Faculty of Physics
M.V.Lomonosov Moscow State University
Biophysics and medical physics

## Radiation technology in medicine: Part 2. Using isotopes in nuclear medicine

### A.P. Chernyaev$^{1,2}$, P.Y. Borschegovskaya$^1$, A.A. Nikolaeva$^1$, S.M. Varzar$^1$, V.T. Samosadniy$^3$, G.A. Krusanov$^1$.

Moscow University Physics Bulletin 2016. 71. N 4. P. 339

In this article, we discuss the role of radionuclide technologies among other nuclear methods used in medicine. We analyze the condition and perspectives of the development of nuclear technology with regard to using radionuclides in medicine, for brachytherapy in particular. We review the modern use of radionuclide facilities in medicine.

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Condensed matter physics

## A Comparison on Absorption Coefficients for Secondary Electron Emission Obtained from Two Different Formulas

### Zhang Peng

Moscow University Physics Bulletin 2016. 71. N 4. P. 420

In this work, the absorption coefficients for secondary electron emission, and, that appeared respectively in the two different formulas, and were derived with a standard deviation rate analysis method based on a Monte Carlo simulated secondary electron yield. Both the energy dissipation in depth for primary electrons, and the depth distribution for the number of secondary electrons including cascade electrons, were obtained by the same Monte Carlo method, in which the discrete inelastic scattering model was employed. The calculation results for Cu and Mg show that the -curve differs significantly from the -curve, and thus as well as from , for varied incidence angles (00-800) and low-energy primary electrons (up to 3 keV). The absorption coefficient -values derived from a realistic depth distribution of cascade secondary electrons, , then describe more accurately the nature of attenuation behavior of secondary electrons than -values that associated with the approximate formula.

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## Short-term reversible changes in the dielectric dispersion of a barium titanate single crystal

### N.D. Gavrilova$^1$, I.A. Malyshkina$^1$, V.K. Novik$^2$

Moscow University Physics Bulletin 2016. 71. N 4. P. 400

An effect of spontaneous fluctuation of the dispersion frequency was detected during investigations of the dielectric dispersion of a BaTiO$_3$ single crystal while measuring under the electric field only. A decrease in the dispersion frequency by three orders of magnitude and its subsequent return to the previous value was observed. A possible mechanism of this phenomenon is suggested, which involves the dynamics of the screening process.

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## An optical study of high-pressure water-jet dynamics

### I.A. Znamenskaya, D.A. Nersesyan, N.N. Sysoev, E.Y. Koroteeva, Y.N. Shirshov

Moscow University Physics Bulletin 2016. 71. N 4. P. 405

This paper considers the results of an optical study of high-speed fluid jets ejected from a nozzle at 400 MPa. The objective was to study two-phase flows under extreme conditions and to analyze the possibility of the optimization of the device design. The process of a high-speed water jet as it exits the focusing tube of the Flow WaterJet Mach3 abrasive cutting machine, along with its development, and the state of the stationary flow are considered. The shadow method was used to investigate the initial stage of high-speed water-jet formation, as well as the jet-head dynamics during the first 200–400 µs after ejection at 400 MPa. A Photron FASTCAM SA5 high-speed camera with a frame rate of one million shots per second and an exposure time of 1 µs and a FLIR SC7000 infrared thermal camera with a frame rate of 400 shot/s and an exposure time of 1 ms were employed in order to study the jet-formation process. The spatiotemporal characteristics of the jet-development process were analyzed. The jet velocity and the starting jet head acceleration were measured by post-processing of digital images.

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## Investigation of the chiral properties of configurations of (H$_2$O)$_n$, K$^+$(H$_2$O)$_m$ and Na$^+$(H$_2$O)$_m$ ($n=4-8$, $m=5-10$) small water clusters at 1 K

Moscow University Physics Bulletin 2016. 71. N 4. P. 413

The Monte Carlo procedure and a new method to determine the chirality of water environments and their classification were used for the first time to study the chiral properties of small water clusters such as (H$_2$O)$_n$, K$^+$(H$_2$O)$_m$, and Na$^+$(H$_2$O)$_m$ ($n = 4–8$, $m = 5–10$) at a temperature of 1 K. The probability that the studied water clusters will be chiral becomes higher at an increase in their size. It is revealed that a small water cluster devoid of impurities is not dominated by one of the arrangements (right or left). The addition of K$^+$ or Na$^+$ impurity ions does not change the equilibrium distribution of right and left configurations in the 10 000-sample set.

