Non-Stationary Thermo-Diffusion Processes in Finite One-Dimensional Crystal

Кривцов, А. М.; Murachev, A.S.; Tsvetkov, D.

doi:10.22405/2226-8383-2017-18-3-332-351

Cited by 1 publication

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“…It follows thus from the analysis that the maximum temperature increase caused by the thermal echo decreases as 3 √ pN (30), where p the thermal echo number and N is the number of particles in the crystal. The duration of the thermal echo grows by the same law (34). Between any two thermal echoes the amplitude of the temperature oscillations decreases in proportion to the square root of time (26).…”

Section: Discussionmentioning

confidence: 96%

“…Unlike previous papers [3,24,26,27], where the main attention is focused on infinite crystals, the present paper investigates thermal processes in finite crystals [34]. The systems with a finite number of particles are of practical importance, especially because nanotechnologies are actively developing [35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

“…Except a small vicinity of the right boundary x = µ, where the width of this vicinity can be determined by expression(34) 5. The temperature jump is the difference between the temperature of the crystal at the point in time immediately after the temperature perturbation, and the temperature at the point in time immediately preceding the temperature perturbation.J.…”

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confidence: 99%

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Thermal echo in a finite one-dimensional harmonic crystal

Murachev¹,

Кривцов²,

Tsvetkov³

2019

J. Phys.: Condens. Matter

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An instant homogeneous thermal perturbation in the finite harmonic one-dimensional crystal is studied. Previously it was shown that for the same problem in the infinite crystal the kinetic temperature oscillates with decreasing amplitude described by the Bessel function of the first kind. In the present paper it is shown that in the finite crystal this behavior is observed only until a certain period of time when a sharp increase of the oscillations amplitude is realized. This phenomenon, further refereed to as the thermal echo, is realized periodically, with the period proportional to the crystal size. The amplitude for each subsequent echo is lower than for the previous one. It is obtained analytically that the time-dependance of the kinetic temperature can be described by an infinite sum of the Bessel functions with multiple indexes. It is also shown that the thermal echo in the thermodynamic limit is described by the Airy function.

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