Mathematical and computer simulation of semiconductor systems of various dimensions and the elements of device structures based on them

The article, in the form of a minireview, reflects the results of theoretical, and partly experimental investigations of the electrical, optical and magnetic phenomena in three-dimensional, two-dimensional, one-dimensional and zero-dimensional systems and elements of device structures made of germanium, silicon, carbon and other chemical elements carried out at the Faculty of Physics of Belarusian State University over the past 25 years.

The method of events separation with overlapping signals

In this paper, we propose a method for the rejection of the background from the superposition of signals from different, almost simultaneously occurring events in the calorimeter for the COMET experiment. The basic idea is to use the chi-squared distribution obtained from fitting the recorded shape of the signal with an average waveform. The elaborated method is applied for the reconstruction of events with overlapping signals from the electron and radiative capture of neutrons by the 175Lu nucleus, as well as overlapping signals from two electrons born as a result of the decay of muons in the bound state with an aluminum nucleus with impulses causing a “false” signal of the μ – e conversion. The method showed a good ability to separate events, meanwhile, the separation time is significantly less than the FWHM of the pulse shape.

Advanced scintillation materials for calorimetry at circular colliders

The most probable scenario for the development of experimental high-energy physics in the next 50 years is the creation of a family of Future Circular Colliders (FCC) at CERN, a Circular Electron–Positron Collider at China, and a Future Electron-Ion Collider at Brookhaven (USA), which continue the Large Hadron Collider (LHC) scientific program within the framework of the Standard Model and beyond it. The first generation of colliders to be put into operation will utilize the electron beam as one of the colliding species to provide precise mass spectroscopy in a wide energy range. Similarly to the measurements at the high luminosity phase of the LHC operation, the most important property of the detectors to be used in the experimental setup is a combination of the short response of the detectors and their high time resolution. The radiation tolerance to a harsh irradiation environment remains mandatory but not the main factor of the collider’s experiments using electronic beams. A short response in combination with high time resolution ensures minimization of the influence of the pile-up and spill-over effects at the high frequency of collisions (higher than 50 MGz). The radiation hardness of the materials maintains the long-term high accuracy of the detector calibration. This paper discusses the prospects for using modern inorganic scintillation materials for calorimetric detectors at future colliders.

On analytical methods for calculating the steady-state temperature field in a circular cylindrical shell

The present paper presents two analytical methods for calculating the steady-state temperature field in a circular cylindrical shell. The effectiveness of the methods in terms of accuracy in comparison with the classical approach, based on Bessel functions, is analyzed. The proposed analytical algorithms contain relatively simple computational operations. Since they do not use special functions, the algorithms can be used to solve a wide range of problems.

The radiation of a spin-free particle in the field of a plane electromagnetic wave

In this paper, we obtained a solution for the equation of motion of a charged spinless particle in the field of a plane electromagnetic wave. Relativistic expressions for the cross section of Compton scattering by a charged particle of spin 0 interacting with the field of a plane electromagnetic wave are calculated. Numerical simulation of the total probability of radiation as the function of the electromagnetic wave amplitude is carried out. The radiation probability is found to be consistent with the total cross section for Compton scattering by a charged particle of spin 0.

Functional differentiation of integral operators of special form and some questions of the inverse interpolation

This article is devoted to the problem of operator interpolation and functional differentiation. Some information about the variational derivatives and explicit formulas for the exact solutions of the simplest equations containing the first variational derivatives of the required functional are given. For functionals defined on sets of functions and square matrices, various interpolating polynomials of the Hermitе type with nodes of the second multiplicity, which contain the first variational derivatives of the interpolated operator, are constructed. The presented solutions of the Hermitе interpolation problems are based on the algebraic Chebyshev system of functions. For analytic functions with an argument from a set of square matrices, explicit formulas for antiderivatives of functionals are obtained. The solution of some differential equations with integral operators of a special form and the first variational derivatives is found. The problem of the inverse interpolation of functions and operators is considered. Explicit schemes for constructing inverse functions and functionals, including the case of functions of a matrix variable, obtained using certain well-known results of interpolation theory, are demonstrated. Data representation is illustrated by a number of examples.

