# Discrete and Continuous Models and Applied Computational Science

**Editor-in-Chief**: Yuriy P. Rybakov, Doctor of Science (Physics and Mathematics), Professor, Honored Scientist of Russia

**ISSN: **2658-4670 (Print). **ISSN: **2658-7149 (Online)

**Founded in **1993. ** Publication frequency**: quarterly.

**Peer-Review**: double blind. **Publication language:** English.

**APC**: no article processing charge. **Open Access**: Open Access , DOAJ SEAL

**PUBLISHER**: Peoples’ Friendship University of Russia named after Patrice Lumumba (RUDN University)

**See the Journal History **to get information on previous journal titles.

**Indexation**: Russian Index of Science Citation, Scopus, VINITI RAS, DOAJ, Google Scholar, Ulrich's Periodicals Directory, WorldCat, Cyberleninka, East View, Dimensions, ResearchBib, Lens, Research4Life, JournalTOCs

Discrete and Continuous Models and Applied Computational Science was created in 2019 by renaming RUDN Journal of Mathematics, Information Sciences and Physics. RUDN Journal of Mathematics, Information Sciences and Physics was created in 2006 by combining the series "Physics", "Mathematics", "Applied Mathematics and Computer Science", "Applied Mathematics and Computer Mathematics".

Discussed issues affecting modern problems of physics, mathematical modeling, computer science. The widely discussed issues Teletraffic theory, queuing systems design, software and databases design and development.

Discussed problems in physics related to quantum theory, nuclear physics and elementary particle physics, astrophysics, statistical physics, the theory of gravity, plasma physics and the interaction of electromagnetic fields with matter, radio physics and electronics, nonlinear optics.

Journal has a high qualitative and quantitative indicators. The Editorial Board consists of well-known scientists of world renown, whose works are highly valued and are cited in the scientific community. Articles are indexed in the Russian and foreign databases. Each paper is reviewed by at least two reviewers, the composition of which includes PhDs, are well known in their circles. Author's part of the magazine includes both young scientists, graduate students and talented students, who publish their works, and famous giants of world science.

Subject areas:

- Mathematics
- Modeling and Simulation
- Mathematical Physics

- Computer Science
- Computer Science (miscellaneous)

## Current Issue

### Vol 32, No 2 (2024)

**Year:**2024**Articles:**9**URL:**https://journals.rudn.ru/miph/issue/view/1799**DOI:**https://doi.org/10.22363/2658-4670-2024-32-2

#### Full Issue

##### Marginal asymptotic diffusion analysis of two-class retrial queueing system with probabilistic priority as a model of two-modal communication networks

###### Abstract

In the paper, a retrial queueing system of \(M_2/M_2/1\) type with probabilistic priority and interruptions is considered as a model of a two-modal communication network. Two classes of customers come to the system according Poisson arrival processes. There is one service device (or channel). If a customer finds the server occupying by a customer of the same class, it goes to an orbit and makes a repeated attempt after a random delay. If an arrival customer finds the other class customer on the server, it can interrupt its service with the given probability and start servicing itself. Customers from the orbit behave the same way. There is a multiply access for customers in the orbit. Service times and inter-retrial times have exponential distributions. Customers are assumed heterogeneous, so the parameters of the distributions are different for each class. In the paper, we propose the original marginal asymptotic-diffusion method for finding of the stationary probability distributions of the number of each class customers under the long delays condition.

**Discrete and Continuous Models and Applied Computational Science**. 2024;32(2):140-153

##### Chronology of the development of active queue management algorithms of RED family. Part 3: from 2016 up to 2024

###### Abstract

This work is the first part of a large bibliographic review of active queue management algorithms of the Random Early Detection (RED) family, presented in the scientific press from 1993 to 2023. The third part will provide data on algorithms published from 2016 to 2023.

**Discrete and Continuous Models and Applied Computational Science**. 2024;32(2):154-171

##### Solution of a two-dimensional time-dependent Schrödinger equation describing two interacting atoms in an optical trap

###### Abstract

We introduce a numerical method to solve the two-dimensional time-dependent Schrödinger equation, which characterizes a system of two atoms with a finite-range interaction potential confined within a harmonic oscillator trap. We choose a Gaussian-shaped potential for the interaction potential. Such a system has been previously studied analytically, except that a zero-range interaction potential was used instead. We observe a strong agreement between the results for the two types of interactions. Also, we investigate the one-dimensional time-dependent Schrödinger equation for the relative motion and compute the ground state energy level as a function of the coupling strength.

