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Random sequential addition: A distribution function approach

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Abstract

Random sequential addition (RSA) of hard objects is an irreversible process defined by three rules: objects are introduced on a surface (or ad-dimensional volume) randomly and sequentially, two objects cannot overlap, and, once inserted, an object is clamped in its position. The configurations generated by an RSA can be characterized, in the macroscopic limit, by a unique set of distribution functions and a density. We show that these “nonequilibrium” RSA configurations can be described in a manner which, in many respects, parallels the usual statistical mechanical treatment of equilibrium configurations: Kirkwood-Salsburg-like hierarchies for the distribution functions, zero-separation theorems, diagrammatic expansions, and approximate equations for the pair distribution function. Approximate descriptions valid for low to intermediate densities can be combined with exact results already derived for higher densities close to the jamming limit of the process. Similarities and differences between the equilibrium and the RSAconfigurations are emphasized. Finally, the potential application of RSA processes to the study of glassy phases is discussed.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique des Liquides, Université Pierre et Marie Curie, 75252, Paris Cédex 05, France

    Gilles Tarjus

  2. Institut Charles Sadron (CRM-EAHP), CNRS-ULP, 67083, Strasbourg Cédex, France

    Pierre Schaaf

  3. School of Chemical Engineering, Purdué University, 47907, West Lafayette, Indiana

    Julian Talbot

Authors
  1. Gilles Tarjus
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  2. Pierre Schaaf
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  3. Julian Talbot
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Tarjus, G., Schaaf, P. & Talbot, J. Random sequential addition: A distribution function approach. J Stat Phys 63, 167–202 (1991). https://doi.org/10.1007/BF01026598

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  • DOI: https://doi.org/10.1007/BF01026598

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