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dc.contributor.authorMartiniani, Stefanoen
dc.contributor.authorSchrenk, Julianen
dc.contributor.authorStevenson, Jacob Den
dc.contributor.authorWales, Daviden
dc.contributor.authorFrenkel, Daanen
dc.identifier.citationMartiniani et al. Physical Review E (2016) Vol. 93, Article 012906. doi: 10.1103/PhysRevE.93.012906en
dc.description.abstractWe report the first numerical calculation of the total number of disordered jammed configurations Ω of N repulsive, three-dimensional spheres in a fixed volume V . To make these calculations tractable, we increase the computational efficiency of the approach of Xu et al. (Phys. Rev. Lett. 106, 245502 (2011)) and Asenjo et al. (Phys. Rev. Lett. 112, 098002 (2014)) and we extend the method to allow computation of the configurational entropy as a function of pressure. The approach that we use computes the configurational entropy by sampling the absolute volume of basins of attraction of the stable packings in the potential energy landscape. We find a surprisingly strong correlation between the pressure of a configuration and the volume of its basin of attraction in the potential energy landscape. This relation is well described by a power law. Our methodology to compute the number of minima in the potential energy landscape should be applicable to a wide range of other enumeration problems in statistical physics, string theory, cosmology and machine learning, that aim to find the distribution of the extrema of a scalar cost function that depends on many degrees of freedom.
dc.description.sponsorshipWe acknowledge useful discussions with Daniel Asenjo, Carl Goodrich, Silke Henkes, and Fabien Paillusson. S.M. acknowledges financial support by the Gates Cambridge Scholarship. K.J.S. acknowledges support by the Swiss National Science Foundation under Grant No. P2EZP2-152188 and No. P300P2-161078. J.D.S. acknowledges support by Marie Curie Grant 275544. D.F. and D.J.W. acknowledge support by EPSRC Programme Grant EP/I001352/1, by EPSRC grant EP/I000844/1 (D.F.) and ERC Advanced Grant RG59508 (D.J.W.)
dc.publisherAmerican Physical Society
dc.rightsAttribution-NonCommercial 2.0 UK: England & Wales*
dc.titleTurning intractable counting into sampling: Computing the configurational entropy of three-dimensional jammed packingsen
dc.description.versionThis is the author accepted manuscript. The final version is available from the American Physical Society via
prism.publicationNamePhysical Review Een
dc.contributor.orcidMartiniani, Stefano [0000-0003-2028-2175]
dc.contributor.orcidWales, David [0000-0002-3555-6645]
dc.contributor.orcidFrenkel, Daan [0000-0002-6362-2021]
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/I001352/1)
pubs.funder-project-idEPSRC (EP/N035003/1)
pubs.funder-project-idEuropean Commission (275544)
pubs.funder-project-idEPSRC (EP/I000844/1)

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Attribution-NonCommercial 2.0 UK: England & Wales
Except where otherwise noted, this item's licence is described as Attribution-NonCommercial 2.0 UK: England & Wales