals (cobalt, iron, and chromium) might both decrease and increase the electron work function. Formation of a variety of adsorption structures from metal atoms depending on the temperature is discussed. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 14–19, July, 2007.     

Role of interactions of triplets of atoms in the formation of elastic properties of cubic crystals

It is widely known that the interaction of triplets of particles (which are not reducible to the sum of pair interactions) play an important role in formation the nonlinear and anisotropic properties of crystals. The aim of this work is to establish a general form of the dependence of these properties on interactions of triplets of atoms that is dependent only on the structure of the crystals. To separate the interactions of triplets of atoms from those of quadruples, we assume that the energy of triplets of interacting atoms depends only on the characteristics of a triangle whose vertices are the centers of gravity of interacting atoms. In this model, the internal energy must therefore be invariant upon rearrangement of the numbers of interacting atoms and any rotation of the triangle in isotropic space, P(3) × O(3). To specify the form of energy dependence on characteristics of selected triangles, we constructed an integral rational basis of invariants in dependence on the components of the vectors connecting the vertices of each triangle. Using the example of a simple dependence of the energy on basic invariants, we show how to move from the assumed energy dependence on invariants to the dependence of energy on lattice sums.     

X-ray interferometric method of determination of parameters of permolecular structure of polymers

A new method for determining the density of polymer materials based on determination of the path-length differences in moiré patterns is proposed. The method is characterized by simplicity and accuracy of results. The densities of polychloropren and polystirol have been determined with high accuracy. Knowledge of the dependence of the polymer density on the stretching degree enables one to reveal the dynamics of changes in the permolecular structure at deformation of polymers.     

Application of new methods of interpretation of meteor observations at the Institute of Astrophysics of Tajikistan

New methods of interpretation of meteor observations were developed and published in [1?C9]. The interpretation of ground-based observations of meteors and bolides available today in the scientific literature all over the world suffers from serious contradictions. Observers use the so-called photometric approach for determination of extra-atmospheric masses of meteoric bodies. This approach is based on the formula proposed in 1933 [10] and very simple ideas of how to describe the interaction between the atmospheric air and the surface of a meteoric body. These ideas are provisionally suitable to describe the flow around a body in a free molecular regime. Subsequently, the photometric approach was applied to all the meteor events including bolides. The main effort aimed to elaborate the approach included a choice of new formulas for the radiative efficiency.     

Symmetry of Lagrangians of nonholonomic systems of non-Chetaev’s type

This paper studies the symmetry of Lagrangians of nonholonomic systems of non-Chetaev's type. First, the definition and the criterion of the symmetry of the system are given. Secondly, it obtains the condition under which there exists a conserved quantity and the form of the conserved quantity. Finally, an example is shown to illustrate the application of the result.     

Kinetics of Macrolocalization Patterns of Plastic Flow of Metals

The features of the macroscopic inhomogeneity of plastic deformation in the form of autowaves with a pulsating amplitude are analyzed, and data on the localization of sources of acoustic emission at different stages of plastic flow in the stretching of fcc mono- and polycrystals are presented. The relationship between the local components of the plastic distortion tensor in the strain localization zone is traced. The role of acoustic phenomena accompanying the localization of plastic strain in the development of the process of plastic deformation is considered.     

Amenability of discrete subgroups of the group of diffeomorphisms of the circle

The amenability of several discrete subgroups of the group of diffeomorphisms of the circle is proved.     

混合物状态方程的计算

多介质流体动力学过程的数值模拟往往涉及混合物状态方程的计算. 做图法和Newton 法是混合物状态方程计算常采用的方法, 前者虽直观精度却差, 后者计算效率高却只具有局部收敛性, 当解与其初始猜测值相差较远时Newton法不一定能够获得收敛解. 为此, 本文给出一种具有大范围收敛性的嵌入算法(imbedding method)求解混合物状态方程, 其基本思想是通过引入嵌入参数, 将待解的混合物状态方程和易解的混合物状态方程线性组合, 构成嵌入方程组, 当嵌入参数从0连续地变化到1 时, 嵌入方程组的解由易解的混合物状态方程的解连续地变化为待解的混合物状态方程的解. 嵌入方程组可由Newton法迭代求解, 也可转化为以嵌入参数为自变量的常微分方程组, 从而易于由成熟的计算方法如梯形法等进行求解. 进一步利用热力学基本关系, Maxwell形式的微分方程描述了压力和温度随嵌入参数的演化速率与应变速率和组分质量分数演化速率的关系. 对铅锡混合物热力学量的计算表明了本文算法的有效性.     

Features of Ion-Beam Polishing of the Surface of Sapphire

The effect of an argon ion beam on the surface of sapphire is studied at different technological parameters: the ion energy, and the angle α between the sapphire surface and the ion-beam axis. The roughness of the sapphire surface is analyzed before and after ion polishing. The optimum ion-beam parameters are determined, at which the surface roughness after polishing decreases to 0.8 nm. At angles α = 20°–30°, the relief of the sapphire surface is found to become wavy. The study of the impact of the ion energy on the roughness of the sapphire surface in the 400–1200-eV range reveals that an increase in the energy of the ion beam to 1200 eV is accompanied with a decrease by 8.8 times in the roughness which falls below the level of 3 nm.     

