{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T23:12:21Z","timestamp":1790723541435,"version":"4.1.0"},"reference-count":33,"publisher":"American Physical Society (APS)","issue":"2","license":[{"start":{"date-parts":[[2026,2,18]],"date-time":"2026-02-18T00:00:00Z","timestamp":1771372800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003483","name":"Hebrew University of Jerusalem","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100003483","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100012688","name":"Universit\u00e4t Rostock","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100012688","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["journals.aps.org"],"crossmark-restriction":true},"short-container-title":["Phys. Rev. E"],"accepted":{"date-parts":[[2026,1,21]]},"abstract":"<jats:p>\n                    In this paper the excluded volume of binary similar hyperparticles with small size difference in\n                    <a:math xmlns:a=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <a:mrow>\n                        <a:mi>D<\/a:mi>\n                      <\/a:mrow>\n                    <\/a:math>\n                    -dimensional Euclidean spaces\n                    <b:math xmlns:b=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <b:msup>\n                        <b:mi mathvariant=\"double-struck\">R<\/b:mi>\n                        <b:mn>2<\/b:mn>\n                      <\/b:msup>\n                      <b:mo>,<\/b:mo>\n                      <b:mo>\u00a0<\/b:mo>\n                      <b:msup>\n                        <b:mi mathvariant=\"double-struck\">R<\/b:mi>\n                        <b:mn>3<\/b:mn>\n                      <\/b:msup>\n                    <\/b:math>\n                    , and\n                    <e:math xmlns:e=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <e:msup>\n                        <e:mi mathvariant=\"double-struck\">R<\/e:mi>\n                        <e:mn>4<\/e:mn>\n                      <\/e:msup>\n                    <\/e:math>\n                    is studied using two different statistical geometry approaches. These geometric approaches, concerning orientation geometry and integral geometry, yield the excluded volume of particle pairs. The excluded volume of rectangles, based on orientation geometry, in Euclidean space\n                    <g:math xmlns:g=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <g:msup>\n                        <g:mi mathvariant=\"double-struck\">R<\/g:mi>\n                        <g:mn>2<\/g:mn>\n                      <\/g:msup>\n                    <\/g:math>\n                    is used to derive an explicit equation for the bidisperse packing fraction, which is compatible with the expression published previously. Next, the excluded volumes of pairs of convex particles in\n                    <i:math xmlns:i=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <i:mrow>\n                        <i:mi>D<\/i:mi>\n                        <i:mo>=<\/i:mo>\n                        <i:mn>2<\/i:mn>\n                        <i:mo>,<\/i:mo>\n                        <i:mn>3<\/i:mn>\n                      <\/i:mrow>\n                    <\/i:math>\n                    , and 4, resulting from integral geometry, are presented. These excluded volumes are identical with the specific ones for circles and rectangles (\n                    <j:math xmlns:j=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <j:mrow>\n                        <j:mi>D<\/j:mi>\n                      <\/j:mrow>\n                    <\/j:math>\n                    = 2) and (sphero)cylinders (\n                    <k:math xmlns:k=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <k:mrow>\n                        <k:mi>D<\/k:mi>\n                      <\/k:mrow>\n                    <\/k:math>\n                    = 3), derived by orientation geometry. Furthermore, these orientation geometry-based excluded volumes contain geometric measures: particle volume, surface area, mean curvature, and the second quermassintegral. They allow for the derivation of closed-form expressions for the random packing fraction of binary convex similar hyperparticles in Euclidean spaces\n                    <l:math xmlns:l=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <l:msup>\n                        <l:mi mathvariant=\"double-struck\">R<\/l:mi>\n                        <l:mn>2<\/l:mn>\n                      <\/l:msup>\n                      <l:mo>,<\/l:mo>\n                      <l:mo>\u00a0<\/l:mo>\n                      <l:msup>\n                        <l:mi mathvariant=\"double-struck\">R<\/l:mi>\n                        <l:mn>3<\/l:mn>\n                      <\/l:msup>\n                    <\/l:math>\n                    , and\n                    <o:math xmlns:o=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                      <o:msup>\n                        <o:mi mathvariant=\"double-struck\">R<\/o:mi>\n                        <o:mn>4<\/o:mn>\n                      <\/o:msup>\n                    <\/o:math>\n                    .