Abstract
We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volume of the constituent grains and the number of neighbors in contact that permits a simple combination of the two approaches to develop a theory of random packings. We predict the density of random loose packing (RLP) and random close packing (RCP) in close agreement with experiments and develop a phase diagram of jammed matter that provides a unifying view of the disordered hard sphere packing problem and further shedding light on a diverse spectrum of data, including the RLP state. Theoretical results are well reproduced by numerical simulations that confirm the essential role played by friction in determining both the RLP and RCP limits. Finally we present an extended discussion on the existence of geometrical and mechanical coordination numbers and how to measure both quantities in experiments and computer simulations.
| Original language | English (US) |
|---|---|
| Title of host publication | AIP Conference Proceedings |
| Pages | 271-279 |
| Number of pages | 9 |
| Volume | 1227 |
| DOIs | |
| State | Published - 2010 |
| Externally published | Yes |
| Event | Joint IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows - Reggio Calabria, Italy Duration: Sep 14 2009 → Sep 18 2009 |
Other
| Other | Joint IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows |
|---|---|
| Country | Italy |
| City | Reggio Calabria |
| Period | 9/14/09 → 9/18/09 |
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Keywords
- Granular matter
- Random close packing
- Statistical mechanics
ASJC Scopus subject areas
- Physics and Astronomy(all)
Cite this
Theory of random packings. / Song, Chaoming; Wang, Ping; Makse, Hernán A.
AIP Conference Proceedings. Vol. 1227 2010. p. 271-279.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Theory of random packings
AU - Song, Chaoming
AU - Wang, Ping
AU - Makse, Hernán A.
PY - 2010
Y1 - 2010
N2 - We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volume of the constituent grains and the number of neighbors in contact that permits a simple combination of the two approaches to develop a theory of random packings. We predict the density of random loose packing (RLP) and random close packing (RCP) in close agreement with experiments and develop a phase diagram of jammed matter that provides a unifying view of the disordered hard sphere packing problem and further shedding light on a diverse spectrum of data, including the RLP state. Theoretical results are well reproduced by numerical simulations that confirm the essential role played by friction in determining both the RLP and RCP limits. Finally we present an extended discussion on the existence of geometrical and mechanical coordination numbers and how to measure both quantities in experiments and computer simulations.
AB - We review a recently proposed theory of random packings. We describe the volume fluctuations in jammed matter through a volume function, amenable to analytical and numerical calculations. We combine an extended statistical mechanics approach 'a la Edwards' (where the role traditionally played by the energy and temperature in thermal systems is substituted by the volume and compactivity) with a constraint on mechanical stability imposed by the isostatic condition. We show how such approaches can bring results that can be compared to experiments and allow for an exploitation of the statistical mechanics framework. The key result is the use of a relation between the local Voronoi volume of the constituent grains and the number of neighbors in contact that permits a simple combination of the two approaches to develop a theory of random packings. We predict the density of random loose packing (RLP) and random close packing (RCP) in close agreement with experiments and develop a phase diagram of jammed matter that provides a unifying view of the disordered hard sphere packing problem and further shedding light on a diverse spectrum of data, including the RLP state. Theoretical results are well reproduced by numerical simulations that confirm the essential role played by friction in determining both the RLP and RCP limits. Finally we present an extended discussion on the existence of geometrical and mechanical coordination numbers and how to measure both quantities in experiments and computer simulations.
KW - Granular matter
KW - Random close packing
KW - Statistical mechanics
UR - http://www.scopus.com/inward/record.url?scp=77954605122&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77954605122&partnerID=8YFLogxK
U2 - 10.1063/1.3435397
DO - 10.1063/1.3435397
M3 - Conference contribution
AN - SCOPUS:77954605122
SN - 9780735407725
VL - 1227
SP - 271
EP - 279
BT - AIP Conference Proceedings
ER -