On different derivations of telegrapher's type kinetic equations

Journal of Non-Equilibrium Thermodynamics

Volumn 21, Issue 4, 1996, Pages 361-379

  Olivares Robles, M A ^a,b   Garcia Colin L S ^a,b,c  

^a DEPARTAMENTO DE QUÍMICA   (Mexico)

^b UNIVERSIDAD AUTÓNOMA METROPOLITANA   (Mexico)

^c EL COLEGIO NACIONAL   (Mexico)

Author keywords

[No Author keywords available]

Indexed keywords

BROWNIAN MOVEMENT; EQUATIONS OF MOTION; NUMERICAL METHODS; PHASE EQUILIBRIA; PROBABILITY;

HYPERBOLIC TRANSPORT EQUATION; TELEGRAPHER TYPE KINETIC EQUATIONS; THEORY OF BROWNIAN MOTION;

KINETIC THEORY;

EID: 0030361807     PISSN: 03400204     EISSN: None     Source Type: Journal    
DOI: 10.1515/jnet.1996.21.4.361     Document Type: Article

References (46)

1. Olivares-Robles, M. A., García-Colín, L. S., Mesoscopic derivation of hyperbolic transport equations, Phys. Rev., E50 (1994), 2451 and references therein.
2. Camacho, J., Jou, D., H Theorem for telegrapher type kinetic equations, Physics Letters, A171 (1992), 26.
3. Masoliver, J. Porrá, J. M., Weiss, G., Solutions of the telegrapher's equation in the presence of traps, Phys. Rev., A45 (1992), 2222.
4. Goldstein, S., On diffusion by discontinuous movements and the telegraph equation, Quart. J. Mech. Appl. Math., 4 (1951) 129.
5. Orsingher, E., A planar random motion governed by the two-dimensional telegraph equation, J. Appl. Prob., 23 (1986), 385.
6. Orsingher, E., Hyperbolic equations arising in random models, Stoch. Proc. Appl., 21 (1985), 420.
7. Masoliver, J., Lindenberg, K., Weiss, G. H., A continuous-time generalization of the persistent random walk, Physica, A157 (1989), 891.
8. Masoliver, J., Porrà, J. M., Weiss, G. H., The continuum limit of a two-dimensional persistent random walk, Physica, A182 (1992), 593.
9. Masoliver, J., Porrà, J. M., Weiss, G. H., Some two and three-dimensional persistent random walks, Physica, A193 (1993), 469.
10. Masoliver, J., Weiss, G. H., Telegrapher's equation with variable propagation speeds, Phys. Rev., E49 (1994), 3852.
11. Masoliver, J., Porrà, J. M., Weiss, Solution to the telegrapher's equation in the presence of reflecting boundaries, Phys. Rev., E48 (1993), 939.
12. Ishimaru, A., On difussion of a pulse in densely distributed scatterers, J. Op. Soc. Am., 68 (1978), 1045.
13. Ishimaru, A., Diffusion of light in turbid material, Appl. Opt., 28 (1989), 2210.
14. Bonner, R. F., Havlin, S., Nossal, R., Weiss, G. H., Model for photon migration in turbid biological media, J. Op. Soc. Am., A4 (1987), 423.
15. García-Colín, L. S., Extended non-equilibrium thermodynamics, scope and limitation, Rev. Mex. Fis. (in English), 34 (1988), 344.
16. Jou, D., Casas-Vázquez, J., Lebon, G., Extended irreversible thermodynamics, Springer Verlag, Berlin, 1993.
17. Joseph, D. D., Preziosi, L., Heat waves, Rev. Mod. Phys., 61 (1989), 41.
18. Joseph, D. D., Preziosi, L., Addendum to the paper "Heat waves", Rev. Mod. Phys., 62 (1990), 375.
19. Jou, D., Casas-Vázquez, J., Lebon, G., Extended irreversible thermodynamics, Rep. Prog. Phys., 51 (1988), 1105.
20. Masoliver, J., Weiss, G. H., Finite-velocity diffusion, Eur. J. Phys., 17 (1996), 190.