\n                  <\/jats:p>","DOI":"10.1103\/g37j-lkv2","type":"journal-article","created":{"date-parts":[[2026,1,21]],"date-time":"2026-01-21T15:56:43Z","timestamp":1769011003000},"update-policy":"https:\/\/doi.org\/10.1103\/crossmark-policy","source":"Crossref","is-referenced-by-count":1,"title":["Excluded volume geometry and packing fraction in binary convex hyperparticle mixtures"],"prefix":"10.1103","volume":"113","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8291-5444","authenticated-orcid":true,"given":"H. J. H.","family":"Brouwers","sequence":"first","affiliation":[{"id":[{"id":"https:\/\/ror.org\/02c2kyt77","id-type":"ROR","asserted-by":"publisher"}],"name":"Eindhoven University of Technology"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"16","published-online":{"date-parts":[[2026,2,18]]},"reference":[{"key":"g37j-lkv2Cc1R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01451681","type":"journal-article"},{"key":"g37j-lkv2Cc2R1","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1949.tb27296.x","type":"journal-article"},{"key":"g37j-lkv2Cc3R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.89.128302","type":"journal-article"},{"key":"g37j-lkv2Cc4R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0968-0004(01)01938-7","type":"journal-article"},{"key":"g37j-lkv2Cc5R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevB.30.3933","type":"journal-article"},{"key":"g37j-lkv2Cc6R1","doi-asserted-by":"publisher","DOI":"10.1021\/la950671o","type":"journal-article"},{"key":"g37j-lkv2Cc6R2","doi-asserted-by":"publisher","DOI":"10.1021\/la960869o","type":"journal-article"},{"key":"g37j-lkv2Cc7R1","doi-asserted-by":"publisher","DOI":"10.1016\/S0927-7757(02)00510-1","type":"journal-article"},{"key":"g37j-lkv2Cc8R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.128.028002","type":"journal-article"},{"key":"g37j-lkv2Cc8R2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.129.039901","type":"journal-article"},{"key":"g37j-lkv2Cc8R3","unstructured":"See also discussion in arXiv:2201.07629, arXiv:2201.10951, arXiv:2201.10550, arXiv:2201.12784, arXiv:2204.13901, arXiv:2205.00720, arXiv:2201.06129, arXiv:2202.05078.","type":"other"},{"key":"g37j-lkv2Cc9R1","doi-asserted-by":"publisher","DOI":"10.1016\/j.powtec.2025.121088","type":"journal-article"},{"key":"g37j-lkv2Cc10R1","doi-asserted-by":"crossref","first-page":"510","DOI":"10.3367\/UFNe.2023.11.039606","type":"journal-article","volume":"67","author":"H. J. H. Brouwers","year":"2023","journal-title":"Phys. Uspekhi"},{"key":"g37j-lkv2Cc11R1","doi-asserted-by":"publisher","DOI":"10.1103\/xhhh-hvhg","type":"journal-article"},{"key":"g37j-lkv2Cc12R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.82.2633","type":"journal-article"},{"key":"g37j-lkv2Cc13R1","volume-title":"Packing Problems in Soft Matter Physics","author":"P. K. Morse","year":"2025","type":"book"},{"key":"g37j-lkv2Cc14R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.82.789","type":"journal-article"},{"key":"g37j-lkv2Cc15R1","doi-asserted-by":"publisher","DOI":"10.1063\/1.1747510","type":"journal-article"},{"key":"g37j-lkv2Cc16R1","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.6.40","type":"journal-article"},{"key":"g37j-lkv2Cc17R1","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.6.46","type":"journal-article"},{"key":"g37j-lkv2Cc18R1","doi-asserted-by":"publisher","DOI":"10.1080\/00268977500100361","type":"journal-article"},{"key":"g37j-lkv2Cc19R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.87.022111","type":"journal-article"},{"key":"g37j-lkv2Cc20R1","doi-asserted-by":"publisher","DOI":"10.1088\/1742-5468\/ac8c8b","type":"journal-article"},{"key":"g37j-lkv2Cc21R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.111.024112","type":"journal-article"},{"key":"g37j-lkv2Cc22R1","doi-asserted-by":"publisher","DOI":"10.1007\/BF01445180","type":"journal-article"},{"key":"g37j-lkv2Cc23R1","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-014-1127-3","type":"journal-article"},{"key":"g37j-lkv2Cc24R1","doi-asserted-by":"publisher","DOI":"10.1039\/D3SM01254A","type":"journal-article"},{"key":"g37j-lkv2Cc25R1","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevE.88.012101","type":"journal-article"},{"key":"g37j-lkv2Cc26R1","unstructured":"I. Balberg (private communication).","type":"other"},{"key":"g37j-lkv2Cc27R1","unstructured":"A. P. Chatterjee (private communication).","type":"other"},{"key":"g37j-lkv2Cc28R1","doi-asserted-by":"publisher","DOI":"10.1103\/RevModPhys.25.831","type":"journal-article"},{"key":"g37j-lkv2Cc29R1","doi-asserted-by":"publisher","DOI":"10.1143\/JPSJ.8.686","type":"journal-article"},{"key":"g37j-lkv2Cc30R1","unstructured":"J. Wagner (private communication).","type":"other"}],"container-title":["Physical Review E"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.aps.org\/article\/10.1103\/g37j-lkv2","content-type":"unspecified","content-version":"vor","intended-application":"syndication"},{"URL":"http:\/\/harvest.aps.org\/v2\/journals\/articles\/10.1103\/g37j-lkv2\/fulltext","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,29]],"date-time":"2026-09-29T22:47:56Z","timestamp":1790722076000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.aps.org\/doi\/10.1103\/g37j-lkv2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,2,18]]},"references-count":33,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,2]]}},"URL":"https:\/\/doi.org\/10.1103\/g37j-lkv2","relation":{"has-preprint":[{"id-type":"doi","id":"10.48550\/arXiv.2510.12898","asserted-by":"subject"}]},"ISSN":["2470-0045","2470-0053"],"issn-type":[{"value":"2470-0045","type":"print"},{"value":"2470-0053","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,2,18]]},"assertion":[{"value":"2025-10-16","name":"date_received","label":"Date Received","group":{"name":"publication_dates","label":"Publication dates"}},{"value":"Published by the American Physical Society. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright_statement","label":"Copyright statement","group":{"name":"copyright","label":"copyright"}},{"value":"2026","name":"copyright_year","label":"Copyright year","group":{"name":"copyright","label":"copyright"}},{"value":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/","name":"creative_commons_license","label":"Creative Commons license","group":{"name":"licenses","label":"Licenses"}},{"value":"\u00a92026 The authors","name":"copyright_holder","label":"Copyright holder","group":{"name":"copyright","label":"copyright"}}],"article-number":"025417"}}