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Volumn 7, Issue 3, 1995, Pages 507-525

Hydrodynamics of a one-dimensional granular medium

Author keywords

[No Author keywords available]

Indexed keywords

GAS; GRANULAR MATERIALS; HYDRODYNAMICS;

EID: 0029105874 PISSN: 10706631 EISSN: None Source Type: Journal
DOI: 10.1063/1.868648 Document Type: Article

Times cited : (71)

References (23)

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- Inelastic collapse and clumping in a one dimensional granular medium
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10
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14
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- In this paper (except in Appendix B) we consider f as the distribution function in the velocity space alone, i.e., the commonly used f normalized by the density Ï.

15
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19
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- The same result can be obtained directly from the â€œtest particle equationâ€10 by multiplying it by [formula omitted] and integrating over Ï…. This procedure results in an equation of motion for the granular temperature with an energy sink term identical to the one given in Eq. (36).

20
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21
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- The regression slope is based on all points in the case of [formula omitted] and on the first four points in the case of [formula omitted] i.e., before the â€œinelastic collapseâ€ sets in.

22
- 85034921459
- Notice that if we had taken [formula omitted] in the three-particle distribution function then the average given in Eq. (80) would have vanished.

23
- 85034919580
- The reason that the simulated critical value of e is somewhat lower than the one predicted by Eq. (62), may be attributed to the fact that the Gaussian distribution is not a solution of the homogeneous Boltzmann equation. The latter should evolve to a two-hump distribution (cf. Fig. 3). As the instability (discussed in this paper) evolves so does the distribution function. Considering the fact that an approximate flat distribution is a transient stage in the development of the distribution function from its Gaussian shape to two-hump form, it is clear that the exact critical value of e should be between that predicted by using the Gaussian distribution and the one predicted by employing the flat distribution.

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