A two-temperature model of optical excitation of acoustic waves in conductors

Indeitsev, D. A.; Osipova, E. V.

doi:10.1134/s1028335817030065

Cited by 17 publications

(11 citation statements)

References 4 publications

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“…We would like to note that in the case of CIT only the temperature (as a function of x and t) is needed to calculate the entropy [see Eq. (25)]. The expression for the temperature for a wide class of scalar lattices was obtained in Ref.…”

Section: Discussionmentioning

confidence: 99%

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Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

et al. 2019

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This work presents a thermodynamic analysis of the ballistic heat equation from two viewpoints: classical irreversible thermodynamics (CIT) and extended irreversible thermodynamics (EIT). A formula for calculating the entropy within the framework of EIT for the ballistic heat equation is derived. The entropy is calculated for a sinusoidal initial temperature perturbation by using both approaches. The results obtained from CIT show that the entropy is a non-monotonic function and that the entropy production can be negative. The results obtained for EIT show that the entropy is a monotonic function and that the entropy production is nonnegative. A comparison between the entropy behaviors predicted for the ballistic, for the ordinary Fourier-based, and for the hyperbolic heat equation is made. A crucial difference of the asymptotic behavior of the entropy for the ballistic heat equation is shown. It is argued that mathematical time reversibility of the partial differential ballistic heat equation is not consistent with its physical irreversibility. The processes described by the ballistic heat equation are irreversible because of the entropy increase. *

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Section: Discussionmentioning

confidence: 99%

“…A hyperbolic equation called "ballistic heat equation" was obtained as a mathematical consequence of the equations of lattice dynamics. From an experimental point of view such processes can be observed in low dimensional structures exposed to a laser excitation [25].…”

Section: Introductionmentioning

confidence: 99%

Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

et al. 2019

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“…], is caused by temperature perturbation and T E def = T 0 + ∆T /2 is the equilibrium temperature. As follows, from expression (20) the equilibrium temperature is the temperature reached when N → ∞, t → ∞ (equilibrium state of an infinite crystal).…”

Section: Representation Via Bessel Functionsmentioning

confidence: 99%

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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“…Consider the initial thermal perturbation in the form of a rectangular pulse,

T_{0} false(x false) = T_{0} false(H (x + l) - H (x - l) false), \dot{T} = 0 .

These initial conditions correspond to a temperature perturbation produced by a laser pulse . In classical thermal conductivity, the maximum is observed at the point x = 0, which decays exponentially.…”

Section: Numerical Study Of Heat Propagationmentioning

confidence: 99%

“…These initial conditions correspond to a temperature perturbation produced by a laser pulse. [29] In classical thermal conductivity, the maximum is observed at the point x = 0, which decays exponentially. In the case of anomalous thermal conductivity, the solution attenuates faster near zero, forming four fronts, which pairwise propagate in the opposite directions with the constant velocities.…”

Section: Numerical Study Of Heat Propagationmentioning

confidence: 99%

Thermal processes in a one‐dimensional crystal with regard for the second neighbor interaction

et al. 2019

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An influence of the second neighbor interaction on the process of heat propagation in a one‐dimensional crystal is studied. Previously developed model of the ballistic nature of the heat transfer is used. It is shown that the initial thermal perturbation evolves into two consecutive thermal wave fronts propagating with finite and different velocities. The velocity of the first front corresponds to the maximum group velocity of the discrete crystalline model. The velocity of the second front is determined by the second group‐velocity extremum, which arises at a certain ratio between the stiffnesses of the first and second neighbor interaction in the lattice.

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A two-temperature model of optical excitation of acoustic waves in conductors

Cited by 17 publications

References 4 publications

Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

Change of entropy for the one-dimensional ballistic heat equation: Sinusoidal initial perturbation

Thermal echo in a finite one-dimensional harmonic crystal

Thermal processes in a one‐dimensional crystal with regard for the second neighbor interaction

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