title: ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ ÑÐ°Ð·ÑÑÐ²Ð¾Ð² ÑÐ²ÑÐ·ÐµÐ¹ Ð½Ð° Ð¿ÐµÑÐµÐ½Ð¾Ñ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð² Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð¹ ÑÐµÐ¿Ð¾ÑÐºÐµ
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: Study the breaking of energy transfer bonds in a one-dimensional chain
Creators: name: ÐÐ¾Ð»Ð±Ð°ÑÐ¾Ð², ÐÐ»ÐµÐºÑÐµÐ¹
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: Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ ÑÐµÐ¿Ð¾ÑÐºÐ°
Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ ÑÐµÐ¿Ð¾ÑÐºÐ°
Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½ÑÐ¹ ÐºÑÐ¸ÑÑÐ°Ð»Ð»
Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð» ÐÐµÐ½Ð½Ð°ÑÐ´Ð°-ÐÐ¶Ð¾Ð½ÑÐ°
ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐ½ÐµÑÐ³Ð¸Ñ
ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑ
ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ
Ð°Ð½Ð°Ð»Ð¸ÑÐ¸ÑÐµÑÐºÐ¾Ðµ ÑÐµÑÐµÐ½Ð¸Ðµ
linear chain
nonlinear chain
one-dimensional crystal
Lennard-Jones potential
kinetic energy
kinetic temperature
numerical solution
analytical solution

description: Ð Ð½Ð°ÑÑÐ¾ÑÑÐµÐ¹ ÑÐ°Ð±Ð¾ÑÐµ Ð¿ÑÐ¾Ð²Ð¾Ð´Ð¸ÑÑÑ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ðµ Ð²Ð»Ð¸ÑÐ½Ð¸Ñ ÑÐ°Ð·ÑÑÐ²Ð¾Ð² ÑÐ²ÑÐ·ÐµÐ¹ Ð½Ð° Ð¿ÐµÑÐµÐ½Ð¾Ñ ÑÐ½ÐµÑÐ³Ð¸Ð¸ Ð² Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð¹ ÑÐµÐ¿Ð¾ÑÐºÐµ. Ð ÑÐ¾Ð´Ðµ ÑÐ°Ð±Ð¾ÑÑ Ð±ÑÐ» Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐ¾Ð²ÑÐµÐ¼ÐµÐ½Ð½Ð¾Ð¹ Ð»Ð¸ÑÐµÑÐ°ÑÑÑÑ, Ð¿Ð¾ÑÐ²ÑÑÐµÐ½Ð½Ð¾Ð¹ Ð´Ð°Ð½Ð½Ð¾Ð¹ ÑÐµÐ¾ÑÐ¸Ð¸. ÐÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ñ Ð´Ð²Ðµ Ð¼Ð¾Ð´ÐµÐ»Ð¸ Ð´Ð»Ñ Ð¾Ð´Ð½Ð¾Ð¼ÐµÑÐ½Ð¾Ð¹ ÑÐµÐ¿Ð¾ÑÐºÐ¸. ÐÐµÑÐ²Ð°Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð°Ñ, Ð²ÑÐ¾ÑÐ°Ñ Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½ÑÐ¼ Ð²Ð·Ð°Ð¸Ð¼Ð¾Ð´ÐµÐ¹ÑÑÐ²Ð¸ÐµÐ¼ Ð¼ÐµÐ¶Ð´Ñ ÑÐ°ÑÑÐ¸ÑÐ°Ð¼Ð¸, Ñ Ð¿Ð¾Ð¼Ð¾ÑÑÑ Ð¿Ð°ÑÐ½Ð¾Ð³Ð¾ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»Ð° ÐÐµÐ½Ð½Ð°ÑÐ´Ð°-ÐÐ¶Ð¾Ð½ÑÐ°. ÐÐ»Ñ Ð»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐµÐ¿Ð¾ÑÐºÐ¸ Ð±ÑÐ» Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½ ÑÑÐ°Ð²Ð½Ð¸ÑÐµÐ»ÑÐ½ÑÐ¹ Ð°Ð½Ð°Ð»Ð¸Ð· ÑÐ¾ ÑÑÐ°ÑÑÐµÐ¹, Ð° ÑÐ°ÐºÐ¶Ðµ Ð¿Ð¾ÑÑÑÐ¾ÐµÐ½Ñ Ð³ÑÐ°ÑÐ¸ÐºÐ¸ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ñ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð¹ Ð¸ Ð¿Ð¾ÑÐµÐ½ÑÐ¸Ð°Ð»ÑÐ½Ð¾Ð¹ ÑÐ½ÐµÑÐ³Ð¸Ð¹. ÐÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ ÑÐ°ÑÑÐµÑÑ Ð´Ð»Ñ ÑÐ°Ð·Ð½Ð¾Ð³Ð¾ ÐºÐ¾Ð»Ð¸ÑÐµÑÑÐ²Ð° ÑÐµÐ°Ð»Ð¸Ð·Ð°ÑÐ¸Ð¹ Ð¸ ÑÐ¸ÑÐ»Ð° ÑÐ°ÑÑÐ¸Ñ Ð´Ð»Ñ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾Ð¹ ÑÐµÐ¿Ð¾ÑÐºÐ¸ Ñ Ð¼Ð°Ð»ÐµÐ½ÑÐºÐ¾Ð¹ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾ÑÑÑÑ k = 0.1 . Ð ÐºÐ°ÑÐµÑÑÐ²Ðµ ÑÐ¸ÑÐ»ÐµÐ½Ð½Ð¾Ð³Ð¾ Ð¼ÐµÑÐ¾Ð´Ð° Ð¸ÑÐ¿Ð¾Ð»ÑÐ·Ð¾Ð²Ð°Ð»ÑÑ ÑÐ¸Ð¼Ð¿Ð»ÐµÐºÑÐ¸ÑÐµÑÐºÐ¸Ð¹ Ð¼ÐµÑÐ¾Ð´ Ð²ÑÐ¾ÑÐ¾Ð³Ð¾ Ð¿Ð¾ÑÑÐ´ÐºÐ°, Ð¼ÐµÑÐ¾Ð´ ÐÐµÑÐ»Ðµ, ÐºÐ¾ÑÐ¾ÑÑÐ¹ ÑÐ¾ÑÑÐ°Ð½ÑÐµÑ ÑÐ½ÐµÑÐ³Ð¸Ñ Ð² Ð¿ÑÐ¾ÑÐµÑÑÐµ Ð¸Ð½ÑÐµÐ³ÑÐ¸ÑÐ¾Ð²Ð°Ð½Ð¸Ñ. Ð¢Ð°ÐºÐ¶Ðµ Ð±ÑÐ»Ð¸ Ð¿ÑÐ¾Ð²ÐµÐ´ÐµÐ½Ñ Ð¸ÑÑÐ»ÐµÐ´Ð¾Ð²Ð°Ð½Ð¸Ñ Ñ ÑÐ²ÐµÐ»Ð¸ÑÐµÐ½Ð½Ð¾Ð¹ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾ÑÑÑÑ k = 0.5, 1, 2. . Ð Ð°ÑÑÐ¼Ð¾ÑÑÐµÐ½Ð¾ Ð¸Ð·Ð¼ÐµÐ½ÐµÐ½Ð¸Ðµ Ð¿Ð¾Ð²ÐµÐ´ÐµÐ½Ð¸Ñ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ¾Ð¹ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÑ Ð½Ð° Ð±Ð¾Ð»ÑÑÐ¸Ñ Ð²ÑÐµÐ¼ÐµÐ½Ð°Ñ, Ð° ÑÐ°ÐºÐ¶Ðµ Ð½Ð° Ð¼Ð°Ð»ÑÑ. ÐÐ¾Ð»ÑÑÐµÐ½Ð½ÑÐµ ÑÐµÐ·ÑÐ»ÑÑÐ°ÑÑ Ð¿Ð¾ÐºÐ°Ð·ÑÐ²Ð°ÑÑ, ÑÑÐ¾ Ð¿ÑÐ¸ Ð¿Ð¾Ð²ÑÑÐµÐ½Ð¸Ð¸ Ð½ÐµÐ»Ð¸Ð½ÐµÐ¹Ð½Ð¾ÑÑÐ¸ Ð¼ÐµÐ½ÑÐµÑÑÑ ÐºÑÐ¸Ð²Ð°Ñ, Ðº ÐºÐ¾ÑÐ¾ÑÐ¾Ð¹ Ð°ÑÐ¸Ð¼Ð¿ÑÐ¾ÑÐ¸ÑÐµÑÐºÐ¸ ÑÑÑÐµÐ¼Ð¸ÑÑÑ ÐºÐ¸Ð½ÐµÑÐ¸ÑÐµÑÐºÐ°Ñ ÑÐµÐ¼Ð¿ÐµÑÐ°ÑÑÑÐ°.
description: In the present work, we study the breaking of energy transfer bonds in a one-dimensional chain. In the course of the work, an analysis of modern work devoted to this theory was carried out. Two models of a one-dimensional chain are investigated. The first is ordinary linear, the second with non-linear interaction between the parts, using the Lennard-Jones pair separation. For a linear chain, a comparative analysis was carried out with the article, and graphs of changes in the kinetic and estimated energies were plotted. Calculations were carried out for a different number of realizations and the number of particles for a nonlinear chain with a small nonlinearity k = 0.1 . As a numerical method, the second-order symplectic method, the Verlet method, is used, which conserves energy in the union. Studies have also been carried out with increased non-linearity . k = 0.5, 1, 2. The change in the behavior of the kinetic temperature for long times, as well as for short ones, is excluded. Obtaining the results of the observation that when a nonlinearity occurs, the curve to which the asymptotically related kinetic temperature refers changes.