FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
Heat flow in a one-dimensional semi-infinite harmonic lattice with an absorbing boundary |
Gudimenko A.I. |
2020, issue 1, P. 38–51 DOI: https://doi.org/10.47910/FEMJ202004 |
Abstract |
| Traditionally, absorbing boundary conditions are used to limit the domains of numerical approximation of partial differential equations in infinite domains. |
Keywords: harmonic chain, heat flow, absorbing boundary condition |
Download the article (PDF-file) |
References |
| [1] E. Teramoto, “Heat Flow in the Linear Chain of Harmonically Coupled Particles”, Prog. Theor. Phys., 28:6, (1962), 1059–1064. [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. [3] E .I. Takizawa, K. Kobayasi, “Heat Flow in a System of Coupled Harmonic Oscillators”, Chin J. Phys., 1:2, (1963), 59–73. [4] K. Kobayasi, E.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, E.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. [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. [8] E.L. Lindman, “Free-space boundary conditions for the time dependent wave equation”, J. Comp. Phys., 18, (1975), 66–78. [9] B. Engquist, A. Majda, “Absorbing boundary conditions for the numerical simulation of waves”, Math. Comp., 31:139, (1977), 629–651. [10] B. Engquist, A .Majda, “Radiation boundary conditions for acoustic and elastic wave cal- culations”, Comm. Pure Appl. Math., 32, (1979), 313–357. [11] L. Halpern, “Absorbing Boundary Conditions for the Discretization Schemes of the One- Dimensional Wave Equation”, Mathematics of Computation, 38:158, (1982), 415–429. [12] A. Dhar, “Heat transport in low-dimensional systems”, Advances in Physics, 57:5, (2008), 457–537. [13] Thermal Transport in Low Dimensions, Lecture Notes in Physics, 921, ed. S. Lepri, Springer International Publishing, 2016. [14] E. Schrodinger, “Zur Dynamik elastisch gekoppelter Punktsysteme”, Annalen der Physik, 44, (1914), 916–934. [15] J.W. Gibbs, Elementary principles in statistical mechanics, developed with especial reference to the rational foundation of thermodynamics, New York, 1902. [16] V.I. Arnol'd, A. Avets, Ergodicheskie problemy klassicheskoi mekhaniki, Izhevskaia respublikanskaia tipografiia, Izhevsk, 1999. [17] G.N. Watson, A Treatise on the Theory of Bessel Functions, Cambridge University Press, Cambridge, 1944. |