Molecular dynamics investigation of heat conduction in crystals with defects

Le-Zakharov, A. A.; Кривцов, А. М.

doi:10.1134/s1028335808050066

Cited by 20 publications

(10 citation statements)

References 8 publications

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“…The center of mass velocity of the periodic cell and initial angular momentum with respect to the center of the cell are equal to zero. The particles interact via the spline potential [23]. The corresponding interatomic force F ij acting on particle i due to particle j has the form…”

Section: Example 3: Flux Of Angular Momentum and Torque Acting On Thementioning

confidence: 99%

On angular momentum balance for particle systems with periodic boundary conditions

Kuzkin

2014

Z Angew Math Mech

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The well-known issue with the absence of conservation of angular momentum in classical particle systems with periodic boundary conditions is addressed. It is shown that conventional theory based on Noether's theorem fails to explain the simplest possible example, notably jumps of angular momentum in the case of single particle moving in a periodic cell. It is suggested to consider the periodic cell as an open system, exchanging mass, momentum, angular momentum, and energy with surrounding cells. Then the behavior of the cell is described by balance laws rather than conservation laws. It is shown using the law of angular momentum balance that the variation of the angular momentum in systems with periodic boundary conditions is a consequence of (i) the non-zero flux of angular momentum through the boundaries and (ii) torque acting on the cell due to the interactions between particles in the cell with images in the neighboring cells. Two simple examples demonstrating both phenomena are presented.

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Section: Example 3: Flux Of Angular Momentum and Torque Acting On Thementioning

confidence: 99%

On angular momentum balance for particle systems with periodic boundary conditions

Kuzkin

2014

Z Angew Math Mech

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“…In the present paper we use symplectic leap-frog integration scheme [20]. All interactions in the system are described via the spline potential [21]. The force, acting between two particles i and j, is calculated as follows:…”

Section: Problem Formulation and Simulation Techniquementioning

confidence: 99%

Comparative study of rheological properties of suspensions by computer simulation of Poiseuille and Couette flows

2014

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The article presents results of numerical experiments performed to evaluate the effective rheological properties of a mixture of a fluid with solid particles. The numerical simulation of the Couette and Poiseuille flows shows that in the both cases, the effective viscosity and non-Newtonian properties of the suspension coincide to the accuracy of standard deviation. The authors define the area of applicability of Newtonian fluid model to modeling fluid and proppant mix and determine conditions for plugs at high concentrations of proppant.

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“…However, it is well known that for one-dimensional crystals substantial deviations from Fourier's law are observed [1][2][3][4][5] . These inadequacies can be, in principle, addressed by using special laws of particle interactions [6][7][8][9][10] or sufficiently complex structures 11,12 . Recent experimental data, however, demonstrate that Fouriers law is indeed violated in low-dimensional nanostructures [13][14][15][16][17][18] , where ballistic heat conduction is observed.…”

Section: Introductionmentioning

confidence: 99%

“…This motivates the interest in the simplest lattice models, in particular, in harmonic onedimensional crystals (chains), where these anomalies are most prominent 22,23 . Problems of this type were previously addressed mainly in the context of steady-state heat conduction [1][2][3][4][5][24][25][26][27][28][29][30][31][32][33] , unsteady conduction regimes came into the focus in 12,[34][35][36][37][38][39][40][41][42] .…”

Section: Introductionmentioning

confidence: 99%

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

Гаврилов

Кривцов

Tsvetkov

2018

Continuum Mech. Thermodyn.

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We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures.

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Molecular dynamics investigation of heat conduction in crystals with defects

Cited by 20 publications

References 8 publications

On angular momentum balance for particle systems with periodic boundary conditions

On angular momentum balance for particle systems with periodic boundary conditions

Comparative study of rheological properties of suspensions by computer simulation of Poiseuille and Couette flows

Heat transfer in a one-dimensional harmonic crystal in a viscous environment subjected to an external heat supply

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