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Theoretical and mathematical physics

## Absorption and generation of electromagnetic waves by structural inhomogeneities of solid

### P.I. Pronin, N.Ed. Smirnov

Moscow University Physics Bulletin 2016. 71. N 4. P. 349

The integrability conditions of the electromagnetic field equations in a continuum with defects and their wave solutions are found. The following dislocation effects on the electromagnetic wave propagation in a continuous medium are investigated: the change in the direction of the electromagnetic wave propagation in a continuous medium; the rotation of the polarization plane of electromagnetic field wave in a continuous medium; the excitation of longitudinal components of the electromagnetic wave in a continuous medium and the change in the electromagnetic wave intensity related to this phenomenon. The energy balance equation for the electromagnetic field in a continuum with a stationary distribution of dislocation is found and it is shown that an electromagnetic wave excites exciton modes localized at dislocations in the solid.

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## On improvable bounds for polaron systems in an external potential

### N.N. Bogolubov, A.V. Soldatov

Moscow University Physics Bulletin 2016. 71. N 4. P. 356

A variational approach is proposed that allows one to obtain in a regular way a sequence of improvable upper bounds for the ground-state energy of various polaron models confined in an external electrostatic potential. The proposed approach can be used for an arbitrary electron–phonon interaction constant and allows generalization to the case of polaron-type systems in a constant external magnetic field.

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## On the localization of eigenfunctions of the Laplace operator in rectangular domains

### A.L. Delitsyn

Moscow University Physics Bulletin 2016. 71. N 4. P. 363

The localization problem is considered for eigenfunctions of the Laplace operator in a domain that consists of two rectangles linked by a small hole. The localization of the eigenfunction is proven in a subdomain. The velocity is estimated for the convergence of an eigenvalue of the original problem to a subdomain eigenvalue.

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## Finite-element methods for junction problems for coaxial and radial waveguides

### A.L. Delitsyn

Moscow University Physics Bulletin 2016. 71. N 4. P. 368

We apply the method of mixed finite elements to the junction problem for coaxial and radial waveguides. The problem is reduced to an internal boundary-value problem with nonlocal boundary-value conditions. In the low-frequency range, we compare the results of the finite-element method with the Otto relationship.

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## Commutative partially integrable systems on Poisson manifolds

### A. V. Kurov

Moscow University Physics Bulletin 2016. 71. N 4. P. 375

We show that, as distinct from completely integrable Hamiltonian systems, a commutative partially integrable system admits different compatible Poisson structures on a phase manifold that are related by a recursion operator. The existence of action–angle coordinates around an invariant submanifold of such a partially integrable system is proved.

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Physics of nuclei and elementary particles

## The binding energies and stability of heavy and superheavy nuclei

### N.N. Kolesnikov

Moscow University Physics Bulletin 2016. 71. N 4. P. 381

A realistic model-free description of the energies of heavy and superheavy nuclei is proposed. It is shown that: (a) the charge $Z^∗$ of the most stable isobar increases proportionally to the mass number A: $Z^∗ = = aA+ b$ , where $a = 0.355$, $b = 9.3$; (b) the energy of $\beta$-decay of isobar $Q\beta (A,Z)$ increases as a linear function of difference $Z − Z^∗$: $Q\beta = k(Z − Z^{∗}) + D$, where $k = 1.13$ MeV and $D$ depends of nuclear parity; (c) the energy of $\alpha$-decay of isobars increases independently of parity in proportion to the difference $Z − Z$^{∗}$:$Q\alpha (A,Z) = Q^{∗}\alpha (A) + \lambda (Z − Z^{∗}(A))$, where$\lambda = 2k(1 − 2a) = 0.65$MeV; (d) the reduced energy of$\alpha$-decay,$Q^{∗}\alpha (A)$, is minimal at$A = A_{0} = 232$, where$Q^{∗}\alpha (A_{0}) = 4.9$MeV, and linearly increases at$A ̸= A_0$, then$Q^{∗}\alpha (A0) = \varepsilon |A− _{A}0|$, where$\varepsilon = 0.212$MeV at$A < A_{0}$and$\varepsilon =0.0838$MeV at$A > A_{0}$. Using the obtained formulas, the energies of$\alpha$-decay are calculated for all heavy and superheavy nuclei with root mean square deviation of 0.2 MeV. It is shown that the region near$A = A_{0}$is the domain of most stable (heavy and superheavy) nuclei, and the region$A > 280$is the domain of increased stability. Show Abstract Optics and spectroscopy. Laser physics ## The stability of the stationary generation of a multichannel laser ## The stability of the stationary generation of a multichannel laser ### O.E.Nanii$^1$, A.I.Odintsov$^1$, A.P.Smirnov$^2$, A.I.Fedoseev$^1$Moscow University Physics Bulletin 2016. 71. N 4. P. 389 Stable generation of multi-channel lasers that find application in optical communication systems with spectral multiplexing is studied theoretically. A computational model to determine the frequencies and increments of self-oscillating perturbations depending on the key laser parameters and the characteristics of the channels cross-saturation is proposed. It is shown that for typical conditions of an erbium-doped fiber laser, multichannel generation with a large number of channels (more than ten), although stable, is characterized by large fluctuations of channel power due to the very small decay increments of perturbations caused by small technical fluctuations of the laser parameters. Show Abstract ## The stability of the fractal properties of quasi-periodic multilayered structures ## The stability of the fractal properties of quasi-periodic multilayered structures ### M.G. Davydova$^1$, P.V. Korolenko$^{1,2}$, Yu. V. Ryzhikova$^1$Moscow University Physics Bulletin 2016. 71. N 4. P. 395 The stability of fractal characteristics has been analyzed in the optical spectra of quasi-periodic multilayered systems with the deterministic changes therein. The transformation of the summation principle of their construction, the transition to the approximant model, and the preparation of metamaterial-based layers have been shown to exert a strong influence on the scaling of the parameters in multilayered systems. Show Abstract Biophysics and medical physics ## The dose kernels of pencil and differential pencil photon beams with the spectrum of treatment machines with a$^{60}$Co source in water and their analytical approximation ## The dose kernels of pencil and differential pencil photon beams with the spectrum of treatment machines with a$^{60}$Co source in water and their analytical approximation ### V.A. Klimanov$^{1,2,3}$, A.N. Moiseev$^4$, M.A. Kolyvanova$^{2,3}$, V.L. Romodanov$^1$, A.P. Chernyaev$^2\$