21. García-Colín, L. S., Olivares-Robles, M. A, Hyperbolic type transport equations, Physica, A220 (1995), 165.
22. Chandrasekhar, S., Stochastic problems in physics and astronomy, Rev. Mod. Phys., 15 (1943), 1. (reprinted in Wax, N., Selected papers on noise and stochastic processes, p. 3, Dover, New York, 1954).
23. Chandrasekhar, S., Stochastic problems in physics and astronomy, Rev. Mod. Phys., 15 (1943), 1. (reprinted in Wax, N., Selected papers on noise and stochastic processes, p. 3, Dover, New York, 1954).
24. Weymann, H. D., Finite speed of propagation in heat conduction, diffusion, and viscous shear motion, Am. J. Phys, 35 (1965), 488.
25. Beckenbach, E. F. (ed.), Modern mathematics for the engineer, p. 170, McGraw-Hill, New York, 1961.
26. Morse, P. M., Feshbach, H., Methods of theoretical physics, vol. I, p. 865, McGraw-Hill, New York, 1953.
27. Einstein, A., Investigations on the theory of the Brownian movement, Dover, New York, 1956.
28. Gardiner, C. W., Handbook of stochastic methods, 2nd edition, Chap. I, Springer-Verlag, Berlin, 1985.
29. Risken, H., The Fokker-Planck equation, 2nd edition, Chaps. I-II, Springer-Verlag, Berlin, 1989.
30. Kramers, H. A., Brownian motion in a field of force and the diffusion model of chemical reactions, Physica, 7 (1940), 284.
31. Wilemski, G., On the derivation of Smoluchowski equations with corrections in the classical theory of Brownian motion, J. Stat. Phys., 14 (1976), 153.
32. Davies, R. W., The connection between the Smoluchowski equation and the Kramers-Chandrasekhar equation, Phys. Rev., 93 (1954), 1169.
33. Brinkman, H. C., Brownian motion in a field of force and the diffusion theory of chemical reactions, Physica, 23 (1956), 29.
34. Sack, R. A., A modification of Smoluchowski's diffusion equation, Physica, 22 (1956), 917.
35. Hemmer, P. C., On a generalization of Smoluchowski's diffusion equation, Physica, 27 (1961), 79.
36. Uhlenbeck, G. E., Ornstein, L. S., On the theory of the Brownian motion, Phys. Rev., 36 (1930), 823. (reprinted in N. Wax loc. cit. ref. [22])
37. Uhlenbeck, G. E., Ornstein, L. S., On the theory of the Brownian motion, Phys. Rev., 36 (1930), 823. (reprinted in N. Wax loc. cit. ref. [22])
38. Titulaer, U. M., A systematic solution procedure for the Fokker-Planck equation of a Brownian particle in the high-friction case, Physica, 91A (1978), 321.
39. McQuarrie, D. A., Statistical mechanics, Chap. 20, Harper & Row Publishers, 1976.
40. Brush, S. G., The kind of motion we call heat, vol. II, p. 680, North-Holland, Neterlands, 1986.
41. García-Colín, L. S., Termodinámica de procesos irreversibles, Chap. 8, Colección C.B.I. U.A.M.-Iztapalapa, 1989, (In Spanish)
42. Maxwell, J. C., On the dynamical theory of gases, Philos. Trans. Soc. London, 157 (1867), 49.
43. Onsager, L., Reciprocal relations in irreversible processes I., Phys. Rev., 37 (1931), 405.
44. Kaliski, S., Wave equation for heat conduction, Bull. Acad. Pol. Sci., 13 (1965), 211.
45. Reif, F., Fundamentals of statistical and thermal physics, Chap. 15, McGraw-Hill, New York, 1965.
46. Kâc, M., Probability and related to topics in physical sciences, lectures in applied mathematics Vol. 1, Interscience publishers, New York, 1959 (see pages 145-146).