The effective algorithm of ensuring the integrity of the transmitted information

The problem of ensuring the integrity of the transmitted information in modern information and communication systems is considered in this paper. An optimized algorithm for detecting and correcting errors in the information transmitted over communication lines is proposed. It was developed on the basis of the results of previous studies of the error correction method based on the parity values of the coordinates of a binary matrix. An easy-to-implement, high-speed and efficient error detection algorithm is proposed which is focused on the use of small binary matrices, for example, (4 × 8) or (7 × 8) bits. In such matrices, the possible number of errors that appear in them during the transfer of information is relatively small and easily detected.

The approximation of an isolated epidemic process wave using a combination of exponents

The most commonly used methods for the medium- and long-term forecasting of epidemic processes are based on the classical SIR (susceptible – infected – recovered) model and its numerous modifications. In this approach, the dynamics of the epidemic is approximated using the solutions of differential or discrete equations. The forecasting methods based on the approximation of data by functions of a given class are usually focused on obtaining a short-term forecast. They are not used for the long-term forecasts of epidemic processes due to their insufficient efficiency for forecasting nonstationary processes. In this paper, we formulated a hypothesis that the primary waves of the COVID-19 pandemic, which took place in a number of European countries, including the Republic of Belarus, in the spring-summer of 2020 are isolated and therefore can be regarded as processes close to stationary. On the basis of this hypothesis, a method of approximating isolated epidemic process waves by means of generalized logistic functions with an increased number of exponents was proposed. The developed approach was applied to predict the number of infected people in the Republic of Belarus for the period until August 2020 based on data from the beginning of the epidemic until June 12, 2020.

On the absence of logarithmic singularities in the solutions of Lamé-type equations

The object of this research is linear differential equations of the second order with regular singularities. We extend the concept of a regular singularity to linear partial differential equations. The general solution of a linear differential equation with a regular singularity is a linear combination of two linearly independent solutions, one of which in the general case contains a logarithmic singularity. The well-known Lamé equation, where the Weierstrass elliptic function is one of the coefficients, has only meromorphic solutions. We consider such linear differential equations of the second order with regular singularities, for which as a coefficient instead of the Weierstrass elliptic function we use functions that are the solutions to the first Painlevé or Korteweg – de Vries equations. These equations will be called Lamé-type equations. The question arises under what conditions the general solution of Lamé-type equations contains no logarithms. For this purpose, in the present paper, the solutions of Lamé-type equations are investigated and the conditions are found that make it possible to judge the presence or absence of logarithmic singularities in the solutions of the equations under study. An example of an equation with an irregular singularity having a solution with an logarithmic singularity is given, since the equation, defining it, has a multiple root.

The Yb3+:LuAlO3 crystal as an active medium for picosecond mode-locked lasers

Herein, we report on the mathematical modelling and experimental study of the regime of nonsoliton mode locking in a laser based on the Yb3+:LuAlO3 (Yb:LuAP) crystal with longitudinal pumping by laser diode radiation. Simulation based on the Haus master equation permitted to determine the requirements for the parameters of a saturable absorber (SA), the level of the average output power, the size of the TEM00 mode of the cavity in the active element and on the gate to obtain a stable regime of generation of picosecond laser pulses. Laser experiments were carried out in a fourmirror X-shaped resonator using a semiconductor saturable mirror (SESAM) as a passive modulator and a laser diode with a fiber output of a maximum power up to 30 W at a wavelength of 978.5 nm as a pump source. We obtained a stable passive mode locking with a maximum average output power of up to 12 W and an ultrashort pulse duration of about 2 ps at an optical conversion efficiency of pump radiation into lasing radiation of about 38 %. Laser pulses were obtained at a central wavelength of about 999 nm with a minimum Stokes shift (about 2 %) with respect to the pump radiation, which significantly reduced the thermal load on the active element. Additionally, the preliminary results on the second harmonic generation and synchronous pumping of a parametric light generator using a Yb3+ : LuAlO3 crystal laser as a pump source are presented.