title: Ð Ð°Ð·ÑÐ°Ð±Ð¾ÑÐºÐ° Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð´Ð»Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð¹ Ð´Ð¸ÑÑÑÐ·Ð¸Ð¸ Ð°ÐºÑÐ¸Ð²Ð½ÑÑ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð² ÑÑÐ»Ð¾Ð²Ð¸ÑÑ ÑÑÑÐµÐºÑÐ° ÐºÐ¾Ð³ÐµÑÐµÐ½ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»ÐµÐ½ÐµÐ½Ð¸Ñ Ð½Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑ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 simulating one-dimensional diffusion of active atoms under conditions of the effect of coherent population trapping
Creators: name: Ð¥Ð²Ð°ÑÐ¾Ð², Ð¡ÐµÑÐ³ÐµÐ¹
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: 2021
Subjects: Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ
fortran
python
Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÐµ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ñ Ð¿ÐµÑÐ²Ð¾Ð³Ð¾ Ð¿Ð¾ÑÑÐ´ÐºÐ°
Ð¸Ð½ÑÐµÐ³ÑÐ¾-Ð¸Ð½ÑÐµÑÐ¿Ð¾Ð»ÑÑÐ¸Ð¾Ð½Ð½ÑÐ¹ Ð¼ÐµÑÐ¾Ð´
modeling
first order differential equations
integro-interpolation method

description: ÐÐ°Ð½Ð½Ð°Ñ Ð±Ð°ÐºÐ°Ð»Ð°Ð²ÑÑÐºÐ°Ñ ÑÐ°Ð±Ð¾ÑÐ° Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð° ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼, Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑÐ¸Ñ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°ÑÑ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½ÑÑ Ð´Ð¸ÑÑÑÐ·Ð¸Ñ Ð°ÐºÑÐ¸Ð²Ð½ÑÑ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð² ÑÑÐ»Ð¾Ð²Ð¸ÑÑ ÑÑÑÐµÐºÑÐ° ÐºÐ¾Ð³ÐµÑÐµÐ½ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»ÐµÐ½ÐµÐ½Ð¸Ñ Ð½Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð¸ÑÑÐ¾Ð´Ð½Ð°Ñ ÑÐ¸ÑÑÐµÐ¼Ð° Ð´Ð¸ÑÑÐµÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½ÑÑ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸Ð¹ Ð±ÑÐ»Ð° Ð´Ð¾Ð¿Ð¾Ð»Ð½ÐµÐ½Ð° ÑÐ¾Ð¿ÑÑÐ¶ÐµÐ½Ð½ÑÐ¼Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ð¸ÑÐ¼Ð¸, Ð¿Ð¾ÑÐ»Ðµ ÑÐµÐ³Ð¾ Ð¿ÑÐµÐ¾Ð±ÑÐ°Ð·Ð¾Ð²Ð°Ð½Ð° Ð² ÑÐ¸ÑÑÐµÐ¼Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½ÑÑ Ð°Ð»Ð³ÐµÐ±ÑÐ°Ð¸ÑÐµÑÐºÐ¸Ñ Ð¿ÑÐ¸ Ð¿Ð¾Ð¼Ð¾ÑÐ¸ Ð¸Ð½ÑÐµÐ³ÑÐ¾-Ð¸Ð½ÑÐµÑÐ¿Ð¾Ð»ÑÑÐ¸Ð¾Ð½Ð½Ð¾Ð³Ð¾ Ð¼ÐµÑÐ¾Ð´Ð°. Ð¢Ð°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¸ ÑÐ°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ñ Ð¸ Ð´ÑÑÐ³Ð¸Ðµ ÑÐ¸ÑÐ»ÐµÐ½Ð½ÑÐµ Ð¼ÐµÑÐ¾Ð´Ñ ÑÐµÑÐµÐ½Ð¸Ñ Ð¿Ð¾Ð´Ð¾Ð±Ð½Ð¾Ð³Ð¾ ÑÐ¾Ð´Ð° ÑÐ¸ÑÑÐµÐ¼. ÐÑÐ»Ð¸ ÑÐ°Ð·ÑÐ°Ð±Ð¾ÑÐ°Ð½Ñ Ð´Ð²Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼, Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ ÐºÐ¾ÑÐ¾ÑÑÑ Ð±ÑÐ»Ð¾ Ð¿Ð¾Ð»ÑÑÐµÐ½Ð¾ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ Ð´Ð»Ñ Ð·Ð°Ð´Ð°Ð½Ð½Ð¾Ð³Ð¾ Ð½Ð°Ð±Ð¾ÑÐ° Ð¿Ð°ÑÐ°Ð¼ÐµÑÑÐ¾Ð². ÐÐ°Ð½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ ÑÐ´Ð¾Ð²Ð»ÐµÑÐ²Ð¾ÑÑÐµÑ ÑÑÐ»Ð¾Ð²Ð¸ÑÐ¼ ÑÐµÑÐ°ÐµÐ¼Ð¾Ð¹ Ð·Ð°Ð´Ð°ÑÐ¸, Ð° ÐµÐ³Ð¾ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÑ ÑÐ²Ð»ÑÐµÑÑÑ Ð´Ð¾Ð¿ÑÑÑÐ¸Ð¼Ð¾Ð¹. ÐÑÐ¾Ð¼Ðµ ÑÐ¾Ð³Ð¾, Ð½Ð° Ð¾ÑÐ½Ð¾Ð²Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð½Ð° ÑÐ·ÑÐºÐµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Python Ð±ÑÐ»Ð¾ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ð¾ ÑÐµÑÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ðµ Ñ Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð½Ð¸ÐµÐ¼ ÑÐµÑÑÐ¾Ð²ÑÑ ÑÑÐ½ÐºÑÐ¸Ð¹ Ñ Ð¸Ð·Ð²ÐµÑÑÐ½ÑÐ¼ ÑÐµÑÐµÐ½Ð¸ÐµÐ¼. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÑÐµÐ½Ð¸Ñ Ð±ÑÐ»Ð¸ ÑÑÐ°Ð²Ð½ÐµÐ½Ñ Ñ Ð¾Ð¶Ð¸Ð´Ð°ÐµÐ¼ÑÐ¼Ð¸, Ð° ÑÐ°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¾ Ð¿ÑÐ¾Ð¸Ð·Ð²ÐµÐ´ÐµÐ½Ð¾ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð·Ð°Ð²Ð¸ÑÐ¸Ð¼Ð¾ÑÑÐ¸ Ð¿Ð¾Ð³ÑÐµÑÐ½Ð¾ÑÑÐ¸ Ð¾Ñ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÑÐ°Ð·Ð±Ð¸ÐµÐ½Ð¸Ð¹. Ð ÐµÐ·ÑÐ»ÑÑÐ°ÑÐ¾Ð¼ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐ°Ð±Ð¾ÑÑ ÑÐ²Ð»ÑÑÑÑÑ Ð´Ð²Ðµ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ñ Ð½Ð° ÑÐ·ÑÐºÐ°Ñ Ð¿ÑÐ¾Ð³ÑÐ°Ð¼Ð¼Ð¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ Fortran Ð¸ Python, ÐºÐ¾ÑÐ¾ÑÑÐµ Ð¿Ð¾Ð·Ð²Ð¾Ð»ÑÑÑ Ð¼Ð¾Ð´ÐµÐ»Ð¸ÑÐ¾Ð²Ð°ÑÑ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½ÑÑ Ð´Ð¸ÑÑÑÐ·Ð¸Ñ Ð°ÐºÑÐ¸Ð²Ð½ÑÑ Ð°ÑÐ¾Ð¼Ð¾Ð² Ð² ÑÑÐ»Ð¾Ð²Ð¸ÑÑ ÑÑÑÐµÐºÑÐ° ÐºÐ¾Ð³ÐµÑÐµÐ½ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð»ÐµÐ½ÐµÐ½Ð¸Ñ Ð½Ð°ÑÐµÐ»ÐµÐ½Ð½Ð¾ÑÑÐµÐ¹.
description: This bachelor's work is devoted to the development of programs that can be used in order to simulate one-dimensional diffusion of active atoms under conditions of the effect of coherent population trapping. In the course of the work, the original system of differential equations was supplemented with conjugate equations, after which it was transformed into a system of linear algebraic equations using the integro-interpolation method. Other numerical methods for solving similar systems were also considered. Two programs were developed, with the help of which a numerical solution was obtained for a given set of parameters. This solution satisfies the conditions of the problem being solved, and its error is acceptable. In addition, based on a program in the Python programming language, testing was carried out using test functions with a known solution. The obtained solutions were compared with the expected ones, and a study was made of the dependence of the error on the number of partitions. The result of this work is two programs in the Fortran and Python programming languages that allow simulating one-dimensional diffusion of active atoms under conditions of the effect of coherent population trapping.