**Discrete and Continuous Models and Applied Computational Science**. 2024;32(2):172-180

##### The recent progress in terahertz channel characterization and system design

###### Abstract

As the standardization of 5G New Radio (NR) systems operating in micro- and millimeter-wave frequency bands is over, scientific and industrial communities have begun to address the question of what 6G communications systems might or should be. While technological specifics are still in their early development phase, there is a common agreement that these systems will utilize the lower part of the terahertz band, namely, 100-300 GHz. This band poses a number of specific challenges for system designers, including the effects related to channel characteristics and the conceptually new requirements for electronics. This paper aims to report the current state-of-the-art channel characterization and communications system design. With respect to the former, we consider dynamic human body blockages and micromobility impairments. For the latter, we mainly concentrate on the physical layer devices for direct conversion schemes and the design of the so-called reconfigurable intelligent surfaces that will potentially serve as a cost-efficient blockage mitigation technique.

**Discrete and Continuous Models and Applied Computational Science**. 2024;32(2):181-201

##### Clenshaw algorithm in the interpolation problem by the Chebyshev collocation method

###### Abstract

The article describes a method for calculating interpolation coefficients of expansion using Chebyshev polynomials. The method is valid when the desired function is bounded and has a finite number of maxima and minima in a finite domain of interpolation. The essence of the method is that the interpolated desired function can be represented as an expansion in Chebyshev polynomials; then the expansion coefficients are determined using the collocation method by reducing the problem to solving a well-conditioned system of linear algebraic equations for the required coefficients. Using the well-known useful properties of Chebyshev polynomials can significantly simplify the solution of the problem of function interpolation. A technique using the Clenshaw algorithm for summing the series and determining the expansion coefficients of the interpolated function, based on the discrete orthogonality of Chebyshev polynomials of the 1st kind, is outlined.

**Discrete and Continuous Models and Applied Computational Science**. 2024;32(2):202-212

##### Statistical causality analysis

###### Abstract

The problem of identifying deterministic cause-and-effect relationships, initially hidden in accumulated empirical data, is discussed. Statistical methods were used to identify such relationships. A simple mathematical model of cause-and-effect relationships is proposed, in the framework of which several models of causal dependencies in data are described - for the simplest relationship between cause and effect, for many effects of one cause, as well as for chains of cause-and-effect relationships (so-called transitive causes). Estimates are formulated that allow using the de Moivre-Laplace theorem to determine the parameters of causal dependencies linking events in a polynomial scheme trials. The statements about the unambiguous identification of causeand-effect dependencies that are reconstructed from accumulated data are proved. The possibilities of using such data analysis schemes in medical diagnostics and cybersecurity tasks are discussed.

**Discrete and Continuous Models and Applied Computational Science**. 2024;32(2):213-221

##### Well-posedness of the microwave heating problem

###### Abstract

A number of initial boundary-value problems of classical mathematical physics is generally represented in the linear operator equation and its well-posedness and causality in a Hilbert space setting was established. If a problem has a unique solution and the solution continuously depends on given data, then the problem is called well-posed. The independence of the future behavior of a solution until a certain time indicates the causality of the solution. In this article, we established the well-posedness and causality of the solution of the evolutionary problems with a perturbation, which is defined by a quadratic form. As an example, we considered the coupled system of the heat and Maxwell’s equations (the microwave heating problem).

**Discrete and Continuous Models and Applied Computational Science**. 2024;32(2):222-233

##### Developing a computer system for student learning based on vision-language models

###### Abstract

In recent years, artificial intelligence methods have been developed in various fields, particularly in education. The development of computer systems for student learning is an important task and can significantly improve student learning. The development and implementation of deep learning methods in the educational process has gained immense popularity. The most successful among them are models that consider the multimodal nature of information, in particular the combination of text, sound, images, and video. The difficulty in processing such data is that combining multimodal input data by different channel concatenation methods that ignore the heterogeneity of different modalities is an inefficient approach. To solve this problem, an inter-channel attention module is proposed in this paper. The paper presents a computer vision-linguistic system of student learning process based on the concatenation of multimodal input data using the inter-channel attention module. It is shown that the creation of effective and flexible learning systems and technologies based on such models allows to adapt the educational process to the individual needs of students and increase its efficiency.

**Discrete and Continuous Models and Applied Computational Science**. 2024;32(2):234-241