Moscow University Physics Bulletin

A review of the experiments performed to date and calculations on the study of doses from secondary neutrons during the operation of medical electron accelerators of various manufacturers is presented. The fundamental differences between the heads of the three largest manufacturers (Varian, Elekta, and Siemens) are given. This article contains data on flux densities and doses for different accelerator models and operating modes. The data analysis showed that the dose from secondary neutrons when irradiating patients on a linear medical accelerator with bremsstrahlung should be taken into account, since its contribution can reach 2.04% at a maximum energy of up to 24 MeV. The contribution to the absorbed dose of secondary neutron fluxes must be evaluated when planning radiation therapy; all other things being equal, it is also necessary to choose modes of operation with the lowest rated energy for treating patients.

The periodic problem that arises in the mathematical modeling of the vertical transfer of an anthropogenic impurity in the lower troposphere is considered for the nonlinear diffusion transfer equation. The model problem in dimensionless variables is classified as a nonlinear singularly perturbed reaction—diffusion—advection problem, which is studied by the methods of asymptotic analysis. Using the method of boundary functions and the asymptotic method of differential inequalities based on the principle of comparison, an asymptotic problem solution of arbitrary-order accuracy is constructed with the further substantiation of constructions and the study of this solution for the Lyapunov asymptotic stability property. The results of this work are illustrated using an example that describes the concentration field of a linear substance sink.

We consider the mathematical problem of electromagnetic wave scattering by a plasmonic dimer composed of noble metal nanoparticles with sizes less than tens of nanometers. To develop mathematical models, the efficient discrete sources method is used, which makes it possible to take all peculiar features of such systems into account, including the shapes of particles and the effects of spatial dispersion, which are also known as nonlocal effects. It is shown that in the case of external fields that are independent of the azimuthal harmonics, it is possible to approximate the problem solution using the system of vertical dipoles on the axis of symmetry of the particle. Based on the hybrid scheme of the discrete sources method, the problem of excitation of a dimer by the field of a point charge in uniform straight motion in a homogeneous space is first solved.

The results of a theoretical and computational study of the electron exchange of ions with metal nanoclusters are presented. Scanning tunneling microscopy and electron exchange in scattering of slow ions are used widely in experimental studies of the electronic structure and surface reactivity of metal nanoclusters. Due to the complexity of direct experiments, computer simulation is an important tool for nanostructure analysis. The results of calculation of the eigenvalues of the electron wave function accurately characterize the spatial distribution of the electron density on the nanocluster surface determined using scanning tunneling microscopy. The electron energy inside a small nanocluster is quantized, and the spatial distribution of the electron density is discrete. The quantization of electron energy (discrete electronic structure) has a significant influence on resonant electron processes, including the electron exchange of ions with nanoclusters and electron tunneling in scanning tunneling microscopy. The model problem of electron tunneling from a negative ion to a nanocluster was used as an example to demonstrate that the discrete electronic structure is manifested in the form of a quantum-size effect of electron exchange and a nonmonotonic dependence of the differential conductivity on the bias voltage. A quantitative explanation for the experimentally observed order-of-magnitude enhancement (compared to bulk samples) of the probability of neutralization of alkali metal ions on metal nanoclusters is also provided.

Near-threshold coherent photoproduction of π⁰-meson on the deuteron is investigated. Numerical results for the unpolarized differential and total cross sections, the linear photon Σ-asymmetry, the vector T₁₁ and tensor T_2M (M = 0, 1, 2) deuteron spin asymmetries, and the spin asymmetry \(\tilde{T}_{20}\) of the total cross section are presented. The role of D-wave component of the deuteron wave function on these physical observables is studied. The calculations are based on the impulse approximation in which we use the realistic and high-precision Bonn NN potential (full model) for the deuteron wave function and the unitary isobar MAID-2007 model for the elementary γN → πN amplitude that describes well the threshold region. We have found that the D-wave component has a negligible effect on the unpolarized cross sections and the vector deuteron T₁₁-asymmetry at photon lab-energies close to threshold. On the contrary, we have obtained a significant role of the D-wave part of the deuteron wave function on the Σ, T_2M, and \(\tilde{T}_{20}\) spin asymmetries. The results for the unpolarized differential cross section are compared to the experimental data from TAPS and a satisfactory agreement within the uncertainties has been obtained at forward pion angles. At backward pion angles, our results underestimate the experimental data and a disagreement has been found.