Moscow University Physics Bulletin 2016. 71. N 4. P. 431

This article presents the results of calculations by the Monte Carlo method in the EGSnrc toolkit of the spatial distributions of absorbed energy or dose kernels in water for a pencil beam or differential pencil beam (point spread function) with the spectrum of ROKUS-M treatment machines. The photon spectrum of the ROKUS-M machines was also calculated by the Monte Carlo method. The calculated dose-kernel results were approximated separately for the radial distribution of the primary and the scattered component of dose kernels by sums of exponential functions divided by the squared radius for a differential pencil beam and by the radius for a pencil beam. This approximation makes direct implementation possible for wellknown model-based techniques for finding 3D dose distributions in external radiation therapy. A simple analytical procedure to verify approximation formulas is proposed. It is also applicable in independent checks of dose distributions along the treat beam axis, which is an important guideline of the Radiation Therapy Quality Assurance Program.

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Astronomy, astrophysics, and cosmology

## The gravitational influence of Venus, the Earth, and Jupiter on the 11-year cycle of solar activity

### V.P. Okhlopkov

Moscow University Physics Bulletin 2016. 71. N 4. P. 440

This paper presents the calculations of the resulting tidal force of Jupiter, Venus, and Earth, that act on the Sun. Considering the tidal forces as the difference of gravitational forces that act on the extreme points of the Sun’s diameter and on the center of the Sun, it is shown that there are large variations in the resulting tidal force (RTF) at the moments of linear configurations of Venus, the Earth, and Jupiter, and that the maximum variations of the RTF are in a strong agreement with the minimum values of the JEV planetary index, as introduced by the author in previous works.

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Physics of Earth, atmosphere, and hydrosphere

## Theoretical and experimental studies of the boundaries between two immiscible liquids in a vortex flow with a free surface

### T.O. Chaplina, A.V. Kistovich, E.V. Stepanova

Moscow University Physics Bulletin 2016. 71. N 4. P. 447

This paper discusses an analytical representation of phase boundaries in a composite vortex that result from the circular motion of a given volume of water with a given volume of a light immiscible admixture (oil) on its surface in a cylindrical container. The vortex structure consists of a vortex cavity in the center of a container and an oil body inside the vortex. Under the assumption of axial symmetry, analytical expressions were first derived describing the shape of the phase boundaries. A series of experiments was carried out and numerical calculations were compared with the experimental data. The calculated and measured phase boundary shapes were found to be satisfactorily consistent with each other. Requirements were determined regarding the experimental study of the shape of an oil body in a composite vortex and its stability depending on the governing parameters

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## The use of artificial neural network segmentation of multivariate time series for the analysis of geomagnetic disturbances

### S.A. Dolenko, I.N. Myagkova, I.G. Persiantsev

Moscow University Physics Bulletin 2016. 71. N 4. P. 454

This study is devoted to a preliminary analysis of the segmentation of multivariate time series of the parameters of the solar wind, interplanetary magnetic field, and the Dst index using artificial neural networks, for the period from November 1997 to March 2014. It is shown that this technique allows progress in understanding the dynamics of the Earth’s magnetosphere.

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