title: ÐÐµÑÐµÑ Ð¾Ð´Ð½ÑÐµ Ð¿ÑÐ¾ÑÐµÑÑÑ Ð² ÑÐ²ÐµÑÐ´ÑÑ ÑÐµÐ»Ð°Ñ Ñ ÐºÑÐ¸ÑÑÐ°Ð»Ð»Ð¸ÑÐµÑÐºÐ¾Ð¹ ÑÑÑÑÐºÑÑÑÐ¾Ð¹
title: ÑÑÐµÐ±Ð½Ð¾Ðµ Ð¿Ð¾ÑÐ¾Ð±Ð¸Ðµ
titleType: Subtitle
title: Transient processes in solids with crystal structure
Creators: name: ÐÑÐ·ÑÐºÐ¸Ð½, ÐÐ¸ÑÐ°Ð»Ð¸Ð¹
name: ÐÑÐ¸Ð²ÑÐ¾Ð², ÐÐ½ÑÐ¾Ð½
name: Ð©ÐµÑÐ±Ð¸Ð½Ð¸Ð½, Ð¡ÑÐµÐ¿Ð°Ð½
Publisher: name: ÐÐÐÐÐ¢ÐÐ¥-ÐÐ ÐÐ¡Ð¡
Year: 2023
Subjects: Ð¢Ð²ÐµÑÐ´ÑÐµ ÑÐµÐ»Ð°

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description: We present methods for the analytical description of two transient processes in harmonic (linear) crystals with random initial conditions, namely, equilibration of kinetic and potential energies and redistribution of energy over degrees of freedom of the unit cell. For analytical description, an approach based on the analysis of the covariances of particle displacements and velocities is used. Using a matrix formalism, derivations are carried out for harmonic crystals with a complex lattice of a fairly general form. Exact formulas are derived to describe the changes in kinetic energies (temperatures) corresponding to different degrees of freedom of the unit cell. These formulas are used to analyze transient processes in a number of specific onedimensional and two-dimensional crystals. The effect of weak nonlinearity on the considered transient processes is numerically investigated. This work corresponds to the state educational standard and the content of bachelorâs and masterâs degree courses 01.03 Â«Mechanics and mathematical modelingÂ» and 15.03 Â«Applied mechanicsÂ». The work is suitable for students specializing in mechanics, thermodynamics, and condensed matter physics.