title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸Ñ ÑÐµÐ¿Ð¾ÑÐºÐ¸ Ð´Ð¸Ð¿Ð¾Ð»ÐµÐ¹
title: Ð²ÑÐ¿ÑÑÐºÐ½Ð°Ñ ÐºÐ²Ð°Ð»Ð¸ÑÐ¸ÐºÐ°ÑÐ¸Ð¾Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÐ°
titleType: Subtitle
title: Development of a program for modeling the interaction of a chain of dipoles
Creators: name: ÐÐµÐ¹Ð½Ð¸Ðº, ÐÐ»ÐµÐºÑÐ°Ð½Ð´Ñ
Publisher: name: Ð¡Ð°Ð½ÐºÑ-ÐÐµÑÐµÑÐ±ÑÑÐ³ÑÐºÐ¸Ð¹ Ð¿Ð¾Ð»Ð¸ÑÐµÑÐ½Ð¸ÑÐµÑÐºÐ¸Ð¹ ÑÐ½Ð¸Ð²ÐµÑÑÐ¸ÑÐµÑ ÐÐµÑÑÐ° ÐÐµÐ»Ð¸ÐºÐ¾Ð³Ð¾
Year: 2023
Subjects: Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¸Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸
Ð´Ð¸Ð¿Ð¾Ð»Ð¸
ÐºÐ²Ð°Ð·Ð¸ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ
Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ðµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ðµ Ñ Ð·Ð°Ð¿Ð°Ð·Ð´ÑÐ²Ð°Ð½Ð¸ÐµÐ¼
ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
ÑÐ¿ÐµÑÐ¸Ð°Ð»ÑÐ½ÑÐµ ÑÑÐ½ÐºÑÐ¸Ð¸
Ð¿Ð¾Ð¸ÑÐº Ð¾Ð¿ÑÐ¸Ð¼Ð°Ð»ÑÐ½ÑÑ ÐºÐ¾Ð½ÑÐ¸Ð³ÑÑÐ°ÑÐ¸Ð¹
mathematical models
dipoles
quasi-stationary solution
differential equation with delay
numerical integration
special functions
search for optimal configurations

description: ÐÐ°Ð½Ð½Ð°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð½Ð¾Ð³Ð¾ Ð¿ÑÐ¾Ð´ÑÐºÑÐ° Ð´Ð»Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸ Ð¸ ÑÐ¾Ð¾ÑÐ²ÐµÑÑÑÐ²ÑÑÑÐµÐ¹ ÐµÐ¹ Ð¼Ð°ÑÐµÐ¼Ð°ÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð² Ð¾Ð±Ð»Ð°ÑÑÐ¸ ÐºÐ²Ð°Ð½ÑÐ¾Ð²Ð¾Ð¹ ÑÐ°Ð´Ð¸Ð¾ÑÐ¸Ð·Ð¸ÐºÐ¸. Ð ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²ÐµÐ´ÑÐ½ Ð¾Ð±Ð·Ð¾Ñ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÑ Ð¼ÐµÑÐ¾Ð´Ð¾Ð² Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¸ Ð¸Ñ ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¸, Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¸ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ ÐºÐ²Ð°Ð·Ð¸ÑÑÐ°ÑÐ¸Ð¾Ð½Ð°ÑÐ½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ ÑÐ¸ÑÑÐµÐ¼Ñ Ð¸ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ ÑÑÐ½ÐºÑÐ¸Ð¸ Ð¿Ð¾Ð¿ÑÐ°Ð²ÐºÐ¸, Ð° ÑÐ°ÐºÐ¶Ðµ Ð·Ð½Ð°ÑÐµÐ½Ð¸Ðµ ÐºÑÐ¸ÑÐµÑÐ¸ÐµÐ² Ð´Ð»Ñ ÑÑÐ½ÐºÑÐ¸Ð¸ Ð¿Ð¾Ð¿ÑÐ°Ð²ÐºÐ¸, Ð±ÑÐ»Ð° Ð¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ð° Ð¾Ð¿ÑÐ¸Ð¼Ð¸Ð·Ð°ÑÐ¸Ñ Ð²ÑÑÐ¸ÑÐ»ÐµÐ½Ð¸Ñ ÑÐ¾ÑÑÐ°Ð²Ð»ÑÑÑÐ¸Ñ Ð´Ð°Ð½Ð½ÑÑ ÐºÑÐ¸ÑÐµÑÐ¸ÐµÐ² Ð¿ÑÐ¸ Ð¿Ð¾Ð¼Ð¾ÑÐ¸ ÑÑÐ½ÐºÑÐ¸Ð¹ ÐÐµÑÑÐµÐ»Ñ Ð¸ Ð¡ÑÑÑÐ²Ðµ Ð¸ Ð²ÑÐ¿Ð¾Ð»Ð½ÐµÐ½ ÑÑÐ´ ÑÐµÑÑÐ¾Ð² Ð´Ð»Ñ ÑÐ°Ð·Ð»Ð¸ÑÐ½ÑÑ ÐºÐ¾Ð½ÑÐ¸Ð³ÑÑÐ°ÑÐ¸Ð¹ ÑÐ°ÑÑÐµÐ¸Ð²Ð°ÑÐµÐ»ÐµÐ¹. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¿ÑÐ¾Ð²ÐµÐ´ÑÐ½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ Ð¿Ð¾Ð¼Ð¾Ð³ÑÑ Ð¾Ð¿ÑÐµÐ´ÐµÐ»Ð¸ÑÑ ÐºÐ°ÐºÐ¸Ð¼ Ð¾Ð±ÑÐ°Ð·Ð¾Ð¼ Ð½Ð°Ð¸Ð±Ð¾Ð»ÐµÐµ ÑÑÑÐµÐºÑÐ¸Ð²Ð½Ð¾ ÑÐ°ÑÐ¿Ð¾Ð»Ð°Ð³Ð°ÑÑ ÑÐ°ÑÑÐµÐ¸Ð²Ð°ÑÐµÐ»Ð¸ Ð´Ð»Ñ Ð´Ð¾ÑÑÐ¸Ð¶ÐµÐ½Ð¸Ñ Ð½ÑÐ¶Ð½ÑÑ ÑÑÑÐµÐºÑÐ¾Ð². Ð Ð´Ð°Ð»ÑÐ½ÐµÐ¹ÑÐµÐ¼ ÑÑÐ¾ Ð¿Ð¾Ð·Ð²Ð¾Ð»Ð¸Ñ Ð²Ð²ÐµÑÑÐ¸ ÐºÐ°ÑÐµÑÑÐ²ÐµÐ½Ð½ÑÑ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÑ Ð¼ÐµÐ¶Ð´Ñ Ð·Ð½Ð°ÑÐµÐ½Ð¸ÑÐ¼Ð¸ ÐºÑÐ¸ÑÐµÑÐ¸ÐµÐ² Ð¸ Ð²ÑÐ¾Ð´Ð½ÑÐ¼Ð¸ Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ°Ð¼Ð¸.
description: This work is devoted to the development of a software product for solving a mathematical problem and the corresponding mathematical model in the field of quantum radio physics. The paper provides an overview of numerical integration methods and their implementation, analytically obtains a quasi-stationary solution of the system and the value of the correction function, as well as the value of the criteria for the that function, optimizes the calculation of the components of these criteria using the Bessel and Struve functions, and performs a number of tests for various configurations of diffusers. The results of the work carried out will help determine how to most effectively position the diffusers to achieve the desired effects. In the future, those calculations can be applied to define qualitative dependency between criteria and input parameters.