A billiard-theoretic approach to elementary one-dimensional elastic collisions

American Journal of Physics

Volumn 72, Issue 12, 2004, Pages 1492-1498

  Redner, S ^a  

^a Boston University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 10844272344     PISSN: 00029505     EISSN: None     Source Type: Journal    
DOI: 10.1119/1.1738428     Document Type: Article

References (27)

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11. See, for example, A. Dhar, "Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses," Phys. Rev. Lett. 86, 3554-3557 (2001); P. L. Garrido, P. I. Hurtado, and B. Nadrowski, "Simple one-dimensional model of heat conduction which obeys Fourier's law," ibid. 86, 5486-5489 (2001); O. Narayan and S. Ramaswamy, "Anomalous heat conduction in one-dimensional momentum-conserving systems," ibid. 89, 200601-1-4 (2002). For a recent review, see S. Lepri, R. Livi, and A. Politi, "Thermal conduction in classical low-dimensional lattices," Phys. Rep. 377, 1-80 (2003).
12. See, for example, A. Dhar, "Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses," Phys. Rev. Lett. 86, 3554-3557 (2001); P. L. Garrido, P. I. Hurtado, and B. Nadrowski, "Simple one-dimensional model of heat conduction which obeys Fourier's law," ibid. 86, 5486-5489 (2001); O. Narayan and S. Ramaswamy, "Anomalous heat conduction in one-dimensional momentum-conserving systems," ibid. 89, 200601-1-4 (2002). For a recent review, see S. Lepri, R. Livi, and A. Politi, "Thermal conduction in classical low-dimensional lattices," Phys. Rep. 377, 1-80 (2003).
13. See, for example, A. Dhar, "Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses," Phys. Rev. Lett. 86, 3554-3557 (2001); P. L. Garrido, P. I. Hurtado, and B. Nadrowski, "Simple one-dimensional model of heat conduction which obeys Fourier's law," ibid. 86, 5486-5489 (2001); O. Narayan and S. Ramaswamy, "Anomalous heat conduction in one-dimensional momentum-conserving systems," ibid. 89, 200601-1-4 (2002). For a recent review, see S. Lepri, R. Livi, and A. Politi, "Thermal conduction in classical low-dimensional lattices," Phys. Rep. 377, 1-80 (2003).
14. See, for example, A. Dhar, "Heat conduction in a one-dimensional gas of elastically colliding particles of unequal masses," Phys. Rev. Lett. 86, 3554-3557 (2001); P. L. Garrido, P. I. Hurtado, and B. Nadrowski, "Simple one-dimensional model of heat conduction which obeys Fourier's law," ibid. 86, 5486-5489 (2001); O. Narayan and S. Ramaswamy, "Anomalous heat conduction in one-dimensional momentum-conserving systems," ibid. 89, 200601-1-4 (2002). For a recent review, see S. Lepri, R. Livi, and A. Politi, "Thermal conduction in classical low-dimensional lattices," Phys. Rep. 377, 1-80 (2003).
15. For a general review, see H. M. Jaeger, S. R. Nagel, and R. B. Behringer, "Granular solids, liquids, and gases," Rev. Mod. Phys. 68, 1259-1273 (1996).
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17. S. McNamara and W. R. Young, "Inelastic collapse and clumping in a one-dimensional granular medium," Phys. Fluids A 4, 496-504 (1992); I. Goldhirsch and G. Zanetti, "Clustering instability in dissipative gases," Phys. Rev. Lett. 70, 1619-1622 (1993); S. McNamara and W. R. Young, "Dynamics of a freely evolving, two-dimensional granular medium," Phys. Rev. E 53, 5089-5100 (1996).
18. S. McNamara and W. R. Young, "Inelastic collapse and clumping in a one-dimensional granular medium," Phys. Fluids A 4, 496-504 (1992); I. Goldhirsch and G. Zanetti, "Clustering instability in dissipative gases," Phys. Rev. Lett. 70, 1619-1622 (1993); S. McNamara and W. R. Young, "Dynamics of a freely evolving, two-dimensional granular medium," Phys. Rev. E 53, 5089-5100 (1996).
19. A similar approach to that in the Appendix is given in P. Constantin, E. Grossman, and M. Mungan, "Inelastic collision of three particles on the line as a two-dimensional billiard," Physica D 83, 409-420 (1995); see also, T. Zhou and L. P. Kadanoff, "Inelastic collapse of three particles," Phys. Rev. E 54, 623-628 (1996).
20. A similar approach to that in the Appendix is given in P. Constantin, E. Grossman, and M. Mungan, "Inelastic collision of three particles on the line as a two-dimensional billiard," Physica D 83, 409-420 (1995); see also, T. Zhou and L. P. Kadanoff, "Inelastic collapse of three particles," Phys. Rev. E 54, 623-628 (1996).
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