Stability of families of probability distributions under reduction of the number of degrees of freedom

We consider two classes of probability distributions for configurations of the ideal gas. They depend only on kinetic energy and they remain of the same form when degrees of freedom are integrated out. The relation with equilibrium distributions of Tsallis’ thermostatistics is discussed.     

Analysis of Calculation of the Critical Temperature of Metals

General considerations on the form of the real equation of state make it possible to assume that the ratio of the melting temperature to the critical temperature is constant for each group of elements. This assumption is verified for two groups of elements, the critical temperatures of which are measured. It is shown that, for certain groups of elements, the critical temperatures of which are calculated instead of being measured, this assumption is also valid. The critical temperatures of certain elements are calculated or refined.     

Model of stochastization of the oscillatory regime of superradiance

Based on the analysis of the experimental data on the observation of the fluorescence and superradiance of praseodymium ions in a matrix of lanthanum trifluoride, a model of superradiance of three-level radiators with two close upper levels is developed in the mean-field approximation and studied. The uppermost level is coherently pumped by an ultrashort pulse of electromagnetic field, after which the excitation is transferred to the close energy level, from which the superradiance transition occurs to the lower level. In limiting cases, the considered model is reduced to the known models of superradiance and describes the ordinary regimes of monopulse and multipulse (oscillatory) superradiance. However, in a certain region of parameters, the model under discussion describes such a multipulse superradiance signal in which electromagnetic field spikes composing it follow in time with random intervals and amplitudes, so that the regime of regular chaotic dynamics is demonstrated in a single superradiance signal. In a certain time interval, the proposed model can be described by the Lorenz equations with the parameters corresponding to the chaotic dynamics of spikes composing the superradiance signal. The presented results of the numerical simulation of the model equations qualitatively correspond to the picture of stochastic pulsations observed experimentally.     

Application of a method of linear scaling of frequencies in calculations of the normal vibrations of polyatomic molecules

The frequencies of the harmonic vibrations of 88 compounds consisting of atoms of the first period are calculated in the approximation of the hybrid density functional B3LYP with the 6-31G* basis set. Using 1189 frequencies from experimental IR and Raman spectra of these compounds in the gas phase and the corresponding theoretical frequencies, the coefficients of the function of linear scaling are found by the least squares method. The method of linear scaling of frequencies is applied to the prediction of the 108 vibrational frequencies of a porphin molecule. A conclusion is made that this method is promising for the interpretation of vibrational spectra of complex molecules and, in combination with the Pulay method of scaling of a quantum-mechanical field, for the determination of harmonic force constants.     

Optical investigation of dynamics of phenomena of laser-based lithotripsy

Using time-resolved high-speed shadowgraphy, the dynamics of phenomena due to laser-based lithotripsy is studied. Collapsing mechanism of bubble formed therein is investigated. In order to study the mechanism, the optically implemented mathematical morphology is applied. The study of the shape of the plasma and the collapsing region of the bubble of fluid that we are studying can possibly be used for practical application for laser-based lithotripsy.     

Equations of the general theory of plasticity of crystals

Equations are formulated for the elastic-plastic strains of crystals experiencing an inelastic flow of crystallographic shears. Local invariant relationships, including creep and active plasticity, are constructed. To take account of the microstresses a method of effective field is used. All the relationships are derived in a tensor formulation with reliance on representations about the physical regularities of the development of deformation. The derived system of equations describes a broad class of problems of the physics and mechanics of plasticity of an almost unbounded degree of complexity.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 73–78, June, 1988.     

Current status of equation of state of nuclear matter

The equation of state (EOS) of symmetric nuclear matter (SNM) is a very important ingredient in the study of various phenomena of interest in nuclear physics and astrophysics. Accurate assessment of the value of the SNM incompressibility coefficient, K, which is directly related to the curvature of the EOS, is needed to extend our knowledge of the EOS in the vicinity of the saturation point. We review the current status of K as determined from experimental data on compression modes in nuclei using the mean-field-based random-phase approximation. The text was submitted by the authors in English.     

Continuity of the robustness of contextuality of empirical models

Recently, the robustness of contextuality (RoC) of an empirical model was discussed in [Sci. China-Phys. Mech. Astron. 59, 640303 (2016)], many important properties of the RoC have been proved except for its boundedness and continuity. The aim of this paper is to find an upper bound for the RoC over all of empirical models and prove that the RoC is a continuous function on the set of all empirical models. Lastly, a relationship between the RoC and the extent of violating the noncontextual inequalities is established for an n-cycle contextual box. This relationship implies that the RoC can be used to quantify the contextuality of n-cycle boxes.