Geodesic
Heat flow in a one-dimensional semi-infinite harmonic lattice with an absorbing boundary
Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 38-51.

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Traditionally, absorbing boundary conditions are used to limit the domains of numerical approximation of partial differential equations in infinite domains. In the present paper, the simplest of these conditions is used to obtain an analytical approximation of the solution to the problem of heat propagation in a one-dimensional infinite harmonic lattice consisting of two semi-infinite homogeneous sublattices with different mechanical characteristics. 
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A. I. Gudimenko. Heat flow in a one-dimensional semi-infinite harmonic lattice with an absorbing boundary. Dalʹnevostočnyj matematičeskij žurnal, Tome 20 (2020) no. 1, pp. 38-51. http://geodesic.mathdoc.fr/item/DVMG_2020_20_1_a3/

[1] E. Teramoto, “Heat Flow in the Linear Chain of Harmonically Coupled Particles”, Prog. Theor. Phys., 28:6 (1962), 1059–1064 | DOI

[2] S. Kashiwamura, E. Teramoto, “Effect of an Isotopic Impurity on the Heat Flow in One-Dimensional Coupled Harmonic Oscillators”, Prog. Theor. Phys. Suppl., 1962, no. 23, 207–222 | DOI

[3] É. I. Takizawa, K. Kobayasi, “Heat Flow in a System of Coupled Harmonic Oscillators”, Chin J. Phys., 1:2 (1963), 59–73

[4] K. Kobayasi, É. I. Takizawa, “Effect of an Isotopic Impurity on the Energy Flow in a System of One-Dimensional Coupled Harmonic Oscillators”, Chin J. Phys., 2:1 (1964), 10–22

[5] K. Kobayasi, É. I. Takizawa, “Effect of a Light Isotopic Impurity on the Energy Flow in a System of One-Dimensional Coupled Harmonic Oscillators”, Chin J. Phys., 2:2 (1964), 68–79

[6] R. J. Rubin, “Momentum Autocorrelation Functions and Energy Transport in Harmonic Crystals Containing Isotopic Defects”, Phys, Rev., 131:3 (1963), 964–989 | DOI

[7] R. J. Rubin, W. L. Greer, “Abnormal Lattice Thermal Conductivity of a One-Dimensional, Harmonic, Isotopically Disordered Crystal”, J. Math. Phys., 12:8 (1971), 1686–1701 | DOI

[8] E. L. Lindman, “Free-space boundary conditions for the time dependent wave equation”, J. Comp. Phys., 18 (1975), 66–78 | DOI | Zbl

[9] B. Engquist, A .Majda, “Absorbing boundary conditions for the numerical simulation of waves”, Math. Comp., 31:139 (1977), 629–651 | DOI | MR | Zbl

[10] B. Engquist, A .Majda, “Radiation boundary conditions for acoustic and elastic wave calculations”, Comm. Pure Appl. Math., 32 (1979), 313–357 | DOI | MR | Zbl

[11] L. Halpern, “Absorbing Boundary Conditions for the Discretization Schemes of the One-Dimensional Wave Equation”, Mathematics of Computation, 38:158 (1982), 415–429 | DOI | MR | Zbl

[12] A. Dhar, “Heat transport in low-dimensional systems”, Advances in Physics, 57:5 (2008), 457–537 | DOI

[13] Thermal Transport in Low Dimensions, Lecture Notes in Physics, 921, ed. S. Lepri, Springer International Publishing, 2016 | MR

[14] E. Schrödinger, “Zur Dynamik elastisch gekoppelter Punktsysteme”, Annalen der Physik, 44 (1914), 916–934 | DOI | Zbl

[15] J. W. Gibbs, Elementary principles in statistical mechanics, developed with especial reference to the rational foundation of thermodynamics, New York, 1902 | MR | Zbl

[16] V. I. Arnold, A. Avets, Ergodicheskie problemy klassicheskoi mekhaniki, Izhevskaya respublikanskaya tipografiya, Izhevsk, 1999

[17] G. N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1944 | MR | Zbl