| | |
| | |
Stat |
Members: 3645 Articles: 2'506'133 Articles rated: 2609
26 April 2024 |
|
| | | |
|
Article overview
| |
|
Granular contact forces: proof of "self-ergodicity" by generalizing Boltzmann's {em stosszahlansatz} and $H$ theorem | Philip T. Metzger
; | Date: |
12 Jun 2006 | Subject: | Statistical Mechanics | Abstract: | Ergodicity is proved for granular contact forces. To obtain this proof from first principles, this paper generalizes Boltzmann’s extit{stosszahlansatz} (molecular chaos) so that it maintains the necessary correlations and symmetries of granular packing ensembles. Then it formally counts granular contact force states and thereby defines the proper analog of Boltzmann’s $H$ functional. This functional is used to prove that (essentially) all static granular packings must exist at maximum entropy with respect to their contact forces. Therefore, the propagation of granular contact forces through a packing is a truly ergodic process in the Boltzmannian sense, or better, it is extit{self-ergodic}. Self-ergodicity refers to the non-dynamic, internal relationships that exist between the layer-by-layer and column-by-column subspaces contained within the phase space locus of any particular granular packing microstate. The generalized $H$ Theorem also produces a recursion equation that may be solved numerically to obtain the density of single particle states and hence the distribution of granular contact forces corresponding to the condition of self-ergodicity. The predictions of the theory are overwhelmingly validated by comparison to empirical data from discrete element modeling. | Source: | arXiv, cond-mat/0606298 | Services: | Forum | Review | PDF | Favorites |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
|
| |
|
|
|
| News, job offers and information for researchers and scientists:
| |