The conditions for ensuring the equilibrium steady-state of a high-density hollow electron beam transported in cylindrical drift tubes and focused by a uniform magnetic field are investigated. The results of numerical calculations of the currents limited due to the longitudinal deceleration of electrons by the space charge and the violation of equilibrium transverse magnetic focusing conditions when transporting beams of different configurations in klystron-type devices are presented. The limitations of the working length of the device associated with the excitation of diocotron instability are estimated. The calculation results were compared with the data obtained by the quasi-3D Arsenal—MSU computer code and by the approximate analytical formulas of other authors.

The field of neuroaesthetics, which allows description of the beauty of fractals, has been considered in this work. The arguments for the concept of selection of the spatial frequencies of fractal images in the brain cortex have been discussed. Special attention has been paid to the stability of the scaling parameter of a fractal and its Fourier transform, indicating the ability for rapid optical signal processing in particular brain sites. Rapid Fourier processing of visual signals makes one feel comfortable and causes the sense of beauty when contemplating a fractal object. The results of this study enable one to explain the efficiency of visual art therapy in medicine from the physical viewpoint, as well as to give a physical interpretation to some statements of modern aesthetics.

Electron-vibrational interactions play a key role in limiting charge mobility in organic semi-conductors. This paper reports a theoretical study of the electron—phonon interaction in the 5,5′-diphenyl-2,2′-bitiophene (PTTP) molecule, which belongs to the class of thiophene-phenylene cooligomers, which are of great interest for organic optoelectronics due to their electron-transport and luminescent properties; these results are compared with anthracene, which is a model organic semiconductor. The contributions of various vibrational modes to the reorganization energy of PTTP and the anthracene molecules are revealed and it is shown that these contributions correlate with the intensities of the corresponding bands in the Raman spectrum. In particular, it is found that for the PTTP molecule the so-called I-mode with a frequency of ∼1460 cm⁻¹, which corresponds to collective vibration of atoms of all oligomer units, has the highest intensity in both spectra. These results indicate the promise of Raman spectroscopy for studying electron-vibrational interactions in organic semiconductors. Finally, the mobility of holes in PTTP and anthracene is estimated in the framework of the jump model and the reasons for their difference are analyzed. Based on these results, we propose some ways to reduce the electron-vibrational interaction in thiophene—phenylene cooligomers, which is important for the directional molecular design of organic semiconductors.

The influence of an external magnetic field on the phase-transition temperature for antiferromagnetic thin films is investigated. The computer modeling method for the antiferromagnetic Ising model with a thin film geometry is used. Films with thicknesses from 4 to 16 layers have been investigated. It is shown that the temperature of the antiferromagnetic phase transition decreases according to the square law as the external magnetic intensity increases. The rate of decrease of the phase-transition temperature depends on the film thickness and on the relationship between the exchange integrals on the surface and the bulk of the system. For each system, there is a limit value of the magnetic intensity such that no antiferromagnetic phase transition occurs if it is exceeded. The dependence of the limit value of the magnetic intensity on the relationship between the exchange integrals obeys the square law as well.

The problem of transmission and reflection of X-rays (0.1 Å ≤ λ ≤ 10 Å) from an infinite amorphous homogeneous wedge-shaped dielectric plate has been analytically solved. The obtained solution is a “zero” step in solving the problem of X-ray diffraction on a semi-infinite amorphous homogeneous dielectric wedge within the heuristic geometric diffraction theory.

