Theory of random packings

Chaoming Song, Ping Wang, Hernán A. Makse

Research output: Chapter in Book/Report/Conference proceedingConference contribution

2 Citations (Scopus)

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 languageEnglish (US)
Title of host publicationAIP Conference Proceedings
Pages271-279
Number of pages9
Volume1227
DOIs
StatePublished - 2010
Externally publishedYes
EventJoint IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows - Reggio Calabria, Italy
Duration: Sep 14 2009Sep 18 2009

Other

OtherJoint IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows
CountryItaly
CityReggio Calabria
Period9/14/099/18/09

Fingerprint

statistical mechanics
exploitation
coordination number
friction
simulation
computerized simulation
phase diagrams
temperature
energy

Keywords

  • Granular matter
  • Random close packing
  • Statistical mechanics

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Song, C., Wang, P., & Makse, H. A. (2010). Theory of random packings. In AIP Conference Proceedings (Vol. 1227, pp. 271-279) https://doi.org/10.1063/1.3435397

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 proceedingConference contribution

Song, C, Wang, P & Makse, HA 2010, Theory of random packings. in AIP Conference Proceedings. vol. 1227, pp. 271-279, Joint IUTAM-ISIMM Symposium on Mathematical Modeling and Physical Instances of Granular Flows, Reggio Calabria, Italy, 9/14/09. https://doi.org/10.1063/1.3435397
Song C, Wang P, Makse HA. Theory of random packings. In AIP Conference Proceedings. Vol. 1227. 2010. p. 271-279 https://doi.org/10.1063/1.3435397
Song, Chaoming ; Wang, Ping ; Makse, Hernán A. / Theory of random packings. AIP Conference Proceedings. Vol. 1227 2010. pp. 271-279
@inproceedings{eaa0495ac7974120b418f025fa0ac6d7,
title = "Theory of random packings",
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.",
keywords = "Granular matter, Random close packing, Statistical mechanics",
author = "Chaoming Song and Ping Wang and Makse, {Hern{\'a}n A.}",
year = "2010",
doi = "10.1063/1.3435397",
language = "English (US)",
isbn = "9780735407725",
volume = "1227",
pages = "271--279",
booktitle = "AIP Conference Proceedings",

}

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 -