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Many-body correlations from integral geometry

Research output: Contribution to journalArticle

Original languageEnglish
Article number062126
Number of pages9
JournalPhysical Review E
Issue number6
DateAccepted/In press - 8 Oct 2019
DatePublished (current) - 20 Dec 2019


In a recent letter we presented a framework for predicting the concentrations of many-particle local structures inside the bulk liquid as a route to assessing changes in the liquid approaching dynamical arrest. Central to this framework was the morphometric approach, a synthesis of integral geometry and liquid state theory, which has traditionally been derived from fundamental measure theory. We present the morphometric approach in a new context as a generalisation of scaled particle theory, and derive several morphometric theories for hard spheres of fundamental and practical interest. Our central result is a new theory which is particularly suited to the treatment of many-body correlation functions in the hard sphere liquid, which we demonstrate by numerical tests against simulation.

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