A mathematical model is suggested for description of translation of the cell activation signals generated by interactions of TLR4 and TNFR2 receptors with ligands. The theoretical background to the construction of the model is offered and the main simulation results are presented. The model takes into account the possibility of self-activation of the cell induced by polymerization of receptors, intersection of signal cascades that may result in depletion of substrates of translating proteins and binding sites on the DNA. The probability of the activation event has a local maximum at the last layer of the reaction graph. The process of cell activation is described by use nonlinear system of singularly perturbed differential equations. All requirements on solution existence have been satisfied and approximate solution has been derived. The boundary conditions type is of importance. Suitably, the probability density of signal transmission from TNFR2 to the cell’s DNA has been specified on the membrane, and flow through the membrane has been set for the probability density of signal transmission from TLR4 to the cell’s DNA. These obstacles necessitate the use of a special algorithm for analyzing nonlinear differential systems with a small parameter for different boundary conditions. The probability densities are qualitatively different themselves, have distinctive structure, emphasizing different ways of cell activation. The density functions of the probability of cell activation make it possible to determine approximately the distribution of the effectiveness of activation inhibitors over the reaction graph layers.

The reflectance spectra of five near-Earth asteroids, one Mars crosser, and four classical asteroids of the main belt in the range 0.35–0.95 µm have been observed, calculated, and analyzed. Asteroids with a magnitude up to 17 were observed in 2013–2017 with a 2-m telescope with a CCD spectrograph with extremely low spectral resolution (R ∼ 100) of the Terskol Observatory of the Institute of Astronomy of the Russian Academy of Sciences in order to determine their taxonomic types and composition. These results show that the composition of some of the studied near-Earth asteroids is heterogeneous judging by the variations in their reflectance spectra within adjacent taxonomic classes. It is notable that some of these asteroids are binary. The physical and chemical-mineralogical interpretation of reflectance spectra is presented.

The Tsunami Observer automatic system for assessment of earthquake tsunami hazard has been operating since January 25, 2018. In this report we analyze the results of the system over the past year and a half, comparison of the estimates made by the system and in situ observations data is performed. The time delay of issue of focal mechanism, which is critical to fast tsunami hazards assessment, is discussed.

To optimize heating conditions during the Thellier procedure and to improve the reliability of paleofield determination, thermal stability experiments with titanomagnetite and titanomaghemite obtained by laboratory heating were conducted. The experiments were performed on P72/2 and P72/4 basalts of the rift zone of the Red Sea that contain titanomagnetite with a concentration of the magnetite component equal to (44.7 ± 3.9)% and (46 ± 5)%, respectively. It has been shown that the single-phase oxidation process prevails in annealing of titanomagnetite for 10 hours in a temperature range of 290–410°C in air. An increase in the annealing temperature up to 460–535°C means that single-phase oxidation is replaced by oxi-exsolution. The temperature range of thermal stability of the single-phase oxidized titanomagnetite expands with the degree of oxidation. In particular, at an oxidation state close to 0.9, titanomaghemite is stable up to temperatures of 410–460°C.

The use of the Thellier technique for studying the properties of the chemical remanent magnetization of single-phase oxidized titanomagnetite with an oxidation state above z ≥ 0.6 is limited to approximately 20% of its value. It is possible to stabilize the single-phase oxidized state of titanomagnetite at temperatures above 460°C and thereby to improve the quality of CRM research using the Thellier method by adjusting the value of the oxygen partial pressure.

The aim of this work is to study the fuel depletion of 30 kW miniature neutron source reactor (MNSR). Under operating conditions of two hours per day for five days a week at a peak thermal neutron flux of 1.0E+12 n/cm² s, the estimated core life is 10 years (200 days). The DRAGON5 code is utilizing to generate the fuel group constants and the infinite multiplication factor versus the MNSR reactor operating time, at different burn-up values. The amounts of uranium burnt up and plutonium produced in the reactor core are calculated using the DRAGON5 transport lattice code. The results are in good agreement with previous studies.

The authors apologize for the misprints in the article “Improved Generation of Higher Harmonics and Suppression of the Lowest Harmonics in an X-Ray FEL with a Two-Frequency Undulator” by K. Zhukovsky in Moscow University Physics Bulletin, 2018, Vol. 73, No. 5, pp. 462–469, DOI: https://doi.org/10.3103/S0027134918050193, and communicate the following corrected formula (5) for the Bessel coefficients f_n of the two-frequency undulator: