R e v i e w s

Physics of nuclei and elementary particles

Moscow University Physics Bulletin 2016. **71**. N 3. P. 215

Peculiarities of electromagnetic interactions in silver isotopes are considered. Excited states of Ag isotopes are studied as a function of the mass number A = 95–117. Low-lying excited states reveal clear features that are specific for rotational spectra for the energies E < 4–5 MeV. In the energy domain above the nucleon separation threshold of 5–10 MeV, single-particle excited states overlap and produce a continuous spectrum. For energies E = 10–35 MeV, excitation of giant dipole resonance plays the most important role in Ag isotopes. Experimental data on the cross sections of photonuclear reactions in Ag isotopes are analyzed.

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Chemical physics, physical kinetics, and plasma physics

Moscow University Physics Bulletin 2016. **71**. N 3. P. 279

In this study, thermodynamic instabilities in hydrogen-helium fluid mixture have been analyzed. These kinds of investigations are inevitable for indicating hydrodynamic transitions in Hydrogen-Helium fluid mixture. Therefore, first we have derived equation of state of mixture via Barker-Henderson statistical perturbation theory. Moreover, we have used Yiping radial distribution function in calculating perturbed terms. Via equation of state, we have calculated excess Gibbs free energy and the Gibbs free energy in the long wavelength limit. By means of this energy in hand we could estimate degree of hetero-coordination and segregations of this mixture which is a measure for defining thermodynamic instabilities. At last, these measurements have made us capable of anticipating thermodynamic instabilities and coordination of mixture in different concentrations.

Show AbstractMoscow University Physics Bulletin 2016. **71**. N 3. P. 284

By using the reductive perturbation technique, the Kadomstev-Petviashvili (KP) equation for the first-order potential is derived,which is then transformed into a nonlinear Schrödinger equation (NLS) by using appropriate variable transformations. The latter admits a solitary wave solution. However, when the carrier waves frequency is much smaller than the dust plasma frequency, the DA waves evolve into the nonlinear modulation instability, generating modulated wave packets in the form of Rogue waves. The dependence of rogue waves profiles on the system parameters investigated numerically. The dusty plasma parameters in this system are within the ranges of the dusty plasma parameters corresponding to cometary tails, upper mesosphere and Jupiter's magnetosphere.

Show AbstractTheoretical and mathematical physics

Moscow University Physics Bulletin 2016. **71**. N 3. P. 229

A theoretical investigation has been made for studying the propagation of ion-acoustic waves (IAWs) in a weakly inhomogeneous, collisionless, unmagnetized, three-component plasmas, whose constituents are inertial ions, nonthermal electrons, and Boltzmannian positrons. Employing reductive perturbation method (RPM), the variable coefficients Korteweg–de Varies equation (KdV) is derived. At the critical ion density, the KdV equation is not suitable for describing the system. Thus, a new set of stretched coordinates is considered to derive the modified variable coefficients KdV equation. Above (below) this critical point the system supports compressive (rarefactive) solitons. The effect of plasma parameters on the soliton profile has been considered. It has been shown that the width and the amplitude of the soliton affected by wave propagation speed, ratio of positron-to-electron density, and nonthermal parameter.

Show AbstractMoscow University Physics Bulletin 2016. **71**. N 3. P. 237

Operational solutions to fractional-order ordinary differential equations and to partial differential equations of the Black–Scholes and of Fourier heat conduction type are presented. Inverse differential operators, integral transforms, and generalized forms of Hermite and Laguerre polynomials with several variables and indices are used for their solution. Examples of the solution of ordinary differential equations and extended forms of the Fourier, Schrödinger, Black–Scholes, etc. type partial differential equations using the operational method are given. Equations that contain the Laguerre derivative are considered. The application of the operational method for the solution of a number of physical problems connected with charge dynamics in the framework of quantum mechanics and heat propagation is demonstrated.

Show AbstractCondensed matter physics

Moscow University Physics Bulletin 2016. **71**. N 3. P. 272

We have performed ab-initio total energy calculations using the plane-wave ultrasoft pseudopotential technique based on the first-principles density-functional theory (DFT) to study the structural, elastic, mechanical, electronic, and optical properties of cubic Mg2TiO4. The calculated lattice parameter a is in good agreement with the experimental values. The independent elastic constants are calculated. The mechanical properties, including bulk, shear and Young’s modulus, Poisson’s coefficient, compressibility and Lamé’s constants are obtained using the Voigt-Reuss-Hill method. The Debye temperature is estimated using the Debye-Grüneisen model. Band structure, density of states and charge densities are shown and analyzed. In order to clarify the mechanism of optical transitions of cubic Mg2TiO4, the complex dielectric function, refractive index, extinction coefficient, reflectivity, absorption coefficient, loss function and complex conductivity function are calculated.

Show AbstractPhysics of nuclei and elementary particles

Moscow University Physics Bulletin 2016. **71**. N 3. P. 245

A description is given and calculation results are presented for a high-intensity electron-beam source that can produce sequences of four electron bunches of 1 nC each, following at a frequency of 50 Hz. The root-mean-square normalized transverse beam emittance of the bunch does not exceed 4 mm mrad, the root-mean-square duration is 3 ps, and the energy can be adjusted in the 35–50 MeV range.

Show AbstractOptics and spectroscopy. Laser physics

Moscow University Physics Bulletin 2016. **71**. N 3. P. 253

A version of an experiment with a correlated pair of entangled particles is considered. This experiment demonstrates an interesting effect of variations in the entangled photon polarization that shows the reality of all of the various superposition components and the corresponding state vector of the quantum system. The possible consequences of this are analyzed.

Show AbstractMoscow University Physics Bulletin 2016. **71**. N 3. P. 258

Specific features of the behavior of quantum particles in different experimental situations are considered. The variants of two-beam interference of single photon and other quantum particles, as well as their ability to form “standing” and “progressive” waves with the interference minima, i.e., “dead” zones in the propagation path, are studied. We also consider some type of quantum particle teleportation in an unconventional understanding of this word, where elementary particles overcome regions of the space where they cannot be, or rather the borders where the probability of finding them is zero. At these boundaries there is no pulse impact of particles on anything, it is as if they are unobservable. When observing three-beam interference, it turns out that all three modes should be present simultaneously in the light field prior to photodetection. If each mode involves a photon, it contradicts the energy conservation law, it is indicative of the fact that the observed quantity (number of photons in the field) has no any particular value prior to the measurement (a priori) unless the quantum system is in the eigen state of a measured value (Fock state).

Show AbstractMoscow University Physics Bulletin 2016. **71**. N 3. P. 266

The processes of the formation of phase spatial structures (patterns) in the cross section of a light wave in a passive nonlinear ring resonator are considered. Analytical and numerical calculations are performed. The potential to form roll- and hexagon-type phase patterns, which are the product of competitive dynamics of nonlinear modes in a resonator, and more complex phase patterns associated with cooperative dynamics of nonlinear modes is demonstrated by numerical modeling.

Show AbstractAstronomy, astrophysics, and cosmology

Moscow University Physics Bulletin 2016. **71**. N 3. P. 292

The structure of the magnetic field in the magnetospheric during the storm of February 14, 2009 is studied. The model parameters that characterize the magnetospheric magnetic field are calculated every hour on the basis of solar wind data and the evolution of the magnetic field during the storm is reproduced using the A2000 model of the Earth’s magnetosphere. It is shown that extremely quiet geomagnetic conditions in 2009 promoted the expansion of the magnetosphere and were favorable for the formation of magnetic- island-like structures (plasmoids) in the geomagnetic tail. It is ascertained that negative variations in the Bz component could occur in the nightside magnetosphere in situations where the magnetic flux through the tail lobes exceeded certain thresholds, which depend on the parameters of the magnetospheric current systems. It is shown that the formation of magnetic islands decreases the magnetic flux through the tail lobes and prevents excessively strong development of the magnetic field in the tail.

Show AbstractMoscow University Physics Bulletin 2016. **71**. N 3. P. 299

The article presents the first results of state vector refinement for the «Spectr-R» spacecraft of «Radioastron» mission which is a part of earth-space radio interferometer. The state vector contains three spacecraft’s components for position and three components for velocity in Geocentric Celestial Reference System. Kahlman filtering iteration process based on a radio range and Doppler data allows to refine the components during each iteration. The paper demonstrates, that obtained results on orbit refinement improve orbit accuracy provided by Keldysh Institute of Applied Mathematics.

Show AbstractMoscow University Physics Bulletin 2016. **71**. N 3. P. 309

In this paper, the apparent motions of quasars, which are the reference sources of the international celestial reference system (ICRS), are analyzed. Kinematic parameters from four catalogs compiled by different research groups are used. Apparent motions are expanded on a special set of vector functions on the sphere that are an irreducible representation of the rotation group O(3). The degree of the noninertiality of the barycentric reference system caused by the rotation of the solar system around the galactic center is estimated according to expansion coefficients. The direction and magnitude of the acceleration vector are calculated and compared with the alternative estimates. This method is discussed as a way to test Newton’s law on a large scale.

Show AbstractMoscow University Physics Bulletin 2016. **71**. N 3. P. 317

The detection of gravitational waves by a cluster of satellites is considered. The detector is an optical interferometer formed of several satellites. The calculations for three spacecraft are given. The complete detector response to the monochromatic gravitational wave generated by a binary star is computed.

Show AbstractPhysics of Earth, atmosphere, and hydrosphere

Moscow University Physics Bulletin 2016. **71**. N 3. P. 323

The run-up of long waves on the coast of a bay with a parabolic cross-section, where the region of constant depth along the principal axis of the bay is connected with the linearly inclined segment, is considered. The study is carried out analytically in the framework of the nonlinear shallow-water theory under the approximation that the height of the initial wave is small compared to the basin depth, and the reflection from the inflection point of the bottom is negligibly small. Three types of incident waves, viz., a sinusoidal wave and solitary waves of positive and negative polarities, are considered in detail. It is shown that a sinusoidal wave undergoes nonlinear deformation at a segment of constant depth faster than solitary waves of positive and negative polarities. Solitary waves of negative polarity steepen somewhat faster than solitary waves of positive polarity. Waves of positive polarity steepen at wave front, while waves of negative polarity steepen at wave rear. These differences in steepness may become crucial at the wave run-up stage, since the wave run-up height on the coast of a bay with a parabolic cross-section is directly proportional to the steepness of a wave that arrives at the slope and can lead to the anomalous run-up of waves on the coast.

Show AbstractMoscow University Physics Bulletin 2016. **71**. N 3. P. 329

Abstract—The results of modeling the direct and inverse problems of low-orbital satellite ultraviolet (UV) tomography of the ionospheric 135.6 OI volume emission rate are presented. The direct problem was solved with the orbital geometry of DMSP block 5D3 satellites with SSUSI and SSULI UV spectrographs among the other payloads, the real operating parameters of these instruments (the scan rate and the interval of scan angles), and the set of the model distributions of the volume emission rate that contain irregularities on various scales. The solution of the direct problem yields the radiation intensities in the 135.6 nm line, which is used as the input data for reconstructing the initial (prototype) model distributions of the volume emission rates. The obtained system of linear equations (SLE) was solved using the Algebraic Reconstruction Technique (ART) and Simultaneous Iterative Reconstructive Technique (SIRT) algorithms, which are highly efficient in problems of the low-orbit radio tomography of the ionosphere. It is shown that the initial model distribution can be successively reconstructed if one takes the non-negativity condition of the solution into account, uses weighting functions to decrease the solution in the regions where it is known to be a priori small, and applies inter-iteration smoothing to eliminate the effects of the approximation errors. Here, the averaging parameters should decrease in the course of the iterations. With these constraints fulfilled, the computational costs of the ART- and SIRT-based solutions are similar, while the reconstruction error is approximately 6%. The influence of random errors and bias in the data on the results of the reconstruction is explored. It is shown that with a given error level of the initial data the parameters of the reconstruction algorithms can be adjusted in such a way as to efficiently suppress the influence of the noise with a relative amplitude of 2–3% on the solution.

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